Measurement of $\mathrm{\Lambda }$ transverse polarization in $e^{+}{e}^{-}$ collisions at $\sqrt{s}=3.68-3.71$ GeV

With data samples collected with the BESIII detector at seven energy points at $\sqrt{s}=3.68-3.71$ GeV, corresponding to an integrated luminosity of 333 pb${}^{-1}$, we present a study of the $\mathrm{\Lambda }$ transverse polarization in the $e^{+}{e}^{-}\to \mathrm{\Lambda }\bar{\mathrm{\Lambda }}$ reaction. The significance of polarization by combining the seven energy points is found to be 2.6$\sigma$ including the systematic uncertainty, which implies a non-zero phase between the transition amplitudes of the $\mathrm{\Lambda }\bar{\mathrm{\Lambda }}$ helicity states. The modulus ratio and the relative phase of EM-$psionic$ form factors combined with all energy points are measured to be $R^{\mathrm{\Psi }}=$ 0.71${}_{-0.10}^{+0.10}$ $\pm$ 0.03 and $\mathrm{\Delta }{\mathrm{\Phi }}^{\mathrm{\Psi }}$ = (23${}_{-8.0}^{+8.8}$ $\pm$ 1.6${)}^{\circ }$, where the first uncertainties are statistical and the second systematic.