Measurement of the neutron charge radius and the role of its constituents

Abstract

The neutron is a cornerstone in our depiction of the visible universe. Despite the neutron zero-net electric charge, the asymmetric distribution of the positively- (up) and negatively-charged (down) quarks, a result of the complex quark-gluon dynamics, lead to a negative value for its squared charge radius, $\langle r_{\rm n}^2 \rangle$. The precise measurement of the neutron's charge radius thus emerges as an essential part of unraveling its structure. Here we report on a $\langle r_{\rm n}^2 \rangle$ measurement, based on the extraction of the neutron electric form factor, $G_{\rm E}^{\rm n}$, at low four-momentum transfer squared $(Q^2)$ by exploiting the long known connection between the $N \rightarrow \Delta$ quadrupole transitions and the neutron electric form factor. Our result, $\langle r_{\rm n}^2 \rangle = -0.110 \pm0.008~({\rm fm}^2)$, addresses long standing unresolved discrepancies in the $\langle r_{\rm n}^2 \rangle$ determination. The dynamics of the strong nuclear force can be viewed through the precise picture of the neutron's constituent distributions that result into the non-zero $\langle r_{\rm n}^2 \rangle$ value.