Hyperon polarisation at BESIII - Istituto Nazionale di ... Hyperon polarisation at BESIII Candidato:...

Universita degli Studi di Torino

DIPARTIMENTO DI FISICA

Corso di Laurea Magistrale in Fisica

Tesi di laurea magistrale

Hyperon polarisation at BESIII

Candidato:

Giulio MezzadriRelatore:

Prof. Marco Maggiora

Co-Relatore:

Dott. Marco Destefanis

Contro-Relatore:

Prof. Mauro Anselmino

Anno Accademico 2012-2013

Alla mia famiglia, il mio incrollabile sostegno

Because maybe,

you’re gonna be the one that saves me...

And after all, you’re my wonderwall..

Oasis

Contents

I Introduction 7

1 Physics 8

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2 Particles and Forces in the Standard Model . . . . . . . . . . . . . . . . . 8

1.3 e+e− Annihilation Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3.1 Feynmann Diagramm and Cross Section Calculation . . . . . . . . 10

1.3.2 Synchrotron radiation . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.3.3 Beamstrahlung and Initial State Radiation . . . . . . . . . . . . . . 12

1.4 Charmonium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.5 Hyperons and Strangeness . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.5.1 Strange Quark Physics - The SU(3)F Model . . . . . . . . . . . . . 17

1.5.2 Λ description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.6 Hyperon Polarisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 BESIII Spectrometer 21

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.1.1 BEPCII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2 BESIII Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.1 Multilayer Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . 24

2.2.2 Time of Flight System . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.2.3 Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . . . 27

2.2.4 Muon Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

II Data Analysis 31

3 Analysis e+e− → ΛΛ 32

3.1 Event Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Armenteros-Podalansky Plot . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.4 Efficiency and acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3

CONTENTS 4


4 Analysis e+e− → J/ψ → ΛX 54

4.1 Event Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.3 Efficiency and Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . 56


5 Analysis e+e− → J/ψ → ΛX 63

5.1 Event simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.3 Efficiency and Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . 65


6 Relative Phase 71

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.1.1 Measuring the Phase . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.2 Event Simulation and Selection . . . . . . . . . . . . . . . . . . . . . . . . 73

6.3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

III Conclusion 78

Abstract

The investigation of the hyperons structure could shed new light on many different

open questions in particle physics; probing the spin degrees of freedom is an usual and

effective approach to experimentally evaluate such a structure. Hyperon polarisation

has been already investigated at low energy (among others at DISTO and CLEOc); to

evaluate it in the yet relatively unexplored threshold sector in electron-positron collision,

eventually up to the J/ψ resonance, could allow to extend the investigation of the energy

dependence of the hyperon polarisation itself and of the underlying elementary processess

at quark level.

After an initial focus on the related theoretical issues, the experimental scenario and

those detectors relevant for the event selection and reconstruction will be described in

details.

Afterwards the complete procedure adopted to extract the spin polarisation for both

the exclusive (e+e− → ΛΛ) and inclusive (e+e− → J/ψ → ΛX and e+e− → J/ψ → ΛX)

hyperon production will be reported, from the event selection to its final results.

Finally, one more observable, the relative phase between electromagnetic and strong

J/ψ production amplitudes, has been extracted considering the ΛΛ final state.

The present analysis has been performed on the full set of events collected up to now

with the BESIII spectrometer at different center of mass energies, to perform both the

J/ψ lineshape scan and a detailed investigation of the off-resonance interference pattern.

Part I

Introduction

7

Chapter 1

Physics

1.1 Introduction

The first hypothesis of quark’s existence is found in Gell-Mann’s work [1] as explana-

tion for similar behavior of different particles: Gell-Mann proposed that these elementary

particles group together to form all the known hadrons. In the same period, Feynmann

proposed the idea of partons, point-like elementary particles which brings part of the

momentum of the hadrons. In the following years, many others compontents of the sub-

atomic world were found: the quark c (with the discovery of J/ψ), the quark b and quark

t and the differences between valence and sea quarks were finally pointed out. Those

studies lead to the full definition the Weinberg and Salam’s Standard Model of Particles.

Althought many questions were answered, many others were brought to a new light,

such as hadronization process, quark extraction from the vacuum, and the neutrino mass,

that are still under investigation. Thus, high energy physics remains a very rich field to

probe our understanding of the subatomic world.

1.2 Particles and Forces in the Standard Model

We need to clarify that there are two different types of elementary particles. The

distinction is based on their spin quantum number: bosons, which have integer spin and

follow the Bose-Einstein statistics, and fermions, which have half integer spin and are

described by the Fermi-Dirac statistics.

Bosons are the particles carrying the elementary forces the particles interact with.

There are five type of bosons: photons, mediators of the electromagnetic force, W’s and

Z’s, of the weak force, gluons, mediators of the strong interaction, and gravitons, of the

gravitational force.

Fermions can be divided in two different groups:

8

CHAPTER 1. PHYSICS 9

• leptons, which are pointlike particles interacting by electromagnetic (EM) and weak

interaction

• quarks, interacting by strong force as well.

Quarks bind together to form not-elementary particle called hadrons.

Hadrons can be divided in two different group:

• mesons, which are composed of a quark-antiquark pair;

• baryons, which are composed of three quarks.

Both leptons and quarks are divided in three families, as shown in the tab. 1.1 and

tab 1.2 respectively.

(ud

) (cs

) (tb

)Table 1.1: The three families of quarks.

(νee

) (νµµ

) (νττ

)Table 1.2: The three families of leptons.

The five lighter quark (up (u), down (d), strange (s), charm (c), and bottom (b), from

the lightest to the heaviest) bind together to form hadrons, while the top quark (t) is too

heavy, and it has too many open decay channels so that it cannot form a tt bound state.

The electromagnetic (EM) interaction is well interpred in a quantum field theory called

Quantum Electrodynamics (QED). Also the weak interaction is today well understood.

Both are unified in the Electroweak interaction theory.

The situation is different once the strong interaction is considered. Two regimes may

apply: the hard regime, explained by the Quantum Cromodynamics, in which processes

with large transverse momentum are described in a similar way as by QED, and the soft

regime, in which processes are no more perturbative; the latter regime still has to be

completely understood. Usually a perturbative approach is considered safe only if the

energy scale of the considered processes is larger than 1 GeV.


1.3 e+e− Annihilation Process

The e+e− annihilation vertex is fully interpreted by QED. I will briefly explain how

to define the partial and the total cross section starting from the Feynmann diagram

[2]. Hence, I will introduce the synchrotron radiation [3], initial state radiation [3] and

beamstrahlung processes [3], which are the most important causes of energy loss in e+e−

annihilations.

1.3.1 Feynmann Diagramm and Cross Section Calculation

A Feynmann diagramm is a pictorial representation of an elementary process [2]. This

picture is universally used to perform calculation for the process under investigation. An

example of the process e+e− → qq is depicted in the fig 1.1.

e −

e+

γ∗

q

q

Figure 1.1: Example of a Born level Feynmann diagramm of e+e− → qq.

First of all, to calculate the cross section for an investigated process, it is necessary to

know the matrix M, the so called interaction matrix :

M = (−ie)2v†2γµQu1u

†3γ

νv4δij1

s,

and its hermitian conjugate

M† = (ie)2Qu†1γµv2v†4γνu3δji

1

s,

where u1, u3 are the spinors for particle (e−, q) and v2, v4 are the spinors for antiparticle

(e+, q), s is the Mandelstamm invariant s = (p1 + p2)2, Q is the quark charge, and γµ,ν is

a Dirac matrix, being µ, ν = 0, 1, 2, 3.

The squared matrix is obtained as M†M:

|M|2 = e4 1

s2δijδjiQ

2u†1γµv2v†4γνu3v

†2γ

µu1u†3γ

νv4.

Since each s†γσs is a scalar, they can be reordered in a more useful way:


|M|2 = e4 1

s2δijδjiQ

2u†1γµv2v†2γ

µu1v†4γνu3u

†3γ

νv4.

Two traces can be defined: u†1γµv2v†2γ

µu1 and v†4γνu3u†3γ

νv4.

Both the beam and the target polarisations have now to be considered. One has to

sum over final spin state and to average on the initial spin state, using the 12S+1

relation,

where S is the spin of the incoming particle. Since quarks populates the final state, a

color factor 13

has to be introduced for each quark line:

1

4

1

9Σf |M|2 =

1

4

1

9δijδjiQ

2Σf tr[u†1γµv2v

†2γ

µu1

]tr[v†4γνu3u

†3γ

νv4

].

By using the trace cyclicity properties Σuu† = (γσpσ + m) and Σvv† = (γσpσ − m)

pairs can be formed, where p is the momentum of the fermion, m is its mass, and σ is a

generic 4-vector index σ = 0, 1, 2, 3. Since the masses of e−, e+, q, q are smaller than√s,

leptons and quark masses can be neglected in this calculation.

1

4

1

9Σf |M|2 =

1

4

1

93Q2 tr [6p1γ

µ 6p2γν ] tr [6p4γµ 6p3γν ] .

Thanks to the trace properties, the solution of the latter equation is:

|M|2 ∝ 2 (p1 · p3p2 · p4 + p1 · p4p2 · p3) .

Introducing the other Mandelstamm variables t = (p1 − p4)2 = (p2 − p3)2 and u =

(p1 − p3)2 = (p2 − p4)2, one obtains:

|M|2 =1

4

1

3

1

2

1

s2e4[u2 + t2

].

In order to correctly evaluate the cross section predictions of the considered process,

a flux factor 12s

, and a factor, 1(2π)3n−4 , accounting for all the π in the vertex and in the

photon propagator, have to be introduced. More over a phase space factor has to be

added as well.

The total cross section of the process:

σ(e+e− → ss) =4πe4

9s

can be evaluated considering the factor Q2 = 19, as for the annihilation to a dd couple,

while for the cross section of the process e+e− → uu the different charge Qu = 23

has to

be considered.

It has to be stressed how all the calculations reported above have been performed

within a pure QED framework, and no effect related to QCD is involved. This is one

more reason to favour those experimental scenarios involving annihilating positron and

electron beams.


1.3.2 Synchrotron radiation

Since both electrons and positron are accelerated charged particles, they emit photons:

such an emission is called synchrotron radiation. This effect causes an energy loss in the

beam energy: the annihilation has hence a lower center of mass energy with respect to

the nominal one.

The Larmor equation [3] rules the synchrotron radiation emission:

P =2

3

e2

m20c

3

∣∣∣∣d−→pdt∣∣∣∣2 ,

where P is the power emitted by a non relativistic charged particle of charge e and

mass m0. Since both electrons and positron are relativistic, a modified version of the

Larmor formula applies:

P =2

3

e4c2

(m0c2)4E2B2,

where B is the magnetic field, E is the energy of the particle. This formula was derived

by Iwanenko and Pomeranchuk in 1944 [4]. The power emitted (or, in the case of an

accelerator, lost) by the accelerated particle depends on the square of the energy but it

is also inversely proportional to the fourth power of the mass. Figure 1.2 shows a typical

synchrotron radiation spectrum. Such dependence is the reason why this effect is relevant

only when accelerating electrons and positrons and not for protons or antiprotons.

