Nucleon Structure from Lattice QCD Using a Nearly Physical Pion Mass

TL;DR

The paper reports the first Lattice QCD calculation near the physical pion mass $m_\pi \approx 149$ MeV that agrees with experiment for four isovector nucleon observables: the Dirac and Pauli radii, the anomalous magnetic moment, and the quark momentum fraction, achieved by suppressing excited-state contamination via the summation method. It analyzes ten dynamical ensembles spanning $m_\pi = 149$–$357$ MeV and shows that extrapolations to the physical point are small, with uncertainties dominated by the lowest-mass data. However, the axial charge $g_A$ exhibits inconsistencies at the lightest masses, suggesting a bias from thermal states or other systematics not present for the other observables. Overall, the work validates a methodology to control systematic uncertainties in nucleon structure calculations and highlights remaining questions about $g_A$ and the need for additional spacings and volumes.

Abstract

We report the first Lattice QCD calculation using the almost physical pion mass mpi=149 MeV that agrees with experiment for four fundamental isovector observables characterizing the gross structure of the nucleon: the Dirac and Pauli radii, the magnetic moment, and the quark momentum fraction. The key to this success is the combination of using a nearly physical pion mass and excluding the contributions of excited states. An analogous calculation of the nucleon axial charge governing beta decay has inconsistencies indicating a source of bias at low pion masses not present for the other observables and yields a result that disagrees with experiment.

Figures (6)

• Figure 1: Isovector Dirac radius $(r_1^2)^v$. Fits to the solid square and diamond points are described in Tab. \ref{['tab:fits']}, and the same fits applied to the full set of solid points are shown for comparison. One experimental point is the CODATA recommended value Mohr:2012tt and the other is from the $\mu p$ Lamb shift Pohl:2010zza. The series of open symbols show data before the removal of excited states, with fixed source-sink separation $\Delta t$ increasing from right to left. Their error bars reflect only statistical uncertainties, which grow with $\Delta t$.
• Figure 2: Isovector anomalous magnetic moment $\kappa^v$. See caption of Fig. \ref{['fig:r1v2']}.
• Figure 3: Isovector Pauli radius $\kappa^v(r_2^2)^v$. See caption of Fig. \ref{['fig:r1v2']}.
• Figure 4: Isovector quark momentum fraction $\langle x\rangle_{u-d}$. See caption of Fig. \ref{['fig:r1v2']}.
• Figure 5: Axial charge $g_A$. See caption of Fig. \ref{['fig:r1v2']}.