Charm physics with a Lattice QCD mixed action

In this thesis we study a mixed-action Lattice QCD setup, which combines $N_f=2+1$ $O(a)$-improved Wilson fermions and $N_f=2+1+1$ Wilson twisted mass (Wtm) fermions at maximal twist in the valence. We take advantage of automatic $O(a)$ improvement in the valence sector to extract charm physics results without improvement coefficients.

Our results include the determination of the charm quark mass, as well as of the decay constants of the $D$ and $D_s$ mesons, relevant for electroweak leptonic decays. Quarkonium states are also studied. We carry out an analysis that focuses on controlling the statistical and systematic errors. Systematic effects are considered in the framework of Bayesian statistics. Different model parameterizations are taken into consideration to perform a model average. Our final results are among the most precise in the literature for computations employing Wilson-like fermions and will contribute significantly to the current world averages.