In the case of synchrotron radiation one can define the critical frequency, that is the

maximum emission frequency, as:

ωc =3

2

c

ρ

(E

m0c2

)3

,

where ρ = EβBe

is the bending radius.

1.3.3 Beamstrahlung and Initial State Radiation

Another effect, lowering the center-of-mass energy, is the beamstrahlung. This effect is

described by a parameter Υ, defined as:

Υ =2

3

~ωcE0

,

that is the ratio of the critical frequency to the nominal energy of the beam; its spectrum

can be evaluted by the Sokolov-Ternov equation. This effect is due to the interaction of

an electron with a positron of the bunch going in the opposite way.

Different physics underlies the initial state radiation: this effect is caused by an emis-

sion of a photon before the collision, and it is not due to an acceleration. Beam particles


Figure 1.2: Emission spectrum of synchrotron radiation.

can be represented by f ee (x,Q2), which describes the probability of a particle to collide

with a fraction x of its energy at the scale Q2, and is defined as:

f ee =β

2(1− x)(

β2−1)(

1 +3

8β

)− β

4(1 + x),

where

β =2α

π

(lnQ2

m2− 1

).

The scale Q2 depends on the actual interaction process, and, for central production

processes, it can be defined as Q2 = s = 4E2cm.

1.4 Charmonium

Some sharp resonances were observed in high energy e+e. annihilation processes in

the 70’s. These resonances where interpreted with an approach similar to that adopted

to interprete the positronium, i.e. as heavy hadronic bound states composed of a fermion

and an antifermion.

These bound states were first observed in 1974 at SLAC(Stanford Linear Accelera-

tor Centre), in e+e− collisions at SPEAR [5], and simultaneously at Brookhaven AGS

(Alternate Gradient Synchroton) [6] in proton scattering on a Beryllium target. The

first observed state, the so called J/ψ, was interpreted as a cc bound state, c being the

charm quark, a scheme proposed by Glashow, Iliopoulos and Maiani to explain the flavour

changing neutral currents [2]. The cc bound state are addressed as charmonium.


Figure 1.3: Decay of J/ψ → π+π− can explain the characteristic name ψ [2].

Properties of J/ψ

The first measurement of the J/ψ resonance width was dominated by the experimental

resolution. The true width can be calculated starting from the Breit-Wigner formula: for

a resonance of spin J from two particle of spin s1 and s2, we can write:

σ(E)e+e−→J/ψ→e+e− =4πλ2 (2J + 1) Γ2

e+e−/4

(2s1 + 1) (2s2 + 1)[(E − ER)2 + Γ2/4

] ,where λ is the de Broglie wavelength of the e+ and e− in the center of mass (cms), E

is the energy of cms, ER is the energy of the resonance, Γ is the total width, and Γe+e− is

the partial width of J/ψ → e+e−. Assuming that s1 = s2 = 12

and J = 1, the integrated

cross section is found to be:∫ ∞0

σ(E)dE =3π2

2λ2

(Γe+e−

Γ

)2

Γ.

The parameters necessary to describe the J/ψ resonance are listed in tab 1.3. The

quite small width of the charmonium is related to the large number of channels in which

it can decay. In table 1.4, 1.5 a list of J/ψ decays is given. The decay BR referred to the

exclusive J/ψ → ΛΛ decay, object of the investigation performed in this thesis, is:

BR(J/ψ → ΛΛ) = (1.61± 0.15)× 10−3

[7].

Charmonium energy levels

As it happend for the positronium, the bounds that let a cc couple forming a meson

can be parametrized by potential models.


Name value∫σ(E)dE 800 nb (experimentally)

λ =~cpc

197 MeV fm1500 MeV

Γe+e−/Γ 0.06

Table 1.3: Numerical value of parameters in the width formula [2].

Dacay mode BRhadrons (87.7± 0.5)%e+e− (5.94± 0.06)%µ+µ− (5.93± 0.06)%

Table 1.4: Decay mode of J/ψ and corresponding BR [7].

The positronim is ruled by the Coulomb potential:

VEM = −αr,

where α = 1137

is the EM coupling constant, and r is the distance between e+ and

e−. The J/ψ resonace lineshape cannot be described by a simple Coulomb potential.

Since we are dealing with quarks, at large distances, i.e. at small momentum transfer, the

confinement applies. The form of the potential describing the confinement was deduced

by studying J as function of squared mass for baryons and mesons and it was found to

be linear [2]. So the most probable form is:

VQCD = −4αs3r

+ br,

where αs is the QCD coupling constant, 43

is a color factor, r is the distance between

the cc pair and b is the factor which accounts for the confinement.

The positronium energy levels can be calculated by solving the non-relativistic Schrodinger

equation:

p

mc=

α

2n,

p being the particle momentum of a state characterised by the principal quantum

number n; for a distance equal to the Bohr radius a, pa = n~. Since p << mc, relativistic

effects has to be accounted for only when performing a fine structure analysis. Fig 1.4

shows the charmonium states energy levels presented in spectroscopic description based

on the spatial angular momentum: (S correspond to a null angular momentum, P to L =

1 and so on). The DD threshold corresponds to the minimun energy needed to access an

open charm decay, i.e. a charmonium decay to D mesons.


Hadronic decay mode BRγ∗ (13.5± 0.3)%ggg (64.1± 1.0)%γgg (8.8± 0.5)%

Table 1.5: Hadronic decay mode of J/ψ and corresponding BR [7].

Figure 1.4: Energy level of charmonium states.

The Coulomb-like term dominates the potential at small r; there a non relativistic

approach is effective [2].

1.5 Hyperons and Strangeness

In 1947, Rochester and Butler found a signature of a new neutral particle in their

bubble chambers experiment[8]. Such particle decayed in two forked tracks and they

concluded that this was a new type of elementary particle. During their analysis, they

found out that the behaviuor of this new particle was not an ordinary one.

The fact that these new types of particles were always produced in pairs and had

different behavior for the production and decay processes, led them to introduce a new

quantum number, called strangeness. This new quantum number S is conserved in strong


interactions but can be violated by weak interactions. They also defined hyperon a particle

carrying strangeness.

1.5.1 Strange Quark Physics - The SU(3)F Model

In a quark approach their experiments led to the introduction of a new type of quark,

and static quark model was proposed to describe the properties of hadrons. A symmetry

group SU(3)F under the hypotesis of three quark flavours, was the mathematical ground

on which such a model was introduced.

The wave function of an hyperon can be written as:

Ψ = ψ(space)φ(flavour)χ(spin)ε(color)

and must be antisymmetric, since hyperons are fermions. The colour part can only

be antisymmetric while the space part can be symmetric. The total wave function

φ(flavour) × χ(spin) should be symmetric. The SU(3)F wave functions can be decom-

posed as:

3⊗ 3⊗ 3 = 10S ⊕ 8MS⊕ 8MA

⊕ 1A,

the SU(2) wave functions as:

2⊗ 2⊗ 2 = 4S ⊕ 2MS⊕ 2MA

,

the subscripts meaning:

• S → simmetric wave function with respect to the exchange of two quarks;

• A → antisymmetric wave function with respect to the exchange of two quarks;

• MS(MA) are symmetric (antisymmetric) wave functions with respect to the ex-

change of the first two quarks.

To obtain a globally symmetric wave functions, only the (10,4) and (8,2) combinations

are possible, the numbers being the SU(3)F and SU(2) dimensions.

The introduction of a new quantum number affects also the Gell-Mann-Nishijima

formula [2], that provides the relation between electric charge and quantum numbers. Its

new form becomes:Q

e= I3 +

B + S

2= I3 +

Y

2,

where B represents the baryon number and Y is called hypercharge, and contains the sum

of all additive quantum number of the particle. [9]

Using the hypercharge Y and the third component of the isospin I3 as coordinate axes,

the multiplets can be graphically represented, as shown in fig. 1.5 and in fig. 1.6 for the

baryons with spin S = 32

and S = 12

respectively [1].


Figure 1.5: Baryonic decuplet (10,4).

Figure 1.6: Baryonic octet (8,2).


1.5.2 Λ description

The data analysis in the present thesis aims to investigate the Λ hyperon, the lightest

one. It can be described as formed by three valence quark, and hence is a baryon: it is

composed of u, d, s quarks. Λ production mechanism involves the strong interactions, but

its decay modes are ruled by the weak interaction. The Λ properties are shown in table

1.6, where only the two main decay modes are reported.

Name Valence Quark Mass (GeV/c2) cτ (cm) Decay Branching ratio α

Λ uds 1.11568 7.89pπ−

nπ0

63.935.8

0.6420.65

Λ uds 1.11568 7.89pπ+

nπ0

63.535.8

0.710.65

Table 1.6: Properties of Λ and Λ hyperons.

where α is the weak decay asimmetry parameter, describing the fore-aft asymmetry

of the decay products in the Λ rest frame. The asimmetry parameters of Λ and Λ, exper-

imentally determined, are slightly different: in fact the value of the Λ→ pπ− asimmetry

parameter is α− = (0.645± 0.0013) while the value of the Λ→ pπ+ asimmetry parameter

is α+ = (−0.71± 0.08).

1.6 Hyperon Polarisation

As already explained in sec. 1.5.2, the Λ hyperon can be described as a combination

of three valence quark, u, d and s. The most common description of its behaviour is a

diquark (ud) - quark (s) structure: in such an approach, the ud pair can be considered as

spectators and most of the properties of the hyperon are related to the behaviour of the

s quark. Such an hypothesis is often assumed when performing low energy spin studies.

Λ shows charged and neutral decay modes, as shown in tab 1.6. The charged mode

(Λ → pπ−) is easier to identify because the experimental efficiency in detecting charged

particles is larger if compared with that neutral decay products can be detected with in

an experimental scenarios; this applies in particular when close to threshold. To measure

the angular distribution of the decay products, the proton and the pion, means hence to

directly access the parity violating angular distribution of the self-analysing weak decay:

IΛ(θ∗) =1

4π(1 + α−PΛ cos θ∗)

IΛ(θ∗) =1

4π(1− α+PΛ cos θ∗)

where θ∗ is the emission angle of the proton in the Λ’s rest frame and α is the asimmetry


parameter. The hyperon polarization can be measured by determining the asimmetry of

the decay angular distributions, since the decay proton is emitted preferentially along the

Λ spin direction in the hyperon rest frame. When considering unpolarised lepton beams,

only the transverse polarisation can be non zero; the transverse polarisation is defined

with respect to a quantisation axis normal to the production plane.

