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 ${\rm N_f}$ = 2 dynamical fermions. We use the twisted mass fermionic action defined at maximal twist so that physical quantities are automatically ${\cal O}(a)$ improved. Two lattice spacings are considered. The charm quark mass has been renormalised in the RI-MOM scheme. After a matching to the $\msb$ scheme, we obtain from the simulation at a fine lattice ($a \sim 0.09$ fm) $m_c^{\msb}(m_c) = 1.481 \pm 0.022 \pm 0.092$ 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) $m_c^{\msb}(m_c) = 1.474 \pm 0.041 \pm 0.132$ 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.