Theoretical study of the $\hat{I}\text{c◯}(2012)$ state in the $\hat{I}{\text{c◯}}_c^0\to \ddot{I}{€}^{+}\hat{I}\text{c◯}(2012{)}^{-}\to \ddot{I}{€}^{+}(\bar{K}\hat{I}ž{)}^{-}$ and $\ddot{I}{€}^{+}(\bar{K}\hat{I}ž\ddot{I}€{)}^{-}$ decays

Abstract

We report on a theoretical study of the newly observed $\hat{I}\text{c◯}(2012)$ resonance in the nonleptonic weak decays of $\hat{I}{\text{c◯}}_c^0\to \ddot{I}{€}^{+}\bar{K}\hat{I}{ž}^{\ast }(1530)(\hat{I}\cdot \hat{I}\text{c◯})\to \ddot{I}{€}^{+}(\bar{K}\hat{I}ž{)}^{-}$ and $\ddot{I}{€}^{+}(\bar{K}\hat{I}ž\ddot{I}€{)}^{-}$ via final-state interactions of the $\bar{K}\hat{I}{ž}^{\ast }(1530)$ and $\hat{I}\cdot \hat{I}\text{c◯}$ 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 $\bar{K}\hat{I}{ž}^{\ast }(1530)$ and $\hat{I}\cdot \hat{I}\text{c◯}$. Accordingly, the final $\bar{K}\hat{I}{ž}^{\ast }(1530)$ and $\hat{I}\cdot \hat{I}\text{c◯}$ states are in pure isospin $I=0$ combinations, and the $\hat{I}{\text{c◯}}_c^0\to \ddot{I}{€}^{+}\bar{K}\hat{I}{ž}^{\ast }(1530)(\hat{I}\cdot \hat{I}\text{c◯})\to \ddot{I}{€}^{+}(\bar{K}\hat{I}ž{)}^{-}$ decay is an ideal process to study the $\hat{I}\text{c◯}(2012)$ 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 $\hat{I}\text{c◯}(2012)$ resonance with spin-parity $J^P=3/2^{-}$ is a dynamically generated state from the coupled channels interactions of the $\bar{K}\hat{I}{ž}^{\ast }(1530)$ and $\hat{I}\cdot \hat{I}\text{c◯}$ in $s$-wave and $\bar{K}\hat{I}ž$ in $d$-wave. We also calculate the ratio, $R_{\bar{K}\hat{I}ž}^{\bar{K}\hat{I}ž\ddot{I}€}=\mathrm{Br}[\hat{I}{\text{c◯}}_c^0\to \ddot{I}{€}^{+}\hat{I}\text{c◯}(2012{)}^{-}\to \ddot{I}{€}^{+}(\bar{K}\hat{I}ž\ddot{I}€{)}^{-}]/\mathrm{Br}[\hat{I}{\text{c◯}}_c^0\to \ddot{I}{€}^{+}\hat{I}\text{c◯}(2012{)}^{-}\to \ddot{I}{€}^{+}(\bar{K}\hat{I}ž{)}^{-}$]. The proposed mechanism can provide valuable information on the nature of the $\hat{I}\text{c◯}(2012)$ and can in principle be tested by future experiments.

More references and discussions are added; typos are fixed