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 \(T_{\textrm{b}}\rightarrow \eta _{b}B_{c}^{-}\). The processes \(T_{\textrm{c}}\rightarrow \eta _{c}B_{c}^{+}\) and \(J/\psi B_{c}^{*+}\) 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 \( m=(15698 \pm 95)~\textrm{MeV}\) and width \(\Gamma [T_b]=(36.0 \pm 10.4)~ \textrm{MeV}\) of the tetraquark \(T_{b}\) as well as the parameters \( \widetilde{m}=(9680 \pm 102)~\textrm{MeV}\) and \(\Gamma [T_c]=(54.7 \pm 12.6)~ \textrm{MeV}\) in the case of \(T_{c}\) provide useful information to search for and interpret new exotic states.