Investigation of $\pi N$ contributions to nucleon matrix elements

TL;DR

This paper presents a new lattice QCD method using GEVP to efficiently extract nucleon matrix elements, reducing excited state contamination and avoiding costly three-point functions, with promising results at physical pion mass.

Contribution

The paper introduces an improved GEVP-based approach for nucleon matrix element extraction that minimizes excited state contamination and simplifies computations.

Findings

Excited state contamination from Nπ is minimized.

The GEVP method is most effective for isovector pseudoscalar and axial currents.

Results are demonstrated on a physical-point ensemble with 131 MeV pion mass.

Abstract

We investigate an improved method to extract nucleon matrix elements from lattice 3-point functions using a generalized eigenvalue problem (GEVP) with nucleon and pion-nucleon interpolating fields. Our method avoids the computation of the costly three-point functions that have pion-nucleon interpolators at both source and sink. We demonstrate that excited state contamination from $N\pi$ is minimized in nucleon matrix elements of the scalar, vector, pseudoscalar, axial, and tensor currents and discuss our results based on a physical-point ensemble with a pion mass value of 131 MeV. We find that the GEVP is most significant for the isovector pseudoscalar and axial currents.