D meson Semileptonic Decay Form Factors at q² = 0

We discuss preliminary results for the vector form factors f₊^{π,K} at zero-momentum transfer for the decays D → π`ν and D → K`ν using MILC’s N_f = 2 + 1 + 1 HISQ ensembles at four lattice spacings, a ≈ 0.042,0.06,0.09, and 0.12 fm, and various HISQ quark masses down to the (degenerate) physical light quark mass. We use the kinematic constraint f₊(q²) = f₀(q²) at q² = 0 to determine the vector form factor from our study of the scalar current, which yields f₀(0). Results are extrapolated to the continuum physical point in the framework of hard pion/kaon SU(3) heavy-meson-staggered χPT and Symanzik effective theory. Our calculation improves upon the precision achieved in existing lattice-QCD calculations of the vector form factors at q² = 0. We show the values of the CKM matrix elements |V_cs| and |V_cd| that we would obtain using our preliminary results for the form factors together with recent experimental results, and discuss the implications of these values for the second row CKM unitarity.