Kaonic hydrogen atoms with realistic potentials

Abstract

Kaonic hydrogen is studied with various realistic potentials in an accurate numerical approach based on Sturmian functions. It is found that the mass difference between the ${K}^{\ensuremath{-}}p$ and ${\mathrm{K\ifmmode \bar{}\else \={}\fi{}}}^{0}n$ channels has a considerable effect on theoretical results of the energy shift and decay width of kaonic hydrogen. On average, the theoretical result in the isospin symmetry limit is smaller by a factor of about 20% than the full result where the mass difference between the ${K}^{\ensuremath{-}}p$ and ${\mathrm{K\ifmmode \bar{}\else \={}\fi{}}}^{0}n$ channels is properly treated. The theoretical results based on realistic local potentials, which reproduce well scattering data, are inconsistent with the recent measurement of the energy shift and decay width of the $1s$ kaonic hydrogen state by the DEAR Collaboration.