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International School of Subnuclear Physics Erice, 30 Aug - 6 Sept 2006

Measurement of the CKM angle g with a D 0 Dalitz analysis of the B ± →D (*) K ± decays at BaBar . Nicola Neri INFN Pisa. International School of Subnuclear Physics Erice, 30 Aug - 6 Sept 2006. ( r , h ). a. *. *. *. V td V tb. |V cd V cb |. V ud V ub. *. |V cd V cb |. g. b.

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International School of Subnuclear Physics Erice, 30 Aug - 6 Sept 2006

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  1. Measurement of the CKM angle gwith a D0 Dalitz analysis of the B±→D(*)K± decays at BaBar Nicola Neri INFN Pisa International School of Subnuclear Physics Erice, 30 Aug - 6 Sept 2006

  2. (r,h) a * * * Vtd Vtb |Vcd Vcb| Vud Vub * |Vcd Vcb| g b (1,0) (0,0) CKM matrix and Unitarity Triangle Unitarity of quark mixing matrix • CP violation is proportional to the triangle area • Standard Model fits predicts g • (64±5 )˚ UTFit - Bayesian • (60±5)˚ CKMFit - Frequentist CP violation • Test SM prediction • with tree-level processes Nicola Neri - International School of Subnuclear Physics

  3. f f Towards g bc transition bu transition If same final state  interference  g measurement A(B-D0 K-) = AB A(B-D0 K-) = ABrB e i(dB-g) f = KSpp (Dalitz Analysis) f = CP (GLW) f = DCSD (ADS) strong phase in B decay CKM elements + color suppression Critical parameter Theoretically and experimentally difficult to determine. Gronau, Wyler, Phys. Lett. B265,172 (1991) D. Atwood, I. Dunietz, A. SoniPhys.Rev. D63 (2001) 036005 A. Giri, Y. Grossman, A. Soffer, J. ZupanPhys.Rev. D68 (2003) 054018 Nicola Neri - International School of Subnuclear Physics

  4. (MD0-mp)2 (MD0-mp)2 (mKS+mp)2 (mKS+mp)2 Three-body D decays: Dalitz plot • A point of in a three-body decay phase-space can be determined with two independent kinematical variables. A possible choice is to represent the state in the Dalitz plot kinematical Mandelstam variables: The A(D0 →Kspp) amplitude can be written as AD(s12, s13). Nicola Neri - International School of Subnuclear Physics

  5. g from the Interference term Using AD(s12, s13)in B decay amplitude s12 (GeV2) s12 (GeV2) D0 3-body decay Dalitz distribution |AD(s12, s13) |2 (*) s13 (GeV2) s13 (GeV2) A(B-) = AD(s12, s13) +rB ei(-g+dB)AD(s13, s12) Assuming CP is conserved in D decays CP A(B+ ) = AD (s13, s12) +rB ei(g+dB)AD((s12, s13) |A(B- )|2 =| AD(s12, s13) |2 +rB2 | AD(s13, s12) |2 + +2rBRe[AD(s12, s13) AD(s13, s12)* ei(-g+dB)] The method suffers of a two-fold ambiguity If rB is large, good precision on g AD(s12, s13): fitted on from with Nicola Neri - International School of Subnuclear Physics (*) Def.

  6. Model Dependent Breit-Wigner description of 2-body amplitudes • Three-body D0 decays proceed mostly via 2-body decays (1 resonance + 1 particle) • The D0 amplitude ADcan be fit to a sum of Breit-Wigner functions plus a constant term, see E.M. Aitala et. al. Phys. Rev. Lett. 86, 770 (2001) • For systematic error evaluation, use K-Matrix formalism to overcome the main limitation of the BW model to parameterize large and overlapping S-wave pp resonances. = angular dependence of the amplitude depends on the spin Jof the resonance r Relativistic Breit-Wigner with mass dependent width Gr where sij=[s12,s13,s23] depending on the resonance Ksp-,Ksp+,p+p-. mr is the mass of the resonance Nicola Neri - International School of Subnuclear Physics

