Mass spectrum of a meson nonet is linear

Abstract

It is argued that the mass spectrum of a meson nonet is linear, consistent with the standard Gell-Mann-Okubo mass formula and leading to an extra Gell-Mann-Okubo mass relation for the masses of the isoscalar states. This relation is shown to hold with an accuracy of up to ∼3% for all well-established nonets. It also suggests a new qq assignment for the scalar meson nonet.

Scalar glueball mass in Regge phenomenology

“…Again, as in a previous paper [21] where we discuss the linear mass spectrum of an individual hadronic multiplet first established in [22] and then applied to the problem of the correct qq assignments for problematic meson nonets [15], and the cubic spectrum of a strongly interacting gas as a model for hot hadronic matter, we have again demonstrated that a mass spectrum represents a powerful tools for hadron spectroscopy. We have shown that linear trajectories for mesons and glueballs, and the cubic mass spectrum associated with them, determine a relation between the masses of the lightest states lying on these trajectories, the ρ meson and the scalar glueball, respectively, which implies that the mass of the latter is in the vicinity of 1600 MeV.…”

Towards resolution of the scalar meson nonet enigma: Gell-Mann-Okubo revisited

“…The qq assignment obtained by one of the authors by the application of the linear mass spectrum discussed in ref. [22] to a composite system of the two, pseudoscalar and scalar nonets, is [23] a 0 (1320), K * 0 (1430), f 0 (1525), f 0 (980),…”

On D-wave meson spectroscopy and the (1410)- (1680) problem

“…(where B is related to the quark condensate, and C is a constant within a given meson nonet) motivated by the linear mass spectrum of a nonet and the collinearity of Regge trajectories of the corresponding I = 1 and I = 1/2 states, as discussed in ref. [19]. Note from (29) that both the K 2A and K 2B lie in the mass intervals provided by current experimental data on the K ′ 2 and K 2 states, respectively.…”

“…Since the ρ and ρ 3 states are mass near-degenerate, ρ ≈ ρ 3 (their masses are 1700±20 MeV and 1691 ± 5 MeV, respectively [4]), it then follows from (24) that either ρ 2 ≈ ρ ≈ ρ 3 , or K * ≈ K * 3 . The first possibility leads, through the relations (19), (20) applied to the I = 1 mesons, to b ≈ c ≈ 0, which would in turn, from the same relations for the I = 1/2 mesons, imply K * ≈ K 2A ≈ K * 3 . Although this case may not be excluded on the basis of current experimental data on the meson masses, we consider simultaneous disappearance of both the spin-orbit and tensor terms as dubious.…”