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Testing Lepton Flavour Universality with (Semi)-Leptonic $D_{(s)}$ Decays

Data in $B$-meson decays indicate violations of lepton flavour universality, thereby raising the question about such phenomena in the charm sector. We perform a model-independent analysis of NP contributions in (semi)-leptonic decays of $D_{(s)}$ mesons which originate from $c \to d \bar{\ell} ν_{\ell}$ and $c \to s \bar{\ell} ν_{\ell}$ charge-current interactions. Starting from the most general low-energy effective Hamiltonian containing four-fermion operators and the corresponding short-distance coefficients, we explore the impact of new (pseudo)-scalar, vector and tensor operators and constrain their effects through the interplay with current data. We pay special attention to the elements $|V_{cd}|$ and $|V_{cs}|$ of the Cabibbo--Kobayashi--Maskawa matrix and extract them from the $D_{(s)}$ decays in the presence of possible NP decay contributions, comparing them with determinations utilizing unitarity. We find a picture in agreement with the Standard Model within the current uncertainties. Using the results from our analysis, we make also predictions for leptonic $D_{(s)}^+ \to e^+ ν_e$ modes which could be hugely enhanced with respect to their tiny Standard Model branching ratios. It will be interesting to apply our strategy at the future high-precision frontier.