Proton decay by monopoles and strings

Order-of-magnitude estimates are obtained for fermion-monopole and fermion-string scattering, taking into account the effect of the monopole or string on the fermion wavefunction. As a result, it is concluded that monopoles will catalyze proton decay with a strong cross-section (the Callan-Rubakov effect) whereas for strings the process has a geometrical cross-section. The difference is explained as being due to a long range attractive potential between the fermion and the monopole, and the absence of long range fields in the case of the string