## 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) |
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Article number | 014002 |

Journal | Physical Review D |

Volume | 65 |

Issue number | 1 |

DOIs | |

State | Published - 2002 |

## ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)