To investigate the dependence of the Λ polarisation on the transverse momentum (pt)

means to investigate the hyperon polarisation dependence on the Λ emission angle. The

pt dependence is relevant bacause it usually allow to select between different reaction

mechanisms.

Hyperons polarisation has been recently investigated at COSY in Julich and at SA-

TURNE II in Saclay, respectively by the COSY-11 [10] and by the DISTO [11] collabo-

rations, making use of the scattering of polarised proton beams on hydrogen target.

Chapter 2

BESIII Spectrometer

In this chapter the BEPCII collider and to the BESIII spectrometer will be discussed.

More emphasis will be given to those detector parts involved in the performed analysis.

2.1 Introduction

The BESIII Collaboration is an international collaboration, which involves 31 Univer-

sities from China, 13 from Europe, 5 from USA and 4 more from other Asian countries.

The spectrometer is hosted at the BEPCII collider, placed at the IHEP, Beijing, People’s

Republic of China. The detector depicted in Fig. 2.1 and described in 2.2 is characterised

by a cylindrical symmetry and it is designed to cover almost all the 4π solid angle; the

bending power is provided by a 1 T solenoidal magnet.

Figure 2.1: Picture of BESIII Spectrometer [12].

21

CHAPTER 2. BESIII SPECTROMETER 22

Figure 2.2: Scheme of the BESIII detector [12].

Tracking and momentum reconstruct are provided by a multilayer drift chamber, the

particles are identified by means of a Time-of-Flight system and the dE/dx (energy loss

per units of length) evaluation performed in the drift chamber. The calorimeter is used to

collect the energy deposited by both charged and neutral particles when passing through

the CsI(Tl) crystal. Muon stations, composed of resistive plate chambers, are placed in

the segmeted iron yoke of the magnet.

The physics program which can be accomplished by the BESIII experiment includes:

• test of electroweak interaction with very high precision in both quark and lepton

sectors;

• high statistic studies on spectroscopy and decay properties of light hadrons;

• studies on J/ψ, ψ(2S) and ψ(3770) states production and decay properties with

large data sample, search for glueballs, quark-hybrids, multi-quark states, and other

exotic states via charmonium hadronic and radiative decays;

• studies on τ−physics;

• studies on charm physics, including the decay properties of D and Ds and of charmed

baryons;

• precision measurements of QCD and CKM parameters;


Figure 2.3: Sketch of the collider, with a zoom over the interaction point of the e− (blue)and e+ (red) beams.

• search for new physics via rare and forbidden decays, oscillations and CP violations

in charmed hadrons and τ -leptons.

2.1.1 BEPCII

The Beijing Electron-Positron Collider (BEPCII), shown in Fig. 2.3, is a double ring

multi-bunch collider, with a designed istant luminosity of 1033 cm−2s−1, optimized at a

center of mass energy of 3.78GeV . In addition to τ -charm studies, that was the main

goal of its predecessor BEPC, this new collider can be used as a synchrotron light source.

Tab. 2.1 reports the main BEPCII features.

Due to an expected average multiplicity on the order of four charged particles and

photons in the final states, the most probable momentum of each charged track is ap-

proximately 0.3 GeV/c and most of the particle do not show a momentum larger than 1

GeV/c. Assuming conservatively one half of the design luminosity and a total running

time of 107 sec/year, Tab. 2.2 reports the expected data collection per year.

2.2 BESIII Spectrometer

The BEijing Spectrometer III (BESIII) detector is designed to take advantage of the

high luminosity provided by BEPCII, and the Collaboration is planning to collect large

data samples to accomplish the presented physics program.

The spectrometer is mainly hosted inside the 1 T superconducting solenoid. The coil

is situated outside the electromagnetic calorimeter region, with a mean radius of 1.482 m.


Parameters BEPCIICenter of mass energy (GeV) 2 - 4.6

Circumference (m) 237.5Number of rings 2

RF frequency (MHz) 499.8Peak Luminosity (cm−2s−1) ∼ 1033

Number of bunches 2× 93Beam current (A) 2× 0.91

Bunch spacing (m - ns) 2.4 - 8Bunch length (σz cm) 1.5Bunch width (σx µm) ∼ 380Bunch height (σy µm) ∼ 5.7Relative energy spread 5× 10−4

Crossing angle (mrad) ±22

Table 2.1: Table of parameters of BEPCII [12].

States Energy (GeV) Peak Luminosity (1033cm−2s−1) Physics cross-section (nb) Events/year

J/ψ 3.097 0.6 3400 1× 1010

ψ(2S) 3.686 1.0 640 3× 109

τ+τ− 3.670 1.0 2.4 1.2× 107

D0D0 3.770 1.0 3.6 1.8× 106

D+D− 3.770 1.0 2.8 1.4× 106

DsDs 4.030 0.6 0.32 1× 106

DsDs 4.170 0.6 1.0 2× 106

Table 2.2: Expected data collection per year [12].

The polar angle coverage of the spectrometer is 21 < θ < 159, leading to the geometrical

acceptance ∆Ω/4π = 0.93.

In the next sections, the main characteristics of each detector system will be briefly

described, moving from the interaction point to the most peripheral areas.

2.2.1 Multilayer Drift Chamber

The multilayer drift chamber (MDC) is optimized for tracking the produced particles

with an excellent momentum resolution and good dE/dx measurement capabilities. The

inner and outer radii are 59 mm and 810 mm, respectively: the MDC cell are filled with

a helium based gas mixture He/C3H8 (60:40), to reduce multiple scattering effects [12].

The single cell position resolution is expected to be 130 µm in the r − φ plane and ∼2 mm along the z direction. The transverse momentum resolution is expected to be 0.5%

at 1 GeV in 1 T magnetic field. The polar angle coverage is | cos θ| < 0.93 [12].

In Fig. 2.4 a scheme of the BESIII MDC is presented.


Figure 2.4: Scheme of the BESIII MDC [12].

Performance

Momentum resolution In a multilayer tracking chamber, like the BESIII one, a simple

model can be used to estimate the transverse momentum resolution σpt , which can be

expressed as:

σptpt

=

√(σwirept

pt

)2

+

(σmsptpt

)2

,

where σwirept is the momentum resolution provided by each individual wire spatial

resolution (Fig. 2.5 shows the dependence of the spatial resolution with respect to the

distance from the sense wire), and σmspt is the momentum resolution due to multiple

scattering.

The total momentum resolution of the MDC is expected to be better than 0.5% at pt

= 1 GeV/c [12].

dE/dx performance The factors which contribute to the dE/dx resolution are the

fluctuation of the number of primary ionizations along the track, the recombination loss

of electron-ion pairs at the corners where the electric field of the chamber is lower, and the

fluctations in the avalanche process. The density of the gas is relatively low. Monte Carlo

simulations show that MDC dE/dx resolution is about 6% allowing 3σ π/K separation

up to momenta of ∼ 770 MeV/c.


Figure 2.5: Spatial resolution wrt the distance from the sense wire [12].

2.2.2 Time of Flight System

The Time Of Flight (TOF) system, which consists of a barrel and two end caps, is

composed of plastic scintillator bars read out by fine mesh photomultiplier tubes attached

at the two end faces of the bar. The expected time resolution (∼ 100 ps) allows for a 3σ

π/K separation.

The position of the TOF layers is constrained by the compact design of BESIII: in the

barrel region, the inner radius of the first layer is 810 mm and the second one is 860 mm,

while one layer is placed in the end caps region. The relatively short particle flight path

makes the design of the TOF system challenging.

A cross section view of the TOF system inside the calorimeter is shown in fig. 2.2.

Performance

Time resolution The overall time resolution σ of the spectrometer can be expressed

as

σ =√σ2i + σ2

b + σ2l + σ2

z + σ2e + σ2

t + σ2w

.

The value of each term is reported in Tab. 2.3. The σz depends on the time needed

to collect the signal and is estimated to be around 30 ps and 50 ps for the barrel and end

caps region, respectively.

Excluding σi and σw, the total contribution from those terms not directly related to

the counters (the other five) to the uncertainty of the TOF system is about 66 ps for

the barrel and 87 ps for the end caps region. Using two layer in the barrel improves the

resolution of the intrinsic factor of the TOF system, i.e. σi and σw, by a factor of√

2.


σ Barrel (ps) EndCap (ps)σi: counter intrinsic time resolution 80 ∼ 90 80

σl: uncertainty from 15 mm bunch length 35 35σb: uncertainty from clock system ∼ 20 ∼ 20σθ : uncertainty from θ-angle 25 50σe: uncertainty from electronics 25 25

σt: uncertainty in expected flight time 30 30σw: uncertainty from time walk 10 10

σ1: total time resolution, one layer 100 - 110 110combined time resolution, two layes 80 - 90 -

Table 2.3: TOF time resolution performance for 1 GeV/c muons [12].

Figure 2.6: Kaon identification (up K → K ) and misidentification (down K → πefficiency. [12])

Particle ID Figure 2.6 shows the simulated separation capability of the BESIII barrel

TOF system.

A K/π separation efficiency of 95% and a contamination level of about 5% can be

achieved up to a momentum of 0.9 GeV/c [12].

2.2.3 Electromagnetic Calorimeter

The electromagnetic calorimeter (EMC), composed of CsI(Tl) crystals, is designed to

precisely measure the energies of photons above 20 MeV, and to provide trigger signals.

It has good e/π discrimination capabilities for momenta above 200 MeV.

It is composed of 6240 CsI(Tl) crystals placed outside the TOF counters. The inner


radius of the BESIII EMC is 940 mm. The length of the crystals, 28 cm, corresponds to

15 radiation lengths (X0) and their section varies from the front face (5.2 cm × 5.2 cm)

to the rear face (6.4 cm × 6.4 cm). The design energy resolution of the EM showers is

σE/E = 2.5%√E and the design position resolution is σ = 0.6cm/

√E at an energy of 1

GeV.

The properties of CsI(Tl) scintillating crystals are listed in Tab. 2.4.

Parameter ValuesRadiation length X0 1.85 cm

Moliere radius 3.8 cmDensity 4.53 g/cm3

Light yield (photodiode) 56000 γ’s/MeVPeak emission wavelength 560 nm

Signal decay time 680 ns (64%)3.34 ms (36%)

Light yield temp coefficient 0.3 %/CdE/dx (per mip) 5.6 MeV/cm

Hygroscopic sensivity slight

Table 2.4: Properties of thallium doped CsI(Tl) crystal [12].

Performance

Position and Energy Resolution The energy resolution is affected by many factors

(dead materials, crystal quality, etc.). The photon position resolution is mainly deter-

mined by the cristal segmentation [12]. The EMC composed of 28 cm long CsI crystals

can reach the desired energy resolution of ≤ 2.5% at 1 GeV photon energy.

2.2.4 Muon Counter

The muon detector consists of resistive plate chambers (RPC) hosted in the steel plates

of the magnetic flux return yoke of the solenoidal magnet. Its main functions is to detect

and separate muons from charged pions, expecially at lower momenta. There are nine

layers of RPC in the barrel and eight in the end caps.

