Phenomenological Evidence for the Gluon Content of η and η ′

We discuss the effect of η–η mixing and of axial current anomalies on various decay processes. We describe the 2γ decays of η and η, the radiative decays of low-lying vector mesons as well as the decays η → 3π, J/ψ → ηγ and J/ψ → ηγ in one unified framework, in which they are related to the electromagnetic and strong axial current anomalies, respectively. We also discuss briefly the enhancement of η in Ds decays and suggest a possible relation to gluon-mediated processes. The importance of the decays of the glueball candidates f0(1500) and f0(1590) into ηη ′ channels is also stressed. Submitted to Phys. Lett. B. Directeur de recherches du FNRS Aspirant du FNRS 1. In this paper we study the effect of η–η mixing and of the axial current anomaly on various processes. We show that a consistent picture arises for the radiative decays η → 2γ and η → 2γ, for radiative decays of type V → ηγ, η → V γ of the lowest-lying vector mesons V , as well as for η → 3π and J/ψ → η(η)γ. Whereas for all the other decays we follow closely the approach of Ref. [1], our description of the vector meson decays is based on their relation to the QED triangle anomaly. In Sec. 2 we thus first test our approach for the simpler cases of the decays V → π(K)γ. In Sec. 3 we then establish notations for the η–η system and determine the decay constants f0 and f8 as functions of the mixing angle from the 2γ decays of η and η. Section 4 is devoted to the comparison of our expectations for the widths of V → ηγ, η → V γ with experiment, whereas Sec. 5 deals with the decay η → 3π, which probes the light quark content of η. In Sec. 6 we then investigate the gluon content of η and η, which determines the decays J/ψ → ηγ and J/ψ → ηγ. It is in this channel that our approach yields a dependence of the involved matrix elements on the mixing angle that is significantly different from other models. We briefly comment on this in relation to the approach of Veneziano et al., Ref. [2], and close in Sec. 7 with some remarks on the important rôle of anomalies in other gluon-enriched channels like Ds → η(η)X and in glueball searches. 2. The radiative decays of the lowest-lying vector-meson nonet are traditionally described in terms of magnetic moments of quarks, see e.g. [3], or of unknown couplings related by SUF(3) symmetry [4]. In Refs. [5, 6] the width Γ(ρ → πγ) was related via SUF(3) arguments and vector-meson dominance to the radiative width of π. In this paper we relate the radiative decays of light vector mesons to light pseudoscalars, V → Pγ and P → V γ, directly to the anomaly of the AV V triangle diagram, where A stands for an axial-vector and V for a vector current. Our approach both includes SUF(3) breaking effects and fixes the vertex couplings gV Pγ as defined below . Let us start by considering the correlation function i ∫ dx e2 〈π(q1 + q2)| T J μ (x)J ν (0) |0〉 = ǫμνρσq 1q 2 Fπ,I=0(1)(q 1, q 2), (1)