Universita degli Studi di Ferrara

FACOLTA DI SCIENZE MATEMATICHE FISICHE E NATURALI

Dottorato di Ricerca in Fisica

Ciclo XX

Measurements of Partial Branching Fractions

for Charmless Semileptonic B Decays

with the BABAR Experiment

and Determination of |Vub|

Dottorando:

Dott. Antonio Petrella

Tutore:

Dott. Livio Piemontese

Correlatore:

Dott. Concezio Bozzi

Anni 2005-2007

Contents

Introduction v

1 CKM Matrix and Semileptonic B Decays 1

1.1 The Electroweak Sector of the Standard Model . . . . . . . . . . . . . . . . 1

1.2 Inclusive Semileptonic B Decays . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3 |Vub| Extraction from Charmless Semileptonic B Decays . . . . . . . . . . . 12

1.3.1 Calculation of the Total Decay Rate . . . . . . . . . . . . . . . . . 13

1.3.2 Decay Rates in Restricted Phase Space Region . . . . . . . . . . . . 16

1.3.3 Experimental Approaches . . . . . . . . . . . . . . . . . . . . . . . 21

2 The BABAR Experiment 23

2.1 The PEP-II Asymmetric Collider . . . . . . . . . . . . . . . . . . . . . . . 25

2.1.1 PEP-II Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2 The BABAR Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.2.1 Silicon Vertex Tracker (SVT) . . . . . . . . . . . . . . . . . . . . . . 30

2.2.2 Drift Chamber (DCH) . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2.3 Cerenkov Light Detector (DRC) . . . . . . . . . . . . . . . . . . . . 35

2.2.4 Electromagnetic Calorimeter (EMC) . . . . . . . . . . . . . . . . . . 37

2.2.5 Instrumented Flux Return (IFR) . . . . . . . . . . . . . . . . . . . . 41

2.2.6 Trigger System (TRG) and Data Acquisition (DAQ) . . . . . . . . . 49

3 Event Reconstruction 51

3.1 Charged Particle Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 52

3.2 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

i

3.2.1 Electron Identification . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.2.2 Muon Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.2.3 Charged Kaon Identification . . . . . . . . . . . . . . . . . . . . . . 58

3.3 Neutral Particles Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4 Meson Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.4.1 π0 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.4.2 K0S Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.4.3 D Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.5 Semi-exclusive Reconstruction Method . . . . . . . . . . . . . . . . . . . . 66

3.5.1 Definition of ∆E and mES . . . . . . . . . . . . . . . . . . . . . . . 68

3.5.2 Study of the Y System . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.5.3 ∆E Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.5.4 Multiple Candidates and Definition of Purity . . . . . . . . . . . . . 72

4 Data and Monte Carlo Samples 75

4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2 Monte Carlo Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2.1 Generic bb Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . 76

4.2.2 Resonant Models for B → Xu`ν . . . . . . . . . . . . . . . . . . . . 76

4.2.3 Non-Resonant Model for B → Xu`ν . . . . . . . . . . . . . . . . . . 77

4.2.4 BABAR Hybrid Model for B → Xu`ν . . . . . . . . . . . . . . . . . . 79

4.2.5 Reweighting Hybrid Model for B → Xu`ν . . . . . . . . . . . . . . 80

5 Event Selection 83

5.1 Reconstruction of the Recoil System . . . . . . . . . . . . . . . . . . . . . 84

5.2 Selection of Semileptonic Decays . . . . . . . . . . . . . . . . . . . . . . . . 86

5.2.1 Selection of Charmless Semileptonic Decays . . . . . . . . . . . . . 87

5.3 Fit to the mES Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.3.1 Modeling of mES Distribution with 3 PDFs . . . . . . . . . . . . . 94

5.3.2 Modeling of mES Distribution with 2 PDF . . . . . . . . . . . . . . 99

ii

5.3.3 Study of Truth-Matching Criteria . . . . . . . . . . . . . . . . . . . 101

5.3.4 Strategy for mES Fits . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.3.5 Binned vs. Unbinned Fits . . . . . . . . . . . . . . . . . . . . . . . 104

5.4 Data/Monte Carlo Comparison . . . . . . . . . . . . . . . . . . . . . . . . 106

6 Partial Charmless Branching Fraction Measurements 115

6.1 Measurement Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6.2 Monte Carlo Fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6.3 One Dimensional MX Fit and Results . . . . . . . . . . . . . . . . . . . . . 120

6.4 One Dimensional P+ Fit and Results . . . . . . . . . . . . . . . . . . . . . 125

6.5 Two Dimensional (MX , q2) Fit and Results . . . . . . . . . . . . . . . . . . 130

7 Systematic Uncertainties 137

7.1 Detector-related Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

7.1.1 Charged Particle Tracking . . . . . . . . . . . . . . . . . . . . . . . 137

7.1.2 Neutral Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 138

7.1.3 KL Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.1.4 Lepton Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.1.5 Charged Kaon Identification . . . . . . . . . . . . . . . . . . . . . . 140

7.2 Uncertainties Related to the mES Fits . . . . . . . . . . . . . . . . . . . . 140

7.3 Signal Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.4 Background Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

8 Measurement of |Vub| 147

8.1 Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

8.2 |Vub| Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

8.2.1 (MX , q2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

8.2.2 MX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

8.2.3 P+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

8.3 Compatibility of the |Vub| Determinations . . . . . . . . . . . . . . . . . . . 151

iii

8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

Bibliography 155

iv

Introduction

This thesis presents measurements of inclusive semileptonic decays of B mesons in charm-

less final states, by using a data sample collected by the BABAR detector at the PEP-II

Asymmetric B Factory, located at the Stanford Linear Accelerator Center.

Charmless semileptonic B meson decays give the cleanest determinations of the CKM

matrix element |Vub|. The study of inclusive decays, where no attempt is made to com-

pletely reconstruct the final state, are particularly interesting since the relevant contribu-

tions to the dominant theoretical uncertainty can be factorized and computed systemati-

cally to a high level of accuracy.

The experimental approach presented in this thesis uses Υ(4S) → BB transitions to

study charmless semileptonic decays of a B meson recoiling against a B meson which is

fully reconstructed in an hadronic final state. The dominant background due to semilep-

tonic decays with charm, about a factor 50 larger than charmless decays, is reduced by

kinematic requirements which allow to identify phase space regions with a manageable

signal over background ratio. In general, these requirements introduce sizeable theoretical

uncertainties when the extrapolation to the full phase space, needed in order to determine

|Vub|, is performed. The determination of |Vub| therefore depends on the interplay between

a careful optimization of signal over background ratio and the minimization of theoretical

uncertainties.

This thesis is organized as follows. The theory of inclusive charmless semileptonic

B decays is reviewed in Chapter 1, together with a brief reminder of the electroweak

sector of the standard model and the CKM mechanism. Chapter 2 shows an overview

of the BABAR detector. The experimental techniques used to reconstruct events, identify

particles and resonances, and fully reconstruct a B meson into hadronic final states, are

v

presented in Chapter 3. The event samples used in this thesis, consisting of both real and

simulated data, are detailed in Chapter 4. Chapter 5 shows the selection criteria applied

in order to select the signal sample. Measurements of partial branching fraction for

inclusive charmless decays in regions of restricted phase space are reported in Chapter 6,

the associated systematic uncertainties are discussed in Chapter 7. Determinations of the

CKM matrix element |Vub| and conclusions are presented in Chapter 8.

The results obtained in this thesis work represent the most precise and up-to-date

determinations of |Vub| with inclusive charmless semileptonic decays. They have been

submitted to and shown at the European Physical Society Conference on High Energy

Physics, held in Manchester in July 2007, and at the XXIII International Symposium on

Lepton and Photon Interactions at High Energy, held in Daegu, Korea, in August 2007.

They have been subsequently submitted for publication [1] on Physical Review Letters.

vi

Chapter 1

CKM Matrix and Semileptonic BDecays

1.1 The Electroweak Sector of the Standard Model

The electroweak sector of the SM is a gauge theory based on the local group SUL(2) ⊗UY (1), which describes the symmetries of the matter field. The Yang-Mills electroweak

Lagrangian is [2]

L = −1

4ΣAW

AµνW

Aµν − 1

4BµνB

µν + ΨLiγµDµΨL + ΨRiγ

µDµΨR (1.1)

where the spinors ΨL and ΨR represent the matter fields in their chiral components, and

the field strength tensors are given by:

Wµν = ∂µWν − ∂νWµ − gεABCWBµ W

Cν and Bµν = ∂µBν − ∂νBµ (1.2)

Here WA and B are the SU(2) and U(1) gauge fields, with the coupling constants g and g′

and εABC is the totally anti-symmetric Levi-Civita tensor. The corresponding covariant

derivative is:

DµΨL,R =

[∂µ + igΣtAL,RWAµ + ig′

1

2YL,RBµ

]ΨL,R, (1.3)

where tAL,R and 1/2YL,R are the SU(2) (weak isospin) and U(1) (hypercharge) generators.

The electric charge generator is related to the isospin and hypercharge by:

Q = t3L +1

2YL = t3L +

1

2YR. (1.4)

The left and the right fermion components have different properties under the gauge group.

The left component behave as doublets while the right as singlets. In the symmetric limit

1

the two chiral component cannot interact each other, and thus mass term for fermions

(of the form ΨLΨR) are forbidden. To give mass terms to fermions as well as to gauge

bosons without loosing the symmetry properties, the electroweak theory is realized with

a vacuum state invariant only under the UEM(1) electric charge gauge transformation.

This phenomenon is known as “spontaneous symmetry breaking”. The gauge theories

spontaneous broken allow to introduce mass terms for the gauge boson and the fermion

fields without loosing the gauge invariance, and the renormalizability of the theory. The

mechanism by which, starting from a degenerate vacuum state, mass terms are introduced

is known as Higgs mechanism [3]. The Higgs Lagrangian term is:

LHiggs = (Dµφ)†(Dµφ)− V (φ†φ)− ΨLΓΨRφ− ΨRΓ†ΨLφ†, (1.5)

where φ is the isospin doublet of the Higgs scalar fields and the quantities Γ (which include

all coupling constants) are matrices that make the Yukawa couplings invariant under the

Lorentz gauge groups. The general form of the Higgs potential is:

V (φ†φ) = µ2φ†φ+ λ(φ†φ)2, (1.6)

and it is not possible to include terms with higher dimension without breaking the renor-

malizability of the SM. To have a vacuum state (the minimum of the potential) degenerate,

the µ2 coefficient should be negative, while the coefficient λ should be positive to guarantee

the potential bound from below. Under these hypotheses the vacuum state of the Higgs

field satisfies |φ|2 = −µ2/2λ = v2. The field φ can be expanded around one of its ground

states; in choosing a particular ground state (φ0 =

(0ν

)), the SUL,R(2)⊗UY (1) symmetry

is spontaneously broken.

The mass terms for the gauge bosons are coming from the kinetic part of the Higgs

Lagrangian once it is expanded around the Higgs vacuum state. The correct quantum

numbers of the Higgs field are fixed by the requirement that the Lagrangian (1.5) is gauge

invariant.

Since the SUL(2) ⊗ UY (1) is spontaneously broken into UEM(1), only the linear com-

bination of gauge fields with the quantum numbers of the photon remains mass-less. A

general linear combination between the gauge bosons associated to the generator in Eq. 1.4

2

can be written: (Aµ

Zµ

)=

(− sin θW cos θW

cos θW sin θW

) (W 3

µ

Bµ

)(1.7)

where the angle θW is known as the Weak or Weinberg mixing angle. Once the symmetry

is spontaneously broken through the interaction with the Higgs field, Aµ remains mass-less

while Zµ, W+µ and W−

µ acquire a mass term. W+µ and W−

µ are defined as:

W±µ =

1√2(W 1

µ ± iW 2µ). (1.8)

The bi-linear terms in the fields Zµ and W±µ in Eq. 1.5 can be identified as the mass terms:

M2Z =

v2g2

2 cos2 θW

(1.9)

M2W = cos2 θWM

2Z (1.10)

which implies tan θW = g′/gYφ. In terms of these new fields the fermionic currents are:

J±µ = Σf Ψf (1− γ5)γµt

±Ψf (1.11)

J0µ = Σf Ψ

fγµ

[(1− γ5)t

3 − 2Q sin2 θW

]Ψf , (1.12)

Jemµ = Σf Ψ

fγµQΨf , (1.13)

where Ψf represents the isospin doublet for the fermion fields (see Tab. 1.1) with f acting

Family Quantum Numbers1 2 3 t t3 Y Q = Y/2 + t3

(νe

e

)

L

(νµ

µ

)

L

(ντ

τ

)

L

1/21/2

+1/2−1/2

−1−1

0−1

eR µR τR 0 0 −2 −1

(ud

)

L

(cs

)

L

(tb

)

L

1/21/2

+1/2−1/2

+1/3+1/3

+2/3−1/3

uR cR tR 0 0 4/3 +2/3dR sR bR 0 0 −2/3 −1/3

Table 1.1: Electroweak interaction multiplets. t indicates the isospin, t3 is the third isospin component,Y indicates the hyper-charge and Q indicates the electric charge.

as a family index, (1 − γ5) is the left-handed chiral projector, and t± are the isospin

3

generator associated to the fields W±. The first current describes interactions which

change the electric charge, while the other two, produce transitions charge-conserving.

The Lagrangian (1.1) could be rewritten in two terms: one including interactions between

the neutral current and the Aµ and Zµ bosons, and another describing the interactions of

the W±µ with the charged current:

LED = LCC + LNC, (1.14)

LCC =g2

2√

2(J+

µ W+µ + J−µ W

−µ ), (1.15)

LNC = −eJemµ Aµ +

g2

2 cos θW

J0µZ

µ, (1.16)

where e is defined as e = g2 sin θW .

Starting from the same doublet which gives masses to the gauge bosons it is possible

to introduce mass terms for the fermion fields. This imposes others restrictions on the

Higgs field. To obtain fermion mass terms like:

−ΨLΓΨRφ− ΨRΓΨLφ where φ = iσ2φ†, (1.17)

invariant under SUL,R(2) transformations, the Higgs field is required to have isospin equal

to 1/2. The Γ matrices contain the Yukawa constants, which determine the strength of

the fermion couplings to the Higgs fields.

The fermion mass matrix is obtained from the Yukawa couplings expanding φ around

the vacuum state:

M = ψL MψR + ψRM†ψL , (1.18)

with

M = Γ · v . (1.19)

It is important to observe that by a suitable change of basis we can always make

the matrix M Hermitian, γ5-free, and diagonal. In fact, we can make separate unitary

transformations on ψL and ψR according to

ψ′L = LψL, ψ′R = RψR, (1.20)

4

and consequently

M→M′ = L†MR . (1.21)

This transformation does not alter the general structure of the fermion couplings in L.

Weak charged currents are the only tree level interactions in the SM that may induce a

change of flavor. By emission of a W boson an up-type quark is turned into a down-type

quark, or a ν` neutrino is turned into a `− charged lepton. If we start from an up quark

that is a mass eigenstate, emission of a W turns it into a down-type quark state d′ (the

weak isospin partner of u) that in general is not a mass eigenstate. In general, the mass

eigenstates and the weak eigenstates do not in fact coincide and a unitary transformation

connects the two sets: d′

s′

b′

= V

dsb

, (1.22)

where V is the Cabibbo-Kobayashi-Maskawa matrix (CKM)[4]. Thus in terms of mass

eigenstates the charged weak current of quarks has the form:

J+µ ∝ uγµ(1− γ5)t

+V d, (1.23)

Since V is unitary (i.e. V V † = V †V = 1) and commutes with T 2, T3 and Q (because

all d-type quarks have the same isospin and charge) the neutral current couplings are

diagonal both in the primed and unprimed basis. If the Z down-type quark current is

abbreviated as d′Γd′ then, by changing basis we get dV †ΓV d and V and Γ commute; it

follows that d′Γd′ = dΓd. This is the Glashow - Iliopoulos - Maiani (GIM) mechanism [5]

that ensures natural flavor conservation of the neutral current couplings at the tree level.

With three fermion generations the matrix V could be expressed in terms of three

angles and one irremovable complex phase [6]. The CKM matrix is usually represented

as:

V =

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

. (1.24)

The irremovable phase in the CKM matrix allows possible CP violation.

5

The measurement of the elements of the CKM matrix is fundamental to test the validity

of the SM. Many of them (actually the first two rows of the matrix) are measured directly,

namely by tree-level processes. Using unitary relations one can put constraints on the top

mixing |Vti|. Moreover the B mixing measurements, that involve box diagrams, can give

information also about Vtd and Vtb.

The CKM-matrix can be expressed in terms of four Wolfenstein parameters (λ,A, ρ, η)

with λ = |Vus| = 0.22 playing the role of an expansion parameter and η representing the

CP -violating phase [7]:

V =

1− λ2

2λ Aλ3(ρ− iη)

λ 1− λ2

2Aλ2

Aλ3(1− ρ− iη) −Aλ2 1

+O(λ4). (1.25)

λ is small, and for each element in V , the expansion parameter is actually λ2.

The Wolfenstein parametrization offers a transparent geometrical representation of the

structure of the CKM matrix. The unitarity of the matrix implies various relations among

its elements. Three of them are very useful for understanding the SM predictions for CP

violation:

VudV∗us + VcdV

∗cs + VtdV

∗ts = 0, (1.26)

VusV∗ub + VcsV

∗cb + VtsV

∗tb = 0, (1.27)

VudV∗ub + VcdV

∗cb + VtdV

∗tb = 0. (1.28)

Each of these three relations requires the sum of three complex quantities to vanish and

so can be geometrically represented in the complex plane as a triangle. These are “the

Unitarity Triangles”. If the CP symmetry is violated the area of the triangles is not zero.

The B physics is related to the third triangle at least for what the B factory can access.

The study of the parameters of this triangle encompasses the physics of CP violation in

the SM. The openness of this triangle, due to the fact that all the three sides are of the

same order of magnitude, predicts large CP asymmetries.

It should be remarked that the Wolfenstein parametrization is an approximation and

neglecting O(λ4) terms could be wrong in particular processes. An improved approxi-

6

mated parametrization of the original Wolfenstein matrix is given in [8]. Defining

Vus = λ, Vcb = Aλ2, Vub = Aλ3(ρ− iη), (1.29)

one can then write

Vtd = Aλ3(1− ρ− iη), (1.30)

=(Vcd) = −A2λ5η, =(Vts) = −Aλ4η, (1.31)

where

ρ = ρ(1− λ2/2), η = η(1− λ2/2), (1.32)

turn out to be excellent approximations to the exact expressions. Depicting the rescaled

Unitarity Triangle in the (ρ, η) plane, the lengths of the two complex sides are

Rb ≡√ρ2 + η2 = 1− λ2/2

λ

∣∣∣∣Vub

Vcb

∣∣∣∣ , (1.33)

Rt ≡√

(1− ρ)2 + η2 =1

λ

∣∣∣∣Vtd

Vcb

∣∣∣∣ . (1.34)

The rescaled Unitarity Triangle (Fig. 1.1) is derived from Eq. 1.28 by choosing a phase

convention such that (VcdV∗cb) is real, dividing the lengths of all sides by |VcdV

∗cb|, aligns

one side of the triangle with the real axis and makes the length of this side equal to 1.

The form of the triangle is unchanged. Two vertexes of the rescaled Unitarity Triangle

are thus fixed at (0,0) and (1,0). The coordinates of the remaining vertex are denoted

by (ρ, η). Both angles and sides can be measured in a B factory and they can offer

two independent tests of the Standard Model. Inconsistencies between these two tests

would indicate the presence of New Physics. The constraints on the apex of the Unitarity

Triangle, obtained from different measurements, now overlap in one small area in the

first quadrant in the (ρ, η) plane [9, 10]. The constraints from the lengths of the sides

and independently those from CP violating processes indicate the consistent regions on

the (ρ, η) plane. The |Vub| /|Vcb| constraint shown in Fig. 1.2 can be directly derived

from Eq. 1.33. The CKM elements |Vub| and |Vcb| therefore provide a test of the SM by

7

Figure 1.1: The rescaled Unitarity Triangle, all sides divided by V ∗cbVcd.

8

ρ-1 -0.5 0 0.5 1

η

-1

-0.5

0

0.5

1γ

β

α

sm∆dm∆ dm∆

Kε

cbVubV

ρ-1 -0.5 0 0.5 1

η

-1

-0.5

0

0.5

1

Figure 1.2: Unitarity Triangle constrains from different measurements of the Standard Model parametersin the (ρ, η) plane, updated to the Summer 2006 results [9]. Allowed region for (ρ, η), using all availablemeasurements,is shown with closed contours at 68% and 95% probability. The full lines correspond to95% probability regions for the constraints, given by the measurements of |Vub| /|Vcb| , εK , ∆md/∆ms,α, β, γ, ∆Γd/Γd, ∆Γs/Γs, Ad

SL and the dimuon asymmetry from D0.

9

over-constraining the (ρ, η) plane vertex with other measurements. These elements can

be directly determined from b→ u`ν and b→ c`ν decays respectively.

While |Vcb| has been measured with a 2% uncertainty [11], |Vub| still remains one of

the least known elements of the CKM matrix and dominates the error on the length of

the side opposite to the angle β.

The Unitarity Triangle analysis shows the impressive success of the CKM picture in

describing CP violation in the SM, but, with the increasing precision of the experimental

results, a slight disagreement between sin 2β and |Vub| is appeared in the UT fit, as shown

in Fig. 1.2. This disagreement could be due to some problem with theoretical calculation

and/or with the estimate of the uncertainties on the |Vub| measurements. So an effort

must be done for a substantial improvement of the theoretical and experimental accuracy

for this quantity. In the future, if the |Vub| value will be confirmed by more precise data

and theory calculations, the disagreement in the UT fit might reveal a bound of New

Physics phase in Bd mixing [9].

1.2 Inclusive Semileptonic B Decays

Semileptonic B decays (Fig. 1.3 shows a Feynman diagram of a charmless semileptonic B

decay), due to their simplicity, provide an excellent laboratory in which to measure |Vcb|and |Vub|. These processes also allow us to study the effects of non-perturbative QCD

interactions on the weak-decay process. These goals may sound contradictory: “how can

be measured standard-model parameters if complicated hadronic effects are present?”

Figure 1.3: Feynman diagram for a charmless semileptonic decay B → Xu`ν.

First of all, it is notable that even if the effects of strong interactions on semileptonic

10

decays are difficult to calculate, they are isolated to the hadronic current. As a conse-

quence, these effects can be rigorously parametrized in terms of a small number of form

factors, which are functions of the Lorentz-invariant quantity q2, the square of the mass

of the virtual W.

Particular and specific care is needed in case it is intended to study |Vcb| or |Vub|.For b → c`ν decays, the large masses of both the b and c quarks provide the key to

reliable theoretical predictions based on the Heavy-Quark Effective Theory (HQET) for

exclusive decays and Heavy-Quark Expansions (HQE) for inclusive decays [12, 13, 14].

In the Heavy-Quark Symmetry limit (mb → ∞ and mc → ∞), the hadronic system is

undisturbed by replacing one heavy quark by the other one. Since the b and c quark masses

are not truly infinite, there are corrections to these predictions, but they are relatively

small. So the Heavy-Quark symmetry relates form factors to each other, reducing the

number of independent functions and gives the normalization at zero recoil configurations

(when the daughter charm hadron has zero momentum with respect to the parent b

hadron). Charmless b→ u`ν decays are more difficult because in this case the zero recoil

configuration does not provide a solid normalization point, due to the small value of the

u quark mass.

While the determination of |Vub| is improving, both experimentally and theoretically,

there are still large uncertainties. The problem with exclusive decays is that the strong

hadronic dynamics can not be calculated from first principles, and it has to resort to

models, light-cone sum rules, or lattice QCD calculations to obtain the form factor. So

inclusive decays should provide a straightforward means to measure |Vub|: one considers

the sum over all possible final-state hadrons, ignoring the detailed breakdown among the

individual decay modes that contribute to the semileptonic rate. Experimentally, it is

necessary to observe only the lepton, eliminating reconstruction difficulties that are often

complex decay sequences of the daughter hadrons. Theoretical calculations of inclusive

properties have certain advantages of simplicity as well, since calculations in which the

heavy quark is assumed to decay as a free particle (with the light quark acting merely as

a spectator) provide a good starting point for predictions.

11

1.3 |Vub| Extraction from Charmless Semileptonic B Decays

The theoretical tools that we have for calculating decay rates and spectra in heavy-quark

physics have as underlying theme the separation of short-distance from long-distance

physics, which is natural due to the presence of the large mass scale mQ À ΛQCD, which

is far above the scale of nonperturbative hadronic physics. Factorization theorems state

that short and long-distance contributions to a given observable can be separated into

Wilson coefficient functions Ci and nonperturbative matrix element Mi. Generically, one

has

Observable ∼∑

i

Ci(mQ, µ)Mi(µ) + . . . (1.35)

Such a factorization formula is useful, since by virtue of it the dependence on the high

scale mQ is calculable, and often the number of matrix elements Mi is smaller than the

number of observables that can be expressed in the form shown above. The factorization

scale µ serves as an auxiliary separator between the domains of short and long-distance

physics. Observables are formally independent of the choice of µ; however, they inherit

some residual dependence once the Wilson coefficient Ci are computed at finite order in

perturbation theory. The dependence gets weaker as higher orders in the perturbative

expansion are included.

Processes involving energetic light partons require a more sophisticated form of the

factorization theorem, which generally can be expressed as

Observable ∼∑

i

Hi(Q,µ)Ji(√QΛ, µ)⊗ Si(µ) + . . . (1.36)

Here QÀ ΛQCD is the hard scale of the process, e.g. a heavy-quark mass or the center-

of-mass energy. The hard function Hi capture virtual effects from quantum fluctuation

at the hard scale. The jet functions Ji describe the properties of the emitted collinear

particles, whose characteristic virtuality or invariant mass scales as an intermediate scale√QΛ between Q and QCD scale ΛQCD. For the inclusive processes the jet scale is in

the perturbative domain (√QΛ À ΛQCD). Finally, the soft functions Si describe the

(nonperturbative) physics associated with soft radiation in the process. The symbol ⊗implies a convolution, which arises since the jet and soft functions share some common

12

variables, such as some small momentum components of order ΛQCD.

The theoretical basis of the factorization theorem (Eq. 1.36) is a generalization of the

euclidean operator product expansion to the time-like domain derived in the soft-collinear

effective theory [15, 16, 17, 18].

1.3.1 Calculation of the Total Decay Rate

The total decay rate B → Xu`ν is directly proportional to |Vub|2, and can be calculated

reliably and with small uncertainties using the Operators Product Expansion (OPE), as

a double expansion in powers of ΛQCD/mb and αs(mb) [12], according to Equation 1.35.

The b-quark decay mediated by weak interactions takes place on a time scale that is

much shorter than the time it takes the quarks in the final state to form physical hadronic

states. Once the b-quark has decayed on a time scale t¿ Λ−1QCD, the probability that the

final states will hadronize somehow is unity, and it is needed not to know the probability

of hadronization into specific final states. Moreover, since the energy release in the decay

is much larger than the hadronic scale, the decays is largely insensitive to the details of

the initial state hadronic structure.

This intuitive picture is formalized by the OPE, presented in [19], which expresses the

inclusive rate as an expansion in inverse power of the heavy quark mass with the leading

term corresponding to the free quark decay. Let us consider, as an example, the inclusive

semileptonic b → c decay, mediated by the operator Osl = −4GF/√

2Vcb(Jbc)α(Jlν)α,

where Jαbc = (cγαPLb) and Jβ

lν = (lγβPLν). The decay rate is given by the square of the

matrix element, integrated over phase space (Φ) and summed over final states (Xc),

Γ(B → Xc`ν) ∼∑Xc

∫d[Φ]|〈Xclν|Osl|B〉|2 (1.37)

Since the leptons have no strong interactions, it is convenient to factorize the phase space

into B → XcW∗ and a perturbative calculable leptonic part, W ∗ → lν. The nontrivial

part is the hadronic tensor,

W αβ ∼∑Xc

δ4(pB − q − pXc)|〈B|Jα†bc |Xc〉〈Xc|Jβ

bc|B〉|2 (1.38)

∼ =∫dx e−iq·x〈B|TJα†

bc (x), Jβbc(0)|B〉, (1.39)

13

where the second line is obtained using the optical theorem, and T denotes the time

ordered product of the two operators. This is convenient because the time ordered product

can be expanded in local operators in the mb À ΛQCD limit. In this limit the time ordered

product is dominated by short distances, x ¿ Λ−1QCD, and one can express the nonlocal

hadronic tensor Wαβ as a sum of local operators.

Schematically,

b b

p =mv+k

q q

p =mv-q+kq

b

= �����b ��� � ����Rb����+

0

mb �����b ��� � ����Rb����+

1

m2b �����b ��� � ����Rb

����+ . . . .

(1.40)

At leading order the decay rate is determined by the b quark content of the initial state,

while subleading effects are parametrized by matrix element of operators with increasing

number of derivatives that are sensitive to the structure of the B meson.

There are no O(ΛQCD/mb) corrections, because the b meson matrix element of any

dimension-4 operator vanishes. As the coefficients in front of each operator are calculable

in perturbation theory, this leads to a simultaneous expansion in powers of the strong

coupling constant αS(mb) and inverse powers of the heavy b quark mass (more precisely,

of mb−mq). The leading order of this expansion is the parton model semileptonic width:

Γ0 =G2

F |Vcb| 2m5b

192π3(1− 8ρ+ 8ρ3 − ρ4 − 12ρ2 ln ρ), (1.41)

where ρ = m2q/m

2b . Non-perturbative corrections are suppressed by at least two powers

of mb. The resulting expression for the total rate of the semileptonic B → Xc`ν has the

form

Γb→c = Γ0

[1 + A

[αS

π

]+B

[(αS

π)2β0

]+ 0

[ΛQCD

mb

]+ C

[Λ2

QCD

m2b

]+O(α2

S,Λ3

QCD

m3b

,αS

m2b

)

]

(1.42)

where the coefficients A, B, C depend on the quark masses mc,b. The perturbative

corrections are known up to order α2Sβ0. Non-perturbative corrections are parametrized

by matrix elements of local operators. The O(Λ2QCD/m

2b) corrections are given in terms

14

of the two terms matrix elements

λ1 =1

2MB

〈B|hv(iD)2hv|B〉, λ2 =1

6MB

〈B|hvg

2σµνG

µνhv|B〉 (1.43)

The dependence on these matrix elements is contained in the coefficient C ≡ C(λ1, λ2).

Up to higher order corrections, the connection to an alternative notation is λ1 = −µ2π

and λ2 = µ2G/3. At order 1/m3

b there are two additional matrix elements. Thus, the total

decay rate depends on a set of non-perturbative parameters, including the quark masses

with the number of such parameters depending on the order in ΛQCD/mb one is working.

The same expansion can be written in case of b → u semileptonic transitions, with the

Equation 1.41 and 1.42 that have perturbative corrections, known through order α2S [20],

as follows:

Γb→usl =

G2Fm

5b

192π3|Vub| 2

[A0

(1− µ2

π − µ2G

2m2b

)− 2

µ2G

2m2b

+O( 1

m3b

)], (1.44)

with the leading order corrections given in terms of µ2π e µ2

G. The leading term includes

purely perturbative corrections (embedded in the coefficient A0).

These perturbative effects have been calculated, and no significant uncertainties are

expected from yet uncalculated higher order perturbative effects.

