Spin polarization of $\mathrm{\Lambda }$ hyperons in $e^{+}{e}^{-}\to \mathrm{\Lambda }\bar{\mathrm{\Lambda }}$ at BESIII

The BESIII collaboration here reports the first observation of polarized $\mathrm{\Lambda }$ and $\bar{\mathrm{\Lambda }}$ hyperons produced in two different processes: i) the resonant $e^{+}{e}^{-}\to J\mathrm{/}\psi \to \mathrm{\Lambda }\bar{\mathrm{\Lambda }}$, using a data sample of 1.31 $\times$ 10${}^9$ $J\mathrm{/}\psi$ events and ii) the non-resonant $e^+e^-\to \gamma^* \to \Lambda\bar{\Lambda}$,usinga66.9pb$^{-1}$ data sample collected at $\sqrt{s}=$ 2.396 GeV. In $e^+e^-\to J/\psi\to\Lambda\bar{\Lambda}$, the phase between the electric and the magnetic amplitude is measured for the first time to be $42.3^{$\mathrm{o}$} \pm 0.6^{$\mathrm{o}$} \pm 0.5^{$\mathrm{o}$}$. The multi-dimensional analysis enables a model-independent measurement of the decay parameters for $\mathrm{\Lambda }\to p{\pi }^{-}$ (${\alpha }_{-}$), $\bar{\mathrm{\Lambda }}\to \bar{p}{\pi }^{+}$ (${\alpha }_{+}$) and $\bar{\mathrm{\Lambda }}\to \bar{n}{\pi }^0$ (${\bar{\alpha }}_0$). The obtained value ${\alpha }_{-}=0.750\pm 0.009\pm 0.004$ differs with ~5$\sigma$ from the PDG value. This value, together with the measurement ${\alpha }_{+}=-0.758\pm 0.010\pm 0.007$ allow for the most precise test of CP violation in $\mathrm{\Lambda }$ decays so far: $A_{CP}=({\alpha }_{-}+{\alpha }_{+})\mathrm{/}({\alpha }_{-}-{\alpha }_{+})$ of $-0.006\pm 0.012\pm 0.007$. The decay asymmetry $\bar{\alpha}_0 = -0.692\pm0.016\pm0.006$ismeasuredforthefirsttime\mathrm{.}The$e^+e^- \to \Lambda\bar{\Lambda}$reactionat$\sqrt{s} =$ 2.396 GeV enables a first complete measurement of the time-like electric and magnetic form factor of any baryon, of the modulus of the ratio $R=\mathrm{\mid }{G}_E\mathrm{/}{G}_M\mathrm{\mid }$ and of the relative phase $\mathrm{\Delta }\mathrm{\Phi }={\mathrm{\Phi }}_E-{\mathrm{\Phi }}_M$. With the decay asymmetry parameters from the $J\mathrm{/}\psi$ data, the obtained values are $R=0.96\pm 0.14\pm 0.02$ and $\Delta\Phi = 37^{$\mathrm{o}$} \pm 12^{$\mathrm{o}$} \pm 6^{$\mathrm{o}$}$. In addition, the cross section has been measured with unprecedented precision to be $\sigma = 119.0\pm 5.3\pm5.1$pb,whichcorrespondstoaneffectiveformfactorof$|G|=0.123 \pm 0.003 \pm 0.003$.