Seminar in Hadronic Physics

Four-charged-pion decay of ρ⁰(770) and the a₁-ρ-π Lagrangian

Peter Lichard

Silesian University in Opava & Czech Technical University

The excitation curves of e⁺e^- annihilation into four charged pions in the ρ(770) region are calculated using three existing models with ρ mesons and pions in intermediate states supplemented by Feynman diagrams with the a₁(1260)-π intermediate states. A two-term phenomenological Lagrangian of the a₁-ρ-π interaction is used. The mixing angle is determined by fitting the e⁺ e^- -> π⁺ π^- π⁺ π^- cross section data of the Novosibirsk CMD-2 collaboration and also its combination with the low-energy part of the BaBar collaboration data. It is shown that the inclusion of the a₁ π intermediate states succeeds in obtaining a good agreement with the data. The reliable knowledge of the a₁-ρ-π Lagrangian is important for obtaining trustful rates of the photon and dilepton production from meson gas. The matrix elements used in this work can be utilized, after trivial modifications, for calculating the rates of the photon and dilepton production in the processes where four charged pions participate, e.g., π⁺ π^- π⁺ π^- -> e⁺ e^- or π⁺ π⁺ π^- -> π⁺ γ.