Pseudoscalar and vector tetraquarks \(bb{\overline{c}}{\overline{c}}\)

Abstract

The pseudoscalar and vector four-quark states \(bb{\overline{c}}{\overline{c}}\) are studied in the context of the QCD sum rule method. We model \(T_{\text { \ \ PS}} \) and \(T_{\text {V}}\) as structures built of diquarks \( b^{T}C\gamma _{5}b\), \({\overline{c}}C{\overline{c}}^{T}\) and \(b^{T}C\gamma _{5}b\), \({\overline{c}}C\gamma _{\mu }\gamma _{5}{\overline{c}}^{T}\), respectively, with C being the charge conjugation matrix. The spectroscopic parameters of the tetraquarks \(T_{\text {PS}}\) and \(T_{\text {V}}\), i.e., their masses and current couplings are calculated using QCD two-point sum rule method. We evaluate the full widths of \(T_{\text {PS}}\) and \(T_{\text {V}}\) by taking into account their kinematically allowed decay channels. In the case of the pseudoscalar particle they are processes \(T_{\text {PS}} \rightarrow B_{c}^{-}B_{c}^{*-}\), \(B_{c}^{-}B_{c}^{-}(1^{3}P_{0})\) and \(B_{c}^{*-}B_{c}^{-}(1^{1}P_{1})\). The vector state \(T_{\text {V}}\) can dissociate to meson pairs \(2 B_{c}^{-}\), \(2 B_{c}^{*-}\) and \( B_{c}^{-}B_{c}^{-}(1^{1}P_{1})\). Partial widths of these decays are determined by the strong couplings at relevant tetraquark-meson-meson vertices, which evaluated in the context of the three-point sum rule approach. Predictions obtained for the mass and full width of the pseudoscalar \(m =(13.092\pm 0.095)~\text {GeV}\), \(\Gamma _{\text {PS} }=(63.7\pm 13.0)~\text {MeV}\) and vector \({\widetilde{m}} =(13.15\pm 0.10)~ \text {GeV}\), \(\Gamma _{\text {V}}=(53.5\pm 10.3)~\text {MeV}\) tetraquarks can be useful for analyses of different four-quark resonances.