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 $f_{\pi }$, 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.

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