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PANIC05

PANIC05. POWER CORRECTIONS AND CP PHASES. Tsung-Wen Yeh National Taichung University Taiwan, R.O.C. d. W -. b. u. CP Phases. CP phases are defined through unitarity triangles. d. + 5 other equations. W -. b. u. CP Phases. CP phases are defined through unitarity triangles.

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PANIC05

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  1. PANIC05 POWER CORRECTIONS AND CP PHASES Tsung-Wen Yeh National Taichung University Taiwan, R.O.C.

  2. d W - b u CP Phases • CP phases are defined through unitarity triangles T.W. Yeh-Power corrections and CP phases

  3. d + 5 other equations W - b u CP Phases • CP phases are defined through unitarity triangles unitarity T.W. Yeh-Power corrections and CP phases

  4. + 5 other equations CP Phases • CP phases are defined through unitary triangles unitarity d W - b u T.W. Yeh-Power corrections and CP phases

  5. Roadmap for CP Phases in B Physics R. Fleischer, PITHA 05 talk T.W. Yeh-Power corrections and CP phases

  6. [ CKM constraint dominated by theory error ] • CKM fit predicts : Δmd = 0.47 ps–1 + 0.23 – 0.12 CP Phases in present status A. Höcker, SLAC 05 talk T.W. Yeh-Power corrections and CP phases

  7. CP Phases in M. Neubert, JHEP 9902:014,1999 ; Nucl.Phys.Proc.Suppl.86:477-486,2000 T.W. Yeh-Power corrections and CP phases

  8. CP Phases from Hadronic B Decays • Existing strategies for extracting CP phases from hadronic B decays requires knowledge of hadronic mechanisms T.W. Yeh-Power corrections and CP phases

  9. CP Phases from Hadronic B Decays • Existing strategies for extracting CP phases from hadronic B decays requires knowledge of hadronic mechanisms • OPE at weak scale: nonlocal operator factorized into SD Wilson Coeff. and LD local operators T.W. Yeh-Power corrections and CP phases

  10. CP Phases from Hadronic B Decays • Existing strategies for extracting CP phases from hadronic B decays requires knowledge of hadronic mechanisms • OPE at weak scale: nonlocal operator factorized into SD Wilson Coeff. and LD local operators • RG equations : evolutions of local operators from high scale to low scale T.W. Yeh-Power corrections and CP phases

  11. CP Phases from Hadronic B Decays • Existing strategies for extracting CP phases from hadronic B decays requires knowledge of hadronic mechanisms • OPE at weak scale: nonlocal operator factorized into SD Wilson Coeff. and LD local operators • RG equations : evolutions of local operators from higher scale to lower scale • Hadronic Matrix Elements contain perturbative and nonperturbative QCD contributions at factorization scale T.W. Yeh-Power corrections and CP phases

  12. Theories • Theoretical Approaches based on QCD: • QCD FA : Beneke et al, PRL 83, 1914(99);NPB606,245(01); NP B675, 333 (03) • pQCD : Keum et al, PLB 504, 6(01); PRD 67, 054009 (03) • SCET : Bauer et al, PRD 63, 114030 (01) • Theoretical Approaches based onsymmetry • Strong isospin symmetry SU(2) : Gronau, London, PRL 65:3381(99) • 1+ SU(3) flavor sysmtery :Buras, Fleisher, PLB360:138(95’);Charles, PRD59:054007(99’) • Isospin + QCD FA T.W. Yeh-Power corrections and CP phases

  13. QCD FA • Heavy quark limit : mb >> • Energetical final state meson : E >> • Factorization of m.e. into hard scattering kernel and LC DAs • Factorization holds at O(1/ mb) and • Extension of naive factorization, color transparency • Automatically including rescattering phase T.W. Yeh-Power corrections and CP phases

  14. QCD FA - Topology vertex T.W. Yeh-Power corrections and CP phases

  15. QCD FA - Topology Penguin T.W. Yeh-Power corrections and CP phases

  16. QCD FA - Topology Spectator T.W. Yeh-Power corrections and CP phases

  17. QCD FA - Topology annihilation T.W. Yeh-Power corrections and CP phases

  18. Sources of Power Corrections • FSI-final state interaction • HS-Hard Spectator • DG-dynamical gluon • AT-annihilation topology • SRG-soft radiative gluon • CP-charming penguin • NFCG-nonfactorizable • collinear gluon • Renor-renormalon T.W. Yeh-Power corrections and CP phases

  19. Sources of Power Corrections • FSI-sizable(model) • HS-very small • DG-sinificant • AT-20% • SRG-few % • CP-sizable(model) or very small(LCSR) • NFCG-few to 10 % • Renor-very small T.W. Yeh-Power corrections and CP phases

  20. QCD FA for i=1-4,8,10 for i=5,7 for i=4,6 for i=8,10 • Hard spectator functions diverge at end points – regularized by a model • twist-3 two parton effects included T.W. Yeh-Power corrections and CP phases

