Axial Nucleon form factors from lattice QCD

TL;DR

This study computes nucleon axial structure using lattice QCD with $N_f=2$ twisted mass fermions across three lattice spacings and two volumes to control discretization and finite-volume effects. By evaluating two- and three-point correlation functions and applying nonperturbative renormalization, the authors extract $g_A$, $G_A(Q^2)$, and $G_p(Q^2)$, performing continuum and chiral extrapolations via HB$ mar{HB} obreakslash ext{ChPT}$ SSE. They find a continuum, volume-corrected $g_A=1.12(8)$, with $G_A(Q^2)$ and $G_p(Q^2)$ showing flatter $Q^2$-dependence than experiment and modest volume effects on $G_A$ but more pronounced sensitivity for $G_p$ near $Q^2=0$. The results are consistent with other lattice actions, validating twisted-mass QCD for nucleon structure while highlighting the need for lighter pion masses to reach the physical axial charge more precisely. Overall, the work demonstrates controlled systematic errors and provides detailed axial form-factor data to compare with phenomenology and other lattice programs.

Abstract

We present results on the nucleon axial form factors within lattice QCD using two flavors of degenerate twisted mass fermions. Volume effects are examined using simulations at two volumes of spatial length $L=2.1$ fm and $L=2.8$ fm. Cut-off effects are investigated using three different values of the lattice spacings, namely $a=0.089$ fm, $a=0.070$ fm and $a=0.056$ fm. The nucleon axial charge is obtained in the continuum limit and chirally extrapolated to the physical pion mass enabling comparison with experiment.

Figures (12)

• Figure 1: Connected nucleon three-point function.
• Figure 2: The ratio of Eq. (\ref{['ratio']}) for representative momentum combinations at $\beta=3.9$ and different values of $\mu$. The filled (black) circles show results with a sink-source separation $t_f/a=14$ and the filled (red) squares for $t_f/a=12$, shifted to the left by one time-slice.
• Figure 3: Nucleon mass in units of $r_0$ at three lattice spacings and spatial lattice size $L$ such that $m_\pi L> 3.3$. The solid (black) and dashed (red) lines are fits to ${\cal O}(p^3)$ and ${\cal O}(p^4)$ HB$\chi$PT. The physical point is shown with the asterisks. Results at $\beta=3.9$ and $24^3\times 48$ are shown with filled (red) circles, at $\beta=3.9$ and $32^3\times 64$ with the filled (blue) squares, at $\beta=4.05$ and $32^3\times 64$ with the filled (green) triangles, at $\beta=4.2$ and $32^3\times 64$ with the open (yellow) square and at $\beta=4.2$ and $48^3\times 96$ with the star (magenta).
• Figure 4: The nucleon axial charge. Results using $N_F=2$ twisted mass fermions are shown using the same notation as that of Fig. \ref{['fig:nucleon scale']}. Crosses show results obtained using $N_F=2+1$ DWF, circles are results in a mixed action approach on a lattice of size $20^3\times 64$ and the triangle on a lattice of size $28^3 \times 64$.
• Figure 5: The nucleon axial charge as a function of $Lm_\pi$. The notation is the same as that of Fig. \ref{['fig:axial_charge']}.