Bound State Inequality for High Mass Exchanges in a Scalar Field Model

TL;DR

This paper extends the analysis of bound state conditions in scalar field theories to cases involving very high mass exchanges, building on previous work that focused on low mass exchanges.

Contribution

It introduces a method to determine the coupling strength needed for bound states when the exchanged particles have very high mass.

Findings

Derived a bound state inequality for high mass exchanges

Generalized previous low-mass exchange results

Provided insights into scalar field interactions at high energies

Abstract

Ladder diagrams are relevant for the study of bound states. The condition upon the coupling strength for the existence of a bound state has been deduced in a scalar field theory for the case of low mass exchanges. We apply this approach to the case of very high mass exchanges.