Heavy four-quark mesons $bc\overline{b}\overline{c}$: Scalar particle

Parameters of the heavy four-quark scalar meson $T_{\mathrm{bc\overline{b} \overline{c}}}$ with content $bc \overline{b}\overline{c}$ are calculated by means of the sum rule method. This structure is considered as a diquark-antidiquark state built of scalar diquark and antidiquark components. The mass and current coupling of $T_{\mathrm{bc\overline{b} \overline{c}}}$ are evaluated in the context of the two-point sum rule approach. The full width of this tetraquark is estimated by taking into account two types of its possible strong decay channels. First class includes dissociation of $T_{\mathrm{bc\overline{b}\overline{c}}}$ to mesons $\eta_c\eta_{b}$, $B_{c}^{+}B_{c}^{-}$, $B_{c}^{\ast +}B_{c}^{\ast -}$ and $B_{c}^{+}(1^3P_{0})B_{c}^{\ast-}$. Another type of processes are generated by annihilations $\overline{b}b \to \overline{q}q$ of constituent $b$-quarks which produces the final-state charmed meson pairs $D^{+}D^{-}$, $D^{0} \overline{D}^{0}$, $D^{*+}D^{*-}$, and $D^{*0}\overline{D}^{*0}$. Partial width all of these decays are found using the three-point sum rule method which is required to calculate strong couplings at corresponding meson-meson-tetraquark vertices. Predictions obtained for the mass $m=(12697 \pm 90)~\mathrm{MeV}$ and width $\Gamma[T_{\mathrm{bc\overline{b}\overline{c} }}]=(142.4 \pm 16.9)~ \mathrm{MeV}$ of this state are compared with alternative results, and are useful for further experimental investigations of fully heavy resonances.