Production of the (predicted) $K^{\ast }(4307)$ in $B$ decays

Abstract

In this work we study the production of $K^{\ast }(4307)$ in $B$ decays by determining the $J/\psi {\pi }^{+(0)}{K}^0$ and $J/\psi {\pi }^{-}{K}^{+}$ invariant mass distributions of the processes $B^{+}\to J/\psi {\pi }^{+}{\pi }^0{K}^0$ and $B^{+}\to J/\psi {\pi }^{+}{\pi }^{-}{K}^{+}$, respectively. Such $K^{\ast }(4307)$ has been recently predicted as a three-body state originated from the dynamics involved in the $KD{\bar{D}}^{\ast }$ system, with the $KD$ subsystem forming the $D_{s0}^{\ast }(2317)$ in isospin 0, and the $D{\bar{D}}^{\ast }$ subsystem generating the $X(3872)$ in isospin 0 and the $Z_c(3900)$ in isospin 1. The hidden charm content of $K^{\ast }(4307)$ favors its decay to a state like $J/\psi \pi K$ and the study of $B$-decays with these particles in their final states can constitute a way of finding experimental evidences for such an exotic vector meson, whose width, in spite of its large mass, is still quite narrow (around 18 MeV).