Nucleon Axial Charge in (2+1)-Flavor Dynamical-Lattice QCD with Domain-Wall Fermions

We present results for the nucleon axial charge $g_A$ at a fixed lattice spacing of $1/a=1.73(3)\mathrm{GeV}$ using $2+1$ flavors of domain wall fermions on size ${16}^3\times 32$ and ${24}^3\times 64$ lattices ($L=1.8$ and 2.7 fm) with length 16 in the fifth dimension. The length of the Monte Carlo trajectory at the lightest $m_{\pi }$ is 7360 units, including 900 for thermalization. We find finite volume effects are larger than the pion mass dependence at $m_{\pi }=330\mathrm{MeV}$. We also find a scaling with the single variable $m_{\pi }L$ which can also be seen in previous two-flavor domain wall and Wilson fermion calculations. Using this scaling to eliminate the finite-volume effect, we obtain $g_A=1.20(6)(4)$ at the physical pion mass, $m_{\pi }=135\mathrm{MeV}$, where the first and second errors are statistical and systematic. The observed finite-volume scaling also appears in similar quenched simulations, but disappear when $V\ge (2.4\mathrm{fm}{)}^3$. We argue this is a dynamical quark effect.