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

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 $f_K/f_{\ddot{I}}€$ = 1.189(7) and $(f_{D_s}/f_D)/(f_K/f_{\ddot{I}}€)$ = 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 $\ddot{I}€$, $K$, and $\hat{I}{\cdot }_c$ meson masses. This allows a stringent test against experiment for $D$ and $D_s$ masses for the first time (to within 7 MeV).

4 pages, 2 figures. Published version - changes from original include a more extensive discussion of errors and an error budget table covering more quantities. There are very small changes in some of the values reported