QCD with overlap fermions: Running coupling and the 3-loop beta-function

TL;DR

This paper computes the relation between bare and renormalized QCD couplings using overlap fermions, deriving the 3-loop beta-function coefficient and analyzing its dependence on parameters for improved lattice simulations.

Contribution

It provides a two-loop calculation of the coupling relation and the 3-loop beta-function coefficient for QCD with overlap fermions, including parameter dependence.

Findings

Calculated Z_g for various rho, N, N_f values.

Derived the 3-loop beta-function coefficient.

Analyzed parameter dependence of renormalization factors.

Abstract

We calculate the relation between the bare coupling constant g_0 and the MSbar-renormalized coupling g_MS: g_0 = Z_g(g_0,a \mu) g_MS, 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 (N_f) and colors (N). Since the dependence of Z_g 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 Z_g allows us to derive the 3-loop coefficient of the bare beta-function (beta_L(g_0)) which, unlike the 1- and 2-loop coefficients, is regularization-dependent. The nontrivial dependence of Z_g and of beta_L(g_0) on rho is plotted for various choices of N, N_f.