Higher-Order Corrections to Leptonic Processes and the Renormalization of Weinberg's Theory of Weak Interactions in the Unitary Gauge

Abstract

Higher-order corrections to the leptonic processes such as muon decay and neutrino-lepton scattering are investigated in order to study the problems associated with the renormalization of the Weinberg theory of weak interactions in the unitary gauge. It is shown that there are definite ways to carry out the renormalization programs and the residual divergences (quadratic as well as logarithmic) cancel out systematically. As a result we find that the higher-order corrections to these processes and the neutrino charge radius are all finite. As a by-product, we find that the logarithmic residual divergences in the elastic $\ensuremath{\nu}\ensuremath{-}\ensuremath{\nu}$ scattering also cancel out.