Properties of the tensor state $bc\overline{b}\overline{c}$

Abstract

Spectroscopic parameters and decays of the exotic tensor meson $T$ with content $bc\overline{b}\overline{c}$ are explored in the context of the diquark-antidiquark model. We treat it as a state built of axial-vector diquark $b^{T}C{\hat{I}}_{\hat{I}¼}^{3}c$ and antidiquark $\overline{b}{\hat{I}}_{\hat{I}½}^{3}C{\overline{c}}^T$, where $C$ is the charge conjugation matrix. The mass $m$ and current coupling $\hat{I}›$ of this tetraquark are extracted from two-point sum rules. Our result for $m=(12.70\pm 0.09)\mathrm{GeV}$ proves that $T$ is unstable against strong dissociations to two-meson final states. Its dominant decay channels are processes $T\to J/\ddot{I}ˆ\hat{I}\yen$, $\hat{I}{\cdot }_b\hat{I}{\cdot }_c$, and $B_c^{(\ast )+}{B}_c^{(\ast )-}$. Kinematically allowed transformations of $T$ include also decays $T\to D^{(\ast )+}{D}^{(\ast )-}$ and $D^{(\ast )0}{\overline{D}}^{(\ast )0}$, which are generated by $b\overline{b}$ annihilation inside of $T$. The full width of $T$ is estimated by considering all of these channels. Their partial widths are calculated by invoking methods of three-point sum rule approach which are required to evaluate strong couplings at corresponding tetraquark-meson-meson vertices. Our predictions for the mass and width $\hat{I}{“}_T=(117.4\pm 15.9)\mathrm{MeV}$ of the tensor state $T$ provide useful information for experimental studies of fully heavy four-quark exotic structures.

14 Pages and 5 Figures