Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors

TL;DR

This paper addresses discrepancies in lattice QCD calculations of nucleon axial and pseudoscalar form factors by identifying excited state contamination as the cause and proposing a new projection method to improve accuracy.

Contribution

It introduces a novel projection technique that mitigates excited state effects in lattice calculations of nucleon form factors, enhancing the reliability of the results.

Findings

The new method reduces excited state contamination in form factor calculations.

Accurate form factors are obtained at physical pion masses using the proposed approach.

The z-expansion with asymptotic constraints effectively extrapolates to the physical point.

Abstract

It has been observed in multiple lattice determinations of isovector axial and pseudoscalar nucleon form factors, that, despite the fact that the partial conservation of the axialvector current is fulfilled on the level of correlation functions, the corresponding relation for form factors (sometimes called the generalized Goldberger-Treiman relation in the literature) is broken rather badly. In this work we trace this difference back to excited state contributions and propose a new projection method that resolves this problem. We demonstrate the efficacy of this method by computing the axial and pseudoscalar form factors as well as related quantities on ensembles with two flavors of improved Wilson fermions using pion masses down to 150 MeV. To this end, we perform the $z$-expansion with analytically enforced asymptotic behaviour and extrapolate to the physical point.