We present a lattice determination of the vector and scalar form factors of the D → π ν and D → K ν semileptonic decays, which are relevant for the extraction of the CKM matrix elements |V cd | and |V cs | from experimental data. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with N f = 2 + 1 + 1 flavors of dynamical quarks, at three different values of the lattice spacing (a 0.062, 0.082, 0.089 fm) and with pion masses as small as 210 MeV. Quark momenta are injected on the lattice using non-periodic boundary conditions. The matrix elements of both vector and scalar currents are determined for a plenty of kinematical conditions in which parent and child mesons are either moving or at rest. Lorentz symmetry breaking due to hypercubic effects is clearly observed in the data and included in the decomposition of the current matrix elements in terms of additional form factors. After the extrapolations to the physical pion mass and to the continuum limit we determine the vector and scalar form factors in the whole kinematical region from q 2 = 0 up to q2 accessible in the experiments, obtaining a good overall agreement with experiments, except in the region at high values of q 2 where some deviations are visible. A set of synthetic data points, representing our results for f(q 2 ) for several selected values of q 2 , is provided and also the corresponding covariance matrix is available. At zero 4-momentum transfer we get: f
We present the first lattice N f ¼ 2 þ 1 þ 1 determination of the tensor form factor f . The matrix elements of the tensor current are determined for a plethora of kinematical conditions in which parent and child mesons are either moving or at rest. As in the case of the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed also in the data for the tensor form factor and included in the decomposition of the current matrix elements in terms of additional form factors. After the extrapolations to the physical pion mass and to the continuum and infinite volume limits, we determine the tensor form factor in the whole kinematical region from q 2 ¼ 0 up to q
We present a determination of the CabibboKobayashi-Maskawa matrix elements |V cd | and |V cs | obtained by combining the momentum dependence of the semileptonic vector form factors f D→π + (q 2 ) and f D→K + (q 2 ), recently determined from lattice QCD simulations, with the differential rates measured for the semileptonic D → π ν and D → K ν 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 statistical and systematic 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: |V cd | = 0.2341 (74) and |V cs | = 0.970 (33). The second-row CKM unitarity is fulfilled within the current uncertainties: |V cd | 2 + |V cs | 2 + |V cb | 2 = 0.996 (64). Moreover, using for the first time hadronic inputs determined from first principles, we have calculated the ratio of the semileptonic D → π(K ) decay rates into muons and electrons, which represent a test of lepton universality within the SM, obtaining in the isospin-symmetric limit of QCD: R Dπ LU = 0.985 (2) and R DK LU = 0.975 (1).
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