Abstract
The effective $\overline{K}N$ interaction based on chiral SU(3) coupled-channel dynamics is derived and its extrapolation below the $\overline{K}N$ threshold is studied in detail. Starting from the coupled-channel scattering equations, we eliminate the channels other than $\overline{K}N$ and obtain an effective interaction in the single $\overline{K}N$ channel. An equivalent local potential in coordinate space is constructed such as to reproduce the full scattering amplitude of the chiral SU(3) coupled-channel framework. We discuss several realistic chiral SU(3)-based models in comparison to reach conclusions about the uncertainties involved. It turns out that, in the region relevant to the discussion of deeply bound $\overline{K}$-nuclear few-body systems, the resulting energy-dependent, equivalent local potential is substantially less attractive than the one suggested in previous purely phenomenological treatments.
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