Decay Effect on Near-Threshold Mass Scaling with Complex and Coupled-Channel Potentials

TL;DR

This paper studies how decay channels influence near-threshold mass scaling by analyzing pole trajectories in potential models, revealing that quasibound states do not smoothly transition into resonances and comparing single-channel and coupled-channel approaches.

Contribution

It provides a detailed comparison of pole trajectories in single-channel and coupled-channel models, clarifying the effects of decay channels on near-threshold states.

Findings

Quasibound states below threshold are not continuously connected to resonance states above threshold.

Pole trajectories differ between single-channel and coupled-channel models.

Decay channels significantly affect the mass scaling and pole behavior near thresholds.

Abstract

We investigate the effect of decay channels on the near-threshold mass scaling by employing potential models. By varying the attractive strength of a square-well potential, we examine the pole trajectory associated with the transition of an $s$-wave bound state into a resonance state, incorporating decay-channel effects through both a single-channel complex potential model and a coupled-channel real potential model. As a result, we show that the pole of a quasibound state below the threshold is not continuously connected to that of a resonance state above the threshold. Furthermore, by comparing the results obtained from the single-channel and coupled-channel models, we clarify the correspondence between the pole trajectories in the two approaches.