Triple-$X$ and beyond: hadronic systems of three and more $X(3872)$
Résumé
The X(3872) resonance has been conjectured to be a JPC=1++ charm meson-antimeson two-body molecule. Meanwhile, there is no experimental evidence for larger, few-body compounds of multiple charm meson-antimeson pairs which would resemble larger molecules or nuclei. Here, we investigate such multimeson states to the extent of what can be deduced theoretically from essentials of the interaction between uncharged D0 and D*0 mesons. From a molecular X(3872), we predict a 4X (4++) octamer with a binding energy B4X>2.08 MeV, assuming a D*0D¯0 system close to the unitary limit [as suggested by the mass of the X(3872)]. If we consider heavy-quark spin symmetry explicitly, the D*0D¯*0 (2++) system is close to unitarity, too. In this case, we predict a bound 3X (3++) hexamer with B3X>2.29 MeV and a more deeply bound 4X octamer with B4X>11.21 MeV. These results exemplify with hadronic molecules a more general phenomenon of equal-mass two-species Bose systems composed of equal number of either type: the emergence of unbound four- and six-boson clusters in the limit of a short-range two-body interaction which acts only between bosons of different species. Finally, we also study the conditions under which a 2X (2++) tetramer might form.