Hadronic tensor molecule $B_c^{\ast +}B_c^{\ast -}$

Mass and full decay width of the hadronic tensor molecule $\mathcal{M}_{ \mathrm{T}}=B_c^{\ast +}B_c^{\ast -}$ are examined in the framework of QCD sum rule method. To find the mass $m$ and current coupling $\Lambda$ of this state, we use the two-point sum rules. The result $(12.87 \pm 0.08)~\mathrm{ GeV}$ for $m$ indicates that $\mathcal{M}_{\mathrm{T}}$ can easily decay to pairs of $J/\psi \Upsilon$, $\eta_{b}\eta _{c}$, $B_{c}^{+}B_{c}^{-}$, and $B_{c}^{\ast +}B_{c}^{\ast -}$ mesons. Kinematically permitted ways for $\mathcal{M}_{\mathrm{T}}$ to transform to conventional mesons include also processes $\mathcal{M}_{\mathrm{T}} \to D^{(\ast)+}D^{(\ast )-}$, $D^{(\ast )0}\overline{D}^{(\ast )0}$, and $D_{s}^{(\ast)+}D_{s}^{(\ast)-}$ triggered by annihilation of $b\overline{b}$ quarks in the molecule. The decays to meson pairs $B^{(\ast)+}B^{(\ast )-}$, $B^{(\ast )0}\overline{B}^{(\ast )0}$ , and $B_{s}^{(\ast)0}\overline{B}_{s}^{(\ast )0}$ generated by $c\overline{c } \to$ light quarks are also among possible channels of the hadronic molecule $\mathcal{M}_{\mathrm{T}}$. Technical tools of the three-point sum rule approach are applied to compute partial widths of these decays. Our results for the mass and width $\Gamma_{\mathcal{M}_{\mathrm{T}}}=(154 \pm 19)~ \mathrm{MeV}$ of the tensor molecule $\mathcal{M}_{\mathrm{T}}$ are important for experimental studies of fully heavy exotic structures.