Renormalization ambiguities in Chern-Simons theory

We introduce a new family of gauge-invariant regularizations of Chern-Simons theories which generate one-loop renormalizations of the coupling constant of the form k→k+2scv where s can take any arbitrary integer value. In the particular case s=0 we get an explicit example of a gauge-invariant regularization which does not generate radiative corrections to the bare coupling constant. This ambiguity in the radiative corrections to k is reminiscent of the Coste-Luescher results for the parity anomaly in 2+1 fermionic effective actions