1 Barbara Sciascia – LNF Barbara Sciascia Barbara Sciascia

Blessing of KBlessing of Kl3l3 decays decays

analysisanalysis

Kaon meetingKaon meeting11 May 2007 - LNF11 May 2007 - LNF

2 Barbara Sciascia – LNF

Overview

• Tracking efficiency: final point.• Photon cluster efficiency correction: “hic sunt leones”• TCA efficiency correction: update using KL and K events.• Update in signal systematic errors.• Shapes: new enriched Ke3 and Km3 samples, few statistics to correct tails, keep old syst estimation.

• BR and R results: “Bisogna che tutto cambi perche’ tutto resti com’e`”(G. Tomasi di Lampedusa)• Dependency of BR(K3) mm from 0 value.• Dependency of BR(Kℓ3) mm from K value.

• Memo update: in progress

3 Barbara Sciascia – LNF

BR measurement technique

BR(Kl3) =N(Kl3) 1 1 1 (TAG(i) BR(i))

NTAG (1-fNI) FV SELE TAG(Kl3)

CF

(TRK)DATA TCA)DATA 1)DATA 2)DATA

(TRK) MC TCA) MC 1) MC 2) MC

SELE= SELE_MC

• 4 tag samples 4 independent mm for each decay channel• Different contributions to each tag sample: kaon nuclear interactions act only on negative measurements tag bias range from 0.97 to 1.03 following charges, decays, and tag samples.• FV: effect on the BR measurement -via the geometrical acceptance- of a possible change of kaon lifetime value Estimate of the BR=BR(K) dependency.• Fit procedure, efficiency, and correction of efficiency affect all mm in the same way.

4 Barbara Sciascia – LNF

Overview of tracking corrections

0 - At least 10 from NV: only (VTX, K) parameterization (used for preliminary mm). 1 - K2, only 1 0: pLAB dependence from kinematics, high momenta. 3 - K’, only 2 0: pLAB dependence from kinematics, low momenta. Old (aka 2) - Kl3: p* dependence. New - Kl3: pLAB dependence from fit

• 1+3: correct TRK efficiency with a (VTX,K,pLAB) parameterization; too high statistical error from low momentum part.• Old: correct the TRK efficiency with a (VTX,K,p*) parameterization.• New: correct TRK efficiency with a (VTX,K,pLAB) parameterization.

Different ways give results compatible within the errrors (1).

Sample Ke3 K3 K2 K’

1 (K2) 15 % 85 % -

3 (K’) 10 % 15 % 75 %

Old (aka 2) 60 % 40 % -

New 50 % 26 % 21 % 2%

5 Barbara Sciascia – LNF

Single photon efficiency: the method • Select events with K2 or K2 tag, to unbias the efficiency measurement for the trigger.• Ask for a K2 selection (p* cut) in the signal side. • Get 0 from the missing momentum at vertex.• Look for a 0-photon from the vertex, excluding clusters already used by the tag or connected to a track.• Starting with K2+ selection, estimate the energy and the position of the “other photon”. • Look for a cluster “close to” the other photon.• Use the opening angle between estimated and cluster direction from the vertex, as “close to” criterion: cos(OPE)<0.99

6 Barbara Sciascia – LNF

Single efficiency : correction to SELE_MC

• 2001-2002 Data, and kpm04 and all_phys MC have been used. • The Data/MC ratio of efficiencies is used to correct MC photon energies.

• Barrel and Endcap are corrected separately.

2% of correction @ 100 MeV: too high

7 Barbara Sciascia – LNF

Single efficiency: Data and MC

• The single photon efficiency as a function of estimated energy of the photon, separately for “K and K photons”, and EMC regions (barrel, endcap, curved).

(Data) (MC)

8 Barbara Sciascia – LNF

Single efficiency : correction to SELE_MC

• The Data/MC ratio of efficiencies is used to correct MC photon energies.

