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Signatures of the $Ω(2012)^{-}$ state in $Ξ^*\bar K$ Correlation Functions

Jia-Xin Lin, Pablo Encarnación, Albert Feijoo, Miguel Albaladejo

Abstract

We investigate the $Ω(2012)$ 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 $Ω(2012)$ is dynamically generated as a quasi-bound $Ξ^{\ast}\bar K$-$Ωη$ molecular state, with its coupling to the $Ξ\bar{K}$ channel driven by $d$-wave transitions. Model parameters are constrained by the measured mass, width, and the Belle determination of the branching fraction $\mathcal R^{Ξ\bar Kπ}_{Ξ\bar K}$, yielding $M_{Ω(2012)}=(2012.53\pm0.73)$ MeV and $Γ_{Ω(2012)}=(4.05\pm0.13)$ MeV. Within this framework, we compute the femtoscopic correlation functions of the $Ξ^{\ast0}K^-$, $Ξ^{\ast-}\bar K^0$, and $Ω^-η$ systems. The $Ξ^{\ast}\bar K$ correlation functions exhibit pronounced near-threshold structures that arise from the proximity of the $Ω(2012)$ pole, demonstrating an exceptional sensitivity to its position and coupled-channel composition. In particular, the $Ξ^{\ast0}K^-$ correlation function is identified as a clean and highly selective probe of the $Ω(2012)$ 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 $Ω(2012)$.

Signatures of the $Ω(2012)^{-}$ state in $Ξ^*\bar K$ Correlation Functions

Abstract

We investigate the resonance in the strangeness sector within a coupled-channel chiral unitary approach and present the first quantitative predictions for femtoscopic correlation functions directly sensitive to its dynamics. The is dynamically generated as a quasi-bound - molecular state, with its coupling to the channel driven by -wave transitions. Model parameters are constrained by the measured mass, width, and the Belle determination of the branching fraction , yielding MeV and MeV. Within this framework, we compute the femtoscopic correlation functions of the , , and systems. The correlation functions exhibit pronounced near-threshold structures that arise from the proximity of the pole, demonstrating an exceptional sensitivity to its position and coupled-channel composition. In particular, the correlation function is identified as a clean and highly selective probe of the 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 .
Paper Structure (7 sections, 22 equations, 2 figures, 3 tables)

This paper contains 7 sections, 22 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Formalism
  3. $\Omega(2012)^-$ as a dynamically generated state
  4. Scattering parameters
  5. Correlation function
  6. Results
  7. Conclusions

Figures (2)

  • Figure 1: Correlation functions of $\Xi^{\ast0}K^-, \Xi^{\ast-}\,\overline{\!{K}}{}^0$, and $\Omega^-\eta$ channels with source size $R=1.2\,\text{fm}$. The solid and dashed lines correspond to the cases with and without the $\Xi^\ast$, respectively. The 68% CL color-shaded bands are estimated from the uncertainties in the production weights, the parameters $\Lambda, \alpha, \beta$, and the 10% uncertainty in the source size.
  • Figure 2: The contributions of different coupled channels to $\Xi^{\ast0}K^-$ CF.