By associating hits in muon counters with tracks reconstructed in the MDC and energy

measured in the EMC, the muons can be identified with a low cut-off momentum. The

requirements for the position resolution of the RPC are modest due to multiple scattering

which can occur in the EMC, in the magnet coil, and in the steel layers. The typical

width of the readout strips in the RPC is about 4 cm.

The active part of the muon detectors must be highly reliable and relatively cheap,

since the area to be covered is quite large and almost inaccessible once the detectors are

installed. Muon detectors are fluxed with an Ar/C2F4H2/C4H10 (50:42:8) gas mixture.


Figure 2.7: 3D model of the external muon system [12].

Fig. 2.7 shows a 3D model of BESIII muon system, while Tab. 2.5 reports the muon

detector mechanical parameters. Fig. 2.8 shows the scheme of the positioning of the

barrel and endcap RPC’s.


Figure 2.8: Scheme of the positioning of the barrel and endcap RPC’s [12].

Barrel ParametersInner radius (m) 1.700Outer radius (m) 2.620

Length (m) 3.94Weight (tons) 399

Steel plate thicknesses (cm) 3÷ 15Gap betwnn plates (cm) 4

No. of RPC layers 9Polar angle covarage cos θ ≤ 0.75

End cap ParametersInner radius (m) 2.050Outer radius (m) 2.800

Weight (tons) 4× 52Steel plate thicknesses (cm) 3÷ 8

Gap betwnn plates (cm) 4No. of RPC layers 8

Polar angle covarage 0.75 ≤ cos θ ≤ 0.89

Table 2.5: Mechanical parameters of the muon identifier [12].

Part II

Data Analysis

31

Chapter 3

Analysis e+e−→ ΛΛ

The inclusive process e+e− → ΛΛ is first investigated process. Only their charged

decay channels Λ→ pπ− (Λ→ pπ+) are used to recontruct hyperons, since characterised

by an higher branching ratio and since the experimental efficiency in detecting charged

particles is expected to be larger if compared to that of neutral particles.

For this process, two track candidates selection method were implemented: the clas-

sical particle identification and the kinematic fit, a quite commonly used technique. The

phsyical observables of the ΛΛ process are hence investigated once the events selection

has been performed.

For this analysis, two data samples were used: a first one collected during the 2009

data taking run and a second one collected during the 2012 run. First I have analysed,

using BOSS version 6.6.2, the data collected in 2012: these data were collected to perform

a J/ψ lineshape scan and will also be used to evaluate the relative phase between strong

and electromagnetic J/ψ decay amplitudes. The nominal energies and the integrated

luminosities of each collected center of mass energy are shown in Tab. 3.1. Afterwards, I

have analysed the 79pb−1 J/ψ peak data collected at the J/ψ peak in 2009 using BOSS

version 6.5.5.

To perform efficiency corrections, I have also used the 225M Monte-Carlo J/ψ inclusive

sample, provided by the Collaboration and analysed with the BOSS version 6.5.5. In this

inclusive sample, all the J/ψ decays are simulated with their respective branching ratios

(BR). ROOT [13] version 5.24 has been used for all the analyses.

3.1 Event Simulation

In order to understand the real data scenario, it is necessary to evaluate the behaviour

of Monte Carlo signals produced with the generator BesEvtGen [14] implemented in

BOSS version 6.6.2, the official collaboration software framework. This software allows to

generate events for the final states under investigation, which are then propagated inside

the detector by means of GEANT4.

32

CHAPTER 3. ANALYSIS E+E− → ΛΛ 33

Ecm (GeV) L(pb−1)3.05 14.895± 0.0293.06 15.056± 0.033.083 4.759± 0.0173.0856 17.507± 0.0323.09 15.552± 0.033.093 15.249± 0.033.0943 2.145± 0.0113.0952 1.819± 0.013.0958 2.161± 0.0113.0969 2.097± 0.0113.0982 2.210± 0.0113.099 0.759± 0.0073.1015 1.164± 0.0103.1055 2.106± 0.0113.112 1.719± 0.013.12 1.261± 0.009

Table 3.1: Center of mass energies and luminosity measurements [15].

A typical BesEvtGen simulation card looks like:

Decay J/psi ← set the mother particle (its properties are taken from [7])

1.0000 Lambda0 Anti-Lambda0 PHSP ← PHSP (stays for PHase SPace), indicates the

probability of a certain decay mode and its angular distribution

Enddecay

Decay Lambda0

1.0000 p+ pi- PHSP

Enddecay

Decay Anti-Lambda0

1.0000 anti-p- pi+ PHSP

Enddecay

This generator card was used to produce 104 ΛΛ events and the subsequent decays

into their charged decay channels with a PHSP angular distribution for the 16 center of

mass energies collected, enlisted in Tab. 3.1.

To be sure that we are dealing with a reliable Monte Carlo simulation, the agree-

ment between real data and Monte Carlo simulation has to be probed. Fig 3.1 (Fig 3.2)

compares the distribution cos θΛ(Λ) for events from the data (red points) and from he

Monte Carlo (blue line) simulations. The agreement between data and Monte Carlo is

qualitatively good, in both cases.


Λθcos-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

cou

nt

100

200

300

400

500

600

700

Figure 3.1: Λ polar angle cos θ distributions evaluated for events from the experimentaldata (red) and from the inclusive MC (blue).

Λθcos

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

cou

nt

100

200

300

400

500

600

700

Figure 3.2: Λ polar angle cos θ distributions evaluated for events from the experimentaldata (red) and from the inclusive MC (blue).


3.2 Event Selection

The choice of reconstructing hyperons through their charged decays only implies that

I need to perform the event selection asking for four reconstructed charged tracks and

zero net charge. Moreover I impose additional kinematic cuts: the selected events are

only those ones for which the vertex of all four charged tracks is inside a cylinder with

a radius of 10 cm and a lenght along the z direction of 20 cm; charged tracks must have

a | cos θ| < 0.92 in the LAB frame, i.e. 21 < θ < 153; finally each charged track’s

momentum should be < 2.GeV, since in a four particle decay no candidate can bring

more than half of the total energy of the event.

PID

I use the PID system information (dE/dx and TOF of the particle) in order to identify

the tracks with the probability density function method. For example, to be identified

as proton, a track candidate must have a probability > 0.001 to be a proton, and this

probability has to be higher than the one to be a kaon or a pion. Once obtained this

information, I select those events in which two tracks are identified as proton (p and p)

and two tracks as pion (π+ and π−).

Afterwards, I require that the constructed pπ− and pπ+ pairs survive a vertex fit

algorithm: this selection is operated in order to verify that p(p) and π−(+) come from

a common vertex, that is then tagged as the Λ(Λ) decay vertex. The same algorithm

perform a fit on the parameters of the tracks, tuning the 4-momenta of protons and

pions. To evalutate thr Λ(Λ)’s 4-momentum, I sum over the 4-momenta of the decay

particles.

In order to reduce the possible background, expecially in the energy region under the

J/ψ resonance, I considered the fact that this process can be described as a two-body

decay: as it is known, in a two-body decay daughter particles go back-to-back in the

parent particle’s rest frame. Although the boost of the event center of mass (CM) in the

Laboratory frame (LAB) slightly differs from zero, one can consider the two reference

frames to be almost coincident, so the angle between the reconstructed Λ and Λ should

be 180M; due to the detector finite resolution, a cut on ΛΛ > 178 was imposed (Fig.

3.3 shows the distribution of the angle between the tracks).

The invariant mass distributions of the reconstructed Λ, Λ, fitted with a Breit-Wigner

function plus a flat background, are presented in Fig. 3.4 and 3.5, respectively.

Kinematic Refitting

Once I have verified that a classical PID approach is possible, I want to explore another

well-known procedure that should have, in principle, a better event rejection factor: the


θ0 20 40 60 80 100 120 140 160 180

cou

nts

0

200

400

600

800

1000

1200

1400

1600

1800

Figure 3.3: Angle between Λ and Λ recontructed momenta at the energy of 3.0969 GeV.

inv mass [Gev/c^2]1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nt

0

20

40

60

80

100

120

140 fitsignalbkgn

Figure 3.4: Fit with a Breit-Wigner plus a constant background of invariant mass of theΛ selected using the pid method.

kinematic refit.

In this procedure, a fit is performed again on the tracks’ parameters with one or more

kinematic constraints in order to improve the resolution. This procedure is included in

the BOSS class KalmanKinematicFit, that initialize the Kalman algorithm to perform

the fit. A detailed description of the Kalman algorithm procedure is presented in [16].

I used again the selections on the track’s geometry and kinematics already presented


inv mass [Gev/c^2]1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nt

0

20

40

60

80

100

120fitsignalbkgn

Figure 3.5: Fit with a Breit-Wigner plus a constant background of invariant mass of theΛ selected using the pid method.

in sec. 3.2. Instead of using the PID information, I identified the tracks making use of

their 3-momenta. The mass difference between protons and pions (mp = 938.27 MeV,

and mπ = 139.57 MeV) causes a different energy distribution in the decay.

In Fig. 3.6 and 3.7 the MC and real data 3-momenta distributions of the tracks,

respectively, are plotted for the 16 center of mass energies. It is clear that also at lower

energies, a good separation is present among the different track candidate populations.

I have tagged as pion all the tracks with 3-momenta < 0.5 GeV/c and as proton all the

tracks with higher 3-momentum. In such a way I have identified the tracks without

making use of any PID information. It has to be stressed that such an a procedure is not

expected to reduce the combinatorial background.

As already performed in the PID selection case, I choose those events with pπ− and

pπ+ pairs surviving a vertex fit algorithm. During the vertex fitting procedure, a first

tuning of the tracks parameters is performed: this is why the kinematic fit procedure is

called ”refit”.

In the refit procedure, it is necessary to set the correct kinematic constraints. In the

present analysis, the total four momentum of the event is fixed to (0.011√s, 0., 0.,

√s),

which is equivalent to ask for a total missing mass compatible with zero. The 0.011 factor

is a correction factor in the total 4-momentum, that makes the x component different from

0: this correction has to be applied in order to take into account the angle between the

beams (22 mrad), that cause a boost of the event center of mass in the LAB frame. The


p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

cou

nts

020

40

60

80

100

120

140

160

180

200

p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

cou

nts

0

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p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

cou

nts

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p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

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p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

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p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

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nts

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p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

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nts

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p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

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nts

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250

300

p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

cou

nts

0

50

100

150

200

250

300

Figure 3.6: Distribution of p (red) and π (blue) tracks’ 3-momentum for each center ofmass energy (MC).

p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

cou

nts

0

0.5

1

1.5

2

2.5

3

3.5

4

p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

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p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

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nts

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1.2

1.4

1.61.8

2

p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

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nts

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81012

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p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

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p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2

cou

nts

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0.5

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1.5

2

2.5

3

Figure 3.7: Tracks 3-momenta distributions for pions (blue) and protons (red) for eachcenter of mass energy (real data).


