Binding Energy of Scalar Bound State by Topologically Massive Interaction: Fermion and Anti-fermion System with Heavy Mass

TL;DR

This paper investigates the binding energy of scalar bound states in topologically massive QED using a non-perturbative Bethe-Salpeter approach, revealing a critical topological mass and a logarithmic scaling behavior.

Contribution

It derives and solves a Schrödinger equation from the Bethe-Salpeter framework for massive fermion-antifermion pairs, uncovering novel scaling and critical phenomena.

Findings

Existence of a critical topological mass where bound states vanish.

Logarithmic dependence of binding energy on topological mass.

Chern-Simons term induces a repulsive effect on bound states.

Abstract

A bound state problem in a topologically massive quantum electrodynamics is investigated by using a non-perturbative method. We formulate the Bethe- Salpeter equation for scalar bound states composed of massive fermion and anti-fermion pair under the lowest ladder approximation. In a large mass expansion for the (anti-) fermion, we derive the Schr{\"o}dinger equation and solve it by a numerical method. The energy eigenvalues of bound states are evaluated for various values of a topological mass and also a fermion mass. Then we find a novel logarithmic scaling behaviour of the binding energy in varying the topological mass, fermion mass and also a quantum number. There exists a critical value of the topological mass, beyond which the bound states disappear. As the topological mass decreases, the energy eigenvalues of the bound states, which are negative, also decrease with a logarithmic dependence on the topological mass. A Chern-Simons term gives the bound system a repulsive effect.