Renormalization of a weak-interaction model

We consider the prototype weak-interaction coupling 1/2g Ψ¯\bar \Psi W·γ(1−iγ ₅)ψ of a boson W (massμ) to a spinor field (massm), gauge-transformed to a nonpolynomial form, and set up the detailed renormalization programme for it. The effective cut-off for the longitudinal W interactions is provided by the « Fermi constant »G=g ²/μ ² and the remaining (renormalizable) « infinities » due to the transverse W interactions can be rendered finite by invoking the further gravitational interactions of the fields. The finite radiative corrections are given as an asymptotic series ing andm/μ, assumed small, and we illustrate the procedure by treating spinor-spinor scattering.