QCD radiative effect in the semi-hadronic decay of the τ-particle

Abstract

Recently, QuIGG (1) has given an introductory lectm'e on gauge theories of the strong, weak and electromagnetic interactions. He has discussed various supporting evidences on the widely accepted nature of fundamental constituents known as quarks and gluons. He pointed out there that the branching ratio of the leptonic decay of the z-particle is one of the evidence for the colour degree of quarks in the zeroth approximation. A more detailed analysis (~) including semi-hadronie decays for n pious gave a reasonable explanation for the slight gap between the experimental data and the naive picture. Experimental ly (a), the z--*e-~evz decay was fitted by choosing the Michel parameter O = 0.72 • 0.10 and 0 for V A and V qA, respectively, for mvz = 0. A pure vector or axial-vector coupling leads O = ~. A V q-A interaction is excluded and a pure A or V interaction is unlikely. An upper l imit of mvz < 250 MeV is obtained from a V A fit to the electron spectrum. In the following we shall adopt a pure V A interaction with m v~ = 0 for definiteness. In this paper the QCD radiative correction for the charged intermediate boson and qq vertex is estimated up to the two-loop levels. In what follows the appropriate choices of the QCD scale parameter A is performed for oneand two-loop corrections, separately. Under these choices the Lorentz-invariant energy spectra for the hadron system in the rest frame of ~ leads to one and the same distribution, by assuming that the hadronie final-state interaction is approximated by the gluonic radiative corrections taken into account. In order to single out the radiat ive effect, the speetr~ without radiative correction are also studied in a parallel manner. The idea of the asymptotic free QCD model for the quark-gluon interactions are usually tested from e+e annihilations to hadrons, the deep-inelastic lepton-hadron interactions and the lepton pair productions in hadronic collisions. Here the QCD scale parameter is adjusted from an ~xperimental information. The idea was tested successfully so far without exception. At the present t ime people are going to explain the