Unraveling the structure of $\Lambda$ hyperons with polarized $\Lambda\bar{\Lambda}$ pairs

With data collected in a dedicated energy scan from 2.3864 up to 3.0800 GeV, the BESIII collaboration provides the first complete energy-dependent measurements of the $\Lambda$ electromagnetic form factors in the time-like region. By combining double-tag and single-tag events from the $e^+e^- \to \Lambda \overline\Lambda \to p\pi^-\bar{p}\pi^+$ reaction, we achieve a complete decomposition of the spin structure of the reaction at five energy points, with high statistical and systematic precision. Our data reveal that while the modulus of the ratio between the electric and magnetic form factor, $R(q^2) = |G_E(q^2)/G_M(q^2)|$, remains fairly constant across the considered energy range, the relative phase $\Delta \Phi(q^2) = \Phi_E(q^2) - \Phi_M(q^2)$ changes by more than 90$^{\mathrm{o}}$ between 2.396 and 2.6544 GeV. Using a fit to our data based on dispersion relations, the complex form factor ratio is determined as a function of $q^2$ and the preferred solution has multiple zero-crossings in the complex plane. From the derivative of the ratio at $q^2 = 0$, the root-mean-squared charge radius of the $\Lambda$ is obtained. The two most probable solutions yield a negative root-mean-squared charge radius, indicating an asymmetric charge distribution where the $ds$ quark pair lies close to the center of the $\Lambda$ hyperon.