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Published byKobe Sidders Modified over 2 years ago

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Motivation Theoretical framework Perturbative QCD Approach Numerical Results Summary 2

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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

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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

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

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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

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

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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 －

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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

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

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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 －

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

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♫ 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 －

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Thank you for your attention ! 25

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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

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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 －

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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 －

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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 －

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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 －

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