Binding energy of scalar bound state by topologically massive interaction: fermion and antifermion system with heavy mass
Abstract
A bound state problem in a topologically massive quantum electrodynamics is investigated by using a nonperturbative method. We formulate the BetheSalpeter equation for scalar bound states composed of massive fermion and antifermion pair under the lowest ladder approximation. In a large mass expansion for the (anti)fermion, we derive the Schrödinger 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 ChernSimons term gives the bound system a repulsive effect.
 Publication:

Physics Letters B
 Pub Date:
 May 2002
 DOI:
 10.1016/S03702693(02)018105
 arXiv:
 arXiv:hepth/0203042
 Bibcode:
 2002PhLB..536...49M
 Keywords:

 High Energy Physics  Theory
 EPrint:
 14 pages, 3 figures, references added