Three-Body $J^P=0^{+},1^{+},2^{+}$ $B^{\ast }{B}^{\ast }\bar{K}$ 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 $B^{\ast }\bar{K}$ binds to form the $B_{s1}^{\ast }$ heavy meson and notice that the mass ratio of the $B^{\ast }$ to $\bar{K}$ is $M/m=10.8$, concrete calculations indicate that there should be a three body $B^{\ast }{B}^{\ast }\bar{K}$ bound state between $30-40\mathrm{MeV}$ below the $B_{s1}^{\ast }{B}^{\ast }$ 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 $5-15\mathrm{MeV}$ below the ${\Xi }_{bb}{\Omega }_{bb\frac{1}{2}}^{\ast }$ threshold (where ${\Omega }_{bb\frac{1}{2}}^{\ast }$ 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.

Comments: 8 pages, corresponds to published version