  7. K*(892) r (770) The BaBar Isobar model BaBar Data with BaBar isobar model fit over imposed. Fit Fraction=1.20 390K sig events 97.7% purity Good fit in DCS K*(892) region. K*DCS Nicola Neri - International School of Subnuclear Physics

  8. The BaBar Isobar Model BaBar model 16 resonances + 1 constant term (Non-resonant). Mass and widths are fixed to the PDG values. Except for K*(1430), use E791 values and for s, s`, fit from data. Nicola Neri - International School of Subnuclear Physics

  9. Signal events and DATA sample • DATA at (4S) peak 10.580 GeV 316.3 fb-1 (347 M BB events) • DATA below peak 23.3 fb-1 (4S) rate = L·s(bb) ~ 1.2·1034cm-2s-1 ·1.1 nb ≳ 13 BB evt/sec 9.1 GeV 3.0 GeV 50% B0B0 50% B+B- (4S) (4S) =1 for signal events B- D*0 K- B- D0 K- D0 p0 ,D0 g Ksp+ p- p+ p- Ksp+ p- p+ p- Nicola Neri - International School of Subnuclear Physics

  10. Signal DpBBqq Yields on DATA 347 million of BB pairs at (4S) D0K D*0K D*0D0 D*0K D*0D0g background is >5 times the bkg contribution in each mode. Dp contribution is negligible after all the selection criteria applied in signal region unless for [Dp0]K. The error on the Dp contribution is large and can be explained as a statistical fluctuation (accounted for in systematic error) Nicola Neri - International School of Subnuclear Physics

  11. Dalitz distributions D*K  (D0p0)K DK B- B+ B- B+ D*K  (D0g)K Dalitz plot distribution for signal events after all the selection criteria applied. B- B+ Nicola Neri - International School of Subnuclear Physics

  12. CP parameters extraction Fit for different CP parameters: cartesian coordinates are preferred base. Errors are gaussian and pulls are well behaving. x= Re[rBexpi(dg))]= rBcos(dg) , y= Im[rBexpi(dg)]= rBsin(dg) CP parameter Result CP parameter Result x-=rBcos(d-g) y-=rBsin(d-g) x+=rBcos(d+g) y+=rBsin(d+g) x*-=rBcos(d*-g) y*-=rBsin(d*-g) x*+=rBcos(d*+g) y*+=rBsin(d*+g) Main systematics Dalitz model error. Account for phenomenological D amplitude parameterization uncertainty PDF shapes , Dalitz plot efficiency, qq Dalitz shape Charge correlation of (D0,K) in qq The statistical error dominates the measurement. Nicola Neri - International School of Subnuclear Physics

  13. 1s 2s Cartesian coordinate results D0K D*0K B- B+ B+ d d B- Direct CPV Direct CP violation d=2 rb(*)|sing| Nicola Neri - International School of Subnuclear Physics

  14. Experimental systematic errors >> Experimental systematics Dalitz model systematics Statistical error ≳ Nicola Neri - International School of Subnuclear Physics

  15. Frequentist interpretation of the results rB r*B D*0K D0K 2 s 1 s 1s (2s) excursion s is to be understood in term of 1D proj of a L in 5D. Nicola Neri - International School of Subnuclear Physics Stat Syst Dalitz

  16. () rB Considerations on the results y Dx≈Dy≈rb·Dq B- s(g) ≈ Dx/rb rb Dq 2g x Dq rb Experimentally we can improve the measurement of the CP cartesian coordinates but the improvement on error of g depends on the true value of the rb parameter. Similar behavior for statistical and systematic error. B+ Nicola Neri - International School of Subnuclear Physics

  17. Conclusions and perspectives • We demonstrated that the measurement of g is possible and compatible with SM predictions. • Dalitz method gives the best sensitivity to g but…more statisticsis crucial. • If rB≥0.1 we will know the g value ≤15% precision with 1 ab-1. Toy MC rb=0.1 assumed Dalitz model error projection g=73±29 ([15,136]@95%CL)g=-107±29 ([-165,-44]@95%CL) Near Future Nicola Neri - International School of Subnuclear Physics

