Prediction of possible $DK_1$ bound states

TL;DR

This paper investigates the potential for bound states involving D, K, and D_1 mesons using vector meson exchange, predicting specific bound states and analyzing their decay properties, while ruling out certain interpretations of recent experimental observations.

Contribution

It extends previous studies to include the $ar D_1K$ system and predicts new bound states in the $DK_1$ channel based on vector meson exchange.

Findings

Bound states around 3110 MeV for $DK_1(1270)$ and 3240 MeV for $DK_1(1400)$.

$ar D K_1$ and $ar D_1 K$ systems are too weakly attractive to form bound states.

The $X_1(2900)$ is unlikely to be a $ar D_1 K$ bound state.

Abstract

Stimulated by recent experimental observation of $X_1(2900)$ just below the $\bar D_1K$ threshold, we extend our previous study of $\bar D_1D$ S-wave bound state by vector meson exchange to $\bar D_1K$ system as well as similar $\bar DK_1$, $D_1K$ and $DK_1$ 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 $DK_1(1270)$ and 3240 MeV for $DK_1(1400)$. $D_1 K$ is also attractive but weaker, hardly enough to form bound states. While $\bar DK_1$ 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.