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, $$\langle {r}_{{\rm{n}}}^{2}\rangle$$ ⟨ r 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 $$\langle {r}_{{\rm{n}}}^{2}\rangle$$ ⟨ r n 2 ⟩ measurement, based on the extraction of the neutron electric form factor, $${G}_{{\rm{E}}}^{{\rm{n}}}$$ G E n , at low four-momentum transfer squared (Q2) by exploiting the long known connection between the N → Δ quadrupole transitions and the neutron electric form factor. Our result, $$\langle {r}_{{\rm{n}}}^{2}\rangle =-0.110\pm 0.008\,({{\rm{fm}}}^{2})$$ ⟨ r n 2 ⟩ = − 0.110 ± 0.008 ( fm 2 ) , addresses long standing unresolved discrepancies in the $$\langle {r}_{{\rm{n}}}^{2}\rangle$$ ⟨ r n 2 ⟩ 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 $$\langle {r}_{{\rm{n}}}^{2}\rangle$$ ⟨ r n 2 ⟩ value.

Solution to the proton radius puzzle

The relationship between the static electric form factor for the proton in the rest frame and the Sachs electric form factor in the Breit momentum frame is used to provide a value for the difference in the mean squared charge radius of the proton evaluated in the two frames. Associating the muonic–hydrogen data analysis for the proton charge radius of 0.84087 fm with the rest frame and associating the electron scattering data with the Breit frame yields a prediction of 0.87944 fm for the proton radius in the relativistic frame. The most recent value deduced via electron scattering from the proton is 0.877(6) fm so that the frame dependence used here yields a plausible solution to the proton radius puzzle.