Barbara Sciascia – LNF 1 Barbara Sciascia Measurement of the absolute branching ratio of K  l3 decays and of the R  e ratio Blessing meeting of the final results 14 June LNF

Barbara Sciascia – LNF 2 Outline Introduction Tag: Description of the selection. 4 different samples are used. Signal: Selection. Counting by means of a Fit procedure. Efficiency: From MC. Data/MC corrections for Tracking, Track-to-Cluster, Clustering, and acceptance. Systematics: Tag bias, FilFo, Cosmic veto/T3, Trigger, K  nuclear interaction, Fiducial volume, selection efficiency, efficiency correction, and fit. Results: BR(K   0 e  ), BR(K   0   ), and  (K   0   )/  (K   0 e  ) Conclusions

Barbara Sciascia – LNF 3 Introduction Measurement of the K  semileptonic decays to measure V US Absolute BR measurement via a Tag technique. Use 2 Tag: K  2 +  -trigger K  2 +  0 -trigger 2 Tag  2 Charge  4 independent samples. Counting K  l3 from the fit of a m 2 distribution. Efficiency from MC + corrections from Data/MC efficiency ratio Data sample: , with data quality: DB information, MC run presence, good EMC time calibration, good trigger conditions MC: use all_phys, kpm04, and kpm10pc productions. For handiness divided in 12+1 periods: 5 for the 2001 data, 7 for the 2002 data, 1 for the 2002  -peak-scan. use 12 periods (410 pb -1 )

Barbara Sciascia – LNF 4 Tag selection - 1 Use only TagDecay algorithm of the Event Classification. track from IP, momentum cut: 70 MeV  p K  130 MeV decay vertex in fiducial volume: 40cm   VTX  150 cm daughter track extrapol. to EMC 2-body decays identified in kaon rest frame: 3  cut around p  peak: Tag events using K    (K  2) or K     0 (K  2) decays 4 independent samples: K +  2, K +  2, K -  2, and K -  2 p  (m  ) = 236 MeVp  (m  ) = 205 MeV

Barbara Sciascia – LNF 5 Tag selection - 2 Tag K ±  2: ask for associated  -cluster on barrel with energy > 90 MeV.  - cluster fires at least one sector.  -cluster fires two sectors (  30%) Tag K   2: a) look for a  0 from vertex using the  (  t) technique and   constraint. b)  0 clusters satisfy the Emc trigger (  90%) c) Don’t use   clusters Calorimeter trigger (2 sectors over threshold  50 MeV) satisfied by tag: KKKK  KKKK   

Barbara Sciascia – LNF 6 Tag selection - 3 For each kaon charge, 2+1 different tag samples: K  2+  Trg, K  2+  0 Trig, and K  2+  NoTrg. Tagging efficiency:  8% for each tag sample. 2 tag × 2 charge = 4 samples for the measurements (  60x10 6 tag) The contamination from.not.Kpm events is negligible: 1 tag × 2 charge = 2 control samples (  60x10 6 tag):

Barbara Sciascia – LNF 7 Signal selection 1-prong kaon decay vertex in the fiducial volume (40   VTX  150 cm) daughter track extrapol. to EMC Reject two-body decays: p  (m  )  195 MeV  0 search: 2 neutral clusters in EmC, with ToF matching the K decay vertex (  t)<3  t ) Spectrum of charged daughter mass, m 2 lept, from TOF measurement: t decay K = t lept -L lept /(  lept c) =  t  -L  /c  KKKK  KKKK eeee   Selection of K ± semileptonic decays (K l3 ) Fit m 2 lept spectrum with a linear combination of Ke3 and K  3 shapes, and background contribution.

Barbara Sciascia – LNF 8 Signal selection: m 2 shapes K  0  0 K  0 K nucl.int. K3K3 Ke3 Signals and background have the same signature in m 2. K     0  0  with a  0 undergoing a Dalitz decay Incorrect cluster associated to the track Both give a m 2 lept under the Ke3 peak. K     0  with an early      give a m 2 lept under the K  3 peak

Barbara Sciascia – LNF 9 Background rejection K     0  0 are rejected cutting on E miss -P miss spectrum (<90MeV); the  0 momentum is obtained by mean of a kinematic fit K     0 events are rejected evaluating the missing momentum at the decay vertex, and cutting on momentum of the secondary track in the P miss rest frame (p  *<60 MeV) E miss -P miss (MeV) K   0  0 K   0,    K   0 e  K   0   K   0  0 p  *(MeV) K   0 l 

