ar X iv : h ep - p h / 06 02 19 0 v 1 2 1 Fe b 20 06 A short note on qq̄g hybrid assignment for X ( 1812 ) → ωφ

BES Collaboration has recently observed an enhancement near the ωφ threshold in the double OZI suppressed decay J/ψ → γωφ. This ωφ enhancement is probably due to a new J = 0 X(1812) state. We discuss a possible assignment that the X(1812) is a 1/ √ 2(uū + dd̄)g (or ss̄g) hybrid meson. We suggest further measurements to test these assignments. Based on a sample of 5.8 × 10 J/ψ events, very recently the BES Collaboration has observed an enhancement near threshold in the ωφ invariant mass spectrum from the double OZI suppressed decay of J/ψ → γωφ with a statistical significance of more than 10 σ. As a hadronic resonance state X, this enhancement has the following mass, width, and branching ratio product[1]: M = 1812 −26 ± 18 MeV, Γ = 105± 20± 28 MeV, (1) B(J/ψ → γX)×B(X → ωφ) = (2.61± 0.27± 0.65) 10. (2) Moreover, the spin-parity J = 0 is favored for X(1812) by a partial wave analysis. J/ψ radiative decays into light hadrons proceed through J/ψ → γgg and are viewed as the glue-rich channels. The striking feature of the X(1812) that it decays substantially to an ω, which is a (1/ √ 2)(uū+ dd̄) meson, and a φ, which is a ss̄ meson, may imply that the X(1812) is unlikely to be an ordinary qq̄ meson, because the qq̄ → qq̄ + qq̄ decays (q and q are of different flavors) should be suppressed, compared with the OZI allowed qq̄ → qq̄ + qq̄ decays. Therefore, the X(1812) is likely to be a new type of hadrons other than the conventional qq̄ mesons. In the following we will discuss a possible assignment for the X(1812). That is, the X(1812) is a qq̄g hybrid state. The expected existence of hybrid states is an essential feature of quantum chromodynamics. A hybrid state qq̄g is made of (qq̄)8, a quark and an antiquark in color-octet, combined with an excited gluon g. Hybrid states have been extensively studied in various approaches such as the constituent gluon model[2], the flux tube model[3], the bag model[4, 5], the QCD sum rules[6], and the lattice QCD[7, 8]. The experimental status for hybrid states can be found in a minireview for ”Non-qq̄ candidates” written by the Particle Data Group[9]. As a more fundamental theoretical approach for hybrid studies, lattice QCD has made interesting progress and shows that for an exotic spin-parity J = 1 hybrid, which does not mix with ordinary qq̄ mesons