Three-Body $J^P = 0^+,1^+,2^+$ $B^* B^* \bar{K}$ Bound States

Abstract: 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 non-interacting 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 $B^* \bar{K}$ binds to form the $B^*_{s1}$ heavy meson and notice that the mass ratio of the $B^*$ to $\bar{K}$ is $M /m = 10.8$, concrete calculations indicate that there should be a three body $B^* B^* \bar{K}$ bound state between $30-40\,{\rm MeV}$ below the $B^*_{s1} B^*$ threshold. For the $\Xi_{bb} \Xi_{bb} \bar{K}$ 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 $5-15\,{\rm MeV}$ below the $\Xi_{bb} \Omega^*_{bb\frac{1}{2}}$ threshold (where $\Omega^*_{bb\frac{1}{2}}$ denotes the $\Xi_{bb} \bar{K}$ 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.