K⁎ mesons with hidden charm arising from KX(3872) and KZc(3900) dynamics

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