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 $T_{\mathrm{PS}}$ and $T_{\mathrm{V}}$ 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 $T_{\mathrm{PS}}$ and $T_{\mathrm{V}}$, i.e., their masses and current couplings are calculated using QCD two-point sum rule method. We evaluate the full widths of $T_{\mathrm{PS}}$ and $T_{\mathrm{V}}$ by taking into account their kinematically allowed decay channels. In the case of the pseudoscalar particle they are processes $T_{\mathrm{PS}}\to B_c^{-}{B}_c^{\ast -}$, $B_c^{-}{B}_c^{-}(1^3{P}_0)$ and $B_c^{\ast -}{B}_c^{-}(1^1{P}_1)$. The vector state $T_{\mathrm{V}}$ can dissociate to meson pairs $2B_c^{-}$, $2B_c^{\ast -}$ 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 $m=(13.092\pm 0.095)\mathrm{GeV}$, ${\Gamma }_{\mathrm{PS}}=(63.7\pm 13.0)\mathrm{MeV}$ and vector $\tilde{m}=(13.15\pm 0.10)\mathrm{GeV}$, ${\Gamma }_{\mathrm{V}}=(53.5\pm 10.3)\mathrm{MeV}$ tetraquarks can be useful for analyses of different four-quark resonances.

Comments: 14 Pages, 6 Figures and 2 Tables