Compositeness of near-threshold $s$-wave resonances

TL;DR

This paper introduces a new probabilistic method to analyze the compositeness of near-threshold resonances, revealing they are less composite than shallow bound states, with implications for understanding resonance structures.

Contribution

A novel probabilistic interpretation scheme for complex compositeness of resonances that excludes unphysical decay widths and provides new insights into near-threshold resonance structures.

Findings

Near-threshold resonances have small composite fractions.

The scheme effectively analyzes resonances via effective range expansion.

Contrasts with the compositeness of shallow bound states.

Abstract

The near-threshold clustering phenomenon is well understood by the low-energy universality, for shallow bound states below the threshold. Nevertheless, the characteristics of resonances slightly above the threshold still lack thorough elucidation. We introduce a novel probabilistic interpretation scheme for complex compositeness of resonances, in which resonances with unphysically large decay widths are inherently excluded. Employing this scheme to analyze resonances via the effective range expansion, we demonstrate that near-threshold resonances have small composite fraction, in sharp contrast to shallow bound states below the threshold.