Complete Measurement of the $\Lambda $ Electromagnetic Form Factors

The exclusive process ${e}^{+}{e}^{-}\to \Lambda \overline{\Lambda }$, with $\Lambda \to p{\pi }^{-}$ and $\overline{\Lambda }\to \overline{p}{\pi }^{+}$, has been studied at $\sqrt{s}=2.396\text{}\text{}\mathrm{GeV}$ for measurement of the timelike $\Lambda $ electric and magnetic form factors, ${G}_{E}$ and ${G}_{M}$. A data sample, corresponding to an integrated luminosity of $66.9\text{}\text{}{\mathrm{pb}}^{-1}$, was collected with the BESIII detector for this purpose. A multidimensional 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 $\Delta \Phi ={\Phi }_{E}-{\Phi }_{M}$. The resulting values are $R=0.96±0.14\left(\text{stat}\right)±0.02\left(\text{syst}\right)$ and $\Delta \Phi =37°±12°\left(\text{stat}\right)±6°\left(\text{syst}\right)$, respectively. These are obtained using the recently established and most precise value of the asymmetry parameter ${\alpha }_{\Lambda }=0.750±0.010$ measured by BESIII. In addition, the cross section is measured with unprecedented precision to be $\sigma =118.7±5.3\left(\text{stat}\right)±5.1\left(\text{syst}\right)\text{}\text{}\mathrm{pb}$, which corresponds to an effective form factor of $|G|=0.123±0.003\left(\text{stat}\right)±0.003\left(\text{syst}\right)$. The contribution from two-photon exchange is found to be negligible. Our result enables the first complete determination of baryon timelike electromagnetic form factors.