χ2 distribution, shown in Fig. 3.8, allows to perform a selection on the track candidates.

Figure 3.9 shows the χ2 distribution with respect to the invariant mass of Λ (in the plot

on the left) and Λ (on the right).

2χ0 20 40 60 80 100 120 140 160 180 200

entr

ies

0

500

1000

1500

2000

2500

3000

3500

Figure 3.8: χ2 distribution of the refit procedure.

inv mass [GeV/c^2]Λ1.1 1.105 1.11 1.115 1.12 1.125 1.13

2 χ

0

5

10

15

20

25

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0

2

4

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16

inv mass [GeV/c^2]Λ

1.1 1.105 1.11 1.115 1.12 1.125 1.13

2 χ

0

5

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15

20

25

30

35

40

45

50

0

2

4

6

8

10

12

14

16

Figure 3.9: χ2 distribution as a function of the invariant mass for real data at 3.0969GeV/c2.

Once that the fit is performed, I sum the tracks 4-momenta to get the reconstructed

4-momentum of the event. Using the information of the correlation between Λ and Λ 3-

momenta, I insert a new cut which selects a squared region around the event momentum

peak, clearly visible at each center of mass energy. In Fig. 3.10 and 3.11 the correlation

between the hyperons momenta is shown for the MC and the real data, respectively.

In Fig. 3.12 and 3.13 the obtained Λ and Λ invariant masses, fitted with a Breit-Wigner

plus a flat background, are presented.


(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

20

40

60

80

100

120

140

160

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

20

40

60

80

100

120

140

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

300

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

020406080100120140160180200220240

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

50

100

150

200

250

Figure 3.10: Correlation between 3-momenta of Λ and Λ at MC level.

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.82

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.82

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

0.5

1

1.5

2

2.5

3

3.5

4

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

2

4

6

8

10

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

5

10

15

20

25

30

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

10

20

30

40

50

60

70

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

20

40

60

80

100

120

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

10

20

30

40

50

60

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

01

2

34

5

67

8

9

10

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

1

2

3

4

5

6

7

8

9

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

1

2

3

4

5

6

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.82

(GeV/c)Λ

p0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

(G

eV/c

)Λ

p

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

0

0.5

1

1.5

2

2.5

3

3.5

4

Figure 3.11: Correlation between 3-momenta of Λ and Λ for each center of mass energy(real data).

Summary

I have implemented two different methods to perform an effective event selection, PID

and Kinematic Fitting. I need to fit the data with both methods to understand the better


selection criteria: the aim is to achieve the best signal over background ratio and the

largest statistics.

inv mass [Gev/c^2]1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nt

0

50

100

150

200

250

300

350 fitsignalbkgn

Figure 3.12: Fit with a Breit-Wigner plus a constant background of invariant mass of Λselected using the kinematic refit method.

Both methods lead to a good signal over background ratio, but the statistics surviving

the selection procedure are different. So for each center of mass energy, I select the

procedure leading to the largest surviving statistics. Fig. 3.14 and 3.15 show the final Λ

and Λ mass distributions.


inv mass [Gev/c^2]1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nt

0

50

100

150

200

250

300

350fitsignalbkgn

Figure 3.13: Fit with a Breit-Wigner plus a constant background of invariant mass of Λselected using the kinematic refit method.

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

0.5

1

1.5

2

2.5

3

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

0.5

1

1.5

2

2.5

3

3.5

4

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

0.5

1

1.5

2

2.5

3

3.5

4

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

00.2

0.4

0.6

0.81

1.2

1.4

1.61.8

2

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

0.5

1

1.5

2

2.5

3

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

1

2

3

4

5

6

7

8

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

024

68

1012141618202224

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

10

20

30

40

50

60

70

80

90

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

020406080

100120140160180200220

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

50

100

150

200

250

300

350

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

20

40

60

80

100

120

140

160

180

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

5

10

15

20

25

30

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

2

4

6

8

10

12

14

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

2

4

6

8

10

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

1

2

3

4

5

6

7

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

0.5

1

1.5

2

2.5

3

3.5

4

Figure 3.14: Λ invariant mass for each center of mass energy (real data).

3.3 Armenteros-Podalansky Plot

To obtain an unique proof that the signals that I reconstructed are Λ (Λ) and not

some artifacts, I considered the Armenteros-Podalansky plot [17] Such a test probes the


)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

0.2

0.4

0.6

0.8

1

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

0.2

0.4

0.6

0.8

1

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

0.2

0.4

0.6

0.8

1

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

00.2

0.4

0.6

0.81

1.2

1.4

1.61.8

2

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

0.5

1

1.5

2

2.5

3

3.5

4

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

1

2

3

4

5

6

7

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

5

10

15

20

25

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

10

20

30

40

50

60

70

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

20

40

60

80

100

120

140

160

180

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

50

100

150

200

250

300

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

20

40

60

80

100

120

140

160

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

5

10

15

20

25

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

02

4

6

8

1012

14

16

18

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

2

4

6

8

10

12

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

1

2

3

4

5

6

7

)2 (GeV/cΛinv mass

1.1 1.105 1.11 1.115 1.12 1.125 1.13

cou

nts

0

1

2

3

4

5

6

7

Figure 3.15: Λ invariant mass for each center of mass energy (real data).

correlation of the transverse momentum (pt) of one of the daughter particles and the

asimmetry defined as

asimmetry =pl(+)− pl(−)

pl(+) + pl(−)

where pl is the longitudinal momentum of the positive (+) or negative (-) particle with

respect to the hyperon direction.

Fig. 3.16 show the Armenteros plot evaluated for the MC sample at each considered

center of mass energy. The left parabola indicates the correlation for a Λ, the right one

the correlation for a Λ. Fig. 3.17 shows the Armenteros plot obatined for the real data

sample. When the number of the survived events is larger, the signature becomes more

clear. These plots validate the signal reconstruction.


asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Figure 3.16: Armenteros-Podalansky plot for each center of mass energy (MC).

3.4 Efficiency and acceptance

The agreement between the real data and the performed Monte Carlo simulations has

to be carefully verified, in order to have full control of the acceptance corrections, which

have to be applied and are crucial to investigate the angular distributions.

The polarisation studies will be performed only for those kinematic ranges in which

a qualitative agreement has been proved; all the other kinematic ranges will be excluded

from the procedure evaluating the polarisation. In order to obtain the proper proton

angular distribution information, the corresponding distributions have to be divided by

the efficiency, to account for the limited detector efficiency and acceptance.

Tab. 3.2 reports the value of the reconstruction efficiency, its error and if the qualita-

tive agreement has been achieved or not, for each collected center of mass energy.

Fig 3.18 and Fig 3.19 show the reconstruction efficiencies as functions of the p(p)

emission angle in Λ(Λ) rest frame at 3.0969 GeV.


asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

asimmetry-1 -0.5 0 0.5 1

pt

(GeV

/c)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Figure 3.17: Armenteros-Podalansky plot for each center of mass energy (real data).


Once I have selected the good event candidates for each collected center of mass

energy, the polarisation can be evaluated. As already explained in sec 1.5 , the self-

analysing properties of the Λ decay is the key to access the Λ polarisation. We know in

fact that∂N

∂Ω= N0(1 + α−PΛ cos θΛ),

and

∂N

∂Ω= N0(1− α+PΛ cos θΛ),

where α+,− is the asimmetry coefficient, θΛ,Λ is the proton(p) angle in the Λ(Λ) rest

frame, N0 is a normalization factor and PΛ,Λ is the polarisation of the Λ, Λ. To extract

the hyperon polarisation value, I consider in the Λ(Λ) rest frame the distribution of the

polar angle between the proton(p) and Λ(Λ) directions and I perform a linear fit. The

slope corresponds to the product αPΛ. Since BEPCII is a collider with unpolarized beams,

only transverse polarization can be investigated.

I consider different binning for each collected center of mass energy, in order to obtain

a reasonable statistical significance for each single bin, so that the detector acceptance


Energy (GeV) Efficiency σefficiency agreement3.050 0.21 0.004 no3.060 0.2 0.004 no3.083 0.44 0.005 ok3.0856 0.45 0.005 ok3.090 0.45 0.005 ok3.093 0.45 0.005 ok3.0943 0.45 0.005 ok3.0952 0.45 0.005 ok3.0958 0.44 0.005 ok3.0969 0.45 0.005 ok3.0982 0.45 0.005 ok3.0982 0.45 0.005 ok3.1015 0.45 0.005 ok3.1055 0.45 0.005 ok3.112 0.46 0.005 ok3.120 0.45 0.005 ok

Table 3.2: Reconstruction efficiency at each collected center of mass energy.

Λθcos-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

effi

cien

cy

0.01

0.015

0.02

0.025

0.03

Figure 3.18: Efficiency dependence on the polar emission angle of the decay proton in theΛ rest frame.

can be accounted for and the considered angular distributions can be corrected for the

reconstruction efficiency.

In the continuum region, characterized by a low statistics, no significative results can


Λθcos

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

effi

cien

cy

0.01

0.015

0.02

0.025

0.03

Figure 3.19: Efficiency dependence on the polar emission angle of the decay p in the Λrest

be obtained. On the contrary, due to the large surviving statistics, significant results can

be extracted in the J/ψ peak range. Tab. 3.3 shows results obtained for the hyperon

polarisation. The binning depends on how many events survived the applied cuts applied.

The first three center of mass energies are not listed in table due to the unsatisfactory

agreement between data and MC at 3.05 GeV and 3.06 GeV, and due to the low statistics

collected at 3.083 GeV. Fig 3.20 and Fig 3.21 show the Λ and Λ polarisations dependence

on the center of mass energy; the energies 3.0856 and 3.090 are omitted due to the too

large error bars obtained.

Due to the very limited statistics of the data collected in the continuum region, the

error bars are too large to draw any staistically significant indication on the hyperon

polarisation. Only by studying the 79 pb−1 data sample collected at the J/ψ peak a more

accurate evaluation of the hyperon polarisation will become possible.

J/ψ Resonance Peak Data

The same selection criteria described above have been applied to perform the analysis

of the 79pb−1 collected under the J/ψ resonance peak. The data have been analysed with

BOSS version 6.5.5.


Energy (GeV)

3.092 3.094 3.096 3.098 3.1 3.102 3.104 3.106 3.108 3.11 3.112

po

lari

sati

on

Λ

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Figure 3.20: Λ polarisation dependence on the center of mass energy.

Energy (GeV)

3.092 3.094 3.096 3.098 3.1 3.102 3.104 3.106 3.108 3.11 3.112

po

lari

sati

on

Λ

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Figure 3.21: Λ polarisation dependence on the center of mass energy.

