Study of the $B^{-}\to K^{-}\hat{I}\cdot \hat{I}{\cdot }_c$ decay due to the $D\bar{D}$ bound state

Abstract

We study the $B^{-}\to K^{-}\hat{I}\cdot \hat{I}{\cdot }_c$ decay by taking into account the $S$-wave contributions from the pseudoscalar meson-pseudoscalar meson interactions within the unitary coupled-channel approach, where the $D\bar{D}$ bound state is dynamically generated. In addition, the contribution from the intermediate resonance $K_0^{\ast }(1430{)}^{-}$, with $K_0^{\ast }(1430{)}^{-}\to K^{-}\hat{I}\cdot$, is also considered. Our results show that there is a clear peak around $3720$~MeV in the $\hat{I}\cdot \hat{I}{\cdot }_c$ invariant mass distribution, which could be associated with the $D\bar{D}$ bound state. The future precise measurements of the $B^{-}\to K^{-}\hat{I}\cdot \hat{I}{\cdot }_c$ process at the Belle II and LHCb experiments could be, therefore, used to check the existence of the $D\bar{D}$ bound state, and to deepen our understanding of the hadron-hadron interactions.

14 pages, 9 figures