Measurements of the Electric and Magnetic Form Factors of the Neutron for Timelike Momentum Transfer

We present the first measurements of the electric and magnetic form factors of the neutron in the timelike (positive ${q}^{2}$) region as function of four-momentum transfer. We explored the differential cross sections of the reaction ${e}^{+}{e}^{-}\to \overline{n}n$ with data collected with the BESIII detector at the BEPCII accelerator, corresponding to an integrated luminosity of $354.6\text{}\text{}{\mathrm{pb}}^{-1}$ in total at twelve center-of-mass energies between $\sqrt{s}=2.0–2.95\text{}\text{}\mathrm{GeV}$. A relative uncertainty of 18% and 12% for the electric and magnetic form factors, respectively, is achieved at $\sqrt{s}=2.3935\text{}\text{}\mathrm{GeV}$. Our results are comparable in accuracy to those from electron scattering in the comparable spacelike region of four-momentum transfer. The electromagnetic form factor ratio ${R}_{\mathrm{em}}\equiv |{G}_{E}|/|{G}_{M}|$ is within the uncertainties close to unity. We compare our result on $|{G}_{E}|$ and $|{G}_{M}|$ to recent model predictions, and the measurements in the spacelike region to test the analyticity of electromagnetic form factors.