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

Abstract

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 $D_{s1}^{\ast }(2860)$, 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 $\pi {\bar{K}}^{\ast }{D}^{\ast }$ system where ${\bar{K}}^{\ast }{D}^{\ast }$ forms $0^{+}$, $1^{+}$ and $2^{+}$ states. We do not find a state which can be associated with $X_1(2900)$.