Exploring strange nucleon form factors on the lattice

TL;DR

This study directly computes disconnected strange-quark contributions to nucleon form factors on a 24^3×64 anisotropic lattice with Wilson gauge and fermion actions. Using variance-reduced stochastic traces and a dedicated correlator analysis, it finds G_E^s(Q^2) and G_M^s(Q^2) to be small and compatible with zero, while G_A^s(Q^2) is mildly negative and the bare strange scalar matrix element <N|ss|N>_0 shows a strong signal but suffers from substantial flavor-singlet/non-singlet mixing in Wilson fermions, complicating renormalization. The work highlights significant methodological challenges and outlines concrete plans—2+1 flavor ensembles, longer temporal extent, multigrid solvers, GPUs, and advanced variance reduction—to achieve controlled, renormalized determinations of strange nucleon matrix elements. The results provide crucial benchmarks for the size of disconnected contributions and have implications for proton spin structure and dark matter cross-section interpretations, while underscoring the importance of careful operator mixing corrections in Wilson-like formulations.

Abstract

We discuss techniques for evaluating sea quark contributions to hadronic form factors on the lattice and apply these to an exploratory calculation of the strange electromagnetic, axial, and scalar form factors of the nucleon. We employ the Wilson gauge and fermion actions on an anisotropic 24^3 x 64 lattice, probing a range of momentum transfer with Q^2 < 1 GeV^2. The strange electric and magnetic form factors, G_E^s(Q^2) and G_M^s(Q^2), are found to be small and consistent with zero within the statistics of our calculation. The lattice data favor a small negative value for the strange axial form factor G_A^s(Q^2) and exhibit a strong signal for the bare strange scalar matrix element <N|ss|N>_0. We discuss the unique systematic uncertainties affecting the latter quantity relative to the continuum, as well as prospects for improving future determinations with Wilson-like fermions.

Figures (14)

• Figure 1: Schematic representation of a disconnected diagram, giving a strange form factor of the nucleon. Here $\Gamma$ is the appropriate gamma insertion for the form factor of interest, and $N$ is an interpolating operator for the nucleon.
• Figure 2: Fit of the nucleon correlation function for $Q^2=0$ to a form that includes two forward-propagating states and one backward-propagating state (upper curve, red) and the same form with the coefficient of the backward-propagating set to zero but the other fit parameters held fixed (lower curve, blue).
• Figure 3: Nucleon energy-squared (in lattice units) as a function of momentum, together with a fit to the continuum dispersion relation.
• Figure 4: Subset of results for the scalar form factor at $Q^2=0$, where the current insertion is placed symmetrically between source and sink. The lower curve (red) shows a corresponding cross-section of the fit. The horizontal line (blue) indicates the resulting value of $G_S^s(Q^2=0)_\mathrm{lat}=\langle N|\bar{s}s|N\rangle_0$ for the ground-state nucleon.
• Figure 5: Strange scalar form factor as a function of momentum.