Nucleon axial coupling from Lattice QCD

We present state-of-the-art results from a lattice QCD calculation of the nucleon axial coupling, $g_A$, 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. Relevant three-point correlation functions are calculated using a method inspired by the Feynman-Hellmann theorem, and demonstrate significant improvement in signal for fixed stochastic samples. The calculation is performed at five pion masses of $m_\pi\sim {400, 350, 310, 220, 130}$MeV,threelatticespacingsof$a\sim{0.15, 0.12, 0.09}$~fm, and we do a dedicated volume study with $m_{\pi }L\sim \{3.22,4.29,5.36\}$. Control over all relevant sources of systematic uncertainty are demonstrated and quantified. We achieve a preliminary value of $g_A=1.285(17)$, with a relative uncertainty of 1.33%.