The corrections depend on αS and mb which are scale dependent. The largest term

is proportional to 1/m2b and thus is of order 5%, leading to a reduction in the decay

width by ≈ 4%. Similar results can be derived for differential distibutions, as long as

the distributions are sufficiently inclusive. To quantify this last statement, it is crucial

to remember that the OPE does not apply to fully differential distributions but requires

that such distributions be smeared over enough final state phase space. The size of the

smearing region ∆ introduces a new scale into the expressions for differential rates and

can lead to non-perturbative corrections being suppressed by powers of ΛnQCD/∆

n rather

than ΛnQCD/m

nb . Thus, a necessary requirement for the OPE to converge is ∆ À ΛQCD,

although a quantitative understanding of how experimental cuts affect the size of smearing

regions is difficult.

15

1.3.2 Decay Rates in Restricted Phase Space Region

The measurement of B → Xu`ν suffers from a large background from the decay B →Xc`ν. The reason for the large background is that |Vcb| À |Vub|, meaning that the b quarks

“likes” to decay to a c quark much more than to a u quark. In order to eliminate the

background we have to look at regions of phase space where particles containing charm

cannot be produced.

In order to analyze inclusive decays one can start answering to a simple question

“How many kinematical variables are needed to describe an inclusive event?”. We are

looking at a decay of a B meson into n particles, where n − 1 of them have known

mass. The “particle” X has unspecified invariant mass. In general for a decay into n

particles there are 3n− 4 kinematical variables, but not all of them are determined from

the dynamics. Since we do not have information about the spin of the hadronic state X

or the spin/polarization of the other decay products, the only four vectors we have at

our disposal are PB, the four momentum of the B meson, p1 ≡ PX the four momentum

of X and p2, . . . , pn. Lorentz invariance implies then that the possible variables are the

(n+1)(n+2)/2 scalar products of these n+1 vectors. Since the masses of all the particles

apart from p1 are known, we have n constraints of the form p2i = m2

i , (i = B, 2, . . . , n).

Conservation of momentum would allow us to eliminate all the pairs that contain PB

(since PB =∑n

i=1 pi), i.e. eliminating n + 1 variables. That leaves us with n(n − 1)/2

independent variables. The rest of the variables are undetermined from the dynamics and

can be integrated over. This arguments hols for n ≤ 3, since at 4 dimensions at most 4

vectors (corresponding to n = 3) can be linearly independent. For n > 3 the argument

needs to be modified. For B → Xu`ν we have n = 3 and three relevant variables (see

Table 1.2). There are various choices in the literature for these variables, and in order

to understand them we have to say a few words about the dynamic of the decay. First

we need to distinguish between the hadronic level, which looks at the decay as a decay

of hadrons, and the partonic level, which looks at the decay as a decay of quarks. At

the hadronic level we have a B meson carrying momentum PB ≡ MBv decaying into a

leptonic pair (the lepton and anti-neutrino) carrying momentom total q, and a hadronic

16

Scalar Products Constraints

¡¡P 2B »»»PBPX »»»PBP` »»»PBPν PB = PX + P` + Pν

P 2X PXP` PXPν

¡¡P2l »»»PlPν (PX + P` + Pν)2 = M2

B , P 2` = 0

¡¡P2ν P 2

ν = 0

Table 1.2: Number of kinematic variables for inclusive B decays. Using the constraints on the rightcolumn we can eliminate some of the variables on the left column.

jet carrying momentum PX . Conservation of momentum implies MBv − q = PX . At the

partonic level we look at the decay as a decay of a b quark, carrying momentum mbv, into

a u quark, carrying momentum p (at tree level), and a virtual W carrying momentum q.

The W in turn decays into a lepton ` and an anti-neutrino ν` (more accurately we write

the momentum of the b quark as mbv + k where k is O(ΛQCD) and expand in powers of

k). Conservation of momentum implies mbv − q = p. If we define Λ ≡ MB −mb we find

that PX = p+Λv. Beyond tree level p would be the momentum of the jet of light partons

created in the decay.

There are generically two common choices of variables:

• Leptonic: the energy of the lepton E`, the energy of the neutrino Eν and the

invariant mass of virtual W boson q2, which is also the invariant mass of the leptonic

pair. This choice focuses on the leptons created in the decay.

• Partonic: the energy of the lepton E`, the energy of the partonic jet v · p and the

invariant mass of the partonic jet p2. This choice focuses on the partons created in

the decay.

For example we can only look at events for which P 2X < M2

D. This fact implies that

the “typical” Xu state will have large energy of order mb, since it originates from a decay

of a heavy quark and intermediate invariant mass, because of the experimental cut. Since

MD ∼√mbΛQCD we can write P 2

X ∼ mbΛQCD. This implies that some of the components

of PX are larger than others. We would like the choice of our variables to reflect that. A

pair of variables which satisfy this condition is:

P− = EX + |~PX |, P+ = EX − |~PX |, (1.45)

where EX and PX are the energy and momentum of the hadronic jet, respectively. Note

17

that P+P− = P 2, P+ + P− = 2EX and P+ < P−. The scaling of these variables will

therefore be P− ∼ mb and P+ ∼ ΛQCD. Specifying P+ and P− would determine the

energy and the invariant mass of the lepton pair, but not the individual energies of the

lepton and neutrino. We therefore have to add another variable that would distinguish

between the two:

P` = MB − 2E` (1.46)

We can determine now the phase space region in terms of P+, P` and P−. In the rest frame

of B meson, conservation of energy and momentum gives us the following equations:

E` + Eν + EX = MB (1.47)

~P` + ~Pν + ~PX = 0. (1.48)

Considering the lepton massless implies E` = |~P`| and Eν = |~Pν |. The limits of phase

space are determined by the extremal values of angles between the momenta. Because of

conservation of momentum (Eq. 1.48) we have only two independent angles.

Let θ be the angle between ~P` and ~Pν . Equation 1.48 then implies ~P 2X = E2

` + E2ν +

2EνE` cos θ. Since −1 ≤ cos θ ≤ 1, we have (E` − Eν)2 ≤ |~PX |2 ≤ (E` + Eν)

2. Using

P+ ≤ P−, the upper limits gives us P− ≤MB, and the lower limit P+ ≤ P` ≤ P−.

Let α be the angle between ~P` and ~PX . Equation 1.48 then implies E2ν = (MB −

E` − EX)2 = E2` + |~PX |2 + 2E`|~PX | cosα. Since −1 ≤ cosα ≤ 1, the upper limit gives

(MB−P+)(P−−P`) ≥ 0, and the lower limit (MB−P−)(P`−P+) ≥ 0. Another constraint

comes from the QCD spectrum: the lightest state containing a u quark is the pion, so we

must have M2π ≤ P 2

X = P+P−. Combining all of these constraints we finally have:

M2π

P−≤ P+ ≤ P` ≤ P− ≤MB. (1.49)

One of the benefits of this choice of variables (apart from the easy derivation) is that phase

space (shown in Fig. 1.4) has an extremely simple form. By examining the phase-space

plane we can find regions where the CKM favoured b → c transitions are forbidden and

therefore select cuts that can be used for the experimental measurements:

• cut on the charged lepton energy E`. If E` ≥ (M2B−M2

D)/2MB ≈ 2.31 GeV, the final

18

[GeV]-P0 1 2 3 4 5

[G

eV]

+P

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Figure 1.4: The (P+P−) phase space for B → Xu`ν. Left: The charm free region is the dark greyregion below the black hyperbola, which correspond to M2

X = P+P− = M2D The solid blue line is

q2 = (MB − P+)(MB − P−) = (MB −MD)2. The red dashed line is P+ = M2D/MB . Right: same as left,

but with the actual distribution of b → u`ν superimposed.

hadronic state will have invariant mass smaller than MD. For this cut P` ≤ 0.66 GeV,

which implies that P+ is of order or ΛQCD;

• cut on the hadronic invariant mass M2X . To eliminate charm background we need

M2X ≤M2

D. The cut M2X = M2

D is depicted as a solid hyperbola in Figure 1.4;

• cut on the leptonic invariant mass q2. Any cut of the form q2 ≥ (MB −MD)2 would

not contain charm events. The cut q2 = (MB − P+)(MB − P−) = (MB −MD)2 is

depicted as a solid line in Figure 1.4;

• cut on P+. Red line in Figure 1.4 shows P+ = M2D/MB.

The experimental measurements have to be performed in restricted region of phase

space and then theoretical prediction on the partial decay widths are needed to extrapolate

to the full phase space. From the theoretical point of view, calculating the partial decay

rate in regions of phase space where B → Xc`ν are suppressed is very challenging, as

the HQE convergence in these regions is spoiled requiring the introduction of a non-

perturbative distribution function, whose form is unknown.

The shape function is a universal property of B mesons at leading order. It has been

19

recognized for over a decade [21, 22] that the leading shape function can be measured

in B → Xsγ decays. However, sub-leading shape functions [23, 24, 25, 26, 27] arise at

each order in 1/mb, and differ in semileptonic and radiative B decays. As previously said,

the form of the shape function cannot be calculated but can be constrained by moment

relations, which relate weighted integrals over the shape function to the heavy-quark

parameters mb (b quark mass), µ2π (kinetic energy of the b quark in the B meson) and µG

(chromomagnetic moment of the b quark). The inclusive charmed semileptonic decay rate

depends on these parameters so constraints to their values and, therefore, to the shape

function, can be applied studying B → Xc`ν decays. The same arguments hold for the

“2 body” B → Xsγ decay, which is directly sensitive to mb. An alternative way is to

employ shape-function independent relations between weighted B → Xsγ and B → Xc`ν

spectra [21, 28, 29, 30, 31]. Both approaches are equivalent; yet, not all predictions that

have been obtained using the shape function independent relations are up to the standard

of present-day calculations.

A fairly complete theoretical analysis of inclusive B → Xu`ν spectra was based on

calculation described in [32, 30] and referred to as BLNP approach. It includes complete

perturbative calculations at NLO with Sudakov resummations, subleading shape functions

at three level, and kinematical power corrections at O(αs). An alternative scheme called

“Dressed Gluon Exponentiation” (DGE) [33, 34, 35] employs a renormalon-inspired model

for the leading shape function, which is less flexible in its functional form that the forms

used by BLNP. Also, no attempt is made to include subleading shape functions, which

among other things means that the predictions for more inclusive partial rates would not

be in accord with the operator product expansion beyond the leading power in ΛQCD/mb

The DGE model is therefore less rigorous than the BLNP approach, even though it leads

to numerical results that are compatible with those of BLNP. Very recently, Gambino et

al. (GGOU) [36] released a work in which authors include the recently calculated O(β0α2s)

corrections to the decay rates [37] which were not available for BLNP. They use moment

constraints to model the subleading shape function differently for the various structures

in hadronic tensor. However, no attempt is made to resum the Sudakov logarithms. The

numerical results obtained using the GGOU code are consistent with those of BLNP in

20

both their central values and error estimates. Another calculation based on pure OPE

was proposed some time ago by Bauer, Ligeti and Luke [38]; their idea presupposes the

extraction of |Vub| from inclusive semileptonic decays b → u`ν by applying a cut on the

squared lepton-neutrino invariant mass q2. Such a cut forbids the hadronic final state

from moving fast in the B rest frame, and so the light-cone expansion which gives rise

to the shape function is not relevant in this region of phase space. It is shown that the

BLL calculation is most predictive, also in terms of uncertainties, in phase space regions

defined by a combination of MX and q2 requirements.

1.3.3 Experimental Approaches

The experimental approaches commonly used to measure charmless semileptonic B decays

fall into three categories:

1. Charged lepton momentum “endpoint” measurements. In these analyses, a single

charged electron is used to determine a partial decay rate for B → Xu`ν and no

neutrino reconstruction is employed, resulting in a ∼ 50% selection efficiency. The

decay rate can be cleanly extracted for E` > 2.3 GeV, but this is deep in the shape

function region, where theoretical uncertainties are large. Recent measurements push

down to 2.0 or 1.9 GeV, but the cost is a lower (< 1/10) signal-to-background (S/B)

ratio;

2. “untagged” neutrino reconstruction measurements. In this case, both the charged

electron and the missing momentum are measured, allowing the determination of q2

and providing additional background rejection. This allows a much higer S/B∼ 0.7

at the same E` cut and a selection efficiency ∼ 5%, but at the cost of smaller

accepted phase space for B → Xu`ν decays and uncertainties associated with the

determination of the missing momentum;

3. “tagged” measurements in which one B meson is fully reconstructed. The S/B ratio

can be quite high (∼ 2%) but the selection efficiency is ∼ 10−3. The E` cut is

typically 1.0 GeV and the full range of signal-side variables (q2, MX , P+) is available

for study, each having its own pros and cons. A cut on the hadronic invariant mass

21

(region below the black hyberbola in Fig. 1.4) has the advantage to include ≈ 80%

of b→ u transition, but has a strong dependence on the shape function. The highest

cut that is possible to set on the ligth-cone momentum is P+ < 0.66 (region below

the red line in Fig. 1.4) which provides access to ≈ 70% of charmless semileptonic

b transition, but the dependence on the shape function is high as well. The q2

distribution is less sensitive to non perturbative effetcs and less dependent on the

calculation of theoretical acceptance, but only a small fraction of events is usable

with a pure q2 cut (region below the blue line in Fig. 1.4). Combined MX and q2

cuts mitigate the drawbacks of the two methods while retaining good statistical and

systematic sensitivities. The fraction of b → u event selected with these combined

cuts is ≈ 45%.

In this thesis, the tagged approach has been chosen and three different kinematic

regions are exploited, in order to compare measurementes with different sensitivies to

theoretical uncertainties; these regions are defined by pure MX cuts, pure P+ cuts and

combined (MX , q2) cuts. Table 1.3 shows a summary of the features of each kinematic

requirement. The detailed impact of the theoretical models presented above on the deter-

Kinematic region % of rate Pros ConsMX < MD ∼ 80% lots of rate depends on shape function

(and subleading corrections)P+ < M2

D/MB ∼ 70% lots of rate depends on shape function(and subleading corrections)

q2 > (MB −MD)2 ∼ 20% insensitive to shape function - very sensitive to mb

- Weak Annihilation may be substantial- effective expansion parameter is 1/mc

(MX , q2) combined ∼ 45% insensitive to shape function less rate than MX and P+ cuts

Table 1.3: Comparison of different kinematic cuts.

mination on |Vub| from the experimental measurements discussed in this thesis are shown

in Chapter 8.

22

Chapter 2

The BABAR Experiment

The BABAR experiment at PEP-II B factory [39, 40] has been optimized for CP violation

studies and searches for rare B meson decays. The PEP-II B factory is an high luminosity

(L & 3 × 1033cm−2s−1) e+e− collider operated at the center-of-mass (CM) energy of

10.58 GeV, on the Υ(4S) resonance. This resonance decays almost exclusively in a B0B0

or a B+B− pair with equal probabilities, giving a clean environment characterized by a

good signal-to-noise ratio (σbb/σtot ≈ 0.28) and low track multiplicity per event (≈ 11).

In addition, events reconstruction and background rejection benefit by the kinematic

constraint on the momentum and energy, of each B, in the CM frame.

In PEP-II, the electron beam of 9 GeV collides head-on with the positron beam of

3.1 GeV resulting in a Lorentz boost for the Υ(4S) of βγ = 0.56 in the laboratory frame.

Figure 2.1 shows the boost effect on the polar angle. The asymmetry of the machine is

Figure 2.1: Effect of the Lorentz boost on the polar angle at BABAR .

23

motivated by the need of separating the decay vertexes of the two B mesons, a crucial

point for the determination of the CP asymmetries. The boost allows the separation and

reconstruction of the decay vertexes of both B mesons, the determination of their relative

decay length measured in the center-of-mass frame, the difference of their decaying time

and thus the measurement of time dependent asymmetries. Nevertheless other stringent

requirements on the detector are placed in order to measure the very small branching

ratios of B mesons to CP eigenstates:

- large and uniform acceptance down to small polar angle relative to the boost direc-

tion;

- excellent reconstruction efficiency down to 60 MeV/c for charged particles and

20 MeV for photons;

- very good momentum resolution to separate small signals from background;

- excellent energy and angular resolution to detect photons coming from π0 and η

decays, and from radiative decays in the range from 20 MeV to 4 GeV;

- very good vertex resolution, both transverse and parallel to the beam direction;

- efficient electron and muon identification, with low misidentification probabilities for

hadrons. This feature is crucial for tagging the B flavor, for the reconstruction of

charmonium states and also important for the study of decays involving leptons;

- efficient and accurate identification of hadrons over a wide range of momenta for B

flavor-tagging and for the reconstruction of exclusive states;

- low-noise electronics and a reliable, high bandwidth, data-acquisition and control

system;

- detailed monitoring and automated calibration;

- an on-line computing and network system that can control, process and store the

expected high volume of data;

24

- detector components that can tolerate significant radiation doses and operate reliably

under high background conditions.

2.1 The PEP-II Asymmetric Collider

The PEP-II B factory is part of the accelerator complex at SLAC, shown in Fig. 2.2.

The electron beam is produced by the electron gun near the beginning of the two-mile

long linear accelerator (the “linac”). The gun consists of a thermally heated cathode

filament held under high voltage. Large numbers of electrons are “boiled off” the cathode,

accelerated by the electric field, collected into bunches, and ejected out of the gun into the

linac. The electron bunches are accelerated in the linac with synchronized radio-frequency

(RF) electromagnetic pulses generated in RF cavities through which the beam passes by a

series of 50 Megawatt klystron tubes (klystrons generate the pulses with their own lower

energy electron beams passing through resonant cavities). The steering, bending, and

focusing of the beam is carried out with magnets throughout the acceleration cycle.

Figure 2.2: A schematic depiction of the B factory accelerator complex ad SLAC.

After acceleration to an energy of approximately 1 GeV, the electron beam is directed to

a damping ring, where the beam is stored for some time. As it circulates in the ring, it loses

energy through synchrotron radiation and is continuously re-accelerated by RF cavities.

25

The radiation and careful re-acceleration has the effect of reducing the emittance, or

spatial and momentum spread of the beam, a necessary step in high-luminosity collisions.

The “damped” beam is then re-directed to the linac and accelerated to 8.9 GeV.

Half of the generated electron bunches are used for the generation of the positron

beam. They are accelerated to approximately 30 GeV, extracted from the linac and

directed onto a tungsten target, producing electromagnetic showers that contain large

numbers of electron-positron pairs. The positrons are separated electromagnetically from

the electrons, collected into bunches, accelerated, and sent through the return line to

the source end of the linac. The positron beam is then accelerated and shaped like the

electron beam through the linac and its own damping ring, culminating in an energy of

3.1 GeV.

After reaching their respective collision energies, the electron and positron beams are

extracted from the linac, and directed to the PEP-II storage rings, the High-Energy

Ring (HER) for electrons and Low-Energy Ring (LER) for the positrons, both housed

in the same tunnel of 2.2 km circumference. As they circulate, the are focused further

by a complex of magnets and accelerated by RF cavities to compensate the synchrotron-

radiation losses. In the interaction region IR-2 (one of twelve such regions), where the

BABAR detector is located, they are brought to a collision after a final-focus system

squeezes the beams to the smallest possible emittance. During data taking, each ring

contains about 1600 circulating bunches colliding every 5 ns. The collisions are then

analyzed by the BABAR detector. About 10% of the time the beams are collided at an

energy 40 MeV below the Υ(4S) resonance for calibration of the backgrounds, as no B

mesons are produced then since this energy is below the bb threshold. As data is collected,

the collision and other losses reduce the currents in the rings, necessitating re-injection

of electron and positron bunches. Initially in the life of the B factory from 1999-2002,

data was taken for about an hour or two while the currents diminished, and then addi-

tional current was injected into the rings for a few minutes. Data could not be taken

during injection due to the large backgrounds in the detector and the resulting danger to

instrumentation. (The detector would have to be put into a “safe” but non-operational

state during injection, with, for example, all high-voltage components ramped down to

26

a lower, safer potential). Starting in 2003, a new scheme for injection, called “trickle”

injection, was developed, wherein new bunches are continuously injected at a rate large

enough to replenish beam losses but low enough to not damage the detector. This has

allowed more efficient operation of the B-factory with 30% more integrated luminosity

for a given highest instantaneous luminosity.

The PEP-II collider was designed for an instantaneous luminosity of 3× 1033 cm−2s−1,

but has reached values of 1.2 × 1034 cm−2s−1 due to improvements in the RF cavities,

beam-shaping cavities and magnet systems. The increased luminosity comes from larger

beam currents (up to 3 A in the LER and 2 A in the HER) and reduced emittance.

With these specifications and trickle injection, the machine generates hundreds of pb−1

of integrated luminosity daily during normal operations and has integrated hundreds of

fb−1 throughout its operating lifetime. Fig. 2.3 shows the total (left) and daily (right)

integrated luminosity.

Figure 2.3: PEP-II delivered and BABAR recorder total (left) and daily (right) integrated luminosity inthe data taking period of 1999-2006 (Run1-Run5).

2.1.1 PEP-II Backgrounds

Different factors should be taken into account when trying to set an acceptable background

that allows a smooth and safe BABAR detector operation. Main constraints are:

27

- Radiation levels in EMC and SVT sub-detectors;

- Current tolerated by DCH;

- L1 trigger rate;

- Other subsystems occupancy.

Simulations, data analysis and dedicated measurements of the various background sources,

on their impact on data taking and on detector performance have contributed to form

a detailed knowledge of different background-related underlying phenomena and made

possible their tuning and reduction. PEP-II main background sources [41] are:

• synchrotron radiation in the proximity of the interaction region. A strong source

of background (many kW of power) is due to the beam deflections in the inter-

action region. This component is limited by channeling the radiation out of the

BABAR acceptance with a proper design of the interaction region and the beam orbits,

and placing absorbing masks before the detector components.

• interaction between beam particles and residual gas in either ring can have two dif-

ferent origins: beam-gas bremsstrahlung and Coulomb scattering. Both these two

types of interaction causes an escape of the beam particle from their orbit. This

background represents the primary source of radiation damage for the inner vertex

detector and the principal background for the other detector components.

• electromagnetic showers generated by beam-beam collisions. These showers are due

to energy degraded e+ and e− produced by radiative Bhabha scattering and hitting

the beam pipe within a few meters of the IP. This background is proportional to

the luminosity of the machine and whereas now is under control, it is expected to

increase in case of higher operation values.

2.2 The BABAR Detector

The BABAR detector is a large, multi-purpose hermetic detector with several components.

As shown in Fig. 2.4 the detector consists of two endcaps and a cylindrical barrel hugging

28

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yx

z1149 1149

Instrumented Flux Return (IFR))

BarrelSuperconducting

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Electromagnetic Calorimeter (EMC)

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3-2001 8583A50

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Earthquake Tie-down

Earthquake Isolator

Floor

3-2001 8583A51

Figure 2.4: Longitudinal (top) and end (bottom) views of the BABAR detector. Units are mm.

29

the beam pipe along the z direction and roughly symmetric in the azimuth φ. The

right-handed coordinate system is defined with the z axis pointing in the e− direction, x

pointing horizontally away from the center of PEP-II rings, and y pointing upwards. The

geometrical center is offset from the beam-beam interaction point towards polar angles

to maximize the geometric acceptance for the boosted Υ(4S) decays.

The sub-detectors are arranged in layers of increasing distance from the beam pipe.

The silicon vertex tracker (SVT), the innermost detector, is used for vertexing particle

decays and is the main source of information on the polar angle of charged particles.

The Drift Chamber (DCH) is the main device for measuring charged-particle momenta

with good resolution through gaseous wire-chamber technology. A Detector of Internally

Reflected Cerenkov Light (DRC) is used to separate pions from kaons, while a crystal Elec-

tromagnetic Calorimeter (EMC) is used for energy measurement of photons and electrons

and for electron identification. These components are placed within a 1.5 Tesla solenoidal

magnet that provides the magnetic bending of charged particles needed to measure their

momenta. Outside the magnet is the Instrumental Return Flux (IFR), which is used for the

identification of muons and long-lived neutral hadrons. The detector signals are processed

through detector electronics, and examined by a trigger system that selects physically in-

teresting collision data to be stored. Various online and offline reconstruction procedures

are employed to convert the data into a format amenable to analysis for the study of

relevant B decays and other processes.

2.2.1 Silicon Vertex Tracker (SVT)

The SVT consists of five layers of double-sided silicon sensors segmented in both the z

and φ directions, designed to measure accurately the positions and decay vertexes of B

mesons and other particles. This measurement is most accurate at small distances from

the interaction point, as the trajectory of the particles farther away is affected by multiple

scattering within the detector. Thus, the first three layers are located as close to the

beam pipe as possible. The outer two layers are closer to the Drift Chamber to facilitate

matching of SVT tracks with DCH tracks. They also provide pattern recognition in track

reconstruction, and the only tracking information for charged particles with transverse

30

momenta below 120 MeV/c, as these may not reach the Drift Chamber. The SVT covers

90% of the solid angle in the CM frame. Fig. 2.5 shows schematic views of the SVT.

Figure 2.5: Schematic view of the SVT: longitudinal section (left) and transverse section (right).

The silicon sensors are 300 µm-thick high-resistivity n-type silicon wafers, with n+ and

p+ strips running orthogonally on opposite sides. As high-energy particles pass through

the sensor they displace orbital electrons, producing conducting electrons and positive

holes that then migrate under the influence of an applied depletion voltage. The resulting

electrical signal is read-off from the strips, amplified and discriminated with respect to a

signal threshold by front-end electronics. The time over threshold of the signal is related

to the charge of the signal and is read out by the data acquisition system for triggered

events. The position resolution is in the 10 µm-50 µm range, depending on the orientation

of the strip (φ or z) and the layer number.

The SVT is water-cooled and monitored for temperature, humidity and position vari-

ations. Local and global position alignment is performed frequently in the outline re-

construction software. As the SVT has to withstand a lifetime integrated radiation dose

of 2 Mrad, the sensors have a high threshold for radiation damage. Nevertheless, they

are easily damaged by high instantaneous or integrated doses and an extensive system of

radiation monitoring with PIN and diamond diodes can abort the beams if dangerous level

develop. Up to 2007 the monitoring systems have prevented any significant damage from

occurring and the SVT has performed extremely well, with an average track reconstruction

efficiency of 97%.

31

2.2.2 Drift Chamber (DCH)

The Drift Chamber is the main tracking device. It supplies high precision tracking for

charged particles with transverse momenta pT above ≈ 120 MeV/c, and provides also

particle identification by measuring track ionization losses as function of position (dE/dx),

in particular for tracks with momenta less than 700 MeV/c.

The inner wall of the Drift Chamber is placed close to the SVT outer wall to facilitate

track-matching between the two devices. The chamber is 2.8 m long and consists of 40

cylindrical layers of 12 mm by 19 mm hexagonal cells, each consisting of six field wires

at the corners and one field wire in the center as shown in Fig. 2.6 and Fig. 2.7. The

Figure 2.6: Longitudinal section of the DCH. Dimensions are in mm. The chamber center has an offsetof 370 mm from the interaction point (IP).

field wires are grounded, while the sense wire is held at high voltage, typically around

1900 V. The space around the wires is filled with gas mixture containing 80% helium and

20% isobutane. High-energy particles ionize the gas as the traverse it, and the liberated

electrons are then accelerated toward the sense wires, ionizing additional electrons, which

are in turn accelerated themselves and result in the formation of a gas avalanche of

electric charge. The avalanche collects on the sense wire with drift times of 10-500 ns

and the charge and timing information of the signal is read-off through electronic circuits

AC-coupled to the wire. The gain relative to the charge of primary ionization is about

32

0Stereo

1 Layer

0Stereo

1 Layer

0 2 0 2 0 2

0 3

0 4 0 4

45 5 45 5

47 6 47 6 47 6

48 7 48 7

50 8

-52 9

-5410

-5511

-5712

013 013

014 014

015

016

4 cm

Sense Field Guard Clearing

1-2001 8583A14

Figure 2.7: Layout of the four innermost super-layers.

33

5× 104. The grounded field wires produce a uniform electric field in the cell with evenly

distributed isochrones, or contours of equal drift time, as shown in Fig. 2.8. “Stereo”

wires in 24 of the 40 layers are placed at small angles with respect to the z direction in

order to provide longitudinal information. The chamber has a typical position resolution

of 140 µm.

Sense

Field Guard 1-2001

8583A16

Figure 2.8: Isochrones in a typical DCH cell.

Isobutane has large molecules with rotational degrees of freedom that can absorb elec-

trical energy, and its presence in the gas mixture limits the growth of the avalanche in

order to protect the chamber from damaging levels of accumulated charge. The choice

of the gas mixture is motivated by considerations of aging and avalanche size as well as

minimizing multiple scattering in the chamber, which is accomplished by choosing helium

as the primary gas component and aluminum as the lightweight material for the multiple

field wires. The gas is circulated to flush out any degraded component, with one full

volume of fresh gas (5.2 m3) added every 36 h. In addition, the water content of the gas is

maintained by a water bubbler at 3500±200 ppm and oxygen is removed with a catalytic

filter, both measures designed to prevent Malter-effect discharges in the gas that would

degrade the performance and aging behavior of the chamber.

The DCH has demonstrated excellent performance throughout the life of BABAR with

track-reconstruction efficiencies at the 95% level. This includes the effect of discon-

necting a fraction of the wires in superlayers 5 and 6 the were damaged during the

commissioning phase. The dE/dx response, with a resolution of about 7%, is shown

34

in Fig. 2.9, and a new calibration in 2006 has improved the PID potential of this ca-

pability for high-energy tracks. The achieved resolution on transverse momentum is

σpT/ pT = (0.13 ± 0.01)% × pT + (0.45 ± 0.03)% where pT is given in units of

GeV/c.

Figure 2.9: dE/dx in the DCH as a function of track momentum for different particles: protons (blue),kaons (red), pions (green), muons (black) and electrons (magenta).

2.2.3 Cerenkov Light Detector (DRC)

The DIRC (Detector of Internally Reflected Cerenkov ) is the main PID sub-detector at

BABAR , providing π−K separation of 2.5σ or more over the momentum range 700 MeV/c -

4.2 GeV/c. It is thin and light, minimizing the size and the impact on performance of

the EMC that is located outside the DRC in the radial direction. Cerenkov devices detect

light radiated by particles that move faster than the speed of light in a given medium,

with the Cerenkov angle θC of the radiated photons given by

cos(θC) =1

nβ=

c

nv, (2.1)

where n is the index of refraction of the medium and v is the particle’s velocity. For a

given momentum, particles of different mass will have different velocities, differentiating

particle-mass hypotheses for a track and thus different PID hypotheses.

35

The DRC consists of 144 bars made of fused silica running along the z direction, with

dimensions of 17 mm by 35 mm and 4.9 m in length. The silica serves as the Cerenkov

radiator, with the high index of refraction of n = 1.437 and as a waveguide, with a

low attenuation length. A charged particle passing through radiates Cerenkov photons,

which then propagate to the longitudinal end of the bar, trapped within by total internal

reflections at the flat boundaries of the bar. Each reflection preserves the original Cerenkov

angle. At the end of the bars, the photons pass through a standoff box filled with purified

water that has a similar refractive index of n = 1.346, so that refraction at the silica-

water boundary is minimized. The water must be highly transparent as the photons

pass through about one meter of water in the standoff box, so it is filtered, de-gassed,

de-ionized, exposed to UV radiation to prevent the growth of bacteria, and treated with

a reverse-osmosis unit.

The rear surface of the standoff box is instrumented with 12 sectors of 896 photo-

multiplier tubes (PMTs) each, which collect the photons, convert them to electrons with

photo-cathodes and amplify the signal using the gas-avalanche principle. As the standoff

box is located outside the solenoid magnet, it is possible to limit the magnetic field in its

volume to about 1 Gauss with a bucking coil that counteracts the field of the solenoid.

