Heavy $K^*$ mesons with open charm from $KD^{(*)}D^*$ interactions

In view of the recent discovery of $T_{cc}$, which can be described as a $DD^*$ molecular state, we perform a study of the $KDD^*$ system, and its extension to studying $KD^*D^*$, where $D^*D^*$ is bound as a spin 1 $T_{cc}$-like state, to search for the possible existence of exotic mesons with the open flavors $ccs$ being part of their quark configuration. Considering the additional attractive interactions present in the $KD$ and $KD^*$ subsystems, where the states $D^*_{s0}(2317)$ and $D_{s1}(2460)$ are generated, we solve the Faddeev equations considering the fixed-center approximation for the mentioned three-body systems and find the existence of two doubly charmed $K^*$-like mesons, $K_{cc}^*(4309)$ and $K_{cc}^*(4449)$, with quantum numbers $I(J^P)=1/2\,(1^-)$. Considering the respective three-body thresholds of the two systems, both $K_{cc}$-states are bound by around $60$ MeV. An experimental confirmation will bring evidence for the existence of a degree of exoticity beyond charm +2.