Fig. 3.22 and 3.23 respectively show the Λ and Λ invariant masses. The green lines

represent the fitting functions leading to mΛ = (1.1159±0.0007)GeV and mΛ = (1.1159±0.0007)GeV .


Energy (GeV) number of bins Λ polarisation error Λ polarisation error3.0856 6 -0.26 > 1 0.21 > 13.090 6 -0.86 > 1 0.81 > 13.093 6 -0.03 0.71 0.06 0.633.0943 15 0.18 0.31 -0.18 0.273.0952 15 -0.13 0.16 0.12 0.143.0958 60 0.17 0.11 -0.11 0.13.0969 60 -0.21 0.09 0.17 0.083.0982 60 -0.17 0.1 0.01 0.13.099 15 -0.1 0.35 0.25 0.293.1015 15 0.39 0.5 0.5 0.333.1055 6 -0.62 0.36 -0.2 0.563.112 6 -0.63 0.56 0.56 0.523.120 6 0.81 0.91 -0.63 0.82

Table 3.3: Λ and Λ polarisations for different center of mass energies.

(GeV/c^2)Λinvariant mass 1.11 1.111 1.112 1.113 1.114 1.115 1.116 1.117 1.118 1.119 1.12

cou

nts

0

200

400

600

800

1000

1200

1400

1600

Figure 3.22: Λ invariant mass distribution from the 79 pb−1 data sample.

Fig. 3.24 (Fig 3.25) shows the angular distribution of the proton (p) in thr Λ(Λ) rest

frame: the green line is the linear fit. The polarisation is found to be PΛ = (0.16± 0.03)

and PΛ = (−0.11± 0.02) for Λ and Λ respectively.



cou

nts

0

200

400

600

800

1000

1200

1400

1600

Figure 3.23: Λ invariant mass distribution from the 79 pb−1 data sample.

Λθcos-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

cou

nt

22000

24000

26000

28000

30000

32000

34000

36000

Figure 3.24: Λ polarisation from the 79 pb−1 data sample.

pt dependence analysis

Thanks to the high statistics the dependence of the polarisation on the hyperons

transverse momentum can be investigated as well. Fig 3.26 and Fig 3.27 show the pt


Λθcos

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

cou

nt

24000

26000

28000

30000

32000

34000

36000

Figure 3.25: Λ polarisation from the 79 pb−1 data sample.

distributions for Λ’s and Λ’s .

Fig. 3.28 and 3.29 show the polarisation dependence on the Λ and Λ hyperons pt.

respectively. Once considering the large sample collected under the J/ψ resonance peak,

the hyperon polarisation depart from zero at larger transverse momenta (pt).


(GeV/c)Λtransverse momentum 0.2 0.4 0.6 0.8 1 1.2

cou

nts

0

500

1000

1500

2000

2500

3000

3500

Figure 3.26: Λ pt distribution.


cou

nts

0

500

1000

1500

2000

2500

3000

3500

Figure 3.27: Λ pt distribution.


(GeV/c)t

pΛ0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

po

lari

sati

on

Λ

-0.1

-0.05

0

0.05

0.1

0.15

Figure 3.28: Λ polarisation dependence on pt.

(GeV/c)t

pΛ0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

po

lari

sati

on

Λ

-0.1

-0.05

0

0.05

0.1

0.15

Figure 3.29: Λ polarisation dependence on pt.

Chapter 4

Analysis e+e−→ J/ψ → ΛX

The inclusive process is investigated analysing the 2pb−1 collected at the center of

mass energy of 3.0969 GeV during the J/ψ scan data, with BOSS version 6.6.2, and the

79pb−1 collected under the J/ψ resonance peak, with BOSS version 6.5.5. I used CERN

ROOT version 5.24 for the analysis.

4.1 Event Simulation

To understand the behaviour of the real data, one has to understand which processes

can contribute to the Λ production. In Tab 4.1 the considered processes are summarized,

where both the total BR and the BR normalized to the total Λ inclusive production are

listed.

Decay BR BRnorm

ΛΣ(1385)0 2 10−4 0.072ΛΣ0 9 10−5 0.032pK−Λ 8.9 10−4 0.319ΛΛη 2.6 10−4 0.093ΛΛπ0 2.6 10−4 0.023

ΛnK0s + c.c. 6.5 10−5 0.117

ΛΣ−π+ (or c.c.) 1.5 10−4 0.298γΛΛ 1.3 10−4 0.047

Table 4.1: List and BR of the processes included in the inclusive process simulation.

I have excluded from this list the ΛΛ process, that I have already analysed.

Fig. 4.1 compares the polar angular distributions of the hyperon decay products in

the hyperon’s rest frame for the data (red dots) and the inclusive Monte Carlo (blue line).

54

CHAPTER 4. ANALYSIS E+E− → J/ψ → ΛX 55

Λθcos

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

cou

nt

100

200

300

400

500

600

700

800

Figure 4.1: Polar angular distributions of the hyperon decay products in the hyperon’srest frame for the data and the inclusive Monte Carlo.

4.2 Event Selection

In the analysys of the inclusive process, only the Λ has to be reconstructed, by selecting

as in the case of the exclusive channel only the Λ charged decay channel (Λ → pπ+). I

select those events with at least two charged tracks and zero net charge. Moreover, the

track’s origin should be in a cylinder with a radius of 10 cm and a length of 20 cm, with

respect to z-direction. I select those events in which the tracks do not have a momentum

higher than 2. GeV/c and their cos θ is lower than 0.92. Once I identify the good track

candidates, I loop over all the positive and negative charged tracks, to search the tracks

pairs that could be better fit to a vertex, in the hypothesys that the positive tracks is a

pion and the negative one is a p. After the vertex selection, I use the SecondaryVertexFit

class, that performs the fit of the parameters of the Λ candidate. I define a parameter

called ratio = dLσdL

, presented in Fig. 4.2, where dL is the distance of the secondary vertex

from interaction point, and σdL is the error of the fit. An effective background rejection

can be achieved by asking for a ratio > 2.

Since this is an inclusive process, the Λ is coupled with different particles (there

should be at least another strange particle due to the strangeness conservation in strong

interaction). All possible couplings are presented in Tab. 4.1.

Once I identify the Λ, I impose a cut on the invariant mass of the hyperon, 1.11GeV/c2 <

MΛ < 1.12GeV/c2, since no kinematic fit is possible.


dL ratio0 2 4 6 8 10 12 14 16 18 20

cou

nts

0

100

200

300

400

500

600

700

800

900

310×

Figure 4.2: Distribution of the variable ratio = dLσdL

.

In Fig. 4.3 shows for the scan data sample the reconstructed Λ invariant mass. Fig.

4.4 shows the Λ recoil mass, which is the mass that should have what is back-scattered

from the Λ It is clear that the signal of Λ is properly reconstructed.

Since ΛΛ has been already investigated in the previous chapter, for further studies I

exclude the region of the recoil mass which contains the Λ signal, i.e. I select mrecoil >

1.16GeV/c2 to investigate the correlation between Λ and non-Λ particles.

4.3 Efficiency and Acceptance

Efficiency corrections and acceptance are important in the analysis of the polarisation.

Only after having corrected the p angular distributions in the Λ rest frame I deduce the

correct information on the polarisation.

The acceptance at forward p emission angle is pretty reduced: this behaviour is due

to the fact that slower π+, that are emitted back with respect to anti-proton direction in

the hyperon’s rest frame, after the boost get not enough momentum to leave a signal in

the tracker and, thus, to be reconstructed. So the condition to have a pair p − π+, that

is what I search for in my event selection, is not fired and the event is rejected.

The efficiency plotted in Fig. 4.5 as a function of cos θ, where θ is the angle between

the p and Λ, is evaluated dividing the number of reconstructed J/ψ by the total number

of the generated ones.


inv mass (GeV/c^2)1.11 1.111 1.112 1.113 1.114 1.115 1.116 1.117 1.118 1.119 1.12

cou

nts

50

100

150

200

250

300

Figure 4.3: Λ invariant mass (scan data).


Taking advantage of the Λ self-analysing weak decay, as performed for the analysis of

the exclusive channel, the distribution of the angle between the p in the parent particle

rest frame and the direction of the hyperon, give access to the hyperon polarisation.

A fit hence of the distribution:

∂N

∂Ω= N0 (1− α+PΛ cos θ) ,

with a linear function provides the slope α+PΛ value, where α+ is the asimmetry of Λ

charged decay (α+ = (0.71 ± 0.01)), and PΛ is the value of the transverse polarisation.

Fig. 4.6 shows the p angular distribution: the fit is the green line and data are the red

dots.

The polarisation is hence evatuated to be PΛ = (−0.09± 0.04) for the scan data.

J/ψ Resonance Peak Data Once that the cuts are optimized, I perform the same

analysis on the 79 pb−1 J/ψ peak data sample using the BOSS version 6.5.5.

The invariant mass and the recoil mass are shown in Fig 4.7 and in Fig. 4.8 respectively.

Fig. 4.9 shows the fit of the p angular distribution in the Λ rest frame.

The polarisation value obtained is PΛ = (0.16± 0.02).


recoil mass (GeV/c^2)1 1.2 1.4 1.6 1.8 2

cou

nts

0

50

100

150

200

250

300

350

400

Figure 4.4: Λ recoil mass (scan data).

Λθcos

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

effi

cien

cy

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure 4.5: Reconstruction efficiency dependence on the p emission angle (scan data).


Since the statistics is good enough, the dependence of the polarization on the hyperon

transverse momentum can be investigated as well. In Fig. 4.10 the distribution of the


Λθcos

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

cou

nt

200

250

300

350

400

450

Figure 4.6: Fit of the angular distribution of the p in the Λ rest frame (scan data).


cou

nts

2000

4000

6000

8000

10000

12000

14000

16000

Figure 4.7: Invariant mass of Λ signal (peak data).

transverse momentum of the selected events is shown. The three bins of momentum inves-

tigated are reported in Tab. 4.2 together with the value determined for the polarisation.


recoil invariant mass (GeV/c^2)1.2 1.4 1.6 1.8 2

cou

nts

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Figure 4.8: Λ recoil mass (peak data).

Λθcos

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

cou

nt

10000

12000

14000

16000

18000

20000

22000

24000

26000

28000

Figure 4.9: Fit to the angular distribution of the p (peak data).

The same results are plotted in Fig. 4.11.

The other inclusive process, J/ψ → ΛX, can be now investigated as well in order to

have a complete picture of the pt dependence of the hyperons polarisation.



cou

nts

0

2000

4000

6000

8000

10000

12000

14000

Figure 4.10: Λ transverse momentum distribution (peak data).

pt PΛ σPΛ

0.5 0.17 0.030.7 0.04 0.030.9 0.06 0.05

Table 4.2: PΛ polarisation dependence on the transverse momentum (peak data).


