Update: Precision D_s decay constant from full lattice QCD using very fine lattices

TL;DR

This paper refines the calculation of the $D_s$ meson decay constant and mass using advanced lattice QCD techniques on very fine lattices, providing results consistent with experiments and offering insights into CKM matrix elements.

Contribution

The study presents updated $D_s$ decay constant and mass determinations using finer lattices and improved tuning, enhancing precision over previous lattice QCD results.

Findings

$m_{D_s} = 1.9691(32)$ GeV, consistent with experiment

$f_{D_s} = 0.2480(25)$ GeV, slightly below experimental average

Estimated $V_{cs} = 1.010(22)$ from decay rate and lattice data

Abstract

We update our previous determination of both the decay constant and the mass of the $D_s$ meson using the Highly Improved Staggered Quark formalism. We include additional results at two finer values of the lattice spacing along with improved determinations of the lattice spacing and improved tuning of the charm and strange quark masses. We obtain $m_{D_s}$ = 1.9691(32) GeV, in good agreement with experiment, and $f_{D_s}$ = 0.2480(25) GeV. Our result for $f_{D_s}$ is 1.6$\sigma$ lower than the most recent experimental average determined from the $D_s$ leptonic decay rate and using $V_{cs}$ from CKM unitarity. Combining our $f_{D_s}$ with the experimental rate we obtain a direct determination of $V_{cs} = 1.010(22)$, or alternatively $0.990 {+0.013 \atop -0.016}$ using a probability distribution for statistical errors for this quantity which vanishes above 1. We also include an accurate prediction of the decay constant of the $\eta_c$, $f_{\eta_c}$ = 0.3947(24) GeV, as a calibration point for other lattice calculations.