  18. Back-up slides Nicola Neri - International School of Subnuclear Physics

  19. Dalitz model systematics • pp S-wave: • Use K-matrix pp S-wave model instead of the nominal BW model • pp P-wave: • Change r(770) parameters according to PDG • Replace Gounaris-Sakurai by regular BW • pp and Kp D-wave • Zemach Tensor as the Spin Factor for f2(1270) and K*2(1430) BW • Kp S-wave: • Allow K*0(1430) mass and width to be determined from the fit • Use LASS parameterization with LASS parameters • Kp P-wave: • Use BJ/psi Ks p+ as control sample for K*(892) parameters • Allow K*(892) mass and width to be determined from the fit • Blatt-Weiskopf penetration factors • Running width: consider a fixed value • Remove K2*(1430), K*(1680), K*(1410), r(1450) This is a more realistic and detailed estimate of the model systematics ! Nicola Neri - International School of Subnuclear Physics

  20. Bias on x-, x+ for alternative Dalitz models Residual for the x-, x+ coordinates wrt the nominal CP fit. Yellow band is the nominal fit statistical error (x100 Run1-5 statistics) Nicola Neri - International School of Subnuclear Physics

  21. Bias on y-, y+ for alternative Dalitz models Residual for the y-, y+ coordinates wrt the nominal CP fit. Yellow band is the nominal fit statistical error (x100 Run1-5 statistics) Nicola Neri - International School of Subnuclear Physics

  22. Background parameterization: Dalitz shape for background events • BB and continuum events are divided in real D0 and fake D0. The real D0 fraction is evaluated on qq and BB Monte Carlo counting: • cross-check on DATA using the mES<5.272 GeV sidebands and fitting the D0 mass. • For the bkg real D0 : D0 Dalitz signal shape For the bkg fake D0 (combinatorial) 2D symmetric 3rd order polynomial asymmetric function : • cross-check on DATA using the mES<5.272 GeV and D0 mass sidebands .BB combinatorics - MC .qq combinatorics – MC fit function fit function Asymmetric Asymmetric Nicola Neri - International School of Subnuclear Physics

  23. Background parameterization: fraction of true D0 • The real D0 fraction is evaluated directly on DATA using the mES<5.272 GeV sidebands and fitting the D0 mass distribution. The signal is a Gaussian with fixed s = 6 MeV/c2 (MC value) and m = 1864.5 MeV/c2 (PDG value). On Monte Carlo we find the fraction for true D0 to be: MC continuum evt MC BB events MC BB + qq weighted evt . DATA (On-Res) we use this error for conservative systematic error evaluation Nicola Neri - International School of Subnuclear Physics

  24. Background characterization: true D0 and flavor-charge correlation D0=KSpp e- e+ cc D0 K- + other particles estimated on Monte Carlo events Nicola Neri - International School of Subnuclear Physics

  25. Final results • We have measured the cartesian CP fit parameters for DK (x±,y±) and D*K (x*± ,y*±) • using 316 fb-1 BaBar data: CP parameter Result CP parameter Result x-=rBcos(d-g) y-=rBsin(d-g) x+=rBcos(d+g) y+=rBsin(d+g) x*-=rBcos(d*-g) y*-=rBsin(d*-g) x*+=rBcos(d*+g) y*+=rBsin(d*+g) Statistical error Experimental systematics D0 amplitude model uncertainty • This measurement supersedes the previous one on 208 fb-1 with significant • improvements in the method and smaller errors on the cartesian CP parameters. • Using a Frequentist approach we have extracted the values of the CP parameters: 1s (2s) excursion Stat Syst Dalitz s is to be understood in term of 1D proj of a L in 5D. Nicola Neri - International School of Subnuclear Physics

  26. CP-violating phase CP Violation in the Standard Model • CP symmetry can be violated in any field theory with at least one CP-odd phase in the Lagrangian • This condition is satisfied in the Standard Model through the three-generation Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix Wolfenstein parameterization: corresponds to a particular choice of the quark-phase convention Nicola Neri - International School of Subnuclear Physics

