$V_{cs}$ determination from $D \to{}K \ell \nu$

TL;DR

This paper presents a highly precise lattice QCD calculation of $V_{cs}$ from $D o K u ar{ u}$ decays, combining theoretical form factors with experimental data to achieve sub-percent accuracy.

Contribution

The study provides the first sub-percent level determination of $|V_{cs}|$ by combining advanced lattice calculations with multiple experimental methods.

Findings

$|V_{cs}|=0.9663(80)$ with sub-percent precision

Three different methods yield consistent results

Lattice form factors agree well with experimental data

Abstract

Semileptonic $D \to{}K \ell \nu$ decays provide one angle of attack to get at the CKM matrix element $V_{cs}$, complementary to the study of leptonic $D_s$ decays. Here, HPQCD present the results of a recently published, improved determination of $V_{cs}$. We discuss a new, precise determination of $D\to K$ scalar and vector form factors from a lattice calculation on eight different $N_f=2+1+1$ MILC gluon field ensembles using the HISQ action, including three with physical light quark masses. When combined with experimental results, we are able to extract $|V_{cs}|=0.9663(80)$ to a sub percent level of precision for the first time. This is achieved using three different methods, which each combine our form factors with different sets of experimental results in different ways, with the results in very good agreement. Our primary method is to use $q^2$-binned data for the differential decay rate, but we also calculate $V_{cs}$ from the total branching fraction and from the value $|V_{cs}|f_+(0)$, which is also quoted by some experiments.