# Chiral perturbation theory and nucleon-pion-state contaminations in lattice QCD

## TL;DR

This paper uses baryon chiral perturbation theory to estimate how nucleon-pion multi-particle states contaminate lattice QCD calculations of nucleon properties, revealing a 5-10% overestimation at typical source-sink separations.

## Contribution

It provides leading order calculations of nucleon-pion-state contamination in lattice QCD observables using chiral perturbation theory, highlighting the limitations of current lattice separations.

## Key findings

- Nucleon-pion states cause 5-10% overestimation of charges and moments.
- Contamination increases with smaller source-sink separations.
- Chiral perturbation theory is limited at current lattice separations.

## Abstract

Multi-particle states with additional pions are expected to be a non-negligible source of excited-state contamination in lattice simulations at the physical point. It is shown that baryon chiral perturbation theory can be employed to calculate the contamination due to two-particle nucleon-pion states in various nucleon observables. Leading order results are presented for the nucleon axial, tensor and scalar charge and three Mellin moments of parton distribution functions (quark momentum fraction, helicity and transversity moment). Taking into account phenomenological results for the charges and moments the impact of the nucleon-pion-states on lattice estimates for these observables can be estimated. The nucleon-pion-state contribution results in an overestimation of all charges and moments obtained with the plateau method. The overestimation is at the 5-10% level for source-sink separations of about 2 fm. The source-sink separations accessible in contemporary lattice simulations are found to be too small for chiral perturbation theory to be directly applicable.