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

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.

Comments: 21 pages, 5 figures, v2: Title changed, references added and rewriting of some sentences. It matches the published version in PRD