Complete Measurement of the Λ Electromagnetic Form Factors

Abstract

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