Toward precise $\hat{I}¾$ gauge fixing for the lattice QCD

Abstract

Lattice QCD provides a first-principles framework for solving Quantum Chromodynamics (QCD). However, its application to off-shell partons has been largely restricted to the Landau gauge, as achieving high-precision $\hat{I}¾$-gauge fixing on the lattice poses significant challenges. Motivated by a universal power-law dependence of off-shell parton matrix elements on gauge-fixing precision in the Landau gauge, we propose an empirical precision extrapolation method to approximate high-precision $\hat{I}¾$-gauge fixing. By properly defining the bare gauge coupling and then the effective $\hat{I}¾$, we validate our $\hat{I}¾$-gauge fixing procedure by successfully reproducing the $\hat{I}¾$-dependent RI/MOM renormalization constants for local quark bilinear operators at 0.3\% level, up to $\hat{I}¾\sim 1$.

12 pages, 15 figures, accepted by PRD