RI/MOM Renormalization Window and Goldstone Pole Contamination

TL;DR

This study compares different non-perturbative methods for calculating lattice renormalization constants, finding that Goldstone pole contamination is less significant than discretization effects at current couplings.

Contribution

It provides a detailed comparison of RI/MOM and Ward Identity methods for Z_P/Z_S, highlighting the relative impact of Goldstone pole contamination versus discretization effects.

Findings

Discrepancy of 10-15% between methods at current couplings.

Goldstone pole contamination is subdominant compared to cutoff effects.

RI/MOM results are consistent with Ward Identity determinations within errors.

Abstract

We perform a comparative study of the ratio of lattice (Wilson fermion) renormalization constants Z_P/Z_S, obtained non-perturbatively from the RI/MOM renormalization conditions and from Ward Identities of on- and off-shell Green's functions. The off-shell Ward Identity used in this work relies on correlation functions with non-degenerate quark masses. We find that, due to discretization effects, there is a 10-15% discrepancy between the two Ward Identity determinations at current bare couplings (beta values). The RI/MOM result is in the same range and has a similar systematic error of 10-15%. Thus, contrary to a previous claim, the contamination of the RI/MOM result from the presence of a Goldstone pole at scales of about 2 GeV is subdominant, compared to finite cutoff effects.