Theoretical study of the $Omega(2012)$ state in the $Omega_c^0 to pi^+ Omega(2012)^- to pi^+ (bar{K}Xi)^-$ and $pi^+ (bar{K}Xipi)^-$ decays

We report on a theoretical study of the newly observed $Omega(2012)$ resonance in the nonleptonic weak decays of $Omega_c^0 to pi^+ bar{K}Xi^*(1530) (eta Omega) to pi^+ (bar{K}Xi)^-$ and $pi^+ (bar{K}Xipi)^-$ via final-state interactions of the $bar{K}Xi^*(1530)$ and $eta Omega$ pairs. The weak interaction part is assumed to be dominated by the charm quark decay process: $c(ss) to (s + u + bar{d})(ss)$, while the hadronization part takes place between the $sss$ cluster from the weak decay and a quark-antiquark pair with the quantum numbers $J^{PC} = 0^{++}$ of the vacuum, produces a pair of $bar{K}Xi^*(1530)$ and $eta Omega$. Accordingly, the final $bar{K}Xi^*(1530)$ and $eta Omega$ states are in pure isospin $I= 0$ combinations, and the $Omega_c^0 to pi^+ bar{K}Xi^*(1530)(eta Omega) to pi^+ (bar{K}Xi)^-$ decay is an ideal process to study the $Omega(2012)$ resonance. With the final-state interaction described in the chiral unitary approach, up to an arbitrary normalization, the invariant mass distributions of the final state are calculated, assuming that the $Omega(2012)$ resonance with spin-parity $J^P = 3/2^-$ is a dynamically generated state from the coupled channels interactions of the $bar{K}Xi^*(1530)$ and $eta Omega$ in $s$-wave and $bar{K}Xi$ in $d$-wave. We also calculate the ratio, $R^{bar{K}Xipi}_{bar{K}Xi} = {rm Br}[Omega_c^0 to pi^+ Omega(2012)^- to pi^+ (bar{K}Xi pi)^-] / {rm Br}[Omega_c^0 to pi^+ Omega(2012)^- to pi^+ (bar{K}Xi)^-$]. The proposed mechanism can provide valuable information on the nature of the $Omega(2012)$ and can in principle be tested by future experiments.