Probing the hadronic molecular nature of the $\Omega (2012)$, $\Omega (2380)$, and ${\Omega }_c(3120)$ via femtoscopy correlation functions

Abstract

We investigate the femtoscopic correlation functions of systems associated with the $\Omega (2012)$, $\Omega (2380)$, and ${\Omega }_c(3120)$ resonances, with the aim of elucidating their internal structures. By employing effective potential models that incorporate both $s$-wave and $d$-wave interactions, we calculate the correlation functions for the relevant coupled channels. Our numerical results reveal pronounced enhancement structures in the ${\Xi }^0{K}^{-}$ and ${\Xi }_c^{+}{K}^{-}$ correlation functions, which provide direct evidences for the dynamically generated $\Omega (2012)$ and ${\Omega }_c(3120)$ states. Furthermore, significant low-momentum enhancements are observed in the ${\Xi }^{\ast 0}{K}^{-}$ and ${\Xi }^{\ast 0}{K}^{\ast -}$ channel, which are attributed to the $\Omega (2012)$ and $\Omega (2380)$ resonances. These theoretical calculations provide crucial insights for future high-precision measurements at the LHC and RHIC, offering a novel and independent approach to determine the dynamically generated hadronic molecular nature of these $\Omega$ excited states.