Tensor states $\mathrm{{\rm Y}}{B}_c^{\ast -}$ and $J\mathrm{/}\psi B_c^{\ast +}$

Tensor states ${\mathcal{M}}_{\mathrm{T}}^{\mathrm{b}}=\mathrm{{\rm Y}}{B}_c^{\ast -}$ and ${\mathcal{M}}_{\mathrm{T}}^{\mathrm{c}}=J\mathrm{/}\psi B_c^{\ast +}$ are explored using techniques of QCD sum rule method. These hadronic molecules, composed of only heavy quarks, have asymmetric quark contents $bb\bar{b}\bar{c}$ and $cc\bar{c}\bar{b}$, respectively. The masses $m=(15864\pm 85)\mathrm{M}\mathrm{e}\mathrm{V}$ and $\tilde{m}=(9870\pm 82)\mathrm{M}\mathrm{e}\mathrm{V}$ prove that these structures are unstable against dissociations to constituent mesons. Full widths of molecules ${\mathcal{M}}_{\mathrm{T}}^{\mathrm{b}}$ and ${\mathcal{M}}_{\mathrm{T}}^{\mathrm{c}}$ are calculated by considering their dominant and subleading decay channels. The subleading channels are processes generated by annihilations of $\bar{b}b$ and $\bar{c}c$ quarks. For the molecule ${\mathcal{M}}_{\mathrm{T}}^{\mathrm{b}}$ dominant decays are ${\mathcal{M}}_{\mathrm{T}}^{\mathrm{b}}\to \mathrm{{\rm Y}}{B}_c^{\ast -}$ and ${\mathcal{M}}_{\mathrm{T}}^{\mathrm{b}}\to {\eta }_b{B}_c^{-}$, whereas subleading channels are transformations to ${\mathcal{M}}_{\mathrm{T}}^{\mathrm{b}}\to B^{(\ast )-}{\bar{D}}^{(\ast )0}$ and ${\bar{B}}_{(s)}^{(\ast )0}{D}_{(s)}^{(\ast )-}$ mesons. In the case of ${\mathcal{M}}_{\mathrm{T}}^{\mathrm{c}}$ we explore decays to $J\mathrm{/}\psi B_c^{\ast +}$, ${\eta }_c{B}_c^{+}$, $B^{(\ast )+}{D}^{(\ast )0}$ and $B_{(s)}^{(\ast )0}{D}_{(s)}^{(\ast )+}$ mesons. Predictions $\mathrm{\Gamma }[{\mathcal{M}}_{\mathrm{T}}^{\mathrm{b}}]=120_{-12}^{+17}\mathrm{M}\mathrm{e}\mathrm{V}$ and $\mathrm{\Gamma }[{\mathcal{M}}_{\mathrm{T}}^{\mathrm{c}}]=(71\pm 9)\mathrm{M}\mathrm{e}\mathrm{V}$ for the widths of these molecules characterize them as relatively broad structures.