Chiral Corrections to Nucleon Two- and Three-Point Correlation Functions

TL;DR

This paper analyzes how multi-particle pion-nucleon and pion-delta states affect nucleon two- and three-point correlation functions in lattice QCD, revealing implications for extracting nucleon properties like the axial charge.

Contribution

It provides a chiral perturbation theory framework to quantify multi-particle contributions to nucleon correlators and their volume scaling effects.

Findings

Multi-pion couplings scale with phase space considerations.

Multi-particle states are suppressed but differently in finite volume.

Finite volume effects can lead to overestimation of the nucleon axial charge.

Abstract

We consider multi-particle contributions to nucleon two- and three-point functions from the perspective of chiral dynamics. Lattice nucleon interpolating operators, which have definite chiral transformation properties, can be mapped into chiral perturbation theory. Using the most common of such operators, we determine pion-nucleon and pion-delta couplings to nucleon two- and three-point correlation functions at leading order in the low-energy expansion. The couplings of pions to nucleons and deltas in two-point functions are consistent with simple phase-space considerations, in accordance with the Lehmann spectral representation. An argument based on available phase space on a torus is utilized to derive the scaling of multiple-pion couplings. While multi-pion states are indeed suppressed, this suppression scales differently with particle number compared to that in infinite volume. For nucleon three-point correlation functions, we investigate the axial-vector current at vanishing momentum transfer. The effect of pion-nucleon and pion-delta states on the extraction of the nucleon axial charge is assessed. We show that couplings to finite volume multi-particle states could potentially lead to overestimation of the axial charge. Hence pion-nucleon excited states cannot explain the trend seen in lattice QCD calculations of the nucleon axial charge.