Thus, conventional PMTs, which do not tolerate high magnetic fields, can be used. To

limit the number of PMTs, there is only one standoff box, located at the backward end

of the detector to exploit the forward boost environment of the collisions. The forward

ends of the silica bars have mirrors perpendicular to the axis of the bars, so that forward-

pointing photons are reflected and reach the backward end of the bars as well. The

detector is depicted schematically in Fig. 2.10. The total photon detection efficiency is

at the 5% level, with the average number of detected photons ranging from 20 at normal

track incidence to 65 at large polar angles.

As the Cerenkov angle of the emitted photons is preserved, it can be reconstructed

from the PMT signals, the timing information and the track momentum vectors obtained

by matching the signal with tracks from the DCH and SVT. The resolution on the single-

photon Cerenkov angle θC,γ is 10.2 mrad, while the resolution that can be obtained for a

36

Figure 2.10: DRC scheme: radiation area and imaging region.

track from all its radiated photons is

θC,track =θC,γ√Nγ

(2.2)

where Nγ is the number of detected photons. This yields typical track angular resolutions

of 3 mrad.

The DRC is intrinsically a three-dimensional imaging device, giving the position and

arrival time of the PMT signals. The three-dimensional vector pointing from the center

of the bar end to the center of the PMT is computed and then is extrapolated (using

Snell’s law) into the radiator bar in order to extract, given the direction of the charged

particle, the Cerenkov angle. Timing information is used to suppress background hits

and to correctly identify the track emitting the photons. Fig. 2.11 shows light rings

reconstructed by the DRC.

2.2.4 Electromagnetic Calorimeter (EMC)

The electromagnetic calorimeter has been designed to measure with excellent resolution

the energy and angular distribution of electromagnetic showers with an energy in the

range from 20 MeV (for photons from decays of slow π0 or η0) to 4 GeV (for photons and

electron from weak processes). An efficient and pure selection of electrons is necessary

37

Figure 2.11: Cerenkov light ring reconstruction using the DRC.

for B flavor tagging via semileptonic decays, for the reconstruction of vector mesons like

J/ψ, or of several exclusive final states of B and D mesons. Furthermore QED processes

like e+e− → e+e−(γ) and e+e− → γγ need to be efficiently detected because they are

useful for calibration and luminosity determination.

The EMC (Fig. 2.12) is made of 6580 CsI Tallium activated crystals (Fig. 2.13) The

transverse segmentation is at the scale of Moliere radius to optimize the angular resolution

while limiting the number of crystals and readout channels. The crystals serve as radiators

for the traversing electrons and photons, with a short radiation length of 1.85 cm. The

crystal scintillate under the influence of the showers and the light is passed through total

internal reflection to the outer face of the crystal, where it is read out by silicon PIN diodes.

As these diodes are well suited for operation in the high magnetic fields in the EMC, part

of the motivation for the crystal choice was that the frequency spectrum of CsI(Tl) is

detected by silicon PIN sensors with the high quantum efficiency of 85%. The EMC is

cooled by water and Flourinert coolant and monitored for changes in the environmental

and radiation conditions and for changes in the light response of individual crystals.

38

Figure 2.12: EMC longitudinal section (top-half only, dimension in mm) showing how the 56 crystal ringsare placed. Detector has an axial symmetry along z axis.

Figure 2.13: EMC crystal scheme.

39

The energy response of the EMC is calibrated using low-energy photons from a radioac-

tive source and high-energy photons from radiative e+e− Bhabha events. As electromag-

netic showers spread throughout several crystals, a reconstruction algorithm is used to

associate activated crystals into clusters and either to identify them as photon candidates

or to match individual maxima of deposited energy to extrapolated tracks from the DCH-

SVT tracker. Additional PID is obtained from the spatial shape of the shower. The energy

and angular resolutions are determined to be

σE

E=

(2.32± 0.30)%4√E(GeV)

⊕ (1.85± 0.12)%, (2.3)

σθ = σφ =(3.87± 0.07) mrad√

E(GeV)⊕ (0.00± 0.04) mrad. (2.4)

In both cases, the first term is due to fluctuations in the number of photons and to

electronic noise of the photon detector and electronics, while the second term arises from

the non-uniformity of light collection, leakage and absorption due to materials between

and in front of the crystals and calibration uncertainties. Fig. 2.14 shows the agreement

between data and simulation of the angular resolution of the EMC and its π0 reconstruction

performance.

Figure 2.14: Left: angular resolution in the EMC as function of photon energy. The solid curve is a fit toEq. 2.4. Right: the reconstructed diphoton peak at the π0 mass region.

40

2.2.5 Instrumented Flux Return (IFR)

The IFR is the primary muon detector at BABAR and is also used for the identification

of long-lived neutral hadrons (primarily K0L’s). The IFR is divided into a hexagonal bar-

rel, which covers 50% of the solid-angle in the CM frame, and two endcaps (Fig. 2.15).

Originally it consisted of layers of steel of varying thickness interspersed with Resistive

Figure 2.15: Overview of the original IFR Barrel sectors and forward and backward end-doors.

Plate Chambers (RPCs), 19 layers in the barrel and 18 in each endcap1. The steel serves

as a flux return for the solenoidal magnet as well as a hadron absorber, limiting pion

contamination in the muon ID. RPCs where chosen as they were believed to be a reliable,

inexpensive option to cover the 2000 m2 of instrumented area in this outermost region of

BABAR with the desired acceptance, efficiency and background rejection for muons down

to momenta of 1 GeV/c.

The RPCs detect high energy particles through gas-avalanche formation in high electric

field. The chambers consist of 2 mm-thin bakelite sheets kept 2 mm apart by an array of

spacers located every 10 cm (Fig. 2.16). The space between is filled with a non-flammable

gas mixture of 56.7% argon, 38.8% freon 134a and 4.5% isobutane, while the sheets are

held at a potential of 7600V. The inside surface of the bakelite is smoothed with a linseed-

1Additional cylindrical RPCs where placed just outside the solenoid magnet to improve the matching between IFR andEMC showers

41

Figure 2.16: Planar RPC section with HV connection scheme.

oil coating so that the electric field is uniform, thus preventing discharges in the gas and

large dark currents. The RPCs operate in streamer mode, wherein the avalanche grows

into a streamer, a mild, controlled form of electrical discharge in the gas. The streamer

charge is read out in both φ and z directions by aluminum strips located outside and

capacitively coupled to the chamber. The streamer is kept from producing electrical

breakdown of the gas by the quenching action of the freon and isobutane molecules, as

described for the DCH.

In streamer mode, the gas gain is at the 108 level. The factor 10-1000 increase in gain

over avalanche mode greatly simplifies the readout electronics. Moreover, the charge of

the streamer is independent of the primary-ionization charge, resulting in an effectively

digital signal with high efficiency. Initially, the RPCs performed over 90% efficiency as

expected geometrically from inactive space in the detector, resulting in a muon detection

efficiency of 90% for a pion misidentification rate of 6–8% in the momentum range of

1.5 < p < 3.0 GeV/c, as shown in Fig. 2.17.

Shortly after the start of data-taking with BABAR in 1999, the performance of the

RPCs started to deteriorate rapidly. Numerous chambers began drawing dark currents

and developing large areas of low efficiency. The overall efficiency of RPCs started to

drop and the number of non-functional chambers (with efficiency less than 10%) rose

dramatically (Fig. 2.18), deteriorating muon ID. The problem was traced to insufficient

42

Figure 2.17: Initial muon-identification performance of BABAR RPCs.

Figure 2.18: Deterioration with time of the average RPC efficiency (red). The green dots show thefraction of RPCs with efficiency lower than 10%.

43

curing and R&D of the linseed-oil coating and to the high temperature at which the

RPCs were operated initially. Uncured oil droplets would form columns under the action

of the strong electric field and the high temperature (up to 37 C), bridging the bakelite

gap and resulting in large currents and dead space. Various remediation measures were

attempted, including flowing oxygen through the chambers to cure the oil and introducing

water cooling of the IFR, but they did not solve the problem. Extrapolating the efficiency

trend showed a clear path towards losing muon ID capability at BABAR within a couple

of years of operations, so an upgrade of the IFR detector was deemed necessary by the

collaboration.

The forward endcap was retrofitted with new improved RPCs in 2002. The new cham-

bers were screened much more stringently with QC tests and had a much thinner linseed-

oil coating that was properly cured and tested. They have performed well since then.

The backward endcap was not retrofitted, as its acceptance in the CM frame is small.

In the barrel, the collaboration decided to upgrade the detector with Limited Streamer

Tube (LST) technology. The RPCs were removed and replaced by 12 layers of LSTs and

6 layers of brass to improve hadron absorption. (The last layer of RPCs is inaccessible,

so the old chambers there were disconnected from all utilities but kept in place). Since

the author was partially involved in this upgrade as the project was a laborious and

careful but time-sensitive project undertaken at a mature age of the experiment, it will

be described in more detail than the other components of the detector.

The LSTs consist of PVC comb of eight 15 mm by 17 mm cells about 3.5 m in length,

encased in PVC sleeve, with a 100 µm gold-plated beryllium-copper wire running down

the center of each cell (Fig. 2.19). The cells in the comb are covered with graphite, which

is grounded, while the wires are held at 5500 V and held in place by wire holders located

every 50 cm. The gas mixture consists of 3.5% argon, 8% isobutane, and 88.5% carbon

dioxide. Like the RPCs and their name implies, the LSTs are operated in streamer mode.

The signal is read off directly from the wires through AC-coupled electronics (granularity

of two wires per channel in the φ direction) and from strips running perpendicular to

the tubes and capacitively coupled to the wires (35 mm pitch in the z direction). After

the mechanical assembly, the tubes were conditioned under progressively higher applied

44

Figure 2.19: The mechanical structure of BABAR LSTs.

45

voltages to burn off dirt accumulated during construction. Only tubes that could hold

the operational voltage without drawing excessive currents were accepted.

One of the crucial performance characteristics was the “singles’-rate”, or counting-

rate, plateau. As the streamer signals are effectively digital, given a constant incident

flux of particles, the chamber should show a counting-rate plateau over a range of applied

voltage where the charge of every streamer is above the read-out threshold (Fig. 2.20).

The plateau provides operational tolerance of the applied HV, allowing operations of the

LSTs at the middle of the plateau to safeguard against fluctuations in efficiency due to

changes in the gas gain from pressure or voltage fluctuations. Defects in the surface of

the graphite or dirt accumulated on the wire can result in large discharges in the tube

(including the Malter effect) that raise the singles’ rate and spoil the plateau (Fig. 2.20

right). In addition, a short plateau is an indication of poor aging behavior. Thus, the

quality of the plateau is a powerful QC test.

Figure 2.20: Left: a singles’ rate plateau seen versus applied voltage for several LSTs. Right: defects inthe chamber can spoil the plateau.

The LSTs were constructed at PolHiTech, an Italian company located in Carsoli, out-

side Rome. The construction and QC procedures outlined above were conducted under

the supervision of BABAR personnel. After all QC tests, the tubes were held under high

voltage for a month to verify that no premature aging behavior occurred. Thereafter,

they were assembled into modules of two to three tubes at Princeton University and The

Ohio State University and then shipped to SLAC for the installation, which occurred in

two stages: two sextants of the hexagonal barrel in summer of 2004 and the remaining

46

four sextants in the Fall of 2006. QC procedures were performed at every step to make

sure that only the best tubes were installed in the detector.

The project involved the manufacture of 1500 LSTs including contingency, with more

than 1200 installed in the detector. It also necessitated the design an fabrication of custom

read-out electronics (done by INFN Ferrara in Italy), HV power supplies (The Ohio State

University) and gas system (SLAC). The project was completed successfully, safely and

ahead of schedule. After installation, the tubes have performed very well since 2005 in

two sextants and since the beginning of 2007 in all sextants, with failure rate below 0.5%

for both the tubes and z-strips. The efficiencies of all layers are at the geometrically

expected level of 90%. Regular testing of singles’-rates with cosmic rays has verified

continuing excellent behavior with long single’s-rate plateaus (Fig. 2.21). Figure 2.22

Figure 2.21: Singles’ rate measurements with cosmic rays for diagnostic of installed LST module.

shows muon tracks in the LST part of the IFR, while in Fig. 2.23 efficiency maps for all

the six barrel sextants instrumented with LST are shown.

47

Timestamp: 7f:020000:41d633/a603358b:W

The PEP-II/BaBar B-Factory

Run: 68724

HER: 8.985 GeV, LER: 3.112 GeV

Date Taken: Tue Nov 14 10:25:46.270537000 2006 PST?

Figure 2.22: Event display of a cosmic muon event as seen by LSTs.

Figure 2.23: Efficiency map: each rectangle represents one sextant.

48

2.2.6 Trigger System (TRG) and Data Acquisition (DAQ)

The basic requirements for the trigger system is the selection of events of interest with a

high, stable and well-understood efficiency while rejecting background events and keeping

the total event rate under 1 kHz. At design luminosity, beam-induced background rates

are typically about 20 kHz each for one or more tracks in the Drift Chamber with pT >

120 MeV/c or at least one EMC cluster with E > 100 MeV.

The total trigger efficiency is required to exceed 99% for all BB events and at least

95% for continuum events. Less stringent requirements apply to other event types, e.g.

τ+τ− events should have a 90-95% trigger efficiency, depending on the specific τ± decay

channels.

The BABAR trigger system is implemented as a two-level hierarchy. The Level 1 (L1) is

hardware based, consisting in several dedicated microprocessor systems that analyze data

from the front-end electronics (FEEs) of the DCH, EMC and IFR to form primitive physics

objects used to make the trigger decision. These include tracks of minimum transverse

momentum that penetrate to a particular depth into the DCH and energy clusters in

the EMC above set thresholds. The selections are optimized to maintain nearly perfect

BB efficiency while removing most of the beam-induced backgrounds in the process of

reducing the data collection rate from about 20 kHz to a few kHz, which can be processed

by the next trigger level. Some “prescaled” events of random beam-beam crossing and

special event types are also collected for efficiency, diagnostic and background studies.

The trigger decision is made and communicated within the 12.8 µs buffer limit of the

FEEs. The L1 trigger has greater than 99.5% efficiency for BB processes.

After an L1 accept decision, the L1 output is passed on to the Level 3 (L3) trigger,

which consist of software based algorithm run on a farm of PCs. The L3 triggers also

has access to the complete event data and refines the L1 decision with more sophisticated

selections, such as requirements on a track’s distance of closest approach to the interaction

point or the total invariant mass of an event. It maintains the BB selection efficiency at

more than 99% while reducing the data rate to about 200 Hz. Each event corresponds to

about 30 kB of detector information.

49

An event that results in an L3 accept decision is processed by the data-acquisition

electronics and event-building software. In this process, charged tracks are reconstructed

from DCH and SVT information and extrapolated to the outer part of the detector, in-

corporating knowledge of the distribution of material in the detector and the magnetic

field. The momentum of tracks is measured from the sagitta in the curves of the tracks.

PID is refined with DRC, EMC and IFR as well as with attempts to match objects in those

sub-detectors with tracks in the DCH. Fundamental physical objects reconstructed in the

detector are also used to assemble candidates for composite particles. Lists of particle

candidates as well as the original digitized data is stored on tape in collections that are

retrieved later for high-level analysis by individual groups of users.

Throughout event reconstruction various calibrations such as alignment constants and

energy-scale adjustments in the EMC are applied to detector information to refine recon-

struction performance. Calibration information is updated frequently during data taking

to keep it consistent with running conditions. Data-quality scripts monitor detector be-

havior and various physics processes to verify that the collected data is not compromised

by deviations from expected behavior of the detector or accelerator. A parallel system

based on the EPICS slow-control environment is used to monitor and control the detec-

tor elements for all subsystems. Detector, accelerator and environmental conditions are

recorded in another “ambient” database. The entire data-taking process is supervised

at all times by at least two BABAR shifters on the detector side and several accelerator

operators on the PEP-II side.

50

Chapter 3

Event Reconstruction

Given the low branching ratio for charmless SL decays, it is essential to reconstruct

the maximum number of signal events in order to have precise measurements. This

suggests to collect inclusive samples of B decays, where little or no requirements are

made on the rest of the event. On the other hand, the poor signal over background ratio,

and the consequent need to apply kinematic cuts in order to reduce background from

semileptonic decays with charm, calls for a detailed knowledge of decay kinematics. This

can be achieved by partially or fully reconstructing the rest of the event, which results

in a low reconstruction efficiency. However, given the high-statistics sample collected at

B Factories, it is possible to find a reasonable compromise between these two apparently

contradicting requirements.

This analysis is based on the study of the recoil of B mesons fully reconstructed in

a hadronic mode (Breco). One of the two B mesons from the decay of the Υ(4S) is

reconstructed in a fully hadronic mode (see Fig. 3.1). Then, the remaining particles of

the event are then supposed to belong to the other B (Brecoil).

Due to the exclusive reconstruction of the Breco, the properties of the recoil can be

studied in a very clean environment. As it will be shown in detail in Chapter 5, charge

conservation can be required and the missing mass of the event should be compatible

with zero. Moreover, since the kinematics is over-constrained, the resolution on the re-

constructed quantities, such as the mass MX of the hadronic system X, is improved. The

momentum of the recoiling B is also known and therefore it’s possible to apply a Lorentz

transformation to the charged lepton four-momentum and compute it in the B rest frame.

51

Figure 3.1: Semileptonic events on the recoil of a fully reconstructed B meson.

The charge of the B is known, so B0 and B+ decays can be studied separately. The flavor

of the B is known, therefore the correlation between the charge of the lepton and the

flavor of the B can be used to reject B → D → lepton cascade events, as described

in Sec. 6.1. The only drawback is that the efficiency of this method is quite low and is

dominated by the B reconstruction efficiency.

The charged and neutral particles reconstruction is described in this chapter together

with the algorithm used for the full hadronicB reconstruction, the so-called Semi-exclusive

reconstruction [42] (Sec. 3.5).

3.1 Charged Particle Reconstruction

The charged particle tracks are reconstructed by processing the information from both

tracking systems, the SVT and the DCH. Charged tracks are defined by five parameters

(d0, φ0, ω, z0, tanλ) and their associated error matrix, measured at the point of closest

approach to the z-axis. d0 and z0 are the distances between the point and the origin of

the coordinate system in the x−y plane and along the z-axis respectively. The angle φ0 is

the azimuth of the track, λ is the angle between the transverse plane and the track tangent

vector at the point of closest approach and the x-axis, and ω = 1/pt is the curvature of

the track. d0 and ω are signed variables and their sign depends on the charge of the

track. The track finding and the fitting procedures use the Kalman filter algorithm [43]

that takes into account the detailed distribution of material in the detector and the full

magnetic field map.

For what concerns this analysis, the definition of charged track is based on some specific

52

quantities:

• distance of closest approach to the beam spot measured in the x - y plane (|dxy|)and along the z axis (|dz|). A cut on those variables rejects fake tracks and back-

ground tracks not originating near the beam-beam interaction point. We require

|dxy| < 1.5 cm and |dz| < 5 cm;

• maximum momentum: to remove tracks not compatible with the beam energy we

require plab < 10 GeV/c , where plab refers to the laboratory momentum of the track,

against misreconstructed tracks;

• polar angle acceptance: the polar angle, in the laboratory frame, is required to be

0.41 < θlab < 2.54 in order to match the acceptance of the detector. This ensures a

well-understood tracking efficiency and systematics.

No restrictions on the impact parameter have been imposed for secondary tracks from

Ks decays. No cut on the minimum number of hits on track is used in order to maximize

the efficiency for low momenta tracks.

In addition, special criteria are used to reject tracks due to specified tracking errors.

Tracks with a transverse momentum p⊥ < 0.18 GeV/c don’t reach the EMC and therefore

they will spiral inside the DCH (“loopers”). The tracking algorithms of BABAR will not

combine the different fragments of these tracks into a single track. Therefore dedicated

cuts have been developed to reject track fragments compatible with originating from

looper based on their distance from the beam spot. Looper candidates are identified as

two tracks with a small difference in p⊥, φ and θ. Of such a pair only the track fragments

with the smallest distance |dz| to the beam interaction point is retained. These cuts

remove roughly 13% of all low-momentum tracks in the central part of the detector. On

average, the mean observed charged multiplicity per B meson is reduced by less than 1%.

Two tracks very closely aligned to each other are called ”ghosts”. These cases arise

when the tracking algorithms splits the DCH hits belonging to a single track in two track

fragments. If two tracks are very close in phase space only the track with the largest

number of DCH hits is retained. This ensures that the fragment with the better momentum

measurement is kept in the analysis.

53

A summary of the track selection criteria is shown in Table 3.1.

Track selection Cutdistance in x− y plane |dxy| < 1.5 cm

distance in z axis |dz| < 5 cmmaximum momentum plab < 10 GeV/cminimum momentum P⊥,lab > 0.06 GeV/c

maximum momentum for SVT-only tracks plab < 0.2 GeV/c if NDCH = 0geometrical acceptance 0.410 < θlab < 2.54 rad

Reject tracks if ∆p⊥,lab< 0.12 GeV/c (loopers)

∆p⊥,lab< 0.15 GeV/c (ghost)

loopers (∆p⊥,lab < 0.25 GeV) Same sign: |∆φ| < 0.1 & |∆θ| < 0.1(| cos θ| < 0.2) Opposite sign: |∆φ| < 0.1 & |π − |∆θ|| < 0.1

ghosts (p⊥ < 0.35GeV ) |∆φ| < 0.1 & |∆θ| < 0.1N1

DCH < 45−N2DCH

Table 3.1: Summary of track selection cuts as adopted from [44]. N1DCH and N2

DCH are the numbers ofDCH hits for ghost candidate tracks. Track 1, the one with most DCH is selected.

3.2 Particle Identification

3.2.1 Electron Identification

The EMC is crucial for electron identification. Different criteria are established to select

electrons with different level of purity and efficiency. Electrons are primarily separated

from charged hadrons by taking into account the ratio of the energy E deposited in the

EMC to the track momentum p, E/p. In addition, the dE/dx energy loss in the DCH and

the DRC Cerenkov angle are required to be consistent with the values expected for an

electron. This offers a good e/π separation in a wide range.

The track selection criteria are tightened for electrons selection to suppress background

and to ensure a reliable momentum measurement and identification efficiency. There are

requirements in addition for transverse momentum p⊥ > 0.1 GeV/c, and NDCH ≥ 12 for

the number of associated drift chamber hits. Furthermore, only electron candidates with

a laboratory momentum plab > 0.5 GeV/c are considered.

Electrons are identified using a likelihood-based selector [45], which uses a number of

discriminating variables:

• Ecal/plab, the ratio of Ecal, the energy deposited in the EMC, and plab the momentum

54

in the laboratory rest frame measured using the tracking system; LAT , the lateral

shape of the calorimeter deposit (defined by Eq. 3.3); ∆Φ, the azimuthal distance

between the centroid of the EMC cluster and the impact point of the track on the

EMC; and Ncry, the number of crystals in the EMC cluster;

• dE/dx, the specific energy loss in the DCH;

• the Cerenkov angle θC and NC , the number of photons measured in the DRC.

First, muons are rejected on the basis of dE/dx ratio value and the shower energy

relative to the momentum. For the remaining tracks, likelihood functions are computed

assuming the particle is an electron, pion, kaon, or proton. These likelihood functions are

based on probability density functions that are derived from pure particle data control

samples for each of the discriminating variables. For hadrons, we take into account the

correlations between energy and shower-shapes. Using combined likelihood functions

L(ξ) = P (E/p, LAT,∆Φ, dE/dx, θC |ξ) (3.1)

= PEMC(E/p, LAT,∆Φ|ξ) PDCH(dE/dx|ξ) PDRC(θC |ξ)

for the hypotheses ξ ∈ {e, π,K, p}, the fraction

Fe =feL(e)∑ξ fξL(ξ)

, (3.2)

is defined, where, for the relative particle fractions, fe : fπ : fK : fp = 1 : 5 : 1 : 0.1 is

assumed. A track is identified as an electron if Fe > 0.95.

The electron identification efficiency has been measured using radiative Bhabha events,

as function of laboratory momentum plab and polar angle θlab. The misidentification rates

for pions, kaons, and protons are extracted from selected data samples. Pure pions are

obtained from kinematically selected K0S → π+π− decays and three prong τ± decays.

Two-body Λ and D0 decays provide pure samples of protons and charged kaons.

The performance of the likelihood-based electron identification algorithm is summa-

rized in Fig. 3.2, in terms of the electron identification efficiency and the per track prob-

ability that an hadron is misidentified as an electron.

55

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.10.20.30.40.50.60.70.80.9

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0

0.002

0.004

0.006

0.008

0.01

- e-π - K

[GeV/c]labp

Eff

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20 40 60 80 100 120 1400

0.10.20.30.40.50.60.70.80.9

1

0

0.002

0.004

0.006

0.008

0.01

- e-π - K

[deg]labθ

Eff

icie

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Mis

iden

tific

atio

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Figure 3.2: Electron identification and hadron misidentification probability for the likelihood-based elec-tron selector as a function of momentum (left) and polar angle (right). Note the different scales foridentification and misidentification on the left and right ordinates, respectively.

The average hadron fake rates per track are determined separately for positive and

negative particles, taking into account the relative abundance from Monte Carlo simu-

lation of BB events, with relative systematic uncertainties of 3.5%, 15% and 20% for

pions, kaons, and protons, respectively. The resulting average fake rate per hadron track

of plab > 1.0 GeV/c, is of the order of 0.05% for pions and 0.2% for kaons.

3.2.2 Muon Identification

Muons are identified by measuring the number of traversed interaction lengths in the entire

detector and comparing it with the number of expected interaction lengths predicted for a

muon of the same momentum. Moreover, the projected intersections of a track with RPC

or LST planes are computed and, for each readout plane, all clusters (groups of adjacent

hits in one of the two readout coordinates) detected within a maximum distance from the

predicted intersection are associated with the track. An additional π/µ discriminating

power is provided by the average number and the RMS of the distribution of the RPC

and LST hits per layer. The average number of hits per layer is expected to be larger

for pions, producing an hadronic interaction, than for muons. Other variables exploiting

clusters distribution shapes are constructed and criteria, based on all these variables, are

applied to select muons. The muon selection performance has been tested on samples of

kinematically identified muons from µµee and µµγ final states and pions from three-prong

56

τ decays and K0S decays.

The muon selection procedure is as follows:

• tight criteria on tracking: p⊥ > 0.1 GeV/c, NDCH ≥ 12, 0.360 < θlab < 2.37 and

plab > 1.0 GeV/c;

• the energy deposited in the EMC is required to be consistent with the minimum

ionizing particle hypothesis, 50 MeV < Ecal < 400 MeV;

• the number of IFR layers associated with the track has to be NL ≥ 2;

• the interaction lengths of material traversed by the track has to be λmeas > 2.2;

• The number of interaction lengths expected for a muon of the measured momentum

and angle to traverse is estimated by extrapolating the track up to the last active layer

of the IFR. This estimate takes into account the IFR efficiencies which are routinely

measured and stored. The difference ∆λ = λexp − λmeas is required to be < 1.0

for tracks with momentum greater than 1.2 GeV/c. For track momenta between

0.5 GeV/c and 1.2 GeV/c, a variable limit is placed: ∆λ < [(plab − 0.5)/0.7];

• the continuity of the IFR cluster is defined as Tc = NL

L−F+1, where L and F are the last

and first layers with hits. Tc is expected to be 1.0 for muons penetrating an ideal

detector whereas is expected smaller for hadrons. We require Tc > 0.3 for tracks

with 0.3 < θlab < 1.0 (i.e. in the Forward End Cap to remove beam background);

• the observed number of hit strips in each RPC or LST layer is used to impose the

conditions on the average number of hits, m < 8, and the standard deviation, σm < 4;

• the strip clusters in the IFR layers are combined to form a track and fit to a third de-

gree polynomial, with the quality of the fit selected by the condition χ2fit/DOF < 3.

In addition, the cluster centroids are compared to the extrapolated charged track,

with the requirement χ2trk/DOF < 5.

The muon identification efficiency has been measured using µ+µ−(γ) events and two-

photon production of µ+µ− pairs. The misidentification rates for pions, kaons, and protons

are extracted from selected data samples. The performance of the muon identification

57

p [GeV/c]1 2 3 4 5

0

0.2

0.4

0.6

0.8 < 57.00θ≤Forward , 17.00

+µ−µ

p [GeV/c]1 2 3 4 5

0

0.2

0.4

0.6

0.8 < 115.00θ≤Barrel , 57.00

+µ−µ

p [GeV/c]1 2 3 4 5

0

0.2

0.4

0.6

0.8 < 155.00θ≤Backward , 115.00

+µ−µ

[Deg]θ20 40 60 80 100 120 140

0

0.2

0.4

0.6

0.8 p[GeV/c]<1.70≤Low P , 1.10

+µ−µ

[Deg]θ20 40 60 80 100 120 140

0

0.2

0.4

0.6

0.8 p[GeV/c]<5.00≤High P , 1.90+µ−µ

Figure 3.3: Muon identification efficiency for the tight muon selector as a function of momentum (top)and polar angle (bottom).

algorithm is summarized in Fig. 3.3, in terms of the muon identification efficiency. The

errors shown are statistical only, the systematic error is dominated by variations in the

performance of the IFR as a function of position and time.

3.2.3 Charged Kaon Identification

A standard selector, based only on track candidates with an associated momentum above

300 GeV/c and exploiting variables based on information from the DRC, the DCH and

the SVT, is used to identify charged kaons. Likelihood functions are computed separately

for charged particles, as products of three terms, one for each detector subsystem and

then combined, similarly to the electron algorithm previously described. Fig. 3.4 shows a

comparison of the charged kaon efficiency versus the charged pion misidentification.

3.3 Neutral Particles Reconstruction

Neutral particles (photons, π0, neutral hadrons) are detected in the EMC as clusters of

close crystals where energy has been deposited. They are required not to be matched to

58

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0.10.20.30.40.50.60.70.80.9

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0.02

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0.06

0.08

0.1 - K + K-π +π

[GeV/c]labp

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20 40 60 80 100 120 1400

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0.02

0.04

0.06

0.08

0.1- K+ K-π +π

[deg]labθ

Eff

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Figure 3.4: Charged kaon identification and pion misidentification probability for the tight kaon microselector as a function of momentum (left) and polar angle (right). The solid markers indicate the efficiencyfor positive particles, the empty markers the efficiency for negative particles. Note the different scales foridentification and misidentification on the left and right ordinates, respectively.

any charged track extrapolated from the tracking volume to the inner surface of the EMC.

For this analysis a neutral particle is selected by its local maximum energy depositions

in the EMC. These energy clusters originate mostly from photons, thus momenta and

angles are assigned to be consistent with photons originating from the interaction region.

The list of neutrals is also used to reconstruct the neutral pions. In Sec. 3.4.1 is described

the selection of the π0 candidates used in the Breco reconstruction.

Photon candidates are required to have an energy Eγ > 30 MeV in order to reduce the

impact of the sizeable beam-related background of low energy photons. Some additional

backgrounds, due to hadronic interactions, either by KL or neutrons, can be reduced by

applying requests on the shape of the calorimeter clusters.

The variable LAT , used to discriminate between electromagnetic and hadronic showers

in the EMC, is defined as

LAT =

N∑i=3

Eir2i

∑Ni=3Eir2

i + E1r20 + E2r2

0

, (3.3)

where N is the number of crystals associated with the electromagnetic shower, r0 is

the average distance between two crystals, which is approximately 5 cm for the BABAR

calorimeter, Ei is the energy deposited in the i-th crystal, numbering them such that

E1 > E2 > . . . > EN and ri, φi are the polar coordinates in the plane perpendicular to

59

the line pointing from the interaction point to the shower center centered in the cluster

centroid. Considering that the summations start from i = 3, they omit the two crystals

containing the highest amounts of energy. Since electrons and photons deposit most of

their energy in two or three crystals, the value of LAT is small for electromagnetic showers.

