Heavy-quark spin symmetry partners of the $X(3872)$ revisited

Abstract

We revisit the consequences of the heavy-quark spin symmetry for the possible spin partners of the $X(3872)$. We confirm that, if the $X(3872)$ were a $D{\bar{D}}^{\ast }$ molecular state with the quantum numbers $J^{PC}=1^{++}$, then in the strict heavy-quark limit there should exist three more hadronic molecules degenerate with the $X(3872)$, with the quantum numbers $0^{++}$, $1^{+-}$, and $2^{++}$ in line with previous results reported in the literature. We demonstrate that this result is robust with respect to the inclusion of the one-pion exchange interaction between the $D$ mesons. However, this is true only if all relevant partial waves as well as particle channels which are coupled via the pion-exchange potential are taken into account. Otherwise, the heavy-quark symmetry is destroyed even in the heavy-quark limit. Finally, we solve the coupled-channel problem in the $2^{++}$ channel with nonperturbative pions beyond the heavy-quark limit and, contrary to the findings of previous calculations with perturbative pions, find for the spin-2 partner of the $X(3872)$ a significant shift of the mass as well as a width of the order of 50 MeV.

17 pages, 3 figures, 1 table, version published in Phys.Lett.B

References in corpus (8)

• Big-Bang Nucleosynthesis
• Heavy quarkonium: progress, puzzles, and opportunities
• Pion Interactions in the X(3872)
• The Heavy Quark Spin Symmetry Partners of the X(3872)
• Reconciling the X(3872) with the near-threshold enhancement in the D^0\bar{D}^{*0} final state
• Employing spin symmetry to disentangle different models for the XYZ states
• Exotic Heavy Quarkonium Spectroscopy: A Mini-review
• Remarks on the study of the X(3872) from Effective Field Theory with Pion-Exchange Interaction

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