Precise determination of low-$Q$ nucleon electromagnetic form factors and their impact on parity-violating $e$-$p$ elastic scattering

The extraction of the strangeness form factors from parity-violating elastic electron-proton scattering is sensitive to the electromagnetic form factors at low $Q^2$. We provide parametrizations for the form factors and uncertainties, including the effects of two-photon exchange corrections to the extracted electromagnetic form factors. We study effect of the correlations between different form factors, in particular as they impact the parity-violating asymmetry and the extraction of the strangeness form factors. We provide a prescription to extract the strangeness form factors from the asymmetry that provides an excellent approximation of the full two-photon correction. The corrected form factors are also appropriate as input for other low-$Q$ analyses, although the effects of correlations and two-photon exchange corrections may be different.

Figure 1

Uncertainties in the fits for $G_{\mathrm{Ep}}$ (solid) and $G_{\mathrm{Mp}}/{\mu }_p$ (dashed). The uncertainty is the random and systematic uncertainties, combined in quadrature.

Figure 2

Total uncertainty for the fit to $G_{\mathrm{En}}$.

Figure 3

Total uncertainty for the fit to the TPE-uncorrected value of ${\sigma }_{\mathrm{red}}$ at the kinematics of several past and planned measurements. The kinematics are shown for the JLab (squares), Mainz (circles), and Bates (diamonds) completed and planned measurements. The hollow symbols correspond to forward angle ($⩽{35}^{°}$) measurements, whereas the solid symbols are for large angle measurements ($⩾{110}^{°}$). The forward angle points depend mainly on $Q$ and are largely independent of angle, except for the two JLab points at 0.6 GeV, corresponding to $6^{°}$ (lower point) and ${12}^{°}$ (upper point).

Figure 4

Comparisons of different calculations of $A_{\mathrm{PV}}$ to the calculation including the full TPE effects. Top left plot is $A_{\mathrm{PV}}^{\mathrm{Born}}$ and shows the true size of the TPE correction. Bottom left plot is the ratio obtained when neglecting TPE in both the extraction of the EM form factors and the calculation of $A_{\mathrm{PV}}$, i.e., the error made in the analysis of previous experimental results. The top right is the approximation presented here, neglecting the additional parametrization of the TPE effect on the numerator of Eq. (1), and the bottom right is the final prescription, including this correction [Eq. (9)].