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

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.

Comments: 18 pages, 12 figures, v2: fixed minor typos and improved discussion, corrected description of another reference, included an additional volume in excited-state-contamination prediction (Fig 9)