Time Dependence of Nucleon Correlation Functions in Chiral Perturbation Theory

TL;DR

This paper uses chiral perturbation theory to analyze how nucleon correlation functions are affected by low-energy excitations at finite times, revealing potential biases in lattice QCD calculations of nucleon properties.

Contribution

It derives the spectral representation of nucleon two-point functions and finite time corrections, highlighting how excited states influence axial current correlators in chiral effective theory.

Findings

Pion-nucleon states increase the axial correlator

Pion-delta interference decreases the axial correlator

Improved operators may underestimate the nucleon axial charge

Abstract

We consider corrections to nucleon correlation functions arising from times that are far from the asymptotic limit. For such times, the single nucleon state is contaminated by the pion-nucleon and pion-delta continuum. We use heavy baryon chiral perturbation theory to derive the spectral representation of the nucleon two-point function. Finite time corrections to the axial current correlation function are also derived. Pion-nucleon excited state contributions drive the axial correlator upward, while contributions from the interference of pion-delta and pion-nucleon states drive the axial correlator downward. Our results can be compared qualitatively to optimized nucleon correlators calculated in lattice QCD, because the chiral corrections characterize only low-energy excitations above the ground state. We show that improved nucleon operators can lead to an underestimation of the nucleon axial charge.