Pole structure and compositeness

TL;DR

This paper introduces a universal criterion for determining whether a bound state is elementary or composite, based on expectation values of particle number operators, and applies it to analyze complex states like the X(3872).

Contribution

It develops a new universal criterion for elementariness and provides a closed formula for the compositeness of bound states in two-particle systems, extending to resonances.

Findings

New criterion for elementariness of bound states

Closed formula for compositeness in two-particle continuum

Discussion of X(3872) as a potential multi-pole virtual state

Abstract

We present in this talk a series of new results on the nature of a bound state or resonance based on the calculation of the expectation values of the number operators of the free particles in the state of interest. In this way, a new universal criterion for the elementariness of a bound state emerges. In the case of large particle wavelengths compared to the range of their interaction, a new closed formula for the compositeness of a bound state in a two-particle continuum is obtained. The extension of these results to resonances with respect to the open channels can be given by making use in addition of suitable phase-factor transformations as also reviewed here. We end with a discussion on the $X(3872)$ as possible double- or triple-pole virtual state, which would be the first case in particle phenomenology.