Nonperturbative Renormalization in the RI-SMOM Scheme and Gribov Uncertainty in the RI-MOM Scheme for Staggered Bilinears

TL;DR

This paper compares nonperturbative renormalization factors for staggered bilinear operators using RI-SMOM and RI-MOM schemes, analyzing Gribov effects and providing insights into scheme differences and uncertainties.

Contribution

It introduces nonperturbative renormalization results in RI-SMOM schemes for staggered bilinears and examines Gribov ambiguity effects in RI-MOM, highlighting scheme comparisons and uncertainties.

Findings

RI-SMOM and RI-MOM schemes yield comparable renormalization factors.

Gribov ambiguity has negligible impact on $Z_q$ in RI-MOM.

Results improve understanding of scheme dependence in lattice renormalization.

Abstract

We present results of renormalization factors for bilinear operators obtained using the nonperturbative renormalization method (NPR) in the RI-SMOM schemes. The operators are constructed using HYP staggered quarks on the MILC asqtad lattice ($N_f=2+1$). We compare results in the RI-SMOM schemes with those in the RI-MOM scheme for the $V\otimes S$ and $S\otimes S$ operators. Since we use Landau gauge fixing, we study the effect of Gribov ambiguity on the wave function renormalization $Z_q$ in the RI-MOM scheme. We find that the Gribov uncertainty is negligibly small for $Z_q$ in the RI-MOM scheme.