Barbara Sciascia – LNF 10 Signal selection: m 2 final shapes The previous cuts reject about 95% of background events The efficiency on the signal is: about 80% for both Ke3 and K  3 The residual background is about 2% of the selected K  l3 sample, and has the m  2 signature. Bkg K3K3 Ke3 K  0 K nucl.int. K  0  0

Barbara Sciascia – LNF 11 Fit of m 2 distribution Same behavior for all tag samples. K   2 tag sample shown. Correlation matrix from the fit: about 1% Ke3-K  3 correlation Fit results: Fitting all the sample, or fitting each one of 12 periods separately and adding together the events found, gives the same grand total within the errors.

Barbara Sciascia – LNF 12 The ingredients of the measurement BR(Kl3) = N(Kl3)  (  TAG (i) BR(i) ) N TAG (1-f NI )  FV  SELE  TAG (Kl3) Fit results Tag bias correction, from MC plus f NI correction  (TRK) DATA  TCA) DATA  1 ) DATA  2 ) DATA 4 tag samples  (TRK) MC  TCA) MC  1 ) MC  2 ) MC  SELE =  SELE_MC  CF Cosmic veto/T3 and FilFo correction to the Tag bias, from Data and MC K  nuclear interaction correction Fiducial volume efficiency  58%   About 14% for each sample

Barbara Sciascia – LNF 13 Tracking efficiency corrections: overview Neutral vertex technique (NV): reconstruction efficiency for kaon 1-prong decay chain from events with a neutral vertex reconstructed along the expected kaon decay path, obtained from the tag kaon (K  2 or K  2) and the  -boost information. Many samples can be defined: 0 - At least 1  0: only (  VTX,  K ) parameterization. 1 - K  2: also p LAB dependence, high momenta. 2 - Kl3: p  * dependence. 3 - K  ’: also p LAB dependence, low momenta. At blessing time, sample 0: from NV get a (  VTX,  K ) parameterization of the correction. No p LAB correction applied. MC and Data checks show the need of a momentum correction. Use sample 2 to correct the efficiency with a (  VTX,  K,p  *) parameterization. Estimate the systematic error of the correction from the comparison between the 2 and 1+3 samples.

Barbara Sciascia – LNF 14 TRK efficiency correction: reliability Method reliability: 50 <  K < 130 deg

Barbara Sciascia – LNF 15 Tracking efficiency corrections: Kl3 Ask for only 1  0 from NV Using the 2-body hypothesis, estimate the pion extrapolation to EMC. Reject events with a cluster associated with the extrapolation point. The “rest” has Kl3 purity of about 60%, and contamination from K  2 and K  ’ In this NV sample, look for a reconstructed kink+extrapolation to EMC (  VTX,  K,p  *) parameterization of the tracking correction:  VTX : 5 bins between 40 and 150 cm.  K : 3 bin between 50 o and 130 o. In each (  VTX,  K ) bin the correction is applied as a function of p  * (average over p LAB distribution). The Data/MC correction ranges between 70% and 90% following essentially the  VTX and the p  * values.

Barbara Sciascia – LNF 16 Tracking efficiency corrections: (K  ’,K  2) For both samples the missing momentum at vertex is an estimation of p LAB >(<) 140 MeV From NV with 1  0, estimate p  * and select events with p  *>170 MeV K  2: Kl3 about 12%, K  2 85% From NV with 2  0 ’s K  ’: Kl3 about 10%, K  ’ 75% (  VTX,  K,p LAB ) parameterization of the tracking correction Large errors on Data/MC correction, mostly for the low momentum range (K  ’). p   (MeV) K2K2 K’K’

Barbara Sciascia – LNF 17 TCA efficiency The Track-to-cluster association (TCA) efficiency for both electrons and muons is evaluated using K L e3 K L  3 events, identified by tight kinematical selection +NN (thanks to A.Sibidanov). Measured on period by period basis (only one period efficiencies and corrections are shown)

Barbara Sciascia – LNF 18 Single photon efficiency: the method Select events with K  2 or K  2 tag, to unbias the efficiency measurement for the trigger. Ask for a K  2 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 K  2+  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

Barbara Sciascia – LNF 19 Single  efficiency: Data and MC The single photon efficiency as a function of estimated energy of the photon, has been measured separately for different tags (K  2 or K  2) and charges. The efficiency behavior at high energy (similar to the K L      0 measurement) indicate a not completely correct acceptance definition.

