Elementarity of composite systems

TL;DR

This paper investigates the concept of elementarity in composite systems, showing that dynamically generated states have a zero wave function renormalization constant, and discusses the implications and ambiguities of this in physical interpretations.

Contribution

It demonstrates that the wave function renormalization constant Z is zero for s-wave composite states, clarifies the conditions under which this holds, and discusses interpretational ambiguities.

Findings

Wave function renormalization constant Z equals zero for composite states.

Zero-energy bound states can have finite elementary mass despite Z=0.

Interpretational ambiguity exists due to Z not being a physical observable.

Abstract

The "compositeness" or "elementarity" is investigated for s-wave composite states dynamically generated by energy-dependent and independent interactions. The bare mass of the corresponding fictitious elementary particle in an equivalent Yukawa model is shown to be infinite, indicating that the wave function renormalization constant Z is equal to zero. The idea can be equally applied to both resonant and bound states. In a special case of zero-energy bound states, the condition Z = 0 does not necessarily mean that the elementary particle has the infinite bare mass. We also emphasize arbitrariness in the "elementarity" leading to multiple interpretations of a physical state, which can be either a pure composite state with Z = 0 or an elementary particle with Z \ne 0. The arbitrariness is unavoidable because the renormalization constant Z is not a physical observable.