Complete measurement of $Λ$ electromagnetic form factors
The exclusive process $e^+e^-\rightarrowΛ\barΛ$, with $Λ\to pπ^-$ and $\barΛ \to \bar{p}π^+$, has been studied at $\sqrt{s} =$ 2.396 GeV for measurement of the $Λ$ 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 $ΔΦ=Φ_E-Φ_M$. The resulting values are obtained using the recent and most precise measured value of the asymmetry parameter $α_Λ$ = $0.750~\pm~0.010$ to be $R~=~0.96\pm0.14~(\rm stat.)\pm~0.02~(\rm sys.)$ and $ΔΦ=37^{\mathrm{o}}\pm~12^{\mathrm{o}}~(\rm stat.)\pm~6^{\mathrm{o}}~(\rm sys.)$, respectively. In addition, the cross section is measured with unprecedented precision to be $σ= 118.7~\pm~5.3~(\rm stat.)\pm~5.1~(\rm sys.)$ pb, which corresponds to an effective form factor of $|G|=0.123~\pm~0.003~(\rm stat.)\pm~0.003~(\rm sys.)$. 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.