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Internal structure of near-threshold states using compositeness

Tomona Kinugawa, Tetsuo Hyodo

TL;DR

The paper tackles the problem of deciphering the internal structure of near-threshold states by quantifying clustering with the compositeness $X$. It uses a nonrelativistic EFT model where a bare state couples to scattering to study shallow bound states, showing that as the binding energy $B$ approaches zero, $X\to 1$, and that for typical shallow bindings a large fraction of parameter space yields cluster-dominant structures, supporting the threshold energy rule. For above-threshold resonances, it employs the effective range expansion and a novel interpretation scheme for complex $X$, yielding a probabilistic decomposition $(\mathcal{X},\mathcal{Y},\mathcal{Z})$ with a fixed $\alpha$, and finds that near-threshold narrow resonances have $\mathcal{Z}\gtrsim 0.8$, i.e., non-cluster-dominant. The results demonstrate a qualitative distinction between sub-threshold bound states and near-threshold resonances and provide a theoretical foundation for interpreting clustering in near-threshold exotic hadrons.

Abstract

Understanding the internal structure of near-threshold states is essential for revealing the nature of exotic hadrons. Motivated by this challenge, we discuss the clustering structures of near-threshold $s$-wave eigenstates using the compositeness, which characterizes the clustering nature of the states. We show that shallow bound states usually possess cluster-dominant structures, while near-threshold narrow resonances are non-cluster-dominant. Through this study, we establish a theoretical foundation for the threshold energy rule, which has been known empirically.

Internal structure of near-threshold states using compositeness

TL;DR

The paper tackles the problem of deciphering the internal structure of near-threshold states by quantifying clustering with the compositeness . It uses a nonrelativistic EFT model where a bare state couples to scattering to study shallow bound states, showing that as the binding energy approaches zero, , and that for typical shallow bindings a large fraction of parameter space yields cluster-dominant structures, supporting the threshold energy rule. For above-threshold resonances, it employs the effective range expansion and a novel interpretation scheme for complex , yielding a probabilistic decomposition with a fixed , and finds that near-threshold narrow resonances have , i.e., non-cluster-dominant. The results demonstrate a qualitative distinction between sub-threshold bound states and near-threshold resonances and provide a theoretical foundation for interpreting clustering in near-threshold exotic hadrons.

Abstract

Understanding the internal structure of near-threshold states is essential for revealing the nature of exotic hadrons. Motivated by this challenge, we discuss the clustering structures of near-threshold -wave eigenstates using the compositeness, which characterizes the clustering nature of the states. We show that shallow bound states usually possess cluster-dominant structures, while near-threshold narrow resonances are non-cluster-dominant. Through this study, we establish a theoretical foundation for the threshold energy rule, which has been known empirically.
Paper Structure (4 sections, 10 equations, 3 figures)

This paper contains 4 sections, 10 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Structure of shallow bound states
  3. Structure of near-threshold resonances
  4. Summary

Figures (3)

  • Figure 1: The dependence of the compositeness $X$ on the model parameter $\nu_{0}/E_{\rm typ}$ for a shallow bound state with $B = 0.01E_{\rm typ}$.
  • Figure 2: The elementarity of resonances $\mathcal{Z}$ on the complex energy plane of the second Riemann sheet, where resonance poles exist.
  • Figure 3: Schematic illustration of the nature of near-threshold $s$-wave eigenstates.