  One of the fundamental goals of particle physics is to gain microscopic
understanding of the strong interaction. Electromagnetic form factors quantify
the structure of hadrons in terms of charge and magnetization distributions.
While the nucleon structure has been investigated extensively, data on hyperons
is still scarce. It has recently been demonstrated that electron-positron
annihilations into hyperon-antihyperon pairs provide a powerful tools to
investigate their inner structure. We present a novel method useful for
hyperon-antihyperon pairs of different types which exploits the cross section
enhancement due to the vacuum polarization effect at the $J/\psi$ resonance.
Using the 10 billion $J/\psi$ events collected with the BESIII detector, this
allows a thorough determination of the hyperon structure . The result is
essentially a precise snapshot of a
$\bar\Lambda\Sigma^0$~($\Lambda\bar\Sigma^0$) pair in the making, encoded in
the form factor ratio and the phase. Their values are measured to be $R =
0.860\pm0.029({\rm stat.})\pm0.010({\rm syst.})$,
$\Delta\Phi_1=(1.011\pm0.094({\rm stat.})\pm0.010({\rm syst.}))~\rm rad$ for
$\bar\Lambda\Sigma^0$ and $\Delta\Phi_2=(2.128\pm0.094({\rm
stat.})\pm0.010({\rm syst.}))~\rm rad$ for $\Lambda\bar\Sigma^0$, respectively.
Furthermore, charge-parity (CP) breaking is investigated for the first time in
this reaction and found to be consistent with CP symmetry.
