Hidden local symmetry and the reaction e⁺e^- → $\pi^{+}_{}$ $\pi^{-}_{}$ $\pi^{+}_{}$ $\pi^{-}_{}$ at energies $\sqrt{{s}}$ ⩽ 1 GeV

Abstract

Based on the generalized hidden local symmetry as the chiral model of pseudoscalar, vector, and axial vector mesons, the excitation curve of the reaction e ⁺ e ^- → $\pi^{+}_{}$ $\pi^{-}_{}$ $\pi^{+}_{}$ $\pi^{-}_{}$ is calculated for energies in the interval 0.65 ⩽ $\sqrt{{s}}$ ⩽ 1 GeV. The theoretical predictions are compared to available data of CMD-2 and BaBaR. It is shown that the inclusion of heavy isovector resonances ρ(1450) and ρ(1700) is necessary for reconciling calculations with the data. It is found that at $\sqrt{{s}}$ ≈ 1 GeV the contributions of the above resonances are much larger, by a factor of 30, than the ρ(770) one, and amount to a considerable fraction ∼ 0.3-0.6 of the latter at $\sqrt{{s}}$ ∼ m _ρ .