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

1 Barbara Sciascia – LNF Barbara Sciascia Barbara Sciascia

Measurement of the Measurement of the absolute branching ratio absolute branching ratio of Kof K

l3l3 decays and of the decays and of the

RRee ratio ratioBlessing meeting of the final results Blessing meeting of the final results

14 June 2006 - LNF14 June 2006 - LNF

2 Barbara Sciascia – LNF

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(K0e), BR(K0), and (K0)/(K0e)

• Conclusions


Introduction• Measurement of the K semileptonic decays to measure VUS

• Absolute BR measurement via a Tag technique.• Use 2 Tag: K2 + -trigger K2 + 0-trigger• 2 Tag 2 Charge 4 independent samples.• Counting Kl3 from the fit of a m2 distribution.• Efficiency from MC + corrections from Data/MC efficiency ratio

• Data sample: 2001+2002, 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)


Tag selection - 1

• Use only TagDecay algorithm of the Event Classification. • track from IP, momentum cut: 70 MeV pK 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 (K2) or K0 (K2) decays• 4 independent samples: K+2, K+2, K-2, and K-2

p(m) = 236 MeV p(m) = 205 MeV


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 K2: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:

KK

KK


Tag selection - 3

• For each kaon charge, 2+1 different tag samples: K2+Trg, K2+0Trig, and K2+NoTrg. Tagging efficiency: 8% for each tag sample.• 2 tag × 2 charge = 4 samples for the measurements ( 60x106 tag)

• The contamination from .not.Kpm events is negligible:

• 1 tag × 2 charge = 2 control samples ( 60x106 tag):


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)<3t)

• Spectrum of charged daughter mass, m2

lept, from TOF measurement:

tdecayK = tlept -Llept /(leptc) = t-L/c

KK

KK

ee

Selection of K± semileptonic decays (Kl3)

• Fit m2lept spectrum with a linear

combination of Ke3 and K3 shapes, and background contribution.


Signal selection: m2 shapes

K00

K0

K nucl.int.

K3Ke3• Signals and background have the same signature in m2. • K00 with a 0 undergoing a Dalitz decay• Incorrect cluster associated to the track• Both give a m2

lept under the Ke3 peak.

• K0 with an early give a m2

lept under the K3 peak


Background rejection

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

• K0 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


Signal selection: m2 final shapes • The previous cuts reject about 95% of background events• The efficiency on the signal is: about 80% for both Ke3 and K3

• The residual background is about 2% of the selected Kl3 sample, and has the m

2 signature.

Bkg

K3Ke3

K0 K nucl.int.

K00


Fit of m2 distribution

• Same behavior for all tag samples.• K2 tag sample shown.•Correlation matrix from the fit: about 1% Ke3-K3 correlation

• Fit results:

•Fitting all the 2001-2002 sample, or fitting each one of 12 periods separately and adding together the events found, gives the same grand total within the errors.


The ingredients of the measurement

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

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

Fit results

Tag bias correction,from MC plus fNI 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/T3and FilFo correctionto the Tag bias, from Data and MC

K nuclear interaction correction

Fiducial volumeefficiency 58%

About 14% for each sample


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 (K2 or K2) and the -boost information.

• Many samples can be defined: 0 - At least 1 0: only (VTX, K) parameterization. 1 - K2: also pLAB dependence, high momenta. 2 - Kl3: p* dependence. 3 - K’: also pLAB dependence, low momenta.• At blessing time, sample 0: from NV get a (VTX, K) parameterization of the correction. No pLAB 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.


TRK efficiency correction: reliability

Method reliability:50 < K< 130 deg


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 K2 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 50o and 130o.• In each (VTX,K) bin the correction is applied as a function of p* (average over pLAB distribution).• The Data/MC correction ranges between 70% and 90% following essentially the VTX and the p* values.


Tracking efficiency corrections: (K’,K2)

• For both samples the missing momentum at vertex is an estimation of pLAB>(<) 140 MeV

• From NV with 1 0, estimate p* and select events with p*>170 MeV • K2: Kl3 about 12%, K2 85%

• From NV with 2 0’s• K’: Kl3 about 10%, K’ 75%

• (VTX,K,pLAB) parameterization of the tracking correction

• Large errors on Data/MC correction, mostly for the low momentum range (K’).

p(MeV)

K2

K’


TCA efficiencyThe 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).

