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

TL;DR

This paper calculates the $D ightarrow K$ semileptonic decay form factor using HISQ quarks on the lattice, achieving a fourfold reduction in theoretical error and providing a precise determination of the CKM matrix element $|V_{cs}|$.

Contribution

The study introduces a lattice QCD calculation of the $D ightarrow K$ form factor with improved accuracy and no operator matching, refining the theoretical input for CKM matrix element extraction.

Findings

Determined $f^{D ightarrow K}_0(0) = 0.747(19)$ with reduced error.

Provided a precise value of $|V_{cs}| = 0.961(11)(24)$ from combined lattice and experimental data.

Achieved a fourfold improvement in the theoretical error over previous lattice calculations.

Abstract

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.