Monopole-induced baryon-number violation in ‘‘realistic’’ grand unified theories

We consider the embedding of the SU(2) monopole of 't Hooft and Polyakov into ``realistic'' grand unified theories (GUT's) and find a complication that may possibly interfere with the Callan-Rubakov effect. The fine tuning that keeps the weak-interaction scale much smaller than the GUT scale is necessarily upset in the vicinity of a magnetic monopole, and there is a probability of order one that the Weinberg-Salam Higgs field will have a GUT-scale expectation value at the monopole core. This means that the fermions could have a large effective mass at the core which could act as a barrier to exclude the fermions from the baryon-number-violating interactions inside the monopole core. In this paper we determine whether such a barrier is likely to cause a significant suppression of the Callan-Rubakov effect. Our analysis involves a variational determination of a position-dependent mass for the fermions in Callan's soliton formalism. Once the position-dependent mass of the solitons has been determined, simple energy arguments allow us to determine if the Callan-Rubakov effect will be suppressed. We find that in ordinary GUT's, the small Yukawa couplings between the Weinberg-Salam Higgs field and the light fermions keep the effective soliton masses very small so baryon-number violation is not affected, but if the Yukawa couplings are larger than ${10}^{\mathrm{\ensuremath{-}}3}$ (instead of the usual ${10}^{\mathrm{\ensuremath{-}}5}$) or with the appropriate tuning of Higgs-field parameters, the soliton masses can become large at the core, and the Callan-Rubakov effect can be prevented. In the event that the Callan-Rubakov effect is suppressed, we find that baryon-number violation is still possible through the weak-anomaly-induced process discussed by Schellekens and Sen. However, this process is not likely to be important phenomenologically. We also correct an ambiguity with the bosonization procedure that was noticed by Yamagishi.