Barbara Sciascia – LNF 20 Single  efficiency : correction to  SELE_MC 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.

Barbara Sciascia – LNF 21 Ke3  and K  3  acceptance The signal selection efficiency is sensitive to the presence of a photon in the final state. The simulation includes an IR-finite treatment (no energy cutoff) of radiation for all K decay. By neglecting the radiative BR(Ke3) changes of about 2%. The K +  2 sample is shown; all samples show the same trend. E  >30 MeV, 2.1×10 -2 E  > 30 MeV, 0.7×10 -3 K - e3  K-3K-3

Barbara Sciascia – LNF 22 BR(Kl3(  )) measurement -1 Fractional statistical contributions to the error: range from 1.8% to 5.9% following tag sample and signal. Ke3 dominated by the tracking efficiency corrections. K  3: tracking + TCA corrections

Barbara Sciascia – LNF 23 BR(Kl3) measurements -2 Comparison of independent measurements and corrections (statistical error only):  2 probabilities between 20% and 50% Very different tag bias values involved in the comaparison: from -3% (  TB =0.9694) to +4% (  TB =1.0371) Kaon nuclear interaction applied only to negative measurements. BR(Ke3) % BR(K  3) %

Barbara Sciascia – LNF 24 Systematics: overview The tag bias can be measured only on MC. The corrections to TB coming from Cosmic veto / T3 and Filfo have been evaluated on MC and downscaled Data samples (  CF ). Good agreement between Data and MC trigger efficiencies. No need of correction to tag bias for the auto triggering tags; but rely on MC trigger for tag bias evaluation. Kaon nuclear interactions: enter in the acceptance and in the tag bias evaluation. Have been measured on data. The effect on the BR measurement coming from a different value of the kaon lifetime has been evaluated using private MC samples. Study of the systematic error from Data/MC correction for tracking, clustering, and TCA efficiencies. Study of the systematic errors due to the selection cuts and to the fit procedure.

Barbara Sciascia – LNF 25 Measurement of K  nuclear interactions-1 Kaon nuclear interactions (NI) poorly known below 240 MeV. NI are needed to correct the kaon flux and enter in the Tag bias evaluation. Exploiting the charge dependency of K nuclear interactions,  NI (K + )<<  NI (K  ), the fraction of nuclear interacting negative kaons (f NI ) can be measured along the kaon decay path. MC(kine):.9827(5)

Barbara Sciascia – LNF 26 Measurement of K  nuclear interactions-2 The expressions can be estimated in MC and Data, and measure directly f NI using K  2 decays. Set as systematic error on f NI the MC(kine)-MC(method) difference. Use the measured f NI value also for tag bias. TagKINEMethod (MC)Method (Data) K2K2.9827(5).9864(27).9922(32) K2K2.984(1).9837(48)1.0040(57)

Barbara Sciascia – LNF 27 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   2,K  all 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.

Barbara Sciascia – LNF 28 Trigger Due to the auto triggering tags, the trigger does not enter directly in the measurement. However the tag bias rely on the MC trigger. Two methods to compare trigger behavior on Data and MC applied to charged kaon events. 1. Measure EmC-trigger efficiency wrt the DC trigger:  (EMC/DC) From MC, evaluate the correlation factor, C TRG, between DC and EmC Trigger, and correct  (EMC/DC) from data, using C TRG (statistical errors only): C TRG  Data MC Truth KK   KK   Data and MC truth difference at the 0.1 % level with both methods C  EMC (Data) KK  0.23 KK  Two-hemisphere method. Dividing the event cluster into two exclusive parts allow to measure a “hemisphere trigger efficiency”, from which a trigger efficiency per event can be built. The “division of the event” has a degree of arbitrariness, which has been used to set the error of the method.

