D → π and D → K semileptonic form factors with Nf = 2 + 1 + 1 twisted mass fermions

We present a lattice determination of the vector and scalar form factors oftheD→π(K)`νsemileptonic decays, which are relevant for the extraction of the CKMmatrix elements|Vcd|and|Vcs|from experimental data. Our analysis is based on the gaugeconfigurations produced by the European Twisted Mass Collaboration withNf=2+1+1flavors of dynamical quarks. We simulated at three different values of the lattice spacingand with pion masses as small as 210 MeV. The matrix elements of both vector and scalarcurrents are determined for a plenty of kinematical conditions in which parent and childmesons are either moving or at rest. Lorentz symmetry breaking due to hypercubic effectsis clearly observed in the data and included in the decomposition of the current matrixelements in terms of additional form factors. After the extrapolations to the physical pionmass and to the continuum limit the vector and scalar form factors are determined in thewhole kinematical region fromq2=0 up toq2max=(MD−Mπ(K))2accessible in theexperiments, obtaining a good overall agreement with experiments, except in the regionat high values ofq2where some deviations are visible