Fully heavy asymmetric scalar tetraquarks

The scalar tetraquarks $T_{b}$ and $T_{c}$ with asymmetric contents $bb \overline{b}\overline{c}$ and $cc \overline{c}\overline{b}$ are explored using the QCD sum rule method. These states are modeled as the diquark-antidiquarks composed of the axial-vector components. The masses and current couplings of $T_{b}$ and $T_{c}$ are calculated using the two-point sum rule approach. The predictions obtained for the masses of these four-quark mesons prove that they are unstable against the strong two-meson fall-apart decays to conventional mesons. In the case of the tetraquark $T_{b}$ this is the decay $T_{\mathrm{b}}\to \eta _{b}B_{c}^{-}$. The processes $T_{\mathrm{c}}\rightarrow \eta _{c}B_{c}^{+}$ and $J/\psi B_{c}^{\ast +}$ are kinematically allowed decay modes of the tetraquark $T_{c}$. The widths of corresponding processes are evaluated by employing the QCD three-point sum rule approach which are necessary to estimate strong couplings at the tetraquark-meson-meson vertices of interest. The mass $m=(15698 \pm 95)~\mathrm{MeV}$ and width $\Gamma[T_b]=(36.0 \pm 10.4)~ \mathrm{MeV}$ of the tetraquark $T_{b}$ as well as the parameters $\widetilde{m}=(9680 \pm 102)~\mathrm{MeV}$ and $\Gamma[T_c]=(54.7 \pm 12.6)~ \mathrm{MeV}$ in the case of $T_{c}$ provide useful information to search for and interpret new exotic states.