Note on predictions for $c\bar{s}$ quarkonia using a three-loop static potential

TL;DR

This paper improves the theoretical modeling of charm-strange quarkonium by incorporating full three-loop QCD corrections, leading to more accurate predictions of the spectrum and decay widths.

Contribution

It introduces a refined potential model with three-loop corrections and a variational approach constrained by the relativistic virial theorem for $c\bar{s}$ quarkonia.

Findings

Accurately describes the $D_s$ spectrum.

Compatible with existing data on radiative decays.

Provides improved mass predictions for $c\bar{s}$ states.

Abstract

We extend our treatment of the the spectroscopy and decays of the charm-strange quarkonium system to include the effect of using the full three-loop QCD correction to the static short distance potential. As before, our potential model consists of the relativistic kinetic energy term, a scalar linear confining term including its relativistic corrections and the perturbative QCD spin-dependent terms. A set of unperturbed wave functions for the various states is obtained using a variational technique that is further constrained by requiring that the wave functions also satisfy the relativistic virial theorem. These are then used in a perturbative treatment of the potential to fit the mass spectrum of the $c\bar{s}$ system and calculate the radiative decay widths. Our results accurately describe the $D_s$ spectrum and are compatible with the little data that is available for the radiative decays of the $D_s$ states.