A study of quark-gluon vertices using the lattice Coulomb gauge domain wall fermion

TL;DR

This paper investigates the quark-gluon vertex functions in Coulomb gauge using lattice domain wall fermions, comparing the running coupling with other gauge measurements to enhance understanding of non-perturbative QCD effects.

Contribution

It provides a non-perturbative calculation of the quark-gluon vertex functions in Coulomb gauge with lattice DWF, and compares the running coupling with ghost-gluon and Landau gauge results.

Findings

The quark propagator shows small fluctuations in Coulomb gauge.

The running coupling $eta_{s,g_1}(q)$ is compared with other gauge measurements.

Results support consistency between Coulomb and Landau gauge analyses.

Abstract

I calculate the quark-gluon vertex of the tensor type $\Gamma(p,q)=g_3(p,q)p_4 \Slash{\Vec q}$, vector type $g_2(p,q)\Vec q$ and scalar type $g_1(p,q)$, for a small spacial momentum transfer $q=\bf q$ using the gauge configuration of the Domain Wall Fermion (DWF) provided by the RBC-UKQCD collaboration. The quark propagator of Coulomb gauge in the cylinder cut, i.e. the four momentum $p$ is directed along the diagonal of the hyper-cubic space has small fluctuation and I use this propagator in the evaluation of the operators by applying the non-perturbative renormalization method. The $q$ dependence of the running coupling $\alpha_{s,g_1}(q)$ is compared with $\alpha_I(q)$ measured by the ghost-gluon vertex in Coulomb gauge and $\alpha_s(q)$ measured in Landau gauge.