Resonance Chiral Lagrangian analysis of $\tau^- \to \eta^{(\prime)} \pi^- \pi^0 \nu_\tau$ decays

TL;DR

This paper uses Resonance Chiral Lagrangian theory to analyze tau decays involving eta and pion mesons, fitting unknown couplings to experimental data and predicting related decay processes and cross sections.

Contribution

It introduces a novel application of Resonance Chiral Lagrangian analysis to tau decay modes involving eta mesons, incorporating QCD constraints and fitting to recent experimental data.

Findings

Determined effective couplings from tau decay data.

Predicted decay rates for tau to eta' pi pi nu.

Provided low-energy cross section estimates for e+e- to eta pi pi.

Abstract

The hadronization structure of $\tau^- \to \eta \pi^- \pi^0 \nu_\tau$ 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 $\tau^- \to \eta \pi^- \pi^0 \nu_\tau$ branching ratio and decay spectrum to recent data. Predictions for the partner decay $\tau^- \to \eta^\prime \pi^- \pi^0 \nu_\tau$ and the low-energy behavior of the cross section $\sigma (e^+e^-\to \eta\pi^+\pi^-)$ are also discussed.