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

TL;DR

This paper uses two-flavor lattice QCD to compute the nucleon axial charge and pion decay constant, analyzing finite size effects and extrapolating to the physical point, achieving results consistent with experimental values.

Contribution

It provides the first combined lattice QCD analysis of $g_A$ and $f_$ with detailed finite size and chiral extrapolations, including the ratio $g_A/f_$.

Findings

The ratio $g_A/f_$ shows universal behavior as quark mass decreases.

Extrapolated $g_A^R$ at physical point is 1.24(4), matching experimental data.

The low-energy constant 4l_44 is determined as 4.2(1).

Abstract

The axial charge of the nucleon $g_A$ and the pion decay constant $f_\pi$ 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 $m_\pi=130\,\mbox{MeV}$. Both quantities, $g_A$ and $f_\pi$, suffer from large finite size effects, which to leading order ChEFT and ChPT turn out to be identical. By considering the naturally renormalized ratio $g_A/f_\pi$, 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 $f_\pi$ as input and $r_0=0.50(1)$ to set the scale. In a subsequent calculation we attempt to extrapolate $g_A$ and $f_\pi$ separately to the infinite volume. Both volume and quark mass dependencies of $g_A$ and $f_\pi$ are found to be well decribed by ChEFT and ChPT. We find at the physical point $g_A^R=1.24(4)$ and $f_\pi^R=89.6(1.1)(1.8)\,\mbox{MeV}$. Both sets of results are in good agreement with experiment. As a by-product we obtain the low-energy constant $\bar{l}_4=4.2(1)$.