Quarkonium $h$ States As Arbiters of Exoticity

Abstract

The mass splitting between the quarkonium spin-singlet state $h$ ($J^{PC}=1^{+-}$) and the spin average of the quarkonium spin-triplet states $\chi$ ($J^{PC}=0^{++},1^{++},2^{++}$) is seen to be astonishingly small, not only in the charmonium and bottomonium cases where the relevant masses have been measured, but in positronium as well. We find, both in nonrelativistic quark models and in NRQCD, that this hyperfine splitting is so small that it can be used as a test of the pure $Q\bar{Q}$ content of the states. We discuss the $2P$ states of charmonium in the vicinity of $3.9$ GeV, where the putative exotics $X(3872)$ and $X(3915)$ have been seen and a new ${\chi }_{c0}(2P)$ candidate has been observed at Belle.

arXiv comment6 pages. Typos repaired (with thanks to correspondents), citations added

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Cited by in corpus (13)

• The $XYZ$ states: experimental and theoretical status and perspectives
• Renormalized quark-antiquark Hamiltonian induced by a gluon mass ansatz in heavy-flavor QCD
• Scalar mesons and the fragmented glueball
• P-wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy
• Charmonium spectrum in an unquenched quark model
• ${\chi }_b(3P)$ Multiplet Revisited: Ultrafine Mass Splitting and Radiative Transitions
• Are the XYZ states unconventional states or conventional states with unconventional properties?
• Charmonium: Conventional and $XYZ$ States in a Relativistic Screened Potential Model
• Splittings of low-lying charmonium masses at the physical point
• Can the hyperfine mass splitting formula in heavy quarkonia be applied to the $B_c$ system?
• A fully non-perturbative charm-quark tuning using machine learning
• Heavy-Quark Hybrid Mass Splittings: Hyperfine and "Ultrafine"
• Predictions for Bottomonium from a Relativistic Screened Potential Model