Radiative corrections and enhanced power corrections for the shape function in inclusive B decays

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Radiative corrections and enhanced power
corrections for the shape function in inclusive
B decays

• Kazuhiro Tanaka (Juntendo U)

H. Kawamura (RIKEN) J. Kodaira (KEK)
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OPE
Light-cone expansion
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?factorization formula
Bigi et al. (94), Neubert (94) Korchemsky,
Sterman (94) Bauer, Pirjol, Sterwart (02)
perturbative
nonperturbative
??
??
unknown
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Shape function
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Loop corrections for RG evolution
Grozin, Korchemsky (96) Bauer,Manohar (04),
Bosch et al. (04)
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Cusp divergence
Polyakov (80) Korchemsky (89)
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Korchemsky, Sterman (94) Bauer, Manohar (04)
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Solution of RG eq.
IR renormalon ambiguity have to be compensated by
the power corrections from nonperturbative
effects
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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
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0
Light-cone expansion
Nachtmann corr.
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4-particle correlation!!
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new enhanced power corrections
independent set
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One-loop matching
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? to minimize complication due to alien
operators? to maximize gauge invariance in
Feynman rules
Background field method
Fock-Schwinger gauge
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Grozin, Korchemsky (96)
coincide with Bauer, Manohar (04), consistent
with Bosch, Lange, Neubert, Paz (04)
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? check of cancellation of IR divergence
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Summary
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