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

In conjunction with recent numerical \hbox{$λ~\partial_0 A_0 + \nabla\cdot\vec{A} =0$} ``$λ$-gauge'' results reported in a companion paper, we construct an $N\to\infty$ Wilson loop picture of $λ$-gaugefixing in which (I)the $λ$-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 $λ$-dependence, are given by the $β=0$ $λ$-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 $β=0$ quark matrix elements. We find that $M_q^{(λ)}$ decreases with increasing $λ$; the quark propagator dispersion relation is not covariant when $λ\ne 1$; and $ΔI=1/2$ matching coefficients are $λ$-independent. These strong coupling features are qualitatively consistent with numerical $β=5.7$ and $6.0$ results briefly described here for comparison purposes but mainly presented in a companion paper.

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