Charge radii of the nucleon from its flavor dependent Dirac form factors

Abstract

In this work, we extracted the proton and the neutron charge radii from the collective analysis of the proton and the neutron elastic form factors simultaneously. We performed a flavor decomposition of these form factors under charge symmetry and determined the mean-square radii of the quark distributions, which in turn are related in a model-independent way to the proton and the neutron charge radii. In the proton case we find \(\langle r_p \rangle = 0.852 \pm0.002_{\rm (stat.)} \pm0.009_{\rm (syst.)}~({\rm fm})\), consistent with the smaller measured values for its charge radius. The current method improves on the accuracy of the \(\langle r_p \rangle\) extraction based on the form factor measurements. Furthermore, we find no discrepancy in the \(\langle r_p \rangle\) determination among the different electron scattering measurements, all of which, utilizing the current method of extraction, result in a smaller \(\langle r_p \rangle\) value. In the neutron case, we have performed the first extraction of the neutron charge radius utilizing the nucleon form factor data, and we find \(\langle r_n^2 \rangle = -0.122 \pm0.004_{\rm (stat.)} \pm0.010_{\rm (syst.)}~({\rm fm}^2)\). The determination of \(\langle r_n^2 \rangle\) has, in the past, relied solely on measurements of the neutron-electron scattering length. Of the measurements adopted by the particle data group, the discrepancies in published results imply an underestimation of the underlying systematic uncertainties associated with that method of extraction. Upcoming measurements for the nucleon form factors will allow significant improvement on the precision of the \(\langle r_n^2 \rangle\) determination, and will address the discrepancies of the neutron-electron scattering length measurements.