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

TL;DR

A highly improved quark discretization on MILC gluon fields that include realistic sea quarks is used, fixing the u/d, s, and c masses from the pi, K, and eta(c) meson masses, which allows a stringent test against experiment for D and D(s) masses for the first time.

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 $f_K/f_π$ = 1.189(7) and $(f_{D_s}/f_D)/(f_K/f_π)$ = 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 $π$, $K$, and $η_c$ meson masses. This allows a stringent test against experiment for $D$ and $D_s$ masses for the first time (to within 7 MeV).

Figures (2)

• Figure 1: Masses of the $D^+$ and $D_s$ meson as a function of the $u/d$ mass in units of the $s$ mass at three values of the lattice spacing. The very coarse results are the top ones in each set, then coarse, then fine. The lines give the simultaneous chiral fits and the dashed line the continuum extrapolation as described in the text. Our final error bars, including the overall scale uncertainty, are given by the shaded bands. These are offset from the dashed lines by an estimate of electromagnetic, $m_{u}\ne m_{d}$ and other systematic corrections to the masses. The experimental results are marked at the physical $m_{d}/m_s$.
• Figure 2: $D$, $D_s$, $K$ and $\pi$ decay constants on very coarse, coarse and fine ensembles, as a function of the $u/d$ quark mass. The chiral fits are performed simultaneously with those of the corresponding meson masses, and the resulting continuum extrapolation curve is given by the dashed line. For $\pi, K$ we have $\chi^2/\mathrm{dof} = 0.2$ and for $D, D_s$, $\chi^2/\mathrm{dof}=0.6$, each for 28 pieces of data. The shaded band gives our final result. At the left are experimental results from CLEO-c cleocfdscleocfd (with the $\tau$ decay result above the $\mu$ decay result for $D_s$) and BaBar babar ($D_s$ only) and from the Particle Data Tables pdg06 for $K$ and $\pi$. For the $K$ we have updated the result quoted by the PDG to be consistent with their quoted value of $V_{us}$.