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.

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

References in corpus (5)

• Spin-dependent potentials from lattice QCD
• Where is the χ_{c0}(2P)?
• Could the $X(3915)$ and the $X(3930)$ Be the Same Tensor State?
• Is the X(3915) the chi_{c0}(2P)?
• $P-$state Positronium for Precision Physics: an Ultrafine Splitting at ${\alpha }^6$

Cited by in corpus (5)

• Scalar mesons and the fragmented glueball
• Charmonium spectrum in an unquenched quark model
• Charmonium: Conventional and $XYZ$ States in a Relativistic Screened Potential Model
• A fully non-perturbative charm-quark tuning using machine learning
• Predictions for Bottomonium from a Relativistic Screened Potential Model