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We present results from an ongoing computation of masses of $D$ mesons, $D_s$mesons and charmonium, including both ground states and several parity andangular momentum excitations. We employ 2+1+1 flavours of dynamical maximallytwisted mass fermions at three lattice spacings and three $u/d$ quark masses ateach lattice spacing. We consider different combinations of valence quarkdiscretizations, with either identical or opposite signs in front of thetwisted mass terms. In the end, our setup allows for a good control ofdifferent kinds of systematic effects, in particular the quark mass dependenceof the resulting meson masses and cut-off effects. We obtain good agreementwith experiment for the majority of states and we discuss improvements thatwill be made to finalize the analysis.

Mass spectra of mesons containing charm quarks - continuum limit results from twisted mass fermions