# $N\pi$-state contamination in lattice calculations of the nucleon axial form factors

## TL;DR

This paper uses chiral perturbation theory to estimate and correct for nucleon-pion-state contamination in lattice QCD calculations of nucleon axial form factors, improving agreement with experimental data.

## Contribution

It provides a leading-order analytical estimate of nucleon-pion-state contamination in lattice calculations and demonstrates effective removal of this contamination from lattice data.

## Key findings

- Nucleon-pion-state contamination is about 5% for G_A at 2 fm separation.
- Contamination causes 10-40% underestimation of G_P at small Q^2.
- Removal of contamination aligns lattice results with experimental data.

## Abstract

The nucleon-pion-state contribution to QCD two-point and three-point functions used in lattice calculations of the nucleon axial form factors are studied in chiral perturbation theory. For small quark masses this contribution is expected to be the dominant excited-state contamination at large time separations. To leading order in chiral perturbation theory the results depend on only two experimentally known low-energy constants and the nucleon-pion-state contribution to the form factors can be estimated. The nucleon-pion-state contribution to the axial form factor $G_{\rm A}(Q^2)$ is at the 5 percent level for a source-sink separation of 2 fm and shows almost no dependence on the momentum transfer $Q^2$. In contrast, for the induced pseudoscalar form factor $\tilde{G}_{\rm P}(Q^2)$ the nucleon-pion-state contribution shows a rather strong dependence on $Q^2$ and leads to a 10 to 40 percent underestimation of $\tilde{G}_{\rm P}(Q^2)$ at small momentum transfers. The ChPT results can be used to analytically remove the nucleon-pion-state contribution from lattice data. Performing this removal for lattice data generated by the PACS collaboration we find agreement with experimental data and the predictions of the pion-pole dominance model. The removal works surprisingly well even for source-sink separations as small as 1.3 fm.