Study of the Change from Walking to Non-Walking Behavior in a Vectorial Gauge Theory as a Function of Nf

Abstract

We study a vectorial gauge theory with gauge group SU(Nc) and a variable number, Nf, of massless fermions in the fundamental representation of this group. Using approximate solutions of Schwinger-Dyson and Bethe-Salpeter equations, we calculate meson masses and investigate how these depend on Nf. We focus on the range of Nf extending from near the boundary with a non-Abelian Coulomb phase, where the theory exhibits a slowly running ("walking") gauge coupling, toward smaller values where the theory has non-walking behavior. Our results include determinations of the masses of the lowest-lying flavor-adjoint mesons with J^{PC} = 0^{-+}, 1^{--}, 0^{++}, and 1^{++} (the generalized π, ρ, a0, and a1). Related results are given for flavor-singlet mesons and for the generalization of f_π. These results give insight into the change from walking to non-walking behavior in a gauge theory, as a function of Nf .