Nucleon axial charge and pion decay constant from two-flavor lattice QCD

TL;DR

The paper addresses the challenge of computing the nucleon axial charge $g_A$ and the pion decay constant $f_ pi$ from first-principles in two-flavor lattice QCD. It uses $N_f=2$ nonperturbatively $O(a)$-improved Wilson fermions on multiple volumes and lattice spacings, including near-physical pion masses, and analyzes finite-size effects with finite-volume ChEFT/ChPT. A key idea is to form the ratio $g_A/f_ pi$, which cancels leading finite-size and renormalization uncertainties, allowing a precise extraction of $g_A^R$; the study reports $g_A^R=1.29(5)(3)$ from the ratio and $g_A^R=1.24(4)$, $f_ pi^R=89.6(1.1)(1.8)\,\mathrm{MeV}$ from infinite-volume fits. The results are in good agreement with experimental values, and the analysis yields the low-energy constant $\bar{l}_4=4.2(1)$, contributing to the understanding of nucleon structure and chiral dynamics.

Abstract

The axial charge of the nucleon $g_A$ and the pion decay constant $f_π$ are computed in two-flavor lattice QCD. The simulations are carried out on lattices of various volumes and lattice spacings. Results are reported for pion masses as low as $m_π=130\,\mbox{MeV}$. Both quantities, $g_A$ and $f_π$, suffer from large finite size effects, which to leading order ChEFT and ChPT turn out to be identical. By considering the naturally renormalized ratio $g_A/f_π$, we observe a universal behavior as a function of decreasing quark mass. From extrapolating the ratio to the physical point, we find $g_A^R=1.29(5)(3)$, using the physical value of $f_π$ as input and $r_0=0.50(1)$ to set the scale. In a subsequent calculation we attempt to extrapolate $g_A$ and $f_π$ separately to the infinite volume. Both volume and quark mass dependencies of $g_A$ and $f_π$ are found to be well decribed by ChEFT and ChPT. We find at the physical point $g_A^R=1.24(4)$ and $f_π^R=89.6(1.1)(1.8)\,\mbox{MeV}$. Both sets of results are in good agreement with experiment. As a by-product we obtain the low-energy constant $\bar{l}_4=4.2(1)$.

Figures (7)

• Figure 1: The effective mass $m_N$ of the nucleon on the $48\times 64$ lattice at $\beta=5.29$, $\kappa=0.13640$, corresponding to our smallest pion mass. The horizontal line shows the fit and error band. The fit range for this nucleon mass was $t=8-16$.
• Figure 2: The ratio R as a function of the source-sink time separation $t$ on the $24^3\times 48$ lattice at $\beta=5.29$, $\kappa=0.13590$.
• Figure 3: The ratio $g_A(L)/af_\pi(L)$ as a function of $m_\pi L$ at $\beta=5.29$, $\kappa=0.13632$.
• Figure 4: The ratio $g_A(L)/f_\pi(L)$ as a function of $m_\pi^2(L)$, together with the experimental value ($\times$). The curve shows a fit of eq. (\ref{['chpt']}) to the data.
• Figure 5: The pion mass $am_\pi$ as a function of lattice size for two ensembles at $\beta=5.29$. The solid line shows a fit of eq. (\ref{['com']}) to the data. The dashed line shows the NLO result, eq. (\ref{['fsmpi']}), fitted to the smallest mass point.