Barbara Sciascia

Blessing of Kl3 decays analysis Kaon meeting 11 May 2007 - LNF Barbara Sciascia

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 Rme results: “Bisogna che tutto cambi perche’ tutto resti com’e`” • (G. Tomasi di Lampedusa) • Dependency of BR(Km3) mm from l0 value. • Dependency of BR(Kℓ3) mm from tK value. • Memo update: in progress

BR measurement technique N(Kl3) 111 (eTAG(i) BR(i)) aCF BR(Kl3) = NTAG(1-fNI)eFVeSELEeTAG(Kl3) e(TRK)DATAe(TCA)DATA e(g1)DATAe(g2)DATA   eSELE= eSELE_MC e(TRK) MCe(TCA) MC e(g1) MCe(g2) 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(tK) dependency. • Fit procedure, efficiency, and correction of efficiency affect all mm in the same way.

Overview of tracking corrections • 0 - At least 1p0 from NV: only (rVTX, qK) parameterization (used for preliminary mm). • 1 - Kp2, only 1 p0: pLAB dependence from kinematics, high momenta. • 3 - Kt’, only 2 p0: pLAB dependence from kinematics, low momenta. • Old (aka 2) - Kl3: pp* dependence. • New - Kl3: pLAB dependence from fit • 1+3: correct TRK efficiency with a (rVTX,qK,pLAB) parameterization; • too high statistical error from low momentum part. • Old: correct the TRK efficiency with a (rVTX,qK,pp*) parameterization. • New: correct TRK efficiency with a (rVTX,qK,pLAB) parameterization. • Different ways give results compatible within the errrors (1s).

Single photon efficiency: the method • Select events with Km2 or Kp2 tag, to unbias the efficiency measurement for the trigger. • Ask for a Kp2 selection (pp* cut) in the signal side. • Get bp0 from the missing momentum at vertex. • Look for a p0-photon from the vertex, excluding clusters already used by the tag or connected to a track. • Starting with Kp2+g 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(qOPE)<0.99

2% of correction @ 100 MeV: too high Single g efficiency : correction to eSELE_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.

Single g efficiency: Data and MC e(Data) e(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).

Single g efficiency : correction to eSELE_MC • The Data/MC ratio of efficiencies is used to correct MC photon energies. • Corrections obtained with cosq >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.

Cluster efficiency: summary • Single photon efficiency: too tight cut in the g acceptance. • 2% of correction @ 100 MeV: too high • Modify: from cosq>0.99 to cosq>0.70 and D(dt) matching. • Time matching: the one applied for p0 signal selection • Check: correction stable wrt acceptance cut, use cosq >0.6, >0.7 , >0.8, and >0.9, corrections. • Change the BR results, not Rme

TCA efficiency • The Track-to-cluster association (TCA) efficiency for both electrons and muons is evaluated using KLe3 KLm3 events, identified by tight kinematical selection +NN • (thanks to A.Sibidanov and to M.Testa for their work/support) • BR(Km3) and Rme mms sensitive to TCAm correction • For high momentum muons use also Kp2, with identified pm kink, and Km2 events. Different corrections in agreement within the errors. Use a “KLm3, Km2 combination”. • Correct separately for Barrel and EndCap, and per charge

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. Km3 No difference for electrons Important for Km3 due to the different kinematic distribution of KLm3 and Km3 decays. Ke3

Background rejection • Reject two-body decays: p(mp)  192.5 MeV Kpp0, pmn Kp0en Kp0mn Kp0ln Kpp0p0 Kpp0p0 pm*(MeV) • Kpp0-with an early pmn- events are rejected evaluating the missing momentum at the decay vertex, and cutting on momentum of the secondary track in the Pmiss rest frame (pm*<60 MeV) Emiss-Pmiss (MeV) • Kpp0p0 are rejected cutting on Emiss-Pmiss spectrum (<90MeV); the p0 momentum is obtained by mean of a kinematic fit

Signal systematics - 1 Ke3 • Estimate the systematic error coming from the cut applied to reject bkg events: 1- p(mp)  192.5 MeV: 190 MeV-195 MeV 2- Emiss-Pmiss <90MeV: 88 MeV-NoCut 3- pm*>60 MeV: 50 MeV - 70 MeV Km3

Signal systematics - 2 Ke3 • 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) Km3 PLAB> 50 MeV > 70 MeV > 90 MeV

Signal systematics - 3 Ke3 • To check the correction applied for the cluster efficiency, require a minimum energy to p0 clusters: EMIN(Clu) > 20 MeV > 30 MeV > 40 MeV Km3

Signal systematics - 4 Ke3 • To check the robustness of the cluster efficiency correction wrt the acceptance cut, vary the opening angle (cos(q)>0.7) and use the CLU correction obtained: cos(q) > 0.6 > 0.8 > 0.9 Km3

Signal systematics - 5 Ke3 Ke3 Km3 Km3 Transversal vertex position (low/high) Kaon polar angle (vertical or not)

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.

