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We discuss preliminary results for the vector form factors $f_+^{\{\pi,K\}}$at zero-momentum transfer for the decays $D\to\pi\ell\nu$ and $D\to K \ell\nu$using MILC's $N_f = 2+1+1$ HISQ ensembles at four lattice spacings, $a \approx0.042, 0.06, 0.09$, and 0.12 fm, and various HISQ quark masses down to the(degenerate) physical light quark mass. We use the kinematic constraint$f_+(q^2)= f_0(q^2)$ at $q^2 = 0$ to determine the vector form factor from ourstudy of the scalar current, which yields $f_0(0)$. Results are extrapolated tothe continuum physical point in the framework of hard pion/kaon SU(3)heavy-meson-staggered $\chi$PT and Symanzik effective theory. Our calculationimproves upon the precision achieved in existing lattice-QCD calculations ofthe vector form factors at $q^2=0$. We show the values of the CKM matrixelements $|V_{cs}|$ and $|V_{cd}|$ that we would obtain using our preliminaryresults for the form factors together with recent experimental results, anddiscuss the implications of these values for the second row CKM unitarity.

$D$ meson Semileptonic Decay Form Factors at $q^2 = 0$