Multiplying the energies by the squared distances enhances the effect for hadronic showers,

compared with electromagnetic ones.

Another useful shape variable is the so-called S9S25, that is the ratio of the energy

deposited in the 9 closest crystals from the cluster centroid over the energy deposited in

the 25 closest clusters. Are assigned to the neutral particles all the local energy maxima,

not matching with charged tracks, and stored in a list the relative parameters, determined

by assuming that the particle is a photon.

Clusters, which are considered as neutral candidates, although they are close to tracks,

need to be rejected. These unmatched clusters are due to inefficiencies in the matching

algorithms and lead to double counting of their energies. In order to study them, the

distance in φ(dφ) and θ(dθ) with respect to all the tracks which do not have a matched

cluster, were considered. In this analysis, a cut on the 3-D angle

α = cos−1 [cos θcl cos θtr + sin θcl sin θtr cos(φcl − φtr)] (3.4)

was considered, where θcl,tr and φcl,tr are the polar coordinates for clusters and tracks

respectively. Clusters which satisfy α < 0.08 with the closest track that is not matched

to another EMC cluster are considered unassociated clusters and not used in the further

analysis [44].

Tab. 3.2 shows a detailed summary of the selection criteria applied on the neutral

candidates.

Cut Selection criteriaNumber of crystals Nc Nc > 2Cluster energy Eclus Eclus > 50 MeV

LAT LAT < 0.6Geometrical acceptance θclus 0.32 < θclus < 2.44

unmatched clusters α > 0.08

Table 3.2: Summary of the photon selections.

60

3.4 Meson Reconstruction

This section describes the reconstruction of the mesons used in the full reconstruction

of the B. A number of control samples have been employed to perform all the relevant

studies; in most cases, the optimizations have been obtained by using only part of the

available data, and it has been assumed that the results are valid for the entire sample as

well.

3.4.1 π0 Reconstruction

A wide energy spectrum of π0’s ranging from particles almost at rest up to several GeV

is needed in this analysis. For instance, lowest energy π0’s are used to reconstruct the

D∗0 → D0π0 decays while the decay products in the B → Dππ0 channel have quite large

momentum.

The π0’s are reconstructed using pairs of neutral clusters with a lower energy at 30 MeV

and applying a cut on the LAT variable. The π0 candidate has to have an energy above

200 MeV. A mass windows of 110-155 MeV/c2, corresponding to (−4σ, +3σ), is required.

In Fig. 3.5 the invariant masses distributions for simulated events and data are shown.

Mgg (GeV)

Simulation

mean = 0.13520 +/- 0.00003

sigma = 0.00640 +/- 0.00002

Mgg (GeV)

Data

mean = 0.13440 +/- 0.00003

sigma = 0.00686 +/- 0.00002

Figure 3.5: Distribution of the invariant mass of the π0 candidates for simulated events and for data.

61

3.4.2 K0S Reconstruction

K0S are reconstructed in the channel K0

S → π+π− by pairing all possible tracks of opposite

sign and looking for the 3D point (vertex) which is more likely to be common to the two

tracks. The algorithm is based on a χ2 minimization and uses as starting point for the

vertex finding the point of closest approach of the two tracks in 3D. No constraint is

applied on the invariant mass of the pair, but a ±3σ cut around the nominal value is

imposed: 0.486 < mπ+π− < 0.510 GeV/c2. The invariant mass distribution of the π+π−

obtained from data is shown in Fig. 3.6. A comparison between data and Monte Carlo

for the K0S momentum and polar angle is shown in Fig. 3.7. The channel K0

S → π0π0 is

not reconstructed in this analysis.

MKs(GeV)0.4750.480.4850.490.495 0.5 0.5050.510.5150.520

1000

2000

3000

4000

5000

6000

7000

8000

9000

2x10

mean = (497.305 +/- 0.005) 10-3

sigma1 = ( 1.924 +/- 0.021) 10-3

sigma2 = ( 4.349 +/- 0.031) 10-3

Figure 3.6: Mass distributions for K0S → π+π− on data. The distribution is fitted with a sum of a double

Gaussian and a first order polynomial function.

3.4.3 D Reconstruction

The reconstruction of the B mesons in hadronic modes utilizes charmed D mesons decay-

ing in a variety of channels. These channels and their branching fractions are summarized

in Tab. 3.3.

The D0 is reconstructed in the modes D0 → Kπ, D0 → K3π, D0 → Kππ0 and

62

[GeV]labp0 0.5 1 1.5 2 2.5 3

En

trie

s/B

in

0

50

100

150

200

250

300

[deg]labθ0 20 40 60 80 100 120 140 160

En

trie

s/B

in

0

20

40

60

80

100

120

140

160

180

Figure 3.7: K0S momentum (left) and polar angle (right) distributions in data (solid markers) and Monte

Carlo simulation (hatched histogram), normalized to the same area.

D0 → K0Sππ. The charged tracks originating from a D meson are required to have a

minimum momentum of 200 MeV/c for the channel D0 → Kπ and 150 MeV/c for the

remaining three modes. The D0 candidates are required to lie within ±3σ of the nominal

D0 mass. All D0 candidates must have momentum greater than 1.3 GeV/c and lower

than 2.5 GeV/c in the Υ(4S) frame. The lower bound is needed to reduce combinatorics,

the upper one is the kinematic endpoint of the D0 coming from a B → D0X decay or

B → D∗+X with D∗+ → D0π+. A vertex fit is performed and a χ2 probability greater

than 0.1% is required. The selection criteria are summarized in Tab. 3.4.

D+ candidates are reconstructed in the modes D+ → K−π+π+, D+ → K−π+π+π0,

D+ → K0Sπ

+, D+ → K0Sπ

+π0, D+ → K0Sπ

+π+π+. We require that the kaon used in

the K−π+π+ and K−π+π+π0 modes have a minimum momentum of 200 MeV/c while

the pions are required to have momentum greater than 150 MeV/c. For the K0Sπ

+X

modes, the minimum charged track momentum is required to be 200 MeV/c. D+ can-

didates are required to have an invariant mass within ±3σ, calculated on an event-by-

event basis, of the nominal D+ mass. The D+ candidates must have momentum greater

than 1.0 GeV/c in the Υ(4S) frame for the three cleanest modes (D+ → K −π+π+,

D+ → K0Sπ

+ and D+ → K0Sπ

+π0) and greater than 1.6 GeV/c for the two remaining

ones (D+ → K−π+π+π0 and D+ → K0Sπ

+π+π+). Moreover, all D+ candidates must

have momentum lower than 2.5 GeV/c in the Υ(4S) frame, as the D0 case. A vertex fit

is performed and a χ2 probability greater than 0.1% is required. The selection criteria

63

Decay mode Branching Fraction(%)D∗ → D0 π; D0 → Kπ 2.55± 0.06D∗ → D0 π; D0 → K3π 5.0± 0.2D∗ → D0 π; D0 → Kππ0 8.8± 0.6D∗ → D0 π; D0 → K0

S ππ (K0S → π+π−) 1.35± 0.08

D+ → Kππ 9.5± 0.3D+ → K0

S π (K0S → π+ π− ) 0.94± 0.06

D+ → Kπππ0 5.5± 2.7D+ → K0

S πππ (K0S → π+ π− ) 2.38± 0.31

D+ → K0S ππ0 (K0

S → π+ π− ) 3.5± 1.0D∗0 → D0 π0 ; D0 → Kπ 2.35± 0.12D∗0 → D0 π0 ; D0 → K3π 4.6± 0.3D∗0 → D0 π0 ; D0 → Kππ0 8.1± 0.7D∗0 → D0 π0 ; D0 → K0

S ππ (K0S → π+π−) 1.2± 0.1

D∗0 → D0 γ; D0 → Kπ 1.44± 0.19D∗0 → D0 γ; D0 → K3π 2.82± 0.18D∗0 → D0 γ; D0 → Kππ0 5.0± 0.4D∗0 → D0 γ; D0 → K0

S ππ (K0S → π+π−) 0.7± 0.1

D0 → Kπ 3.80± 0.07D0 → K3π 7.72± 0.28D0 → Kππ0 14.1± 0.5D0 → K0

S ππ 2.03± 0.12

Table 3.3: D mesons decays used in the Semi-exclusive B reconstruction.

D0 → Kπ D0 → Kππ0 D0 → K3π D0 → K0S ππ

mD invariant mass window ± 15 MeV/c2 ± 25 MeV/c2 ± 15 MeV/c2 ± 20 MeV/c2

Charged Tracks : lower p∗ cut > 200 MeV/c > 150 MeV/cD0 upper p∗ cut < 2.5 GeV/cD0 lower p∗ cut > 1.3 GeV/c

Vertex Fit χ2 > 0.01

Table 3.4: Summary of criteria applied for the D0 selection.

64

are summarized in Tab. 3.5.

D+ → Kππ D+ → K0S π D+ → K0

S ππ0 D+ → Kπππ0 D+ → K0S πππ

mD invariant mass window ± 20 MeV/c2 ± 20 MeV/c2 ± 30 MeV/c2 ± 30 MeV/c2 ± 30 MeV/c2

D+ lower p∗ cut > 1.0 GeV/c > 1.6 GeV/cD+ upper p∗ cut < 2.5 GeV/c

Charged Tracks : lower p∗ cut > 200 MeV/cVertex fit χ2 > 0.01

Table 3.5: Summary of criteria applied for the D+ selection.

D∗+ candidates are formed by combining a D0 with a pion which has momentum

greater than 70 MeV/c. Due to the limited phase space available from the D∗−D0 mass

difference ∆m, the pion coming from the D∗ has a low momentum, below 450 Mev/c,

and is referred to as soft pion (see Fig. 3.8). Only the reconstruction of the D∗+ → D0π+

channel is discussed here, since D∗+ → D+π0 events enter in the B → D+X category

of the Semi-exclusive reconstruction, as explained in Sec. 3.5. A vertex fit for the D∗+

is performed using a constraint to the beam spot to improve the angular resolution for

the soft pion. A fixed σy = 30 µm is used to model the beam spot spread in the vertical

direction, to avoid bias in the D∗+ vertex fit. The fit is required to converge, but no cut

is applied on the probability of χ2. After fitting, selected D∗+ candidates are required to

have ∆m within ±3σ of the measured nominal value (see Fig. 3.8). ∆m distribution is

fitted with a double Gaussian distribution. The width is taken to be a weighted average

of the core and broad Gaussian distributions. The selection criteria are summarized in

Tab. 3.6.

Criteria CutD∗+ → D0 π+

Vertexing and χ2 beam spot constraint (σy = 30 µm), convergencem(Dπ+)−m(D0) ±3σ MeV/c2

p∗(π+) [70,450] MeV/c

Table 3.6: Summary of criteria applied for the D∗+ selection.

D∗0 candidates are reconstructed by combining a selected D0 with a either a π0 or a

photon having a momentum less than 450 MeV/c in the Υ(4S) frame. The minimum

momentum for the π0 corresponds to 70 MeV while the photons are required to have an

energy greater than 100 MeV. ForD∗0 → D0π0 decay, selectedD∗0 candidates are required

to have ∆m within 4 MeV/c2 of the nominal value while a wider window, 127 MeV/c2 <

65

0

10

20

30

40

50

60

70

80

0 0.05 0.1 0.15 0.2 0.25 0.3

Soft pion momentumSoft pion momentumSoft pion momentump(π))_soft

Soft pion momentum

Signal MCData

0

50

100

150

200

250

0.136 0.138 0.14 0.142 0.144 0.146 0.148 0.15

D*-D0 Mass DifferenceD*-D0 Mass DifferenceD*-D0 Mass Difference∆M (GeV)

D*-D0 Mass Difference

Signal MCData

Figure 3.8: Distribution of soft pion momentum in the Υ(4S) frame (left) and m(D∗+π−)−m(D0) massdistribution for D∗+ candidates in the B → D∗+π−, D0 → Kπ mode. Units in both plots are GeV.Vertical lines indicate the signal windows used in the selection.

∆m < 157 MeV/c2, is used for D∗0 → D 0γ. The selection criteria are summarized in

Tab. 3.7.

Criteria CutD ∗0 → D 0π0

m(D 0π0)−m(D 0) ±4 MeV/c2

p∗(π0) [70 , 450] MeV/cp∗(D ∗0) 1.3 < p∗ < 2.5 GeV/c

D ∗0 → D 0γm(D 0γ)−m(D 0) [127 , 157] MeV/c2

E∗(γ) [100 , 450] MeVp∗(D ∗0) 1.3 < p∗ < 2.5 GeV/c

Table 3.7: Summary of criteria applied for the D∗0 selection.

3.5 Semi-exclusive Reconstruction Method

The aim of the Semi-exclusive reconstruction is to get as many as possible B mesons

in fully hadronic modes in order to study the properties of the recoiling B meson in

Υ(4S) → BB transitions.

The sum of a few, very pure exclusive modes ensures very high purity but low efficiency.

66

Decay mode Branching Fraction (%)B → D∗±Y 22.5± 1.5B → D±Y 22.8± 1.4

B → D∗0/D∗0Y 26.0± 2.7B → D0/D0Y 64.0± 3.0

B → D+s Y 10.1± 3.1

B → D−(∗)D(∗)s 4.9± 1.2

B → D(∗)D(∗)K 7.1+2.3−1.7

B0 → D−(∗)D+(∗) ∼ 1.0

Table 3.8: Inclusive and Exclusive branching fractions relevant to this analysis as measured in [46].

On the other hand a fully inclusive approach with high multiplicities is not feasible since

the level of combinatoric background would be too high. A compromise has been set up,

where only favored modes are considered and an algorithm which combines the final state

particles neglecting the intermediate states as inclusive as possible is used.

Since B0 mesons mostly decay into charged D(∗) mesons while B− mesons decay into

the neutral D0(∗) mesons, only B− → D0(∗)Y , B0 → D+(∗)Y modes are considered.

Tab. 3.8 shows the relevant branching fractions for B mesons decaying predominantly

into fully hadronic final states.

The Semi-exclusive reconstruction approach comprises the following steps:

• reconstruct all possible decay modes B → DY , where the D refers to a charm meson

(D0, D+, D∗0, D∗±), and Y system is a combination of π+, π0, K+ and K0S, with

total charge equal to ±1, and composed of n1π± + n2K

± + n3K0S + n4π

0, where

n1 + n2 < 6, n3 < 3 and n4 < 3;

• study the structure of the Y system looking for resonances in the signal and studying

the shape of the background (Sec. 3.5.2);

• identify submodes and create sub-categories according to the their multiplicity and

to the structure of the Y system (e.g. Dππ0, mππ0 < 1.5 GeV/c2). For each mode,

the most relevant parameter is the apriori-purity of the mode: the ratio S/√S +B,

where S and B are the signal and combinatorial background respectively, as esti-

mated from a mES fit on data (Sec. 3.5.2);

• determine a mode by mode combinatorial background rejection, in order to account

67

for different background levels depending on the number of charged tracks and, above

all, on the number of π0s in the reconstructed mode (Sec. 3.5.3);

• rank the submodes according to their purity and yields and study the significance as a

function of the number of used modes in order to maximize the statistical significance

of the sample (Sec. 3.5.4);

• group the submodes with similar purity;

• resolve the multiple candidates (Sec. 3.5.4).

The starting point of the Semi-exclusive selection is the D0, D+, D∗, D∗0 meson

reconstruction, described in Sec. 3.4.3. Charged pions, kaons, π0 and K0S candidates are

then combined to the D meson to form the B candidate.

3.5.1 Definition of ∆E and mES

Two main variables are used to select B candidates, to extract the yields and to define a

sideband region to study the background: ∆E and mES.

The energy difference ∆E is defined as:

∆E = E∗B −

√s/2, (3.5)

where E∗B is the energy of the B candidate in the Υ(4S) rest frame (CM) and

√s is the

total energy of the e+e− system in the CM rest frame. The resolution of this variable

is affected by the detector momentum resolution and by the particle identification since

a wrong mass assignment results in a shift in ∆E. Due to the energy conservation,

signal events are Gaussian distributed in ∆E around zero. Continuum and part of the bb

background have a ∆E distribution that can be modeled with a polynomial distribution.

Instead, some other bb background, due to misidentification, gives shifted Gaussian peaks.

The resolution of this variable depends essentially on the reconstructed B mode and π0

multiplicity and it can varies from 20 to 40 MeV.

The beam energy-substituted mass mES is defined as

mES =√

(√s/2)2 − p∗2B , (3.6)

68

mes(GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28

Eve

nts

/ (

0.00

0523

485

)

0

200

400

600

800

1000

1200

1400

= 0.94262χ

mes(GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28

Eve

nts

/ (

0.00

0523

485

)

0

200

400

600

800

1000

1200

1400

UDS+CCBAR MC

-2

0

2

-2

0

2

Figure 3.9: Left: fit of the Argus function (Eq. 3.7) to the mES distributions for candidates in thecontinuum background (udsc).

where p∗B is the B candidate momentum in the CM rest frame. It is clear that, since |p∗B| ¿√s/2, the experimental resolution on mES is dominated by beam energy fluctuations. To

an excellent approximation, the shapes of themES distributions for B meson reconstructed

in a final states with charged tracks only are Gaussian and practically identical. Otherwise

the presence of neutrals in the final states, in case their showers are not fully contained

in the calorimeter, can introduce tails.

It is important to notice that, since the sources of experimental smearing are uncorre-

lated (beams energy for mES and detector momentum resolution for ∆E), mES and ∆E

also are basically uncorrelated.

The background shape in mES is parametrized using the Argus function [47]:

dN

dmES

= N ·mES ·√

1− x2 · exp(−χ · (1− x2)

)(3.7)

where x = mES/mmax and χ is a free parameter determined from the fit. The mmax,

that represents the endpoint of the Argus distribution, is fixed in the fit to Monte Carlo

mES distributions. The Argus function provides a good parametrization of the continuum

(uuddccss), as Fig. 3.9 shows.

69

)2 (GeV/cESm5.22 5.24 5.26 5.28

2E

ntri

es /

0.5

MeV

/c

0

2000

4000

6000

8000(a)

)2 (GeV/cESm5.22 5.24 5.26 5.28

2E

ntri

es /

0.5

MeV

/c

0

2000

4000

6000

8000

)2 (GeV/cESm5.24 5.26 5.28

(b)

)2 (GeV/cESm5.24 5.26 5.28

Figure 3.10: The mES distribution for data (points with statistical errors) is shown together with theresults of the fit (solid line) for selected semileptonic decays from B+B− events (a) and B0B0 events (b).The dashed line shows the contribution from combinatorial and continuum background.

The signal component is fitted using a modified Gaussian function [48], which will be

described in detail in Chapter 5. The total fit (Argus and signal function) to the data

sample is shown in Fig. 3.10. The radiative tail of this function can take into account

cases where the energy of the neutral candidates is not fully deposited in the EMC crystals.

The left tail of the distribution depends on the reconstructed B mode and in particular

on the number of π0.

The maximum total number of floating parameters in the mES fits is 7. Two of them

refer to the Argus shape, while the remaining five parameters belong to the signal function.

In the following the number of signal and background events (indicated as S and B in

the plots) are estimated as the area of the signal and the Argus functions integrated for

mES > 5.27 GeV.

3.5.2 Study of the Y System

The choice of the submodes is crucial in the reconstruction method. The identification of

the clean modes allows to set up the most efficient and pure selection among the multiple

candidates in different modes. A detailed study of the Y system, looking for resonances

in the signal and background shape is performed.

As an example, the invariant mass of the Y = ππ0 system in the B → D∗ππ0 mode is

shown in Fig. 3.11. There is a large contribution below 1.5 GeV/c2 due to the ρ resonance,

but there is also a small amount of signal at ∼ 2.4-2.6 GeV/c2, but not clear enough for

70

Figure 3.11: Mass distribution of the Y system ππ0 in data for the B → D∗ππ0 decay mode. Thenormalized background, as evaluated from sidebands, is overlaid.

a specific selection. Therefore two sub-modes are defined depending on whether mππ0

is smaller than 1.5 Gev/c2 or greater than 1.5 GeV/c2, without requiring the sub-mode

belonging to a precise resonance structure. In this way the clean B → D∗ππ0 sub-mode

(mππ0 < 1.5 GeV/c2) has been separated from the low purity ones (mππ0 > 1.5 GeV/c2).

Finally, the total number of the reconstructed B decay modes are 52 and 53 for the D0

and D+ seeds, respectively. The total number of the decay modes is 1097. A summary is

shown in Tab. 3.9.

3.5.3 ∆E Selection

Once all possible reconstruction modes are identified, a window in ∆E is applied in order

to pick up among several candidates in a given submode.

The ∆E resolutions are determined from the ∆E distributions before the best candi-

date selection; they depend essentially on the number of charged tracks and, above all,

on the number of π0s in Y system (since the reconstructed D is mass constrained). For

the modes without π0s a fit with a linear background and a Gaussian is performed and

71

Channel pre-seed mode number of B modes total number of modesB± → D0Y D0 → Kπ 52 208

D0 → Kππ0 52D0 → K0

Sππ 52D0 → Kπππ 52

B → D+Y D+ → Kππ 53 265D+ → Kπππ0 53D+ → K0

Sπ 53D+ → K0

Sππ0 53B± → D∗0 D∗0 → D0π0, D0 → Kπ 52 416

D+0 → D0π0, D0 → Kππ0 52D ∗0 → D0π0, D0 → K0

Sππ 52D ∗0 → D0π0, D0 → Kπππ 52

D∗0 → D0γ, D0 → Kπ 52D∗0 → D0γ, D0 → Kππ0 52D∗0 → D0γ, D0 → K0

Sππ 52D∗0 → D0γ, D0 → Kπππ 52

B0 → D∗+Y D∗+ → D0π, D0 → Kπ 52 208D∗+ → D0π, D0 → Kππ0 52D∗+ → D0π, D0 → K0

Sππ 52D∗+ → D0π, D0 → Kπππ 52

Total 1097

Table 3.9: Summary of the number of Semi-exclusive modes.

2σ symmetric windows are taken. In the case of modes with at least a π0, the situation

is worse. First of all there are too many candidates per event. Requiring that only the 10

candidates with the smallest |∆E| are taken, can create a bias in the ∆E distribution. Due

to studies of the decay modes, the chosen windows are: |∆E| < 45 MeV for candidates

without π0 and K0S, |∆E| < 50 MeV for candidates with up to one π0 and two K0

S and

−90 < ∆E < 60 MeV for all the others.

3.5.4 Multiple Candidates and Definition of Purity

Multiple candidates can be reconstructed in the same submode; candidates reconstructed

in different submodes per event are also possible.

If there are multiple candidates in the same submode only the one with lowest ∆E is

chosen and one candidate per submode is selected.

The selection of the best B decay among different submodes cannot use ∆E because

the modes with higher combinatoric background would be privileged with respect to the

clean ones. An unbiased criterion for choosing a signal event is based on an a-priori

72

Figure 3.12: Dependence of the quality factor S/√

S + B as a function of the yield when adding modesfor the B0 → D+Y case. Statistic corresponds to 80 fb−1.

probability. The a-priori probability here is given by the purity of the mode, determined

by fitting the mES distribution and determining the signal and background contributions

in the signal region (mES > 5.27 GeV). The selection of the best B in the event is based

on the choice of the reconstructed mode with the highest purity.

The decay modes are ranked according to their purity and are added to the sample of

reconstructed B one at a time. At each addition of a mode the yield increases and the

purity mostly decreases. This method is very useful once the composition of the modes has

to be optimized for the analysis of the recoil. The significance S/√S +B is computed as

a function of the number of added modes and the best composition is chosen. An example

for the B0 → D+Y case is shown in Fig. 3.12.

The final yields depend on the cut on the purity. The yields for different levels of

purity on the Breco sample are shown in Tab. 3.10.

The study of the recoiling B can improve the purity of the sample, since the application

of selection criteria on the recoil, for instance the request of an hard lepton, removes

most of the non bb events without changing the mES shape above the signal threshold

(5.27 GeV/c2) and allows to use most of the Semi-exclusive modes.

73

Decay mode a-priori pur.> 80% a-priori pur.> 50% a-priori pur.> 10%B+ → D0 X 75524 ± 322 213774 ± 684 376055 ± 1316B0 → D+ X 43726 ± 258 101594 ± 518 220528 ± 948B+ → D∗0 X 73470 ± 337 174866 ± 665 297632 ± 1161B0 → D∗+ X 81646 ± 335 198685 ± 676 219462 ± 768Total B+ 148994 ± 477 388640 ± 1010 673712 ± 1752Total B0 125372± 414 300279 ± 871 439990 ± 1232Total 274366 ± 631 688919± 1308 1113702 ± 2116

Table 3.10: Yields from Semi-exclusive reconstruction for different levels of purity for 316 fb−1 of data.

74

Chapter 4

Data and Monte Carlo Samples

4.1 Data

The total dataset used in this analysis correspond to an integrated on-peak luminosity

of 347.4 fb−1, recorded by BABAR in the years 1999-2006. They correspond to about 383

million of BB pairs. Table 4.1 summarizes data event samples divided by run period.

Data Set integrated luminosity on peak NBB(106)Run 1 20.4 fb−1 22.4Run 2 61.1 fb−1 67.5Run 3 32.3 fb−1 35.6Run 4 100.3 fb−1 110.5Run 5 133.3 fb−1 147.2

Table 4.1: Data event samples.

4.2 Monte Carlo Samples

The Monte Carlo samples used in this analysis are summarized in Table 4.2.

Data Set 1’ B mode 2’ B mode equiv. lumin.B0 generic Generic Generic 1080 fb−1

B± generic Generic Generic 1095 fb−1

|Vub| pure res. generic b → u`ν exclusive Generic 3689 fb−1

|Vub| pure non-res. generic b → u`ν inclusive Generic 1743 fb−1

Table 4.2: Monte Carlo event samples used in this analysis.

75

4.2.1 Generic bb Monte Carlo

Generic bb Monte Carlo represents the full simulation of all possible decays of the B meson

and it should represent the data and an unbiased event sample. This sample is actually

used to model the data.

4.2.2 Resonant Models for B → Xu`ν

Exclusive charmless semileptonic B → Xu`ν decays are simulated as a combination of

three-body decays to narrow resonances, Xu = π, η, ρ, ω, η′.

These decays are simulated using the ISGW2 model [49]. To be consistent with the

latest measurements, generation values of branching ratios (detailed in Table 4.3) have

been adjusted in a reweighting procedure to match the current PDG values [46] (see also

Tab. 4.4). The hadronic invariant mass spectrum at the generator level for these decays

is shown in Fig. 4.1 (left).

mode BR hadron mass [GeV] mode BR hadron mass [GeV]B0 → π−`+ν 180 · 10−6 0.1396 B+ → π0`+ν 90 · 10−6 0.135

B+η`+ν 30 · 10−6 0.5488B0 → ρ−`+ν 260 · 10−6 0.7669 B+ → ρ0`+ν 130 · 10−6 0.77

B+ → ω`+ν 130 · 10−6 0.782B+ → η′`+ν 60 · 10−6 0.9575

B0 → a−0 `+ν 14 · 10−6 0.983 B+ → a00`

+ν 7 · 10−6 0.983B0 → a−1 `+ν 165 · 10−6 1.26 B+ → a0

1`+ν 82 · 10−6 1.26

B0 → a−2 `+ν 14 · 10−6 1.318 B+ → a02`

+ν 7 · 10−6 1.318B0 → b−1 `+ν 102 · 10−6 1.233 B+ → B0

1`+ν 48 · 10−6 1.233B+ → f0

0 `+ν 4 · 10−6 1.00B+ → f ′00 `+ν 4 · 10−6 1.4B+ → f0

1 `+ν 41 · 10−6 1.283B+ → f ′01 `+ν 41 · 10−6 1.422B+ → f0

2 `+ν 4 · 10−6 1.274B+ → f ′02 `+ν 4 · 10−6 1.525B+ → h0

1`+ν 24 · 10−6 1.17

B+ → h′01 `+ν 24 · 10−6 1.41exclusive 735 · 10−6 exclusive 730 · 10−6

inclusive 1365 · 10−6 inclusive 1365 · 10−6

total 2100 · 10−6 total 2095 · 10−6

Table 4.3: Branching fractions and hadron masses used in the generator for b → u`ν decay.

76

)2 (GeV/cXM0 1 2 3 4 50

1000

2000

3000

4000

5000

6000

resonantXM

)2 (GeV/cXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

200

400

600

800

1000

1200

1400

1600

1800

Non resonantXM

Figure 4.1: MX distributions at generator-level for pure resonant (left) and pure non-resonant (right)b → u`ν Monte Carlo.

4.2.3 Non-Resonant Model for B → Xu`ν

The BABAR simulation code models the inclusive charmless semileptonic B decays into

hadronic states with masses larger than 2mπ using a prescription by De Fazio and Neubert

(DFN) [50]; other theoretical models, like the ones described in Sec. 1.3.2 are not yet

implemented. However, predictions from the DFN model in this analysis are used only

to calculate the detector reconstruction efficiency for events in restricted phase-space

regions. In this respect, differences with the more detailed theoretical models shown in

Chapter 1 are negligible and indeed, as it will be shown in Chapter 7, the systematic

uncertainties due to the limited knowledge of the parameters involved in the definition

of the signal model, are among the smallest ones. The most recent theoretical models

are nevertheless used to compute the acceptances needed to relate the partial charmless

semileptonic branching fraction to |Vub| (see Chapter 8).

The DFN model calculates the triple-differential decay rate, d3Γ / dq2 dE` dsH

(sH = M2X), up to O(αs) corrections. The non perturbative corrections to this ob-

servable (the S function in Eq. 1.35) can be associated with the motion of b quark inside

the B meson, and are commonly referred as “Fermi motion”.

Fermi motion effects are included in the heavy-quark expansion by re-summing an

infinite set of leading-twist correction into a shape function F (k+), which governs the

light-cone momentum distribution of the heavy quark inside the B meson [21, 22]. The

77

physical decay distributions are obtained from a convolution of parton model spectra with

this function.

As already mentioned in Chapter 1, the shape function is a universal characteristic

of the B meson governing inclusive decay spectra in processes with mass-less partons in

the final state, such as B → Xu`ν and B → Xsγ. The convolution of the parton spectra

with this function is such that in the perturbative formulae for the decay distributions the

b-quark mass mb is replaced by the momentum dependent mass mb +k+ and similarly the

parameter Λ = MB −mb is replaced by Λ− k+. Here k+ takes values between −mb and

Λ, with a distribution centered around k+ = 0 and with a characteristic width of O(Λ).

Several functional forms for the shape function have been suggested in the literature

but they are all subject to constraints on the moments of this function, An = 〈kn+〉, which

are related to the forward matrix elements of local operator on the light cone [21]. The

first three moments must satisfy

A0 =

∫F (k+)dk+ = 1 (4.1)

A1 =

∫k+F (k+)dk+ = 0 (4.2)

A2 =

∫k2

+F (k+)dk+ =µ2

π

3(4.3)

where µ2π is the average momentum squared of the b quark inside the B meson [51]. The

form of the shape function is unknown and usually is adopted the simple form [52]

F (k+) = N(1− x)ae(1+a)x; x =k+

Λ≤ 1 (4.4)

which is such that A1 = 0 by construction (neglecting exponentially small terms in mb/Λ),

whereas the condition A0 = 1 fixes the normalization N . The parameter a can be related

to the second moment, yielding A2 = µ2π/3 = Λ2/(1 + a). Thus the b quark mass (or Λ)

and the quantity µ2π are the two parameters of the function.