• Corrections obtained with cos >0.6,0.7,0.8 photon acceptance are in agreement within the errors. Use 0.7 for the mm and use the other as systematic check.

9 Barbara Sciascia – LNF

Cluster efficiency: summary

• Single photon efficiency: too tight cut in the acceptance. 2% of correction @ 100 MeV: too high

• Modify: from cos>0.99 to cos>0.70 and (t) matching.• Time matching: the one applied for 0 signal selection • Check: correction stable wrt acceptance cut, use cos >0.6, >0.7 , >0.8, and >0.9, corrections.

• Change the BR results, not Re

10 Barbara Sciascia – LNF

TCA efficiency• The Track-to-cluster association (TCA) efficiency for both electrons and muons is evaluated using KLe3 KL3 events, identified by tight kinematical selection +NN(thanks to A.Sibidanov and to M.Testa for their work/support)• BR(K3) and Re mms sensitive to TCA correction

• For high momentum muons use also K2, with identified kink, and K2 events. Different corrections in agreement within the errors. Use a “KL3, K2 combination”.

•Correct separately for Barrel and EndCap, and per charge

11 Barbara Sciascia – LNF

TCA efficiency

Wrt 2006 mm, correct as a function of momentum (20 MeV/bin) and EMC impact angle (0.2/bin), instead of Plab only.

Ke3

K3

No difference for electrons

Important for K3 due to the different kinematic distribution of KL3 and K3 decays.

12 Barbara Sciascia – LNF

Background rejection

• K00 are rejected cutting on Emiss-Pmiss spectrum (<90MeV); the 0 momentum is obtained by mean of a kinematic fit

• K0 with an early events are rejected evaluating the missing momentum at the decay vertex, and cutting on momentum of the secondary track in the Pmiss rest frame (p*<60 MeV)

Emiss-Pmiss (MeV)

K00

K0,

K0e

K0

K00

p*(MeV)

K0l

• Reject two-body decays: p(m) 192.5 MeV

13 Barbara Sciascia – LNF

Signal systematics - 1

• Estimate the systematic error coming from the cut applied to reject bkg events:1- p(m) 192.5 MeV: 190 MeV-195 MeV2- Emiss-Pmiss <90MeV: 88 MeV-NoCut3- p*>60 MeV: 50 MeV - 70 MeV

Ke3

K3

14 Barbara Sciascia – LNF

Signal systematics - 2

• No cut is applied to PLAB in signal selection; require PLAB> xx MeV to check the stability of the momentum-dependent corrections (TRK and TCA)

PLAB > 50 MeV > 70 MeV > 90 MeV

Ke3

K3

15 Barbara Sciascia – LNF

Signal systematics - 3

• To check the correction applied for the cluster efficiency, require a minimum energy to 0 clusters:EMIN(Clu) > 20 MeV > 30 MeV > 40 MeV

Ke3

K3

16 Barbara Sciascia – LNF

Signal systematics - 4

• To check the robustness of the cluster efficiency correction wrt the acceptance cut, vary the opening angle (cos()>0.7) and use the CLU correction obtained:cos() > 0.6 > 0.8 > 0.9

Ke3

K3

17 Barbara Sciascia – LNF

Signal systematics - 5

Ke3

K3

Transversal vertex position (low/high) Kaon polar angle (vertical or not)

Ke3

K3

18 Barbara Sciascia – LNF

Summary on systematics: Ke3• The systematics have been carefully evaluated for each tag sample and for each decays, taking correlation into account.

• Nuclear interaction corrections affect only negative mm.

• The final error is dominated by the error of the correction efficiency (tracking).

• For most the tag bias corrections, the systematic error is the correction itself.

19 Barbara Sciascia – LNF

Summary on systematics: K3

• The systematics have been carefully evaluated for each tag sample and for each decays, taking correlation into account.

• Nuclear interaction corrections affect only negative mm.

• The final error is dominated by the error of the correction efficiency (tracking and muon track-to-cluster efficiencies).

