Investigating $\mathbf{N \to N\pi}$ axial matrix elements

TL;DR

This paper addresses excited state contamination in nucleon axial matrix element calculations by explicitly studying $N o N ext{pi}$ transitions using specialized correlation functions and the GEVP method on lattice QCD data.

Contribution

It introduces a novel approach using nucleon-pion interpolators and the GEVP to directly analyze excited state effects in axial matrix elements.

Findings

Successful construction of $N o N ext{pi}$ three-point functions

Application of GEVP to disentangle excited states

Results at different pion masses demonstrating method effectiveness

Abstract

Excited state contamination is one of the most challenging sources of systematics to tackle in the determination of nucleon matrix elements and form factors. The signal-to-noise problem prevents one from considering large source-sink time separations for the three-point functions to ensure ground state dominance. Instead, relevant analyses consider multi-state fits. Excited state contributions are particularly significant in the axial channel. In this work, we confront the problem directly. Since the major source of contamination is understood to be related to pion production, we consider three-point correlation functions with a nucleon operator at the source and a nucleon-pion interpolating operator at the sink, which allows studies of $N \to N\pi$ matrix elements. We discuss the construction of these three-point correlation functions and we solve the generalized eigenvalue problem (GEVP) using different sets of nucleon and nucleon-pion interpolators. The analysis is performed on the CLS ensemble A653 with $m_\pi \approx 420$ MeV. Results were generated with valence quark masses corresponding to $m_\pi \approx 1750$ MeV and $m_\pi \approx 420$ MeV.