Constraining the $\bar{K}N$ interaction from the $1S$ level shift of kaonic deuterium

TL;DR

This study performs precise three-body calculations of kaonic deuterium to connect the $1S$ level shift measurements with the antikaon-nucleon interaction, aiming to improve understanding of the $KN$ force.

Contribution

It introduces a highly accurate three-body calculation method for kaonic deuterium, linking atomic level shifts to the $KN$ interaction, especially constraining the isospin $I=1$ component.

Findings

The $1S$ level shift of kaonic deuterium is $670-i508$ eV.

The level shift is sensitive to the isospin $I=1$ component of the $KN$ interaction.

A 25 ext% measurement accuracy can significantly constrain the $KN$ interaction.

Abstract

Motivated by the precise measurement of the $1S$ level shift of kaonic hydrogen, we perform accurate three-body calculations for the spectrum of kaonic deuterium using a realistic antikaon-nucleon ($KN$) interaction. In order to describe both short- and long-range behavior of the kaonic atomic states, we solve the three-body Schr\"odinger equation with a superposition of a large number of correlated Gaussian basis functions covering distances up to several hundreds of fm. Transition energies between $1S$, $2P$ and $2S$ states are determined with high precision. The complex energy shift of the $1S$ level of kaonic deuterium is found to be $670-i508$ eV. The sensitivity of this level shift with respect to the isospin $I=1$ component of the $KN$ interaction is examined. It is pointed out that an experimental determination of the kaonic deuterium level shift within an uncertainty of 25\% will provide a constraint for the $I=1$ component of the $KN$ interaction significantly stronger than that from kaonic hydrogen.