Remarks on gauge vortex scattering

In the abelian Higgs model, among other situations, it has recently been realized that the head-on scattering of n solitons distributed symmetrically around the point of scattering is by an angle πn, independent of various details of the scattering. In this note, it is first observed that this result is in fact not entirely surprising: the above is one of only two possible outcomes. Then, a generalization of an argument given by Ruback for the case of two gauge theory vortices in the Bogomolʹnyi limit is used to show that in the geodesic approximation the above result follows from purely geometric considerations.