On the width of the $K^-$D atom ground state

TL;DR

This paper predicts the strong-interaction width and shift of the $K^-$D atom's ground state using global fits to kaonic atom data and chiral interaction models, aiding upcoming experimental measurements.

Contribution

It provides the first comprehensive prediction of the $K^-$D atom ground state width and shift based on global fits and chiral models, connecting to three-body calculations.

Findings

Predicted $K^-$D 1S ground state width of about 1.2 to 1.3 keV.

Predicted upward level shift of approximately 700 eV.

Results are consistent with three-body $K^-$D atom calculations.

Abstract

Experiments at DA$\Phi$NE-Frascati and at J-PARC are scheduled to produce $K^-$D atoms and observe their X-ray cascade down to the 1$S$ ground state (g.s.), thereby measuring its strong-interaction width and shift away from a purely Coulomb state. A width $\Gamma_{1S}\lesssim 1$ keV will ensure good resolution of the X-ray transitions feeding the 1$S$ g.s. Here we study the expected $K^-$D 1$S$ g.s. width from the perspective of global fits to level shifts and widths in heavier kaonic atoms across the periodic table, using $K^-$ nuclear optical potentials constructed from $\bar K N$ chiral interaction models. Special attention is paid to the subthreshold energy at which the $\bar K N$ subsystem interacts in the $K^-$D atomic g.s. Within this approach we predict strong-interaction upward level shift of close to 700 eV and width of about 1.2 to 1.3 keV for the $K^-$D atom 1$S$ g.s., in fair agreement with genuinely three-body $K^-$D atom calculations. Comparison is made with $\pi^-$D atom phenomenology.