$K^{\ast }$ mesons with hidden charm arising from $KX(3872)$ and $K{Z}_c(3900)$ dynamics

Abstract

Inspired by the recent discovery of the pentaquark states $P_c(4450)$ and $P_c(4380)$, which can be viewed as excited nucleon states with hidden charm, we study the three-body interaction of a kaon and a pair of $D{\bar{D}}^{\ast }$ in isospin 0 and 1. We show that the two body interactions stringently constrained by the existence of the $D_{s0}^{\ast }(2317)$, $D_{s1}^{\ast }(2460)$, $X(3872)$, and $Z_c(3900)$, which are widely believed to contain large $DK$, $D^{\ast }K$, and $D{\bar{D}}^{\ast }$ components, inevitably lead to the existence of a heavy $K^{\ast }$ meson with hidden charm. Concrete coupled channel three-body calculations yield its mass and width as $(4307\pm 2)-i(9\pm 2)$ MeV with $I(J^P)=1/2(1^{-})$. This state, if found experimentally, definitely cannot be accommodated in a $q\bar{q}$ picture, and therefore presents a clear case of an exotic hadron.

Comments: updated version