Quarkonium h states as arbiters of exoticity

Abstract

The mass splitting between the quarkonium spin-singlet state h (J P C = 1 +− ) and the spin average of the quarkonium spin-triplet states χ (J P C = 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 QQ 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 χc0(2P ) candidate has been observed at Belle.

χb(3P) multiplet revisited: Hyperfine mass splitting and radiative transitions

“…where C F is the color factor of bottomonium, n l being the number of light fermion species appearing in loop corrections, and N c is the number of colors in QCD. The computed δM n,L=1 values using NRQCD for the bottomonium (with m b = 4.5 GeV and α s (m b ) = 0.2) are; δM 1P = 3.77 keV, δM 2P = 1.12 keV, and δM 3P = 0.47 keV [22]. The remarkable smallness…”

“…Recently, Lebed and Swanson also pointed out the remarkable importance of the P-wave heavy quarkonia [22]. For 1P and 2P charmonia, the ultrafine splitting is found to be astonishingly small.…”

“…The non-perturbative effects can make an additional contribution to this term, so that it is no longer a pure delta function. This give rise to introduce the smearing of the delta function in the quark models [17,22]. However, one could use different non-perturbative forms for the spin-spin operator that contributes to the ultrafine splitting.…”

Large-${N_{\mathrm{c}}^{}}$ QCD and tetraquarks

“…It has been applied to tetraquark phenomenology by Maiani, Piccinini, Polosa and Riquer [27,28]. Other approaches with the diquark mechanism can be found in [29][30][31][32].…”

P -wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy

“…This suppression is indeed seen experimentally (actually, experimentally, the suppression is stronger than expected. For a discussion on this issue see [52]).…”