$D$ to $K$ semileptonic decay form factors from HISQ light and charm quarks

Abstract

We present a study of $D\to K,l\hat{I}½$ 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 $f_0^{D\to K}(0)\equiv f_{+}^{D\to K}(0)=0.747(19)$ 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 $f_{+}^{D\to K}(0)\ast |V_{cs}|$ 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.

7 pages, 6 figures, and 1 table. Talk given at Lattice 2010, June 14-19, 2010, Villasimius, Italy