Nucleon structure with pion mass down to 149 MeV

TL;DR

This work uses ten $2+1$ flavor lattice ensembles with BMW clover-improved Wilson fermions to study isovector nucleon observables $(r_1^2)^v$, $g_A$, $g_T$, and $g_S$ down to $m_ ext{π}=149$ MeV. By employing three source-sink separations and the summation method, the authors identify and mitigate excited-state contamination, enabling chiral extrapolations that bring several observables into agreement with experimental values, notably the isovector Dirac radius. Results indicate persistent but manageable challenges for $g_A$ due to finite-temperature effects, while $g_T$ and $g_S$ remain noisier but consistent with near-physical extrapolations; finite-volume and discretization effects appear subdominant within current precision. The study underscores the importance of near-physical quark masses and robust excited-state control for credible lattice QCD predictions of nucleon structure, with implications for constraining beyond-Standard-Model physics through $g_T$ and $g_S$.

Abstract

We present isovector nucleon observables: the axial, tensor, and scalar charges and the Dirac radius. Using the BMW clover-improved Wilson action and pion masses as low as 149 MeV, we achieve good control over chiral extrapolation to the physical point. Our analysis is done using three different source-sink separations in order to identify excited-state effects, and we make use of the summation method to reduce their size.

Figures (4)

• Figure 1: Isovector Dirac radius $(r_1^2)^v$, as determined from dipole fits to $F_1(Q^2)$. The two experimental points both use the PDG Beringer:1900zz value for $(r_E^2)^n$, and $(r_E^2)^p$ is taken from either the PDG or from the result from measurement of the Lamb shift in muonic hydrogen Pohl:2010zza. Left: Results from ensembles using the three different lattice actions. Wilson action points are taken from the middle source-sink separation. Right: The full set of Wilson action results. Measurements using the three source-sink separations and the summation method are slightly displaced horizontally. The points corresponding to the smallest source-sink separation are placed at the measured value of $m_\pi^2$, except for the ensembles with $m_\pi\approx 250$ MeV and $m_\pi\approx 350$ MeV, where the different volumes are displaced horizontally and the dotted lines indicate the approximate measured values of $m_\pi^2$.
• Figure 2: Axial charge $g_A$. The experimental value is from Ref. Beringer:1900zz. See caption of Fig. \ref{['fig:r1v2']}.
• Figure 3: Tensor charge $g_T$. The physical pion mass is indicated by the vertical line. See caption of Fig. \ref{['fig:r1v2']}.
• Figure 4: Scalar charge $g_S$. The physical pion mass is indicated by the vertical line. See caption of Fig. \ref{['fig:r1v2']}.