Nucleon axial charge in 2+1-flavor dynamical DWF lattice QCD

The current status of some nucleon isovector observables, the vector charge, $g_V$, axial charge, $g_A$, quark momentum fraction, $\langle x \rangle_{u-d}$, and quark helicity fraction, $\langle x \rangle_{\Delta u - \Delta d}$, calculated using recent RBC/UKQCD 2+1-flavor dynamical domain-wall fermions (DWF) lattice QCD ensembles are reported: with Iwasaki gauge action at inverse lattice spacing, $a^{-1}$, of about 1.7 GeV, linear lattice extent, $L$, of about 2.7 fm, pion mass, $m_\pi$, of about 420 and 330 MeV, and with Iwasaki$\times$DSDR gauge action at $a^{-1}$ of about 1.4 GeV, $L$ of about 4.6 fm, and $m_\pi$ of about 250 and 170 MeV. The calculations have been refined with enhanced statistics, in particular through successful application of the all-mode-averaging (AMA) technique for the 170- and 330-MeV ensembles. As a result, the precision agreement seen in the charge ratio, $g_A/g_V$, for 420-MeV and 250-MeV ensembles that share the finite-size scaling parameter $m_\pi L$ of about 5.8 is more significant with new values of 1.17(2) and 1.18(4) respectively. We also studied the dependence on the source-sink separation in the lightest ensemble of 170-MeV, by comparing the cases with the separation of about 1.0 and 1.3 fm and did not see any dependence: contamination from the excited states are well under control in our choice of source and sink smearing. The axial charge, $g_A$ and the ratio, $g_A/g_V$, shows a long-range autocorrelation that extends the entire range of configurations that were so far analyzed, almost 700 hybrid Molecular Dynamics time, in the lightest ensemble of $m_\pi=170$ MeV. The other observables do not show any autocorrelation with the interval of 16 trajectories.