Energy dependence of $K^-$-"$pp$" effective potential derived from coupled-channel Green's function

TL;DR

This study derives an energy-dependent effective potential for the $K^-$ and $pp$ system from a coupled-channel model, highlighting its behavior near decay thresholds and implications for resonance pole positions.

Contribution

It introduces a method to obtain an energy-dependent local potential from a coupled-channel framework for the $ar{K}N$ and $ar{K}( ext{NN})$ systems, emphasizing decay threshold effects.

Findings

Imaginary part of potential approximates phase space suppression near decay threshold.

Potential influences the pole position of the $ar{K}( ext{NN})$ resonance.

Energy dependence is crucial for accurate modeling of $K^-$-nuclear interactions.

Abstract

We investigate the energy dependence of a single-channel effective potential between the $K^-$ and the "$pp$"-core nucleus, which can be obtained as an $K^-$-"$pp$" equivalent local potential from a coupled-channel model for $\bar{K}(NN)$-$\pi(\Sigma N)$ systems. It turns out that the imaginary part of the resultant potential near the $\pi \Sigma N$ decay threshold can well approximate the phase space suppression factor of $K^-pp \to \pi \Sigma N$ decay modes. The effects on the pole position of the $\pi(\Sigma N)$ state in the $\pi \Sigma N$ channel are also discussed.