D→K, lν 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 f₀(q²) for D→K, lν 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 f₀(q²). The method uses the kinematic “z”variable instead of q² or the kaon energy E_K and is applicable over the entire physical q² range. We find f₀^D→K(0)≡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 ∼4 compared to previous lattice determinations. Combining the new theory result with recent experimental measurements of the product f₊^D→K(0)*|V_cs| from BABAR and CLEO-c leads to a very precise direct determination of the CKM matrix element |V_cs|, |V_cs|=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 find 2.986±0.087GeV^-1 and show that this agrees with experiment.