Measured on period by period basis (only one period efficiencies and corrections are shown)


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


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 (K2 or K2) and charges.• The efficiency behavior at high energy (similar to the KL0 measurement) indicate a not completely correct acceptance definition.


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.


Ke3 and K3 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


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.

• K3: tracking + TCA corrections


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

(K3

) %


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.


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 (fNI) can be measured along the kaon decay path.

MC(kine): .9827(5)


Measurement of K nuclear interactions-2

• The expressions can be estimated in MC and Data, and measure directly fNI using K2 decays. • Set as systematic error on fNI the MC(kine)-MC(method) difference.• Use the measured fNI value also for tag bias.

Tag KINE Method (MC) Method (Data)

K2 .9827(5) .9864(27) .9922(32)

K2 .984(1) .9837(48) 1.0040(57)


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.


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, CTRG, between DC and EmC Trigger, and correct (EMC/DC) from data, using CTRG (statistical errors only):

CTRGData MC Truth

K 92.752 0.003

92.896 0.007

K 92.949 0.003

93.007 0.007• Data and MC truth difference at the 0.1 % level with both methods

CEMC(Data)

K 92.64 0.23

K 92.83 0.25

2. 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.


Tag bias

• The auto-triggering K2 K2 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 ith decay channel is:

Tag K+2 K+2 K-2 K-2

Ke3 0.9694(11) 1.0137(34) 0.9884(10) 1.0328(23)

K 0.9756(13) 1.0210(36) 0.9963(10) 1.0371(25)

• The error comes from the statistics used for both TB evaluation and TB corrections.


• 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 K2 tags, and at the 0.1% level for the K2 tag samples.

Tag bias: Data/MC corrections

FilFo|TRGDATA(i)

< BR(k) FilFo|TRG(k)>DATA FilFo|TRGMC(i)

< BR(k) FilFo|TRG(k)>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 10-4 level for all tag sample. The contribution to BR error is negligible.

CV|FilFoDATA(i)

< BR(k) CV|FilFo(k)>DATA CVFilFoMC(i)

< BR(k) CV|FilFo(k)>MC


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.


Tag bias: FilFo correction - 2• Machine background rejection accounts for about one half (0.7%) of the correction for K2 tag.• Little contribution from “true” machine background.• Some charged kaon event topology match the “small/big cell ratio” criterium.

Tag K2 + SignalTag K2 only

• Due to a tricky combination of different rejection criteria, K2 tagged events are more FilFo-rejected than K2 tagged.


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% - -

Trg 0.26% 0.26% 0.18% 0.18%

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.• 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.


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’,K2) which have very different contaminations (40% vs 90%)

Ke3 0.4%, K+e3 0.03 % K3 0.5%, K+3 0.01%, (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(k3)


Tracking efficiency correction-22- 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(k3) BR(k3)

BR(ke3) BR(ke3)


TCA and Tracking correctionsData/MC efficiency• From the difference of BRs calculated

in the pLAB<140MeV and pLAB>140 MeV subsamples.• Different correction in the two regions, especially for muons (K3 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 pLAB>90 MeV, and obtain cut acceptance from MC.• pLAB<90MeV region: larger TRK and TCA Data/MC corrections.

90 MeV

90 MeV


0 corrections

• From the difference of BRs calculated in the Emin<70MeV and Emin>70 MeV subsample.

• Emin more sensitive to clustering efficiency correction.

• Negligible contribution to the error.


Selection efficiency systematics

K0,

K0e

K0

K00

p*(MeV)

Systematics due to the selection are evaluated varying the cut values. The most relevant contribution comes from the K2 rejection cut (p*).

• The chosen cuts minimizes the correlation between Ke3 and K3 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 K3.



195 MeV

• From the pstar vs the pstar

distribution check the effects of the pstar

<195 MeV cut vs the pstar

>60 MeV cut.• Very narrow residual pstar

peak.• m2

signature in m2 distribution.• Systematic error from BRs difference w/wo pstar

cut: - about 0.1% for Ke3, - about 0.4% for K3.


