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K ±  ±  0  0

K ±  ±  0  0. Measuring Branching Ratio and Dalitz plot parameters. A. Ventura E. Gorini M. Primavera. B ranching Ratio World data.  ’  K ±  ±  0  0. PDG ( units 10 –2 ). 1.73±0.04 (fit) 1.77±0.07 (average). Best experiment is 3.5% error,

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K ±  ±  0  0

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  1. K±±00 Measuring Branching Ratio and Dalitz plot parameters A. Ventura E. Gorini M. Primavera

  2. Branching Ratio World data ’ K±±00 PDG(units 10–2) 1.73±0.04 (fit) 1.77±0.07 (average) Best experiment is 3.5% error, and bases on only 1307 events: CHIANG 72 (1.84±0.06)10–2 K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  3. Present statistics analized at KLOE • Data: 6.33 pb–1 (December 2001) • MC: 1.8 106all (~0.6 pb–1) • 7.0 105K–K+, K±±00,Kall (~13 pb–1) – DBV-12 default datarec version – MC samples include proper DC & EMC bckg simulations K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  4. Filter algorithm (I)Preliminary requirements • Cosmic Veto  (DC+EMC) Trigger • Any of the 5 EvCl algorithms • K± track • a unique 2-tracks vertex in DC involving the K± • Distance between the two tracks’ first/last hit < 50 cm • Angle at vertex between the two tracks > 2°* * Redundant cut with new retracking K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  5. Filter algorithm (II)Further requirements • 4 “ontime” non-associated clusters with Ei>15 MeV coming from thecharged vertex:|ti–tj–(Li–Lj)/c|<3t(Ei,Ej) i,j=1,..,4 • Best pairing of the quartet of clusters: 80 MeV < m12 , m34 < 190 MeV ( 3m cut ) • 460 MeV < m < 530 MeV ( 3m cut ) • Charged product track momentum: |pdau| < 135 MeV in K± frame all contamination ~0.5% (MC) K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  6. Photons from 0s in ’on MC and Data Energy distribution: Ei [20,180]MeV MC gen MC rec  00 K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  7. Tagging strategies K±±0 • Daughter momentum: 199 MeV < |pdau| < 211 MeV in K frame • Missing mass at K vertex: 122 MeV < mm < 148 MeV • 2 ontime non-associated clusters: 90 MeV < m < 180 MeV all contamination ~0.35% (MC) K± ± • Daughter momentum: 226 MeV < |pdau| < 245 MeV in K frame • Missing mass at K vertex: |mm|< 5 MeV all contamination ~0.3% (MC) K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  8. BR measurement method [N’]tag Ntag 1 ’ 1 [1–BR(0)]2 BR(K±00) = BR(0)=(98.80±0.03)%,tag = 0,  ’ = K vtx4onTpair M pdau • ’does not depend onFILFO ,EvCl ,tag • ’independence from trigto be tested K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  9. Evaluating efficiencies on MC and on Data • All the cuts applied have been separately studied on proper Samplesof Normalization (SoNs) in order to evaluate efficiencies directly from data. • Equivalent MC samples have been used just to control and reduce contamination in all SoNs. • Each  is meant to be convoluted with the corresponding KLOE acceptance and to be averaged over ’ kinematics K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  10. Evaluating efficiencies: K SoN#1 : tag+4 • A K° or a K on one side, as defined for tagging • 4 non-tag neutral clusters with E>15MeV (“”) : • 20 MeV < Ei < 180 MeV • 125 MeV < Ej+Ek< 195 MeV • (j=min and k=max) or (j=2nd and k=3rd) • 1 cluster >110 MeV • 2 clusters <60 MeV • max(|tj–tk|) < 9 ns (j,k=1,..,4) 98% K°°(MC) ;~2200 events/pb–1 on data K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  11. Evaluating efficiencies: K Kaon tracks in tag+4 K MC Data MC Data  |pFH| # of “” cot  Track’s length Track’s radius at First Hit • New tracking algorithms still to be used on analysis K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  12. Evaluating efficiencies: vtx SoN#2 : tag+4+K • A tag+4 subsample with the other K reconstructed vtx = v TTcos|v • v : finding a 2-tracks vertex • TT: distance between tracks < 50 cm • cos: angle between tracks > 2° • |v: no other decay vertices for K K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  13. Evaluating efficiencies: vtxvs # of “” MC Data v TT cos |v K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  14. Evaluating efficiencies: 4onT A possible parametrization: 4onT = tw6 [1–Pwtw4]N • tw : finding 2 clusters (photons) coming from the same vertex (0) in a 3ttime window • Pw : physical probability for a “” not coming from a given 0 to be ontime with its 2 correct clusters (e.g.: accidentals, split clusters, TCA faults, …) • N : mean number of non-’ “”s in a generic ’ event K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  15. Evaluating efficiencies: tw SoN#3 : Kp+1 • (K track + dautrack) at a 2-trks vertex • 199 MeV < pdau< 211 MeV in K frame • Missing mass at vtx: 122 MeV<mmiss<148 MeV •  cluster 0 associated with dau track •  neutral cluster 1 : E1<(>)Emiss/2 ontime with 0 and such that: |E1–E1*|<35.7%/E1(GeV) , with E1*=m°2/2[Emiss– pmissc1] 1 2   0 99.7% cluster 1 from K°(MC) ; ~60000 events/pb–1 on data K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  16. Evaluating efficiencies: twin Kp+1 tw • tw : finding a cluster 2 such that: • E2>(<)Emiss/2 • 2ontime with 1 • 80 MeV<m12<190 MeV MC Data MC Data E tw as a function of the cluster 2 expected energy Cluster 2 not found (90.94±0.07)% on MC (86.11±0.04)% on Data tw = Distance between cluster 2 and the expected impinging point K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  17. Evaluating efficiencies: Pw SoN#4 : Kp+2 1 2 • A Kp+1 subsample in which cluster 2 has been found • Pwtw4: finding a “wrong” cluster W which is ontime with clusters 1 and 2 0 Pw W (2.16±0.07)% on MC (3.39±0.03)% on Data MC Data Pw = K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  18. Evaluating efficiencies: N The mean number of non-’ “”s in a ’ event (N) can be estimated • in tag+4 , • in tag+4+K , • in the final analysis sample itself • Nany possible “” observed in a ’ event apart the 4 ’ neutral clusters MC Data (1.27 ± 0.02)% on MC (1.531±0.008)% on Data N= N+4 K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  19. Evaluating efficiencies: pair SoN#5 : Kp+1+1 • A Kp sample in which both the 2 clusters have been separately found with the procedure as for kp+1 and are ontime. 1 2 pair = 2 0 •  : the 2 clusters in Kp+1+1 satisfy: 80 MeV<m12<190 MeV N MC Data (0.975±0.002)% on MC (0.941±0.001)% on Data E  = K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  20. Efficiencies: summary } K0tag ’ 0.203±0.014 0.096±0.004 K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  21. Estimation of statistical error on BR(’) • MC (~1.8·106 all events) N’ =2204 , [N’]°tag=169 , Ntag=49912 BR(’) = (1.71±0.16stat)% • Data (~6.33 pb-1, December 2001) N’ =20778 , [N’]°tag=726 , N°tag=421626 BR(’) = (1.83±0.09stat)% • ~ 115’|0tag events/pb-1 • 2001 data are enough for BR(’)below0.8stat% • Systematics to be tested at % level K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  22. Dalitz plot parameters World data X = (s1 – s2)/m2 Y = (s3 – s0)/m2 si = (PK – Pi)2 i = 1,2,3  s0 = isi/3 = (mK2 + m2 +2m°2)/3 F(X,Y;g,h,k) = 1+gY+hY2+kX2 LINEAR COEFFICIENTg 0.652±0.031(average) QUADRATIC COEFFICIENTh 0.057±0.018(average) ASYMMETRY (g+- g-) / (g++ g-) NEVER MEASURED QUADRATIC COEFFICIENTk 0.0197±0.0045±0.0029(BATUSOV 98) K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  23. Kinematical fit (for Dalitz plot only) • Based on 4-momentum conservation, m’s and s0 Clusters energy resolutions (MC)  m m K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  24. X and Y resolutions (MC) X=(3390)10-3 Y=(2051)10-3 X[-2.39,2.39] Y[-1.39,1.31] • Dalitz plot floored by 10x20 bins in [-3,3]x[-2,2] K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  25. Dalitz plots and efficiencies (MC) GENerated REConstructed Y Y X X (X,Y) # REC # GEN (X,Y) = (X,Y)dX (from data) (X,Y)dY (Y)is also evaluable from data (Y=.033) (X,Y)dX K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  26. Extraction of Dalitz plot parameters F F(X,Y;g,h,k) = 1+gY+hY2+kX2 • 2= bins[(Fexp – Ftheo)/Fexp]2 minimized with g, h, k free • A0(g,h,k) = F(X,Y;g,h,k)dxdy normalization applied • Maximum Likelihood method under study 6.33 pb-1  ~15500 K°° (MCnormalized) Y X VERY PRELIMINARY K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  27. Event selection and errors estimation • ~3330 K00 / pb–1 for BR(before kine fit) • ~2500 K00 / pb–1 for g,h,k (after kine fit) • All 2001 data should yield ~0.5stat% on Dalitz plot • parameters and asymmetries K±±00measuring branching ratio and Dalitz plot parameters A. Ventura – KLOE Otranto 2002

