Static potential in scalar QED$_3$ with non-minimal coupling

TL;DR

This paper calculates the static potential in scalar QED3 with a non-minimal coupling, showing it remains logarithmic at large distances but exhibits a short-range repulsive force at small separations, affecting bound state formation.

Contribution

It demonstrates that non-minimal Pauli-type coupling in scalar QED3 does not alter the long-distance logarithmic potential but introduces a short-range repulsive force, independent of a Chern-Simons term.

Findings

The static potential remains logarithmic at large distances.

Non-minimal coupling causes a short-range repulsive force.

Repulsion occurs regardless of the Chern-Simons term presence.

Abstract

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 ($\eps j^{\mu}\partial^{\nu}A^{\alpha}$), 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 M$\ddot{o}$ller 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.