Isospin violation in τ → 3πντ

Abstract

Isospin violating signals in the τ⁻ → (3π)⁻ν_τ decay mode are discussed. For the τ⁻ → π⁻π⁻π⁺ν_τ decay mode, isospin violation arises from the vector current contribution in the τ⁻ → ωπ⁻ν_τ decay with the subsequent isospin violating ω decay into π⁺π⁻. We demonstrate that such effects may be observed in presently available data through the measurement of the interference effects of these vector current contributions with the dominating axial vector current,i. e. through a measurement of the structure functionsW_F, WG, WH andW_I. In the case of the τ⁻ → π⁰π⁰π⁻ν_τ decay mode, a vector current contribution is generated by ηπ⁰ mixing in the decay chain τ⁻ → ηϱ⁻ν_τ → π⁰π⁰π⁻ν_τ. We find that this effect is rather small, the magnitude of the associated interference terms being too low for present statistics.