(GeV/c)Λ t

p0.4 0.5 0.6 0.7 0.8 0.9 1

ΛP

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Figure 4.11: Λ polarisation dependence on the transverse momentum (peak data).

Chapter 5

Analysis e+e−→ J/ψ → ΛX

The 2 pb−1 3.0969 GeV data collected during the J/ψ scan are analysed with the

BOSS version 6.6.2 while the 79 pb−1 data collected under the J/ψ peak are analys with

BOSS version 6.5.5. I use ROOT 5.24 version for both the performed analysis.

5.1 Event simulation

As reported in sec. 4 for the other inclusive process, also in this case the list of the

processes that can contribute to the inclusive Λ production has to be defined. Tab. 5.1

shows the considered processes.

Decay BR BRnorm

Λ ¯Σ(1385)0 2 10−4 0.072ΛΣ0 9 10−5 0.032pK+Λ 8.9 10−4 0.319ΛΛη 2.6 10−4 0.093ΛΛπ0 2.6 10−4 0.023

ΛnK0s + c.c. 6.5 10−5 0.117

ΛΣ+π− (or c.c.) 1.5 10−4 0.298γΛΛ 1.3 10−4 0.047

Table 5.1: List and BR of the processes included in the inclusive process simulation.

In order to have the correct input in the generation process I normalize each branching

ratio to the total branching ratio of the processes. I exclude from the list the exclusive

process ΛΛ, that I have already investigated.

Fig. 5.1 compares the distributions of the polar angke of the decay proton in the Λ

rest frame obtained from the data (red dots) and from the inclusive Monte Carlo (blue

line).

63


Λθcos-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

cou

nt

100

200

300

400

500

600

700

Figure 5.1: Comparison of the distributions of the polar angle of the decay proton in theΛ rest frame obtained from the data (red dots) and from the inclusive Monte Carlo (blueline).

5.2 Event Selection

Since this is the complementary channel of what I have already discussed in sec 4, the

event selection is the same as already performed for the J/ψ → ΛX inclusive channel. I

require the track’s origin to be in a cylinder of a radium of 10 cm and of a length of 20

cm. I select those events in which the tracks do not have momentum higher than 2 GeV/c

and | cos θ| is lower than 0.92. I require events with at least 2 charged tracks. Once that

this first selection is done, I loop over all the charged tracks to search for those p and π−

pairs which fit to a common vertex. After that, I require that the selected particles fit a

secondary vertex. Using the fitted parameter, I cut on the ratio dLσdL

, the same variable

used in Λ inclusive process, that should be higher than 2, and on the invariant mass, in

the region 1.11GeV/c2 < MΛ < 1.12GeV/c2. In Fig 5.2 and 5.3 the invariant mass of the

Λ and the recoil mass respectively are shown.

As in the Λ analysis, I do not include in my further studies the ΛΛ exclusive channel,

so I require a recoil mass Mrecoil > 1.16GeV/c2 to exclude the exclusive process.


inv mass (GeV/c^2)1.11 1.111 1.112 1.113 1.114 1.115 1.116 1.117 1.118 1.119 1.12

cou

nts

100

200

300

400

500

600

700

Figure 5.2: Λ invariant mass (scan data).

recoil mass (GeV/c^2)1 1.2 1.4 1.6 1.8 2

cou

nts

0

100

200

300

400

500

600

700

800

900

Figure 5.3: Λ recoil mass (scan data).

5.3 Efficiency and Acceptance

The efficiency is calculated by dividing the total number of the reconstructed J/ψ by

the total number of generated one. In Fig. 5.4 the efficiency is plotted as a function of


the cos θ, where θ is the decay angle of the proton in the Λ rest frame.

Λθcos-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

effi

cien

cy

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Figure 5.4: Recostruction efficiency dependence on the proton decay angle in the Λ restframe.

Those proton emitted at a very forward angle are detected with very low efficiency,

since slower π−, emitted backward with respect to the proton direction, after the boost to

the Laboratory frame get not enough momentum to be tracked and, thus, reconstructed,

and so the event shows no reconstructed pπ− pair as required and is hence rejected.


The investigation of the polarisation of the inclusive channel is similar to the one

performed for the ΛX inclusive channel. To obtain the polarization it is necessary to

study the angular distribution of the proton in the Λ rest frame. A linear fit is then

performed and the slope value is α−PΛ, where α− is the asimmetry of the weak decay

(α− = 0.642± 0.016).

For the J/ψ scan data, Fig. 5.5 shows the p angular distribution and the green line is

the linear fit. The obtained polarisation value is PΛ = 0.12± 0.04

J/ψ Resonance Peak Data

Once that I have optimized the cuts with the data collected for the J/ψ lineshape

scan, I performed the same analysis on the 79 pb−1 collected under the J/ψ resonance


Λθcos-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

cou

nt

60

80

100

120

140

160

180

Figure 5.5: Fit to the angular distribution of the proton in Λ rest frame (J/ψ scan data).

peak.

In Fig 5.6 and 5.7 the invariant mass and the recoil mass are respectively shown.


cou

nts

5000

10000

15000

20000

25000

Figure 5.6: Λ invariant mass distribution from the 79 pb−1 peak data.


recoil invariant mass (GeV/c^2)1.2 1.4 1.6 1.8 2

cou

nts

0

5000

10000

15000

20000

25000

30000

Figure 5.7: Λ recoil mass distribution from the 79 pb−1 peak data.

In Fig. 5.8 the p angular distribution, the fit is the green line, is shown. The value of

the polarisation is found to be PΛ = (−0.16± 0.03).

Λθcos-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

cou

nt

20000

30000

40000

50000

60000

Figure 5.8: Fit to the the angular distribution of the p in Λ rest frame using the 79 pb−1

data.



Due to the high collected statistics, the investigation of the dependence of the polar-

ization on the transverse momentum can be performed. The total statistics is subdivided

in three transverse momentum ranges, each bin of a 0.2 GeV/c width. Figure 5.9 shows

the distribution of the transverse momentum of the selected Λs.


cou

nts

0

5000

10000

15000

20000

25000

Figure 5.9: Λ transverse momentum distribution.

Tab. 5.2 reports the values of the polarisation obtained for the different bins in the

Λ transverse momentum. Fig. 5.10 shows the polarisation dependence on the transverse

momentum.

pt PΛ σPΛ

0.5 -0.23 0.040.7 -0.1 0.040.9 0.05 0.06

Table 5.2: Polarisation dependence on the Λ transverse momentum.


(GeV/c)Λ t

p0.4 0.5 0.6 0.7 0.8 0.9 1

ΛP

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Figure 5.10: Λ polarisation dependence on the transverse momentum.

Chapter 6

Relative Phase

I’ll report here on the last outcome of the analyses I have performed, i.e. the evaluation

of the relative phase between the strong and electromagnetic J/ψ production amplitudes

performed considering the exclusive final state ΛΛ. Such an investigation is part of a more

extended experimental effort in progress at BESIII and lead by the Italian component of

the Collaboration.

6.1 Introduction

An interference pattern between the J/ψ decay and the non-resonant amplitudes was

obeserved in the e+e− → µ+µ− final state [18]. The 93 KeV J/ψ narrow width is often

interpred as a proof that perturbative regime holds in this energy region. In the pertur-

bative QCD approch, both resonant strong A3g and electromagnetic Aγ amplitudes are

predicted to be real, as well as the non-resonant continuum Aem. If these assumptions

are correct, maximal interference should occur between the above mentioned amplitudes

corrisponding to a 0/180 relative phase.

On the contrary, experimental data on NN final states [18] point toward a 90 relative

phase, consistent to a non-interference pattern. A model indipendent approach requires

to probe the dependence on Q2 of the cross sections for different exclusive final states in

the J/ψ energy range, looking for those interference patterns that could eventually show

out.

Tha aim of this analysis is to evaluate hence for the first time the Q2 dependence in

the J/ψ energy range of the cross section of the exclusive ΛΛ production, in order to

access the relative phase between electromagnetic and strong J/ψ production amplitudes

considering this specific final state, and to probe the validity of pQCD in this regime for

a process involving strangeness production.

71

CHAPTER 6. RELATIVE PHASE 72

6.1.1 Measuring the Phase

The cross section can be parametrised as:

σ [nb] = 12πBinBout

[ cW

]2

· 107 ·[

C1 + C2eiΦ

Wris −W − iΓ/2+ C3e

iΦ

]2

,

where C1, C2, C3 are proportional to the strong, the electromagnetic and the non-

resonant amplitude respectively, Φ is the relative phase and Bout is the branching ratio of

the final states.

To perform simulations, I need to extrapolate the cross section at 3 GeV. We know that

the cross section has an energy dependence σ(√s) ∝ 1√

s10 , where s is the squared center

of mass energy of the considered process. The value of the cross section at 3 GeV is found

to be σ3 = 2.862 pb. This value is obtained performing an exponential fit, as shown in Fig

6.1, using the ΛΛ cross section already experimentally determined at different center of

mass energies by the BaBar [19] and DM2 [20] Collaborations. In the plot of Fig 6.1, the

red line is the fit of the data and the yellow region depicts its error.

]2W [GeV/c2.5 3 3.5 4 4.5 5

[pb]

ΛΛσ

0

10

20

30

40

50

60

70

Figure 6.1: Fit of the cross section at 3 GeV for ΛΛ final state, where W is the invariantmass of the considered processes

The above described calculations can lead to different energy dependences of the cross

section, according to which phase value has been considered:


• interference pattern: both amplitudes are almost real and have same (φ = 0) or

opposite (φ = 180) sign;

• no-interferece pattern: the EM amplitudes, ruled by QED, are almost real, the

strong one is imaginary (φ = 90).

Fig 6.2 shows three scenarios: the black line shows the constructive interference sce-

nario (φ = 0), the red line the non interference scenario (φ = 90) and the blue line the

destructive interference scenario (φ = 180).

[MeV]cmE3040 3050 3060 3070 3080 3090 3100 3110 3120

[nb]

ΛΛσ

-310

-210

-110

1

10

Graph

Figure 6.2: Possible pattern for each phase value. (black line Φ = 0, red line Φ = 90,blue line Φ = 180.)

6.2 Event Simulation and Selection

In order to evaluate the relative phase between strong and electromagnetic amplitudes

in e+e− collision, it is necessary to perform an energy scan below the J/ψ peak. The

considered data have been collected at the same center of mass energies as those analysed

in the previous chapters of this thesis for the investigation of e+e− → ΛΛ. (see section 3).

I performed Monte Carlo simulations for each center of mass energy, using the generator

BesEvtGen, within the BOSS version 6.6.2 (section 3.1).

In this analysis, I apply the same cuts that I have already applied in section 3, requiring

for the selection of good candidate events:

• 4 charged tracks and zero net charge;

• track vertex inside a |z| < 20 cm, |r| < 10 cm cylinder;


• track momentum lower than 2 GeV;

• selection method (as explained in section 3.2):

– PID for the center of mass energies 3.05 GeV, 3.06 GeV;

– Kinematic fitting for the other center of mass energies.

