QCD with overlap fermions: Running coupling and the 3-loop β-function
Date
2007ISSN
1550-7998Source
Physical Review D - Particles, Fields, Gravitation and CosmologyVolume
76Issue
11Google Scholar check
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We calculate the relation between the bare coupling constant g0 and the MS̄-renormalized coupling gMS̄, g0=Zg(g0,aμ̄)gMS̄, 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 ρ cannot be extracted analytically, we tabulate our results for different values in the allowed range of ρ (0<ρ<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 β-function (βL(g0)) which, unlike the 1- and 2-loop coefficients, is regularization-dependent. The nontrivial dependence of Zg and of βL(g0) on ρ is plotted for various choices of N, Nf. © 2007 The American Physical Society.