On the effect of excited states in lattice calculations of the nucleon axial charge

TL;DR

This paper investigates the impact of excited states on lattice calculations of the nucleon axial charge, revealing that including final-state interactions and the Roper resonance explains the negative contamination observed empirically.

Contribution

It demonstrates that accounting for $N o N \pi$ interactions and the Roper resonance can reproduce lattice correlator behavior, challenging previous ChPT predictions.

Findings

Empirical lattice results show negative excited-state contamination.

Including $N \pi$ interactions explains the observed behavior.

Sign change in the $N o N \pi$ axial-vector transition amplitude is crucial.

Abstract

Excited-state contamination is one of the dominant uncertainties in lattice calculations of the nucleon axial-charge, $g_A$. Recently published results in leading-order chiral perturbation theory (ChPT) predict the excited-state contamination to be independent of the nucleon interpolator and positive. However, empirical results from numerical lattice calculations show negative contamination (downward curvature), indicating that present-day calculations are not in the regime where the leading-order ChPT predictions apply. In this paper we show that, under plausible assumptions, one can reproduce the behavior of lattice correlators by taking into account final-state $N \pi$ interactions, in particular the effect of the Roper resonance, and by postulating a sign change in the infinite-volume $N \to N \pi$ axial-vector transition amplitude.