Investigating $\hat{I}{\cdot }_1^{\prime }(1855)$ exotic states in $J/\ddot{I}ˆ\to \hat{I}{\cdot }_1^{\prime }(1855)\hat{I}{\cdot }^{(\prime )}$ decays

Abstract

An analysis of the $J/\ddot{I}ˆ\to \hat{I}\cdot \hat{I}{\cdot }^{\prime }{\hat{I}}^3$ decay by the BESIII collaboration claims the observation of an exotic state $\hat{I}{\cdot }_1(1855)$ with $I^G{J}^{PC}=0^{+}{1}^{-+}$. To establish its C-parity partner $\hat{I}{\cdot }_1^{\prime }(1855)$ in the picture of the $K{\bar{K}}_1(1400)$ molecular state, we propose that $J/\ddot{I}ˆ\to \hat{I}{\cdot }_1^{\prime }(1855)\hat{I}{\cdot }^{(\prime )}$ receives the main contributions from the final state interaction of $K{K}^{\ast }$($K^{+}{K}^{\ast -}$, $K^{-}{K}^{\ast +}$, $K^0{\bar{K}}^{\ast 0}$, and ${\bar{K}}^0{K}^{\ast 0}$). Specifically, $K$ and $K^{\ast }$ in $J/\ddot{I}ˆ\to K{K}^{\ast }$ decays transform as $\hat{I}{\cdot }_1^{\prime }(1855)\hat{I}{\cdot }^{(\prime )}$, by exchanging a $K_1(1400)$. We predict $\mathcal{B}(J/\ddot{I}ˆ\to \hat{I}{\cdot }_1^{\prime }(1855)\hat{I}\cdot )=(6.3_{-3.5}^{+12.6})\times 10^{-6}$, and $\mathcal{B}(J/\ddot{I}ˆ\to \hat{I}{\cdot }_1^{\prime }(1855)\hat{I}{\cdot }^{\prime })=(6.5_{-4.6}^{+6.6})\times 10^{-6}$, which can be studied in the $J/\ddot{I}ˆ\to K^{\ast }{\bar{K}}^{\ast }\hat{I}{\cdot }^{(\prime )}$ decays.

Accepted by Physics Letters B