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

Excited-state contamination is one of the dominant uncertainties in lattice calculations of the nucleon axial-charge, gA. Recently published results in leading-order chiral perturbation theory (ChPT) predict the excited-state contamination to be independent of the nucleon interpolator and positive [1-3]. We reproduce these results using ChPT in infinite volume along with the Lellouch-Lüscher formalism to relate finite- and infinite-volume matrix elements. We then go beyond ChPT by using the experimentally determined Nπ scattering phase to estimate the correction due to the final-state interactions, both on the discrete energy levels and on the Lellouch-Lüscher factors. We find that, while individual Lellouch-Lüscher factors differ significantly, the overall effect on the excited-state contamination is small. 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. We show that, under plausible assumptions, one can reproduce the behavior of lattice correlators by postulating a sign change in the infinite-volume N→Nπ axial-vector transition amplitude roughly in the region of the Roper resonance. Improved data, either from experiment or from a lattice QCD calculation, would allow for a direct test of this postulate.