Three-particle $N\pi\pi$ state contribution to the nucleon two-point function in lattice QCD

TL;DR

This paper calculates the contribution of three-particle $N\pi\pi$ states to the nucleon two-point function in lattice QCD using chiral perturbation theory, finding it negligible for practical nucleon mass calculations.

Contribution

It provides the first leading-order estimate of three-particle $N\pi\pi$ state effects on nucleon two-point functions in lattice QCD, showing their minimal impact.

Findings

Impact on nucleon mass is at most per mille level.

Three-particle $N\pi\pi$ contributions are negligible in current lattice QCD calculations.

Estimates are based on experimental low-energy coefficients.

Abstract

The three-particle $N\pi\pi$-state contribution to the QCD two-point function of standard nucleon interpolating fields is computed to leading order in chiral perturbation theory. Using the experimental values for two low-energy coefficients the impact of this contribution on lattice QCD calculations of the nucleon mass is estimated. The impact is found to be at the per mille level at most and negligible in practice.