  The BESIII collaboration here reports the first observation of polarized
$\Lambda$ and $\bar{\Lambda}$ hyperons produced in two different processes: i)
the resonant $e^+e^- \to J/\psi\to\Lambda\bar{\Lambda}$, using a data sample of
1.31 $\times$ 10$^9$ $J/\psi$ events and ii) the non-resonant $e^+e^-\to
\gamma^* \to \Lambda\bar{\Lambda}$, using a 66.9 pb$^{-1}$ 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 $\Lambda\to p\pi^-$
($\alpha_-$), $\bar{\Lambda}\to\bar{p}\pi^+$ ($\alpha_+$) and
$\bar{\Lambda}\to\bar{n}\pi^0$ ($\bar{\alpha}_0$). The obtained value
$\alpha_-=0.750\pm0.009\pm0.004$ differs with ~5$\sigma$ from the PDG value.
This value, together with the measurement $\alpha_+=-0.758\pm0.010\pm0.007$
allow for the most precise test of CP violation in $\Lambda$ decays so far:
$A_{CP} = (\alpha_- + \alpha_+)/(\alpha_- - \alpha_+)$ of
$-0.006\pm0.012\pm0.007$. The decay asymmetry $\bar{\alpha}_0 =
-0.692\pm0.016\pm0.006$ is measured for the first time. The $e^+e^- \to
\Lambda\bar{\Lambda}$ reaction at $\sqrt{s} =$ 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 $R=|G_E/G_M|$ and of the relative phase
$\Delta\Phi=\Phi_E-\Phi_M$. With the decay asymmetry parameters from the
$J/\psi$ data, the obtained values are $R=0.96\pm0.14\pm0.02$ 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, which corresponds to an effective form factor of $|G|=0.123 \pm
0.003 \pm 0.003$.
