Three-body $J^P=0^{+}$, $1^{+}$, $2^{+}$ $B^{*}{B}^{*}\overline{K}$ bound states

Three-body systems with short-range interactions display universal features that have been extensively explored in atomic physics, but apply to hadron physics as well. Systems composed of two noninteracting identical particles (species H) of mass $M$ and a third particle (species P) of mass $m$ that interacts attractively with the other two have the property that they are more likely to bind for larger values of the mass ratio $M/m$. This is particularly striking if the HHP system is in P-wave (while the interacting pair is in S-wave), in which case one would not normally expect the formation of a three-body state. If we assume that the $B^{*}\overline{K}$ binds to form the $B_{s1}^{*}$ heavy meson and notice that the mass ratio of the $B^{*}$ to $\overline{K}$ is $M/m=10.8$, concrete calculations indicate that there should be a three-body $B^{*}{B}^{*}\overline{K}$ bound state between 30–40 MeV below the $B_{s1}^{*}{B}^{*}$ threshold. For the ${\mathrm{\Xi }}_{bb}{\mathrm{\Xi }}_{bb}\overline{K}$ system the mass imbalance is about $M/m=20.5$ and two bound states are expected to appear, a fundamental and an excited one located at 50–90 and 5–15 MeV below the ${\mathrm{\Xi }}_{bb}{\mathrm{\Omega }}_{bb\frac{1}{2}}^{*}$ threshold (where ${\mathrm{\Omega }}_{bb\frac{1}{2}}^{*}$ denotes the ${\mathrm{\Xi }}_{bb}\overline{K}$ bound state). We indicate the possibility of analogous P-wave three-body bound states composed of two heavy baryons and a kaon or antikaon and investigate the conditions under which the Efimov effect could appear in these systems.