Accessing the strong interaction between $\mathrm{\Lambda }$ baryons and charged kaons with the femtoscopy technique at the LHC

The interaction between $\mathrm{\Lambda }$ baryons and kaons/antikaons is a crucial ingredient for the strangeness $S=0$ and $S=-2$ sector of the meson$-$baryon interaction at low energies. In particular, the $\mathrm{\Lambda }\bar{\mathrm{K}}$ might help in understanding the origin of states such as the $\mathrm{\Xi }(1620)$, whose nature and properties are still under debate. Experimental data on $\mathrm{\Lambda }$$-$$\mathrm{K}$ and $\mathrm{\Lambda }$$-$$\bar{\mathrm{K}}$ systems are scarce, leading to large uncertainties and tension between the available theoretical predictions constrained by such data. In this Letter we present the measurements of $\mathrm{\Lambda }$$-$K${}^{+}\oplus \bar{\mathrm{\Lambda }}$$-$K${}^{-}$ and $\mathrm{\Lambda }$$-$K${}^{-}\oplus \bar{\mathrm{\Lambda }}$$-$K${}^{+}$ correlations obtained in the high-multiplicity triggered data sample in pp collisions at $\sqrt{s}=13$ TeV recorded by ALICE at the LHC. The correlation function for both pairs is modeled using the Lednicky$-$Lyuboshits analytical formula and the corresponding scattering parameters are extracted. The $\mathrm{\Lambda }$$-$K${}^{-}\oplus \bar{\mathrm{\Lambda }}$$-$K${}^{+}$ correlations show the presence of several structures at relative momenta $k^{\ast }$ above 200 MeV/$c$, compatible with the $\mathrm{\Omega }$ baryon, the $\mathrm{\Xi }(1690)$, and $\mathrm{\Xi }(1820)$ resonances decaying into $\mathrm{\Lambda }$$-$K${}^{-}$ pairs. The low $k^{\ast }$ region in the $\mathrm{\Lambda }$$-$K${}^{-}\oplus \bar{\mathrm{\Lambda }}$$-$K${}^{+}$ also exhibits the presence of the $\mathrm{\Xi }(1620)$ state, expected to strongly couple to the measured pair. The presented data allow to access the $\mathrm{\Lambda }$K${}^{+}$ and $\mathrm{\Lambda }$K${}^{-}$ strong interaction with an unprecedented precision and deliver the first experimental observation of the $\mathrm{\Xi }(1620)$ decaying into $\mathrm{\Lambda }$K${}^{-}$.