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We compute masses of $D$ meson, $D_s$ meson and charmonium states using$N_f=2+1+1$ Wilson twisted mass lattice QCD. All results are extrapolated tophysical light quark masses, physical strange and charm quark masses and to thecontinuum. Our analysis includes states with spin $J = 0,1,2$, parity$\mathcal{P} = -,+$ and in case of charmonium also charge conjugation$\mathcal{C} = -,+$. Computations are based on a large set of quark-antiquarkmeson creation operators. We investigate and quantify all sources of systematicerrors, including fitting range uncertainties, finite volume effects, isospinbreaking effects and the choice of the fitting ansatz for the combined chiraland continuum extrapolation such that the resulting meson masses can becompared directly and in a meaningful way to experimental results. Withincombined statistical and systematic errors, which are between below two permille and three percent, our results agree with available experimental resultsfor most of the states. In the few cases where we observe discrepancies, wediscuss possible reasons.

Continuum limit of the $D$ meson, $D_s$ meson and charmonium spectrum from $N_f=2+1+1$ twisted mass lattice QCD