  27. * |Vcd Vcb| Unitarity triangle • CP violation is proportional to the area CP violation  (r,h) a * * Vtd Vtb Vud Vub * |Vcd Vcb| g b (1,0) (0,0) Nicola Neri - International School of Subnuclear Physics

  28. A 2 2  B B g g d CP violation in decay or direct CP violation  CP violation For example A=A1+A2: two amplitudes with a relative CP violating phase g(CP-odd) and a CP conserving phase d (CP-even) Nicola Neri - International School of Subnuclear Physics

  29. BaBar Detector 1.5T solenoid DIRC (PID) 144 quartz bars 11000 PMs EMC 6580 CsI(Tl) crystals e+ (3.1GeV) Drift Chamber 40 stereo layers e- (9.0 GeV) Silicon Vertex Tracker 5 layers, double-sided sensors Instrumented Flux Return iron / RPCs/LSTs (muon / neutral hadrons) Nicola Neri - International School of Subnuclear Physics

  30. Dalitz: BaBar vs Belle Results HFAG Experiment Mode γ/φ3 (°) δB (°) rB Belle‘06 N(BB)=392M DK–D→KSπ+π–53± +15–18 ± 3 ± 9 146 ± 19 ± 3 ± 23 0.16 ± 0.05 ± 0.01 ± 0.05 D*K–D*→Dπ0D→KSπ+π–53 ± +15–18 ± 3 ± 9 302 ± 35 ± 6 ± 23 0.18 +0.11–0.10 ± 0.01 ± 0.05 BABAR'06 N(BB)=347M DK–D→KSπ+π–92 ± 41 ± 10 ± 13 118 ±64 ±21 ±28 <0.142 D*K–D*→D(π0,γ) D→KSπ+π– 92 ± 41 ± 10 ± 13 298 ±59 ±16 ±13 <0.206 BaBar measurement is very important since it stresses one more time the difficulty to measure g in a regime where the uncertainty on rb is quite large. Nicola Neri - International School of Subnuclear Physics

  31. BaBar vs Belle experimental results BABAR'06 - N(BB)=347M CP parameter Result CP parameter Result x-=rBcos(d-g) y-=rBsin(d-g) x+=rBcos(d+g) y+=rBsin(d+g) x*-=rBcos(d*-g) y*-=rBsin(d*-g) x*+=rBcos(d*+g) y*+=rBsin(d*+g) Belle’06 - N(BB)=386M CP parameter Result CP parameter Result −0.13 +0.17−0.15 ± 0.02 −0.34 +0.17−0.16 ± 0.03 0.03 ± 0.12 ± 0.01 0.01 ± 0.14 ± 0.01 given on rb,g,d given on rb,g,d 0.03 +0.07−0.08 ± 0.01 0.17 +0.09−0.12 ± 0.02 −0.14 ± 0.07 ± 0.02 −0.09 ± 0.09 ± 0.01 x-=rBcos(d-g) y-=rBsin(d-g) x+=rBcos(d+g y+=rBsin(d+g) x*-=rBcos(d*-g) y*-=rBsin(d*-g) x*+=rBcos(d*+g) y*+=rBsin(d*+g) Experimental measurement of the CP parameters x,y is more precise wrt Belle even with slightly smaller statistics. Different error on g is due to Belle larger central values. Nicola Neri - International School of Subnuclear Physics Statistical error Experimental systematics D0 amplitude model uncertainty

  32. Outline • Theoretical framework • D0 decay amplitude parameterization • Selection of the D(*)K events • CP parameters from the D0 Dalitz distribution • Systematic errors • Extraction of g • Conclusions Nicola Neri - International School of Subnuclear Physics

