Renormalized sum rules for structure functions of heavy meson decays

Journal Article · Thu Feb 01 04:00:00 EST 1996 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.53.1378· OSTI ID:278568

Grozin, A G ^[1]; Korchemsky, G P ^[2]

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1. Physics Department, Open University, Milton Keynes, MK7 6AA (United Kingdom)
2. Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York 11794-3840 (United States)

We consider the properties of the structure functions of inclusive heavy meson decays {ital B}{r_arrow}{ital X}{sub {ital c}} and treat the {ital c} quark mass as a free parameter. We show that in two extreme cases of heavy and light {ital c} quarks the structure functions of heavy-heavy and heavy-light transitions are given by a Fourier transform of the matrix elements of Wilson lines containing a timelike and a lightlike segment, correspondingly. Using the renormalization properties of Wilson lines we find the dependence of the structure functions on the factorization scale, the structure function of the heavy-heavy transition is renormalized multiplicatively, while that of the heavy-light transition obeys the GLAP-type evolution equation. We propose a generalization of the sum rules for the moments of the structure functions (Bjorken, Voloshin, and the {open_quote}{open_quote}third{close_quote}{close_quote} sum rules) with a soft exponential factorization cutoff, which correctly incorporates both perturbative and nonperturbative effects. We analyze nonperturbative corrections by first considering infrared renormalon contributions to the Wilson lines. Uncertainties induced by the leading renormalon pole at {ital u}=1/2 are exactly canceled by a similar uncertainty in the heavy quark pole mass. The leading nonperturbative corrections associated with the next renormalon at {ital u}=1 are parametrized by the matrix element {mu}{sub {pi}}{sup 2} which is proportional to the heavy quark kinetic energy. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 278568
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 3 Vol. 53; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
FACTORIZATION
FOURIER TRANSFORMATION
KINETIC ENERGY
MASS
MATRIX ELEMENTS
MESONS
QUARKS
RENORMALIZATION
STRUCTURE FUNCTIONS
SUM RULES
WEAK HADRONIC DECAY