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We consider the process of annihilation of e^+ e^- to three pion final state for the case of moderately high energies. The final state emission of virtual and real photon is considered explicitly. The calculations are performed in frames of QED with point-like mesons and pion part of chiral perturbation theory. Some numerical estimates are given

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

Process<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:mn>3</mml:mn><mml:mi>π</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>γ</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>with final state radiative corrections

Processe+e−→3π(γ)with final state radiative corrections