Radiative Decay of Polarized τ-Leptons, τ ⇛ ντ + π + γ

Abstract

Using the standard form of the matrix element, which contains the so-called structural part as well as Inner Bremsstrahlung (IB) contribution, we calculate the structure functions for τ− → ντ + π− + γ in terms of the vector and axial form factors of the transition W → π− + γ. We work out the Dalitz plot for all three possible exclusive asymmetries and show that they are all non-zero. We discuss the consequences of the radiative zero in the IB amplitude. We show that inclusive asymmetries in τ− → ντ + π− + γ can be calculated analytically without knowledge of any concrete parametrization of the form factors v(t) and a(t). The t-dependence of v(t) and a(t) is computed in the framework of the vector dominance model using the conservation of vector current hypothesis for the v(0) and the existing experimental data for the ratio γ = a(0)/v(0) from π− → e− + ν(e) + γ decay. We demonstrate the sensitivity of exclusive and inclusive asymmetries to the sign of the vector form factor. The predicted polarization effects are large in magnitude.