Improved Vcs determination using precise lattice QCD form factors for D→Kℓν

Abstract

We provide a 0.8%-accurate determination of ${V}_{cs}$ from combining experimental results for the differential rate of $D\ensuremath{\rightarrow}K$ 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 $|{V}_{cs}|=0.9663(53{)}_{\mathrm{latt}}(39{)}_{\mathrm{exp}}(19{)}_{{\ensuremath{\eta}}_{\mathrm{EW}}}(40{)}_{\mathrm{EM}}$, where the uncertainties come from lattice QCD, experiment, short-distance electroweak, and electromagnetic corrections, respectively. This last uncertainty, neglected for $D\ensuremath{\rightarrow}K\ensuremath{\ell}\ensuremath{\nu}$ 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 flavor universality violation. We find the ratio of branching fractions for ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}$ with $\ensuremath{\mu}$ and $e$ in the final state to be ${R}_{\ensuremath{\mu}/e}=0.9779(2{)}_{\mathrm{latt}}(50{)}_{\mathrm{EM}}$ in the Standard Model, with the uncertainty dominated by that from electromagnetic corrections.