  Latest Lattice results on $D$ form factors evaluation from first principles
show that the standard model (SM) branching ratios prediction for the leptonic
$D_s \to \ell \nu_\ell$ decays and the semileptonic SM branching ratios of the
$D^0$ and $D^+$ meson decays are in good agreement with the world average
experimental measurements. It is possible to disprove New Physics hypothesis or
find bounds over several models beyond the SM. Using the observed leptonic and
semileptonic branching ratios for the D meson decays, we performed a combined
analysis to constrain non standard interactions which mediate the $c\bar{s}\to
l\bar{\nu}$ transition. This is done either by a model independent way through
the corresponding Wilson coefficients or in a model dependent way by finding
the respective bounds over the relevant parameters for some models beyond the
standard model. In particular, we obtain bounds for the Two Higgs Doublet Model
Type-II and Type III, the Left-Right model, the Minimal Supersymmetric Standard
Model with explicit R-Parity violation and Leptoquarks. Finally, we estimate
the transverse polarization of the lepton in the $D^0$ decay and we found it
can be as high as $P_T=0.23$.
