1 / 54

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.

anoush
Download Presentation

PANIC05

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related