Separable potential model for $K^{-}N$ interactions at low energies

TL;DR

This paper develops a separable potential model for low-energy K- N interactions, fitting experimental data and solving bound state problems to improve understanding of kaonic hydrogen and related scattering phenomena.

Contribution

It introduces a separable potential model that matches chiral amplitudes and accurately describes low-energy K- N interactions, including bound states and scattering data.

Findings

Successfully fits low-energy K- p data

Accurately predicts kaonic hydrogen 1s level characteristics

Describes the πΣ mass spectrum and K- n amplitude energy dependence

Abstract

The effective separable meson-baryon potentials are constructed to match the equivalent chiral amplitudes up to the second order in external meson momenta. We fit the model parameters (low energy constants) to the threshold and low energy $K^{-}p$ data. In the process, the $K^{-}$-proton bound state problem is solved exactly in the momentum space and the 1s level characteristics of the kaonic hydrogen are computed simultaneously with the available low energy $K^{-}p$ cross sections. The model is also used to describe the $\pi \Sigma$ mass spectrum and the energy dependence of the $K^{-}n$ amplitude.