γ 5 symmetries and relativistic corrections in beta decay

Abstract

Making the postulate that the four-fermion interaction must be invariant under the mass reversal transformation ψ → γ 5 ψ and m → − m, for every pair of the four fields simultaneously, we obtain the V-A interaction where C v = − C A, C' v = − C' A and C v/ C' v is arbitrary. This invariance property is very useful in finding a similarity between the nth and the ( n±1) th forbidden transitions in beta decay. In particular, corrections due to the relativistic matrix elements are given for the various formulae describing all kinds of the phenomena in the allowed beta decay. The Coulomb corrections and the finite de Broglie wavelength effect are taken into account simultaneously.