We determine the decay constants of the pi and K mesons on gluon field configurations from the MILC collaboration including u, d, s and c quarks. We use three values of the lattice spacing and u/d quark masses going down to the physical value. We use
the w_0 parameter to fix the relative lattice spacing and f_pi to fix the overall scale. This allows us to obtain a value for f{K^+}/f{pi^+} = 1.1916(21). Comparing to the ratio of experimental leptonic decay rates gives |Vus| = 0.22564(28){Br(K^+)}(20){EM}(40){latt}(5){Vud} and the test of unitarity of the first row of the Cabibbo-Kobayashi-Maskawa matrix: |Vud|^2+|Vus|^2+|Vub|^2 - 1 = 0.00009(51).
We illustrate a technique for fitting lattice QCD correlators to sums of exponentials that is significantly faster than traditional fitting methods --- 10--40 times faster for the realistic examples we present. Our examples are drawn from a recent an
alysis of the Upsilon spectrum, and another recent analysis of the D -> pi semileptonic form factor. For single correlators, we show how to simplify traditional effective-mass analyses.
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).
We explore the possibility of studying $Btopi l u$ semileptonic decays at large recoil momentum. Our methods include the use of a random-wall source for the pion to reduce statistical errors, and different smearing functions are used for the B meson
to improve the overlap with the ground state. We observe, in general, a factor of 3-4 improvement in the signal-to-noise ratio in correlation functions if random-wall propagators are used.
