Signatures of Odd-Parity $s$-wave ${\Xi }^{\ast }$ States in Femtoscopic Correlation Functions

Abstract

We investigate the ${\Xi }^{\ast }$ resonances within the molecular picture, where these states are dynamically generated as poles in the unitarized scattering amplitudes arising from the coupled-channel interactions of $K^{\ast -}\Lambda$, $K^{\ast -}{\Sigma }^0$, ${\rho }^{-}{\Xi }^0$, $\overline{K}{}^{\ast 0}{\Sigma }^{-}$, ${\rho }^0{\Xi }^{-}$, $\omega {\Xi }^{-}$, and $\varphi {\Xi }^{-}$. The interaction kernel is derived from the local hidden gauge formalism, while the unitarization procedure employs a hybrid method that combines cutoff and dimensional regularizations in the evaluation of the loop function. From a detailed spectroscopic analysis, we identify two $S=-2$ baryon states whose properties are compatible with some of the ${\Xi }^{\ast }$ resonances listed in the Review of Particle Physics. To explore their possible experimental signatures, we compute the femtoscopic correlation functions for all the vector-baryon pairs considered in the present study, using realistic estimates of production weights and varying source sizes $R=1,1.1,1.2,1.3,1.5$ fm.