Nucleon decay and the parameters of the sigma model

Abstract

We discuss nucleon decay mediated by electroweak instantons using the description of a nucleon as a soliton in the non-linear sigma model. We show that the requirement that the decay amplitudes evaluated in the soliton model and at the quark level be equal leads to non-trivial constraints on the parameters of the sigma model. In particular, the dimensionless coupling constant of the Skyrme model is calculable; we find e = 5.48 N c −1 2 (3.16 for N c = 3, in a semi-quantitative agreement with the recent fit, e fit = 5.45). We also conjecture that higher derivative terms in the sigma model lagrangian are absent, unless there are miraculous cancellations between them in the amplitude of nucleon decay.