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

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 $f_π$, and investigate the chiral symmetry breaking and mass anomalous dimension $γ_{m}$ in the presence of IR cutoffs $Λ_{\mathrm{IR}}$. We find that the chiral symmetry breaking is suppressed \ if IR cutoff $Λ_{\mathrm{IR}}$ becomes larger than the critical \ value near the dynamical mass ($Λ_{\mathrm{IR}}$ $\simeq m_{D}$) In the conformal phase the $γ_{m}$ is strongly suppressed by IR cutoffs for $Λ_{\mathrm{IR}}$ $\simeq m_{p}$. We, then, obtain finite size hyperscaling (FSS) relation by adapting a linearized approximation for the SD equation, and examine the $γ_{m}$ The results offer valuable insight and suggestion for analyses in lattice gauge theories.

5 pages,2 figures; Presented at Sakata Memorial KMI Workshop on "Origin of Mass and Strong Coupling Gauge Theories" (SCGT15)