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Resonance Chiral Lagrangian analysis of $τ^- \to η^{(\prime)} π^- π^0 ν_τ$ decays

The hadronization structure of $τ^- \to ηπ^- π^0 ν_τ$ decays is analyzed using Chiral Perturbation Theory with resonances, considering only the contribution of the lightest meson resonances at leading order in the $1/N_C$ expansion. After imposing the asymptotic behavior of vector spectral functions ruled by QCD, unknown effective couplings are determined by fitting the $τ^- \to ηπ^- π^0 ν_τ$ branching ratio and decay spectrum to recent data. Predictions for the partner decay $τ^- \to η^\prime π^- π^0 ν_τ$ and the low-energy behavior of the cross section $σ(e^+e^-\to ηπ^+π^-)$ are also discussed.