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

Motivated by the 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_IR). We find that the chiral symmetry breaking is suppressed if IR cutoff (Λ_IR) becomes larger than the critical value near the dynamical mass $\left({\text{Λ}}_{\text{IR}}^{*}\sim m_D\right).$ In the conformal phase the γ_m is strongly suppressed by IR cutoffs for Λ_IR ≳ 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.