  33. Selection criteria for B±D(*)K± decay modes D0K D*0K (D0p0)D*0K (D0g) |cos qT| <0.8 <0.8 <0.8 |mass(D0)-PDG| <12MeV <12MeV <12MeV |mass(Ks)-PDG| <9MeV <9MeV <9MeV E (g) ----- >30 MeV >100MeV |mass(p0)-PDG| ----- <15MeV ----- Kaon Tight Selector Yes Yes Yes |DM-PDG| ----- <2.5MeV <10.0MeV cos aKs >0.99 >0.99 >0.99 |DE | <30MeV <30MeV <30MeV ---------------------------------------------------------------------------------------- efficiency 15% 7% 9% ---------------------------------------------------------------------------------------- signal events 398±23 97±1393±12 cos aKssuppress fake Ks |cos qT| suppress jet-like events Kaon Tight Selector (LH)and |DE|<30 MeV suppress D(*)p events Nicola Neri - International School of Subnuclear Physics

  34. Likelihood for Dalitz CP fit A(B-)= |AD(s12,s13) +rBei(-g+dB)AD(s13,s12)|2 |AD(s12,s13)|2 |AD(s13,s12)|2 From MC and D0 sideband data a=D0,D0 fSig,Dh,Cont,BB from data (extended likelihood  yields) True D0 fraction from MC and data (mES sidebands) Charge-flavor correlation from MC Nicola Neri - International School of Subnuclear Physics

  35. (D0g)K – (D0p0)K cross-feed • From Monte Carlo simulation the cross-feed between the samples is due to events of (D0p0)K where we loose a soft g and we reconstruct it as a (D0g)K. • Since the cross-feed goes in one direction (D0p0)K  (D0g)K, it is correct to assign common events to the (D0p0)K signal sample. • After all the cuts and after this correction applied we expect <5% of signal (D0g)K from cross-feed. • A systematic effect to the cross-feed has been assigned adding a signal component according to the (D0p0)K Dalitz PDF and performing the CP fit. • The systematic bias of the fit with and without (D0p0)K has been quoted as systematic error. • Negligible wrt the other systematic error sources. Nicola Neri - International School of Subnuclear Physics

  36. Dalitz model systematic error:K*(1430) parameters Mass =1.412 +/- 0.006 GeV Width = 294 +/- 23 MeV PDG (from LASS) Current BaBar model for K*0(1430): Mass =1.459+/-0.007 GeV Width = 175 +/- 12 MeV E791 Isobar model for K*0(1430): Mass =1.495 +/- 0.01 GeV Width = 183 +/- 9 MeV BaBar Isobar model [float] for K*0(1430): The Isobar model, the fit prefer small value of K*(1430), both seen in E791 and BaBar, although PDG list the width 294 MeV Mass and width are not unique parameters, depend on the parameterization and Non-Resonant model Nicola Neri - International School of Subnuclear Physics

  37. K*(892) and K*(1430) with new parameters Perfect! Nicola Neri - International School of Subnuclear Physics

  38. Data Dsppp Data Zemach Tensor vs Helicity model Affects seriously on spin 2 Monte Carlo simulation using f2(1270)pp MC MC In Dsp-p+p+ the non-resonant term is much smaller (5%) in Zemach Tensor while the non-resonant term is (25%) if Helicity model is used  D wave systematics Nicola Neri - International School of Subnuclear Physics

  39. Dalitz model systematic error:K*(892) parameters • In PDG those measurements are from 1970’s. Very low statistics ~5000 events • we have ~200000 K*(892) events • If we allow mass and width to float, we get the width 46 +/- 0.5 MeV, mass 893 +/- 0.2 MeV • Partial wave analysis of BJ/psi K p decay (BaBar) can use as control sample • Mass=892.9+/-2.5 MeV • Width=46.6 +/-4.7 MeV • Their values are consistent with our floatedvalues No S-wave! Very clean measurement  Consider as systematics compared with PDG Nicola Neri - International School of Subnuclear Physics

  40. Procedure for Dalitz model systematics • Generate a high statistics toy MC (x100 data statistics) experiment using nominal (BW) model. • The experiment is fitted using the nominal and each alternative model. • Produce experiment-by-experiment differences for all (x,y) parameters for each alternative Dalitz model. • For each CP coordinates, consider the squared sum of the residuals over all the alternative models as the systematic error. • Since the model error increases with the value of rb we conservatively quote a model error corresponding to ~rb+1s valuethat we fit on data. • This is a quite conservative estimate of the systematics and we believe it is fair to consider the covariance matrix among the CP parameters to be diagonal. Nicola Neri - International School of Subnuclear Physics