Summary on systematics: Km3 • 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).

Results: BR(Kl3) 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 Km3 • Efficiency and tag bias corrections, as well as selection cuts induce a 65.62% of correlation between the Ke3-Km3 branching ratio measurements.

Rme = G(Km3)/G(Ke3) • As a check, using the SAME samples of BR mm: • Calculate Rme = G(Km3)/G(Ke3) in the four tag samples used for BR mm. • Rme = (Nm3/Ne3) (ee3/em3) bTB • bTB 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 Km3 coming from the fit and from the efficiency corrections has been taken into account in calculating dRm/e • Error dominated by statistics of efficiency corrections.

Rme = G(Km3)/G(Ke3) G(Km3)/G(Ke3) • Average: Rme=0.6508(53)Stat(73)Syst • From theory: Rme=0.6646(61) • Integrals (Ie3 and Im3) and dSU(2), dem corrections from Moulson (FlaviaNet) at CKM06.

l0 dependency of BR(Km3) • Wrong/old scalar form factor value in MC (l0 = 0.030). • Weight MC to obtain BR(Km3) at the present value (l0 = 0.015). • Evaluate BR(Km3) dependency on l0 value: • BR(Km3) = P1 - P2*l0 • Limited knowledge of l0 value, gives negligible contribution to the systematic error. BR(Km3)

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 Km2,Kall with tKPDG(12.37ns)f, f = 0.98, f = 1.02 • Variation of eFV as a function of f. • tK KLOE preliminary (P.Massarotti) in agreement within the errors with PDG (and MC). • From eFV=eFV(tK) dependency, conservatively assume as systematic error the eFV variation due to s(tK) 0.6% fractional: 0.3%. • Estimate of the BR=BR(tK) dependency.

tK dependency of BR(Kℓ3) • In MC tK = 12.36 ns • PDG 06 tK = 12.384 ns • From the BR=BR(tK) dependency: evaluate BR @ tK (PDG 06 fit) • Change BR’s of 0.1% • Should change Ke3-Km3 correlation, and Rme errors. Detailed calculation to be done before the results presentation.

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 tK (e3 and m3) and l0 (m3) have been determined. • BR final results have a fractional accuracy of 1.1% for (Ke3) and 1.2% for (Km3). • The Rme 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….

Presence of an intelligent design! Along the years… KLOE 06/2: wrong CLU correction, better TCA, PLAB dependence (from Fit) for TRK correction. Ke3 Km3 Rme KLOE 06/1: wrong CLU correction, better TCA correction, no PLAB cut, rough momentum dependence for TRK correction. Moulson CKM06 Theory KLOE 05 KLOE 05 KLOE 05: wrong CLU corrections, no good TCA corrections, cut on PLAB>90 MeV, no momentum dependence for TRK corrections. KLOE 07: the best we can do today…

Corrections to eMC CLU Ke3 TCA Ke3 CLU Km3 TCA Km3

Corrections to eMC TRK Ke3 ALL Ke3 TRK Km3 ALL Km3

Summary on Tag bias evaluation • 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.

Fit shapes - 1 • 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: • Count Ke3 events in the (-15000MeV2,6800MeV2) region, in which the Ke3 acceptance is about 97%. • Count Km3 events in the (3400MeV2,30000MeV2) region, in which the Km3 acceptance is about 99%.

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 Km3-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 K-m2 sample. • Assume 10% of uncertainty on the “not-included” part: 0.3% for Ke3, 0.1% for Km3

c2 between mm on different tag samples c2 between All (4) mm: 2.32612 (DoF=3) c2 between tag 1 and 4: 0.38439 (DoF=1) c2 between tag 1 and 6: 0.88506 (DoF=1) c2 between tag 3 and 4: 0.42146 (DoF=1) c2 between tag 3 and 6: 0.92128 (DoF=1) Ke3 c2 between All (4) mm: 0.79551 (DoF=3) c2 between tag 1 and 4: 0.11204 (DoF=1) c2 between tag 1 and 6: 0.44156 (DoF=1) c2 between tag 3 and 4: 0.02534 (DoF=1) c2 between tag 3 and 6: 0.22561 (DoF=1) Km3 c2 between All (4) mm: 1.09061 (DoF=3) c2 between tag 1 and 4: 0.14180 (DoF=1) c2 between tag 1 and 6: 0.16244 (DoF=1) c2 between tag 3 and 4: 0.83655 (DoF=1) c2 between tag 3 and 6: 0.69193 (DoF=1) G(Km3)/G(Ke3) (taking correlation into account)

Barbara Sciascia