Kaonic hydrogen atom and kaon-proton scattering length

TL;DR

This paper investigates the discrepancies in kaon-proton scattering lengths derived from kaonic hydrogen energy shifts, highlighting inconsistencies between different extraction methods and assessing the implications for experimental measurements.

Contribution

It demonstrates the inconsistency between scattering lengths obtained via the Deser-Trueman formula and direct solutions, and evaluates the impact on interpreting experimental data.

Findings

Discrepancy between scattering lengths from different methods

Most chiral SU(3) models align with DEAR data when considering decay widths

Caution advised in extracting scattering lengths from planned measurements

Abstract

Kaonic hydrogen is studied with various realistic potentials in an accurate numerical approach based on Sturmian functions. The kaon-proton scattering length extracted from the 1s energy shift of the kaonic hydrogen by applying the Deser-Trueman formula is severely inconsistent with the one derived by directly solving the scattering Schoedinger 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. After taking into account the large discrepancy between the extracted and directly-evaluated scattering lengths, we found theoretical predictions of most chiral SU(3) based models for the kaonic hydrogen decay width are consistent with the DEAR data. We warn the SIDDHARTA collaboration that it may not be reasonable to extract kaon-nucleon scattering lengths, by using the Coulomb-interaction corrected Deser-Truemab formula, from the planned measurement of kaonic hydrogen.