Dispersive representation of the pion vector form factor in τ→π π ν_τ decays

Abstract

We propose a dispersive representation of the charged pion vector form factor that is consistent with chiral symmetry and fulfills the constraints imposed by analyticity and unitarity. Unknown parameters are fitted to the very precise data on τ^- π^- π⁰ ν_τ decays obtained by Belle, leading to a good description of the corresponding spectral function up to a π π squared invariant mass s ≃ 1.5 GeV². We determine the ρ(770) mass and width pole parameters and obtain the values of low energy observables. The significance of isospin breaking corrections is also discussed. For larger values of s, this representation is complemented with a phenomenological description to allow its implementation in the new TAUOLA hadronic currents.