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.
Highlights
The three boson system in the unitary limit shows a geometric spectrum of shallow bound states, the Efimov effect [1]
The bottom-line is that three-body systems with large mass imbalances are more likely to bind
Hadron to be a bottom baryon and the P hadron to be a kaon or antikaon, the HP interaction is of a Weinberg-Tomozawa type and in a few cases might be strong enough as to bind the HP subsystem [29]. If this is the case, this will likely imply the existence of HHP bound states. At this point the natural question arises of whether the P-wave Efimov effect will be present in these systems if the HP interaction is resonant
Summary
The three boson system in the unitary limit shows a geometric spectrum of shallow bound states, the Efimov effect [1]. The bottom-line is that three-body systems with large mass imbalances are more likely to bind This is interesting in view of the recent renaissance of heavy hadron spectroscopy triggered by the discovery of the Xð3872Þ [9] (which has been theorized to be a shallow twobody bound state [10,11,12]). If this is the case, this will likely imply the existence of HHP bound states At this point the natural question arises of whether the P-wave Efimov effect will be present in these systems if the HP interaction is resonant.
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