Gauge Dependence of Effective Quark Mass and Matrix Elements in Gaugefixed Large $N$ Strong Coupling Lattice QCD

TL;DR

This paper develops a large N Wilson loop framework for gauge fixing in lattice QCD, revealing how effective quark masses and matrix elements depend on gauge parameter lambda, with results consistent with numerical simulations.

Contribution

It introduces a novel Wilson loop approach to analyze lambda-gauge fixing in large N lattice QCD, providing formulas for quark matrix elements and their lambda dependence.

Findings

Quark mass decreases as lambda increases

Quark propagator becomes non-covariant for lambda ≠ 1

Matching coefficients are lambda-independent

Abstract

In conjunction with recent numerical \hbox{$\lambda~\partial_0 A_0 + \nabla\cdot\vec{A} =0$} ``$\lambda$-gauge'' results reported in a companion paper, we construct an $N\to\infty$ Wilson loop picture of $\lambda$-gaugefixing in which (I)the $\lambda$-gauge expectation value of a link chain $C$ is the weighted sum over Wilson loops made by joining to $C$ all selfavoiding chains $\widetilde{C}$ closing $C$. (II)Weights $A_{\widetilde{C}}$, containing all the $\lambda$-dependence, are given by the $\beta=0$ $\lambda$-gauge expectation value of $\widetilde{C}$. (III)$A_{\widetilde{C}}$ equals path-products of coefficients from the trace expansion of the gaugefixing Boltzmann weight. From (II) and (III) we deduce formulas for $\beta =0$ quark matrix elements. We find that $M_q^{(\lambda)}$ decreases with increasing $\lambda$; the quark propagator dispersion relation is not covariant when $\lambda\ne 1$; and $\Delta I=1/2$ matching coefficients are $\lambda$-independent. These strong coupling features are qualitatively consistent with numerical $\beta=5.7$ and $6.0$ results briefly described here for comparison purposes but mainly presented in a companion paper.