Measurement of $e^{+}{e}^{-}\to p\bar{p}$ around $\psi (2S)$ with scan method

This paper uses the data corresponding to an integrated luminosity of $495$~pb${}^{-1}$ in the center-of-mass energy region from 3.58~GeV to 3.71~GeV to study the relative phase between strong and electromagnetic amplitudes in the $\psi (2S)\to p\bar{p}$ decay. The cross sections and the effective form factors around $\psi (2S)$ of proton-antiproton pairs are presented thereby filling the gap in the experimental results around the $\psi (2S)$ resonance for the first time, and the results are consistent with the previous BESIII and BaBar results. The relative phase is extracted from the cross-section line shape as ${\mathrm{\Phi }}_{g,\gamma }=(105.9\pm 9.4{)}^{\circ }$ or ${\mathrm{\Phi }}_{g,\gamma }=(-105.3\pm 9.1{)}^{\circ }$. Correspondingly, two solutions for the $\psi (2S)\to p\bar{p}$ branching fractions are obtained as $\mathcal{B}=(3.21\pm 0.13)\times {10}^{-4}$ and $\mathcal{B}=(3.47\pm 0.19)\times {10}^{-4}$. These results support the universality of the phase and provide new insights into its underlying mechanism.