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

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, $⟨r_{\mathrm{n}}^2⟩$. The precise measurement of the neutron’s charge radius thus emerges as an essential part of unraveling its structure. Here we report on a $⟨r_{\mathrm{n}}^2⟩$ measurement, based on the extraction of the neutron electric form factor, $G_{\mathrm{E}}^{\mathrm{n}}$, at low four-momentum transfer squared $(Q^2)$ by exploiting the long known connection between the $N\to \mathrm{\Delta }$ quadrupole transitions and the neutron electric form factor. Our result, $\langle r_{\rm n}^2 \rangle = -0.110 \pm0.008~({\rm fm}^2)$,addresseslongstandingunresolveddiscrepanciesinthe$\langle r_{\rm n}^2 \rangle$ 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 $⟨r_{\mathrm{n}}^2⟩$ value.