Barbara Sciascia – LNF 29 Tag bias The auto-triggering K  2 K  2 tags imply  TRG|TAG (i)=1  i. The effects of cosmic veto/T3 as well as that of FilFo (FILtro di FOndo) have been taken from MC. The different behavior of FilFo and CV/T3 on Data and MC have been measured on control samples, and used to correct the MC tag bias value. The values of tag bias per tag sample and per signal, accounting also for FilFo and cosmic veto/T3 corrections, are: TagBias(i) =  BR(k)  TAG (k)  TRG | TAG (k)  FilFo|TRG (k)  CV|FilFo (k)  TAG (i)  TRG | TAG (i)  FilFo|TRG (i)  CV|FilFo (i) The general formula of the tag bias for the i th decay channel is: Tag K+2K+2K+2K+2K-2K-2K-2K-2 Ke (11)1.0137(34)0.9884(10)1.0328(23) K  (13)1.0210(36)0.9963(10)1.0371(25) The error comes from the statistics used for both TB evaluation and TB corrections.

Barbara Sciascia – LNF 30 FilFo. The correction is: It has been evaluated on MC and on the 1:10 downscaled events of the first 50 pb -1 of Datarec22 reprocessed Data. It is about 1.5% for K  2 tags, and at the 0.1% level for the K  2 tag samples. Tag bias: Data/MC corrections  FilFo|TRG DATA (i) DATA  FilFo|TRG MC (i) MC Cosmic veto. The correction coming from the CV and the T3 filter: has been evaluated on MC and on Data downscaled samples; it is at the level for all tag sample. The contribution to BR error is negligible.  CV|FilFo DATA (i) DATA  CVFilFo MC (i) MC

Barbara Sciascia – LNF 31 Tag bias: FilFo correction - 1 Cosmic ray rejection accounts for one half of the correction (  0.8%) Some rejection criteria matched by charged kaon timing and/or topology Energy and/or time difference between plane 5 and plane 1 Crossing velocity.

Barbara Sciascia – LNF 32 Tag bias: FilFo correction - 2 Machine background rejection accounts for about one half (0.7%) of the correction for K  2 tag. Little contribution from “true” machine background. Some charged kaon event topology match the “small/big cell ratio” criterium. Tag K  2 + SignalTag K  2 only Due to a tricky combination of different rejection criteria, K  2 tagged events are more FilFo-rejected than K  2 tagged.

Barbara Sciascia – LNF 33 Summary on Tag bias evaluation Tag K+2K+2K+2K+2K-2K-2K-2K-2 Fractional systematic error CV0.04%0.02%0.03%0.04% FilFo 0.36%0.06%0.37%0.05% NI0.09%0.13%-- Trg0.26% 0.18% Tot0.45%0.30%0.41%0.19% Tag Bias (Statistical) (Systematic) Ke (11)(44)1.0137(34)(30)0.9884(10)(40)1.0328(23)(20) K  (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 f NI systematic contribution has been chosen as the whole correction. Due to the “auto-trigger” requirement, the systematic trigger error comes from the reliability of the MC-trigger wrt the real one. This has been studied with two different methods and gives a systematic error of about 0.2% The stability of tag bias value wrt the kinematical selection of the tag has been checked; the contribution to the systematic error is negligible.

Barbara Sciascia – LNF 34 Tracking efficiency correction-1 Estimate the systematic error from the comparison of the BR’s results calculated using for tracking correction the samples, Kl3 and (K  ’,K  2) which have very different contaminations (40% vs 90%) K  e3 0.4%, K + e % K   3 0.5%, K +  %, (fractional). Use the Kl3 correction because of the smaller statistical error. Check the correction by comparing the branching ratio calculated in sub samples with very different tracking corrections. Halving the Kl3 signal sample into independent samples following the Low/High values of the variables used for the tracking corrections. The average correction in the two sub-samples differs of about 20%: from  75% to  95%. 1 – Transverse vertex position (  VTX ) BR(ke3) BR(k  3)

Barbara Sciascia – LNF 35 Tracking efficiency correction-2 2- Kaon polar angle (  K ) 3- Momentum dependence (p  *) The systematics calculated from the comparison is negligible. These checks were WRONG using the old (blessing measurement) tracking correction… or better THESE CHECKS CAUSED THE CHANGE ON TRACKING CORRECTION STRATEGY. BR(k  3) BR(ke3)

Barbara Sciascia – LNF 36 TCA and Tracking corrections Data/MC efficiency From the difference of BRs calculated in the p LAB 140 MeV subsamples. Different correction in the two regions, especially for muons (K  3 events) Test both TCA and TRK correction (TRK correction is applied as a function of p*  ). Negligible contribution to the error. For preliminary BR results: due to old  -TCA correction require p LAB >90 MeV, and obtain cut acceptance from MC. p LAB <90MeV region: larger TRK and TCA Data/MC corrections. 90 MeV

Barbara Sciascia – LNF 37  0 corrections From the difference of BRs calculated in the E min 70 MeV subsample. E min more sensitive to clustering efficiency correction. Negligible contribution to the error.

