Classification of Coupled-Channel Near-Threshold Structures

TL;DR

This paper classifies near-threshold heavy quarkonium structures using a coupled-channel effective field theory, linking scattering amplitude behaviors to pole trajectories and renormalization group fixed points.

Contribution

It introduces a systematic method to interpret near-threshold structures through pole evolution and provides a practical dictionary for experimental analysis.

Findings

Scattering amplitude line shapes are linked to pole trajectories.

Pole evolution is connected to renormalization group fixed points.

The classification aids in understanding exotic hadron candidates.

Abstract

Since 2003, plenty of resonant structures have been observed in the heavy quarkonium regime. Many of them are close to the thresholds of a few pairs of heavy hadrons. They are candidates of exotic hadrons and have attracted immense attentions. Based on a coupled-channel nonrelativistic effective field theory, we classify the near-threshold structures of a symmetry-related two-channel system by studying the evolution of the scattering amplitude line shapes and pole positions with the variation of the single-channel scattering length and channel coupling strength. We show that the evolution of the scattering amplitude line shapes can be understood from the pole trajectories in the complex energy plane, and the pole evolution can be traced back to the renormalization group fixed points. We provide a dictionary of correspondence between the evolution of line shapes and pole trajectories along with varying interaction and channel coupling strengths, which can be used to understand the experimental observations of the near-threshold structures.