D∗D∗ D ̄ and D∗D∗ D ̄ ∗ three-body systems D∗D∗ D ̄ and D∗D∗ D ̄ ∗ THREE-BODY SYSTEMS M. PAVON VALDERRAMA

Abstract

The hidden charm X(3872) resonance is usually thought to be a D∗0D̄0 meson-antimeson molecule with quantum numbers JPC=1++. If this is the case, there is the possibility that there might be three body bound states with two charmed mesons and a charmed antimeson. Here we argue that the theoretical existence of this type of three body molecules is expected from heavy quark spin symmetry. If applied to the two body sector, this symmetry implies that the interaction of the D∗0D̄∗0 meson-antimeson pair in the JPC=2++ channel is the same as in the JPC=1++ D∗0D̄0 case. From this we can infer that the JP=3- D∗0D∗0D̄∗0 molecule will be able to display the Efimov effect if the scattering length of the 2++ channel is close enough to the unitary limit. Heavy quark spin symmetry also indicates that the JP=2- D∗0D∗0D̄0 molecule is analogous to the JP=3- D∗0D∗0D̄∗0 one. That is, it can also have a geometric spectrum. If we consider these triply heavy trimers in the isospin symmetric limit, the Efimov effect disappears and we can in principle predict the fundamental state of the 2- D∗D∗D̄ and 3- D∗D∗D̄∗ systems. The same applies to the B∗B∗B̄∗ system: if the Zb(10650) is an isovector B∗B̄∗ molecule then the 0- isodoublet and the 1-, 2- isoquartet B∗B∗B̄∗ trimers might bind, but do not display Efimov physics. Finally from heavy flavour symmetry it can be argued that scattering in the BD two-body system might be resonant. This would in turn imply the possibility of Efimov physics in the BBD three body system.