D → K, lv semileptonic decay scalar form factor and |Vcs| from lattice QCD

We present a new study of D semileptonic decays on the lattice which employs the highly improved staggered quark action for both the charm and the light valence quarks. We work with MILC unquenched N-f = 2 + 1 lattices and determine the scalar form factor f(0)(q(2)) for D -> K, lv semileptonic decays. The form factor is obtained from a scalar current matrix element that does not require any operator matching. We develop a new approach to carrying out chiral/continuum extrapolations of f(0)(q(2)). The method uses the kinematic "z'' variable instead of q(2) or the kaon energy E-K and is applicable over the entire physical q(2) range. We find f(0)(D -> K)(0) equivalent to f(+)(D -> K)(0) = 0.747(19) in the chiral plus continuum limit and hereby improve the theory error on this quantity by a factor of similar to 4 compared to previous lattice determinations. Combining the new theory result with recent experimental measurements of the product f(+)(D -> K)(0)*vertical bar V-cs vertical bar from BABAR and CLEO-c leads to a very precise direct determination of the CKM matrix element vertical bar V-cs vertical bar, vertical bar V-cs vertical bar = 0.961(11)(24), where the first error comes from experiment and the second is the lattice QCD theory error. We calculate the ratio f(+)(D -> K)(0)/f(Ds) and and find 2.986 +/- 0.087 GeV-1 and show that this agrees with experiment.