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 Q2. 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