Energy dependence of $K^-$-$pp$ effective potential derived from coupled-channel Greens function

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.