Accurate evaluation of the 1s wave functions of kaonic hydrogen

Abstract

Kaonic hydrogen is studied with realistic potentials in an accurate numerical approach based on Sturmian functions. It is found that the ground-state wave function of the exotic atom with realistic strong interactions is considerably different from the hydrogen-like ones at small distances. The K − p scattering length extracted from the 1s energy shift of the kaonic hydrogen by applying the DeserTrueman formula is severely inconsistent with the one derived directly by solving the Schödinger equation. We pay special attention to the recent measurement of the energy shift and decay width of the 1s kaonic hydrogen state by the DEAR Collaboration. Our work strongly supports the argument that the DEAR data of the K − p scattering length extracted with the Deser-Trueman formula from the measured 1s energy shift and decay width are not accurate, if not to say, unreliable.