Pion form factor and reactions e^+e^---> omega pi⁰ and e^+e^---> pi^+ pi^- pi^+ pi^- at energies up to 2-3 GeV in the many-channel approach

Using the field-theory-inspired expression for the pion electromagnetic form factor F_\pi, a good description of the data in the range -10<s<1 GeV^2 is obtained upon taking into account the pseudoscalar-pseudoscalar (PP) loops. When the vector-pseudoscalar (VP) and the axial vector-pseudoscalar (AP) loops are taken into account in addition to the PP ones, a good description of the BABAR data on the reaction e^+e^--->pi^+ pi^- is obtained at energies up to 3 GeV. The inclusion of the VP and AP loops demands the treatment of the reactions e^+e^---> omega pi^0 and e^+e^---> pi^+ pi^- pi^+ pi^-. This task is also made, with the SND data on the omega pi^0 production and the BABAR data on the pi^+ pi^- pi^+ pi^- production, both in e^+e^- annihilation, upon taking into account \rho(770) and the heavier \rho(1450), \rho(1700), and \rho(2100) resonances. The problems with inclusion of the VP and AP loops are pointed out and discussed.