Heavy scalar molecule $B_{c}^{+} B_{c}^{-}$

Mass and full width of the heavy scalar molecule $\mathcal{M}$ composed of the mesons $B_{c}^{+}$ and $B_{c}^{-}$ are calculated in the QCD sum rule framework. To find its mass and current coupling, we apply the two-point sum rule method. The width of the hadronic molecule $\mathcal{M} =B_{c}^{+}B_{c}^{-}$ is evaluated by taking into account its dissociation to $\eta_c\eta_{b}, J/\psi \Upsilon$, and $B_{c}^{+}B_{c}^{-}$ mesons. Decays into $D$ and $B$ meson pairs with appropriate charges and quantum numbers triggered by $\overline{b}b$ and $\overline{c}c$ annihilations to light quark-antiquarks are also included in the analyses. Because the partial widths of $\mathcal{M}$ molecule's decay channels depend on the strong couplings at $\mathcal{M}$-meson-meson vertices, we estimate them by invoking tools of the three-point sum rule method. Our predictions $m=(12725 \pm 85)~\mathrm{ MeV}$ and $\Gamma[\mathcal{\ M}]=(155 \pm 23)~ \mathrm{MeV}$ for the parameters of the molecule $\mathcal{\ M}$ provide useful information for experimental studies of numerous heavy resonances.