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Analysis of ratio BR( K     0 )/BR(K    )

Analysis of ratio BR( K     0 )/BR(K    ). Motivation Selection and cuts Trigger efficiency Signal and Background fit Selection efficiency Result and conclusion. M. Martemianov V. Kulikov. Motivation / I.

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Analysis of ratio BR( K     0 )/BR(K    )

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  1. Analysis of ratio BR(K  0)/BR(K ) • Motivation • Selection and cuts • Trigger efficiency • Signal and Background fit • Selection efficiency • Result and conclusion M. Martemianov V. Kulikov

  2. Motivation / I ChPT theory for K decays gives total amplitude as mixture of two isospin (I=0 and I=2) amplitudes :  • CPM (chiral pole model) predicts amplitude A(K+ + 0) by formula • PDG values : GF= 1.16610-5 GeV (Fermi constant) • sinc = 0.2196 and cos c = 0.9734 (c - Cabibbo angle) • f+(0) = 0.96 and f  = 93 MeV

  3. Motivation / II • Using PDG constants and the most precise experiment : • Difference between prediction and experiment : 3.8 % • First step : measurement of Best experiment, LEAR (CERN), 1992 at precision around (less ?) 1 % Precision 1.5 %

  4. Statistical estimation of result • DST - version N 15 for kpm - stream • Run numbers : 23542-27133 (2387 DST - files) • All runs of 2002 year • Total statistics : 283.5 pb-1 • Number of pions candidates : 1.649  106 • Number of muons candidates : 4.919  106 • Selected  - window : 190 - 220 MeV/c • Selected  - window : 220 - 260 MeV/c •  - hyphotesis for secondary particles Statistical error on the level of 0.1 %

  5. Tag strategy • Ktrigger - trigger efficiency, extracted from EXP. data • Kfit- efficiency of signals and background rejection, based on MC data and performed of EXP data, • Ksel- selection efficiency, from MC and EXP. data • Kvetocos - efficiency of cosmic veto rejection, EXP. data

  6. Secondary track selection • Kaon candidates from ECLO2 • Only events with two kaonsand Charge1 x Charge2 < 0 • Selection by momenta in the first point in DC 40 < PK < 160 MeV/c • At least one secondary kaon vertex with 40 cm < Rxy < 150 cm, |Z| < 210 cm • 20 MeV/c < P sec < 320 MeV/c • Rejection of “Splitted” tracks (events with |PK- P_sec| < 40 MeV/c . AND . DF < 80 . OR . DF > 1720) , where DF = | - |  - acos (PK P sec)||  “Wrong” orientation of tracks 0 Splitted tracks

  7. Trigger efficiency / I Drift Chamber 1 K+ K+  ,  K K 2 • + - trigger : • Based on DC track information • Two tracks go to ECL • Rejection tracks fired same ENDCAP • Auto - triggering for K+, based on EMC trigger • Trigger effciency = 100 % • Pion trigger (from K+ +0) based on the maximal number of clusters = 3, muon trigger (from K+ +) number of clustres = 1

  8. Trigger efficiency / II • Linear fit for both trigger (p0) •  - auto - triggering : p0 = 0.3348  0.0008(stat.) •  - auto - triggering : p0 = 0.3341  0.0007(stat.) • Trigger difference : 0.0007  0.0008 (trigger error = 0.2 % ) •  - tag, no auto-triggering : p0 = 0.3356  0.0004(stat.) •  - auto - triggering : p0 = 0.3341  0.0008(stat.) • Trigger difference : 0.0014  0.0008 (trigger error = 0.4 % )

  9. 0 - selection • Number of clusters > 2 • No association to charged track • Ecl > 25 MeV • | t | < 3 ns • Search a minimum : | (Ecl1 + Ecl2) - M(0) | • 50 < M(0) < 210 MeV •  space < 30 0, where  space - angle between 0 momenta from ECL and calculated from DC  space | Mfit(0) - M(0) |  0.7 MeV

  10. Selection of K  decays • Rejected clusters associated to the neutral tracks • Minimum | (Ecl1 + Ecl2) - M(0) | if 0 has common clusters for both vertex MC • Procedure needs to get a clear signal for the both peak in windows • Good selection of  - decay, small contamination of 0 - events survived • Selection didn’t change the shape of two peak’s shape All selected events Events with reconstructed as pions from K 0 Events selected as muons from K 

  11. Three-body decays • Four main modes in geanfi : • K      • K e0 • K  0 • K    0 0   Sum = 15.3 % 0 - selection doesn’t change shape of three - body decays 2 = 1.2 MC data MC data + 0 - sel. MC data

  12. Description of  - peak Exp. tails  - backg.  three-body backg. • Step N2 : • Experiment - extracting launch shape of peak for experimental data • Two contributions :  and three - body background Step N1 : Pure MC - extracting launch shape of peak (3 Gaussians at the same mean value + 2 exponential functions due to effect of multiple scattering)

