The Study of Pole Trajectory within a bare state in the coupled channel model

TL;DR

This paper explores the behavior of pole trajectories in a relativistic coupled channel model with a bare state, revealing how interactions influence bound and resonance poles using Hamiltonian Effective Field Theory.

Contribution

It introduces a relativistic coupled channel model with a bare state and analyzes pole distributions, trajectories, and compositeness, highlighting differences from non-relativistic cases.

Findings

Relativistic effects significantly alter pole distributions compared to non-relativistic models.

Attractive and repulsive interactions distinctly affect bound and resonance poles.

Including a bare state allows detailed analysis of pole origins and their trajectories.

Abstract

We investigate two-particle scattering and two-particle scattering with a bare basis state using Hamiltonian Effective Field Theory (HEFT). We analyze the distribution of two-body scattering poles in the momentum and energy planes under relativistic conditions. Compared to the non-relativistic case, there are significant differences in the distribution of bound state poles and resonance poles in the relativistic case, primarily due to the square root term in the relativistic formula. By considering pure two-particle scattering, we examine the relationship between the form factor and the number of poles. Additionally, we clearly elucidate the effects of attractive and repulsive interactions on the bound state poles and resonance poles. More importantly, we extend our model by including a bare state and explore the poles originating from the bare state or coupled channels through the trajectories of pole positions, as well as the compositeness of bound states.