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

In this work we study the production of $K^*(4307)$ in $B$ decays by determining the $J/ψπ^{+(0)}K^{0}$ and $J/ψπ^- K^+$ invariant mass distributions of the processes $B^+\to J/ψπ^+π^0 K^0$ and $B^+\to J/ψπ^+π^- K^+$, 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 $J/ψπK$ 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).

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