Monopoles, baryon decay and charge conservation

Abstract

The mechanism of baryon decay via monopoles is analyzed. For this purpose we quantize isodoublet fermion fields in the presence of a 't Hooft-Polyakov monopole. When the electromagnetic interactions are switched off, we find a condensation of a fermion pair\(\bar \psi _ - ^{(i)} \gamma ^0 \gamma ^5 \psi _ + ^{(i)} \) as well as that of\(\bar \psi _ - ^{(i)} \gamma ^0 \gamma ^5 \psi _ + ^{(i)} \bar \psi _ + ^{(j)} \gamma ^0 \gamma ^5 \psi _ - ^{(j)} \). Here, the indices ± stand for the electric charge and (i,j) for the flavour. Hence, the charge symmetry is spontaneously broken. However, when the Coulomb interactions are switched on, it is proved that all fermion condensates carrying non-zero electric charges are removed; the condensates carrying zero electric charge, which induce baryon decay in the standardSU (5) model, are not removed by switching on the Coulomb interactions. In these analyses, the key element is the charge mixing boundary condition imposed on the fermion wave-function at the monopole center; the chiral anomaly does not play any role.