# Pole mass of the heavy quark: Perturbation theory and beyond

## Abstract

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] [italmore »

- Authors:

- (TH Division, CERN, CH-1211 Geneva 23 (Switzerland) Department of Physics, University of Notre Dame du Lac, Notre Dame, Indiana 46556 (United States) Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455 (United States) St. Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188350 (Russian Federation) Budker Institute of Nuclear Physics, Novosibirsk 630090 (Russian Federation))

- Publication Date:

- OSTI Identifier:
- 7171977

- DOE Contract Number:
- AC02-83ER40105

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review, D (Particles Fields); (United States)

- Additional Journal Information:
- Journal Volume: 50:3; Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; PERTURBATION THEORY; QUARKS; MASS; CORRECTIONS; QUANTUM CHROMODYNAMICS; SEMILEPTONIC DECAY; SINGULARITY; WIDTH; DECAY; DIMENSIONS; ELEMENTARY PARTICLES; FERMIONS; FIELD THEORIES; PARTICLE DECAY; POSTULATED PARTICLES; QUANTUM FIELD THEORY; WEAK PARTICLE DECAY; 662240* - Models for Strong Interactions- (1992-); 662230 - Quantum Chromodynamics- (1992-); 662350 - Decays of Mesons- (1992-)

### Citation Formats

```
Bigi, I.I., Shifman, M.A., Uraltsev, N.G., and Vainshtein, A.I.
```*Pole mass of the heavy quark: Perturbation theory and beyond*. United States: N. p., 1994.
Web. doi:10.1103/PhysRevD.50.2234.

```
Bigi, I.I., Shifman, M.A., Uraltsev, N.G., & Vainshtein, A.I.
```*Pole mass of the heavy quark: Perturbation theory and beyond*. United States. doi:10.1103/PhysRevD.50.2234.

```
Bigi, I.I., Shifman, M.A., Uraltsev, N.G., and Vainshtein, A.I. Mon .
"Pole mass of the heavy quark: Perturbation theory and beyond". United States. doi:10.1103/PhysRevD.50.2234.
```

```
@article{osti_7171977,
```

title = {Pole mass of the heavy quark: Perturbation theory and beyond},

author = {Bigi, I.I. and Shifman, M.A. and Uraltsev, N.G. and Vainshtein, A.I.},

abstractNote = {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.},

doi = {10.1103/PhysRevD.50.2234},

journal = {Physical Review, D (Particles Fields); (United States)},

issn = {0556-2821},

number = ,

volume = 50:3,

place = {United States},

year = {1994},

month = {8}

}