Renormalizationgroup calculation of the colorCoulomb potential
Abstract
We report here on the application of the perturbative renormalizationgroup to the Coulomb gauge in QCD. We use it to determine the highmomentum asymptotic form of the instantaneous colorCoulomb potential V(k>) and of the vacuum polarization P(k>,k_{4}). These quantities are renormalizationgroup invariants in the sense that they are independent of the renormalization scheme. A schemeindependent 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/(11N2N_{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.
 Publication:

Physical Review D
 Pub Date:
 January 2002
 DOI:
 10.1103/PhysRevD.65.014002
 arXiv:
 arXiv:hepth/0008248
 Bibcode:
 2002PhRvD..65a4002C
 Keywords:

 12.38.Bx;
 11.10.Hi;
 12.39.Pn;
 Perturbative calculations;
 Renormalization group evolution of parameters;
 Potential models;
 High Energy Physics  Theory;
 High Energy Physics  Lattice
 EPrint:
 24 pages, 1 figure, TeX file. Minor modifications, incorporating referee's suggestions