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 Motivation  Theoretical framework  Perturbative QCD Approach  Numerical Results  Summary 2

 The B → πρ 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

 Effective Hamiltonian is the basic tool to study B physics are Wilson coefficients are Effective operators 4

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 The amplitude of is  The key is to tackle : Naïve factorization Generalized Factorization QCD factorization (QCDF) Soft-collinear effective theory (SCET) Perturbative QCD approach (PQCD) … 8

Six quark interaction inside the dotted line 9 4-quark operator

 The End-point singularity (x→0,1).  Introducing the transverse momentum of the light quark can remove the end-point singularities of hard kernel. 10

 Large double logarithms  K T resummation –-Sudakov form factor  Suppressed the long distance contributions  Improve the applicability of PQCD － 11 －

 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 －

 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]  Ф ： universal  H ： process dependent 13

14 Feynman diagrams which may contribute at leading order to B → πρ, πω decays Calculate in leading order (LO)

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 －

Feynman diagrams for NLO contributions: the vertex corrections (a-f); the quark-loops(g-h) and the chromo-magnetic penguin contributions (i-j). － 16 －

♫ CP averaging branching ratios ♫ Direct CPV ♫ Mixing induced CPV 17

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 We calculate the branching ratios and CP-saymmetries of the B → πρ, πω decays in the perturbative QCD factorization approach up to the NLO contributions 。  NLO correction have significant e ff 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 －

Thank you for your attention ! 25

 C=0.3 comes from the best fit to the next-to-leading-logarithm threshold resummation in moment space. （由 mellin 变换决定的） 26

 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 －

 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 (PRD ) － 28 －

 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 －

 the NLO contributions can be included in a simple way:  the vertex corrections have been absorbed into the redefinition of the Wilson coe ffi cient 30

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 the hard-scattering form factor ζJ is relatively large and comparable with the soft form factor ζ. Besides, this term has a large Wilson coe ffi cient. － 36 －