# $N\pi$-state contamination in lattice calculations of the nucleon pseudoscalar form factor

## TL;DR

This paper uses chiral perturbation theory to predict nucleon-pion-state contamination in lattice calculations of the nucleon pseudoscalar form factor, revealing significant effects that impact the accuracy of lattice QCD results.

## Contribution

It provides the first leading-order calculation of nucleon-pion-state contamination in the pseudoscalar form factor within lattice QCD, highlighting its impact on the plateau method and the Goldberger-Treiman relation.

## Key findings

- Contamination varies between -20% and +50% at 2 fm separation.
- Nucleon-pion-state contamination causes violations of the Goldberger-Treiman relation.
- Chiral perturbation theory predictions agree with lattice results for small source-sink separations.

## Abstract

The nucleon-pion-state contribution in the QCD 3-point function of the pseudoscalar density is calculated to leading order in chiral perturbation theory. It predicts a nucleon-pion-state contamination in lattice estimates for the pseudoscalar form factor $G_{\rm P}(Q^2)$ determined with the plateau method. Depending on the momentum transfer $Q^2$ the contamination varies between -20% and +50% for a source-sink separation of 2 fm. The nucleon-pion-state contamination also causes violations in the generalized Goldberger-Treiman relation among the pseudoscalar and the axial nucleon form factors, the dominant source being the nucleon-pion-state contamination in the induced pseudoscalar form factor $\tilde{G}_{\rm P}(Q^2)$. Comparing the chiral perturbation theory predictions with lattice results of the PACS collaboration we find reasonable agreement even for source-sink separations as small as 1.3 fm.