$N\pi$-states and the projection method for the nucleon axial and pseudoscalar form factors

TL;DR

This paper evaluates a proposed projection method for removing excited state contamination in lattice QCD calculations of nucleon form factors, finding it ineffective and sometimes counterproductive, especially for pseudoscalar form factors.

Contribution

The study critically assesses the effectiveness of the projection method in eliminating nucleon-pion-state contamination using chiral perturbation theory.

Findings

Projection method has little impact on axial form factors.

It increases contamination in pseudoscalar form factors.

Goldberger-Treiman relation remains satisfied despite contamination.

Abstract

The RQCD collaboration proposed a projection method to remove the excited state contamination in lattice OCD calculations of nuclear form factors. The effectiveness of this method in removing the two-particle nucleon-pion-state contamination is examined using chiral perturbation theory. It is shown that the projection method has practically no impact in the calculation of the axial and induced pseudoscalar form factors. In the pseudoscalar form factor the projection method strongly enhances the nucleon-pion-state contamination. The generalized Goldberger-Treiman relation is satisfied even though large nucleon-pion-state contaminations are present in individual form factors. Therefore, the projection method is not a solution to the excited state problem in nucleon form factor calculations.