In the simulation the hadron Xu is produced with a non-resonant and continuous

invariant mass spectrum according to the DFN model. Finally, the fragmentation of the

Xu system into final state hadrons is performed by JETSET [53]. Invariant hadronic mass

spectrum for pure non-resonant charmless semileptonic B decays at the generator level is

shown in Fig. 4.1 (right).

78

Figure 4.2: ∆χ2 = 1 contour plot in the (mb, µ2π) plane for the combined fit to all moments (solid line),

the fit to hadron and leptons moment only (dashed lines), and the fit to photon moments only (dottedline).

A reweighting of the Fermi motion distribution is used to obtain distributions for

different values of Λ and µ2π. Several experimental measurements of these heavy quark

parameters are available. In this thesis, the determination from the B → Xsγ spectrum

as measured by Belle, CLEO and BABAR and from b→ c`ν moments measured by several

experiments and extracted by Flacher and Buchmuller [11]

mb = 4.590± 0.039 GeV (4.5)

µ2π = 0.401± 0.040 GeV2,

and also comprehensively presented by the HFAG group [54], has been used. In Figure 4.2

a fit to the heavy quark parameters using constraints from different measurements are

displayed.

4.2.4 BABAR Hybrid Model for B → Xu`ν

Neither the resonant, or the non-resonant models alone are adequate for a proper simu-

lation of charmless semileptonic decays. The non-resonant generator for instance is not

able to produce hadronic final states with masses below 2mπ and it does not produce

any resonant structure in the hadron mass. Therefore the resonant and non-resonant

79

components are combined such that the total branching fraction is consistent with the

measured value [55, 56] and that the fraction of events below a given threshold in MX

is similar to the non-resonant case (except local discontinuity due to the resonant struc-

ture). This requirement is imposed in order to minimize theoretical uncertainties related

to the hadronization in the charmless decay and to ensure that the OPE is valid. This

reweighting procedure is common among the other |Vub| analyses performed in BABAR .

4.2.5 Reweighting Hybrid Model for B → Xu`ν

The hybrid model described in the previous paragraph considers the non-resonant model

only above 1.264 GeV/c2, while it is in principle possible to go down to the allowed

kinematic limit. So the non-resonant events have been reweighted in the hybrid model

in order to have a better agreement between the model and the measured fraction of

resonant and non-resonant events.

The (MX , q2, E`) phase space is dived into an 8×8×8 grid; the number of non-resonant

(resonant) events in each bin is denoted as N inr (N i

r), then the weights w are determined

in the following way:

• the ratio between the number of non-resonant and resonant events after reweighting

is equal to the imposed one∑

iwi ·N inr

Nr

= R =B(b→ u)− B(Xu`ν resonant)

B(Xu`ν resonant)(4.6)

• the fraction of hybrid events in a given bin Hybi/Hyb is the same as the fraction of

non-resonant events form the reference sample in that bin Ref i/Ref :

Hybi

Hyb=

wi ·N inr +N i

r

Nr +∑

iwi ·N inr

=N i

nr

Nnr

=Ref i

Ref(4.7)

where Hyb = Nr +Nnr = Nr +∑

iwi ·N inr.

Solving these two equations the weights are

wi =Ref i −Nr

N inr

(4.8)

• if the wi is negative, is set to zero. To preserve the overall normalization between the

reference sample and the hybrid, a global weight is applied to the inclusive component

80

of the hybrid corresponding to and the weights for the inclusive is recomputed. The

correct weight corrwi it then

corrwi = wiGlobalW · T − E

Y(4.9)

where GlobalW is the ratio Reference Inclusive/sum of Hybrid, T is the branching

ratio of the total hybrid, E (Y ) is the branching ratio of exclusive (inclusive) part of

the hybrid model. This preserves not only the normalization between the reference

inclusive and the hybrid but also the exclusive/inclusive BRs.

Since the generation values are not updated to the latest measurements, inclusive and

exclusive branching ratios are reweighted to the measured values as reported in Table 4.4.

The experimental errors on these measurements are one of the sources of the systematic

uncertainties.

All branching fractions and theory parameters involved in this reweighting technique

are varied within their errors in the evaluation of the associated uncertainty. The uncer-

tainty due to the specific parametrization given in Equation 4.4 has also been evaluated

by using other two empirical parametrization (see Sec. 7.3).

Decay mode generation value new value with error generation value new value with error(B0) (B0) (B+) (B+)

B → π`ν 1.80 1.36± 0.08 0.90 0.77± 0.12B → η`ν 0.30 0.84± 0.36B → ρ`ν 2.60 2.14± 0.59 1.30 1.16± 0.32B → ω`ν 1.30 1.30± 0.54B → η′`ν 0.60 0.84± 0.84

other resonant 2.95 0.00 (see note *) 2.90 0.00 (see note *)non-resonant 13.65 22.20 (see note **) 13.65 23.04 (see note **)Total sample 21.00 25.70± 3.83 20.95 27.95± 4.17

Table 4.4: Comparison between the BABAR generated branching fraction and the latest measurementswith corresponding errors (in 10−4) to which they are rescaled. *: Since there are no measurements forother resonances (a,b,f ,. . . ), these BR are set to 0.**: The fraction for inclusive events is adjusted topreserve the correct overall normalization of the hybrid sample.

Figure 4.3 shows the comparison, for charged and neutralB, between pure non-resonant

signal Monte Carlo and its rescaled component in the hybrid model along with the rescaled

resonant component. The hybrid model is represented by the black line.

81

05000

100001500020000250003000035000400004500050000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

B0 decays

HybridResonant (hybrid)Inclusive (hybrid)Inclusive only

mass of Xu (GeV)

05000

100001500020000250003000035000400004500050000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

B+ decays

HybridResonant (hybrid)Inclusive (hybrid)Inclusive only

mass of Xu (GeV)

Figure 4.3: MX distribution for the resonant (“exclusive”), the pure non-resonant (“inclusive”) b → u`νMC and for the reweighted combination of exclusive and non-resonant MC (“hybrid”) for B0 (top) andB+ (bottom) decays.

82

Chapter 5

Event Selection

In this thesis, the Υ(4S) → BB process is used to study semileptonic decays of the

B meson recoiling against a B meson whose decay into hadronic final states is fully

reconstructed. Compared with to untagged analyses, where little information on the

companion B is used, this tagging technique offers many advantages:

• the Brecoil decay products consist of particles that are not used to reconstruct the

Breco meson; in other terms, it is possible to assign particles to the Brecoil in an

inclusive and unambiguous way, and compute the relevant hadronic variables;

• it is possible to require charge conservation in the event and impose the missing mass

of the event (due to the undetected neutrino) to be compatible with zero;

• the momentum of the recoiling B is known and therefore it is possible to apply

a Lorentz transformation and compute the relevant kinematic variables in the rest

frame of the decaying B;

• charge and flavor of the B mesons are known, and the correlation between the charge

of the lepton and flavor of the Breco can be exploited to reject B → DX → `Y

background events.

The only disadvantage of this technique is a low reconstruction efficiency, typically in the

0.1− 0.4% range.

The idea to isolate B → Xu`ν decays in regions where the b → c transitions are

forbidden is conceptually simple (see Fig. 5.1 left plots), but the measurement of kine-

83

)2 gen (GeV/cXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Arb

itra

ty U

nit

s

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

u generated→ for bXM

)2 rec (GeV/cXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Arb

itra

ty U

nit

s

0

0.005

0.01

0.015

0.02

0.025

0.03

u reconstructed→ for bXM

)2 rec (GeV/cXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Arb

itra

ty U

nit

s

0

0.1

0.2

0.3

0.4

0.5

c generated→ for bXM

)2 rec (GeV/cXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Arb

itra

ty U

nit

s

0

0.005

0.01

0.015

0.02

0.025

0.03

c reconstructed→ for bXM

Figure 5.1: Generation-level distribution (left set of plots) of the invariant mass of the hadronic recoilsystem in semileptonic b → u`ν (top) and b → c`ν (bottom). The invariant mass distribution after theevent reconstruction are shown on the right.

matic variables is not trivial. Undetected particles and reconstruction errors distort the

measured distribution (see Fig. 5.1 right plots) and lead to a large background from the

dominant b → c`ν transition . The data samples are divided in two event sub-samples,

one that is enriched in b→ u transitions by a veto on the presence of kaons in the recoil

system, and one that is enriched in b → c transitions by requiring the detection of at

least one charged or neutral kaon. The latter can be used as a control sample to check

the agreement between data and Monte Carlo for background, so that the remaining

background in the b → u enriched sample in the phase space region under study can be

obtained by extrapolation from the b→ c dominated region.

5.1 Reconstruction of the Recoil System

Events containing a B meson decaying in a fully reconstructed hadronic final state are

selected by the Semi-exclusive reconstruction technique (see Sec. 3.5). The following steps

84

are employed to identify and study semileptonic decays in the recoil system:

- charged particles and neutral clusters are selected according to the criteria of Sec. 3.1

and 3.3;

- leptons are identified using standard BABAR algorithms for electrons and muon (see

Sec. 3.2.1 and 3.2.2);

- charged and neutral kaons are used to separate B → Xu`ν from the dominant

B → Xc`ν decays (see Sec. 3.2.3 and 3.4.2);

- the hadronic system X, the charged lepton ` and the undetected neutrino ν make

up the rest of the event (except for lost particles) recoiling against the Breco.

The hadronic system X is reconstructed from charged tracks and energy depositions in

the calorimeter that are not associated with the Breco candidate or the identified lepton.

The measured four-momentum pmX of the X system can be written as

pmX =

Nch∑i=1

pchi +

Nγ∑j=1

pγj (5.1)

where p are four-momenta and the indices ch and γ refer to the selected number of charged

tracks, and photons. Care is taken to eliminate fake charged tracks (see Section 3.1), as

well as low-energy beam-generated photons and energy depositions in the calorimeter

(Section 3.3) due to charged particles. The reconstruction of K0S mesons is used for veto

purposes only, without applying any mass constraints.

The neutrino four-momentum pν is estimated from the missing momentum four-vector

pmiss = pΥ(4S) − pmBreco

− pmX − pm

` = QCM − pmreco − pm

X − pm` (5.2)

where all momenta are measured in the laboratory frame, pΥ(4S) refers to the Υ(4S) meson

and QCM is the four-momenta of the colliding beams. The measured invariant mass

squared, m2miss = p2

miss, is an important estimator of the quality of the reconstruction

of the total recoil system. Undetected particles and measurement uncertainties affect

the determination of the four-momenta of the X system and neutrino, and lead to a

85

large leakage of B → Xc`ν background from the high MX into the low MX region and,

similarly, in other kinematic regions which would otherwise be background-free. Likewise

any sizable energy loss of the leptons via bremsstrahlung or internal radiation will impact

the measurement of these two quantities. However, the effect of initial state radiation is

small, due to the fact that the width of the Υ(4S) resonance is rather small.

5.2 Selection of Semileptonic Decays

The following requirements have been optimized to select a sample of Nmeassl semileptonic

B decays:

- cut on the purity per seed for reconstructed B modes. The Semi-exclusive

reconstruction allows to select samples of a given purity; clearly, the higher is the

purity, the smaller is the sample. The impact of the purity selection on the statistical

error was studied on the basis of data. The ratio S/(S + B), for events passing all

selection criteria as a function of the purity for the four charm seeds is shown in

Figure 5.2, while in Table 5.1 the optimal cuts are summarized, as a function of the

Semi-exclusive reconstruction decay channel.

- Lepton with a momentum in the B rest frame p∗` > 1 GeV/c. Semileptonic

B decays are identified by the presence of a high momentum electron or muon. A

minimum lepton momentum, in the B rest frame, is required to reduce background

leptons from secondary charm or τ± decays, and fake leptons. It is possible to boost

the lepton momentum to the rest frame of the recoiling B since the momenta of

the Υ(4S) and the reconstructed B are known. The cut p∗` > 1 GeV/c removes

Seed Mode Cut on Purity S B

B0 → D∗X 24% 228± 18 51± 12B0 → D+X 9% 510± 31 357± 26B± → D0X 9% 615± 33 470± 27B± → D∗0X 8% 307± 23 172± 19

Total 1660± 54 1050± 44

Table 5.1: Signal yield S and background B per seed, for the 81.9 fb−1 data sample, as obtained fromfits to the mES distribution for the optimum choice of the purity of the sample.

86

single mode purity0 10 20 30 40 50 60 70

0

2

4

6

8

10

12

14

s/sqrt(s+b) vs int purity D*

D*

single mode purity0 10 20 30 40 50 60 70

0

2

4

6

8

10

12

14

s/sqrt(s+b) vs int purity Dc

D+

single mode purity0 10 20 30 40 50 60 70

0

2

4

6

8

10

12

14

16

18

s/sqrt(s+b) vs int purity D*0

D*0

single mode purity0 10 20 30 40 50 60 70

0

2

4

6

8

10

12

14

16

18

s/sqrt(s+b) vs int purity D0

D0

Figure 5.2: Statistical significance S/(S + B) as a function of the purity (in %) for the four charm seedsof the reconstructed B sample after all cuts: clockwise (starting from the upper left plot) the seeds areB0 → D∗+X, B0 → D+X, B± → D0X, B+ → D∗0X.

about 10% of the fraction of signal events, as shown in Figure 5.3. The theoretical

uncertainty in the small fraction of the spectrum lost by this cut is small.

- Lepton Charge and B Flavor Correlation. In semileptonic decays of B mesons

the lepton charge is correlated with the B flavor. This leads to the relation

QBrecoilQ` > 0 for primary leptons and QBrecoil

Q` < 0 for secondary leptons (here

QBrecoilrefers to the b quark charge and Q` to the lepton charge in the semileptonic

decay). The former condition is imposed on charged B decays. No requirements

are made on neutral B decays, due to flavor oscillations; this implies a small mixing

correction to be applied on the results (see Sec. 6.1).

5.2.1 Selection of Charmless Semileptonic Decays

Further requirements refine the previously selected sample, enrich it with charmless

semileptonic decays, and reject as much charm background as possible. The relevant

87

lepton momentum (GeV/c)0 0.5 1 1.5 2 2.5 30

100

200

300

400

500

600

ν ul→b ν ul→b

lepton momentum (GeV/c)0 0.5 1 1.5 2 2.5 30

1000

2000

3000

4000

5000

6000

7000

ν cl→b ν cl→b

lepton momentum (GeV/c)0 0.5 1 1.5 2 2.5 30

1000

2000

3000

4000

5000

6000

7000

8000

lepp

ν Xl→B νlu X→B

lepp

Figure 5.3: The momentum p∗` of the lepton in the recoiling B rest frame after all analysis cuts. Top leftplot shows the spectrum for b → u`ν transitions, bottom left for b → c`ν. Right plot shows spectra fortotal and charmless semileptonic decays.

variables involved are:

- Number of Leptons, N` = 1. In b → c`ν transitions it is possible to find out a

second lepton originated in cascade decays of the charm particles, whereas secondary

leptons coming from b→ u`ν decays are very rare. Therefore, charmless decays can

be isolated by requesting one and only one lepton with p∗` > 1 GeV/c in the event.

On the other hand, additional leptons are accepted when measuring Nmeassl , which is

a quantity dominated by b → c`ν transitions. The number of detected leptons per

event is shown in Fig. 5.4. A cut at 1 GeV/c offers a reasonable compromise be-

tween the uncertainties due to available statistics, lepton identification, background

estimate and theoretical models.

- Total Charge of the event, Qtot = 0. The reconstructed kinematical variables

of the recoil system are distorted if one or more charged particles are lost, therefore

charge conservation Qtot = QBreco +QBrecoil= 0 is imposed. This requirement rejects

not only events with missing reconstructed charged particles, but also those with an

additional charged particle due to γ → e+e− conversions or tracking errors. This cut

is also important to reject B → Xc`ν events, that are more prone to inefficiencies in

88

Number of leptons-0.5 0 0.5 1 1.5 2 2.5 3 3.50

2000

4000

6000

8000

10000

ν ul→b ν ul→b

Number of leptons-0.5 0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

310×ν cl→b ν cl→b

Number of leptons-0.5 0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

310×lN

ν Xl→B νlu X→B

lN

Figure 5.4: Number of identified leptons per event with p∗` > 1 GeV/c after all analysis cuts. Top leftplot shows the distribution for b → u`ν transitions, bottom left for b → c`ν. Right plot shows spectrafor total and charmless semileptonic decays.

particle detection, due to their higher charged multiplicity. As an example, a sizeable

fraction of decays with low momentum pions coming from D∗ decays are rejected by

a requirement on the total charge of the event. Figure 5.5 shows the distributions of

Qtot.

- Missing mass squared, m2miss < 0.5 GeV2/c4. The only undetected particle in a

semileptonic B decay should be the neutrino. Therefore a cut on the missing mass

of the recoil is a powerful tool to reject events in which one or more particles are

undetected or poorly measured. As illustrated in Fig. 5.6, the m2miss distribution

is much wider and extends to higher values for b → c`ν decays. A cut in this

variable results in a valuable background suppression, due to higher multiplicities

and/or the presence of an additional neutrino or KL in charm decays. The optimal

requirement m2miss < 0.5 GeV2/c4 is chosen because a tighter cut introduces large

systematic uncertainties due to differences in m2miss resolution in data and Monte

Carlo simulations, and a looser cut results in poor signal-to-background ratio and

thus unacceptable statistical and systematic errors due to background subtraction.

89

Total event charge-4 -3 -2 -1 0 1 2 3 40

2000

4000

6000

8000

10000

ν ul→b ν ul→b

Total event charge-4 -3 -2 -1 0 1 2 3 40

20

40

60

80

100

310×ν cl→b ν cl→b

Total event charge-4 -3 -2 -1 0 1 2 3 40

20

40

60

80

100

310×totQ

ν Xl→B νlu X→B

totQ

Figure 5.5: total charge of events selected after all analysis cuts. Top left plot shows the distributionfor b → u`ν transitions, bottom left for b → c`ν. Right plot shows spectra for total and charmlesssemileptonic decays.

)4/c2Missing mass squared (GeV-4 -2 0 2 4 6 8 100

200

400

600

800

1000

1200

1400

1600

ν ul→b ν ul→b

)4/c2Missing mass squared (GeV-4 -2 0 2 4 6 8 100

2000

4000

6000

8000

10000

12000

14000

ν cl→b ν cl→b

)4/c2Missing mass squared (GeV-4 -2 0 2 4 6 8 100

2000

4000

6000

8000

10000

12000

14000

16000

2mm

ν Xl→B νlu X→B

2mm

Figure 5.6: Missing mass squared after all analysis cuts. Top left plot shows the distribution for b → u`νtransitions, bottom left for b → c`ν. Right plot shows spectra for total and charmless semileptonictransitions.

90

- Partially-Reconstructed Missing Mass Squared, m2miss,PR < −3 GeV2/c4.

One of the dominant backgrounds (∼ 50% of the entire B → Xc`ν) decays is due to

B0 → D∗`ν decays, with D∗ → D0π. This decay can be identified exploiting the

fact that the mass difference between the D∗ and the D0 is close to the pion mass

and therefore the pion produced in the D∗ decay is soft and basically collinear with

the D∗. Using the approximation that the direction of flight of the pion is the same

as the D∗ one, and taking into account that the soft pion energy in the D∗ rest frame

is fixed (E′π = 145.0 MeV), the pion energy in the laboratory frame is

Eπ = γ(E′π − βP

′π) (5.3)

where β and γ refer to the D∗ boost and P′π = 39.0 MeV/c is the soft pion momentum

in the D∗ frame. The D∗ energy in the laboratory frame can be computed, by

)4/c2PR Missing mass squared (GeV-45 -40 -35 -30 -25 -20 -15 -10 -5 0 50

10

20

30

40

50

60

70

80

90

ν ul→b ν ul→b

)4/c2PR Missing mass squared (GeV-45 -40 -35 -30 -25 -20 -15 -10 -5 0 50

200

400

600

800

1000

1200

1400

1600

1800

ν cl→b ν cl→b

)4/c2PR Missing mass squared (GeV-45 -40 -35 -30 -25 -20 -15 -10 -5 0 50

200

400

600

800

1000

1200

1400

1600

1800

2PR mm

ν Xl→B νlu X→B

2PR mm

Figure 5.7: m2miss,PR after all analysis cuts for neutral B meson decays with a positively identified soft

pion. Top left plot shows the distribution for b → u`ν transitions, bottom left for b → c`ν. Right plotshows spectra for total and charmless semileptonic decays.

neglecting the second term in equation 5.3, as

ED∗ = γMD∗ = EπMD∗

E ′π

. (5.4)

91

Given that the 4-momentum PD∗ of the D∗ is now known, the missing invariant mass

can be computed as

m2miss,PR = |Precoil − PD∗ − Plepton|2. (5.5)

Its distribution peaks at zero for background and varies smoothly for signal, as it

can be seen in Figure 5.7.

- Number of Kaons, NK± = NKS= 0. Since kaons are produced in nearly all

charm semileptonic decays, whereas they are highly suppressed in B → Xu`ν decays,

rejecting events where a kaon has been detected in the recoil system reduces the

background from B → Xc`ν decays. Both the number of identified charged kaons and

the number of detected KS are therefore required to be zero (see Figure 5.8). Studies

performed show that EMC and IFR information does not permit the identification of

KL and KS → π0π0 with a sufficient degree of purity. Charged kaons are identified

[40] with an efficiency varying between 60% at the highest and almost 100% at the

lowest momenta. The KS → π+π− decays are reconstructed with an efficiency of

80% from pairs of oppositely charged tracks with an invariant mass between 486 and

510 MeV/c2.

Number of Kaons-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

2000

4000

6000

8000

10000

ν ul→b ν ul→b

Number of Kaons-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

20

40

60

80

100

120

140

310×ν cl→b ν cl→b

Number of Kaons-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

20

40

60

80

100

120

140

310×KN

ν Xl→B νlu X→B

KN

Figure 5.8: Number of identified charged kaons after all analysis cuts. Top left plot shows the distributionfor b → u`ν transitions, bottom left for b → c`ν. Right plot shows spectra for total and charmlesssemileptonic decays.

92

The criteria for the selection of semileptonic events, after having found a Breco can-

didate, and of the final sample enriched in b → u`ν signal events are summarized in

Table 5.2.

Semileptonic selection at least one leptonp∗` > 1 GeV/c

correlation between lepton charge and B flavorFinal selection only one lepton

mm2 < 0.5 GeV2/c4

Sum of all charged particles equal to zeroReject events with kaons in Brecoil

Reject events with partially reconstructed D∗±`∓ν

Table 5.2: Selection criteria for semileptonic events and final selection.

5.3 Fit to the mES Distribution

As mentioned in Section 3.5.1, the kinematic consistency of reconstructed Breco candidates

with actual B decays and the subtraction of combinatorial backgrounds are determined

by performing a fit to mES distributions. In this thesis, a large number of fits to mES

distributions are performed, on samples of very different statistical power and signal

purity. It is therefore important to properly subtract combinatorial backgrounds and

insure that the parametrization of the fitting function used in the mES fits is accurate,

reproduces well the data and keeps systematic uncertainties to a minimum.

In other BABAR analyses [57], the only combinatorial background generally considered

is due to random associations of tracks and neutral clusters in BB and continuum events.

This background does not peak in mES and is subtracted by performing an unbinned like-

lihood fit to the mES distribution. In this fit, the combinatorial background is described

by an Argus function and the signal is described by a Crystal Ball function [58] peaking

at the B meson mass. This parametrization works quite well for moderate data samples,

but its shortcomings are visible in some regions of the mES distribution when using larger

datasets.

In principle, a B meson can be reconstructed in a different decay mode (defined in

the Semi-exclusive reconstruction algorithm) than is actually decaying into. Daughters

of the two B mesons can be lost or assigned to the wrong B in the reconstruction. The

93

mES distribution of these events exhibits a broad peaking component, which is referred

to as “peaking background”. A typical example is due to the swapping of charged and

neutral soft pions from D∗ decays, which have nearly the same kinematic properties, give

an incorrect charge assignment to the reconstructed B mesons and a peaking background

in mES. Since it is not possible to include this peaking component in the Argus back-

ground function, new functions describing the mES distributions have been studied and

are presented in the next sections.

5.3.1 Modeling of mES Distribution with 3 PDFs

The parametrization of the two backgrounds to be considered when fitting the mES dis-

tribution has been determined following the studies of [48]. An Argus shape is used for

non-peaking backgrounds, originating from both continuum (e+e− → qq, q = (u, d, s, c))

and BB events. The shape of BB background peaking in mES can be determined by using

Monte Carlo truth matching and selecting events where the generated and reconstructed

decays do not match. Figure 5.9 shows the mES distribution from BB Monte Carlo events

with incorrect truth-matching. The shape can be in principle described by the sum of an

Argus and a Crystal Ball function

fcb(x) =

{Ncbe

− 12

(x−xc)2

σ2 , x ≥ xc − ασ

Ncbe− 1

2α2(nσ

α)n 1

(xc−ασ+ nσα −x)n x < xc − ασ

(5.6)

However this function does not model the sharp cutoff at the endpoint, leading to prob-

lems in the last bins when trying to fit this function to the total mES distribution. To

model this endpoint region a “cutoff” Crystal Ball function is used:

fccb(x) =

{0 x > xmax

fcb − e−500(xmax−x)ffcb(2xmax − x) x < xmax(5.7)

which by construction drops down to 0 at x = xmax. The factor e−500(xmax−x) ensures this

behavior and confine it to the endpoint region. The value 500 is found empirically. The

fit results are shown in Table 5.3.

Decays with correct truth-matching, where the B meson is reconstructed in the same

mode that is decaying into, are defined as signal candidates. The mES distribution of

these candidates is displayed in Fig. 5.10, showing an almost gaussian shape with a slight

94

mes(GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28

Eve

nts

/ (

0.00

0691

)

0

2000

4000

6000

8000

10000

12000

14000

= 2.67402χ

mes(GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28

Eve

nts

/ (

0.00

0691

)

0

2000

4000

6000

8000

10000

12000

14000

MC Comb. Background: ccb+Argus

-5

0

-5

0

Figure 5.9: Fit of the Argus and “cutoff” Crystal Ball function to mES distribution of Breco candidateswith incorrect truth-matching. The semileptonic selection criteria of Table 5.2 have been applied on therecoiling B. The fitted function is plotted in blue and the single contributions from Argus and “cutoff”Crystal Ball are plotted in yellow and red. The bottom plot shows the pull distribution, namely thedifference between the fit and the points, divided by the statistical error for each bin.

Parameter Fitxc − 5279 MeV [MeV] 0.90± 0.04

σ [MeV] 5.10± 0.09α 0.465± 0.020n 20± 17

xcut − 5289 MeV [MeV] 0.90± 0.09

Table 5.3: Results from fitting “cutoff” Crystal Ball function to B-background Monte Carlo.

tail to the left. Usually such a distribution is modeled by a Crystal Ball function (Fig 5.10

left), which is however inadequate when the data sample to be fitted exceeds some tens

of thousand events. A three region function is then built starting from a Crystal Ball

function. The right side of the function is described by the sum of the derivative of

tanh(x)

ftanh′(x) =e−x

(1 + e−x)2(5.8)

and a gaussian function

fsigR(x) = Nr

σR1

ftanh′(x− xc

σR1

) +N1− r

σR2

fgauss(x− xc

σR2

) (5.9)

The left side of the function is described by a modified Crystal Ball function, where the

95

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-5

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10

Figure 5.10: Left: fit of a Crystal Ball function to the mES distribution of Breco candidates with correcttruth-matching from BB Monte Carlo for run period Run1-4. Right: fit of Eq. 5.12 to the mES distribu-tion of the same Breco candidates but for Run1-5 data period. We see that the fit of the 3-wise functionhas a better agreement with the mES distribution resulting in better χ2. The semileptonic selectioncriteria of Table 5.2 have been applied on the recoiling B.

gaussian part has been substituted by ftanh′(x):

fsigL(x) =

Ncb

exp(−x−xcσL

)

(1+exp(−x−xcσL

))2x ≥ xc − αsigσL

NcbB

(A+xc−x)nsig x < xc − αsigσL

(5.10)

with

A = −2αsigσL

1− eαsig, B =

eαsig

(1 + eαsig)2(A+ αsigσL)nsig . (5.11)

Both functions fsigR(x) and fsigL(x) are combined into the final signal function:

fsig(x) = N ×{CfsigL(mES, xc, σL, αsig, nsig) x ≤ xc

fsigR(mES, xc, r, σr1, σr2) x > xc(5.12)

with

C = fsigR(xc)/fsigL(xc). (5.13)

Figure 5.10-right shows the result of fitting the signal function fsig(x), with all parameters

floating free, to the mES distribution using only signal candidates. The function fits well

in all three regions (left tail, peak, right tail). Table 5.4 shows the results of the fit.

A function that is the sum of an Argus function for non-peaking (continuum and B)

backgrounds, a “cutoff” Crystal Ball function for the peaking B-background and the

signal function fsig is used to describe the mES distribution on data:

fmES= Nagfag(mES) +Ncbfccb(mES) +Nsigfsig(mES) (5.14)

96

Parameter Fitxc − 5279 MeV [MeV] 0.50± 0.01

σL [MeV] 0.00202± 0.00005αsig 4.20± 0.01nsig 1.27± 0.01

σR1 [MeV] 1.59± 0.03σR2 [MeV] 2.30± 0.10

r 0.94± 0.03

Table 5.4: Results from fitting the signal function to signal candidates from Monte Carlo.

Studies show that all the parameters of the peaking background function need to be fixed

in order to get a converging fit. In addition, the parameters αsig, nsig, σR2 and r of the

signal function fsig(x) need to be fixed. Table 5.5 shows the results of the fit on Monte

Carlo (Fig. 5.11). As the endpoint is fixed in Monte Carlo, the corresponding parameters

also have been fixed for the Argus and “cutoff” Crystal Ball.

Component Parameter Fitxc − 5279 MeV [MeV] 0.75± 0.02

σL [MeV] 0.00192± 0.00009αsig 4.20 (fixed)

Signal nsig 1.27 (fixed)σR1 [MeV] 1.58± 0.02σR2 [MeV] 2.30 (fixed)

r 0.94 (fixed)xc − 5279 MeV [MeV] 0.90 (fixed)

σ [MeV] 5.10 (fixed)Peaking background α 0.465 (fixed)

n 20 (fixed)xcut − 5289 MeV [MeV] 0.90 (fixed)

Non-peaking background χ −22.6± 0.02xmax − 5289 MeV [MeV] 0.10 (fixed)

Table 5.5: Results from fitting the mES function to BB Monte Carlo.

Figure 5.12 shows the mES distribution in data. Due to variations in the beam energy,

the endpoint of the mES distribution is not constant over time. Hence xmax cannot be

assumed constant and is left free in the fit. To extract the number of signal B’s, we

fit Eq. 5.14 to the observed mES distribution with the normalizations Nag, Ncb and Nsig

being free parameters. The peaking background shape is taken from Monte Carlo and

fixed. The signal shape is also taken from Monte Carlo but only a few parameters are

fixed, as indicated in Table 5.6.

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MC: Argus+ccb+Thorsten sig

-5

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-5

0

Figure 5.11: Fit to the mES function (Eq. 5.14) to the mES distribution of Breco candidates from BBMonte Carlo. The semileptonic selection criteria of Table 5.2 have been applied on the recoiling B. Thefitted function is plotted in blue and the single contributions from Argus, “cutoff” Crystal Ball and signalfunction are plotted in yellow, red and green.

)2 (GeV/cESm5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3

2E

ntri

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.5 M

eV/c

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8000

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signal + all BGcomb. BG

peaking BG

)2 (GeV/cESm5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3

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8000

5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3-20

-10

0

5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3-20

-10

0

Figure 5.12: Fit of the mES function (Eq. 5.14) to the mES distribution of Breco candidates in data. Thesemileptonic selection criteria of Table 5.2 have been applied on the recoiling B.

