Flavor decomposition of the nucleon electromagnetic form factors

Background: The spatial distribution of charge and magnetization in the proton and neutron are encoded in the nucleon electromagnetic form factors. The form factors are all approximated by a simple dipole function, normalized to the charge or magnetic moment of the nucleon. The differences between the proton and neutron form factors and the deviation of ${G}_{E}^{n}$ from zero are sensitive to the difference between up- and down-quark contributions to the form factors.Purpose: Recent measurements of ${G}_{E}^{n}$ up to 3.4 (GeV/$c$)${}^{2}$ allow for a much more detailed examination of the form factors. The flavor-separated form factors provide information on the quark flavor dependence of the nucleon structure and test theoretical models of the form factors.Methods: We combine recent measurements of the neutron form factors with updated extractions of the proton form factors, accounting for two-photon exchange corrections and including an estimate of the uncertainties for all of the form factors to obtain a complete set of measurements up to ${Q}^{2}\ensuremath{\approx}4$ (GeV/$c$)${}^{2}$. We use this to extract the up- and down-quark contributions which we compare to recent fits and calculations.Results: We find large differences between the up- and down-quark contributions to ${G}_{E}$ and ${G}_{M}$, implying significant flavor dependence in the charge and magnetization distributions. The rapid falloff of the ratio ${G}_{E}^{p}/{G}_{M}^{p}$ does not appear in the individual quark form factors, but arises from a cancellation between the up- and down-quark contributions. We see indications that the down-quark contributions to the Dirac and Pauli form factors deviate from the suggested 1/${Q}^{4}$ scaling behavior suggested by a previous analysis. While recent models provide a generally good qualitative description of the data, the down-quark contribution to ${G}_{E}/{G}_{M}$ and ${F}_{2}/{F}_{1}$ are not reproduced by any of the models. Finally, we note that, while the inclusion of recent ${G}_{M}^{n}$ data from the CLAS Collaboration modifies the high-${Q}^{2}$ behavior slightly, the tension between these data and previous measurements at lower ${Q}^{2}$ has a more significant impact, suggesting the need for additional data in this region.