The Pole mass of the heavy quark. Perturbation theory and beyond

Feb, 1994
26 pages
Published in:
  • Phys.Rev.D 50 (1994) 2234-2246
e-Print:
Report number:
  • TPI-MINN-94-4-T,
  • UMN-TH-1239-94,
  • CERN-TH-7171-94,
  • UND-HEP-94-BIG03

Citations per year

1994200220102018202501020304050
Abstract:
The key quantity of the heavy quark theory is the quark mass mQm_Q. Since quarks are unobservable one can suggest different definitions of mQm_Q. One of the most popular choices is the pole quark mass routinely used in perturbative calculations and in some analyses based on heavy quark expansions. We show that no precise definition of the pole mass can be given in the full theory once non-perturbative effects are included. Any definition of this quantity suffers from an intrinsic uncertainty of order \Lam /m_Q. This fact is succinctly described by the existence of an infrared renormalon generating a factorial divergence in the high-order coefficients of the αs\alpha_s series; the corresponding singularity in the Borel plane is situated at 2π/b2\pi /b. A peculiar feature is that this renormalon is not associated with the matrix element of a local operator. The difference \La \equiv M_{H_Q}-m_Q~{pole} can still be defined in Heavy Quark Effective Theory, but only at the price of introducing an explicit dependence on a normalization point μ\mu: \La (\mu ). Fortunately the pole mass mQ(0)m_Q(0) {\em per se} does not appear in calculable observable quantities.
  • heavy quark
  • quark: mass
  • mass: quark
  • mass: pole
  • pole: mass
  • perturbation theory: higher-order
  • operator product expansion
  • infrared problem
  • effect: renormalon
  • mass: correction