Discerning new physics in charm meson leptonic and semileptonic decays

Current experimental information on the charm meson decay observables in which the $c\to s\ell\nu_\ell$ transitions occur is well compatible with the Standard Model predictions. Recent precise lattice calculations of the $D_s$ meson decay constant and form factors in $D\to K\ell\nu$ decays offer a possibility to search for the small deviations from the Standard Model predictions in the next generation of the high intensity flavour experiments. We revisit constraints from these processes on the new physics contributions in the effective theory approach. We investigate new physics effects which might appear in the differential distributions for the longitudinally and transversely polarised $K^\ast$ in $D\to K^\ast\ell\nu_\ell$ decays. Present constraints from these observables are rather weak, but could be used to constrain new physics effects in the future. In the case of $D\to K\ell\nu$ we identify observables sensitive on new physics contribution coming from the scalar Wilson coefficient, namely the forward-backward and the transversal muon asymmetries. By allowing that new physics modifies only the second lepton generation but not the first one, we identify allowed region for the differential decay rate for the process $D\to K\mu\nu_\mu$ and find that it is allowed to deviate from the Standard Model prediction by only few percent. The lepton flavour universality violation can be tested in the ratio $R_{\mu/e}(q^2)\equiv \frac{d\Gamma^{(\mu)}}{dq^2}/\frac{d\Gamma^{(e)}}{dq^2}$. If the first lepton generation behaves as in the Standard Model, we find, using current constraint on the scalar Wilson coefficient, that the ratio $R_{\mu/e}(q^2)$ is currently allowed to be within the range $(0.9, 1.2)$, depending on the value of $q^2$.