- Berkowitz, E
- Brantley, D
- Bouchard, C
- Chang, CC
- Clark, MA
- Garron, N
- Joo, B
- Kurth, T
- Monahan, C
- Monge-Camacho, H
- Nicholson, A
- Orginos, K
- Rinaldi, E
- Vranas, P
- Walker-Loud, A
- et al.

We report on a lattice QCD calculation of the nucleon axial charge, $g_A$,
using M\"{o}bius Domain-Wall fermions solved on the dynamical $N_f=2+1+1$ HISQ
ensembles after they are smeared using the gradient-flow algorithm. The
calculation is performed with three pion masses, $m_\pi\sim\{310,220,130\}$
MeV. Three lattice spacings ($a\sim\{0.15,0.12,0.09\}$ fm) are used with the
heaviest pion mass, while the coarsest two spacings are used on the middle pion
mass and only the coarsest spacing is used with the near physical pion mass. On
the $m_\pi\sim220$ MeV, $a\sim0.12$ fm point, a dedicated volume study is
performed with $m_\pi L \sim \{3.22,4.29,5.36\}$. Using a new strategy
motivated by the Feynman-Hellmann Theorem, we achieve a precise determination
of $g_A$ with relatively low statistics, and demonstrable control over the
excited state, continuum, infinite volume and chiral extrapolation systematic
uncertainties, the latter of which remains the dominant uncertainty. Our final
determination at 2.6\% total uncertainty is $g_A = 1.278(21)(26)$, with the
first uncertainty including statistical and systematic uncertainties from
fitting and the second including model selection systematics related to the
chiral and continuum extrapolation. The largest reduction of the second
uncertainty will come from a greater number of pion mass points as well as more
precise lattice QCD results near the physical pion mass.