Large pion pole in Z_{S}^{MOM}/Z_{P}^{MOM} from Wilson action data

TL;DR

This paper demonstrates a significant Goldstone boson contribution in the quark pseudoscalar vertex using Wilson action data, showing it dominates over discretization errors across a broad momentum range.

Contribution

It provides the first clear evidence of a large pion pole in Z_{S}^{MOM}/Z_{P}^{MOM} from unimproved Wilson fermion data, challenging recent claims.

Findings

Goldstone boson contribution is large and consistent across different beta values.

Discretization errors are smaller than the Goldstone pole contribution.

Subtracting the non-perturbative contribution aligns results with one-loop BPT.

Abstract

We show that, contrarily to recent claims, data from the Wilson (unimproved) fermionic action at three different beta values demonstrate the presence of a large Goldstone boson contribution in the quark pseudoscalar vertex, quantitatively close to our previous estimate based on the SW action with c_{SW}=1.769. We show that discretisation errors on Z_{S}^{MOM}/Z_{P}^{MOM} seem to be much smaller than the Goldstone pole contribution over a very large range of momenta. The subtraction of this non perturbative contribution leads to numbers close to one-loop BPT.