Masses of $D$ mesons, $D_s$ mesons and charmonium states from twisted mass lattice QCD

We compute masses of $D$ mesons, $D_s$ mesons and charmonium states using Wilson twisted mass lattice QCD. We present results for spin $J=0,1,2,3$, parity $\mathcal{P}=-,+$ and in case of charmonium also charge conjugation $\mathcal{C}=-,+$. Computations are based on quark-antiquark creation operators and performed at three different unphysically heavy $u\mathrm{/}d$ quark masses allowing an extrapolation to the physical $u\mathrm{/}d$ quark mass. Within combined statistical and systematic errors, which are around $2 % \ldots 3 %$, our results agree with available experimental results. Particular focus is put on the $J^{\mathcal{P}}=1^{+}$ mesons $D_1(2430)$ and $D_1(2420)$. We separate and classify these close-by states according to the total angular momentum of their light degrees of freedom, $j\approx 1\mathrm{/}2$ and $j \approx 3/2$\mathrm{.}Thisisafirstimportantsteptostudydecays$B^{(\ast)} \rightarrow D_1 + l + \nu$, for which a long-standing conflict between theory and experiment exists.