Improved $V_{cs}$ determination using precise lattice QCD form factors for $D \rightarrow K \ell \nu$

TL;DR

This paper precisely determines the CKM matrix element V_{cs} using advanced lattice QCD form factors combined with experimental data, achieving 0.8% accuracy and enabling detailed Standard Model tests and lepton flavor universality checks.

Contribution

First precise V_{cs} determination with sub-percent accuracy using comprehensive lattice QCD form factors and physical quark ensembles, improving previous uncertainties and testing the Standard Model.

Findings

V_{cs} = 0.9663(53) with combined uncertainties

Form factors cover full q^2 range for decay analysis

Test of lepton flavor universality with R_{μ/e} ratio

Abstract

We provide a 0.8\%-accurate determination of $V_{cs}$ from combining experimental results for the differential rate of $D \rightarrow K$ semileptonic decays with precise form factors that we determine from lattice QCD. This is the first time that $V_{cs}$ has been determined with an accuracy that allows its difference from 1 to be seen. Our lattice QCD calculation uses the Highly Improved Staggered Quark (HISQ) action for all valence quarks on gluon field configurations generated by the MILC collaboration that include the effect of $u$, $d$, $s$ and $c$ HISQ quarks in the sea. We use eight gluon field ensembles with five values of the lattice spacing ranging from 0.15 fm to 0.045 fm and include results with physical $u/d$ quarks for the first time. Our calculated form factors cover the full $q^2$ range of the physical decay process and enable a Standard Model test of the shape of the differential decay rate as well as the determination of $V_{cs}$ from a correlated weighted average over $q^2$ bins. We obtain $|V_{cs}|= 0.9663(53)_{\text{latt}}(39)_{\text{exp}}(19)_{\eta_{EW}}(40)_{\text{EM}}$, where the uncertainties come from lattice QCD, experiment, short-distance electroweak and electromagnetic corrections, respectively. This last uncertainty, neglected for $D \rightarrow K \ell \nu$ hitherto, now needs attention if the uncertainty on $V_{cs}$ is to be reduced further. We also determine $V_{cs}$ values in good agreement using the measured total branching fraction and the rates extrapolated to $q^2=0$. Our form factors enable tests of lepton flavour universality violation. We find the ratio of branching fractions for $D^0 \rightarrow K^-$ with $\mu$ and $e$ in the final state to be $R_{\mu/e}=0.9779(2)_{\text{latt}}(50)_{\mathrm{EM}}$ in the Standard Model, with the uncertainty dominated by that from electromagnetic corrections.