The CVC prediction for the τ⁻→h ⁻π⁰ v _τ branching ratio

Abstract

Theoretical predictions for the τ⁻→h ⁻π⁰ v _τ branching ratio can made using the measurede ⁺ e ⁻→π⁺π⁻ cross section and the conserved vector current (CVC) hypothesis. We use a parameterization, that was developed by other authors to study the η meson, to fit thee ⁺ e ⁻→π⁺π⁻ cross section. The parameterization includes both the ρ and ω resonances and the ρ′(1450) and ρ″(1700) resonances. The result is a good description of the data up to center-of-mass energies 2200 MeV. We compare our result against the fits made by others using the same and different parameterizations of the cross section. Most fits model the cross section except at higher center-of-mass energies where the other fits fail to describe the data. With this parameterization of the cross section, we calculate that the ratio of the τ⁻→π⁻π⁰ v _τ branching ratio relative to the$\tau ^ - \to e^ - \bar v_e v_\tau$ branching ratio isR _ρ=1.37±0.06 and that the ratio of the τ⁻→π⁻π⁰ v _τ branching ratio relative to the tau lifetime isL _ρ=(8.40±0.38)×10⁻⁴ffs⁻¹. Using a recent set of world averages for the$\tau ^ - \to e^ - \bar v_e v_\tau$ branching ratio and τ lifetime, and including a 0.5% correction for the τ⁻→K ⁻π⁰ v _τ branching ratio, we predict that the τ⁻→h ⁻π⁰ v _τ branching ratio is (25.1±1.4)%. This result is in good agreement with all measurements of the τ⁻→h ⁻π⁰ v _τ branching ratio.