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Interpretation of CP Asymmetries in B→ππ: Theoretical Frameworks and Experimental Inputs

This research outlines the analysis of CP asymmetries in B→ππ decays within the theoretical frameworks of strong isospin symmetry SU(2) and SU(3) flavor symmetry. Using predictions from QCD factorization and experimental inputs from global CKM fits, the study discusses constraints on various parameters and the significance of different contributions. It also highlights the challenges in interpreting time-dependent asymmetry measurements and the need for further theoretical validation from data.

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Interpretation of CP Asymmetries in B→ππ: Theoretical Frameworks and Experimental Inputs

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  1. Interpreting CP asymmetries in

  2. B CP asymmetries Tree diagram: Penguin diagram: Rt /Rc  Ru /Rc g b need |P/T| and =arg(P/T)

  3. Theoretical frameworks strong isospin symmetry SU(2) (GL) CP-averaged Br(B) only (00 not seen yet) EW penguins neglected 1 + SU(3) flavour symmetry(BF,Ch) OZI-suppressed annihilation penguins neglected No correction of SU(3) breaking 1 + |P| from K0- (GR,BBNS) Rth from QCD factorisation Neglect annihilation diagram in K0-  remains unconstrained QCD factorisation(BBNS) Use the prediction of both |P/T| and  Non-factorisable 1/mb contributions fixed to default value use Br(B0K+-) and |P| = |PK| 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.B606:245-321,2001

  4. Experimental inputs Global CKM fit using standard constraints (referred as standard CKM fit in this talk) ICHEP02 Aspen03 sign convention changed! ICHEP’02 Branching fractions (x10-6) WA = BaBar + Belle + CLEO not seen 32 CL range: CKMFitter: Hoecker et al., Eur.Phys.J.C21,225,2001 and http://ckmfitter.in2p3.fr

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

  6. Constraints in the (r,h) plane: SU(3) BABAR Belle no significant constraints Charles 99

  7. Constraints in the (r,h) plane: |P+–| from K0- BABAR Belle

  8. Constraints in the (r,h) plane:QCD Factorisation BABAR Belle BABAR Belle Negative C and small positive  negative 

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

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

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

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

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

  14. 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 B0 00

  15. Conclusion • 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-K0-) • 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

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