LAUSR

We present results on the renormalization functions of the quark field and fermion bilinears with up to one covariant derivative. For the fermion part of the action, we employ the twisted mass formulation with ${N}_{f}=2$ and ${N}_{f}=4$ degenerate dynamical quarks, while in the gluon sector, we use the Iwasaki-improved action. The simulations for ${N}_{f}=4$ have been performed for pion masses in the range of 390--760 MeV and at three values of the lattice spacing, $a$, corresponding to $\ensuremath{\beta}=1.90$, 1.95, 2.10. The ${N}_{f}=2$ action includes a clover term with ${c}_{\mathrm{sw}}=1.57551$ at $\ensuremath{\beta}=2.10$, and three ensembles at different values of ${m}_{\ensuremath{\pi}}$. The evaluation of the renormalization functions is carried out in the ${\mathrm{RI}}^{\ensuremath{'}}$ scheme using a momentum source. The nonperturbative evaluation is complemented with a perturbative computation, which is carried out at one-loop level and to all orders in the lattice spacing, $a$. For each renormalization function computed nonperturbatively, we subtract the corresponding lattice artifacts to all orders in $a$, so that a large part of the cutoff effects is eliminated. The renormalization functions are converted to the $\overline{\mathrm{MS}}$ scheme at a reference energy scale of $\ensuremath{\mu}=2\text{ }\text{ }\mathrm{GeV}$ after taking the chiral limit.