On the nature of near-threshold bound and virtual states

TL;DR

This paper extends Weinberg's criterion to classify near-threshold states as bound, virtual, or resonant, clarifying the nature of these states based on their pole positions and residues.

Contribution

It demonstrates that Weinberg's criterion can be applied to shallow virtual states, providing a clearer classification of near-threshold states.

Findings

Virtual states are predominantly molecular in nature.

Non-molecular states are mainly bound states or resonances.

Classification scheme has limitations in certain cases.

Abstract

Physical states are characterised uniquely by their pole positions and the corresponding residues. Accordingly, in those parameters also the nature of the states should be encoded. For bound states (poles on the real $s$-axis below the lowest threshold on the physical sheet) there is an established criterion formulated originally by Weinberg in the 1960s, which allows one to estimate the amount of compact and molecular components in a given state. We demonstrate in this paper that this criterion can be straightforwardly extended to shallow virtual states (poles on the real $s$-axis below the lowest threshold on the unphysical sheet) which should be classified as molecular. We argue that predominantly non-molecular or compact states exist either as bound states or as resonances (poles on the unphysical sheet off the real energy axis) but not as virtual states. We also discuss the limitations of the mentioned classification scheme.