Are Y(4260) and {\rm Z${}_2^{+}$(4250)} ${\mathrm{D}}_1\mathrm{D}$ or ${\mathrm{D}}_0{\mathrm{D}}^{\ast }$ Hadronic Molecules?

In this work, we have investigated whether Y(4260) and ${\mathrm{Z}}_2^{+}(4250)$ could be ${\mathrm{D}}_1\mathrm{D}$ or ${\mathrm{D}}_0{\mathrm{D}}^{\ast }$ molecules in the framework of meson exchange model. The off-diagonal interaction induced by $\pi$ exchange plays a dominant role. The $\sigma$ exchange has been taken into account, which leads to diagonal interaction. The contribution of $\sigma$ exchange is not favorable to the formation of molecular state $\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}{\mathrm{I}}^{\mathrm{G}}({\mathrm{J}}^{\mathrm{P}\mathrm{C}})=0^{-}(1^{--})$, however, it is beneficial to the binding of molecule ${\rm with I^{G}(J^{P})=1^{-}(1^{-})}$. Light vector meson exchange leads to diagonal interaction as well. For ${\mathrm{Z}}_2^{+}(4250)$, the contribution from $\rho$ and $\omega$ exchange almost cancels each other. For the currently allowed values of the effective coupling constants and a reasonable cutoff $\mathrm{\Lambda }$ in the range 1-2 GeV, We find that Y(4260) could be accommodated as a ${\mathrm{D}}_1\mathrm{D}$ and ${\mathrm{D}}_0{\mathrm{D}}^{\ast }$ molecule, whereas the interpretation of ${\rm Z^{+}_2(4250)}$asa${\rm D_1D}$or${\rm D_0D^{*}}$ molecule is disfavored. The bottom analog of Y(4260) and ${\mathrm{Z}}_2^{+}(4250)$ may exist, and the most promising channels to discovery them are ${\pi }^{+}{\pi }^{-}\mathrm{{\rm Y}}$ and ${\pi }^{+}{\chi }_{b1}$ respectively.