On Ratios of the Renormalized and the Bare Coupling Constants in the Beta Decay Interaction

Abstract

The ratio of the renormalized and the bare coupling constants in the (j-decay interaction is calculated in two ways. The first is evaluation of the contribution from the process in which a neutron and an antiproton, which virtually exchange an infinite number of pions, are annihilated into an electron-neutrino (or antineutrino) pair. For this purpose a dispersion relation for the vertex function of the (j-decay is assumed. Using this relation the ratio is calculated in the ladder approximation of Federbush, Goldberger and Treiman. The result is that the ratio is smaller than unity. The second way is calculating the ratio so as to include the main contribution from virtual nucleon pairs. For this purpose we derive an equation for the vertex operator of the (j-decay. The vertex operator is calculated using Goto and Machida's approximation. The result is that the ratio for the axial vector coupling constants is larger than unity, while that for the vector coupling constants is smaller than unity. The experimental value for the ratio (~1·2) is reproduced at a rather small cutoff energy (~ one-pion rest mass).