$D \rightarrow K, l \nu$ Semileptonic Decay Scalar Form Factor and $|V_{cs}|$ from Lattice QCD

TL;DR

This paper uses advanced lattice QCD techniques with the HISQ action to precisely determine the scalar form factor for D to K semileptonic decays and extract the CKM matrix element |V_{cs}| with unprecedented accuracy.

Contribution

The study introduces a new chiral/continuum extrapolation method using the kinematic 'z' variable, significantly improving the precision of the form factor and |V_{cs}| determination.

Findings

The scalar form factor at zero momentum transfer is 0.747(19).

The CKM matrix element |V_{cs}| is determined as 0.961(11)(24).

The ratio f^{D→K}_+(0)/f_{D_s} agrees with experimental results.

Abstract

We present a new study of D semileptonic decays on the lattice which employs the Highly Improved Staggered Quark (HISQ) 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 $D \rightarrow K, l \nu$ 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 $f^{D \rightarrow K}_0(0) \equiv f^{D \rightarrow K}_+(0) = 0.747(19)$ 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 the most precise direct determination of the CKM matrix element $|V_{cs}| $ to date, $|V_{cs}| = 0.961(11)(24)$, where the first error comes from experiment and the second is the lattice QCD theory error. We calculate the ratio $f^{D \rightarrow K}_+(0)/f_{D_s}$ and find $2.986 \pm 0.087$ GeV$^{-1}$ and show that this agrees with experiment.