Three-body universality in the B meson sector

TL;DR

This paper investigates the potential for three-body bound states involving B and B* mesons near the Z_b(10610) and Z'_b(10650) resonances, concluding that Efimov states are unlikely, and provides phase shift predictions.

Contribution

It demonstrates the absence of Efimov states in the B meson sector and offers phase shift predictions using a non-relativistic effective field theory.

Findings

No universal three-body bound states due to Efimov effect.

Predicted phase shifts for B and B* meson scattering.

Constraints on three-body interactions in heavy meson systems.

Abstract

The charged exotic mesons Z_b(10610) and Z'_b(10650) observed by the Belle collaboration in 2011 are very close to the B* Bbar and B* Bbar* thresholds, respectively. This suggests their interpretation as shallow hadronic molecules of B and B* mesons. Using the masses of the Z_b(10610) and Z'_b(10650) as input, we rule out the possibility for universal bound states of three B and B* mesons arising from the Efimov effect based on their spin-isospin structure. As a consequence, we can predict the phase shifts for the scattering of B and B* mesons off the exotic mesons Z_b(10610) and Z'_b(10650) to leading order in a non-relativistic effective field theory with contact interactions based on two-body information alone.