  41. CA D0 K*(892)- p+ s13 (GeV2) weight = DCS D0 K0*(1430)+p- DCS D0 K*(892)+p- D0 Ksr s12 (GeV2) Sensitivity tog points : weight = 1 Strong phase variation improves the sensitivity to g. Isobar model formalism reduces discrete ambiguities on the value of g to a two-fold ambiguity. Nicola Neri - International School of Subnuclear Physics

  42. Reconstruction of exclusive B±D(*)K± decays Y(4S) =1 for signal events B- K- D*0 B- D0 K- Ksp+ p- D0 p0 ,D0 g p+ p- Ksp+ p- p+ p- Nicola Neri - International School of Subnuclear Physics

  43. Signal DpBBqq Background characterization: relative fraction of signal and bkg samples • Continuum events are the largest bkg in the analysis. We apply a cut |cos(qT)|<0.8 and we use fisher PDF for the continuum bkg suppression. Fisher = F [LegendreP0,LegendreP2,|cos qT|,|cos qB*|] • The Fisher PDF helps to evaluate the relative fraction of BB and continuum events directly from DATA. D0K D*0K - D*0D0g D*0K - D*0D0 Nicola Neri - International School of Subnuclear Physics

  44. Efficiency Map for D*→D0p We use ~200K D* MC sample D0 Phase Space to compute the efficiency map . 2D 3rd order polynomial function used for the efficiency map. Purity 97.7% Red = perfectly flat efficiency Blu = 3rd order polynomial fit Efficiency is almost flat in the Dalitz plot. The fit without eff map gives very similar fit results. Nicola Neri - International School of Subnuclear Physics

  45. Isobar model formalism As an example a D0 three-body decay D0ABC decaying through an r=[AB] resonance In the amplitude we include FD, Fr the vertex factors of the D and the resonance r respectively. H.Pilkuhn, The interactions of hadrons, Amsterdam: North-Holland (1967) D0 three-body amplitude can be fitted from DATA using a D0 flavor tagged sample from events selecting with • We fit for a0 ,ar amplitude values and the relative phase f0 , fr among resonances, • constant over the Dalitz plot. Nicola Neri - International School of Subnuclear Physics

  46. Efficiency Map for B->DK (*) • Because of the different momentum range we use a different parametrization respect to the D* sample. We use ~1M B->D(*)K signal MC sample with Phase Space D0 decay to compute the efficiency mapping. • Fit for 2D 3rd order polynomial function to parametrize the efficiency mapping: Efficiency is rather flat in the Dalitz plot. CP Fit without eff map to quote the systematic error on CP parameters Nicola Neri - International School of Subnuclear Physics

  47. K-Matrix formalism for pp S-wave • K-Matrix formalism overcomes the main limitation of the BW model to parameterize large and overlapping S-wave pp resonances. Avoid the introduction of not established s, s´ scalar resonances. • By construction unitarity is satisfied SS†=1 S=1+2iT T=(1-iK·r)-1K where S is the scattering operator T is the transition operator r is the phase space matrix K-matrix D0 three-body amplitude F1 = pp S-wave amplitude Pj(s) = initial production vector Nicola Neri - International School of Subnuclear Physics

  48. The CLEO model CLEO model 10 resonances + 1 Non Resonant term. Nicola Neri - International School of Subnuclear Physics

  49. The CLEO model With >10x more data than CLEO, we find that the model with 10 resonances is insufficient to describe the data. CLEO model 10 resonances + 1 Non Resonant term. BaBar Data refitted using CLEO model. Nicola Neri - International School of Subnuclear Physics

  50. The BELLE model Belle model 15 resonances + 1 Non Resonant term. Added DCS K*0,2(1430), K*(1680) and s1 , s2 respect to the CLEO Model.With more statistics you “see” a more detailed structure. Added Added Added Added Added Nicola Neri - International School of Subnuclear Physics

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