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

Abstract

I calculate the quark-gluon vertex of the tensor type $\Gamma (p,q)=g_3(p,q)p_4\text{Slash}\text{Vec}q$, vector type $g_2(p,q)\text{Vec}q$ and scalar type $g_1(p,q)$, for a small spacial momentum transfer $q=\mathbf{q}$ 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.

Comments: 7 pages, 4 figures, A mistake in the momentum scale in the domain wall fermion mass parameter is corrected and references updated. Proceedings of the Lattice2008 (130)