Schwinger-Dyson Study for Walking/Conformal Dynamics with IR Cutoffs

TL;DR

This study uses Schwinger-Dyson equations to analyze conformal and walking dynamics in gauge theories with IR cutoffs, providing insights into chiral symmetry breaking, mass anomalous dimension, and finite size hyperscaling relevant for lattice simulations.

Contribution

It introduces a numerical SD equation approach with IR cutoffs to explore chiral symmetry and anomalous dimensions in conformal/walking gauge theories, offering new analytical tools.

Findings

Chiral symmetry breaking is suppressed when IR cutoff exceeds the dynamical mass.

Mass anomalous dimension is strongly suppressed by IR cutoffs near the pole mass.

Finite size hyperscaling relation is derived and used to analyze the data.

Abstract

Motivated by recent progress on many flavor QCD on a lattice, we investigate conformal/walking dynamics by using Schwinger-Dyson (SD) equation within an improved ladder approximation for two-loop running coupling. By numerically solving the SD equation, we obtain a pole mass $m_{p}$, pion decay constant $f_{\pi}$, and investigate the chiral symmetry breaking and mass anomalous dimension $\gamma_{m}$ in the presence of IR cutoffs $\Lambda_{\mathrm{IR}}$. We find that the chiral symmetry breaking is suppressed \ if IR cutoff $\Lambda_{\mathrm{IR}}$ becomes larger than the critical \ value near the dynamical mass ($\Lambda_{\mathrm{IR}}$ $\simeq m_{D}$) In the conformal phase the $\gamma_{m}$ is strongly suppressed by IR cutoffs for $\Lambda _{\mathrm{IR}}$ $\simeq m_{p}$. We, then, obtain finite size hyperscaling (FSS) relation by adapting a linearized approximation for the SD equation, and examine the $\gamma_{m}$ The results offer valuable insight and suggestion for analyses in lattice gauge theories.