Production of the (predicted) $K^*(4307)$ in $B$ decays

Abstract

In this work we study the production of $K^*(4307)$ 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 $K^*(4307)$ has been recently predicted as a three-body state originated from the dynamics involved in the $K D\\bar D^*$ system, with the $KD$ subsystem forming the $D^{*}_{s0}(2317)$ in isospin 0, and the $D\\bar D^*$ subsystem generating the $X(3872)$ in isospin 0 and the $Z_c(3900)$ in isospin 1. The hidden charm content of $K^*(4307)$ 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).