A new method for the beta function in the chiral symmetry broken phase

TL;DR

This paper introduces a novel lattice-based method to non-perturbatively determine the beta function in gauge theories within the chiral symmetry broken phase, bridging the gap between weak and strong coupling regimes.

Contribution

The authors develop a new lattice simulation technique to measure the beta function non-perturbatively in the p-regime, complementing existing methods at zero fermion mass.

Findings

Beta function is small but non-zero at g^2=6.7

Method applied to SU(3) with two sextet fermions

Supports near-conformal behavior relevant for composite Higgs models

Abstract

We describe a new method to determine non-perturbatively the beta function of a gauge theory using lattice simulations in the p-regime of the theory. This complements alternative measurements of the beta function working directly at zero fermion mass and bridges the gap between the weak coupling perturbative regime and the strong coupling regime relevant to the mass spectrum of the theory. We apply this method to ${\mathrm {SU(3)} }$ gauge theory with two fermion flavors in the 2-index symmetric (sextet) representation. We find that the beta function is small but non-zero at the renormalized coupling value $g^2 = 6.7$, consistent with our previous independent investigation using simulations directly at zero fermion mass. The model continues to be a very interesting explicit realization of the near-conformal composite Higgs paradigm which could be relevant for Beyond Standard Model phenomenology.