Heavy-Quark spin symmetry breaking in the Born-Oppenheimer approximation

Abstract

Heavy-quark spin symmetry is explicitly broken by the mass splitting between a heavy-light pseudoscalar meson and its vector partner. This fact plays a pivotal role in the physics of states whose mass lies close to the threshold of an open-flavor meson pair, like $X(3872)$. We show that this source of heavy-quark spin symmetry breaking can be systematically included within the diabatic representation of the Born-Oppenheimer approximation. We verify that including all the appropriate coupled channels guarantees conservation of total angular momentum, parity, and charge-conjugation parity. This marks a fundamental step towards a unified, first-principles study of quarkonia and meson molecules with hidden flavor.

arXiv comment28 pages; v2: added new appendix, edited text in sections I and V, corrected several typos in various equations, introduced additional references; v3: version accepted in JHEP, several minor modifications and additions in the text and equations, new references, typos corrected

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• Model-independent predictions for decays of hidden-heavy hadrons into pairs of heavy hadrons
• Model-independent predictions for decays of double-heavy hadrons into pairs of heavy hadrons
• Effect of continuum states on the double-heavy hadron spectra
• Assessing the validity of the Born-Oppenheimer approximation in potential models for doubly heavy hadrons