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.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)