On two dimensional coupled bosons and fermions

TL;DR

This paper investigates a large-N_c coupled boson-fermion model, revealing the absence of boson-antiboson bound states in a linear approximation and identifying fermion-antifermion bound states with energies below the two-mass threshold.

Contribution

It introduces a linear approximation to a coupled boson-fermion model, showing the potential for fermion-antifermion bound states and analyzing scattering properties.

Findings

No boson-antiboson bound states in the approximation

Existence of fermion-antifermion bound states below threshold

Implications for scattering theory above the two-mass threshold

Abstract

We study complex bosons and fermions coupled through a generalized Yukawa type coupling in the large-N_c limit following ideas of Rajeev [Int. Jour. Mod. Phys. A 9 (1994) 5583]. We study a linear approximation to this model. We show that in this approximation we do not have boson-antiboson and fermion-antifermion bound states occuring together. There is a possibility of having only fermion-antifermion bound states. We support this claim by finding distributional solutions with energies lower than the two mass treshold in the fermion sector. This also has implications from the point of view of scattering theory to this model. We discuss some aspects of the scattering above the two mass treshold of boson pairs and fermion pairs. We also briefly present a gauged version of the same model and write down the linearized equations of motion.