Mutual fractional statistics of relativistic Chern-Simons solitons

Recently low-energy dynamics of two distinct species of the Chern-Simons solitons has been studied by a direct analysis of the relevant classical Lagrangian. In the case of long-range interactions of solitons, this dynamics does not seem to give the mutual statistics. We comment on the mutual fractional statistics of such solitons by explicitly computing the effective Lagrangian which expresses the statistics of composite vortices.