Variational Approach to the Calculation of gA

TL;DR

The nucleon axial charge $g_A$ has proven difficult to obtain accurately in lattice QCD due to excited-state contamination. This study applies a variational correlation-matrix method to construct optimized interpolators that isolate the ground state and extract $g_A$ from a ratio of three- and two-point functions, achieving rapid ground-state dominance and more stable fits. The results show a robust $g_A^R$ around $1.15$ on the present ensemble and highlight significant reductions in excited-state systematics compared with traditional methods, even at smaller source-sink separations. The approach is generalizable to other form factors and to quantities like the quark momentum fraction, offering a practical route to more reliable lattice predictions at near-physical quark masses.

Abstract

We present a lattice QCD calculation of the nucleon axial charge, gA, using a variational approach. After a brief outline of how the variational method is applied to the calculation of form factors, we present results for gA using this method. We find that ground state dominance is rapid, evident in the early onset of a clear plateau in the correlation function ratio proportional to gA. Through a comparison with results obtained via traditional methods, we show how excited state effects can suppress gA by as much as 8% if sources are not properly tuned.

Figures (4)

• Figure 1: A comparison of un-renormalized $g_A$ as a function of sink time. The first two figures are using the traditional approach of smeared source $\rightarrow$point sink and, smeared source $\rightarrow$smeared sink, both for 35 sweeps of smearing. The final figure is the result from a $4 \times 4$ correlation matrix.
• Figure 2: An overlay of the results from fig. 1. The data sets have been offset from the time slice for clarity -- the circles (blue) are the results for the variational approach, the triangles (purple) are the smeared source $\rightarrow$smeared sink, while the squares (red) are the smeared source $\rightarrow$point sink. The fitted value from the variational approach has been included (blue shaded region) to highlight where the traditional approach is consistent with the improved method.
• Figure 3: Comparison of the renormalized value of $g_A$. The first four pairs of points are the results for the conventional, point sink (squares) and smeared sink (triangles) approach with increasing levels of smearing to the right. The rightmost point (circle) is the result extracted using variational approach. There is a clear dependence on the level of smearing to the extracted result.
• Figure 4: Results for $g_A$ with different number and combinations of operators used in the variational analysis.