Application of the hidden local symmetry effective chiral Lagrangian to evaluation of the ω(782), ϕ(1020) → 5π decay widths

Abstract

The amplitudes obtained from the effective chiral Lagrangian with anomalous terms based on hidden local symmetry are applied to the evaluation of the partial widths of the decays ω → 2π+2π−π0 and ω → π+π−3π0. Combining the Okubo-Zweig-Iizuka rule, applied to the five-pion final state, with the Adler condition of vanishing of the amplitude at the vanishing of four-momentum of any final pion in the chiral limit, the ϕ → 2π+2π−π0 and ϕ → π+π−3π0 decay amplitudes are also calculated. The partial widths of the above decays are evaluated, and the resonance excitation curves in e+e− annihilation are obtained, assuming reasonable particular relations among the free parameters characterizing the anomalous terms of the Lagrangian. The evaluated branching ratios \(Br_{\phi \to \pi + \pi - 3\pi ^0 } \approx 2 \times 10^{ - 7} \) and \(Br_{\phi \to 2\pi + 2\pi - \pi ^0 } \approx 5 \times 10^{ - 7} \) are such that with the luminosity L = 500 pb−1, attained at the DAΦNE ϕ factory, one may already possess about 1340 events of the decays ϕ → 5π.