D→K,lνsemileptonic 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 $D\to K$, $l\nu$ 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 $f_0^{D\to K}(0)\equiv f_{+}^{D\to K}(0)=0.747(19)$ in the chiral plus continuum limit and hereby improve the theory error on this quantity by a factor of $\sim 4$ compared to previous lattice determinations. Combining the new theory result with recent experimental measurements of the product $f_{+}^{D\to K}(0)*|V_{cs}|$ 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 $f_{+}^{D\to K}(0)/f_{D_s}$ and find $2.986\pm 0.087{\mathrm{GeV}}^{-1}$ and show that this agrees with experiment. DOI: http://dx.doi.org/10.1103/PhysRevD.82.114506 © 2010 The American Physical Society