A self-consistent bound state model for meson

TL;DR

This paper investigates bound state formation in a 1+1 dimensional Yukawa theory, showing that in a specific limit, many bound states resemble non-relativistic particles, with unstable excited states and a stable ground state that can be interpreted as a fermion-antifermion bound pair.

Contribution

It introduces a self-consistent bound state model for mesons in Yukawa theory, analyzing the behavior of bound states in a particular parameter limit and their quantum stability.

Findings

Low-lying bound states are well-described by the non-relativistic Schrödinger equation.

Excited bound states are unstable and decay rapidly.

The ground state mass can be tuned to match the scalar mass.

Abstract

We study the 1+1 dimensional Yukawa theory, in a certain limit of its parameters g,M,m (as suggested by the study of causality in presence of bound states in this model). We study the bound state formation in the model. In the limit $g\to\infty,M\to\infty$, in a certain specific manner, we show that there are a large number of bound states of which at least the low lying states are described by the non-relativistic Schrodinger equation. We show that, in this limit, the excited bound states are unstable and deem to decay quickly (lifetime $\tau\to 0 $) by emission of scalar (s) in this particular limit. The mass of the ground state is not significantly affected by higher order quantum corrections and by proper choice of parameters, involving only small changes, can be adjusted to be equal to the mass of the scalar. As a result of quantum effects, the state of the meson mixes with the lowest bound state and may be dominated by the latter .We show that in this detailed sense, a scalar meson in Yukawa model can be looked upon as a bound state of a fermion-anti fermion pair formed.