This paper examines the shape of the mass peaks (the “line shape”) seen when the particle called Ω(2012) is produced and then decays into two different final states: Ξ^- π^+ K^- and Ξ^0 K^-. The authors test the idea that Ω(2012) is not a simple three‑quark particle but a molecular state: a bound system formed chiefly from a Ξ* baryon and an anti‑kaon (K̄), with another channel called Ωη mixed in and the Ξ K̄ channel appearing as a decay mode. They compare their calculated mass distributions directly with published experimental results and find overall agreement, which supports the molecular interpretation of Ω(2012).

To make the comparison the authors model how the resonance is produced and how its components convert into the observed final particles. They assume an initial “doorway” three‑quark state hadronizes (creates a meson–baryon pair) and then the meson and baryon interact. The interactions are treated in a coupled‑channel approach, which means several possible two‑body combinations (Ξ* K̄, Ωη, and Ξ K̄) are allowed to mix and scatter into one another. The scattering matrix is built from a potential and loop functions that describe propagation of the intermediate meson‑baryon pairs. For the three‑body decay (Ξ π K̄) the calculation also includes the finite, energy‑dependent width of the intermediate Ξ* resonance and the experimentally determined coupling of Ξ* to Ξ π (the paper quotes a coupling g = 0.0044 MeV^-1 computed from the measured Ξ* decay width).

At a qualitative level this produces peaks in the predicted mass distributions at the location of Ω(2012), and the authors add a simple smooth background to match nonresonant events in the experiment. Using parameter sets taken from a previous study, which already reproduced the Ω(2012) mass and total width, they reproduce the shape and size of the experimental peaks in both decay channels. The authors emphasize that matching the full line shapes (the detailed mass distributions) is a more demanding and informative test of the molecular picture than comparing only a single number—the ratio R of the three‑body to two‑body decay widths.