Observation of Transverse Polarization and Determination of Psionic Form Factors of The. Hyperon at √s=3.773 Gev

Using a data sample of e(+)e(-) collision data corresponding to an integrated luminosity of 20.3 fb(-1) collected by the BESIII detector at the BEPCII collider, we present an observation of transverse polarization and a complete determination of the psionic formfactors of the. hyperon in e(+)e(-) -> Lambda(Lambda) over bar decaywith the entangled Lambda - (Lambda) over bar pair at root s = 3.773 GeV. The relative phase between the psionic form factors is determined to be Delta phi = (1.53 +/- 0.36 +/- 0.03) rad with a significance of 5.5 sigma taking into account systematic uncertainty. This result indicates a nonzero phase between the transition amplitudes of the Lambda(Lambda) over bar helicity states. Additionally, we measure the angular distribution parameter and the modulus of the ratio between the psionic formfactors to be eta = 0.86 +/- 0.05 +/- 0.03 and R(s) +/- |G(E)(s)=GM (s)| = 0.47 +/- 0.08 +/- 0.05, where the first uncertainty is statistical and the second systematic.