D→K, lν semileptonic decay scalar form factor and |V_cs| 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<sub>f</sub>=2+1 lattices and determine the scalar form factor f<sub>0</sub>(q<sup>2</sup>) 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 f<sub>0</sub>(q<sup>2</sup>). The method uses the kinematic “z”variable instead of q<sup>2</sup> or the kaon energy E<sub>K</sub> and is applicable over the entire physical q<sup>2</sup> range. We find f<sub>0</sub><sup>D→K</sup>(0)≡f<sub>+</sub><sup>D→K</sup>(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<sub>+</sub> <sup>D→K</sup>(0)*|V<sub>cs</sub>| from BABAR and CLEO-c leads to a very precise direct determination of the CKM matrix element |V<sub>cs</sub>|, |V<sub>cs</sub>|=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<sub>+</sub> <sup>D→K</sup>(0)/f<sub>D</sub> <sub>s</sub> and find 2.986±0.087 GeV-1 and show that this agrees with experiment