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.