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Revisiting the B → πρ , πω Decays in the Perturbative QCD Approach beyond the leading order

Revisiting the B → πρ , πω Decays in the Perturbative QCD Approach beyond the leading order. By Zhou Rui ( 周锐 ) Collaborator: Cai -Dian Lu, Xiang-dong Gao. Outline. Motivation Theoretical framework Perturbative QCD Approach Numerical Results Summary. Motivation.

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Revisiting the B → πρ , πω Decays in the Perturbative QCD Approach beyond the leading order

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  1. Revisiting the B → πρ, πω Decays in the Perturbative QCD Approach beyond the leading order By Zhou Rui(周锐) Collaborator: Cai-Dian Lu, Xiang-dong Gao

  2. Outline • Motivation • Theoretical framework • Perturbative QCDApproach • Numerical Results • Summary

  3. Motivation • 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.

  4. Theoretical framework • Effective Hamiltonian is the basic tool to study B physics are Wilson coefficients are Effectiveoperators

  5. tree operators

  6. QCD-penguin and QED-penguin

  7. Magnetic Penguins

  8. 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) • …

  9. Picture of PQCD Approach--kT因子化 Six quark interaction inside the dotted line 4-quark operator

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

  11. the Sudakov form factor • Large double logarithms • KT resummation –-Sudakovform factor • Suppressed the long distance contributions • Improve the applicability of PQCD

  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:

  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] • Ф：universal • H ：process dependent

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

  15. Calculate in next-to-leading order (NLO) we add two sorts of subleading corrections which include: • the NLO Wilson coefficient , the NLO Sudakov factor. • the NLO hard kernel contains the vertex corrections; the quark-loop and the chromo-magnetic penguin contributions.

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

  17. Numerical Results • CP averaging branching ratios • Direct CPV • Mixing induced CPV

  18. The CP-averaged branching ratio (10^-6)

  19. The scale dependence of in LO and NLO pQCD

  20. The pQCD predictions for the direct CP-violating asymmetries (in units of %)

  21. The pQCD predictions for the CP-violating parameters S_f and the total CP-violating parameters A_CP of B0 → π0ρ0, π0ω (in units of %)

  22. The LO and NLO pQCD predictions for the CP-violating parameters Cf , Sf ,∆C and ∆S (f = π−ρ+) of B→ π±ρ∓ (in units of %)

  23. Summary • 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 effects 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. KT 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 (PRD72 114005)

  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 decay amplitude • the NLO contributions can be included in a simple way: • the vertex corrections have been absorbed into the redefinition of the Wilson coefficient

  30. Wilson coefficients and Effective operators

  31. the hard-scattering form factor ζJ is relatively large and comparable with the soft form factor ζ. Besides, this term has a large Wilson coefficient.

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