Flavor Dependence of the S-parameter

TL;DR

This paper computes the S-parameter at two loops in the conformal window of gauge theories, revealing how it depends on flavor number and supporting the conjecture that the normalized S-parameter at the conformal window's upper end is minimal.

Contribution

It extends previous work by providing a two-loop perturbative calculation of the S-parameter across the conformal window, linking perturbative and non-perturbative results.

Findings

S increases as flavor number decreases

Normalized S at the conformal window's upper end is minimal

Results serve as benchmarks for lattice computations

Abstract

We extend the results of [arXiv:1006.0207 [hep-lat]] by computing the S-parameter at two loops in the perturbative region of the conformal window. Consistently using the expression for the location of the infra-red fixed point at the two-loop order we express the S-parameter in terms of the number of flavors, colors and matter representation. We show that S, normalized to the number of flavors, increases as we decrease the number of flavors. Our findings support the conjecture presented in [arXiv:1006.0207 [hep-lat]] according to which the normalized value of the S-parameter at the upper end of the conformal window constitutes the lower bound across the entire phase diagram for the given underlying asymptotically free gauge theory. We also show that the non-trivial dependence on the number of flavors merges naturally with the non-perturbative estimate of the S-parameter close to the lower end of the conformal window obtained using gauge duality [arXiv:1007.0254 [hep-ph]]. Our results are natural benchmarks for lattice computations of the S-parameter for vector-like gauge theories.