Linear Sigma EFT for Nearly Conformal Gauge Theories

TL;DR

This paper develops a generalized linear sigma model as an effective field theory to describe nearly conformal gauge theories, capturing the light scalar state observed in lattice studies and explaining its mass relations.

Contribution

It introduces a novel EFT framework that includes explicit chiral symmetry breaking terms, accurately modeling the scalar and pion masses in nearly conformal gauge theories.

Findings

The EFT reproduces the light scalar ($\sigma$) and pion ($\pi$) mass spectrum.

It relaxes the inequality $M_{\sigma}^2 \ge 3 M_{\pi}^2$, aligning with lattice data.

The model remains weakly coupled despite large explicit symmetry breaking.

Abstract

We construct a generalized linear sigma model as an effective field theory (EFT) to describe nearly conformal gauge theories at low energies. The work is motivated by recent lattice studies of gauge theories near the conformal window, which have shown that the lightest flavor-singlet scalar state in the spectrum ($\sigma$) can be much lighter than the vector state ($\rho$) and nearly degenerate with the PNGBs ($\pi$) over a large range of quark masses. The EFT incorporates this feature. We highlight the crucial role played by the terms in the potential that explicitly break chiral symmetry. The explicit breaking can be large enough so that a limited set of additional terms in the potential can no longer be neglected, with the EFT still weakly coupled in this new range. The additional terms contribute importantly to the scalar and pion masses. In particular, they relax the inequality $M_{\sigma}^2 \ge 3 M_{\pi}^2$, allowing for consistency with current lattice data.