Some aspects of a Chern-Simons-like coupling in an external magnetic field

For a gauge theory which includes a light massive vector field interacting with the familiar photon U(1)_{QED} via a Chern-Simons- like coupling, we study the static quantum potential. Our analysis is based on the gauge-invariant, but path-dependent, variables formalism. The result is that the theory describes an exactly screening phase. Interestingly enough, this result displays a marked departure of a qualitative nature from the axionic elctrodynamics result. However, the present result is analogous to that encountered in the coupling between the familiar photon U(1)_{QED} and a second massive gauge field living in the so-called hidden-sector U(1)_h, inside a superconducting box.