The large-mass regime of the dilaton-pion low-energy effective theory

TL;DR

This paper investigates the large-mass regime of the dilaton-pion effective theory in SU(3) gauge theory with 8 fermions, highlighting how hyperscaling relations persist and discussing the conditions for the small-mass regime.

Contribution

It provides an analysis of the large-mass regime where the dilaton-pion theory applies despite non-small fermion masses, and estimates the fermion mass scale for the small-mass regime.

Findings

Large-mass regime where dilaton-pion theory is valid despite sizable fermion masses

Hyperscaling relations similar to conformal theories in this regime

Estimated fermion mass threshold for entering the small-mass regime

Abstract

Numerical data of the SU(3) gauge theory with $N_f=8$ fermions in the fundamental representation suggest the existence of a large-mass regime, where the fermion mass is not small relative to the confinement scale, but nevertheless the dilaton-pion low-energy theory is applicable thanks to the parametric proximity of the conformal window. In this regime, the leading hyperscaling relations are similar to those of a mass-deformed conformal theory, so that distinguishing infrared conformality from confinement requires the study of subleading effects. Assuming that the $N_f=8$ theory confines, we estimate how light the fermion mass should be to enter the small-mass regime, where the pions become much lighter than the dilatonic scalar meson.