# An accurate calculation of the nucleon axial charge with lattice QCD

Evan Berkowitz,
David Brantley,
Chris Bouchard,
Chia Cheng Chang,
M. A. Clark,
Nicholas Garron,
Balint Joo,
Thorsten Kurth,
Chris Monahan,
Henry Monge-Camacho,
Amy Nicholson,
Kostas Orginos,
Enrico Rinaldi,
Pavlos Vranas,
Andre Walker-Loud

Apr 2017

### Abstract

We report on a lattice QCD calculation of the nucleon axial charge, $g_A$, using M$$"obius Domain-Wall fermions solved on the dynamical $N_f=2+1+1$ HISQ ensembles after they are smeared using the gradient-flow algorithm. The calculation is performed with three pion masses, $m_\pi\sim\310,220,130$ MeV. Three lattice spacings ($a\sim\0.15,0.12,0.09$ fm) are used with the heaviest pion mass, while the coarsest two spacings are used on the middle pion mass and only the coarsest spacing is used with the near physical pion mass. On the $m_\pi\sim220$ MeV, $a\sim0.12$ fm point, a dedicated volume study is performed with $m_\pi L \sim \3.22,4.29,5.36$. Using a new strategy motivated by the Feynman-Hellmann Theorem, we achieve a precise determination of $g_A$ with relatively low statistics, and demonstrable control over the excited state, continuum, infinite volume and chiral extrapolation systematic uncertainties, the latter of which remains the dominant uncertainty. Our final determination at 2.6$$% 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.

###### Research Scientist

My research interests include artificial intelligence and quantum computing applied to particle physics and quantum many-body systems.