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

TL;DR

This study evaluates nucleon isovector observables ($g_V$, $g_A$, and related moments) using 2+1-flavor dynamical domain-wall fermion lattice QCD across four ensembles with varying lattice spacing, volume, and pion mass. The authors employ enhanced statistics, including all-mode averaging (AMA), to measure $g_A/g_V$ and find a persistent ~10% deficit relative to experiment, with $g_A/g_V$ values around $1.17$–$1.18$ for ensembles with $m_\pi L \approx 5.8$. They find no evidence of excited-state contamination for these observables and report a striking long-range autocorrelation in $g_A$ on the lightest ensemble, suggesting possible finite-volume effects. The work highlights the need for larger volumes and further methodological refinements to reconcile lattice results with experimental nucleon structure and outlines plans to extend AMA and pursue physical-mass, larger-volume calculations in collaboration with other lattice groups.

Abstract

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, \(\langle x \rangle_{Δu - Δd}\), 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, \(m_π\), 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 \(m_π\) 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 \(m_πL\) 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 \(m_π=170\) MeV. The other observables do not show any autocorrelation with the interval of 16 trajectories.

Figures (4)

• Figure 1: nameref-fig:gAgVmpi fith LAB: fig:gAgVmpi Dependence of the ratio, $g_A/g_V$, of isovector axial charge, $g_A$, and vector charge, $g_V$, calculated with recent RBC+UKQCD 2+1-flavor dynamical DWF ensembles, on the pion mass squared, , $m_\pi^2$ (left), and the finite-size scaling parameter, $m_\pi L$ (right). Solid symbols are the present results, while the faded ones are from our earlier publications. While the precision agreement of the two ensembles at $m_\pi L$ of about 5.8 has increased its significance (right), the dependence on $m_\pi^2$ does not show any sign of approaching the experiment as the pion mass squared decreases toward physical value (left).
• Figure 2: nameref-fig:NotExcited fith LAB: fig:NotExcited Comparison of two source-sink separations, 7 and 9 lattice units, or 1.0 and 1.3 fm: Jack-knifed differences between the two separations (solid red symbols) fail to show any sign of excited-state contamination in any of the observables, the isovector vector charge, $g_V$, axial charge, $g_A$, quark momentum fraction, $\langle x \rangle_{u-d}$, and helicity fraction $\langle x \rangle_{\Delta u - \Delta d}$. Faded symbols are the values of the observables themselves for the long (red) and short (blue) separations, respectively.
• Figure 3: nameref-fig:gAgV2halves fith LAB: fig:gAgV2halves Very long-range autocorrelation is observed in both the isovector axial charge, $g_A$, and its ratio, $g_A/g_V$ to the vector charge in the lightest ensemble with $m_\pi$ of 170 MeV. On the left we present the plateaux of the ratio, $g_A/g_V$, for the first (trajectory from 748 to 1084, red) and the second (1100 to 1420, blue) halves, respectively: fitted in the range from 2 to 7 lattice units, the values of1.26(5) for the first and 1.07(5) are almost four standard deviations away from each other. On the right we present quarter-wise average along the hybrid MD time, from 748 to 892, 908 to 1084, 1100 to 1292, and 1308 to 1420: the values seem to drift monotonically from what is consistent with the experiment of 1.2701(25) in the first quarter to a value around 1.0 in the last quarter.
• Figure 4: nameref-fig:blocking fith LAB: fig:blocking Blocked Jack-knife analyses for the four observables, $g_V$ at upper left, $g_A$ upper right, $\langle x \rangle_{u-d}$ lower left, and $\langle x \rangle_{\Delta u - \Delta d}$ lower right. When two successive configurations are blocked together in the lightest ensemble with $m_\pi$ of 170 MeV, the statistical error grows significantly for the isovector axial charge, $g_A$, and its ratio, $g_A/g_V$ to the vector charge (not shown), in consistency with the long-range autocorrelation. In contrast, no other observable shows such growth.