Radiative corrections in the SU(2)/sub L/ x U(1) theory: A simple renormalization framework

A simple renormalization framework to carry out practical calculations in the SU(2)/sub L/ x U(1) theory is discussed. The basic counterterms associated with the mass matrix of the gauge bosons and their interactions with quarks and leptons are generated and determined in a straightforward manner. They can then be applied, in a systematic fashion, to study the radiative corrections to the various processes of interest: μ decay, β decay, ν-induced reactions, and other leptonic and semileptonic processes. The role played by costheta/sub W/ is discussed in some detail. Using the results and methods of the current-algebra formulation of radiative corrections, an effective Lagrangian is derived for μ decay in which the contributions of the heavy particles and some of the photonic corrections are reduced to a renormalization factor of the zeroth-order amplitude. This analysis determines the connection between the renormalized constants of the present framework and G/sub μ/. The corrections to the relation m/sub W/=(piα/√2G/sub μ/)/sup 1/2//sintheta/sub W/ are discussed. This leads to some relevant observations concerning certain model-dependent hadronic contributions to these corrections and their cancellation in the comparison between charged-current transitions and neutral-current processes occurring at large momentum transfers