1. M. Martemianov, ITEP, October 2003 Analysis of ratio BR(K     0 )/BR(K    ) M. Martemianov V. Kulikov Motivation Selection and cuts Trigger efficiency Signal and Background fit Selection efficiency Result and conclusion

2. M. Martemianov, ITEP, October 2003 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 : G F = 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. M. Martemianov, ITEP, October 2003 Motivation / II  Using PDG constants and the most precise experiment :  Difference between prediction and experiment : 3.8 % Best experiment, LEAR (CERN), 1992  First step : measurement of at precision around (less ?) 1 % Precision 1.5 %

4. M. Martemianov, ITEP, October 2003 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  10 6  Number of muons candidates : 4.919  10 6 Statistical estimation of result  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. M. Martemianov, ITEP, October 2003  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  K vetocos - efficiency of cosmic veto rejection, EXP. data Tag strategy

6. M. Martemianov, ITEP, October 2003   0 Splitted tracks “Wrong” orientation of tracks  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 |P K - P_sec| 172 0 ), where DF = |  - |  - acos (P K  P sec)|| Secondary track selection  Kaon candidates from ECLO2  Only events with two kaons and Charge1 x Charge2 < 0  Selection by momenta in the first point in DC 40 < P K < 160 MeV/c

7. M. Martemianov, ITEP, October 2003 Trigger efficiency / I  ,   22 11 KK K+K+ Drift Chamber  KK K+K+  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  + - trigger :  Based on DC track information  Two tracks go to ECL  Rejection tracks fired same ENDCAP

8. M. Martemianov, ITEP, October 2003 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. M. Martemianov, ITEP, October 2003  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 | M fit (  0 ) - M(  0 ) |  0.7 MeV  space

10. M. Martemianov, ITEP, October 2003 Selection of K     decays All selected events Events with reconstructed as pions from K      0 Events selected as muons from K      Rejected clusters associated to the neutral tracks  Minimum | (Ecl1 + Ecl2) - M(  0 ) | if  0 has common clusters for both vertex  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 MC

11. M. Martemianov, ITEP, October 2003 Four main modes in geanfi :  K        K   e   0  K      0  K     0  0 Three-body decays  Sum = 15.3 %   0 - selection doesn’t change shape of three - body decays  2 = 1.2 MC data MC data +  0 - sel.

12. M. Martemianov, ITEP, October 2003 Description of  - peak  Exp. tails 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) three-body backg.  - backg.

13. M. Martemianov, ITEP, October 2003 Description of  - peak  Step N1 : Pure MC - extracting launch shape of peak (4 Gaussians, each 2 Gaussians have the same mean value + 2 exponential functions) Exp. tails Step N2 :  Experiment - extracting launch shape of peak for experimental data  One contribution :  - background  -backg.

14. M. Martemianov, ITEP, October 2003 Fit of two peaks  Fit gives a full description of all type of kaon decays in DC  f(x) three - extracted from MC

15. M. Martemianov, ITEP, October 2003 Total statistics  All data diveded on 5 sets 

16. M. Martemianov, ITEP, October 2003 Fit quality

17. M. Martemianov, ITEP, October 2003 Correction coefficient on background Ratio as function of data set Linear fit gives : 0.3352  0.0003(stat.) Stat error : 0.09 % Correction coeff. physical background Linear fit gives : Kfit = 0.9255  0.0012(fit.) Fit error : 0.13 %

18. M. Martemianov, ITEP, October 2003 Comparison data / MC Fit can be checked by MC data using the same way : K MC = 97.10  0.25 % Kfit = 96.66  0.24 % Ratio = 0.3174  0.0006 Ratio  Kmc = (0.30863  0.00055) MC Kfit = 0.9255  0.0012 Ratio = 0.3352  0.0003 Ratio  Kfit = 0.3102  0.0012 MC : EXP :  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. M. Martemianov, ITEP, October 2003 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. M. Martemianov, ITEP, October 2003 Selection efficiency/ II  Distributions on MC and EXP are the same  Cut for tracks length on all tracks (> 40 cm) gives   decay = 1.0443  0.0016 (stat.) Calculation of  decay  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. M. Martemianov, ITEP, October 2003 Selection efficiency/ IV 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 Calculation of  window  Based on fit parameters  Calculates the percentage muons and pions inside window  Different for MC and EXP data

22. M. Martemianov, ITEP, October 2003 Selection efficiency/ V Calculation of  vertex  KK K+K+ ++ KK K+K+ EMC - cluster Two EMC clusters only for charged tracks,  + - seleclted by momenta Investigated vertex  vertex =  vertex   cuts Investigated vertex Two EMC clusters only for charged tracks,  + - seleclted by momenta, two clusters from gammas 22 11

23. M. Martemianov, ITEP, October 2003 Selection efficiency/ VI 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) Selected muons Selected pions Efficiency of vertex efficiency for muons and pions as function of kaons momenta

24. M. Martemianov, ITEP, October 2003 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) MC distribution of the secondary particles in the laboratory system for muons and pions  from K    from K    0

25. M. Martemianov, ITEP, October 2003 Summary of selection efficiency

26. M. Martemianov, ITEP, October 2003 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  10 6 4466 55  64 1.00073  0.00010  +  0,    0 0.621  10 6 111 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. M. Martemianov, ITEP, October 2003 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. M. Martemianov, ITEP, October 2003 Comparison with world data

29. M. Martemianov, ITEP, October 2003 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