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

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

2002-03-06

arxiv.org/abs/hep-th/0203042v2

Phys.Lett. B536 (2002) 49-58

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 3 figures, references added; version accepted for publication in Phys. Lett. B

Scientific paper

10.1016/S0370-2693(02)01810-5

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.

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