Coupled-channel analysis of the possible $D^{(\ast )}{D}^{(\ast )}$, ${\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}$ and $D^{(\ast )}{\bar{B}}^{(\ast )}$ molecular states

We perform a coupled-channel study of the possible deuteron-like molecules with two heavy flavor quarks, including the systems of $D^{(\ast )}{D}^{(\ast )}$ with double charm, ${\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}$ with double bottom and $D^{(\ast )}{\bar{B}}^{(\ast )}$ with both charm and bottom, within the one-boson-exchange model. In our study, we take into account the S-D mixing which plays an important role in the formation of the loosely bound deuteron, and particularly, the coupled-channel effect in the flavor space. According to our calculation, the states $D^{(\ast )}{D}^{(\ast )}[I(J^P)=0(1^{+})]$ and $(D^{(\ast )}{D}^{(\ast )}{)}_s[J^P=1^{+}]$ with double charm, the states ${\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}[I(J^P)=0(1^{+}),0(2^{+}),1(0^{+}),1(1^{+}),1(2^{+})]$, $({\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}{)}_s[J^P=0^{+},1^{+},2^{+}]$ and $({\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}{)}_{ss}[J^P=0^{+},1^{+},2^{+}]$ with double bottom, and the states $D^{(\ast )}{\bar{B}}^{(\ast )}[I(J^P)=0(0^{+}),0(1^{+})]$ and $(D^{(\ast )}{\bar{B}}^{(\ast )}{)}_s[J^P=0^{+},1^{+}]$ with both charm and bottom are good molecule candidates. However, the existence of the states $D^{(\ast )}{D}^{(\ast )}[I(J^P)=0(2^{+})]$ with double charm and $D^{(\ast )}{\bar{B}}^{(\ast )}[I(J^P)=1(1^{+})]$ with both charm and bottom is ruled out.