Observation of Transverse Polarization and Determination of Psionic Form Factors of the $\mathrm{\Lambda }$ Hyperon at $\sqrt{s}=3.773$ 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 form factors of the $\mathrm{\Lambda }$ hyperon in $e^{+}{e}^{-}\to \mathrm{\Lambda }\bar{\mathrm{\Lambda }}$ decay with the entangled $\mathrm{\Lambda }-\bar{\mathrm{\Lambda }}$ pair at $\sqrt{s}=3.773$ GeV. The relative phase between the psionic form factors is determined to be $\mathrm{\Delta }\mathrm{\Phi }=(1.53\pm 0.36\pm 0.03)$~rad with a significance of 5.5 $\sigma$ taking into account systematic uncertainty. This result indicates a non-zero phase between the transition amplitudes of the $\mathrm{\Lambda }\bar{\mathrm{\Lambda }}$ helicity states. Additionally, we measure the angular distribution parameter and the modulus of the ratio between the psionic form factors to be $\eta =0.86\pm 0.05\pm 0.03$ and $R(s)=\mathrm{\mid }{G}_E(s)\mathrm{/}{G}_M(s)\mathrm{\mid }=0.47\pm 0.08\pm 0.05$, where the first uncertainty is statistical and the second systematic.