20 Barbara Sciascia – LNF

Results: BR(Kl3)

Br (Stat) (Syst)%

Ke3 4.892 (49) (39)

Ke3 4.944 (52) (39)

K3 3.190 (42) (28)

K3 3.212 (38) (27)

Ke3 4.916 (35) (39)

K3 3.202 (28) (27)

Average of the four result per charge and per decay taking correlations into account:

• The statistical errors are dominated by the contribution of TRK correction for Ke3 and TRK+TCA corrections for K3• Efficiency and tag bias corrections, as well as selection cuts induce a 65.62% of correlation between the Ke3-K3 branching ratio measurements.

21 Barbara Sciascia – LNF

Re = (K3)/(Ke3)

As a check, using the SAME samples of BR mm:• Calculate Re = (K3)/(Ke3) in the four tag samples used for BR mm.• Re = (N3/Ne3) (e3/3) TB • TB is the tag bias correction for the ratio, and ranges from 0.4% to 0.8% following the tag sample.

• The correlation between Ke3 and K3 coming from the fit and from the efficiency corrections has been taken into account in calculating R/e

• Error dominated by statistics of efficiency corrections.

22 Barbara Sciascia – LNF

Re = (K3)/(Ke3)

• Average: Re=0.6508(53)Stat(73)Syst

• From theory: Re=0.6646(61)Integrals (Ie3 and I3) and SU(2), em corrections from Moulson (FlaviaNet) at CKM06.

Re

K2 0.6514(64)(65)(20)

K2 0.6543(111)(71)(20)

K2 0.6497(62)(72)(20)

K2 0.6490(128)(79)(20)

(K3)/(Ke3)

2/nDoF between tags

1.091/3 All

0.142/1 1 and 3

0.162/1 1 and 4

0.837/1 2 and 3

0.692/1 2 and 4

23 Barbara Sciascia – LNF

0 dependency of BR(K3)

• Wrong/old scalar form factor value in MC (0 = 0.030).• Weight MC to obtain BR(K3) at the present value (0 = 0.015).

• Evaluate BR(K3) dependency on 0 value: BR(K3) = P1 - P2*0

• Limited knowledge of 0 value, gives negligible contribution to the systematic error.

BR

(K3

)

24 Barbara Sciascia – LNF

Fiducial volume efficiency• Effect on the BR measurement -via the geometrical acceptance- of a possible change of kaon lifetime value.• Ott mm: underestimated error.

• Two private MC samples K2,Kall with K

PDG(12.37ns)f, f = 0.98, f = 1.02• Variation of FV as a function of f.

• K KLOE preliminary (P.Massarotti) in agreement within the errors with PDG (and MC).• From FV=FV(K) dependency, conservatively assume as systematic error the FV variation due to (K) 0.6% fractional: 0.3%.

• Estimate of the BR=BR(K) dependency.

25 Barbara Sciascia – LNF

K dependency of BR(Kℓ3)

• In MC K = 12.36 ns• PDG 06 K = 12.384 ns

• From the BR=BR(K) dependency: evaluate BR @ K (PDG 06 fit)

• Change BR’s of 0.1%• Should change Ke3-K3 correlation, and Re errors.

Detailed calculation to be done before the results presentation.

26 Barbara Sciascia – LNF

Conclusions• The charged kaon semileptonic branching ratios have been measured in 4 independent samples (2 Tag x 2 Charge). They are all compatible within the errors.

• Different contributions to each tag sample: kaon nuclear interactions act only on negative measurements tag bias range from 0.97 to 1.03 following charges, decays, and tag samples.

• MC efficiencies have been corrected using efficiencies from data control samples.• The errors are dominated by the statistics of the control sample used to correct the tracking efficiency.• BR’s dependency from K (e3 and 3) and 0 (3) have been determined.

• BR final results have a fractional accuracy of 1.1% for (Ke3) and 1.2% for (K3).• The Re has been measured with 1.4% of fractional accuracy, and is in agreement within the errors with the theoretical prevision.

