Weak decays of stable doubly heavy tetraquark states

In light of the recent discovery of the ${\mathrm{\Xi }}_{cc}^{++}$ by the LHCb Collaboration, we study the stable doubly heavy tetraquarks. These states are compact exotic hadrons which can be approximated as the diquark-antidiquark correlations. In the flavor SU(3) symmetry, they form a SU(3) triplet or antisextet. The spectra of the stable doubly heavy tetraquark states are predicted by the Sakharov-Zeldovich formula. We find that the $T_{bb\overline{u}\overline{d}}^{-}(\mathbf{3})$ is about 73 MeV below the $B{B}^{*}$ threshold at SET I. We then study the semileptonic and nonleptonic weak decays of the stable doubly heavy tetraquark states. The doubly heavy tetraquark decay amplitudes are parametrized in terms of flavor SU(3)-irreducible parts. Ratios between decay widths of different channels are also derived. At the end, we collect the Cabibbo allowed two-body and three-body decay channels, which are most promising to search for the stable doubly heavy tetraquark states at the LHCb and Belle II experiments.

Figure 1

Flavor SU(3) weight diagrams for the triplet and antitriplet hadrons. Panel (a) corresponds with doubly heavy tetraquark triplet; panel (b) corresponds with the charmed bottom baryons triplet; panel (c) and (e) stand for the anticharm mesons triplet and the charmed mesons antitriplet; panel (d) and (f) represent the anticharm antibaryons triplet and the charmed baryons antitriplet respectively.

Figure 2

Flavor SU(3) weight diagrams for the sextet, antisextet, antidecuplet, antioctet, and octet hadrons. Panel (a) corresponds with the charmed baryons sextet; panel (b) corresponds with the anticharm baryons antisextet; panel (c) and (d) represent the light antibaryons antidecuplet and the light antibaryon antioctet respectively; panel (e) stands for the light mesons octet.

Figure 3

Feynman diagrams for semileptonic decays of doubly bottomed tetraquark. Panels (a),(b) correspond to the decays into a pair of mesons. In panel (c), there is only one meson in the final states. Panels (d),(e) denote the decays into baryonic states. In panels (b),(c),(e), the two $b\overline{u}$ quarks in the initial state can annihilate, but such contributions are usually power suppressed.

Figure 4

Feynman diagrams for semileptonic decays of doubly charmed tetraquarks. Panels (a),(b) correspond to the decays into a pair of mesons, and in panel (c), there is only one meson in the final state. In panels (b),(c), the two $c\overline{d}/\overline{s}$ quarks in the initial state can annihilate, and usually such contributions are power suppressed.

Figure 5

Feynman diagrams for nonleptonic decays of doubly heavy tetraquarks. Panels (a),(b) correspond to the two mesons W-exchange process; panels (c),(d) correspond to the baryon and antibaryon processes; and panels (e),(f),(g),(h),(i),(j) correspond to three mesons processes [Panels (e),(f) match with $J/\psi$ plus the $B$ meson and the light meson; panels (g),(h) match with the $B_{\overline{c}}$ plus $D$ and light meson; and panels (i),(j) match with the $B$ plus $\overline{D}$ and $D$ meson].

Figure 6

Feynman diagrams for nonleptonic decays of doubly heavy tetraquarks. Panels (a),(b) correspond with the two mesons W-exchange process; panels (c),(d) correspond with the baryon and antibaryon process; and panels (e),(f),(g),(h),(i),(j) correspond with the $B$ plus $D$ and light meson processes.

Figure 7

Feynman diagrams for nonleptonic decays of doubly bottomed tetraquarks. Panels (a),(b) correspond with $B$ plus $\overline{D}$ or $B_c$ plus light meson W-exchange processes, respectively. Panels (c),(d) correspond with the baryon and antibaryon process and panels (e),(f),(i),(j) match with $B$ plus $\overline{D}$ and light mesons. Panels (g),(h) match with $B_c$ plus two light mesons.

Figure 8

Feynman diagrams for nonleptonic decays of doubly heavy tetraquark $T_{bc\overline{q}\overline{q}}$. Panel (a) corresponds with two mesons by the new W-exchange process. Panels (b),(c),(d) correspond with three mesons by the new W-exchange process.

Figure 9

Feynman diagrams for nonleptonic decays of doubly charmed tetraquark $T_{cc\overline{q}\overline{q}}$. Panels (a),(b) correspond with a charmed meson and light meson final states by the W-exchange process. Panels (c),(d),(e),(f),(g),(h) correspond with a charmed meson and two light meson final state processes.