2016/10/31 by Maxwell T. Hansen, Harvey B. Meyer
Physics and Astronomy · #Amplitude #Atomic physics #Chiral perturbation theory #Excited state #Lattice (music) #Lattice QCD #Nuclear physics research studies #Nucleon #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Scattering #hep-lat
paper · pdf · doi:10.1016/j.nuclphysb.2017.08.017
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)
arxiv created 2016/11/30 · openalex publication_date 2017/09/01 · arxiv updated 2018/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 [1] , [2] , [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 → N π 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.