Heavy quark spin partners of the $Y(4260)$ in coupled-channel formalism

The charmoniumlike state $Y(4260)$ is described as predominantly a $D_1 \bar{D}$ molecule in a coupled-channel quark model [Phys. Rev. D \textbf{96}, 114022 (2017)]. The heavy quark spin symmetry (HQSS) thus implies the possible emergence of its heavy quark spin partners with molecular configuration as $D_1 \bar{D}^*$ and $D_2^* \bar{D}^*$ below these charmed mesons' thresholds. We analyze the probabilities of various intermediate charmed meson loops for $J^{PC}=1^{--}$ exotic state $Y(4360)$ and find that the channel $D_1 \bar{D}^*$ couples more strongly around its mass regime, and the coupling behavior remains the same even if the mass of $Y(4360)$ is pushed closer to $D_1 \bar{D}^*$ threshold. This enlightens that the most favorable molecular scenario for the $Y(4360)$ could be $D_1 \bar{D}^*$, and hence it can be interpreted as HQSS partner of the $Y(4260)$. We also find the strong coupling behavior of $D_2^* \bar{D}^*$ channel with the $\psi(4415)$, which makes it a good candidate for a dominant $D_2^* \bar{D}^*$ molecule. We discuss the important decay patterns of these resonances to disentangle their long- and short-distance structures.