current status of e⁺e⁻→π⁺π⁻η study. experiment and theory

In this note I review the current status of electron-positron annihilation into the π⁺π⁻η final state from both experimental and theoretical sides. The theoretical studies of the reaction are discussed in framework of three theoretical approaches: the Vector Meson Dominance Model, the Resonance Chiral Theory with vector and axial-vector resonances and within the extended nonlocal version of the Nambu-Jona-Lasinio model. In the case of the Vector Meson Dominance model the three vector ρ-mesons are included, i.e. the main ρ(770) state and the excited ρ(1400) and ρ(1700) states. For the theoretical approach based on the Resonance Chiral Theory lagrangian the theoretical prediction includes either the lightest ρ(770) state only or the superposition of the main state ρ(770) with the ρ(1400), ρ(1700) states. Finally, the theoretical calculations in the framework of the Nambu-Jona-Lasinio model include both the lightest ρ(770) state and its first excited state ρ(1400) . To sum up the theoretical predictions of these three approaches are compared with the recent experimental data from Novosibirsk groups (SND and CMD experiments) and from the BaBar Collaboration. In addition, main points of studies on application of the Conservation Vector Current hypothesis to estimate the cross channel decay width, τ→π⁻π⁰ητ , are discussed. The last subject is an investigation of the OZI and G-parity violated decay ϕ→π⁺π⁻η.