Why the vacuum charge of a fermion-monopole system vanishes discontinuously as fermion mass vanishes

Using nonrelativistic scattering theory we attribute the vacuum charge induced by a fermion on a monopole to the branch cut introduced by the kinematic (k2+m2)-1/2 in the momentum representation of the charge density. The absence of this cut in the zero mass case leads to the discontinuity in the charge. (orig.)