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With data samples collected with the BESIII detector at seven energy pointsat $\sqrt{s}= 3.68 - 3.71$ GeV, corresponding to an integrated luminosity of333 pb$^{-1}$, we present a study of the $\Lambda$ transverse polarization inthe $e^+e^-\to\Lambda\bar\Lambda$ reaction. The significance of polarization bycombining the seven energy points is found to be 2.6$\sigma$ including thesystematic uncertainty, which implies a non-zero phase between the transitionamplitudes of the $\Lambda\bar\Lambda$ helicity states. The modulus ratio andthe relative phase of EM-$psionic$ form factors combined with all energy pointsare measured to be $R^{\Psi} =$ 0.71$^{+0.10}_{-0.10}$ $\pm$ 0.03 and$\Delta\Phi^{\Psi}$ = (23$^{+8.8}_{-8.0}$ $\pm$ 1.6$)^\circ$, where the firstuncertainties are statistical and the second systematic.

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