Twisted mass QCD in the charm sector

We present preliminary results for the charm quark mass $m_c$ and the $D$ and $D_s$ mesons decay constants $f_D$ and $f_{D_s}$ from a lattice QCD calculation with ${\mathrm{N}}_{\mathrm{f}}$ = 2 dynamical fermions. We use the twisted mass fermionic action defined at maximal twist so that physical quantities are automatically $\mathcal{O}(a)$ improved. Two lattice spacings are considered. The charm quark mass has been renormalised in the RI-MOM scheme. After a matching to the $\text{msb}$ scheme, we obtain from the simulation at a fine lattice ($a\sim 0.09$ fm) $m_c^{\text{msb}}(m_c)=1.481\pm 0.022\pm 0.092$ GeV, $f_D=205\pm 13\pm 17$ MeV, $f_{D_s}=271\pm 6\pm 6$ MeV and from the simulation at the finer lattice ($a\sim 0.07$ fm) $m_c^{\text{msb}}(m_c)=1.474\pm 0.041\pm 0.132$ GeV, $f_D=230\pm 31\pm 8$ MeV and $f_{D_s}=264\pm 5\pm 8$ MeV. We chose three renormalisation conditions to determine $m_c$: the spread between the final results contributes to the systematic error. At both lattice spacings, particularly at the finer one, the error on $m_c$ is dominated by present uncertainty on the renormalisation constant $Z_P$, which should be reduced before performing a reliable continuum limit.