  13. Description of  - peak Exp. tails  -backg.  Step N1 : Pure MC - extracting launch shape of peak (4 Gaussians, each 2 Gaussians have the same mean value + 2 exponential functions) • Step N2 : • Experiment - extracting launch shape of peak for experimental data • One contribution :  - background

  14. Fit of two peaks • Fit gives a full description of all type of kaon decays in DC • f(x)three - extracted from MC

  15. Total statistics • All data diveded on 5 sets 

  16. Fit quality

  17. Correction coefficient on background Correction coeff. physical background Ratio as function of data set Linear fit gives : Kfit=0.9255  0.0012(fit.) Fit error :0.13 % Linear fit gives : 0.3352  0.0003(stat.) Stat error : 0.09 %

  18. Comparison data / MC Fit can be checked by MC data using the same way : MC : EXP : Kfit = 0.9255  0.0012 Ratio = 0.3352  0.0003 Ratio  Kfit = 0.3102  0.0012 KMC = 97.10  0.25 % Kfit = 96.66  0.24 % Ratio = 0.3174  0.0006 Ratio  Kmc = (0.30863  0.00055)MC • On MC fit and real number of ratio coefficient are very close (difference = 0.44  0.35) (contribution to the syst. error) • Total MC correction coefficient : Ksel. = 1.080  0.002

  19. Selection efficiency / I Ksel = decay vertex  window • decay - correction on decay of charged pions • vertex - selection of vertex for pions and muons • window - correction of signals for all momentum range • decay - can be extracted on MC only using a convenient cut on the track length of secondary particles • vertex, window - estimated on MC and EXP, must be different in MC and EXP. Data due different momentum resolution

  20. Selection efficiency/ II Calculation of decay • Distributions on MC and EXP are the same • Cut for tracks length on all tracks (> 40 cm) gives • decay = 1.0443  0.0016 (stat.) • Main part of this value (1.036) can be calculated from PDG pion decay length, its mass and averaged laboratory momentum (205 MeV/c). • The rest can be attributed to pion decay at larger than 40 cm length with spoiled reconstraction of the pion track due to the presence of pion decay product.

  21. Selection efficiency/ IV Calculation of window • Based on fit parameters • Calculates the percentage muons and pions inside window • Different for MC and EXP data • Exp. data • Correction for pions : 96.3 % • Correction for muons : 99.5 % • Correction coefficient for windows by fit : 1.030  0.002(stat.) (0.2 %) • MC. data • Correction for pions : 97.2 % • Correction for muons : 99.2 % • Correction coefficient for windows by fit : 1.019  0.003 • MC real coefficient : 1.020  0.003

  22. Selection efficiency/ V Calculation of vertex vertex = vertex  cuts EMC - cluster K+ Investigated vertex Investigated vertex K+ K  + K 1 2 Two EMC clusters only for charged tracks, + - seleclted by momenta Two EMC clusters only for charged tracks, + - seleclted by momenta, two clusters from gammas

  23. Selection efficiency/ VI Selected muons Selected pions Efficiency of vertex efficiency for muons and pions as function of kaons momenta Mean value of efficiency (sum by all kaons momenta gives vertex efficiency : Pions : 86.79  0.18 %, Muons : 86.65  0.08 % Difference : 0.14  0.20 %(contribution of stat error for vertex efficiency)

  24. Selection efficiency/ VI Calculation of cuts • Calculated by MC and corrected by EXP • Includes cuts to reject splitted tracks and cuts on momenta of secondary tracks • MC : cuts = 1.0137  0.0016(stat) • Difference between MC and EXP based only on momenta cuts on high region (main contribution based on muons)and differnece equal to 0.5 % • EXP : cuts = 1.0086  0.0020(stat)  from K   from K  0 MC distribution of the secondary particles in the laboratory system for muons and pions

  25. Summary of selection efficiency

  26. Cosmic veto S = N(vetocos=0) + N(vetocos=1,t3flag=0)+N(t3flag=1) Kvetocos = 1+64N(t3flag=1) / S • Check cosmic veto for runs 26111-27133 Type of events vetocos = 0 vetocos =1 t3flag = 1 Kvetocos +,   4.789106 4466 5564 1.00073  0.00010  +0, 0 0.621106 111 5 64 1.00051  0.00020 No difference between rejection of different type of event by cosmic veto on the level 210 4

  27. Corrections and erros *) Taken from previous experiments, we plan to recalculate the coefficient, but now use the same value to compare with pevious experiments.

  28. Comparison with world data

  29. Conclusion • was measured • Result has a good agreement with world data • Statistical error is negligible due to the huge sample of kaon decays (more than 6.5 M). • Systematic error ( 0.65 %) dominates. It improves accuracy for the ratio by a factor of 2.7 • In principal, result can be updated by further investigation of MC / EXP uncertanties and true calculation of K  decay

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