6.3 Data Analysis

To evaluate the phase between electromagnetic and strong amplitudes, I need to de-

termine the cross section at each center of mass energy . Since the integrated luminosities

L are known (see Tab. 6.1), it is possible to determine the cross section from the relation:

σ(e+e− → ΛΛ) =NΛΛ

εL,

where NΛΛ is the number of the reconstructed ΛΛ pairs, ε is the reconstruction efficiency,

which can be calculated by the means of the simulated data as the ratio between recon-

structed events and the generated ones. To obtain the reconstruction efficiency I used

the already generated MC sample produced for the exclusive channel for the polarization

analysis.

Ecm (GeV) L(pb−1)3.050 14.895± 0.0293.060 15.056± 0.033.083 4.759± 0.0173.0856 17.507± 0.0323.090 15.552± 0.033.093 15.249± 0.033.0943 2.145± 0.0113.0952 1.819± 0.013.0958 2.161± 0.0113.0969 2.097± 0.0113.0982 2.210± 0.0113.099 0.759± 0.0073.1015 1.164± 0.0103.1055 2.106± 0.0113.112 1.719± 0.013.120 1.261± 0.009

Table 6.1: Integrated luminosities [15].

The errors for these quantities can be evaluated according to the following scheme:


• for the number of events, I assume a poissonian error: σNΛΛ=√NΛΛ;

• for the efficiency, I assume a binomial distribution (since it has only 2 results:

reconstructed or not), so that the error can be evaluated as: σε =√

ε(1−ε)Ngenerated

.

Tab. 6.2 and 6.3 report the number of events and the reconstruction efficiencies, and

the cross section values determined for each center of mass energy.

Energy (GeV) NΛΛ σNΛΛEfficiency σefficiency

3.050 5 2.24 0.21 0.0043.060 7 2.65 0.2 0.0043.083 6 2.45 0.44 0.0053.0856 7 2.65 0.45 0.0053.090 16 4. 0.45 0.0053.093 40 6.32 0.45 0.0053.0943 154 12.41 0.45 0.0053.0952 488 22.09 0.45 0.0053.0958 1426 37.76 0.44 0.0053.0969 2485 49.85 0.45 0.0053.0982 1154 33.97 0.45 0.0053.0982 173 13.15 0.45 0.0053.1015 107 10.34 0.45 0.0053.1055 78 8.83 0.45 0.0053.112 30 5.48 0.46 0.0053.120 23 4.8 0.45 0.005

Table 6.2: List of energy, number of events and efficiency for the scan center of massenergies.

To extract the relative phase, I need to perform a fit of the cross sections evalutated

for the 16 center of mass energies collected by the BESIII Collaboration during 2012 data

taking.

This fit is performed by mean of a complex fitting function, which was already devel-

oped in the BESIII Turin group in order to perform a fit of the e+e− → pp cross section

considering the data collected at the same center of mass energies. The peculiarity of this

fitting approach is that the fitting function itself consist of a Monte Carlo simulation (see

6.3). The MC simulates with 106 extractions the radiative corrections at each center of

mass energy. The estimated value of the radiative correction, divided by the number of

extractions, provides the functional dependence.

The fit depends on three variables:

• φ, which is the relative phase between the amplitudes;

• σ3, which is the cross section of the process at 3 Gev, and it is an extimation of

the cross section in the non-resonant region, and anchor the fit function to the

continuum;


Energy (GeV) Cross-section (nb) σcross−section (nb)3.050 1.64 10−3 7.32 10−4

3.060 2.31 10−3 8.73 10−4

3.083 2.86 10−3 1.17 10−3

3.0856 8.88 10−4 3.35 10−3

3.090 2.28 10−3 5.69 10−4

3.093 5.87 10−3 9.29 10−4

3.0943 1.61 10−1 1.3 10−2

3.0952 5.95 10−1 2.7 10−2

3.0958 1.49 3.96 10−2

3.0969 2.64 5.29 10−2

3.0982 1.16 3.41 10−2

3.0982 5.1 10−1 3.88 10−2

3.1015 2.02 10−1 1.95 10−2

3.1055 8.17 10−2 9.25 10−3

3.112 3.81 10−2 6.96 10−3

3.120 4.03 10−2 8.4 10−3

Table 6.3: Cross sections for the scan center of mass energies.

• Bout, which is an extimation of the BR of the considered process.

The best fit obtaining the best agreement with the cross section values experimentally

determined is shown in Fig 6.3. The agreement is pretty good, nevertheless the fit needs

some more refinement in the continuum region. The σ fluctiations are due to the low ΛΛ

statistics available.

The best fit provides a relative phase of Φ = (1.42557±0.260296) rad, that corresponds

to

Φ = (81.68± 14.91).

The fitting procedure provides also the cross section at continuum, that is σe = (1.106±0.496) pb, and the branching ratio Bout = (0.753± 0.011) 10−3.

The value experimentally obtained for the phase does not match the theoretical pre-

dictions from pQCD, but it is consistent with the value experimentally determined in

other preliminary analyses performed at BESIII considering different final states[21]. The

BR found from the fit of the data corresponds approximately to half of the value listed

in [7]. Further investigations aimed to determine the origin of this discrepancy are in

progress; an hypotesis that has been advanced is that an even relatively small shift in the

evaluation of the center of mass energy, and hence of the J/ψ resonance peak energy, can

significantly affect the value of the BR obtained from the fitting procedure.


]2Mass [MeV/c3050 3060 3070 3080 3090 3100 3110 3120

[nb]

ΛΛσ

-310

-210

-110

1

Figure 6.3: Fit of the ΛΛ cross sections. (the fit is the red line).

Part III

Conclusion

78

79

Hyperon Polarisation

Two different event selection approches has been tested, and then separately for each

center of mass energy I have selected the most suitable, i.e. that providing the largest

number of surviving events and the better signal over background ratio. The Λ and the Λ

polarisations have been determined for the exclusive production of the ΛΛ pairs, for the

first time with e+e− beams in the J/ψ sector and in the lower energy continuum. The

hyperon polarisation is compatible with zero in the continuum region and is statistically

uncompatible with zero in the J/ψ resonance region: PΛ = 0.16± 0.03 and PΛ = −0.11±0.02. A precise evaluation of the hyperon polarisation could also allow to access the

relative phase between the hyperon electric and magnetic form factors [22].

The polarisation has been evaluated as well for the inclusive J/ψ → ΛX production,

and is also statistically non compatible with zero: PΛ = 0.16± 0.02.

A similar result has been determined for the charge conjugate process J/ψ → Λ:

PΛ = −0.16± 0.03.

The polarisation evaluated experimentally both in the inclusive both in the exclusive

processes shows a clear dependence on the hypeon transverse momentum: in the case

of the exclusive process, the polarisation is more sizeable at larger transverse momen-

tum, while in the inclusive processes the polarisation is more sizeable at lower transverse

momentum.

The present analysis has shown as the polarisation has opposite signs in the considered

exclusive and inclusive hyperon production processes.

Relative phase

The relative phase between strong and electromagnetic J/ψ production amplitudes

has been determined for the first time: φ = (81.68± 14.91), and found to be compatible

with 90 degrees. A similar picture has been recently reported by BESIII considering other

final states. A 90 relatice phase between amplitudes ruled by QED and QCD implies that

at least one of these amplitudes should be imaginary, and such a possibility is excluded

by QED and QCD.

Bibliography

[1] M. Gell-Mann, The interpretation of the New Particels as Displaced Charged Multi-

plets, Il Nuovo Cimento 4 (S2): 848 (1956)

[2] D.H. Perkins, Introduction to High Energy physics, Cambridge Press.

[3] D. Schulte, Beam-Beam Interaction, CERN.

[4] Iwanenko D., Pomeranchuk I., On the maximal energy attainable in betatron, Physical

Review 65 (1944) 343.

[5] J. Aubert et al., Experimental observation of a Heavy Particle J, Physical Review

Letters 33 (1974).

[6] J. Augustin et al.,Discovery of a Narrow Resonance in e+e− Annihilation., Physical

Review Letters 33 (1974).

[7] J. Beringer et al. (Particle Data Group), The Review of Particle Physics, Phys. Rev.

D86,010001 (2012)

[8] G. D. Rochester and C. C. Butler, Evidence for the Existence of New Un- stable

Elementary Particles, Nature, 92:855 (1947).

[9] K. Nishijima (1955), Charge Indipendence Theory of V Particles, Progress of Theo-

retical Physics 13(3): 285.

[10] S. Brauksiepe, et al., COSY-11 an Internal Experimental Facility for Threshold Mea-

surements, Nucl. Instr. Meth. A 376, 3 (1996)

[11] F. Balestra et al., Spin Transfer in Exclusive Λ Production from pp Collisions at 3.67

GeV/c, Phys. Rev. Lett. 83, 1534-1537 (1999)

[12] M. Ablikim et al. (BESIII collaboration), Design and Construction of BESIII.

[13] http://root.cern.ch/drupal/

[14] R.G. Ping, C.Y. Pang, Monte Carlo Generators for Tau-Charm-Physics at BESIII

80

BIBLIOGRAPHY 81

[15] B.X. Zhang, Luminosity measurement for J/ψ phase and lineshape study, private

communication.

[16] R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, Trans-

action of the ASME Journal of Basic Engineering 82D (1960)

[17] J. Podolansky and R. Armenteros, Phil. Mag., 45(13), 1954

[18] J. Augustin et al., PRL 33, 1076 (1974)

[19] B. Aubert et al. (BABAR Collaboration), Phys. Rev. D 76, 092006 (2007)

[arXiv:0709.1988[hep-ex]])

[20] D. Bisello et al. (DM2 Collaboration), Z. Phys. C 48, 23 (1990)

[21] M. Destefanis, Measurement of the Phase between Strong and Electromagnatic J/ψ →pp Decay Amplitudes, BAM-106 on Hypernews.

[22] B. Aubert et al. (BABAR collaboration), Study of e+e− → ΛΛ,ΛΣ0,Σ0Σ0 using

initial state radiation with BABAR, Physical Rewiew D 76, 092006(2007).

And without any reference in the text:

[-] M. Ablikim et al. (BESIII collaboration), Physics at BESIII.

[-] M. Ablikim et al. (BESIII collaboration), Study of the J/ψ decays to ΛΛ and Σ0Σ0.,

hep-ex/050602v1 (2005)

[-] M. Destefanis, Hyperon Studies at GSI: Λ reconstruction in p-p Collision at 2.2 GeV

with Hades and in p-p Interaction for the Future PANDA Experiment. Ph.D thesis

(2008),

[-] M. Gell-Mann , Phys. Lett. 16(1964), pag 214-215

[-] M. Maggiora, Measuring the phase between strong and EM J/ψ decay amplitude.

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