Barbara Sciascia – LNF 38 Selection efficiency systematics K   0,    K   0 e  K   0   K   0  0 p  *(MeV) Systematics due to the selection are evaluated varying the cut values. The most relevant contribution comes from the K  2 rejection cut (p  *). The chosen cuts minimizes the correlation between Ke3 and K  3 in the fit. BR as a function of the p  * cut efficiency (from 40 to 90 MeV). The systematic errors from p  * cut are 0.3% fractional on Ke3, and 0.6% on K  3.

Barbara Sciascia – LNF 39 Selection efficiency systematics 195 MeV From the p star  vs the p star  distribution check the effects of the p star  60 MeV cut. Very narrow residual p star   peak. m 2  signature in m 2 distribution. Systematic error from BRs difference w/wo p star  cut: - about 0.1% for Ke3, - about 0.4% for K  3.

Barbara Sciascia – LNF 40 Definition of an enriched Kl3 sample Tag events by using the K  2 decay without “auto-trigger”: about 70% of the kinematical selected sample. Apply the same signal selection cuts. Control sample larger than the one used for the measurement. Define “enriched” Ke3 and K  3 samples using (E/p,E miss -P miss ) plane: Purity (by MC):  98% for both signals (for K  3 apply also m 2 >3200MeV 2 ) Used to check fit shapes.

Barbara Sciascia – LNF 41 Fit shapes - 1 Count K  3 events in the (3400MeV 2,30000MeV 2 ) region, in which the K  3 acceptance is about 99%. Count Ke3 events in the (-15000MeV 2,6800MeV 2 ) region, in which the Ke3 acceptance is about 97%. Compare fit output obtained using different shapes to fit the m 2 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:

Barbara Sciascia – LNF 42 Fit shapes 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 K  3-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   2 sample. Assume 10% of uncertainty on the “not-included” part: 0.3% for Ke3, 0.1% for K  3

Barbara Sciascia – LNF 43 Fit window selection Fit also m2 tails outside the fit window: -(122MeV) 2,(173 MeV) 2 Systematic from the BRs difference measured including or not including the tails in the fit window: about 0.1% for Ke3 about 0.4% for K  3

Barbara Sciascia – LNF 44 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.

Barbara Sciascia – LNF 45 Summary on systematics: K  3 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).

Barbara Sciascia – LNF 46 Results: BR(Kl3) Br (Stat) (Syst) (%) K  e (84) (44) K  e (93) (46) K3K (88) (47) K3K (80) (47) Ke (62) (45) K3K (59) (47) Average of the four result per charge and per decay taking correlations into account: The errors are dominated by the statistical contribution through the statistics of TRK correction for Ke3 and TRK+TCA corrections for K  3 Efficiency and tag bias corrections induce a 41.7% of correlation between the Ke3-K  3 branching ratio measurements.

Barbara Sciascia – LNF 47 R  e =  (K  3)/  (Ke3) Calculate R  e =  (K  3)/  (Ke3) in the four tag samples used for BR mm. R  e = (N  3 /N e3 ) (  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 K  3 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. Average: R  e =0.649(7) Stat (10) Syst From theory: R  e =0.6606(31); comparison with KLOE mm  2 = 0.91/1 ( + ’, + ’’ from pole=0.8753(54)GeV, 0 = (95))

Barbara Sciascia – LNF 48 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. Using a different tracking correction, doesn’t change BR values The final results have a fractional accuracy of 1.5% for BR(Ke3) and 2.2% for BR(K  3). The R  e has been measured with 1.9% of fractional accuracy, and is in agreement with the theoretical prevision.

Barbara Sciascia – LNF 49 Spare slides

Barbara Sciascia – LNF 50 Tracking efficiency corrections-spare p   (MeV) K2K2 Kl3

Barbara Sciascia – LNF 51 Tracking efficiency correction: systematics We need the Data/MC tracking efficiency ratio for signal:  D S /  MC S. The correction evaluated on the control sample can be parameterized as: Estimate the systematic error from the comparison of the BR’s results calculated using for tracking correction the samples, Kl3 and (K  ’,K  2) which have very different contaminations (40% vs 80%) K  e3 0.4%, K + e % K   3 0.5%, K +  %, (fractional).  D (  MC ) is the background contamination on data (on MC)  D B (  MC B ) is the efficiency for the background. Possible bias if MC doesn’t reproduce  D B /  D S and the contamination  D.

