Extraction of $\lvert V_{cd} \rvert$ and $\lvert V_{cs} \rvert$ from experimental decay rates using lattice QCD $D \to \pi(K) \ell \nu$ form factors

We present a determination of the Cabibbo-Kobayashi-Maskawa matrix elements $\lvert V_{cd}\rvert$ and $\lvert V_{cs}\rvert$ obtained by combining the momentum dependence of the semileptonic vector form factors $f_+^{D \to \pi}(q^2)$ and $f_+^{D \to K}(q^2)$, recently determined from lattice QCD simulations, with the differential rates measured for the semileptonic $D \to \pi \ell \nu$ and $D \to K \ell \nu$ decays. Our analysis is based on the results for the semileptonic form factors produced by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ flavors of dynamical quarks in the whole range of values of the squared 4-momentum transfer accessible in the experiments. The correlations between the lattice data as well as those present in the experimental data are properly taken into account. With respect to the standard procedure based on the use of only the vector form factor at zero 4-momentum transfer, we obtain more precise and consistent results: $\lvert V_{cd} \rvert = 0.2349 ~ (72)$ and $\lvert V_{cs} \rvert = 0.968 ~ (34)$. The second-row CKM unitarity is fullfilled within the current uncertainties: $|V_{cd}|^2 + |V_{cs}|^2 + |V_{cb}|^2 = 0.993 ~ (66)$.