Absence of higher order corrections to the non-Abelian Chern-Simons coefficient

We extend the Coleman-Hill analysis to non-Abelian Chern-Simons theories co ntaining a tree level topological mass term. We show, in the case of a pure Yang-Mills-Chern-Simons theory, that there are no corrections to the coeff icient of the Chern-Simons term beyond one loop in the axial gauge. Our arg uments use constraints coming only from small gauge Ward identities as well as the analyticity of the amplitudes, much like the proof in the Abelian c ase. Some implications of this result are also discussed. (C) 2000 Elsevier Science B.V. All rights reserved.