6 Static potential in scalar QED 3 with non - minimal coupling

Here we compute the static potential in scalar QED 3 at leading order in 1/N f. We show that the addition of a non-minimal coupling of Pauli-type (ǫ µνα j µ ∂ ν A α), although it breaks parity, it does not change the analytic structure of the photon propagator and consequently the static potential remains logarithmic (confining) at large distances. The non-minimal coupling modifies the potential, however, at small charge separations giving rise to a repulsive force of short range between opposite sign charges, which is relevant for the existence of bound states. This effect is in agreement with a previous calculation based on Möller scattering, but differently from such calculation we show here that the repulsion appears independently of the presence of a tree level Chern-Simons term which rather affects the large distance behavior of the potential turning it into constant.