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.
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Submitted on : Tuesday, January 19, 2016 - 5:41:26 PM
Last modification on : Wednesday, October 3, 2018 - 8:48:04 PM

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  • HAL Id : hal-01259018, version 1
  • ARXIV : 1510.03603

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Kohtaroh Miura, Kei-Ichi Nagai, Akihiro Shibata. Schwinger-Dyson Study for Walking/Conformal Dynamics with IR Cutoffs. Sakata Memorial KMI Workshop on "Origin of Mass and Strong Coupling Gauge Theories" (SCGT15), Mar 2015, Nagoya Japan. ⟨hal-01259018⟩

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