# Quarkonium $h$ States As Arbiters of Exoticity

## TL;DR

This paper investigates the tiny hyperfine mass splitting in quarkonium $h$ states across different systems, proposing it as a test for their pure quark-antiquark nature and discussing implications for exotic states near 3.9 GeV.

## Contribution

It introduces the use of hyperfine splitting as a diagnostic tool for quarkonium purity and analyzes recent experimental candidates for $2P$ states in charmonium.

## Key findings

- Hyperfine splitting is extremely small across systems.
- Small splitting can test the pure $Q\bar Q$ content.
- Discussion of exotic states near 3.9 GeV.

## 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.