On spin-1 massive particles coupled to a Chern-Simons field

TL;DR

This paper investigates the scattering behavior of spin-1 particles coupled to a Chern-Simons field, analyzing different models and their renormalization properties, revealing similarities with Aharonov-Bohm scattering at low energies.

Contribution

It introduces and compares three models of spin-1 particles coupled to a Chern-Simons field and examines their scattering amplitudes and renormalization at one loop.

Findings

Low energy scattering resembles Aharonov-Bohm effect for spin 1/2

Models are power counting renormalizable at one loop due to Ward identities

Different coupling schemes affect ultraviolet behavior and renormalization

Abstract

We study spin one particles interacting through a Chern-Simons field. In the Born approximation, we calculate the two body scattering amplitude considering three possible ways to introduce the interaction: (a) a Proca like model minimally coupled to a Chern-Simons field, (b) the model obtained from (a) by replacing the Proca's mass by a Chern-Simons term and (c) a complex Maxwell-Chern-Simons model minimally coupled to a Chern-Simons field. In the low energy regime the results show similarities with the Aharonov-Bohm scattering for spin 1/2 particles. We discuss the one loop renormalization program for the Proca's model. In spite of the bad ultraviolet behavior of the matter field propagator, we show that, up to one loop the model is power counting renormalizable thanks to the Ward identities satisfied by the interaction vertices.