On the particle spectrum and the conformal window

TL;DR

This paper investigates the spectrum and conformal properties of SU(3) gauge theory with twelve fermion flavors, providing nonperturbative insights into the infrared fixed point and the associated anomalous dimension, with implications for conformal window theories.

Contribution

It offers the first nonperturbative determination of the fermion mass anomalous dimension and a unified lattice spectrum analysis across the conformal and Coulomb phases.

Findings

Fermion mass anomalous dimension gamma* = 0.235(46).

Spectrum consistent with universal scaling in the Coulomb phase.

Restoration of U(1) axial symmetry observed.

Abstract

We study the SU(3) gauge theory with twelve flavours of fermions in the fundamental representation as a prototype of non-Abelian gauge theories inside the conformal window. Guided by the pattern of underlying symmetries, chiral and conformal, we analyze the two-point functions theoretically and on the lattice, and determine the finite size scaling and the infinite volume fermion mass dependence of the would-be hadron masses. We show that the spectrum in the Coulomb phase of the system can be described in the context of a universal scaling analysis and we provide the nonperturbative determination of the fermion mass anomalous dimension gamma*=0.235(46) at the infrared fixed point. We comment on the agreement with the four-loop perturbative prediction for this quantity and we provide a unified description of all existing lattice results for the spectrum of this system, them being in the Coulomb phase or the asymptotically free phase. Our results corroborate the view that the fixed point we are studying is not associated to a physical singularity along the bare coupling line and estimates of physical observables can be attempted on either side of the fixed point. Finally, we observe the restoration of the U(1) axial symmetry in the two-point functions.