QCD with overlap fermions: Running coupling and the 3-loop beta-function
Abstract
We calculate the relation between the bare coupling constant g0 and the MSbar-renormalized coupling gMS: g0 = Zg(g0,a μ) gMS, to 2 loops in perturbation theory. We employ the standard Wilson action for gluons and the overlap action for fermions. For convenience, we have worked with the background field technique, which only requires evaluation of 2-point Green's function for the problem at hand. Our results depend explicitly on the number of fermion flavors (Nf) and colors (N). Since the dependence of Zg on the overlap parameter rho cannot be extracted analytically, we tabulate our results for different values in the allowed range of rho (0 < rho < 2), focusing on values which are being used most frequently in simulations. Knowledge of Zg allows us to derive the 3-loop coefficient of the bare beta-function (betaL(g0)) which, unlike the 1- and 2-loop coefficients, is regularization-dependent. The nontrivial dependence of Zg and of betaL(g0) on rho is plotted for various choices of N, Nf.