# $N\pi$-excited state contamination in nucleon 3-point functions using ChPT

## TL;DR

This paper uses ChPT to analyze how $N ext{π}$ excited states contaminate nucleon 3-point functions, revealing their impact on form factors and relations like Goldberger-Treiman, with implications for lattice QCD results.

## Contribution

It provides a leading-order ChPT calculation of $N ext{π}$-state contamination in nucleon 3-point functions, highlighting effects on form factors and lattice data interpretation.

## Key findings

- $N ext{π}$ contamination causes linear time dependence in axial current data.
- Strong momentum transfer dependence distorts pseudoscalar form factors.
- Contamination leads to violations of the Goldberger-Treiman relation in lattice results.

## Abstract

The $N\pi$-state contribution to nucleon 3-pt functions involving the pseudoscalar density $P(x)$ and the time component $A_4(x)$ of the axial vector current are computed to LO in ChPT. In case of the latter the $N\pi$ contribution is O($M_N$) enhanced compared to the single-nucleon ground state contribution. In addition, a relative sign in two terms of the $N\pi$ contribution leads an almost linear dependence on the operator insertion time, as it is observed in lattice data. In case of the pseudoscalar density the $N\pi$ contribution is strongly dependent on the momentum transfer, leading to a distortion of the pseudoscalar nucleon form factor. Finally, the $N\pi$ state contamination in the form factors result in a violation of the generalized Goldberger-Treiman relation as observed in various lattice calculations.