D*D*(D)over-bar and D*D*(D)over-bar* three-body systems

The hidden charm X(3872) resonance is usually thought to be a D*(0)(D) over bar (0) meson-antimeson molecule with quantum numbers J(PC) = 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*(0)(D) over bar*(0) meson-antimeson pair in the J(PC) = 2(++) channel is the same as in the J(PC) = 1(++) D*(0)(D) over bar (0) case. From this we can infer that the J(P) = 3(-)D*D-0*(0)(D) over bar*(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 J(P) = 2(-) D*D-0*(0)(D) over bar*(0) molecule is analogous to the J(P) = 3(-) D*D-0*(0)(D) over bar*(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*(D) over bar and D*D*(D) over bar* systems. The same applies to the B*B*(B) over bar* system: if the Z(b) (10650) is an isovector B*(B) over bar* molecule then the 0(-) isodoublet and the 1(-), 2(-) isoquartet B*B*(B) over bar* 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.