Effective pion mass term and the trace anomaly

TL;DR

This paper derives the transformation properties of the pion mass term in an effective theory near the conformal window, linking it to the trace anomaly and the fixed-point anomalous dimension.

Contribution

It establishes the exponent $y=3-\gamma_m^*$ for the pion mass term, connecting effective theory parameters with fundamental gauge theory properties.

Findings

Derived the exponent y=3-γ_m* for the pion mass term.

Linked the effective theory to the trace anomaly of the underlying gauge theory.

Confirmed consistency with the fixed-point anomalous dimension.

Abstract

Recently, we developed an effective theory of pions and a light dilatonic meson for gauge theories with spontaneously broken chiral symmetry that are close to the conformal window. The pion mass term in this effective theory depends on an exponent $y$. We derive the transformation properties under dilatations of the renormalized fermion mass, and use this to rederive $y=3-\gamma_m^*$, where $\gamma_m^*$ is fixed-point value of the mass anomalous dimension at the sill of the conformal window. This value for $y$ is consistent with the trace anomaly of the underlying near-conformal gauge theory.