Measurement of the CKM angle with a D 0 Dalitz analysis of the B D (*) K decays at BaBar International School of Subnuclear Physics Erice, 30 Aug - 6 Sept 2006 Nicola Neri INFN Pisa September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 2 CKM matrix and Unitarity Triangle CP violation is proportional to the triangle area CP violation Standard Model fits predicts (64 5 ) UTFit - Bayesian (60 5 ) CKMFit - Frequentist Test SM prediction with tree-level processes (0,0) (1,0) (,)(,) V td V tb * |V cd V cb | * * V ud V ub * Unitarity of quark mixing matrix September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 3 b c transition b u transition A(B - D 0 K - ) = A B A(B - D 0 K - ) = A B r B e i( B - ) Gronau, Wyler, Phys. Lett. B265,172 (1991) D. Atwood, I. Dunietz, A. Soni Phys.Rev. D63 (2001) A. Giri, Y. Grossman, A. Soffer, J. Zupan Phys.Rev. D68 (2003) If same final state interference measurement CKM elements + color suppression strong phase in B decay Towards Critical parameter f f f = K S (Dalitz Analysis) f = CP (GLW) f = DCSD (ADS) Theoretically and experimentally difficult to determine. September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 4 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(D 0 K s ) amplitude can be written as A D (s 12, s 13 ). (m KS +m 2 (M D0 -m ) 2 (m KS +m 2 (M D0 -m ) 2 September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 5 A(B - ) = A D (s 12, s 13 ) +r B e i (- + B ) A D (s 13, s 12 ) A(B + ) = A D (s 13, s 12 ) +r B e i ( + B A D ((s 12, s 13 ) CP |A(B - )| 2 =| A D (s 12, s 13 ) | 2 + r B 2 | A D (s 13, s 12 ) | r B Re[A D (s 12, s 13 ) A D (s 13, s 12 )* e i(- + B ) ] A D (s 12, s 13 ): fitted on If r B is large, good precision on D 0 3-body decay Dalitz distribution | A D (s 12, s 13 ) | 2 (*) from the Interference term The method suffers of a two-fold ambiguity Using A D (s 12, s 13 ) in B decay amplitude Assuming CP is conserved in D decays with from s 13 (GeV 2 ) (*) Def. s 13 (GeV 2 ) s 12 (GeV 2 ) September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 6 Model Dependent Breit-Wigner description of 2-body amplitudes Three-body D 0 decays proceed mostly via 2-body decays (1 resonance + 1 particle) The D 0 amplitude A D can 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 resonances. = angular dependence of the amplitude depends on the spin J of the resonance r Relativistic Breit-Wigner with mass dependent width r where s ij =[s 12,s 13,s 23 ] depending on the resonance Ks -,Ks +, + -. m r is the mass of the resonance September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 7 The BaBar Isobar model Good fit in DCS K*(892) region. BaBar Data with BaBar isobar model fit over imposed. Fit Fraction=1.20 K K DCS 390K sig events 97.7% purity September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 8 The BaBar Isobar Model Mass and widths are fixed to the PDG values. Except for K*(1430), use E791 values and for , `, fit from data. BaBar model 16 resonances + 1 constant term (Non-resonant). September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 9 Signal events and DATA sample DATA at (4S) peak GeV fb -1 (347 M BB events) DATA below peak 23.3 fb -1 (4S) =1 for signal events D 0 0,D 0 K-K- B-B- ++ -- K s + - D *0 D0D0 B-B- K-K- ++ -- K s + GeV3.0 GeV rate = L (bb) ~ 1.210 34 cm -2 s -1 1.1 nb 13 BB evt/sec (4S) 50% B 0 B 0 50% B + B - (4S) September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 10 Yields on DATA D0KD0K D* 0 K D* 0 D 0 D* 0 K D* 0 D 0 BD0KBD0K398 23 signal events ~60% purity mES>5.272 GeV/c 2 B D* 0 K D* 0 D 0 97 13 signal events ~80% purity B D* 0 K D* 0 D 0 93 12 signal events ~50% purity 347 million of BB pairs at (4S) Signal D BB qq background is >5 times the bkg contribution in each mode. D contribution is negligible after all the selection criteria applied in signal region unless for [D 0 ]K. The error on the D contribution is large and can be explained as a statistical fluctuation (accounted for in systematic error) September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 11 Dalitz distributions B-B- B+B+ DK D*K (D 0 0 )K D*K (D 0 )K B-B- B+B+ B-B- B+B+ Dalitz plot distribution for signal events after all the selection criteria applied. September 1st 2006 Erice 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[r B exp i(d g) ]= r B cos(d g), y = Im[r B exp i(d g) = r B sin(d g) The statistical error dominates the measurement. x* - =r B cos( ) y* - =r B sin( ) x* + =r B cos( ) y* + =r B sin( ) CP parameterResult x - =r B cos( ) y - =r B sin( ) x + =r B cos( ) y + =r B sin( ) CP parameterResult Dalitz model error. Account for phenomenological D amplitude parameterization uncertainty PDF shapes, Dalitz plot efficiency, qq Dalitz shape Charge correlation of (D 0,K) in qq Main systematics September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 13 Cartesian coordinate results B+ B- d D0KD0K Direct CPV B+ B- D* 0 K Direct CP violation d=2 r b (*) | sin | d September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 14 Experimental systematic errors Experimental systematicsDalitz model systematics Statistical error >> September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 15 Frequentist interpretation of the results Stat Syst Dalitz 2 1 D0KD0K D* 0 K is to be understood in term of 1D proj of a L in 5D. 1 (2 ) excursion rBrB r*Br*B September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 16 Considerations on the results 22 B+B+ B-B- x y rBrB ()() x yrb rb ( ) x/rb Experimentally we can improve the measurement of the CP cartesian coordinates but the improvement on error of depends on the true value of the rb parameter. Similar behavior for statistical and systematic error. September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 17 Conclusions and perspectives We demonstrated that the measurement of is possible and compatible with SM predictions. Dalitz method gives the best sensitivity to but more statistics is crucial. If r B 0.1 we will know the value 15% precision with 1 ab -1. Near Future =7329 =-10729 Toy MC r b =0.1 assumed Dalitz model error projection September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 18 Back-up slides September 1st 2006 Erice 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 f 2 (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 + 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 K 2 *(1430), K*(1680), K*(1410), (1450) This is a more realistic and detailed estimate of the model systematics ! September 1st 2006 Erice 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) September 1st 2006 Erice 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) September 1st 2006 Erice Nicola Neri - International School of Subnuclear Physics 22 Background parameterization: Dalitz shape for background events BB and continuum events are divided in real D 0 and fake D 0. The real D 0 fraction is evaluated on qq and BB Monte Carlo counting: cross-check on DATA using the mES