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Non-quark model mesons include
- exotic mesons, which have quantum numbers not possible for mesons in the quark model;
- glueballs or gluonium, which have no valence quarks at all;
- tetraquarks, which have two valence quark-antiquark pairs; and
- hybrid mesons, which contain a valence quark-antiquark pair and one or more gluons.
All of these can be classed as mesons, because they are hadrons and carry zero baryon number. Of these, glueballs must be flavor singlets; that is, have zero isospin, strangeness, charm, bottomness, and topness. Like all particle states, they are specified by the quantum numbers which label representations of the Poincaré symmetry, q.e., JPC (where J is the angular momentum, P is the intrinsic parity, and C is the charge conjugation parity) and by the mass. One also specifies the isospin I of the meson.
Typically, every quark model meson comes in SU(3) flavor nonet: an octet and a flavor singlet. A glueball shows up as an extra (supernumerary) particle outside the nonet. In spite of such seemingly simple counting, the assignment of any given state as a glueball, tetraquark, or hybrid remains tentative even today. Even when there is agreement that one of several states is one of these non-quark model mesons, the degree of mixing, and the precise assignment is fraught with uncertainties. There is also the considerable experimental labor of assigning quantum numbers to each state and crosschecking them in other experiments. As a result, all assignments outside the quark model are tentative. The remainder of this article outlines the situation as it stood at the end of 2004.
Lattice predictions 
- 0++ with mass of 1,611±163 MeV/c2 and
- 2++ with mass of 2,232±310 MeV/c2
The 0−+ and exotic glueballs such as 0−− are all expected to lie above 2 GeV/c2. Glueballs are necessarily isoscalar, with isospin I = 0.
The ground state hybrid mesons 0−+, 1−+, 1−−, and 2−+ all lie a little below 2 GeV/c2. The hybrid with exotic quantum numbers 1−+ is at 1.9±0.2 GeV/c2. The best lattice computations to date are made in the quenched approximation, which neglects virtual quarks loops. As a result, these computations miss mixing with meson states.
The 0++ states 
The data show five isoscalar resonances: f0(600), f0(980), f0(1370), f0(1500), and f0(1710). Of these the f0(600) is usually identified with the σ of chiral models. The decays and production of f0(1710) give strong evidence that it is also a meson.
Glueball candidate 
The f0(1370) and f0(1500) cannot both be a quark model meson, because one is supernumerary. The production of the higher mass state in two photon reactions such as 2γ → 2π or 2γ → 2K reactions is highly suppressed. The decays also give some evidence that one of these could be a glueball.
Tetraquark candidate 
The f0(980) has been identified by some authors as a tetraquark meson, along with the I = 1 states a0(980) and κ0(800). Two long-lived (narrow in the jargon of particle spectroscopy) states: the scalar (0++) state D*±
sJ(2317) and the vector (1+) meson D*±
sJ(2460), observed at CLEO and BaBar, have also been tentatively identified as tetraquark states. However, for these, other explanations are possible.
The 2++ states 
Two isoscalar states are definitely identified—f2(1270) and the f′2(1525). No other states have been consistently identified by all experiments. Hence it is difficult to say more about these states.
The 1−+ exotics and other states 
The two isovector exotics π1(1400) and π1(1600) seem to be well established experimentally. They are clearly not glueballs, but could be either a tetraquark or a hybrid. The evidence for such assignments is weak.
The π(1800) (0−+), ρ(1900) (1−−) and the η2(1870) (2−+) are fairly well identified states, which have been tentatively identified as hybrids by some authors. If this identification is correct, then it is a remarkable agreement with lattice computations, which place several hybrids in this range of masses.
See also 
- Quark model, mesons, baryons, quarks, and gluons
- Exotic hadrons and exotic baryons
- Quantum chromodynamics, flavor, and the QCD vacuum
- GlueX, an experiment which will explore the spectrum of glueballs and exotic mesons
- W.-M. Yao et al. (Particle Data Group) (2006). "Review of Particle Physics: Non-qq mesons". Journal of Physics G 33: 1. arXiv:astro-ph/0601168. Bibcode:2006JPhG...33....1Y. doi:10.1088/0954-3899/33/1/001.