  21. QCD FA for i=1-4,8,10 for i=5,7 for i=4,6 3 PARTON for i=8,10 • Hard spectator functions has no 3 parton contributions • Coefficient functions for O6 and O8 are corrected by 3 parton T.W. Yeh-Power corrections and CP phases

  22. QCD FA • annihilation functions contain end point divergences • 3 parton effects can be neglected in annihilation functions T.W. Yeh-Power corrections and CP phases

  23. Amplitudes defined in QCDFA T.W. Yeh-Power corrections and CP phases

  24. Amplitudes defined in QCDFA T.W. Yeh-Power corrections and CP phases

  25. Amplitudes defined in QCDFA T.W. Yeh-Power corrections and CP phases

  26. Strong Phases in QCDFA T.W. Yeh-Power corrections and CP phases

  27. T.W. Yeh-Power corrections and CP phases

  28. T.W. Yeh-Power corrections and CP phases

  29. 3pt 24.9 -21.2 20.9 -16.1 2.2 -13.2 60.5 1.28 7.3 -47.8 27.9 15.0 T.W. Yeh-Power corrections and CP phases

  30. + + + + + + T.W. Yeh-Power corrections and CP phases

  31. Comparison between EXPT and QCD FA • LO+2PT TW3 contributions for • theoretic uncertainty are large due to input parameters and higher order corrections A. Höcker, SLAC 05 talk T.W. Yeh-Power corrections and CP phases

  32. Exploring CKM in QCD FA 2 parton 3 parton R R T.W. Yeh-Power corrections and CP phases

  33. Exploring CKM in QCD FA • Inputs: R* and εexp T.W. Yeh-Power corrections and CP phases

  34. 2 parton 3 parton T.W. Yeh-Power corrections and CP phases

  35. SA SP EWP EWA Exploring CKM in QCD FA BN01 • Assume PDG2004 T.W. Yeh-Power corrections and CP phases

  36. 2 parton 3 parton 3 parton -2 parton T.W. Yeh-Power corrections and CP phases

  37. 3 parton 2 parton HFAG 05’ T.W. Yeh-Power corrections and CP phases

  38. 2 parton 3 parton T.W. Yeh-Power corrections and CP phases

  39. 2 parton 3 parton T.W. Yeh-Power corrections and CP phases

  40. 2 parton 3 parton T.W. Yeh-Power corrections and CP phases

  41. 2 parton 3 parton T.W. Yeh-Power corrections and CP phases

  42. 3 parton 2 parton T.W. Yeh-Power corrections and CP phases

  43. 2 parton 3 parton T.W. Yeh-Power corrections and CP phases

  44. I will only discuss power corrections in QCDF T.W. Yeh-Power corrections and CP phases

  45. Hard Spectator Gluons • Radiative gluons connecting the spectator quark and the partons of the emitted meson • Gluons carry momentum of scale • except and , other 8 effective operators participate • Amplitudes are of ~ few % of Tree T.W. Yeh-Power corrections and CP phases

  46. Annihilation Topology • Radiative gluons involve in annihilation diagrams • Gluons carry momentum of scale • except , other 10 effective operators participate • Amplitudes are of ~ few -- 20% of Tree • Uncertainty ~30-40% due to a regularization for end-point divergence T.W. Yeh-Power corrections and CP phases

  47. Nonfactorizable soft Gluons • soft gluons involve in vertex diagrams • Gluons carry momentum of scale • except , other 10 effective operators participate • Significant for some PP and VP with • Require Sum Rule assumptions (optical theorem for correlators) K.W. Yang,PRD69 (2004) 054025 T.W. Yeh-Power corrections and CP phases

  48. S Collinear Expansion • QCD factorization, LO partons can carry only collinear momenta into hard scattering center • systematical expansion of parton momenta w.r.t. coll. momenta • non-collinear parts of parton momenta as higher order effects [EFP, 82,83] • parton model + Feynman diagram calculation techniques [J. Qui, 90,92] • only dynamical gluon contributions included • exclusive process applicable [T.W. Yeh, 00,02,] + S' v v=0 T.W. Yeh-Power corrections and CP phases

  49. NonFactorizable DG Factorizable DG Dynamical Gluons • Collinear gluons of the emitted light meson enter into the hard scattering center • Scale analysis indicate that collinear partons dominate • FDG ~ , while NFDG ~ • FDG corrections enhanced by their hard kernel ~ 50 % of two parton twist-3 contributions T.W. Yeh-Power corrections and CP phases

  50. Vertex Diagrams • Adding Collinear gluon to the vertex diagrams in QCD FA: • 112 diagrams • Up to , only 8 factorizable DG diagrams remain • Only participate and collinear (soft) div.’s cancelled out • About 20 % of two parton twist-3 vertex corrections T.W. Yeh-Power corrections and CP phases

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