We present a study of $D \rightarrow K, l \nu$ semileptonic decays on the lattice which employs the HISQ action for both the charm and the light quarks. We work with MILC unquenched $N_f = 2 + 1$ lattices and determine the scalar form factor $f_0(q^2)$. This form factor is obtained from a scalar current matrix element that does not require any operator matching. We find $f^{ D \rightarrow K}_0(0) \equiv f^{ D \rightarrow K}_+(0) = 0.747(19)$ 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 \rightarrow 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.
Categories: hep-lat