1. 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)

2. OPE
Light-cone expansion

3. 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

4. Shape function

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

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

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. Light-cone expansion
Nachtmann corr.

11. 4-particle
correlation!!

12. new enhanced power corrections
independent set

14. One-loop matching

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

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

17. ●　check of cancellation of IR divergence

19. Summary