High Precision determination of the pi, K, D and D_s decay constants from lattice QCD

TL;DR

This paper reports highly precise lattice QCD calculations of $D$ and $D_s$ decay constants, achieving 2% errors, and provides important tests and determinations of CKM matrix elements by combining theoretical and experimental data.

Contribution

The study introduces a highly improved quark discretization method on MILC gluon fields, significantly reducing errors in decay constant calculations and enabling stringent tests against experimental meson masses.

Findings

$f_{D_s}$ = 241(3) MeV, $f_D$ = 207(4) MeV

$f_{D_s}/f_D$ = 1.164(11), $f_K/f_{\pi}$ = 1.189(7)

Determined CKM elements $V_{us}$ and $V_{cs}/V_{cd}$ with improved precision.

Abstract

We determine $D$ and $D_s$ decay constants from lattice QCD with 2% errors, 4 times better than experiment and previous theory: $f_{D_s}$ = 241(3) MeV, $f_D$ = 207(4) MeV and $f_{D_s}/f_D$ = 1.164(11). We also obtain $f_K/f_{\pi}$ = 1.189(7) and $(f_{D_s}/f_D)/(f_K/f_{\pi})$ = 0.979(11). Combining with experiment gives $V_{us}$=0.2262(14) and $V_{cs}/V_{cd}$ of 4.43(41). We use a highly improved quark discretization on MILC gluon fields that include realistic sea quarks fixing the $u/d, s$ and $c$ masses from the $\pi$, $K$, and $\eta_c$ meson masses. This allows a stringent test against experiment for $D$ and $D_s$ masses for the first time (to within 7 MeV).