Renormalized sum rules for structure functions of heavy mesons decays

Nov, 1994
20 pages
Published in:
  • Phys.Rev.D 53 (1996) 1378-1390
e-Print:
Report number:
  • OUT-4102-53,
  • ITP-SB-94-47,
  • OUT--4102--53,
  • ITP--SB--94--47

Citations per year

1995200220092016202301234567
Abstract: (arXiv)
We consider properties of the structure functions of inclusive heavy meson decays BXcB\to X_c and treat the cc quark mass as a free parameter. We show that in two extreme cases of heavy and light cc quark 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 time--like and a light--like 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 heavy--heavy transition is renormalized multiplicatively while that of 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 ``third'' sum rules) with a soft exponential factorization cut--off, 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 u=12u=\frac12 are exactly cancelled by the similar uncertainty in the heavy quark pole mass. The leading nonperturbative corrections associated with the next renormalon at u=1u=1 are parameterized by the matrix element μπ2\mu_\pi^2 which is proportional to the heavy quark kinetic energy.
Note:
  • 20 pages, LaTeX style
  • B: semileptonic decay
  • semileptonic decay: B
  • decay: inclusive reaction
  • inclusive reaction: decay
  • quark: charm
  • structure function: renormalization
  • dependence: factorization
  • sum rule
  • infrared problem: renormalon
  • correction: nonperturbative