$X(4260)$ Revisited: A Coupled Channel Perspective

We calculate the probabilities of various charmed meson molecules for $X(4260)$ under the framework of ${}^3P_0$ model. The results indicate that even though heavy quark spin symmetry forbids $S$ wave coupling of $D_1\bar{D}$ to the ${}^3S_1$ charmonia ($\psi(nS)$), the $D$ wave coupling is allowed and not negligible. Under this symmetry, the $D_1\bar{D}$ can couple to ${}^3D_1$ charmonia ($\psi(nD)$) via both $S$ and $D$ wave, and the overall coupling is around three times larger than that of $\psi(nS)$. The $X(4260)$ cannot be a pure molecule but a mixture of a charmonium and various charmed meson components. Since the $D_1\bar{D}$ couples strongly to $\psi(nD)$, our results suggest that in the $D_1\bar{D}$ molecular picture, the charmonium core of $X(4260)$ is $\psi(nD)$ instead of $\psi(nS)$. As a result, the experimental fact that the $R$ ratio has a dip around 4.26 GeV can be understood in the $D_1\bar{D}$ molecular picture of the $X(4260)$.