$D_1(2420)$ and its interactions with a kaon: open charm states with strangeness

In this work we present an attempt to describe the $X_1(2900)$ found by the LHCb collaboration, in the experimental data on the invariant mass spectrum of $D^-K^+$, as a three-meson molecular state of the $K\rho\bar D$ system. We discuss that the interactions in all the subsystems are attractive in nature, with the $\rho \bar D$ interaction generating $\bar D_1(2420)$ and the $K \rho$ resonating as $K_1(1270)$. We find that the system can form a three-body state but with a mass higher than that of $X_1(2900)$. We investigate the $K \rho D$ system too, finding that the three-body dynamics generates an isoscalar state, which can be related to $D_{s1}^*(2860)$, and an exotic isovector state. This latter state has a mass similar to that of the $X_0(2900)$ and $X_1(2900)$ states found by LHCb, but a very small width ($\sim 7.4 \pm 0.9$ MeV) and necessarily requires more than two quarks to describe its properties. We hope that our findings will encourage experimental investigations of the isovector $K \rho D$ state. Finally, in the pursuit of finding a description for $X_1(2900)$, we study the $\pi\bar K^* D^*$ system where $\bar K^*D^*$ forms $0^+$, $1^+$ and $2^+$ states. We do not find a state which can be associated with $X_1(2900)$.