Recent update of nucleon axial-vector charge with the PACS10 superfine lattice

Abstract

We update the results of the nucleon axial-vector charge with the third ensemble of the PACS10 gauge configurations, which are generated by the PACS Collaboration at the physical point with lattice volume larger than $(10\;{\rm fm})^4$ and three different lattice spacings, 0.085 fm (coarse), 0.063 fm (fine) and 0.041 fm (superfine). Although the results of the first two ensembles generated at the coarse and fine lattice spacings are published, our study using the third one generated at the superfine lattice spacing is still underway. In this work, the low-energy relations arising from the partially conserved axial-vector current (PCAC) relation are also examined in terms of the nucleon three-point functions to verify whether the lattice QCD data correctly reproduces the physics in the continuum within the statistical accuracy.

Figures (3)

• Figure 1: Left: The bare value of the nucleon axial-vector charge $g_A^\mathrm{bare}$ as functions of the current insertion time slice $t$ for $t_\mathrm{sep}/a=20$ and 29 in lattice units. Right: The renormalized nucleon axial-vector charge ($g_A$) as functions of $t_\mathrm{sep}$ in the physical unit.
• Figure 2: The values of $m_\mathrm{PCAC}^\mathrm{nucl}$ computed with $t_\mathrm{sep}/a=20$ (right triangle) and 29 (left triangle) for all momentum transfers as functions of the current insertion time $t$. In each panel, the value of $m_\mathrm{PCAC}^\mathrm{pion}$ is indicated by the horizontal band.
• Figure 3: Comparison between $m_{\rm PCAC}^{\rm pion}$ (horizontal band) and $m_{\rm PCAC}^{\rm nucl}$ (open symbols) in each panel. Results for $t_{\rm sep}/a=\{20, 29\}$ are plotted from top to bottom.