Interpreting CP asymmetries in. B   CP asymmetries Tree diagram: Penguin diagram: need |P/T| and  =arg(P/T) R t /R c R u /R c   

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Presentation transcript:

Interpreting CP asymmetries in

B   CP asymmetries Tree diagram: Penguin diagram: need |P/T| and  =arg(P/T) R t /R c R u /R c   

Theoretical frameworks 1.strong isospin symmetry SU(2) (GL) CP-averaged Br(B   ) only (  0  0 not seen yet) EW penguins neglected SU(3) flavour symmetry (BF,Ch) OZI-suppressed annihilation penguins neglected No correction of SU(3) breaking |P  | from K 0  - (GR,BBNS) R th from QCD factorisation Neglect annihilation diagram in K 0  -  remains unconstrained 4.QCD factorisation (BBNS) Use the prediction of both |P/T| and  Non-factorisable 1/m b contributions fixed to default value use Br(B 0  K +  - ) and |P  | = |P K  | GL: Gronau, London, Phys.Rev.LettD65:3381,1990 BF: Buras,Fleisher, Phys.Lett.B360:138,1995 Ch: Charles, Phys.Rev.D59:054007,1999 GR: Gronau, Rosner, Phys.Rev.D65:013004,2002 BBNS: Beneke et al., Nucl.Phys.B606: ,2001

Experimental inputs ICHEP’02 Branching fractions (x10 -6 ) WA = BaBar + Belle + CLEO Global CKM fit using standard constraints (referred as standard CKM fit in this talk) BaBarBelle S   0.34– 1.23  0.42 C  – 0.30  0.25– 0.77  0.28  sign convention changed! not seen CKMFitter: Hoecker et al., Eur.Phys.J.C21,225,2001 and ICHEP02 Aspen03  32  CL range:

BABAR Belle Constraints in the (  ) plane from isospin analysis BABAR Belle Gronau,London,Sinha,Sinha bound: Grossman-Quinn 98; Charles 99; Gronau-London-Sinha-Sinha 01 no significant constraints

Constraints in the (  ) plane: SU(3) BABAR Belle Charles 99 no significant constraints

Constraints in the (  ) plane: |P  +  – | from K 0  - BABAR Belle

BABAR Belle Constraints in the (  ) plane:QCD Factorisation Negative C  and small positive  negative  BABAR Belle

What about  ? BABAR Belle At present, significant theoretical input needed to extract 

QCD Factorisation: uncertainty from hard spectator interaction and annihilation diagram BABAR Belle no zoom Non-factorisable power-suppressed contribution parameters free

Constraints/predictions on |P/T| and  (C , S  ) and ( ,  ) from standard CKM fit non-factorisable contributions free theoretical parameters varied within a given range uncertainty from ( ,  ) non-factorisable contributions fixed

Predicting C  and S  using ,  from standard CKM fit Only predictive approach: QCD Factorisation. poor knowledge of sin2   large uncertainty in S 

Constraint on Br(B   0  0 ) Inputs = C , Br(B   +  - ), Br(B   +  0 ) Moriond’02 Belle measurements ! ! Gronau-London-Sinha-Sinha 01 S  C 

How about More Statistics? Isospin analysis for present central values, but 500 fb –1 (BaBar C ,,S  and WA branching fractions) and even more... The only hope for BaBar and Belle is not to observe B 0   0  0

Various strategies to interpret time-dependent asymmetry measurements C , S  studied: –Significant constraints on  from QCD Factorisation but still need validation from data –Qualitative information when constraining the penguin amplitude using Br(B -  K 0  - ) – Mild assumption frameworks based on SU(2) and SU(3) do not lead to significant constraints If central value of BR(  0  0 ) stays large, isospin analysis probably cannot be performed by first generation B factories Conclusion