Analysis of the $Y(4220)$ and $Y(4390)$ as molecular states with QCD sum rules

In this article, we assign the $Y(4390)$ and $Y(4220)$ to be the vector molecular states $D{\bar{D}}_1(2420)$ and $D^{\ast }{\bar{D}}_0^{\ast }(2400)$, respectively, and study their masses and pole residues with the QCD sum rules in details. The present calculations only favor assigning the $Y(4390)$ to be the $D{\bar{D}}_1(1^{--})$ molecular state.