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The fermion and meson sectors of the quark-level SU(2) linear sigma model are dynamically generated from a meson-quark Lagrangian, with the quark (q) and meson (σ, π) fields all treated as elementary, having neither bare masses nor expectation values. In the chiral limit, the masses are predicted to be mq = fπg, mπ = 0, mσ = 2mq, and we also find that the quark-meson coupling is g = 2π/ √ Nc, the three-meson coupling is g ′ = m 2 σ /2fπ = 2gmq and the four-meson coupling is λ = 2g 2 = g ′ /fπ, where fπ ≃ 90 MeV is the pion decay constant and Nc = 3 is the colour number. By gauging this model one can generate the couplings to the vector mesons ρ and A1, including the quark-vector coupling constant gρ = 2π, gρππ, gA 1 ρπ and the masses mρ ∼ 700 MeV, mA 1 ≃ √ 3mρ; of course the vector and axial currents remain conserved throughout.

We survey various U A (1) problems and attempt to resolve the two puzzles related to the eta mesons that have experimental verification. Specifically, we first explore the Goldstone structure of the η and η ′ mesons in the context of η-η ′ mixing using ideas based on QCD. Then we study the eta decays η → 3π 0 , η ′ → 3π 0 and η ′ → ηππ. Finally we arrive at essentially the same picture in the dynamical scheme based on consistently coupled Schwinger-Dyson and Bethe-Salpeter integral equations. This chirally well-behaved bound-state approach clarifies the distinction between the usual axial-current decay constants and the γγ decay constants in the η-η ′ complex. Allowing for the effects of the SU(3) flavor symmetry breaking in the quark-antiquark annihilation, leads to the improved η-η ′ mass matrix.

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The octet-singlet mixing angle θ P in the pseudoscalar meson nonet is deduced from the rich set of accurate data on J/ψ decays into a vector and a pseudoscalar meson. Corrections due to non-ideal ω-φ mixing have been included for the first time and turn out to be crucial to find θ P = −16.9 • ±1.7 • , which is appreciably less negative than previous results coming from similar analyses.The value of the η-η′ mixing angle θ P in the pseudoscalar-meson nonet has been discussed many times in the last thirty years. A well-known contribution to this discussion is the phenomenological analysis performed by Gilman and Kauffman [1] almost a decade ago. The approximate value θ P ≃ −20 • was proposed by these authors through a rather exhaustive discussion of the experimental evidence available at that time. Another, more recent analysis by two of the present authors [2] concluded that a somewhat less negative value, θ P = −14 • ±2 • , seems to be favoured. A significant difference between these two independent analyses concerns the set of rich data on J/ψ decays into a vector and a pseudoscalar meson, J/ψ → V P , which were included in the first analysis [1] but not in the second one [2]. The purpose of the present note is to extract a value for θ P from this relevant set of J/ψ → V P decay data. In this sense, we will follow quite closely the similar analyses in Refs. [3,4,5] except that the apparently negligible effects of non-ideal mixing in the vector-meson nonet will be now taken into account. Ignoring these effects, i.e., assuming that the physical ω and φ coincide precisely with the ideally mixed states ω 0 ≡ (uū + dd)/ √ 2 and φ 0 ≡ ss, lead to 5]). Introducing the small, but certainly non-vanishing, departure of ω and φ from the above ideally mixed states ω 0 and φ 0 , and using essentially the same set of J/ψ → V P data as in Refs. [3, 4, 5], we will obtain θ P = −16.9 • ± 1.7 • .Experimental information concerning strong and electromagnetic J/ψ decays into a vector and a pseudoscalar meson, J/ψ → V P with V = ρ, ω, φ or K * and P = π, η, η′ or K, comes mainly from the MARK III [3] and DM2 [4] detectors. We have collected all this information on the J/ψ → V P branching ratios (BR), as averaged by the PDG compilation [6], in the first column of Table 1. The highly accurate value for BR(ρπ) comes from Ref. [3] and other papers listed in [6]; the upper limit for BR(φπ) has been established by [3]; and the nine remaining BR's, with relative experimental errors ranging from about 8 to 17 %, come from Refs. [3] and [4]. Altogether they constitute an excellent and exhaustive set of data which remains unchanged in the recent editions of the PDG compilations. Part of these data were already used in the analyses of Refs. [3,4,5]; our purpose here consists also in improving these analyses by using the complete set.Attempts to understand these decays in a phenomenological context started immediately after the appearence of the data and all these attempts were based on the same essential model with slight variations [3,4,5,7]....