Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?

TL;DR

This paper evaluates a linear sigma model as an effective field theory for walking gauge theories near the conformal window, successfully fitting lattice data where traditional chiral perturbation theory fails.

Contribution

It introduces and tests a linear sigma model as a new EFT approach for describing light states in walking gauge theories, improving fits to lattice data.

Findings

Linear sigma model fits lattice data better than chiral perturbation theory.

The model reduces chi-squared/d.o.f. significantly in data fitting.

Supports the sigma model as a viable EFT for near-conformal gauge theories.

Abstract

In recent years, many investigations of confining Yang Mills gauge theories near the edge of the conformal window have been carried out using lattice techniques. These studies have revealed that the spectrum of hadrons in nearly conformal ("walking") gauge theories differs significantly from the QCD spectrum. In particular, a light flavorsinglet scalar appears in the spectrum which is nearly degenerate with the pseudo-NambuGoldstone bosons (PNGBs) at the lightest currently accessible quark masses. This state is a viable candidate for a composite Higgs boson. Presently, an acceptable effective field theory (EFT) description of the light states in walking theories has not been established. Such an EFT would be useful for performing chiral extrapolations of lattice data and for serving as a bridge between lattice calculations and phenomenology. It has been shown that the chiral Lagrangian fails to describe the IR dynamics of a theory near the edge of the conformal window. Here we assess a linear sigma model as an alternate EFT description by performing explicit chiral fits to lattice data. Our model provides an acceptable combined fit to the PNGB mass and decay constant, reducing the $\chi^2$/d.o.f. by more than an order of magnitude compared to next-to-leading order chiral perturbation theory.