LEPTONIC TAU-DECAYS - HOW TO DETERMINE THE LORENTZ STRUCTURE OF THE CHARGED LEPTONIC WEAK INTERACTION BY EXPERIMENT

The purely leptonic decays ++» and +e+e» are both described by the most general (local, derivative-free, lepton-number-conserving) four-fermion interaction Hamiltonian characterized by ten complex coupling constants. The V-A hypothesis of the standard model can be proven experimentally, as has been done for decay, from the results of only five key experiments. These five decay experiments would determine upper limits for all eighteen non-(V-A) terms and a lower limit for the V-A coupling. Most of these experiments can be carried out at an e+e- collider with unpolarized beams near pair production threshold as well as in the region of the resonances. Analytical decay distributions are derived in terms of suitable laboratory observables. With their help statistical errors for the decay parameters e, e, e, e and K are calculated assuming an ideal detector. For 107 produced +- pairs these errors are in the range of (2-20)×10-3 except the error for e(e=0.53). The parameters and that describe the isotropic part of the spectrum are found to be strongly correlated. Therefore any experiment should be analyzed simultaneously with respect to both parameters. An experimental value of is required for the derivation of the Fermi coupling constant for the muonic decay. By measuring the + polarization from + decay the polarization parameter can be deduced with an error of 15%. The measurements of e and e will allow us to constrain five of the ten complex coupling constants for the decay +e+e» the measurements of and will even constrain eight complex coupling constants for the decay ++». The determination of the remaining coupling constants would require the measurement of the cross section for the inverse decay e--e or of correlations between one of the neutrinos and the + or + for the muonic decay. © 1990 The American Physical Society.