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We analyze the hadronization structure of $\tau \to \eta \pi^- \pi^0\nu_\tau$ decays. In the isospin limit only the vector current contributes tothis process. We compute the relevant form factor within Resonance ChiralTheory, at leading order in the $1/N_C$ expansion, and considering only thecontribution of the lightest vector resonances. The couplings in the resonancetheory are constrained by imposing the asymptotic behaviour of vector spectralfunctions ruled by $QCD$. We reproduce the branching ratio of this mode andpredict the low-energy behaviour of$\sigma\left(e^+e^-\to\eta\pi^+\pi^-\right)$ using isospin symmetry.

$\tau^-\to\eta\pi^-\pi^0\nu_\tau$ and $\sigma(e^+e^-\to \eta\pi^+\pi^-)$ at low energies