Triple-X and beyond: hadronic systems of three and more X(3872)

Abstract

The $X(3872)$ resonance has been conjectured to be a $J^{PC}=1^{++}$ 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 multi-meson states to the extent of what can be deduced theoretically from essentials of the interaction between uncharged $D^0$ and $D^{\ast 0}$ mesons. From a molecular $X(3872)$, we predict a $4X$ ($4^{++}$) octamer with a binding energy \mbox{$B_{4X}>2.08\mathrm{MeV}$,} assuming a $D^{\ast 0}{\bar{D}}^0$ system close to the unitary limit (as suggested by the mass of the $X(3872)$). If we consider heavy-quark spin symmetry explicitly, the $D^{\ast 0}{\bar{D}}^{\ast 0}$ ($2^{++}$) system is close to unitarity, too. In this case, we predict a bound $3X$ ($3^{++}$) hexamer with $B_{3X}>2.29\mathrm{MeV}$ and a more deeply bound $4X$ octamer with $B_{4X}>11.21\mathrm{MeV}$. These results exemplify with hadronic molecules a more general phenomenon of equal-mass two-species Bose systems comprised 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.

arXiv comment7 pages, 3 figures, corresponds to the published version

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