On bound-states of the Gross Neveu model with massive fundamental fermions

TL;DR

This paper investigates the existence of bound states in the two-dimensional Gross-Neveu model with massive fermions, finding a metastable bound state around a local minimum that decays via tunneling.

Contribution

It provides a detailed analysis of bound states in the massive Gross-Neveu model, revealing the presence of a metastable state and its decay properties, which was not previously established.

Findings

No bound states around the lowest minimum

Existence of a metastable bound state around a local minimum

Decay rate of the metastable state depends on fermion mass and coupling

Abstract

In the search for QFT's that admit boundstates, we reinvestigate the two dimensional Gross-Neveu model, but with massive fermions. By computing the self-energy for the auxiliary boundstate field and the effective potential, we show that there are no bound states around the lowest minimum, but there is a meta-stable bound state around the other minimum, a local one. The latter decays by tunneling. We determine the dependence of its lifetime on the fermion mass and coupling constant.