Pole mass of the heavy quark: Perturbation theory and beyond

The key quantity of the heavy quark theory is the quark mass [ital m][sub [ital Q]]. Since quarks are unobservable one can suggest different definitions of [ital m][sub [ital Q]]. One of the most popular choices is the pole quark mass routinely used in perturbative calculations and in some analyses...

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Bibliographic Details
Published in:Physical review. D, Particles and fields Particles and fields, 1994-08, Vol.50 (3), p.2234-2246
Main Authors: Bigi, II, II, Shifman, MA, Uraltsev, NG, Vainshtein, AI
Format: Article
Language:English
Subjects:
662230 - Quantum Chromodynamics- (1992-)
662240 - Models for Strong Interactions- (1992-)
662350 - Decays of Mesons- (1992-)
CORRECTIONS
DECAY
DIMENSIONS
ELEMENTARY PARTICLES
FERMIONS
FIELD THEORIES
MASS
PARTICLE DECAY
PERTURBATION THEORY
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
POSTULATED PARTICLES
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARKS
SEMILEPTONIC DECAY
SINGULARITY
WEAK PARTICLE DECAY
WIDTH
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Summary:The key quantity of the heavy quark theory is the quark mass [ital m][sub [ital Q]]. Since quarks are unobservable one can suggest different definitions of [ital m][sub [ital 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 nonperturbative effects are included. Any definition of this quantity suffers from an intrinsic uncertainty of order [Lambda][sub QCD]/[ital m][sub [ital Q]]. This fact is succinctly described by the existence of an infrared renormalon generating a factorial divergence in the high-order coefficients of the [alpha][sub [ital s]] series; the corresponding singularity in the Borel plane is situated at 2[pi]/[ital b]. A peculiar feature is that this renormalon is not associated with the matrix element of a local operator. The difference [bar [Lambda]][equivalent to][ital M][sub [ital H][ital Q]]-[ital m][sub [ital Q]][sup pole] can still be defined by heavy quark effective theory, but only at the price of introducing an explicit dependence on a normalization point [mu]: [bar [Lambda]]([mu]). Fortunately the pole mass [ital m][sub [ital Q]](0) [ital per] [ital se] does not appear in calculable observable quantities.
ISSN:0556-2821
1089-4918
DOI:10.1103/PhysRevD.50.2234