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

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.

Figures (3)

• Figure 1: Pole trajectories in the complex momentum plane by the single-channel model with $-15 \leq V_{0}\leq -0.1\ [b^{-2}\mu^{-1}]$ and $W_{0}=-1\ [b^{-2}\mu^{-1}]$.
• Figure 2: Pole trajectories in the complex momentum plane by the coupled-channel model with $-15 \leq V_{0}\leq -0.1\ [b^{-2}\mu^{-1}]$ and $V_{12}=2\ [b^{-2}\mu^{-1}]$. Left: [tt/bb] sheet, right: [bt/tb] sheet.
• Figure 3: Pole trajectories in the complex momentum plane by the coupled-channel model with $-15 \leq V_{0}\leq -0.1\ [b^{-2}\mu^{-1}]$ and $V_{12}=2\ [b^{-2}\mu^{-1}]$. Left (right) half plane is the [bt/tb] ([tt/bb]) sheet.