TESTS OF QUANTUM CHROMODYNAMICS IN THE DECAY OF THE TAU-LEPTON AND IN ELECTRON POSITRON-ANNIHILATION INTO HADRONS

We present a method to derive upper and lower bounds for a large class of quantities measurable in e+e- annihilation into hadrons and in τ-decay. The theoretical input are the asymptotic expansions for the vacuum polarization functions of vector and axial vector currents in the euclidean region as given by QCD. Since our method allows straightforward inclusion of (as yet uncalculated) higher order terms in αs, there is the potential of making high precision tests of QCD even with experiments at rather moderate energies. We argue, therefore, that it may be very worthwhile to pursue experiments at e+e- storage rings below the J/Ψ resonance and to measure the branching ratios for the decays of the τ-lepton with high accuracy. In the latter case we can also get information on the behaviour of the weak axial vector current which should be very interesting in connection with chiral symmetry breaking. © 1979 Springer-Verlag.