98

Component Parameter Fitxc − 5279 MeV [MeV] 0.62± 0.13

σL [MeV] 0.0016± 0.0001αsig 4.20 (fixed)

Signal nsig 1.27 (fixed)σR1 [MeV] 1.90± 0.56σR2 [MeV] 2.30 (fixed)

r 0.94 (fixed)xc − 5279 MeV [MeV] 0.90 (fixed)

σ [MeV] 5.10 (fixed)Peaking background α 0.465 (fixed)

n 20 (fixed)xcut − 5289 MeV [MeV] 0.31± 0.05

Non-peaking background χ −22.1± 0.4xmax − 5289 MeV [MeV] 0.10± 0.03 (fixed)

Table 5.6: Results from fitting the mES function to data.

The parametrization of the mES distribution with 3 PDFs is accurate for high statistics

data samples, hence adequate to calculate the number of semileptonic decays Nmeassl .

However, severe instabilities show up in low statistics samples, such as the ones selected

to measure b → u transitions, Nmeasu . This is mainly due to the shape of the signal and

peaking background being very similar in the B mass region of the mES distribution.

Studies have been performed to determine whether fixing the ratio S/P , where S is the

number of signal events and P is the number of peaking background events, can help to

stabilize the fit. This was certainly the case, but large systematic uncertainties due to the

knowledge of S/P were also introduced. Therefore the 3 PDF model has been eventually

dropped.

5.3.2 Modeling of mES Distribution with 2 PDF

As already shown, the main problem when modeling the mES distribution for high statis-

tics samples is the presence of the peaking background due to errors in the association of

daughter particles to the reconstructed B. Simply neglecting peaking background events

can potentially introduce a bias in the high MX end of the spectrum, where larger particle

multiplicity makes it more likely for particles to be swapped between the two B mesons.

This possibility has been studied by selecting a sample of well-reconstructed B mesons

and looking for biases and changes in resolution after adding increasing amounts of peak-

99

ing background. Figure 5.13 shows a comparison of the MX resolution achieved, where

the amount of peaking background varies according to the truth-matching algorithms

described in Sec. 5.3.3. It is evident that small contamination due to peaking background

still provides a good resolution. Therefore the “cutoff” Crystal Ball function for modeling

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.1

0.2

0.3

0.4

0.5

0.6

Figure 5.13: Comparison between the MX resolution obtained by selecting only well-reconstructed Bmesons (black points) and by allowing some peaking background contamination. The contamination isdefined by the truth-matching algorithms described in Table 5.9, where the points relative to codes 1 to4 are, respectively, in red, green blue and yellow.

the peaking background has been dropped and the fit includes the Argus and the signal

functions described in the previous section; in this case part of the peaking background

is taken into account by the Argus function, the rest is considered as signal.

Figure 5.14 (left) shows an example of the result of fitting the signal and continuum

background to the mES distribution for a generic Monte Carlo sample. To allow the con-

vergence of the fit, the parameters α, n, σR2 and r of the signal function fsig(x) (Eq. 5.12)

need to be fixed. Table 5.7 shows the result of the fit. These values are used as starting

values for all subsequent fits in the analysis.

Figure 5.14 (right) shows the mES distribution in data. The fitted function describes

the distribution well over the full range. The results of the fit is shown in Table 5.8

Clearly, a good mES parametrization is not sufficient per se to avoid any biases in the

event yields and analysis results, due to the neglection of peaking backgrounds. However,

it is expected that the criteria applied on the recoiling B, when going from the semileptonic

100

to the final selection, do not modify substantially the fraction of peaking background.

Since all measurements shown in the next chapter are normalized to the semileptonic

event selection, it is expected that any bias due to the peaking backgrounds should be

small. This is indeed the case, as demonstrated in Section 5.3.4.

mes(GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28

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allMC_enr_SL_haspi0-1.intp0.00 = 2.26702χ

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allMC_enr_SL_haspi0-1.intp0.00

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0

Figure 5.14: Example of a fit of 2-PDF model to mES distribution of Breco candidates in BB MonteCarlo (left) and data (right). The semileptonic selection criteria of Table 5.2 have been applied on therecoiling B.

5.3.3 Study of Truth-Matching Criteria

Up to now, the standard BABAR truth-matching algorithm has been used to determine

whether a B meson is correctly reconstructed or not. It is well known that several truth-

matching criteria can be defined. Generally speaking, truth-matching algorithms are less

efficient and accurate for soft particles and in dense environments. The Semi-exclusive

reconstruction is particularly challenging from this point of view, being based on the

reconstruction of high multiplicity modes and low momentum particles. Ideally, truth-

matching should be tailored to each single Breco mode, which is an unpractical task, given

that about 1000 modes are reconstructed.

An alternative approach to check the reliability of truth-matching and its impact on

final results involves a looser definition of well-reconstructed Breco decays, which can be

adopted as basis of a pseudo-truth-matching algorithm; as in standard truth-matching,

the peaking background component can be estimated from Monte Carlo and subtracted

from the signal yields obtained in data.

101

The signal sample is defined based on the shape of the resulting mES distribution.

The number of generated ngen and reconstructed nreco daughter particles of the Breco are

subdivided according to their charge (nchggen, nchg

reco, nneugen , nneu

reco); the number of reconstructed

daughter particles that are truth-matched, nchgtm , and nneu

tm , are also split according to their

charge, i.e. to whether they are coming from the Breco according to simulation information.

The following quantities can be defined: mchg = nchgreco − nchg

tm , mneu = nneureco − nneu

tm , lneu =

nchggen − nchg

tm and lneu = nneugen − nneu

tm .

Different choices for mneu, lneu, mchg, lchg lead to differences in the identification of

the signal component. An example is shown in Fig. 5.16 and 5.17, where, using generic

Monte Carlo samples, the truth-matched signal and background components are shown

for different truth-matching algorithms (see Table 5.9), and the result of the fit to the full

mES distribution in Figure 5.18 is overlaid.

It can be noticed that no truth-matching algorithm actually reproduces the fit results,

but it is possible to estimate the bias that is introduced and correct for it. The choice

mneu < 3, lneu < 3 and mchg = lchg = 0 gives the best agreement for the resulting “signal”

mES distribution with the modified Crystal Ball function.

Truth-matching algorithms can be used on generic Monte Carlo to estimate the peak-

ing background contamination both for semileptonic and for signal selection. For each

selection and for each Breco reconstructed charge, the ratio Stm/Sfit can be computed,

where Stm is the number of signal events that satisfy the truth-matching criteria, and Sfit

is the number of signal events obtained by fitting the mES distribution. This ratio can be

used to correct the signal yields of mES fits on data where, by definition, it is not possible

to apply any kind of truth-matching. The statistical uncertainty on the ratio Stm/Sfit is

computed by taking into account the correlation between the yields from mES fits and

the ones from truth-matching, which are obtained on the same Monte Carlo sample.

5.3.4 Strategy for mES Fits

The fitting strategy chosen for mES distributions represents a compromise between the

accuracy of the final measurements and the practical implementation of more detailed

techniques aimed at subtracting peaking backgrounds.

102

Parameter Fitxc - 5279 MeV [MeV] 0.92± 0.03σL [MeV] 2.24± 0.01α 4.64± 0.02n 1.55± 0.02σR1 [MeV] 1.19± 0.02σR2 [MeV] 1.55± 0.07r 0.95± 0.01χ −24.18± 0.63xmax - 5289 MeV [MeV] 0.28± 0.01

Table 5.7: Results from fitting the mES function toBB Monte Carlo. The parameters α, n, σR1 andxmax are kept fixed in the fit, but their uncertaintiesare used in the evaluation of the systematic uncer-tainties due to the fitting technique.

Parameter Fitxc - 5279 MeV [MeV] 0.92± 0.03σL [MeV] 2.14± 0.01α 4.64± 0.02n 2.08± 0.01σR1 [MeV] 1.31± 0.02σR2 [MeV] 3.25± 0.07r 0.71± 0.01 (fixed)χ −21.28± 1.29xmax - 5289 MeV [MeV] 0.24± 0.01

Table 5.8: Results from fitting the mES function todata. The parameters α, n, σR1 and xmax are keptfixed in the fit, but their uncertainties are used inthe evaluation of the systematic uncertainties dueto the fitting technique.

CODE mneu lneu mchg lchg

1 0 0 0 02 < 3 0 0 03 < 3 < 2 0 04 < 3 < 3 0 05 < 3 < 3 < 2 06 < 3 < 3 < 2 < 27 < 2 < 2 < 2 < 28 mchg + mneu < 2 lchg + lneu < 39 reconstructed Breco mode equals generated Breco mode

Table 5.9: Truth-matching algorithms.

103

In the following, the measurements of partial branching fractions subject of this thesis

work and further detailed in the next chapter, are compared in two different scenarios for

the mES fits:

• a parametrization with 2 PDFs, without peaking background subtraction;

• a parametrization with 2 PDFs, where peaking background is subtracted by using

the truth-matching algorithm which gives the smallest bias (see previous section).

The systematic uncertainty associated to the peaking background subtraction in the

latter scenario has been evaluated by randomizing 100 times the peaking background

correction according to a gaussian distribution whose mean and sigma are the central

value and the statistical error of the ratio Stm/Sfit, respectively, and by performing the

measurements of partial branching fractions on the Monte Carlo sample for each ran-

domization. The RMS of the distribution of the 100 results thus obtained (see Fig. 5.15)

is taken as systematic error and added in quadrature to the other uncertainties. The

resulting error is optimistic, since it neglects any additional systematic uncertainty in

Stm/Sfit and refers to the truth-matching algorithm that gives the smallest bias in the

event yields. Nevertheless, it can be compared to the uncertainty due to the bias intro-

duced by neglecting peaking background completely. As shown in Table 5.10, the bias

on the analysis results determined by fitting all mES distributions without subtracting

peaking backgrounds corresponds to an uncertainty which, summed in quadrature with

the others, is comparable to the optimistic one that comes from the peaking background

subtraction procedure. For this reason, a 2-PDF model without peaking background

subtraction will be used in the following to fit the mES distributions, the resulting biases

will be corrected for and a systematic uncertainty equal to the bias will be assumed. Nev-

ertheless, the model where peaking background is subtracted according to truth-matching

will be used as a validation of the results.

5.3.5 Binned vs. Unbinned Fits

Due to the large number of events that survive the semileptonic selection, it is not very

practical to perform every fit as an unbinned maximum likelihood fit. On the other

104

Entries 100

Mean 0.02152

RMS 0.0007613

Constant 1.67± 11.95

Mean 0.00008± 0.02147

Sigma 0.000077± 0.000723

BRBR0.018 0.019 0.02 0.021 0.022 0.023 0.024 0.0250

2

4

6

8

10

12

Entries 100

Mean 0.02152

RMS 0.0007613

Constant 1.67± 11.95

Mean 0.00008± 0.02147

Sigma 0.000077± 0.000723

xRun 1-5: MEntries 100

Mean 0.0214

RMS 0.0008636

Constant 1.342± 9.564

Mean 0.00010± 0.02143

Sigma 0.0000968± 0.0008859

BRBR0.018 0.019 0.02 0.021 0.022 0.023 0.024 0.0250

2

4

6

8

10

12

14Entries 100

Mean 0.0214

RMS 0.0008636

Constant 1.342± 9.564

Mean 0.00010± 0.02143

Sigma 0.0000968± 0.0008859

+Run 1-5: P

Entries 100

Mean 0.02132

RMS 0.001006

Constant 1.213± 8.584

Mean 0.00013± 0.02125

Sigma 0.000115± 0.001003

BRBR0.018 0.019 0.02 0.021 0.022 0.023 0.024 0.0250

2

4

6

8

10

12Entries 100

Mean 0.02132

RMS 0.001006

Constant 1.213± 8.584

Mean 0.00013± 0.02125

Sigma 0.000115± 0.001003

2/qxRun 1-5: M

Figure 5.15: Distribution of the 100 ratio of branching ratio (Ru/sl) measurements obtained by randomlyvarying the Stm/Sfit according to a gaussian distribution whose RMS is the Monte Carlo statistical erroron Stm/Sfit (see text). The top left, top right and bottom plots refer to MX , P+ and (MX , q2) analyses,respectively. The generation value for Ru/sl is 0.0215.

Ru/sl (10−4) Ru/sl (10−4) Ru/sl (10−4)generation value truth-matching + sys fit mES

MX analysis 215 215± 11± 12 220± 12± 11P+ analysis 215 215± 12± 13 219± 12± 12

(MX , q2) analysis 215 214± 15± 16 222± 16± 16

Table 5.10: Comparison among the partial ratio of branching fractions generated on Monte Carlo (firstcolumn), fitted on Monte Carlo using the truth-matching approach and adding the systematic error onpeaking background evaluation (second column), and fitted using the mES fit approach without subtract-ing the peaking background (third column). In the last column, a systematic uncertainty correspondingto 100% of the observed bias has been added in quadrature to the other uncertainties.

105

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Figure 5.16: Truth-matched distributions for the signal component in Run4 BB Monte Carlo, afterall analysis cuts have been applied, according to the various truth-matching algorithms described inTable 5.9. The signal PDF, as determined from the mES fit in Figure 5.18 has been overlaid in eachsub-plot.

side, the unbinned fit is needed when fitting low statistics samples. These are either

single bins in MX , P+ and (MX , q2) or small data samples, e. g. the b→ u`ν Monte Carlo

sample. Datasets with less than Nt = 20000 events are fitted using an unbinned maximum

likelihood fit, all other datasets are fitted using a binned one. With this threshold most

of the fits are unbinned. The Nt threshold has been varied from 10000 up to 100000 and

removed it entirely. No appreciable differences in the fitted yields and the ratio of partial

branching ratios have been found.

5.4 Data/Monte Carlo Comparison

A good description of the relevant variables by the Monte Carlo simulation is important

for this inclusive analysis. Distributions showing data and Monte Carlo agreement for

Run5 are shown in Figures 5.19 to 5.28, according to event type (signal-enriched or -

depleted) for the full running period. The distributions for other run periods are very

106

similar.

Since b → u`ν events are basically free of kaons, the total number of kaons (neutral

or charged) in the recoil system is a powerful tool to discriminate between signal and

background. On the basis of this kaon veto, two data samples are defined:

1. the signal-enriched sample (events with NK± = NK0S

= 0), and

2. the signal-depleted sample with (NK± > 0 or NK0S> 0).

The plots for each variable were produced using data and generic Monte Carlo samples.

All the selection cuts were applied, except the one on the plotted variable. All spectra

were background-subtracted with the appropriate mES sideband distribution after having

performed a binned mES fit for each bin of the observed variable. Error on data points

is the fit error on yields. Data and Monte Carlo were normalized to equal area; each pair

of histograms was then tested for compatibility by calculating the χ2/d.o.f..

mes (GeV)5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29

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A RooPlot of "mes (GeV)"

Figure 5.17: Truth-matched distributions for the background component in Run4 BB Monte Carlo, afterall analysis cuts have been applied, according to the various truth-matching algorithms described inTable 5.9. The background PDF, as determined from the mES fit in Figure 5.18 has been overlaid ineach sub-plot.

107

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A RooPlot of "mes (GeV)"

-5

0

5

-5

0

5

Figure 5.18: Fit to mES distribution for Run4 BB Monte Carlo, after all analysis cuts have been applied.The two PDF functions for signal and background that have been determined on this plot are overlaidto the truth-matched signal and background events in Figure 5.16 and 5.17.

108

The overall data-Monte Carlo agreement is good; differences between data and Monte

Carlo considered as systematic uncertainties are discussed in Chapter 7.

The following observations can be made:

• Figure 5.19 illustrates the multiplicities of charged particles. The charged multiplicity

observed in data has a good agreement with the Monte Carlo distributions. The

signal-depleted distributions start only with a minimum of two tracks, since at least

one charged kaon is required in the event selection (in addition to the lepton). The

structure in the signal-enriched distribution is from B+ decays with two tracks in

addition to the lepton.

• The charged lepton momentum distribution (Figure 5.21) shows a good data-Monte

Carlo agreement in both the signal enriched and depleted sample

• Good agreement is observed for the total charge distribution (Figure 5.23).

• Good agreement is also observed for the missing mass squared distribution for the

partial D∗ reconstruction (Figure 5.25) and the reconstructed hadronic recoil mass

MX (Figure 5.26).

• The q2 distributions (Figure 5.27) agree very well.

109

500

1000

1500

2000

2500

3000

nchg data events after all cuts: enriched h400000Entries 10

Mean 3.665

RMS 1.12

Underflow 0

Overflow 0Integral 4967

= 1.80322χ

nchg data events after all cuts: enriched

0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 100.5

1

1.5

1000

2000

3000

4000

5000

6000

nchg data events after all cuts: depleted d400000Entries 10

Mean 4.452

RMS 1.093

Underflow 0

Overflow 0

Integral 1.067e+04

= 3.93282χ

nchg data events after all cuts: depleted

0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 100.5

1

1.5

Figure 5.19: Charged track multiplicity (side-bandsubtracted) in data and generic Monte Carlo forb → u`ν enhanced (top row) and depleted (bottomrow) event samples.

200

400

600

800

1000

nneu data events after all cuts: enriched h400000Entries 15

Mean 5.435

RMS 2.554

Underflow 0

Overflow 0Integral 4952

= 1.12802χ

nneu data events after all cuts: enriched

0 2 4 6 8 10 12 140 2 4 6 8 10 12 140.5

1

1.5

500

1000

1500

2000

2500

nneu data events after all cuts: depleted d400000Entries 15

Mean 4.198

RMS 2.119

Underflow 0

Overflow 0

Integral 1.063e+04

= 1.94092χ

nneu data events after all cuts: depleted

0 2 4 6 8 10 12 140 2 4 6 8 10 12 140.5

1

1.5

Figure 5.20: Photon multiplicity (side-band sub-tracted) in data and generic Monte Carlo for b →u`ν enhanced (top row) and depleted (bottom row)event samples.

110

200

400

600

800

1000pcms data events after all cuts: enriched h400000

Entries 15

Mean 1.658

RMS 0.3234

Underflow 0

Overflow 0

Integral 4980

= 1.28532χ

pcms data events after all cuts: enriched

1 1.21.41.61.8 2 2.22.42.62.8 31 1.21.41.61.8 2 2.22.42.62.8 30.5

1

1.5

200400600800

100012001400160018002000

pcms data events after all cuts: depleted d400000Entries 15

Mean 1.589

RMS 0.3104

Underflow 0

Overflow 0

Integral 1.063e+04

= 0.56132χ

pcms data events after all cuts: depleted

1 1.21.41.61.8 2 2.22.42.62.8 31 1.21.41.61.8 2 2.22.42.62.8 30.5

1

1.5

Figure 5.21: Charged lepton momentum distribu-tion in the CM frame (side-band subtracted) in dataand generic Monte Carlo for b → u`ν enhanced (toprow) and depleted (bottom row) event samples.

500

1000

1500

2000

2500

3000

mm2 data events after all cuts: enriched h400000Entries 40

Mean 2.78

RMS 2.87

Underflow 0

Overflow 0

Integral 2.082e+04

= 1.63932χ

mm2 data events after all cuts: enriched

-4 -2 0 2 4 6 8 101214-4 -2 0 2 4 6 8 1012140.5

1

1.5

1000

2000

3000

4000

5000

6000mm2 data events after all cuts: depleted d400000

Entries 40

Mean 0.7529

RMS 1.715

Underflow 0

Overflow 0

Integral 1.765e+04

= 1.15352χ

mm2 data events after all cuts: depleted

-4 -2 0 2 4 6 8 101214-4 -2 0 2 4 6 8 1012140.5

1

1.5

Figure 5.22: Missing mass squared distribution(side-band subtracted) in data and generic MonteCarlo for b → u`ν enhanced (top row) and depleted(bottom row) event samples.

111

1000

2000

3000

4000

5000

6000

qtot data events after all cuts: enriched h400000Entries 9

Mean 0.03677

RMS 0.7495

Underflow 0

Overflow 0

Integral 8810

= 1.51032χ

qtot data events after all cuts: enriched

-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 40.5

1

1.5

2000

4000

6000

8000

10000

12000

14000

qtot data events after all cuts: depleted d400000Entries 9

Mean -0.0001751

RMS 0.6564

Underflow 0

Overflow 0

Integral 1.69e+04

= 1.56592χ

qtot data events after all cuts: depleted

-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 40.5

1

1.5

Figure 5.23: Total charge distribution (side-bandsubtracted) in data and generic Monte Carlo forb → u`ν enhanced (top row) and depleted (bottomrow) event samples.

1000

2000

3000

4000

5000

6000

nks+nkp data events after all cuts: enriched h400000Entries 10

Mean 0.5

RMS 0

Underflow 0

Overflow 0Integral 4976

= 0.00002χ

nks+nkp data events after all cuts: enriched

0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 100.5

1

1.5

2000

4000

6000

8000

10000

nks+nkp data events after all cuts: depleted d400000Entries 10

Mean 1.753

RMS 0.5304

Underflow 0

Overflow 0

Integral 1.066e+04

= 0.73982χ

nks+nkp data events after all cuts: depleted

0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 100.5

1

1.5

Figure 5.24: Sum of charged and neutral kaons(side-band subtracted) in data and generic MonteCarlo for b → u`ν enhanced (top row) and depleted(bottom row) event samples. Please note that thisquantity is used to define the enriched/depletedsample hence the enriched sample shows zeros only.

112

100

200

300

400

500

600

700

800

wdeltam data events after all cuts: enriched h400000Entries 40

Mean -21.81

RMS 26.46

Underflow 0

Overflow 0Integral 4942

= 0.84212χ

wdeltam data events after all cuts: enriched

-140-120-100-80-60-40-20 0-140-120-100-80-60-40-20 00.5

1

1.5

200400600800

1000120014001600180020002200

wdeltam data events after all cuts: depleted d400000Entries 40

Mean -23.62

RMS 27.93

Underflow 0

Overflow 0

Integral 1.063e+04

= 1.10892χ

wdeltam data events after all cuts: depleted

-140-120-100-80-60-40-20 0-140-120-100-80-60-40-20 00.5

1

1.5

Figure 5.25: Missing mass squared distributionfor the partial D∗+ reconstruction (side-band sub-tracted) in data and generic Monte Carlo for b →u`ν enhanced (top row) and depleted (bottom row)event samples selecting neutral B s only.

200

400

600

800

1000

1200

1400

1600mxhad data events after all cuts: enriched h400000

Entries 20

Mean 1.954

RMS 0.5654

Underflow 0

Overflow 0

Integral 4949

= 1.43822χ

mxhad data events after all cuts: enriched

0 0.5 1 1.5 2 2.5 3 3.5 40 0.5 1 1.5 2 2.5 3 3.5 40.5

1

1.5

500

1000

1500

2000

2500

3000

3500

mxhad data events after all cuts: depleted d400000Entries 20

Mean 2.171

RMS 0.4466

Underflow 0

Overflow 0

Integral 1.062e+04

= 0.79592χ

mxhad data events after all cuts: depleted

0 0.5 1 1.5 2 2.5 3 3.5 40 0.5 1 1.5 2 2.5 3 3.5 40.5

1

1.5

Figure 5.26: Hadronic recoil invariant mass spec-trum (side-band subtracted) in data and genericMonte Carlo for b → u`ν enhanced (top row) anddepleted (bottom row) event samples.

113

100

200

300

400

500

600

q2 data events after all cuts: enriched h400000Entries 20

Mean 5.786

RMS 3.975

Underflow 0

Overflow 0Integral 4966

= 1.16632χ

q2 data events after all cuts: enriched

0 2 4 6 8 10121416180 2 4 6 8 10121416180.5

1

1.5

200

400

600

800

1000

1200

1400

1600q2 data events after all cuts: depleted d400000

Entries 20

Mean 4.628

RMS 3.188

Underflow 0

Overflow 0

Integral 1.065e+04

= 0.78282χ

q2 data events after all cuts: depleted

0 2 4 6 8 10121416180 2 4 6 8 10121416180.5

1

1.5

Figure 5.27: q2 distribution (side-band subtracted)in data and generic Monte Carlo for b → u`ν en-hanced (top row) and depleted (bottom row) eventsamples.

200

400600800

10001200

140016001800

pplus data events after all cuts: enriched h400000Entries 20

Mean 1.033

RMS 0.5071

Underflow 0

Overflow 0Integral 4965

= 0.55552χ

pplus data events after all cuts: enriched

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.5

1

1.5

500

1000

1500

2000

2500

3000

3500

4000

pplus data events after all cuts: depleted d400000Entries 20

Mean 1.173

RMS 0.457

Underflow 0

Overflow 0

Integral 1.064e+04

= 0.63072χ

pplus data events after all cuts: depleted

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.5

1

1.5

Figure 5.28: P+ distribution in the CM frame (side-band subtracted) in data and generic Monte Carlofor b → u`ν enhanced (top row) and depleted (bot-tom row) event samples.

114

Chapter 6

Partial Charmless BranchingFraction Measurements

6.1 Measurement Technique

Inclusive charmless semileptonic branching ratios are determined in phase space regions

defined by the MX , P+ and (MX , q2) kinematic variables. Rather than perform direct

measurements of the ∆B(B → Xu`ν), a measurements of the partial branching ratios

relative to the inclusive semileptonic one B(B → X`ν) allows to cancel out relevant

contributions to the systematic uncertainties.

To derive partial charmless semileptonic branching ratios, the observed number of

events, corrected for background and efficiency, is normalized to the total number of

semileptonic decays b → q`ν (here q stands for c or u) in the Brecoil event sample. The

measurement of a ratio of branching ratios offers at least three experimental advantages:

1. the efficiency of the Semi-exclusive reconstruction is not needed. This is very impor-

tant because the Semi-exclusive reconstruction efficiency is affected by large uncer-

tainties due to the fact that many of the reconstructed modes are not well described

in Monte Carlo;

2. most of the systematics, due to charged lepton identification, are removed since they

are present in both numerator and denominator of the ratio, and they vanish;

3. the normalization to the number of semileptonic events, that is extracted from a fit

to the mES distribution, is less affected by biases, which affect in almost the same

115

way the numerator and the denominator of this ratio.

The number of observed Brecoil events which survive the semileptonic event selection (Ta-

ble 5.2) is denoted as Nmeassl . It can be related to the true number of semileptonic decays,

N truesl = N true

c +N trueu , and the remaining background BGsl which is to be subtracted,

Nmeassl = εc`ε

ctN

truec + εu` ε

utN

trueu +BGsl = εsl` ε

slt N

truesl +BGsl, (6.1)

thus

N truesl =

Nmeassl −BGsl

εsl` εslt

=Nsl

εsl` εslt

. (6.2)

Here εsl` refers to the efficiency of the semileptonic selection on a semileptonic B decay in

an event tagged with efficiency εslt . As already discussed, additional selection criteria are

imposed to select b → u`ν decays. If we denote as Nmeasu the number of events fitted in

the sample after all requirements, with BGu the background coming from semileptonic

decays other than the signal, the measured number of events can be expressed in terms

of N trueu , the true number of signal events, as

Nu = Nmeasu −BGu = εuselε

ukinε

u` ε

utN

trueu (6.3)

where εusel is the efficiency for detecting B → Xu`ν decays after applying all cuts but the

one on the kinematical variables, relative to the semileptonic event selection, and εukin is

the efficiency for B → Xu`ν decays when cutting on the kinematic variables MX , P+ or

(MX , q2).

To determine Nu, the background (BGu) is subtracted by performing a χ2 fit on the

P+, MX or (MX , q2) distributions, where the background shape is computed from Monte

Carlo simulation, and its normalization is floating. An example of such a χ2 fit is shown in

Fig. 6.1. The P+, MX or (MX , q2) distributions in data and Monte Carlo are determined

by mES fits in individual P+, MX or (MX , q2) bins. For charged B mesons, the charge of

the direct lepton from a semileptonic decay is exactly correlated with the charge of the

flavor of the b quark. For neutral B mesons, the effect of B0 − B0 mixing needs to be

taken into account.

If the sample were made only of direct cascade leptons from neutral B decays, the right

(rs) and wrong (ws) sign events would be related to the direct (B → X`ν) and cascade

116

/ GeVXm0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

500

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1500

2000

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3000

/ GeVXm0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

500

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1500

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3000 ν l uB -> Xν l cB -> X

OtherData

/ GeVXm0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

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2000

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3000

/ GeVXm0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

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3000ν l uB -> Xν l cB -> X

OtherData

/ GeVXm0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

-50

0

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150

200

250

/ GeVXm0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

-50

0

50

100

150

200

250

MCν l uB -> X

Data bkgd subtr.

Figure 6.1: χ2 fit to the MX distribution. Left: fit result with ”other” background (red), b → c`ν (yellow)and signal (green) shapes superimposed. Middle: same as in the left plot with finer binning. Right: MX

distribution subtracted of the backgrounds (binning as in the middle plot).

(D → X`ν) decays by

Nrs = (1− χd)NB + χDND (6.4)

Nws = χdNB + (1− χd)ND (6.5)

where χd = 0.188± 0.003 [46] is the neutral Bd mixing parameter. The contribution from

cascade would be subtracted in an exact way by computing

NB =1− χd

1− 2χd

Nrs − χd

1− 2χd

Nws (6.6)

Actually there are events which do not contain any leptons and events that contain two

D mesons and can therefore have a right sign lepton even if it is not direct. These

components are very small and neglected.

In order to have Monte Carlo distributions as much similar as possible to data, the

ratio of the charged to neutral B yields in Monte Carlo is reweighted to be the same

observed in data.

Monte Carlo and data distribution are divided into 3 flavor subsamples, corresponding

to charged B mesons, right-sign and wrong-sign neutral B mesons. The mES distribution

of events surviving the semileptonic selection is fitted for each subsample in order to deter-

mine the number of semileptonic B decays and subtract the combinatorial backgrounds.

To get convergence, the parameters α, n, r and σR2 of the signal function are fixed in these

fits. The mixing correction of Eq. 6.6 is applied to data and Monte Carlo subsamples,

charge reweighting is applied to Monte Carlo only.

117

The distributions of the kinematic variables (MX , P+, (MX , q2)) are divided into bins

and for each bin a mES fit is performed on events surviving the signal selection, again for

each of the 3 flavor subsamples. In these fits, all parameters of the signal function are

fixed to the values fitted in the semileptonic selection samples; only the shape of the Argus

function and the signal and background normalizations are free to float. The number of

events in each bin of the kinematical variable under study is obtained after applying the

mixing correction and charge reweighting. The remaining background is due to b → c`ν

transitions and to “other” components such cascade decays and non semileptonic decays

that survive the selection criteria; this background is subtracted with a χ2 fit described

further on.

The ratio between the partial branching fraction for the signal decays in a given phase

space region and B → X`ν decays is given by

∆Ru/sl =B(signal)

B(B → X`ν)=N true

u

N truesl

=(Nmeas

u −BGu)/(εuselε

ukin)

(Nmeassl −BGsl)

× εsll εslt

εul εut

. (6.7)

The efficiency ratio (last term of Eq. 6.7) is expected to be close to, but not equal to

unity. Due to the difference in multiplicity and the different lepton momentum spectra,

the tag efficiency εt and lepton efficiency εl are expected to be different for the two classes

of events.

Partial branching fractions for charmless decays in the regions of interest are then

obtained from ∆Ru/sl using the semileptonic branching ratio determined by the HFAG

group by averaging over several experiments [54]

B(B → X`ν) = (10.75± 0.16)%. (6.8)

In order to extract the partial charmless semileptonic branching ratio ∆B(B → Xu`ν)

in a given region of the MX , (MX , q2) or P+ distributions, signal events are defined as

the ones with true values of the kinematic variables in the chosen region. The b → u`ν

events with true values of the kinematic variables outside the signal region are treated as

background. This means that in applying Eq. 6.7, the b→ u`ν events outside the signal

region are included in BGu and the quoted efficiencies refer only to events with true

values of the kinematical variables in the chosen kinematic region. These efficiencies are

118

computed on Monte Carlo, and therefore are based on the DFN model. The associated

theoretical uncertainty on the final result is small compared to the extrapolation error to

the full phase space.

