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→,k4). 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→)=x0g 2(k→/ΛCoul), and of αs≡ g2(k→/ΛCoul)/4π, where x0= 12N/(11N -2Nf), and ΛCoul 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→\(∂g/∂\k→\)=- (b0g3 + b1g5 + b2g 7+ ...), where all coefficients are scheme independent.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)