Kazuhiro Tanaka (Juntendo U)

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Presentation transcript:

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

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

Shape function

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

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

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

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

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

Light-cone expansion Nachtmann corr.

4-particle correlation!!

new enhanced power corrections independent set

One-loop matching

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

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

●　check of cancellation of IR divergence

Summary