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The excitation curve of e+e- annihilation into four charged pions in therho(770) region is calculated using three existing models with rho mesons andpions in intermediate states supplemented by Feynman diagrams with thea_1(1260)pi intermediate states. A two-term phenomenological Lagrangian of thea_1-rho-pi interaction is used. The mixing angle is determined by fitting thee+e- --> pi+pi-pi+pi- cross section data of the Novosibirsk CMD-2 collaborationand also its combination with the low-energy part of the BaBar collaborationdata. It is shown that the inclusion of the a_1-pi intermediate states succeedsin obtaining a good agreement with the data on both cross section and the rho^0--> pi+pi-pi+pi- decay width. When moving to energies above 1 GeV, therho(1450) and rho(1700) resonances are taken into account to get excellentagreement with the BaBar data over the full energy range up to 4.5 GeV.Comment: 15 pages, 6 figures. Largely extended. The title changed to reflect  new conten

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Electron-positron annihilation into four charged pions and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>a</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>ρ</mml:mi><mml:mi>π</mml:mi></mml:math>Lagrangian

Electron-positron annihilation into four charged pions and thea1ρπLagrangian