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

Analysis of ratio BR( K     0 )/BR(K    ). Motaivation Selection and cuts Trigger efficiency Background Geometrical 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 ) • Motaivation • Selection and cuts • Trigger efficiency • Background • Geometrical 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 : 23100-27133 (2379 DST - files) • Total statistics : 281.3 pb-1 • Number of pions candidates : 1.386  106 • Number of muons candidates : 4.152  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. 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

  6. Tag strategy +, + 1 K+ K+ K ,  K 2 • Ktrigger - extracted from exp. data • Kfit - from exp. data and based on MC shape, define signals and backgrounds • Kvert - from MC • Kvetocos - from exp. • Tag for K+ • Trigger effciency  100 % • Measurement ratio on K

  7. Trigger efficiency / I Trigger N1 Trigger N2 Drift Chamber 1 K+ K+  ,  K K 2 • + - trigger : • Two tracks go to ECL • Rejection tracks fired same ENDCAP • Auto - triggering for K+ • Trigger effciency  100 %

  8. Trigger efficiency / II Trajectory, sec. particle cos 2 Intersection point, (XI, YI, ZI)  Last point XC, YC, ZC  cL Rdc vertex c0 kaon  cos 1 • Simple procedure to prolongate last point of track to calorimeter R • Cut : (cos1>-0.2.or. cos2>-0.2).and. (cos1<0.2.or. cos2<0.2) Drift Chamber

  9. Trigger efficiency / III Auto - triggering   - trigger • Linear fit for both trigger (p0) • Auto - triggering : p0 = 0.3337  0.0006(stat.) •  - trigger : p0 = 0.3332  0.0004(stat.) • Trigger difference : 0.0005  0.0006 (trigger error = 0.2 %)

  10. 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

  11. 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 two peak’s shape All selected events Events with reconstructed 0 Events selected as 

  12. Three-body decays • Four main modes in geanfi : • K      • K e0 • K  0 • K    0 0 0 - selection changed shape of three - body decays   Sum = 15.3 % 2 = 1.1 2 = 0.9 Skewed Fermi-Dirac function, f4 Fermi-Dirac function, f3 MC data

  13. Description of  - peak three-body backg.  - backg. Exp. tails  • Step N2 : • Experiment - extracting launch shape of peak for experiment • Two contributions :  and three - body background Step N1 : Pure MC - extracting launch shape of peak (4 Gaussians at the same mean value + 2 exponential functions at the same amplitude)

  14. Description of  - peak  -backg. Exp. tails  • Step N2 : • Experiment - extracting launch shape of peak for experiment • Two contributions :  - background Step N1 : Pure MC - extracting launch shape of peak (4 Gaussians, each 2 Gaussians have the same mean value + 2 exp. functions at the same amplitude)

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

  16. Fit quality • All data diveded on 5 sets 

  17. Correction coefficient on background Correction coeff. physical background Ratio as function of data set Linear fit gives : Kfit=0.9323  0.0013(stat.) Stat error : 0.14 % Linear fit gives : 0.3339  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 = 0.9614  0.0027 Ratio = 0.3263  0.0007 Ratio  Kfit = 0.3137  0.0011 Kfit = 0.9323  0.0013 Ratio = 0.3339  0.0003 Ratio  Kfit = 0.3113  0.0009 • Difference due to a small MC uncertainty, but very close to exp (on a level of 0.7 %), or 0.0021  0.0011 • Kmc (background defined by the code of reaction) and Kmc = 0.9600  0.0028 is on a level of Kfit (MC)

  19. Geometrical efficiency / II Kvert(MC) = 1.060  0.0023 MC. data • Sources of efficiency difference • Pions decay (cut by length > 40 cm) ( 2.6 %) • Selection signals in big windows ( 160. < P < 260. MeV/c ) and (180. < P < 280. MeV/c), ( 2.3 %) • Dependence of vertex reconstruction from the value of momenta (  1.0 %) Track length, cm • Fit by A0 + A1L • Correction for  - decay : • K = 1.0260  0.0004

  20. 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

  21. Systematic error

  22. Comparison with world data

  23. Conclusion • was measured • Result has a good compatibility with world data • Total error  0.9 % (improves world statistics accuracy of ratio on factor 1.7) • In principal, result can be updated by investigation of MC / EXP uncertanties

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