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Based on data samples collected with the BESIII detector at the BEPCIIcollider, the process $e^{+}e^{-} \to \Sigma^{+}\bar{\Sigma}^{-}$ is studied atcenter-of-mass energies $\sqrt{s}$ = 2.3960, 2.6454, and 2.9000~GeV. Using afully differential angular description of the final state particles, thecomplete information of the $\Sigma^{+}$ electromagnetic form factors in thetime-like region is extracted. The relative phase between the electric andmagnetic form factors is determined to be $\sin\Delta\Phi$ =-0.67~$\pm$~0.29~(stat.)~$\pm$~0.18~(syst.) at $\sqrt{s}$ = 2.3960~GeV,$\Delta\Phi$ = 55$^{\circ}$~$\pm$~19$^{\circ}$~(stat.)$\pm$~14$^{\circ}$~(syst.) at $\sqrt{s}$ = 2.6454~GeV, and78$^{\circ}$~$\pm$~22$^{\circ}$~(stat.) $\pm$~9$^{\circ}$~(syst.) at $\sqrt{s}$= 2.9000~GeV. For the first time, the phase of the hyperon electromagnetic formfactors is explored in a wide range of four-momentum transfer. The evolution ofthe phase along with four-momentum transfer is an important input forunderstanding its asymptotic behavior and the dynamics of baryons.

Complete determination of $\Sigma^{+}$ electromagnetic form factors via $e^{+}e^{-} \to \Sigma^{+} \bar{\Sigma}^{-}$