The decay constants F_DS, F_d+, F_BS and F_b from lattice QCD

In this report we summarize results for the leptonic decay constants f_Ds, f_D+, f_Bs and f_B, obtained at the three lattice spacings a ≈ 0.09, 0.125 and 0.15 fm, from the now concluded first computational phase of our on-going project. The decay constants are computed on the MILC collaboration's 2 + 1 flavor asqtad gauge ensembles. We use clover heavy quarks in the Fermilab interpretation and asqtad improved staggered light quarks. For each of the D and B meson systems, a simultaneous chiral and continuum extrapolation is performed with partially quenched lattice results. We show how improvements being implemented now, such as, higher statistics, additional finer lattice spacings and better determinations of inputs to the calculation, are expected to reduce future statistical and systematic uncertainties.