$\mathrm{D}$ and $\mathrm{D_s}$ decay constants in $N_{\rm f}=2+1$ QCD with Wilson fermions

TL;DR

This paper reports precise lattice QCD calculations of D and D_s meson decay constants using extensive ensembles with controlled quark mass dependence, contributing to the understanding of heavy meson decay properties.

Contribution

First high-precision lattice QCD determination of D and D_s decay constants with multiple trajectories and controlled quark mass dependence.

Findings

f_Ds = 246.8(1.3) MeV

f_D = 208.4(1.5) MeV

f_Ds / f_D = 1.1842(36)

Abstract

We present results for the leptonic decay constants of the D and D$_{\rm s}$ mesons from $N_{\rm f}=2+1$ lattice QCD. We employ a set of 49 high statistics gauge ensembles generated by the Coordinated Lattice Simulations (CLS) effort utilising non-perturbatively improved Wilson fermions and the tree-level Symanzik improved gauge action at six values of the lattice spacing in the range $a = 0.098\,$fm down to $a = 0.039\,$fm, with pion masses varying from around $420\,$MeV down to below the physical point. The ensembles lie on three trajectories in the quark mass plane, two trajectories intersecting close to the physical quark mass point and the third one approaching the SU(3) chiral limit, enabling tight control of the light and strange quark mass dependence. We obtain $f_{\mathrm{D_s}}=246.8(1.3)\,$MeV, $f_\mathrm{D}=208.4(1.5)\,$MeV and $f_{\mathrm{D_s}}/f_\mathrm{D}=1.1842(36)$, where the precision of our results is mostly limited by the determination of the scale.