Prediction of possible $D{K}_1$ bound states

Abstract

Stimulated by recent experimental observation of $X_1(2900)$ just below the ${\bar{D}}_{1}K$ threshold, we extend our previous study of ${\bar{D}}_{1}D$ S-wave bound state by vector meson exchange to ${\bar{D}}_{1}K$ system as well as similar $\bar{D}{K}_1$, $D_{1}K$ and $D{K}_1$ systems to look for possible bound states. We find that the potential of $D{K}_1$ is attractive and strong enough to form bound states with mass around 3110 MeV for $D{K}_1(1270)$ and 3240 MeV for $D{K}_1(1400)$. $D_{1}K$ is also attractive but weaker, hardly enough to form bound states. While $\bar{D}{K}_1$ becomes further less attractive, the potential between ${\bar{D}}_{1}K$ is the weakest, definitely too weak to form any bound state, which excludes the recently observed $X_1(2900)$ to be a ${\bar{D}}_{1}K$ bound state. We also give the decay properties of the predicted $D{K}_1$ bound states.

Comments: 9 pages, 2 figures, version appears in EPJA