Stability of bound states in the light-front Yukawa model

TL;DR

This paper demonstrates that in a two-fermion scalar exchange system, bound state solutions are stable without regularization below a critical coupling, which is determined through an eigenvalue equation.

Contribution

It provides a novel analysis of bound state stability in the light-front Yukawa model without the need for cutoff regularization.

Findings

Bound states are stable for coupling constants below a critical value.

The critical coupling constant is calculated from an eigenvalue equation.

Stability is achieved without cutoff regularization.

Abstract

We show that in the system of two fermions interacting by scalar exchange, the solutions for J$^{\pi}$=$0^+$ bound states are stable without any cutoff regularization, for values of the coupling constant $\alpha$ below a critical value $\alpha_c$. This latter is calculated from an eigenvalue equation.