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

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 μ) 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.

20 pages, 6 figures, 2 Tables

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Cited by in corpus (7)

• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Classical Limits of Scalar and Tensor Gauge Operators Based on the Overlap Dirac Matrix
• Large Wilson loops with overlap and clover fermions: Two-loop evaluation of the b-quark mass shift and the quark-antiquark potential
• Relation between bare lattice coupling and MSbar coupling at one loop with general lattice fermions
• Gauge theories with overlap fermions in an arbitrary representation: Evaluation of the 3-loop beta-function
• Perturbative determination of $\mathcal{O}(am)$ improvement on the QCD running coupling
• Linking infrared and ultraviolet parameters of pion-like states in strongly coupled gauge theories