Doubly heavy tetraquarks in QCD sum rules

Abstract

In the framework of QCD sum rules, we investigate the $q{q}^{\ensuremath{'}}\overline{Q}\overline{Q}$ tetraquark structure with quantum number ${J}^{P}={1}^{+}$, which is embedded in two types of configurations, the $[{8}_{c}{]}_{q\overline{Q}}\ensuremath{\bigotimes}[{8}_{c}{]}_{{q}^{\ensuremath{'}}\overline{Q}}$ and $[{1}_{c}{]}_{q\overline{Q}}\ensuremath{\bigotimes}[{1}_{c}{]}_{{q}^{\ensuremath{'}}\overline{Q}}$ with $Q=b$, $c$, $q=u$, and ${q}^{\ensuremath{'}}=d$, $s$. Our finding confirms the lattice QCD result that the bottom tetraquark states could exist and their masses are evaluated. In the calculation, the nonperturbative condensate contributions up to dimension eight in operator product expansion are considered, and those terms linear to the strange quark mass ${m}_{s}$ are kept. It is found that for octet-octet configuration the masses of potential tetraquark states are about 11.28 GeV for the $ud\overline{b}\overline{b}$ system, and 11.36 and 11.39 GeV for the $us\overline{b}\overline{b}$ system, which are above the corresponding two-meson thresholds. For molecular configuration, the corresponding masses are found below the thresholds, that is, 10.36 GeV and 10.51 GeV, respectively. The possible tetraquark decay channels are analyzed and the strong decay rates are evaluated. The mass dependence on the radiative correction and the condensates is estimated. Moreover, the doubly charmed tetraquark states are also considered.