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Kazuhiro Tanaka (Juntendo U)

Radiative corrections and enhanced power corrections for the shape function in inclusive B decays. Kazuhiro Tanaka (Juntendo U). H. Kawamura (RIKEN) J. Kodaira (KEK). OPE. Light-cone expansion. ⇒factorization formula. Bigi et al. (’94), Neubert (’94) Korchemsky, Sterman (’94)

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Kazuhiro Tanaka (Juntendo U)

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  1. Radiative corrections and enhanced power corrections for the shape function in inclusive B decays Kazuhiro Tanaka (Juntendo U) H. Kawamura (RIKEN) J. Kodaira (KEK)

  2. OPE Light-cone expansion

  3. ⇒factorization formula Bigi et al. (’94), Neubert (’94) Korchemsky, Sterman (’94) Bauer, Pirjol, Sterwart (’02) perturbative nonperturbative 形状 関数 unknown

  4. Shape function

  5. Grozin, Korchemsky (’96) Bauer,Manohar (’04), Bosch et al. (’04) Loop corrections for RG evolution

  6. Polyakov (’80) Korchemsky (’89) Cusp divergence

  7. Korchemsky, Sterman (’94) Bauer, Manohar (’04)

  8. Solution of RG eq. IR renormalon ambiguity have to be compensated by the power corrections from nonperturbative effects:

  9. Tree-level matching ● Economic way: Kawamura,Kodaira,Tanaka, Prog.Theor.Phys. 113 (’05)183 Eq. of motion constraints on nonlocal operator ⇒ nonlocal op. basis Taylor expand in the final step ⇒ independent set

  10. 0 Light-cone expansion Nachtmann corr.

  11. 4-particle correlation!!

  12. new enhanced power corrections independent set

  13. One-loop matching

  14. ● to minimize complication due to alien operators● to maximize gauge invariance in Feynman rules Background field method: Fock-Schwinger gauge

  15. Grozin, Korchemsky (’96) [coincide with Bauer, Manohar (‘04), consistent with Bosch, Lange, Neubert, Paz (‘04)]

  16. ●check of cancellation of IR divergence

  17. Summary

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