Electron-positron annihilation into four charged pions and the a1ρπ Lagrangian

The excitation curve of e+e- annihilation into four charged pions in the ρ(770) region is 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 a1ρπ 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 a1π intermediate states succeeds in obtaining a good agreement with the data on both cross section and the ρ0→π+π-π+π- decay width. When moving to energies above 1 GeV, the ρ(1450) and ρ(1700) resonances are taken into account to get excellent agreement with the BABAR data over the full energy range up to 4.5 GeV