Rates and Distributions in Tau Decay

Abstract

Semileptonic decays of polarised $τ$ leptons are investigated. Predictions for the rate, based on CVC and chiral Lagrangians, are contrasted with experiments. Predictions for the angular distributions of three meson final states are given. Emphasis is put on studies in electron-positron annihilation where the neutrino escapes detection and the $τ$ restframe cannot be reconstructed. It is shown that the form factors can be measured in ongoing high statistics experiments. Of particular interest for the three meson case are the distribution of the normal to the Dalitz plane and the distribution around this normal. At LEP these distributions allow for an improved measurement of the $τ$ polarisation. Implications are considered for an experiment where the $τ$ restframe is reconstructed. It is shown that the measurement of impact parameters with the help of vertex detectors allows a full kinematic reconstruction, including the direction of the $τ$ and the missing neutrino momentum.