Barbara Sciascia – LNF 52 Selection efficiency systematics

Barbara Sciascia – LNF 53 Selection efficiency systematics

Barbara Sciascia – LNF 54 Trigger: EMC/DC-1 DC/EMC EMC/DC Measure EmC-trigger efficiency wrt the DC trigger:  (EMC/DC) (errors are statistical only) DataMC KK   KK    (EMC/DC) is stable within the errors wrt the threshold requirement at the 2 nd level DC trigger.  (EMC/DC) Data

Barbara Sciascia – LNF 55 Trigger: EMC/DC-2 C TRG  Data MC Truth KK   KK   From MC, evaluate the correlation factor, C TRG, between DC and EmC Trigger Correct  (EMC/DC) from data, using C TRG Compare with MC truth (errors are statistical only): Difference at the 0.1 % level (0.14% for K  and 0.06% for K  ) First check of the reliability of Tag-bias measurement for what concern Emc-global-trigger.

Barbara Sciascia – LNF 56 Trigger: “Two-hemisphere method”-1 “Two-emisphere method” (KLOE memo 223) successfully used in studying trigger efficiency in neutral kaon analyses KKKK  KKKK eeee   Define:  EMC =1  P(Tag=1)  P(DarkSide=0) where: - P(Tag=1): probability for the selected “Tag Emisphere” of firing only one trigger sector (here the  -cluster) - P(DarkSide=0): probability for “the rest of the event” (included machine bkg clusters) of not firing any sectors

Barbara Sciascia – LNF 57 Trigger: “Two-hemisphere method”-2 The “division of the event” has a degree of arbitrarity which can be kept under control defining a MAX and a min probability for the selected list of clusters: P   P; with  P = P MAX  P Min Good agreement within the errors between MC and Data Reliability of the method:  0.8% of difference wrt the MC truth Correcting data with factor C =  EMC (MC)/  EMC (MCtruth) we get  EMC (Data) values in very good agreement with Mctruth. Good check of trigger effects on tag-bias evaluation.  EMC (Data)  EMC (MC) KK   0.25 KK   0.25  EMC (MCtruth)   C  EMC (Data) KK  0.23 KK  0.25

Barbara Sciascia – LNF 58 Fit of m 2 distribution-spare Fit of Data Use kpm04 + all_phys MC productions Signals: Ke3 and K  3 shapes; bkg: “the rest” Correct MC shapes for: Measured  (  t) (  0 photons from kaon decay vertex) difference between Data and MC (14  18 ps shift). ToF in Emc (“Pezzetto” correction) in m e hypothesis, correct K  3 for the difference  DATA –  MC (20  24 ps shift).

Barbara Sciascia – LNF 59 Fiducial volume efficiency-2 A second order correction in the ratio  SELE_MC  DATA   MC . Final check: direct calculation of  SELE_MC  DATA   MC  using two more private MC samples (f = 0.98, 1.02) with K   2 and K  l3. Check also the possible effect coming from the tag reconstruction. Rec. tag, Ke3 Kine tag, Ke3 Kine tag, K  3 Rec. tag, K  3

Barbara Sciascia – LNF 60 Measurement of K  nuclear interactions-1 Kaon nuclear interactions (NI) poorly known below 240 MeV. NI are needed to correct the kaon flux and enter in the Tag bias evaluation. Exploiting the charge dependency of K nuclear interactions,  NI (K + )<<  NI (K  ), the fraction of nuclear interacting negative kaons (f NI ) can be measured along the kaon decay path. Some calculations are needed:

Barbara Sciascia – LNF 61 Measurement of K  nuclear interactions-2  K (ns) MC(kine):.9827(5) MC(method) The expressions can be estimated in MC and Data, and measure directly f NI using K  2 decays. Set as systematic error on f NI the MC(kine)- MC(method) difference. Use the measured f NI value also for tag bias. 1-f NI TagKINEMethod (MC)Method (Data) K2K2.9827(5).9864(27).9922(32) K2K2.984(1).9837(48)1.0040(57)