Lattice Determination of Heavy-Light Decay Constants

Abstract

We report on the MILC collaboration's calculation of $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$, and their ratios. Our central values come from the quenched approximation, but the quenching error is estimated from $N_F=2$ dynamical staggered lattices. We use Wilson light valence quarks and Wilson and static heavy quarks. We find, for example, $f_B=157 \pm 11 {}^{+25}_{-9} {}^{+23}_{-0} \MeV$, $f_{B_s}/f_B=1.11\pm 0.02{}_{-0.03}^{+0.04}\pm 0.03$, $f_{D_s} = 210 \pm 9 {}^{+25}_{-9} {}^{+17}_{-1} \MeV$ and $f_B/f_{D_s}=0.75\pm 0.03{}_{-0.02}^{+0.04}{}_{-0.00}^{+0.08}$, where the errors are statistical, systematic (within the quenched approximation), and systematic (of quenching), respectively.

arXiv comment4 pages, 2 included figures. We adjust the perturbative correction calculated by Kuramashi to take into account the fact that we match to the continuum at the kinetic mass of the heavy meson, not the pole mass. This produces a 2 to 4 MeV change in final results for decay constants, and has negligible effect on decay constant ratios. We also include further explanation of various features of the analysis

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