Unveiling the elusive $\hat{I}\pounds (1380)$ resonance through coupled-channel dynamics in $\hat{I}{›}_c^{+}\to \hat{I}\cdot \ddot{I}{€}^{+}\hat{I}›$ reaction

Abstract

We investigate the $\hat{I}{›}_c^{+}\to \hat{I}\cdot \ddot{I}{€}^{+}\hat{I}›$ decay measured by the Belle and BESIII Collaborations, focusing on the possible role of the $\hat{I}\pounds (1380)$ state with spin-parity $J^P=1/2^{-}$. In our theoretical framework, the $\hat{I}›(1670)$ and $a_0(980)$ are dynamically generated from meson-baryon and meson-meson final-state interactions, respectively, and the corresponding line shapes of these two states used here are applicable to all relevant hadronic reactions. Furthermore, the contributions from the intermediate $\hat{I}\pounds (1385)$ resonance and the possible $\hat{I}\pounds (1380)$ state are included explicitly. By comparing the invariant mass and angular distributions obtained with and without the $\hat{I}\pounds (1380)$ state, we demonstrate that this state plays an important role in improving the description of the experimental data. We also identify the kinematic regions most sensitive to the possible $\hat{I}\pounds (1380)$ contribution. Future high-precision measurements of this process will be instrumental for testing the existence of the $\hat{I}\pounds$ state with $J^P=1/2^{-}$.

10 pages, 7 figures