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

TL;DR

This paper models the hadronization process in tau decays to eta and pions using Resonance Chiral Theory, constraining parameters with QCD, and predicts related electron-positron annihilation cross sections at low energies.

Contribution

It provides a theoretical calculation of the tau decay form factor and predicts the low-energy behavior of the e+e- to eta pi+ pi- cross section using resonance chiral theory.

Findings

Reproduces the tau decay branching ratio.

Predicts the low-energy e+e- cross section behavior.

Constrains resonance couplings with QCD asymptotics.

Abstract

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