Definition of an enriched Kl3 sample

• Tag events by using the K2 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 K3 samples using (E/p,Emiss-Pmiss) plane:• Purity (by MC): 98% for both signals (for K3 apply also m2>3200MeV2)• Used to check fit shapes.


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:


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


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 K3


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: 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).


Results: BR(Kl3)

Br (Stat) (Syst) (%)

Ke3 5.224 (84) (44)

Ke3 5.309 (93) (46)

K3 3.379 (88) (47)

K3 3.449 (80) (47)

Ke3 5.263 (62) (45)

K3 3.417 (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 K3• Efficiency and tag bias corrections induce a 41.7% of correlation between the Ke3-K3 branching ratio measurements.


Re = (K3)/(Ke3)• 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.

• Average: Re=0.649(7)Stat(10)Syst • From theory: Re=0.6606(31); comparison with KLOE mm 2 = 0.91/1(+’,+’’ from pole=0.8753(54)GeV, 0=0.01587(95))


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(K3).• The Re has been measured with 1.9% of fractional accuracy, and is in agreement with the theoretical prevision.


Spare slides


Tracking efficiency corrections-spare

p(MeV)

K2Kl3


Tracking efficiency correction: systematics• We need the Data/MC tracking efficiency ratio for signal: D

S/MCS.

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’,K2) which have very different contaminations (40% vs 80%)

Ke3 0.4%, K+e3 0.03 % K3 0.5%, K+3 0.01%, (fractional).

D (MC) is the background contamination on data (on MC)D

B (MCB) is the efficiency for the background.

• Possible bias if MC doesn’t reproduce DB/D

S and the contamination D.






Trigger: EMC/DC-1

DC/EMC

EMC/DC

• Measure EmC-trigger efficiency wrt the DC trigger: (EMC/DC) (errors are statistical only)

Data MC

K 94.982 0.003 95.130 0.006

K 95.129 0.003 95.188 0.006

• (EMC/DC) is stable within the errors wrt the threshold requirement at the 2nd level DC trigger.

(EMC/DC) Data


Trigger: EMC/DC-2

CTRGData MC Truth

K 92.752 0.003 92.896 0.007

K 92.949 0.003 93.007 0.007

• From MC, evaluate the correlation factor, CTRG, between DC and EmC Trigger• Correct (EMC/DC) from data, using CTRG • 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.


Trigger: “Two-hemisphere method”-1 • “Two-emisphere method” (KLOE memo 223) successfully used in studying trigger efficiency in neutral kaon analyses

KK

KK

ee

•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


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 = PMAX PMin

• 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 effectson tag-bias evaluation.

EMC(Data) EMC(MC)

K 91.96 0.23 92.21 0.25

K 92.09 0.25 92.27 0.25

EMC (MCtruth)

92.896 0.007

93.007 0.007

CEMC(Data)

K 92.64 0.23

K 92.83 0.25


Fit of m2 distribution-spare

• Fit of 2001+2002 Data • Use kpm04 + all_phys MC productions• Signals: Ke3 and K3 shapes; bkg: “the rest”

Correct MC shapes for:• Measured (t) (0 photons from kaon decay vertex) difference between Data and MC (1418 ps shift). • ToF in Emc (“Pezzetto” correction) in me hypothesis, correct K3 for the difference DATA–MC (20 24 ps shift).


Fiducial volume efficiency-2

• A second order correction in the ratio SELE_MCDATA MC.• Final check: direct calculation of SELE_MCDATA MC using two more private MC samples (f = 0.98, 1.02) with K2 and Kl3.• Check also the possible effect coming from the tag reconstruction.

Rec. tag, Ke3 Kine tag, Ke3

Kine tag, K3Rec. tag, K3


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 (fNI) can be measured along the kaon decay path. Some calculations are needed:


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 fNI using K2 decays. • Set as systematic error on fNI the MC(kine)-MC(method) difference.• Use the measured fNI value also for tag bias.

1-fNI

Tag KINE Method (MC) Method (Data)

K2 .9827(5) .9864(27) .9922(32)

K2 .984(1) .9837(48) 1.0040(57)

Documents

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