Signatures of the $\Omega(2012)^{-}$ state in $\Xi^*\bar K$ 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 $\mathcal R^{\Xi\bar K\pi}_{\Xi\bar K}$, yielding $M_{\Omega(2012)}=(2012.53\pm0.73)$ MeV and $\Gamma_{\Omega(2012)}=(4.05\pm0.13)$ MeV. Within this framework, we compute the femtoscopic correlation functions of the $\Xi^{\ast0}K^-$, $\Xi^{\ast-}\bar K^0$, 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 $\Xi^{\ast0}K^-$ 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 $\Omega(2012)$.