Pion form factor and reactionse+e−→ωπ0ande+e−→π+π−π+π−at energies up to 2–3 GeV in the many-channel approach

Abstract

Using the field-theory-inspired expression for the pion electromagnetic form factor ${F}_{\ensuremath{\pi}}$, a good description of the data in the range $\ensuremath{-}10<s<1\text{ }\text{ }{\mathrm{GeV}}^{2}$ 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 ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ is obtained at energies up to 3 GeV. The inclusion of the VP and AP loops demands the treatment of the reactions ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\pi}}^{0}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. This task is performed with the SND data on $\ensuremath{\omega}{\ensuremath{\pi}}^{0}$ production and the BABAR data on ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ production, both in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation, by taking into account $\ensuremath{\rho}(770)$ and the heavier $\ensuremath{\rho}(1450)$, $\ensuremath{\rho}(1700)$, and $\ensuremath{\rho}(2100)$ resonances. The problems arising from including the VP and AP loops are pointed out and discussed.