The binned kinematic distribution obtained is fitted with a χ2 minimization which

extracts Nu and BGu as defined by Eq. 6.7 using signal and background shapes taken

from simulation, and by determining their relative normalizations with respect to the

experimental distribution. The distribution of the kinematic variable(s) on data (Nu measi )

is fitted to the sum of three distributions, the b→ u`ν events inside the signal region (N inu i),

the b→ u`ν events outside the signal region (N outu i ), and the sum of b→ c`ν and “other”

backgrounds (N bkgi )

µi = CinNin MCu i + CoutN

out MCu i + CbN

bkg MCi . (6.9)

The χ2 function is:

χ2(Cin, Cout, Cbkg) = −∑

i

Nu meas

i − µi√δNu meas

i2 + δN in MC

u i2

2

(6.10)

where the sum runs over the bins, Nu measi is the number of observed events in bin i,

δNu measi and δN in MC

u i are the corresponding statistical errors coming from the mES fits

for data and Monte Carlo respectively. Cin, Cout and Cbkg are the normalizations of the

three components which are free parameters of the fit. The constraint Cin = Cout is

applied. When fitting the MX and P+ distributions, the first bin is chosen to contain all

events within the phase space being considered for the calculation of the partial branching

fraction. In this way, the number of fitted signal events is Nu = N in measu 1 − CoutN

out MCu 1 −

CbkgNbkg MC1 . For the (MX , q

2), Nu is determined by summing over the appropriate q2

bins.

6.2 Monte Carlo Fits

The measurement technique described above has been extensively tested using Monte

Carlo samples.

Generic Monte Carlo was used to study the b → c`ν component, signal Monte Carlo

119

for the b → u`ν component; both were properly reweighted to reproduce the currently

measured values of branching fractions, heavy quark parameters, form factors, and de-

tector effects. Generic and signal Monte Carlo are summed by taking into account their

relative luminosities.

The two approaches described in 5.3.4 were followed. In the approach without peaking

background corrections, all quantities including efficiencies were determined by measuring

yields with mES fits. For the other approach, all the efficiency calculations were performed

by counting truth-matched events surviving the cuts, and the peaking component was

corrected for when determining the number of semileptonic events and the shapes of the

kinematical distributions. For the latter, the peaking background evaluation was done

in bins of the kinematic variable under study. As an example, figures 6.2 to 6.5 show

the Stm/Sfit ratio as a function of MX for the three flavour subsamples in different run

periods. The ratio Stm/Sfit is approximately constant and well behaved for every run

period, regardless of the charge of the reconstructed B meson.

The fit results are shown for the different analyses in tables 6.1 to 6.7, divided in run

periods. A very good agreement can be noticed between the two mES fit approaches

and the generated values. The small biases observed in the approach without peaking

background subtraction will be corrected for in data fits, and a systematic uncertainty

corresponding to 100% of the correction will be assigned.

6.3 One Dimensional MX Fit and Results

The MX data distribution, obtained by following the procedure outlined in Section 6.1,

is fitted by using the two mES fit approaches outlined in Section 5.3.4 and Nu and BGu,

as defined by Eq. 6.7, are determined.

Fits to theMX distribution have been performed for phase space regions defined byMX

smaller than 1.55 GeV/c2 and 1.7 GeV/c2 on data for different run periods, and for the

entire sample. Results for MX < 1.55 GeV/c2 are shown in Table 6.8 and Figure 6.6 for

the approach without peaking background subtraction, and in Table 6.9 and Figure 6.7 for

the approach based on truth-matching. The results for MX < 1.7 GeV/c2 are presented

120

/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

fitt

ed/S

tru

thm

atch

edS

0.8

0.9

1

1.1

1.2

1.3

= 0.70832χRun 1-2 charged

/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

fitt

ed/S

tru

thm

atch

edS

0.2

0.4

0.6

0.8

1

1.2

1.4

= 0.82922χRun 1-2 neutrals Same Sign

/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

fitt

ed/S

tru

thm

atch

edS

0.4

0.6

0.8

1

1.2

1.4

= 0.38802χRun 1-2 neutrals Opposite Sign

Figure 6.2: Left: Stm/Sfit in MX bins for Run1-2 B± (right), unmixed B0 (left), mixed B0 (bottom).The red line represents Stm/Sfit calculated.

Run Period gen. Nsl Nsl

Run1-2 106963 106901Run3 39339 39318Run4 138185 137724Run5 172373 171981

Run1-5 456858 457014

Table 6.1: Generated and fitted values for Nsl in all the analyses.

Run Period gen. Ru/sl Ru/sl (truth-matching) Ru/sl

Run1-2 215× 10−4 (216± 23± 16)× 10−4 (219± 22± 20)× 10−4

Run3 215× 10−4 (216± 35± 25)× 10−4 (215± 35± 30)× 10−4

Run4 215× 10−4 (216± 21± 15)× 10−4 (219± 21± 19)× 10−4

Run5 215× 10−4 (216± 20± 16)× 10−4 (221± 21± 18)× 10−4

Run1-5 215× 10−4 (215± 11± 9)× 10−4 (220± 12± 10)× 10−4

Table 6.2: Generated and fitted values for Ru/sl in the MX analysis. The first fitted value is obtainedwith the truth-matching based approach, the second with the approach based on fits to all data andMonte Carlo mES distributions.

121

/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

fitt

ed/S

tru

thm

atch

edS

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

= 0.29032χRun 3 charged

/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

fitt

ed/S

tru

thm

atch

edS

0.5

1

1.5

2

2.5

3

= 0.13812χRun 3 neutrals Same Sign

/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

fitt

ed/S

tru

thm

atch

edS

0.5

1

1.5

2

2.5

3

= 0.62902χRun 3 neutrals Opposite Sign

Figure 6.3: Left: Stm/Sfit in MX bins for Run3 B± (right), unmixed B0 (left), mixed B0 (bottom).

Run Period gen. Nu Nu gen. εuselε

ukin εu

selεukin gen. εsll εslt

εul εu

t

εsll εslt

εul εu

t

Run1-2 517± 13 518± 54± 13 0.371 0.371 1.22 1.22± 0.05Run3 192± 8 193± 31± 8 0.389 0.389 1.17 1.17± 0.08Run4 630± 15 629± 61± 15 0.346 0.346 1.23 1.23± 0.05Run5 706± 15 706± 65± 15 0.321 0.321 1.20 1.20± 0.04

Run1-5 2045± 26 2046± 109± 26 0.347 0.347 1.21 1.21± 0.02

Table 6.3: Generated and fitted values for Nu, the efficiencies product εuselε

ukin and εsll εslt

εul εu

tin the MX

analysis.

Run Period gen. Ru/sl Ru/sl (truth-matching) Ru/sl

Run1-2 215× 10−4 (215± 23± 17)× 10−4 (220± 23± 21)× 10−4

a Run3 215× 10−4 (214± 37± 18)× 10−4 (223± 39± 34)× 10−4

Run4 215× 10−4 (215± 22± 17)× 10−4 (220± 22± 20)× 10−4

Run5 215× 10−4 (215± 20± 16)× 10−4 (221± 21± 19)× 10−4

Run1-5 215× 10−4 (214± 12± 9)× 10−4 (219± 12± 11)× 10−4

Table 6.4: Generated and fitted values for Ru/sl in the P+ analysis. The first fitted value is obtained withthe truth-matching based approach, the second with the approach based on fits to all data and MonteCarlo mES distributions.

122

/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

fitt

ed/S

tru

thm

atch

edS

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

= 0.28842χRun 4 charged

/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

fitt

ed/S

tru

thm

atch

edS

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

= 0.39972χRun 4 neutrals Same Sign

/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

fitt

ed/S

tru

thm

atch

edS

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

= 0.83862χRun 4 neutrals Opposite Sign

Figure 6.4: Left: Stm/Sfit in MX bins for Run4 B± (right), unmixed B0 (left), mixed B0 (bottom).

Run Period gen. Nu Nu gen. εuselε

ukin εu

selεukin gen. εsll εslt

εul εu

t

εsll εslt

εul εu

t

Run1-2 477± 13 476± 52± 13 0.367 0.367 1.14 1.14± 0.05Run3 180± 7 179± 31± 7 0.391 0.391 1.10 1.10± 0.08Run4 582± 14 590± 59± 14 0.345 0.345 1.15 1.15± 0.04Run5 680± 15 679± 64± 15 0.328 0.328 1.13 1.13± 0.04

Run1-5 1920± 26 1919± 106± 26 0.348 0.348 1.15 1.14± 0.02

Table 6.5: Generated and fitted values for Nu, the efficiencies product εuselε

ukin and εsll εslt

εul εu

tin the P+ analysis.

Run Period gen. Ru/sl Ru/sl (truth-matching) Ru/sl

Run1-2 215× 10−4 (211± 31± 23)× 10−4 (216± 30± 27)× 10−4

Run3 215× 10−4 (213± 49± 37)× 10−4 (210± 47± 42)× 10−4

Run4 215× 10−4 (208± 27± 20)× 10−4 (225± 28± 26)× 10−4

Run5 215× 10−4 (224± 26± 20)× 10−4 (220± 27± 24)× 10−4

Run1-5 215× 10−4 (214± 23± 12)× 10−4 (222± 16± 14)× 10−4

Table 6.6: Generated and fitted values for Ru/sl in the (MX , q2) analysis. The first fitted value is obtainedwith the truth-matching based approach, the second with the approach based on fits to all data and MonteCarlo mES distributions.

123

/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

fitt

ed/S

tru

thm

atch

edS

0.6

0.7

0.8

0.9

1

1.1

= 0.83742χRun 5 charged

/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

fitt

ed/S

tru

thm

atch

edS

0.4

0.6

0.8

1

1.2

1.4

1.6

= 0.46842χRun 5 neutrals Same Sign

/ GeVXM0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

fitt

ed/S

tru

thm

atch

edS

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

= 0.41132χRun 5 neutrals Opposite Sign

Figure 6.5: Left: Stm/Sfit in MX bins for Run5 B± (right), unmixed B0 (left), mixed B0 (bottom).

Run Period gen. Nu Nu gen. εuselε

ukin εu

selεukin gen. εsll εslt

εul εu

t

εsll εslt

εul εu

t

Run1-2 362± 11 357± 52± 11 0.390 0.390 1.16 1.16± 0.05Run3 131± 6 129± 30± 6 0.373 0.372 1.19 1.19± 0.09Run4 469± 13 453± 160± 13 0.387 0.388 1.17 1.17± 0.04Run5 517± 13 539± 63± 13 0.355 0.355 1.13 1.13± 0.04

Run1-5 1479± 22 1467± 106± 22 0.375 0.374 1.15 1.15± 0.02

Table 6.7: Generated and fitted values for Nu, the efficiencies product εuselε

ukin and εsll εslt

εul εu

tin the (MX , q2)

analysis.

124

in Tables 6.10 and 6.11, and Figures 6.8 and 6.9.

The value for ∆Ru/sl obtained by using the full Run1-Run5 dataset and

MX < 1.55 GeV/c2 is

∆Ru/sl(MX < 1.55 GeV/c2) = (109± 8± 4± 10)× 10−4 (6.11)

where the first error is statistical, the second is due to Monte Carlo statistics and the

third is systematic.

Using the above result and the measurement of the inclusive semileptonic branching

fraction (Eq. 6.8), the partial branching fraction for charmless semileptonic B decays is

measured to be

∆B(B → Xu`ν,MX < 1.55 GeV/c2) = (1.18± 0.09stat. ± 0.07sys. ± 0.01SF)× 10−3

(6.12)

where the first error is statistical, the second systematic and the third is due to the

uncertainties of the shape function parameters.

Systematic uncertainties will be discussed in Chapter 7.

6.4 One Dimensional P+ Fit and Results

The P+ data distribution, obtained by following the procedure outlined in Section 6.1, is

fitted by using the two mES fit approaches outlined in Section 5.3.4 and Nu and BGu, as

defined by Eq. 6.7, are determined.

Reference [32] suggests that the region defined by P+ < 0.66 GeV/c2 is optimal for a

reliable calculation of the theoretical phase space acceptance.

Fits to the P+ distribution have been performed for different run periods, and on the

full data sample. Results are shown in Table 6.12 and in Figure 6.10 for the mES fit

approach without peaking background subtraction, and in Table 6.13 and in Figure 6.11

for the algorithm based on truth-matching.

The value for ∆Ru/sl obtained by using the full dataset is

∆Ru/sl(P+ < 0.66 GeV/c2) = (88± 9± 4± 10)× 10−4 (6.13)

125

Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 43031± 574 17544± 344 53097± 393 66458± 520 181074± 706

BGsl 2659± 35 1296± 25 3708± 27 4376± 34 12187± 48Nsl −BGsl 40372± 538 16249± 319 49389± 366 62082± 486 168888± 659

N inu 214± 29 105± 19 205± 32 282± 36 803± 60

Noutu 5± 1 2± 0 7± 1 11± 2 27± 2

Nbkg 208± 9 79± 6 276± 11 362± 14 923± 21εusel 0.409 0.437 0.403 0.376 0.397

εukin 0.858 0.846 0.826 0.827 0.834

(εut εu

` )/(εslt εsl

` ) 1.29± 0.06 1.29± 0.10 1.31± 0.04 1.31± 0.06 1.31± 0.03∆Ru/sl(10−4) 117± 16± 7 135± 24± 11 96± 15± 7 112± 14± 6 110± 8± 4

Table 6.8: Summary of the fit to the MX distribution and results for MX < 1.55 GeV/c2 for the fullsample and for various subsamples. The approach fully based on mES fits without any attempt tosubtract peaking backgrounds has been used. N in

u is the number of signal events in the signal region(MX < 1.55 GeV/c2). The first error on ∆Ru/sl(MX < 1.55 GeV/c2) is statistical, the second is due toMonte Carlo statistics. The non-resonant component in the Monte Carlo has been reweighted accordingto the shape function parameters from the HFAG combination using B → Xc`ν and B → Xsγ decays asdescribed in Section 4.2.5.

Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 37577± 512 15196± 293 46058± 340 57332± 442 156252± 603

BGsl 2221± 30 1056± 20 3210± 24 3849± 30 10352± 40Nsl −BGsl 35355± 481 14141± 273 42848± 316 53483± 412 145900± 563

N inu 194± 26 94± 17 187± 30 254± 32 724± 54

Noutu 5± 1 2± 0 6± 1 9± 1 24± 2

Nbkg 194± 8 73± 5 262± 10 322± 12 850± 18εusel 0.423 0.442 0.423 0.390 0.412

εukin 0.871 0.868 0.837 0.852 0.853

(εut εu

` )/(εslt εsl

` ) 1.31± 0.05 1.27± 0.08 1.32± 0.05 1.30± 0.04 1.31± 0.03∆Ru/sl(10−4) 114± 15± 6 137± 25± 9 94± 15± 5 110± 14± 5 108± 8± 3

Table 6.9: Summary of the fit to the MX distribution and results for MX < 1.55 GeV/c2 for the fullsample and for various subsamples. The mES fit approach based on Monte Carlo truth-matching wasused. N in

u is the number of signal events in the signal region (MX < 1.55 GeV/c2). The first error on∆Ru/sl(MX < 1.55 GeV/c2) is statistical, the second is due to Monte Carlo statistics. The non-resonantcomponent in the Monte Carlo has been reweighted according to the shape function parameters from theHFAG combination using B → Xc`ν and B → Xsγ decays as described in Section 4.2.5.

126

(GeV)xM

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

500

1000

1500

2000

2500

3000

3500

INν ul→b + othν cl→b OUTν ul→b

data

(GeV)xM

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

200

400

600

800

scaled MC

data subtr.

Figure 6.6: One-dimensional MX < 1.55 GeV/c2 analysis: 2-parameter χ2 fit to the MX distributionfor Run1-Run5 data The approach fully based on mES fits without any attempt to subtract peakingbackgrounds has been used. Left: Points are data, the blue, magenta and yellow histograms representrespectively the fitted contributions from b → u`ν events with true MX < 1.55 GeV/c2, the rest of theb → u`ν events, and background events. The signal box is defined by MX < 1.55 GeV/c2. Right: MX

distribution subtracted of the backgrounds. χ2 per degree of freedom = 17.6/8.

(GeV)xM

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

500

1000

1500

2000

2500

3000

INν ul→b + othν cl→b OUTν ul→b

data

(GeV)xM

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

200

400

600

800

scaled MC

data subtr.

Figure 6.7: One-dimensional MX < 1.55 GeV/c2 analysis: 2-parameter χ2 fit to the MX distribution forRun1-Run5 data. The mES fit approach based on Monte Carlo truth-matching was used. Left: Pointsare data, the blue, magenta and yellow histograms represent respectively the fitted contributions fromb → u`ν events with true MX < 1.55 GeV/c2, the rest of the b → u`ν events, and background events.The signal box is defined by MX < 1.55 GeV/c2. Right: MX distribution subtracted of the backgrounds.χ2 per degree of freedom = 12.8/8.

127

Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 43031± 574 17544± 344 53097± 393 66458± 520 180418± 701

BGsl 2659± 35 1296± 25 3708± 27 4376± 34 11480± 45Nsl −BGsl 40373± 538 16249± 319 49390± 366 62082± 486 168937± 657

N inu 259± 36 132± 24 211± 41 303± 47 914± 76

Noutu 5± 1 4± 1 5± 1 9± 2 25± 2

Nbkg 346± 16 135± 10 480± 19 600± 24 1548± 36εusel 0.396 0.419 0.382 0.358 0.381

εukin 0.869 0.843 0.875 0.869 0.867

(εut εu

` )/(εslt εsl

` ) 1.27± 0.06 1.32± 0.11 1.30± 0.05 1.29± 0.04 1.29± 0.05∆Ru/sl(10−4) 147± 21± 9 174± 31± 15 99± 19± 9 121± 19± 9 128± 11± 5

Table 6.10: Summary of the fit to the MX distribution and results for MX < 1.7 GeV/c2 for the fullsample and for various subsamples. The approach fully based on mES fits without any attempt tosubtract peaking backgrounds has been used. N in

u is the number of signal events in the signal region(MX < 1.7 GeV/c2). The first error on ∆Ru/sl(MX < 1.7 GeV/c2) is statistical, the second is due toMonte Carlo statistics. The non-resonant component in the Monte Carlo has been reweighted accordingto the shape function parameters from the HFAG combination using B → Xc`ν and B → Xsγ decays asdescribed in Section 4.2.5.

Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 37577± 512 15196± 293 46058± 340 57332± 442 156252± 603

BGsl 2221± 30 1056± 20 3210± 24 3849± 30 10352± 40Nsl −BGsl 35355± 481 14141± 273 42848± 316 53483± 412 145900± 563

N inu 236± 33 122± 22 193± 38 265± 42 821± 69

Noutu 6± 1 2± 0 4± 1 7± 1 19± 2

Nbkg 321± 15 125± 9 446± 17 543± 21 1431± 32εusel 0.404 0.429 0.402 0.373 0.394

εukin 0.890 0.861 0.887 0.881 0.883

(εut εu

` )/(εslt εsl

` ) 1.30± 0.06 1.29± 0.09 1.31± 0.05 1.28± 0.04 1.29± 0.03∆Ru/sl(10−4) 144± 20± 8 182± 32± 13 97± 19± 7 117± 19± 7 125± 11± 4

Table 6.11: Summary of the fit to the MX distribution and results for MX < 1.7 GeV/c2 for the fullsample and for various subsamples. The mES fit approach based on Monte Carlo truth-matching wasused. N in

u is the number of signal events in the signal region (MX < 1.7 GeV/c2). The first error on∆Ru/sl(MX < 1.7 GeV/c2) is statistical, the second is due to Monte Carlo statistics. The non-resonantcomponent in the Monte Carlo has been reweighted according to the shape function parameters from theHFAG combination using B → Xc`ν and B → Xsγ decays as described in Section 4.2.5.

128

(GeV)xM

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

500

1000

1500

2000

2500

3000

INν ul→b + othν cl→b OUTν ul→b

data

(GeV)xM

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

200

400

600

800scaled MC

data subtr.

Figure 6.8: One-dimensional MX < 1.7 GeV/c2 analysis: 2-parameter χ2 fit to the MX distributionfor Run1-Run5 data. The approach fully based on mES fits without any attempt to subtract peakingbackgrounds has been used. Left: Points are data, the blue, magenta and yellow histograms representrespectively the fitted contributions from b → u`ν events with true MX < 1.7 GeV/c2, the rest of theb → u`ν events, and background events. The signal box is defined by MX < 1.7 GeV/c2. Right: MX

distribution subtracted of the backgrounds. χ2 per degree of freedom = 17.5/8.

(GeV)xM

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

500

1000

1500

2000

2500

3000

INν ul→b + othν cl→b OUTν ul→b

data

(GeV)xM

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

200

400

600

800scaled MC

data subtr.

Figure 6.9: One-dimensional MX < 1.7 GeV/c2 analysis: 2-parameter χ2 fit to the MX distribution forRun1-Run5 data The mES fit approach based on Monte Carlo truth-matching was used. Left: Pointsare data, the blue, magenta and yellow histograms represent respectively the fitted contributions fromb → u`ν events with true MX < 1.7 GeV/c2, the rest of the b → u`ν events, and background events. Thesignal box is defined by MX < 1.7 GeV/c2. Right: MX distribution subtracted of the backgrounds. χ2

per degree of freedom = 12.6/8.

129

where the first error is statistical, the second is due to Monte Carlo statistics and the

third is systematic.

Using the result of the fit, the partial branching fraction for charmless semileptonic B

decays, in the phase space region P+ < 0.66 GeV/c2, is measured to be

∆B(B → Xu`ν, P+ < 0.66 GeV/c2) = (0.95± 0.10stat. ± 0.08sys. ± 0.01SF)× 10−3

(6.14)

where the measurement of the inclusive semileptonic branching fraction reported in Eq. 6.8

has been used. The first error is statistical, the second is systematic and the third is due

to the uncertainties of the shape function parameters.

6.5 Two Dimensional (MX , q2) Fit and Results

The (MX , q2) two-dimensional distribution for data, obtained by following the procedure

outlined in Section 6.1, is fitted by using the two mES fit approaches outlined in Sec-

tion 5.3.4 and Nu and BGu, as defined by Eq. 6.7, are determined.

Previous studies [59] have shown that the phase space region defined by

MX < 1.7 GeV/c2 and q2 > 8 GeV2/c4 is optimal for a good measurement of the

partial branching ratio.

Fits to the (MX , q2) distribution have been performed for different run periods, and on

the full data sample. Results are shown in Table 6.14 and in Figure 6.12 for the approach

without peaking background subtraction, and in Table 6.15 and in Figure 6.13 for the

algorithm based on truth-matching.

In the signal region defined by MX < 1.7 GeV/c2 and q2 > 8 GeV2/c4, the value for

∆Ru/sl obtained by using the full dataset is

∆Ru/sl(MX < 1.7 GeV/c2, q2 > 8 GeV2/c4) = (75± 7± 3± 10)× 10−4 (6.15)

where the first error is statistical, the second is due to Monte Carlo statistics and the

third is systematic.

Using the result of the fit, the partial branching fraction for charmless semileptonic B

decays, for the phase space region defined by (MX < 1.7 GeV/c2, q2 > 8 GeV2/c4), is

130

Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 43031± 574 17544± 344 53097± 393 66458± 520 181074± 706

BGsl 2659± 35 1296± 25 3708± 27 4376± 34 12187± 48Nsl −BGsl 40373± 538 16249± 319 49389± 366 62082± 486 168887± 659

N inu 212± 30 65± 20 164± 35 194± 38 633± 63

Noutu 13± 2 5± 2 14± 3 13± 3 48± 5

Nbkg 245± 12 115± 8 360± 15 459± 18 1183± 27εusel 0.414 0.428 0.395 0.383 0.399

εukin 0.874 0.879 0.862 0.858 0.865

(εut εu

` )/(εslt εsl

` ) 1.21± 0.06 1.21± 0.10 1.22± 0.06 1.23± 0.05 1.23± 0.03∆Ru/sl(10−4) 120± 17± 7 88± 26± 14 80± 17± 8 77± 15± 7 88± 9± 4

Table 6.12: Summary of the fit to the P+ distribution and results for P+ < 0.66 Gev/c2 for the fullsample and for various subsamples. The approach fully based on mES fits without any attempt tosubtract peaking backgrounds has been used. N in

u is the number of signal events in the signal region(P+ < 0.66 GeV/c2). The first error on ∆Ru/sl(P+ < 0.66 GeV/c2) is statistical, the second is due toMonte Carlo statistics. The non-resonant component in the Monte Carlo has been reweighted accordingto the shape function parameters from the HFAG combination using B → Xc`ν and B → Xsγ decays asdescribed in Section 4.2.5.

Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 37577± 512 15196± 293 46058± 340 57332± 442 156252± 603

BGsl 2221± 30 1056± 20 3210± 24 3849± 30 10352± 40Nsl −BGsl 35355± 481 14141± 273 42848± 316 53483± 412 145900± 563

N inu 193± 28 56± 18 146± 32 170± 34 560± 58

Noutu 13± 2 5± 2 13± 3 12± 3 43± 5

Nbkg 232± 11 109± 7 336± 13 422± 16 1100± 24εusel 0.421 0.446 0.414 0.396 0.412

εukin 0.886 0.882 0.871 0.880 0.879

(εut εu

` )/(εslt εsl

` ) 1.23± 0.05 1.18± 0.08 1.23± 0.04 1.23± 0.04 1.23± 0.02∆Ru/sl(10−4) 118± 17± 6 84± 27± 12 77± 17± 7 74± 15± 6 87± 9± 4

Table 6.13: Summary of the fit to the P+ distribution and results for P+ < 0.66 GeV/c2 for the fullsample and for various subsamples. The mES fit approach based on Monte Carlo truth-matching wasused. N in

u is the number of signal events in the signal region (P+ < 0.66 GeV/c2). The first error on∆Ru/sl(P+ < 0.66 GeV/c2) is statistical, the second is due to Monte Carlo statistics. The non-resonantcomponent in the Monte Carlo has been reweighted according to the shape function parameters from theHFAG combination using B → Xc`ν and B → Xsγ decays as described in Section 4.2.5.

131

(GeV)+P

0 1 2 3 4 5

0

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4000

5000

6000 INν ul→b + othν cl→b OUTν ul→b

data

(GeV)+P

0 1 2 3 4 5

0

100

200

300

400

500

600

700

scaled MC

data subtr.

Figure 6.10: One-dimensional P+ analysis: 2-parameter χ2 fit to the P+ distribution for Run1-Run5 data.The approach fully based on mES fits without any attempt to subtract peaking backgrounds has beenused. Left: Points are data, the blue, magenta and yellow histograms represent respectively the fittedcontributions from b → u`ν events with true P+ < 0.66 GeV/c2, the rest of the b → u`ν events, andbackground events. The signal box is defined by P+ < 0.66 GeV/c2. Right: P+ distribution subtractedof the backgrounds. χ2 per degree of freedom = 5.5/5.

(GeV)+P

0 1 2 3 4 5

0

1000

2000

3000

4000

5000

6000

INν ul→b + othν cl→b OUTν ul→b

data

(GeV)+P

0 1 2 3 4 5

0

100

200

300

400

500

600

scaled MC

data subtr.

Figure 6.11: One-dimensional P+ analysis: 2-parameter χ2 fit to the P+ distribution for Run1-Run5data (truth-matching based approach for mES fits). Left: Points are data, the blue, magenta andyellow histograms represent respectively the fitted contributions from b → u`ν events with true P+ <0.66 GeV/c2, the rest of the b → u`ν events, and background events. The signal box is defined byP+ < 0.66 GeV/c2. Right: P+ distribution subtracted of the backgrounds. χ2 per degree of freedom= 6.4/5.

132

measured to be

∆B (B → Xu`ν, MX < 1.7 GeV/c2, q2 > 8 GeV2/c4) =

=(0.81± 0.08stat. ± 0.07sys. ± 0.02SF)× 10−3 (6.16)

where the measurement of the inclusive semileptonic branching fraction reported in

Eq. 6.8 has been used. The first error is statistical, the second is systematical and the

third is due to the uncertainties of the shape function parameters.

133

Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 43031± 574 17544± 344 53097± 393 66458± 520 181074± 706

BGsl 2658± 35 1295± 25 3708± 27 4376± 34 12185± 48Nsl −BGsl 40373± 538 16249± 319 49390± 366 62083± 486 168889± 659

N inu 165± 26 82± 16 125± 30 189± 33 562± 55

Noutu 10± 1 2± 0 7± 1 11± 1 32± 2

Nbkg 181± 4 70± 3 239± 5 299± 6 789± 9εusel 0.415 0.415 0.399 0.377 0.400

εukin 0.869 0.858 0.871 0.913 0.881

(εut εu

` )/(εslt εsl

` ) 1.24± 0.05 1.32± 0.16 1.27± 0.06 1.25± 0.05 1.26± 0.04∆Ru/sl(10−4) 91± 14± 6 107± 20± 10 57± 13± 6 71± 12± 5 75± 7± 3

Table 6.14: Summary of the fit to the (MX , q2) distributions and results for MX < 1.7 GeV/c2 andq2 > 8 GeV2/c4 for the full sample and for various subsamples. The approach fully based on mES

fits without any attempt to subtract peaking backgrounds has been used. N inu is the number of signal

events in the signal region (MX < 1.7 GeV/c2, q2 > 8 GeV2/c4). The first error on ∆Ru/sl(MX <1.7 GeV/c2, q2 > 8GeV2/c4) is statistical, the second is due to Monte Carlo statistics. The non-resonantcomponent in the Monte Carlo has been reweighted according to the shape function parameters from theHFAG combination using B → Xc`ν and B → Xsγ decays as described in Section 4.2.5.

Parameters Run1-Run2 Run3 Run4 Run5 Run1-Run5Nsl 37577± 512 15196± 293 46058± 340 57332± 442 156252± 603

BGsl 2221± 30 1056± 20 3210± 24 3849± 30 10352± 40Nsl −BGsl 35355± 481 14141± 273 42848± 316 53483± 412 145900± 563

N inu 157± 24 75± 15 111± 27 176± 29 516± 50

Noutu 9± 1 1± 0 6± 1 10± 1 28± 2

Nbkg 161± 4 64± 2 225± 4 260± 5 711± 8εusel 0.423 0.439 0.427 0.400 0.417

εukin 0.874 0.829 0.889 0.916 0.891

(εut εu

` )/(εslt εsl

` ) 1.27± 0.05 1.27± 0.09 1.27± 0.05 1.23± 0.04 1.25± 0.03∆Ru/sl(10−4) 95± 14± 5 115± 22± 9 54± 13± 4 73± 11± 4 76± 7± 3

Table 6.15: Summary of the fit to the (MX , q2) distributions and results for MX < 1.7 GeV/c2 and q2 >8 GeV2/c4 for the full sample and for various subsamples. The mES fit approach based on Monte Carlotruth-matching was used. N in

u is the number of signal events in the signal region (MX < 1.7 GeV/c2,q2 > 8 GeV2/c4). The first error on ∆Ru/sl(MX < 1.7 GeV/c2, q2 > 8 GeV2/c4) is statistical, the secondis due to Monte Carlo statistics. The non-resonant component in the Monte Carlo has been reweightedaccording to the shape function parameters from the HFAG combination using B → Xc`ν and B → Xsγdecays as described in Section 4.2.5.

