### Abstract

We report here on the application of the perturbative renormalization-group to the Coulomb gauge in QCD. We use it to determine the high-momentum asymptotic form of the instantaneous color-Coulomb potential V(k→) and of the vacuum polarization P(k→,k
_{4}). These quantities are renormalization-group invariants in the sense that they are independent of the renormalization scheme. A scheme-independent definition of the running coupling constant is provided by k→
^{2}V(k→)=x
_{0}g
^{2}(k→/Λ
_{Coul}), and of α
_{s}≡ g
^{2}(k→/Λ
_{Coul})/4π, where x
_{0}= 12N/(11N -2N
_{f}), and Λ
_{Coul} is a finite QCD mass scale. We also show how to calculate the coefficients in the expansion of the invariant β function β(g)≡\k→\(∂g/∂\k→\)=- (b
_{0}g
^{3} + b
_{1}g
^{5} + b
_{2}g
^{7}+ ...), where all coefficients are scheme independent.

Original language | English (US) |
---|---|

Article number | 014002 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 65 |

Issue number | 1 |

DOIs | |

State | Published - 2002 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*65*(1), [014002]. https://doi.org/10.1103/PhysRevD.65.014002

**Renormalization-group calculation of the color-Coulomb potential.** / Cucchieri, Attilio; Zwanziger, Daniel.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 65, no. 1, 014002. https://doi.org/10.1103/PhysRevD.65.014002

}

TY - JOUR

T1 - Renormalization-group calculation of the color-Coulomb potential

AU - Cucchieri, Attilio

AU - Zwanziger, Daniel

PY - 2002

Y1 - 2002

N2 - We report here on the application of the perturbative renormalization-group to the Coulomb gauge in QCD. We use it to determine the high-momentum asymptotic form of the instantaneous color-Coulomb potential V(k→) and of the vacuum polarization P(k→,k 4). These quantities are renormalization-group invariants in the sense that they are independent of the renormalization scheme. A scheme-independent definition of the running coupling constant is provided by k→ 2V(k→)=x 0g 2(k→/Λ Coul), and of α s≡ g 2(k→/Λ Coul)/4π, where x 0= 12N/(11N -2N f), and Λ Coul is a finite QCD mass scale. We also show how to calculate the coefficients in the expansion of the invariant β function β(g)≡\k→\(∂g/∂\k→\)=- (b 0g 3 + b 1g 5 + b 2g 7+ ...), where all coefficients are scheme independent.

AB - We report here on the application of the perturbative renormalization-group to the Coulomb gauge in QCD. We use it to determine the high-momentum asymptotic form of the instantaneous color-Coulomb potential V(k→) and of the vacuum polarization P(k→,k 4). These quantities are renormalization-group invariants in the sense that they are independent of the renormalization scheme. A scheme-independent definition of the running coupling constant is provided by k→ 2V(k→)=x 0g 2(k→/Λ Coul), and of α s≡ g 2(k→/Λ Coul)/4π, where x 0= 12N/(11N -2N f), and Λ Coul is a finite QCD mass scale. We also show how to calculate the coefficients in the expansion of the invariant β function β(g)≡\k→\(∂g/∂\k→\)=- (b 0g 3 + b 1g 5 + b 2g 7+ ...), where all coefficients are scheme independent.

UR - http://www.scopus.com/inward/record.url?scp=0036144150&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036144150&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.65.014002

DO - 10.1103/PhysRevD.65.014002

M3 - Article

VL - 65

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 1

M1 - 014002

ER -