Phys. Rev. D 88, 093002 (2013) - Pion form factor and reactions ${e}^{\mathbf{+}}{e}^{\mathbf{\ensuremath{-}}}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{0}$ and ${e}^{\mathbf{+}}{e}^{\mathbf{\ensuremath{-}}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\mathbf{+}}{\ensuremath{\pi}}^{\mathbf{\ensuremath{-}}}{\ensuremath{\pi}}^{\mathbf{+}}{\ensuremath{\pi}}^{\mathbf{\ensuremath{-}}}$ at energies up to 2--3 GeV in the many-channel approach

Pion form factor and reactions $e^{+} e^{-} \to ω π^{0}$ and $e^{+} e^{-} \to π^{+} π^{-} π^{+} π^{-}$ at energies up to 2–3 GeV in the many-channel approach

N. N. Achasov and A. A. Kozhevnikov

Phys. Rev. D 88, 093002 – Published 7 November 2013

Abstract

Using the field-theory-inspired expression for the pion electromagnetic form factor $F_{π}$ , 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 $e^{+} e^{-} \to π^{+} π^{-}$ is obtained at energies up to 3 GeV. The inclusion of the VP and AP loops demands the treatment of the reactions $e^{+} e^{-} \to ω π^{0}$ and $e^{+} e^{-} \to π^{+} π^{-} π^{+} π^{-}$ . This task is performed with the SND data on $ω π^{0}$ production and the BABAR data on $π^{+} π^{-} π^{+} π^{-}$ production, both in $e^{+} e^{-}$ annihilation, by taking into account $ρ (770)$ and the heavier $ρ (1450)$ , $ρ (1700)$ , and $ρ (2100)$ resonances. The problems arising from including the VP and AP loops are pointed out and discussed.