# 1. Motivation Theoretical framework Perturbative QCD Approach Numerical Results ...

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1 Slide 2 Motivation Theoretical framework Perturbative QCD Approach Numerical Results Summary 2 Slide 3 The B decays are useful to determine the CKM angle. the CP asymmetries are sensitive to high order contributions. It is necessary to calculate the NLO corrections to those channels in order to improve the reliability of the theoretical predictions. 3 Slide 4 Effective Hamiltonian is the basic tool to study B physics are Wilson coefficients are Effective operators 4 Slide 5 5 Slide 6 6 Slide 7 7 Slide 8 The amplitude of is The key is to tackle : Nave factorization Generalized Factorization QCD factorization (QCDF) Soft-collinear effective theory (SCET) Perturbative QCD approach (PQCD) 8 Slide 9 Six quark interaction inside the dotted line 9 4-quark operator Slide 10 The End-point singularity (x0,1). Introducing the transverse momentum of the light quark can remove the end-point singularities of hard kernel. 10 Slide 11 Large double logarithms K T resummation -Sudakov form factor Suppressed the long distance contributions Improve the applicability of PQCD 11 Slide 12 large double logarithms summed by the threshold resummation,and they lead to St(x) which smears the the end-point singularities on x,we parameteried this term as below: 12 Slide 13 In pQCD approach,the end-point divergence was removed effectively. the non-perturbative contributions were absorbed into the meson wave functions,and the perturbative contributions can be calculated in the hard kernel.the calculation is reliable. In this frame,the amplitude can be written as[PPNP51,85] universal H process dependent 13 Slide 14 14 Feynman diagrams which may contribute at leading order to B , decays Calculate in leading order (LO) Slide 15 we add two sorts of subleading corrections which include: 1. the NLO Wilson coefficient, the NLO Sudakov factor. 2. the NLO hard kernel contains the vertex corrections; the quark-loop and the chromo-magnetic penguin contributions. 15 Slide 16 Feynman diagrams for NLO contributions: the vertex corrections (a-f); the quark-loops(g-h) and the chromo-magnetic penguin contributions (i-j). 16 Slide 17 CP averaging branching ratios Direct CPV Mixing induced CPV 17 Slide 18 18 Slide 19 19 Slide 20 20 Slide 21 21 Slide 22 22 Slide 23 23 Slide 24 We calculate the branching ratios and CP-saymmetries of the B , decays in the perturbative QCD factorization approach up to the NLO contributions NLO correction have signicant e ects on some of the decay channels, most our NLO predictions agree well with the measured values The NLO corrections play an important role in modifying direct CP asymmetries 24 Slide 25 Thank you for your attention ! 25 Slide 26 C=0.3 comes from the best fit to the next-to-leading-logarithm threshold resummation in moment space. mellin 26 Slide 27 K T regularization scheme The vertex corrections can be absorbed into the redefinition of the Wilson coefficients by adding a vertex-function to them 27 Slide 28 The contribution from the so-called quark- loops is a kind of penguin correction with the four quark operators insertion. For the b d transition,the effective Hamiltonian can be written as (PRD72 114005) 28 Slide 29 The magnetic penguin is another kind penguin correction induced by the insertion of the operator O8g The corresponding weak effective Hamiltonian contains the b dg transition can be written as 29 Slide 30 the NLO contributions can be included in a simple way: the vertex corrections have been absorbed into the redenition of the Wilson coe cient 30 Slide 31 31 Slide 32 32 Slide 33 33 Slide 34 34 Slide 35 35 Slide 36 the hard-scattering form factor J is relatively large and comparable with the soft form factor . Besides, this term has a large Wilson coe cient. 36

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