Light kaonic atoms: from "corrected" to "summed up" Deser formula

TL;DR

This paper evaluates the accuracy of corrected and summed-up Deser formulas for kaonic atoms, finding that the summed-up version provides significantly better results for linking level shifts to scattering lengths.

Contribution

It introduces a comparative analysis showing the superiority of the summed-up Deser formula over the corrected version for kaonic atom systems.

Findings

Summed-up Deser formula is more accurate than corrected Deser formula.

The study provides guidance on which formula to use for precise level shift and scattering length connection.

Results support using the summed-up formula in future kaonic atom analyses.

Abstract

Accuracy of "corrected Deser" and "summed up Deser" formulas was checked for the $K^- p$ and $K^- d$ systems. It was found that the last one is much more accurate and should be used for connection the $1s$ level shift to the corresponding scattering length.