Signatures of the $\Omega (2012{)}^{-}$ state in ${\Xi }^{\ast }\bar{K}$ Correlation Functions

Abstract

We investigate the $\Omega (2012)$ resonance in the strangeness $S=-3$ sector within a coupled-channel chiral unitary approach and present the first quantitative predictions for femtoscopic correlation functions directly sensitive to its dynamics. The $\Omega (2012)$ is dynamically generated as a quasi-bound ${\Xi }^{\ast }\bar{K}$-$\Omega \eta$ molecular state, with its coupling to the $\Xi \bar{K}$ channel driven by $d$-wave transitions. Model parameters are constrained by the measured mass, width, and the Belle determination of the branching fraction ${\mathcal{R}}_{\Xi \bar{K}}^{\Xi \bar{K}\pi }$, yielding $M_{\Omega (2012)}=(2012.53\pm 0.73)$ MeV and ${\Gamma }_{\Omega (2012)}=(4.05\pm 0.13)$ MeV. Within this framework, we compute the femtoscopic correlation functions of the ${\Xi }^{\ast 0}{K}^{-}$, ${\Xi }^{\ast -}{\bar{K}}^0$, and ${\Omega }^{-}\eta$ systems. The ${\Xi }^{\ast }\bar{K}$ correlation functions exhibit pronounced near-threshold structures that arise from the proximity of the $\Omega (2012)$ pole, demonstrating an exceptional sensitivity to its position and coupled-channel composition. In particular, the ${\Xi }^{\ast 0}{K}^{-}$ correlation function is identified as a clean and highly selective probe of the $\Omega (2012)$ resonance. These results establish femtoscopic correlation measurements as powerful tools for extracting resonance properties beyond conventional invariant-mass analyses and provide concrete theoretical benchmarks for upcoming experimental studies aimed at elucidating the molecular nature of the $\Omega (2012)$.

Comments: 12 pages, 2 figures