The nucleon axial charge from lattice QCD with controlled errors

TL;DR

This paper addresses the lattice QCD determination of the nucleon axial charge $g_{ m A}$ with $N_f=2$ dynamical quarks, focusing on a rigorous control of systematic errors, especially excited-state contamination. The authors apply the summed operator insertion method to suppress excited-state effects in three-point functions and perform chiral extrapolations including finite-volume corrections; they find $g_{ m A}=1.223(63) ext{ (stat)}^{+0.035}_{-0.060} ext{ (syst)}$, in agreement with the experimental value around $g_{ m A}^{ m exp}\\approx 1.270$. Their results show that the plateau method underestimates $g_{ m A}$ while the summed approach aligns with experiment, highlighting the importance of robust excited-state control in nucleon structure calculations. The work suggests extending the method to lighter pions and to other nucleon observables, such as vector and axial form factors, potentially aided by optimized smearing techniques for nonzero momenta.

Abstract

We report on our calculation of the nucleon axial charge gA in QCD with two flavours of dynamical quarks. A detailed investigation of systematic errors is performed, with a particular focus on contributions from excited states to three-point correlation functions. The use of summed operator insertions allows for a much better control over such contamination. After performing a chiral extrapolation to the physical pion mass, we find gA=1.223 +/- 0.063 (stat) +0.035 -0.060 (syst), in good agreement with the experimental value.

Figures (5)

• Figure 1: The ratio $R(t,t_{\rm s})$ at $\beta=5.2$ and $m_\pi=312\,{\rm{MeV}}$ for several different values of the source-sink separation $t_{\rm s}$.
• Figure 2: The summed ratio $S(t_{\rm s})$ at $m_\pi\approx 320\,{\rm{MeV}}$ for two different lattice spacings (ensembles A5 and F6).
• Figure 3: Chiral behaviour of $g_{\rm{A}}$ extracted from summed insertions (upper panel) and using the standard plateau method (lower panel). Chiral fits of type "A" and "D" (see text) applied for $m_\pi<540\,{\rm{MeV}}$ are represented by the blue/hatched and red bands, respectively. The black point denotes the experimental value.
• Figure 4: Results for $g_{\rm{A}}$ at the physical pion mass for the plateau and summation methods. Solid points refer to a pion mass cut at $m_\pi<540\,{\rm{MeV}}$, while open symbols are used to denote results from fits across the entire pion mass range. Fits A, B and D were applied to the volume-corrected data (see text). The vertical lines represent the experimental value.
• Figure 5: Estimates for $g_{\rm{A}}$ determined from the summation and plateacu methods compared to recent results by ETMC nuclff:ETMC10_nf2, RBC/UKQCD (nuclFF:RBC08_nf2 for $N_{\rm{f}}=2$, ref. nuclFF:RBC09_nf2p1 for $N_{\rm{f}}=2+1$) and LHPC nuclFF:LHPC10_nf2p1. Only statistical errors are shown. The thick vertical line represents the experimental result.