RI/MOM renormalization window and Goldstone pole contamination

We perform a comparative study of the ratio of lattice (Wilson fermion) renormalization constants ZP/ZS, obtained non-perturbatively from the RI/MOM renormalization conditions and from Ward Identities of on- and off-shell Greenʹs 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 (β 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 renormalization scales μ∼a−1 is subdominant, compared to finite cutoff effects.