Abstract: | The exclusive process $e^+e^-
ightarrowLambdaar{Lambda}$, with $Lambda
o ppi^-$ and $ar{Lambda} o ar{p}pi^+$, has been studied at $sqrt{s}
=$ 2.396 GeV for measurement of the $Lambda$ electric and magnetic form
factors, $G_E$ and $G_M$. A data sample, corresponding to an integrated
luminosity of 66.9 pb$^{-1}$, was collected with the BESIII detector for this
purpose. A multi-dimensional analysis with a complete decomposition of the spin
structure of the reaction enables a determination of the modulus of the ratio
$R=|G_E/G_M|$ and, for the first time for any baryon, the relative phase
$DeltaPhi=Phi_E-Phi_M$. The resulting values are obtained using the recent
and most precise measured value of the asymmetry parameter $alpha_{Lambda}$ =
$0.750~pm~0.010$ to be $R~=~0.96pm0.14~(
m stat.)pm~0.02~(
m sys.)$ and
$DeltaPhi=37^{mathrm{o}}pm~12^{mathrm{o}}~(
m
stat.)pm~6^{mathrm{o}}~(
m sys.)$, respectively. In addition, the cross
section is measured with unprecedented precision to be $sigma =
118.7~pm~5.3~(
m stat.)pm~5.1~(
m sys.)$ pb, which corresponds to an
effective form factor of $|G|=0.123~pm~0.003~(
m stat.)pm~0.003~(
m sys.)$.
The contribution from two-photon exchange is found to be negligible. Our result
enables the first complete determination of baryon time-like electromagnetic
form factors. |