134

)2 (

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2 q

05

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136

Chapter 7

Systematic Uncertainties

Theoretical uncertainties appearing when extrapolating measurements of partial branch-

ing fraction for charmless semileptonic decays to the full phase space are taken from theory

papers, and shown in the next chapter. The other systematic uncertainties are extremely

similar to the one described in previous BABAR inclusive semileptonic branching fraction

measurements [57, 60, 61]. Since a ratio of branching fractions is measured, most of them

cancel. The sources of systematic uncertainties on the (partial) ratio of branching fraction

are summarized in Tables 7.5 and 7.6, and can be divided into categories, as described

below.

7.1 Detector-related Effects

7.1.1 Charged Particle Tracking

Any difference between data and Monte Carlo simulation can potentially lead to a distor-

tion in the distribution of the kinematical variables under study, as well as in the efficiency

calculations.

The tracking efficiencies are well reproduced by the Monte Carlo simulations and, as

shown in Figure 5.19, the charged track spectrum is in good agreement between data

and Monte Carlo. A similar agreement has been obtained on other control samples. For

high momentum tracks, e+e− → τ+τ− events, where one τ decaying leptonically and the

other to three charged hadrons (plus an arbitrary number of neutrals), are used. They

are a good control sample for this purpose because the e+e− → τ+τ− cross section is

137

0.94 nb and the branching fraction to ` + 3 hadrons is 11% so this sample allows high

statistics tests. Moreover, the momentum distribution of tracks from τ decays is similar

to the one from B decays. Data and Monte Carlo efficiencies are in good agreement

within the statistical errors. To assign a systematic uncertainty on the charged particle

tracking, a common prescription within BABAR measurements has been followed and no

correction has been applied to Monte Carlo tracks, but a systematic uncertainty per track

has been assigned depending on the run period. The Monte Carlo has been reweighted by

randomly eliminating tracks with probabilities detailed in Table 7.1, and the difference

observed with respect to the default measurements is taken as the systematic uncertainty.

Run period syst. uncertainty (%)Run 1 0.44Run 2 0.32Run 3 0.18Run 4 0.54Run 5 0.65

Table 7.1: Systematic uncertainty per track used in the calculation of tracking systematic uncertainties,divided by run period.

7.1.2 Neutral Reconstruction

Differences between data and Monte Carlo simulation in the photon detection efficiency

and resolution, as well as additional energy depositions in the EMC, can impact the dis-

tributions of the kinematic variables used in this analysis.

Two different control samples are used to check for disagreements between data and

Monte Carlo simulation in efficiency and energy resolution. The study is performed using

the τ hadronic decays that represent an abundant source of neutral pions. The τ → eνν

decay is identified in e+e− → τ+τ− events. The ratio R = N(τ → h±π0 ντ )/N(τ →h±π0 π0 ντ ) is computed both for data and Monte Carlo as a function of the π0 energy in

order to evaluate possible differences in efficiency. The agreement has been found to be

good and the ratio is compatible with the unity in the full range. A systematic uncertainty

of 1.8% per photon is assigned, due to uncertainties in the hadronic interactions in the

EMC, to the photon background being not perfectly modeled in the Monte Carlo, and to

138

the uncertainty in the τ branching fractions in πντ and ρντ final states. The corresponding

systematic uncertainty is about 0.1% for all analyses.

The resolution has been studied taking π0s from both τ → h±π0 ντ and τ → h±π0 π0 ντ

decays. The π0 mass is fitted in energy bins and the resolution (corresponding to the σ

of a Gaussian fit) is then compared between data and Monte Carlo. The Monte Carlo

resolution is changed by applying a smearing factor such to be identical to data. Similar

corrections are applied on Monte Carlo to take into account differences in the energy scale

and effects due to energy deposits close to crystal boundaries and to the edges between

the barrel and the endcap of the EMC. These factors are determined as well with control

samples such as µµγ and B → K∗(K+π−)γ decays. All corrections turn out to be small.

The systematic uncertainty due to the reconstruction of neutral particles has been ob-

tained by repeating the analysis without applying the corrections and taking the difference

with respect to the default measurements.

7.1.3 KL Reconstruction

Systematic uncertainties in the simulation of KL interactions have been estimated accord-

ing to the results shown in [62]. Several corrections are applied on the Monte Carlo in

order to reproduce data. The energy deposition of calorimeter clusters truth-matched to a

KL are corrected by ad-hoc factors. The KL detection efficiency is corrected by rejecting

neutral clusters truth-matched to a KL with a probability, which is a function of the true

KL momentum.

A correction due to the differences between data and simulation for the KL production

rate is also applied, based on studies detailed in [63]. Given that such a correction can

not be accomplished by eliminating neutral clusters, a different approach, also described

in [64], has been employed. Clusters truth-matched to KL’s are randomly transformed

into “pseudo-photons” and in this way the energy and momentum balance in the event

are restored. This is achieved by rescaling the measured energy and momentum of the KL

cluster to the true KL momentum, assuming zero mass. The probability of the correction

depends on the KL momentum: 22% for momenta between 0 and 0.4 GeV/c, 1% for

momenta between 0.4 and 1.4 GeV/c, 9% for momenta larger than 1.4 GeV/c.

139

The systematic uncertainty due toKL reconstruction has been determined by repeating

the measurements without applying the above corrections in the Monte Carlo, and taking

the difference with respect to the default measurements.

7.1.4 Lepton Identification

The systematic uncertainties related to lepton identification efficiencies and misidentifi-

cation probabilities are derived from control samples. For electron efficiency, radiative

Bhabha events are used. For pions, samples of K0S → π+π− and three-prong τ decays

are used. A control sample of kaons is obtained by selecting D ∗+ → D 0π+, D 0 → Kπ

decays, where only kinematic information is used to identify the kaon. Muons with a mo-

mentum spectrum covering the range of interest are extracted from the e+e− → µ+µ−γ

and e+e− → e+e−µ+µ− channels.

The statistical and systematic errors from the data-Monte Carlo comparison in bins

of momentum and polar angle are used to compute the systematic uncertainties due

to particle identification. Each bin is shifted by ±2% for efficiency and by ±15% for

misidentification and the analysis is repeated. The difference in the results is taken

as the systematic uncertainty. The effect of the time dependence (especially in muon

identification) has been investigated by using efficiency corrections depending on run

periods.

7.1.5 Charged Kaon Identification

The systematic uncertainty associated with kaon identification efficiency and misidenti-

fication probabilities (shown in Figure 3.4) are obtained with the same technique used

for lepton identification. Kaon and pion samples are selected from the D∗+ → D0 π+ ,

D0 → Kπ decay chain. Each bin (as a function of the momentum and polar angle) is

shifted by ±2% for efficiency and by ±15% for misidentification.

7.2 Uncertainties Related to the mES Fits

In the fits to the mES distributions, some parameters of the signal function (α, n, σR1, r)

are kept fixed to values determined from high-statistics data sample or simulation. The

140

systematic uncertainty due to the choice of these parameters has been determined by

varying their values within the statistical errors. The small bias introduced in the mES

fitting approach, where the peaking background is not taken into account, is corrected for

and an error of 100% on this bias is assumed as systematic uncertainty.

7.3 Signal Knowledge

Our limited knowledge of the shape function parameters determined from other measure-

ments affects the experimental efficiencies (εsel, εkin). The corresponding uncertainty on

the measurement of partial branching fractions is expected to be small. This uncertainty

is estimated by varying the heavy quark parameter along the ellipse in the (mb,µ2π) plane

corresponding to ∆χ2 = 1 (Figure 7.1 and Table 7.2) and taking the maximum positive

and negative fit deviations from the central point.

/ GeVbm4.6 4.62 4.64 4.66 4.68 4.7 4.72 4.74

2 /

GeV

2 πµ

0.35

0.4

0.45

0.5

0.55

0.6

Figure 7.1: ∆χ2 = 1 contour plot in the (mb, µ2π) plane in the Kagan-Neubert Scheme [11]. The points

around the ellipse are the values used in the evaluation of systematic uncertainties (see also Tab. 7.2).

Systematic effects due to the form of the shape function have been studied by using

alternative parametrization, such as a Gaussian (Eq. 7.1) and a Roman form (Eq.7.2),

shown in Figure 7.2, both of them satisfying the same moments constraints as the original

form of Eq. 4.4.

F (k+; c) = N(1− k+/Λ)ce−b(1−k+/Λ)2 , b =

(Γ

(c+ 2

2

)/Γ

(c+ 1

2

))2

(7.1)

141

Point mb (GeV/c2) µ2π (GeV2/c4)

Central 4.6586 0.49661 4.6184 0.51322 4.6232 0.47533 4.6359 0.44534 4.6591 0.42575 4.6874 0.43786 4.6983 0.46977 4.6978 0.50958 4.6891 0.54359 4.6732 0.570410 4.644 0.580211 4.6253 0.556

Table 7.2: mb and µ2π values for the ∆χ2 = 1 contour plot shown in Fig. 7.1.

Figure 7.2: Left: Functional forms used for the Shape Function. Right: cumulative distribution for eachform.

F (k+; ρ) = Nκ√π

exp

(−1

4

(1

κ

ρ

1− k+/Λ− κ(1− k+/Λ)2

)2), κ =

ρ√πeρ/2K1(ρ/2)

(7.2)

Other effects due to the modeling of charmless semileptonic decays have been evaluated

by varying the branching fractions for the exclusive charmless semileptonic decays within

their known uncertainties (Table 4.4).

Signal Monte Carlo contains events where a gluon splits in an ss pair, resulting in

decays of the heavy Xu states into KK pairs. This happens both in the resonant and

142

the non-resonant contributions. In the hybrid model the fractions of events with gluon

splitting in ss for B+ (B0) are 10.7% (0.1%) for the resonant component and 12.0%

(11.3%) for the non-resonant one. The resonant contribution is almost entirely due to the

f′1 and h

′1 decays that produce only KK pairs. The non-resonant contribution is modeled

using JETSET. The parameter which sets gluon splitting in ss in JETSET is also known

as γs and it is set to γs = 0.30 in Monte Carlo. This parameter has been measured by two

experiments at center of mass energies between 12 and 36 GeV as γs = 0.35 ± 0.05 [65],

γs = 0.27 ± 0.06 [66]. Reference [66] shows how the scaling to lower energies (to 3 GeV,

equivalent to the energies involved in the Xu decays for MX ∼ 1.5 GeV/c2) works fine

compared to [67].

In order to calculate the systematic uncertainty, the fraction of events where a gluon

splits in an ss pair has been varied by ±30%. For non-resonant events this corresponds

to taking as 1σ interval the sum of the intervals from the two experiment.

7.4 Background Knowledge

Exclusive semileptonic branching fractions for B → Xc`ν are known with a certain pre-

cision. Moreover, the individual branching fractions in the Monte Carlo simulations are

known to differ from the current world averages. This difference is corrected by re-

weighting simulated events to match the world averages, shown in Table 7.3. Here D∗∗

refers to either non-resonant or broad D∗∗ states and the corresponding branching frac-

tion is taken as the difference between the total semileptonic rate and the other measured

branching fractions. The systematic uncertainty due to the limited knowledge of the

exclusive semileptonic branching fractions is computed by varying them randomly within

one standard deviation of their world averages, repeating the measurements, iterating the

procedure 100 times, and taking the RMS of the resulting distribution of results.

A similar procedure was followed to estimate the uncertainty, which turns to be negli-

gible, due to the branching ratios of charm mesons (Table 7.4) Uncertainties in the form

factors in the B → D∗`ν decays are also taken into account, by repeating the analyses

after varying the form factors within their experimental error [68].

143

B Decay mode best average (%) Monte Carlo (%)B0 → D−lν 2.13 ±0.14 2.07B0 → D∗−lν 5.53±0.25 5.70B0 → D−

1 lν 0.50±0.08 0.52B0 → D∗−

2 lν 0.39±0.07 0.23B0 → Xclν 10.14±0.38 10.2B+ → D0lν 2.30±0.16 2.24B+ → D∗0lν 5.95 ±0.24 6.17B+ → D0

1lν 0.54±0.06 0.56B+ → D∗0

2 lν 0.42± 0.08 0.30B+ → Xclν 10.92± 0.37 11.04

Table 7.3: Branching fractions for B → Xc`ν decays, current best averages and values used in MonteCarlo simulation, plus shift of the results due to the adjustments of the BR. The non resonant B → D`νXis obtained by difference of the inclusive rate and the other 4 components.

D0 Decay mode PDG MC D+ Decay mode PDG MCD0 → Kπ 0.0380± 0.0070 0.0383 D+ → K0π 0.0294± 0.0012 0.0282D0 → K0π0 0.0228± 0.0024 0.0212 D+ → Kππ 0.0951± 0.0034 0.0920D0 → K0ππ 0.0580± 0.0038 0.0540 D+ → K0ππ0 0.1400± 0.0100 0.1082D0 → Kππ0 0.1410± 0.0050 0.1390 D+ → K0πππ0 0.0550± 0.0270 0.0681D0 → K0π0π0 0.0210± 0.0020 0.0161 D+ → K0πππ 0.0622± 0.0042 0.0716D0 → Kπππ 0.0772± 0.0028 0.0787 D+ → Kππππ 0.0058± 0.0006 0.0075D0 → K0πππ0 0.1060± 0.0120 0.0973 D+ → Kπππ0π0 0.0220± 0.0470 0.0084D0 → Kππ0π0 0.1500± 0.0500 0.1056 D+ → K0ππππ0 0.0540± 0.0300 0.0252D0 → Kππππ0 0.0410± 0.0040 0.0433 D+ → K0πππππ 0.0008± 0.0007 0.0000D0 → ππ 0.00136± 0.00003 0.00150 D+ → Kπππππ0 0.0020± 0.0018 0.0045D0 → π0π0 0.00079± 0.00008 0.0008 D+ → K0K0K 0.0094± 0.0042 0.0100D0 → πππ0 0.0131± 0.0006 0.0159 D+ → ππ0 0.00128± 0.00009 0.0027D0 → ππππ 0.0073± 0.0003 0.0073 D+ → πππ 0.00331± 0.00022 0.0031D0 → πππππ0 0.0041± 0.0005 0.0177 D+ → ππππ0 0.0118± 0.0009 0.0119D0 → ππππππ 0.0004± 0.0001 0.0000 D+ → πππππ 0.00168± 0.00017 0.00210

D+ → ππππππ0 0.0029± 0.0029 0.0007

Table 7.4: D branching ratios, current best measurements and values used in the Monte Carlo.

7.5 Summary

Table 7.5 shows the relative uncertainties (in percent) involved in the MX analyses for the

two kinematic cuts under study. In Table 7.6 the relative systematics uncertainties (also in

percent) for the P+ and (MX , q2) analyses are reported. Statistical errors are slightly larger

than the total systematic uncertainties for all analyses. Systematic uncertainties due to

detector, fit procedure and signal knowledge contribute roughly equally. The approach

to mES fits based on truth-matching seems slightly better than the other one. However

144

Source σ(∆B(B → Xu`ν)) σ(∆B(B → Xu`ν))MX < 1.55 GeV/c2 MX < 1.7 GeV/c2

truth-matching fit all truth-matching fit allStatistical error 7.41 7.27 8.59 8.80Monte-Carlo statistics 2.74 3.22 3.23 3.85Tracking efficiency 0.75 0.71 0.56 0.65Neutral efficiency 1.85 1.42 2.76 2.21PID eff. & misID 1.16 0.86 1.95 1.84KL 0.53 0.51 0.72 0.69

Fit-related:mES fit parameters 2.68 2.99 3.59 4.16peaking background 2.20 2.20

Signal knowledge:SF parameters +0.95

−1.15+0.71−1.01

+2.27−1.77

+1.86−1.67

SF form 0.66 0.56 0.70 0.97Exclusive b → u`ν 2.12 2.08 1.79 1.82Gluon splitting 1.49 1.62 2.04 2.43

Background knowledge:KS veto 0.40 0.44 0.84 0.77B SL branching ratio 0.81 0.87 2.07 1.76D decays 0.38 0.44 0.35 0.41B → D∗ `ν from factor 0.30 0.21 0.31 0.27Total systematics: +5.85

−5.89+6.05−6.09

+7.66−7.52

+7.98−7.94

Total error: +9.54−9.56

+9.63−9.65

+11.43−11.34

+11.59−11.56

Table 7.5: Relative uncertainties in percent for the MX < 1.55 GeV/c2 and the MX < 1.7 GeV/c2

analyses, for the two approaches to the mES fits.

it should be kept in mind that the systematic uncertainties for the former approach are

underestimated, as mentioned in Section 5.3.4. The best measurement in terms of overall

uncertainty is the one in the phase space region defined by MX < 1.55 GeV/c2.

145

Source σ(∆B(B → Xu`ν)) σ(∆B(B → Xu`ν))P+ < 0.66 GeV/c2 MX < 1.7 GeV/c2, q2 > 8 GeV2/c4

truth-matching fit all truth-matching fit allStatistical error 10.34 10.11 9.72 9.72Monte-Carlo statistics 4.08 4.62 3.44 4.29

Detector-related:Tracking efficiency 0.40 0.49 1.32 1.07Neutral efficiency 2.99 2.88 2.90 2.45PID eff. & misID 1.45 1.52 2.84 2.51KL 0.77 0.61 0.85 1.02

Fit-related:mES fit parameters 3.32 3.55 1.86 4.14peaking background 1.80 3.10

Signal knowledge:SF parameters +0.60

−1.16+0.42−1.25

+2.83−1.71

+1.65−2.26

SF form 1.30 1.25 1.37 1.78Exclusive b → u`ν 2.27 2.22 1.94 2.71Gluon splitting 1.23 1.47 0.87 1.02

Background knowledge:KS veto 1.73 1.34 0.40 0.40B SL branching ratio 2.93 2.80 1.41 1.17D decays 0.70 0.73 0.79 0.79B → D∗ `ν from factor 0.40 0.39 0.55 0.55Total systematics: +7.90

−7.97+8.34−8.42

+7.83−7.50

+8.74−8.88

Total error: +13.02−13.06

+13.03−13.08

+12.42−12.21

+13.13−13.22

Table 7.6: Relative uncertainties in percent for the P+ and the (MX , q2) analyses, for the two approachesto the mES fits.

146

Chapter 8

Measurement of |Vub|

The partial branching fractions ∆B(B → Xu`ν) determined in Chapter 7 are translated

into |Vub| values by means of theoretical calculations. These calculations use heavy quark

input parameters which are extracted from data.

8.1 Input Parameters

Moment measurements from B → Xsγ and B → Xc`ν transitions are used in or-

der to extract the non–perturbative input parameters needed to compute |Vub| from

∆B(B → Xu`ν). Different choices are possible. The values of |Vub| quoted in the fol-

lowing correspond to the set of input parameters obtained by fitting simultaneously both

B → Xsγ and B → Xc`ν moments [11].

The values of the input parameters extracted for the different theoretical calculations

are shown in Table 8.1.

BLL BLNP DGEmb(1S) mb(SF ) µ2

π(SF ) mb(MS)B → Xsγ and B → Xc`ν moments 4.73 4.60± 0.04 0.20± 0.04 4.20± 0.04

Table 8.1: Non–perturbative parameters as computed for BLL, BLNP and DGE theoretical schemes.

The fit to the B → Xsγ and B → Xc`ν moments was performed by Flacher and

Buchmuller [11] in the kinetic scheme and then translated to other schemes, except the

1S scheme, for which the result in the MS scheme was converted by using the expres-

sions in Ref. [69].

147

8.2 |Vub| Extraction

The measured values of ∆Ru/sl are converted in ∆B(B → Xu`ν), and finally |Vub| is

determined.

As there is no agreement on the theoretical calculation to be used to determine |Vub|,all currently available computations have been tried, similarly to what is done by the

HFAG [54]. The theoretical uncertainties have been computed as suggested by theory

papers.

In the BLL approach, see [38], the relation between ∆B(B → Xu`ν) and |Vub| is given

by:

|Vub| =√

192π3

τBG2Fm

5b

∆B(B → Xu`ν)

G(8.1)

where τB is the B hadron lifetime from 2007 update of the PDG [70], averaged between

charged and neutral mesons, and G is the ratio of the decay width between the phase

space we are using and all the phase space.

The value of G in Ref. [71], obtained with mb(1S) = 4.70 GeV, is 1.21 × G =

0.324 ± 0.048. The 15% error on G, resulting in a 7% error on |Vub|, is the sum in

quadrature of uncertainties due to: residual shape function effects (6%), higher order

terms in the αs perturbative expansion (6%), a 50 MeV/c2 uncertainty on the b quark

mass (9%), and O(Λ3QCD/m

3) terms in the OPE expansion (8%). The latter two sources

dominate, contributing almost 10% each to the uncertainty on G. To compute G for a

given b quark mass and given (MX , q2) cuts, a linear interpolation [72] is used to rescale

the value for G as computed by BLL [71] for (MX , q2)=(1.7-8.0) to the b quark mass

measured in the 1S scheme (see Table 8.1 for the b-quark mass values). The values

obtained for mb(1S) = 4.73 GeV and mb(1S) = 4.69 GeV, as presented in Table 8.1, are

1.21×G = 0.341± 0.050 and 1.21×G = 0.318± 0.047, respectively.

BLNP give results and uncertainties in terms of the reduced decay rate Γthy, defined

in units of |Vub|2 ps−1:

Γthy =∆Γthy

|Vub|2 (8.2)

where ∆Γthy is the partial width of the B → Xu`ν decay into the phase space of

148

interest predicted by the theory.

|Vub| is given by

|Vub| =√

∆B(B → Xu`ν)

Γthy · τB(8.3)

where τB is the B meson lifetime. The reduce decay rate Γthy is computed by a Math-

ematica notebook, given to BABAR by the authors of BLNP. The value of Γthy depends

on the analyzed phase space. The corresponding values of Γthy for the current analyses

are shown on Table 8.2 with the corresponding error due to the SF parameters (SF ), the

error due to the sub–leading shape functions (ssf), the choice of the intermediate scale

(scale), and finally the error contribution due to the Weak Annihilation (WA).

Γ%(MX , q2) 24.4± 2.0SF ± 0.4ssf ± 2.1scale ± 1.3WA

MX ≤ 1.55 GeV/c2 40.7± 4.3SF ± 1.0ssf ± 2.9scale ± 1.3WA

MX ≤ 1.70 GeV/c2 47.4± 4.3SF ± 0.6ssf ± 3.3scale ± 1.3WA

P+ 39.7± 4.7SF ± 1.2ssf ± 2.5scale ± 1.3WA

Table 8.2: Values of Γ, from the BLNP method, used in the analyses.

Finally, the partial branching fraction can be translated to |Vub| using the DGE calcu-

lation (see Ref. [35]). DGE stands for Dressed Gluon Exponentiation and is a recent new

addition to the phenomenology landscape of inclusive B meson decays. In this framework,

the on-shell b quark calculation, converted into hadronic variables, can be directly used

as an approximation to the meson decay spectrum, without need of a leading-power non–

perturbative function i.e. no shape function. The on-shell mass of the b quark within the

B meson is required as an input (mb). |Vub| is given by

|Vub| =√

∆B(B → Xu`ν)

R · ω · τB (8.4)

where ω is the B → Xu`ν total rate, as computed by DGE [35], and R is the fraction of

phase space selected by the kinematic cuts.

Theoretical uncertainties are assessed by varying the inputs of: mb (in the minimal

subtraction scheme), and the strong coupling constant (αs), the number of light fermion

flavours (NF ), and the method and scale of the matching scheme intrinsic to the approach.

Finally, a contribution to the uncertainties due to weak annihilation, so far missing in

149

DGE, has been added similarly to what has been done for BLNP [73]. See Table 8.3 for

details for the values of R and its error.

R

(MX , q2) 0.3579±1.03mb± 0.20αs ± 1.41NF ± 1.91scale ± 0.90WA

MX ≤ 1.55 GeV/c2 0.5369±4.21mb± 0.04αs ± 2.74NF

± 4.01scale ± 0.90WA

MX ≤ 1.70 GeV/c2 0.5667±4.78mb± 0.12αs

± 1.64NF± 2.27scale ± 0.90WA

P+ 0.6367±3.36mb± 0.07αs

± 1.33NF± 3.94scale ± 0.90WA

Table 8.3: Values of R, from the DGE method, used in the analyses with the corresponding errors.

8.2.1 (MX , q2)

Results on |Vub| obtained from the (MX , q2) analysis by using the three above theoretical

calculations are shown in Table 8.4. The result based on BLL is somewhat higher than

the other two. The uncertainty is also larger, due to a more conservative estimate by BLL

of weak annihilation effects, which are dominant at high q2 regions.

|Vub| for the (MX , q2) analysisCalculation |Vub|(10−3)BLL 4.93± 0.24(stat)± 0.20(syst)± 0.36(theo)BLNP 4.57± 0.22(stat)± 0.19(syst)± 0.30(theo)DGE 4.64± 0.23(stat)± 0.19(syst)± 0.25(theo)

Table 8.4: Results on |Vub| from the (MX , q2) analysis obtained with the three theoretical calculationsdescribed in the text.

8.2.2 MX

By construction, the BLL computations make sense only in phase space regions where

shape function effects are small, so they cannot be used for regions defined by pure

MX cuts. Results on |Vub| obtained with BLNP and DGE are shown in Table 8.5. It is

interesting to notice that the results based on DGE are comparable to the ones obtained in

the (MX , q2) analysis, whereas those based on BLNP are somewhat lower. The theoretical

uncertainty on the measurement with MX ≤ 1.55 GeV/c2 is higher than the one based

on MX ≤ 1.70 GeV/c2, since the latter is less sensitive to shape function effects.

150

|Vub| for the MX analysisCalculation |Vub|(10−3)BLNP (MX ≤ 1.55 GeV/c2) 4.27± 0.16(stat)± 0.13(syst)± 0.30(theo)BLNP (MX ≤ 1.70 GeV/c2) 4.28± 0.18(stat)± 0.17(syst)± 0.25(theo)DGE (MX ≤ 1.55 GeV/c2) 4.56± 0.17(stat)± 0.14(syst)± 0.32(theo)DGE (MX ≤ 1.70 GeV/c2) 4.53± 0.19(stat)± 0.18(syst)± 0.25(theo)

Table 8.5: Results on |Vub| obtained for the MX analysis with by using the BLNP and DGE calculations.

8.2.3 P+

Again, BLL cannot be applied to determine |Vub| from measurements based on regions

delimited by P+ requirements. Results on |Vub| obtained with BLNP and DGE are shown

in Table 8.6. These results are somewhat lower than the others, and closer to the range

determined with measurements of exclusive charmless semileptonic decays [54].

|Vub| for the P+ analysisComputation |Vub|(10−3)BLNP 3.88± 0.19(stat)± 0.16(syst)± 0.28(theo)DGE 3.99± 0.20(stat)± 0.16(syst)± 0.24(theo)

Table 8.6: Results on |Vub| obtained for the P+ analysis by using the BLNP and DGE calculations.

8.3 Compatibility of the |Vub| Determinations

The different |Vub| determinations obtained so far can be compared and checked for com-

patibility, but also to determine whether the features predicted by the theoretical models

for different phase space regions are observed in the experimental results.

However, the phase space regions considered above are not independent but highly

overlapping. Strong correlations among the different determinations of theoretical ac-

ceptances are also expected. Consequently, the |Vub| measurements are not independent

between each other.

Theoretical correlation have been calculated for the BLNP framework in the following

way. Since the theoretical uncertainties are dominated by the knowledge of the heavy

quark parameters, the correlation coefficients among the acceptances in different phase

space regions have been determined by computing the fractions of b → u events corre-

sponding to the three kinematic signal regions in a grid of 50 points in the (mb, µ2π) plane.

151

The resulting correlation coefficients ρ are displayed in Table 8.7.

Correlation coefficient ρ MX < 1.55 GeV/c2 P+ < 0.66 GeV/c2 MX < 1.7GeV/c2

q2 > 8 GeV2/c4

MX < 1.55 GeV/c2 1 0.98020 0.97253P+ < 0.66 GeV/c2 0.98020 1 0.97474MX < 1.7GeV/c2 0.97253 0.97474 1q2 > 8 GeV2/c4

Table 8.7: Correlation coefficients ρ for the different phase space acceptances in the BLNP model.

Taking the values of Γthy from Table 8.2, the ratio of theoretical acceptances between

two different phase space regions can be computed as

ΓMX

ΓMX ,q2

= 1.67± 0.05 (8.5)

ΓP+

ΓMX

= 0.98± 0.03 (8.6)

ΓP+

ΓMX ,q2

= 1.63± 0.05 (8.7)

The statistical correlation can be computed by rewriting Equation 8.4 as

|Vub| =√

1

Γthy · τBN in

u

Nsl

1

εuselεukin

· εsl` ε

slt

εu` εu`

(8.8)

where N inu comes from the χ2 fit described in Section 6.1. The statistical correlation has

been calculated by taking into account the statistical correlation between the number

of measured b → u transitions, Nmeasu , the number of b → u events migrating into the

signal region N outMCu and the number of background events N bkgMC and propagating the

uncertainties accordingly. A 100% correlation has been assumed for all other systematic

uncertainties.

The ratios of partial branching ratios determined in different phase space regions are

then:

∆B(B → Xu`ν)MX

∆B(B → Xu`ν)MX ,q2

= 1.46± 0.13 (8.9)

∆B(B → Xu`ν)P+

∆B(B → Xu`ν)MX

= 0.81± 0.07 (8.10)

∆B(B → Xu`ν)P+

∆B(B → Xu`ν)MX ,q2

= 1.18± 0.14 (8.11)

152

These experimental ratios are in good agreement with the same measurements performed

by the Belle Collaboration [74]. Due to the lack of information about experimental cor-

relations in the Belle paper, only the central values can be quoted:

∆B(B → Xu`ν)MX

∆B(B → Xu`ν)MX ,q2

= 1.47 [74] (8.12)

∆B(B → Xu`ν)P+

∆B(B → Xu`ν)MX

= 0.89 [74] (8.13)

∆B(B → Xu`ν)P+

∆B(B → Xu`ν)MX ,q2

= 1.31 [74] (8.14)

The double ratios between theoretical acceptances and experimental measurements in

different phase space regions should be compatible with unity within errors. Using BLNP

calculations:

theo

exp

∣∣∣∣MX/MX ,q2

= 1.14± 0.14 (8.15)

theo

exp

∣∣∣∣P+/MX

= 1.21± 0.08 (8.16)

theo

exp

∣∣∣∣P+/MX ,q2

= 1.38± 0.15 (8.17)

The MX and (MX , q2) analyses give therefore compatible results, while there is a dis-

agreement at the order of 2.5σ in the P+ analysis, which is confirmed also by the Belle

results.

8.4 Conclusion

The experimental results presented in this thesis work are used to determine the CKM

matrix element |Vub| by resorting to various theoretical models currently available. While

measurements based on MX and (MX , q2) are compatible with theory calculations, there

is a suggestive hint that results based on P+ are somewhat lower than theory predictions

and closer to |Vub| determinations which use exclusive charmless semileptonic decays.

The measurement shown in this thesis are currently the most precise on this subject and

contribute substantially to increase the precision on |Vub| determination by using inclusive

charmless semileptonic decays.

153

The dominant uncertainty is currently due to theory when extrapolating the experi-

mental measurements in restricted regions of phase space to |Vub|. As an outlook, more

efforts should be done on the theory side to reach consensus on a viable model to be used,

a better assessment of theory uncertainties and their reduction. A systematic program of

measurements in several regions of phase space, on final datasets from the B Factories,

will be extremely helpful to increase confidence in the reduction of the theoretical errors.

154

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[72] Z. Ligeti, private communication.

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