And now it’s the referees’ turn,but before….

27 Barbara Sciascia – LNF

Along the years…KLOE 06/2: wrong CLU correction, better TCA, PLAB dependence (from Fit) for TRK correction.

KLOE 06/1: wrong CLU correction, better TCA correction, no PLAB cut, rough momentum dependence for TRK correction.

KLOE 07: the best we can do today…

Ke3 K3 Re

KLOE 05

KLOE 05

Theory

KLOE 05: wrong CLU corrections, no good TCA corrections, cut on PLAB>90 MeV, no momentum dependence for TRK corrections.

Presence of an intelligent design!

Moulson CKM06

28 Barbara Sciascia – LNF

Corrections to MC

CLU Ke3

CLU K3

TCA Ke3

TCA K3

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Corrections to MC

TRK Ke3

TRK K3

ALL Ke3

ALL K3

30 Barbara Sciascia – LNF

Summary on Tag bias evaluationTag K+2 K+2 K-2 K-2

Fractional systematic error

CV 0.04% 0.02% 0.03% 0.04%

FilFo 0.36% 0.06% 0.37% 0.05%

NI 0.09% 0.13% - -

Tot 0.45% 0.30% 0.41% 0.19%

Tag Bias (Statistical) (Systematic)

Ke3 0.9694(11)(44) 1.0137(34)(30) 0.9884(10)(40) 1.0328(23)(20)

K 0.9756(13)(44) 1.0210(36)(31) 0.9963(10)(41) 1.0371(25)(20)

• Systematic errors on Cosmic veto and FilFo corrections have conservatively chosen as half of the correction itself.• The fNI systematic contribution has been chosen as the whole correction.• The stability of tag bias value wrt the kinematical selection of the tag has been checked; the contribution to the systematic error is negligible.

31 Barbara Sciascia – LNF

Fit shapes - 1

• Count K3 events in the (3400MeV2,30000MeV2) region, in which the K3 acceptance is about 99%.

• Count Ke3 events in the (-15000MeV2,6800MeV2) region, in which the Ke3 acceptance is about 97%.

• Compare fit output obtained using different shapes to fit the m2 Data distribution.• Various MC shapes have been used obtaining negligible variations of the fit results.• Trying to use shapes obtained form enriched Kl3 samples, define two different and partially overlapped fit windows:

32 Barbara Sciascia – LNF

Fit shapes - 2

1- Found by the standard fit.2- Fitting the data distribution in the same region using MC for signal and bkg fit input shapes.3- As 2) but using as signal fit input the m2 distribution of the Ke3-enriched or K3-enriched sample.• In each tag sample, estimate a systematic error from the comparison of the three numbers.• All error negligible but 0.5% for the K2 sample.• Assume 10% of uncertainty on the “not-included” part: 0.3% for Ke3, 0.1% for K3

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2 between mm on different tag samples2 between All (4) mm: 2.32612 (DoF=3)2 between tag 1 and 4: 0.38439 (DoF=1)2 between tag 1 and 6: 0.88506 (DoF=1)2 between tag 3 and 4: 0.42146 (DoF=1)2 between tag 3 and 6: 0.92128 (DoF=1)

2 between All (4) mm: 0.79551 (DoF=3)2 between tag 1 and 4: 0.11204 (DoF=1)2 between tag 1 and 6: 0.44156 (DoF=1)2 between tag 3 and 4: 0.02534 (DoF=1)2 between tag 3 and 6: 0.22561 (DoF=1)

(taking correlation into account)

2 between All (4) mm: 1.09061 (DoF=3)2 between tag 1 and 4: 0.14180 (DoF=1)2 between tag 1 and 6: 0.16244 (DoF=1)2 between tag 3 and 4: 0.83655 (DoF=1)2 between tag 3 and 6: 0.69193 (DoF=1)

(K3)/(Ke3)

Ke3

K3