  28. Study on K±00e±e (Ke4) Branching Ratio (2.1 ± 0.4 ) 10–5(PDG fit) (2.54±0.89) 10–5 (BARMIN 88, 10 evts) Highest statistics in: (00e±e)/(0e±e) = (4.2±1.0)10–4 (BOLOTOV 86, 25 evts) Monte Carlo samples used: • signal: ~105K–K+, K±00e±, Kall (~2 fb–1) • 1st bckg: 3.0 106K–K+, K±±00,Kall (~60 pb–1) • 2nd bckg: 1.5106K–K+, K±0e±,Kall (~10 pb–1) A. Ventura – KLOE Otranto 2002 Study on K±00e±e

  29. Ke4 Filter algorithm • All cuts as in K00, except for: • 460 MeV < m < 530 MeV • |pdau|<135 MeV in K frame • K°°fit unsuccessful •  cluster associated to charged product’s track • 2based on 0 missing mass, E conservation (in  mass hypothesis), charged product 1, charged product t.o.f. compatible with e (not  or ): 2 < 5(MC tuned) Ke4 K°° A. Ventura – KLOE Otranto 2002 Study on K±00e±e

  30. Background subtraction (MC) • Contamination due to K±±00: (5.9 ±3.1)% • Contamination due to K±0e±: < 10% • Possible contamination from KL+–0 A. Ventura – KLOE Otranto 2002 Study on K±00e±e

  31. Selection Efficiency on MCand events collection on data • 1515 selected Ke4 events of 102600 MC generated  MC1.48%  ~0.9 Ke4/pb–1 are expected on data • Only2 Ke4 havebeen found in 6.33 pb–1 MC rec Data m m me me In(00e±e)/(±00) many systematics cancel out A. Ventura – KLOE Otranto 2002 Study on K±00e±e

  32. Conclusions and outlook • K 00 , BR Filter and data-extracted efficiencies already tested Trigger effects and systematic errors to be evaluated tag, EvCl, trig corrections to be studied • K 00 , Dalitz Plots parameters MC differential efficiency used for fit to be corrected Maximum Likelihood Method under study • K 00e , BR All 2001 data statistics to be analized Data-extracted efficiencies to correct MC predictions K±±00 and K±00e±e A. Ventura – KLOE Otranto 2002

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