Precision Measurements of the Nucleon Strange Form Factors at $Q^2\sim 0.1{\mathrm{GeV}}^2$

We report new measurements of the parity-violating asymmetry $A_{\mathrm{PV}}$ in elastic scattering of 3 GeV electrons off hydrogen and ${}^4\mathrm{He}$ targets with $⟨{\theta }_{\mathrm{lab}}⟩\approx 6.0°$. The ${}^4\mathrm{He}$ result is $A_{\mathrm{PV}}=\mathbf{(}+6.40\pm 0.23(\mathrm{stat})\pm 0.12(\mathrm{syst})\mathbf{)}\times {10}^{-6}$. The hydrogen result is $A_{\mathrm{PV}}=\mathbf{(}-1.58\pm 0.12(\mathrm{stat})\pm 0.04(\mathrm{syst})\mathbf{)}\times {10}^{-6}$. These results significantly improve constraints on the electric and magnetic strange form factors $G_E^s$ and $G_M^s$. We extract $G_E^s=0.002\pm 0.014\pm 0.007$ at $⟨Q^2⟩=0.077{\mathrm{GeV}}^2$, and $G_E^s+0.09G_M^s=0.007\pm 0.011\pm 0.006$ at $⟨Q^2⟩=0.109{\mathrm{GeV}}^2$, providing new limits on the role of strange quarks in the nucleon charge and magnetization distributions.

Figure 1

Single-particle spectra obtained in dedicated low-current runs. The insets show the same spectra on a logarithmic scale. The vertical lines delineate the extent of the detectors. Inelastic scattering from ${}^4\mathrm{He}$ is entirely contained in the hatched area. The shaded regions, visible only in the log plots, show the contribution from target windows.

Figure 2

68 and 95% C.L. constraints in the $G_E^s-G_M^s$ plane from data from this apparatus ([11, 12] and this Letter). Various theoretical predictions are plotted with published uncertainty estimates, when available. The 1-$\sigma$ bands (a quadrature sum of statistical and systematic errors) and central values (dashed lines) from the new results alone are also shown.