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.

Figure 1

Plateaus of $g_A$. $V=(2.7\mathrm{fm}{)}^3$ and $m_f=0.005$, 0.01, 0.02, and 0.03, from top to bottom.

Figure 2

$g_A$. Dashed and solid lines denote the fit results and chiral extrapolation in infinite volume, respectively. The open circle is extrapolated result at $m_{\pi }=135\mathrm{MeV}$.

Figure 3

$m_{\pi }L$ scaling of $g_A$. Top, middle, and bottom panels are dynamical and mixed action DWF, dynamical Wilson, and quenched DWF results, respectively. In the bottom panel, open symbol is same as in the top panel.