Gauge theories with overlap fermions in an arbitrary representation: Evaluation of the 3-loop β-function

Abstract

This work presents the calculation of the relation between the bare coupling constant g0 and the MS̄-renormalized coupling gMS̄, g0=Zg(g0,aμ)gMS̄, to 2 loops in perturbation theory, with fermions in an arbitrary representation of the gauge group SU(N). Our calculation is performed using overlap fermions and Wilson gluons, and the background field technique has been chosen for convenience. The corresponding results in the fundamental representation appear in our longer publication. The 3-loop coefficient of the bare β-function, b2L, is extracted using the 2-loop expression for Zg, and it is presented as a function of the overlap parameter ρ, the number of fermion flavors (Nf) and the number of colors (N). We also provide the expression for the ratio of energy scales ΛL/ΛMS̄, in an arbitrary representation. A plot of ΛL/ΛMS̄ is given in the adjoint representation. © 2008 The American Physical Society.