  Perturbative and non-perturbative results on the renormalization constants of
the fermion field and the twist-2 fermion bilinears are presented with emphasis
on the non-perturbative evaluation of the one-derivative twist-2 vector and
axial vector operators. Non-perturbative results are obtained using the twisted
mass Wilson fermion formulation employing two degenerate dynamical quarks and
the tree-level Symanzik improved gluon action. The simulations have been
performed for pion masses in the range of about 450-260 MeV and at three values
of the lattice spacing $a$ corresponding to $\beta=3.9, 4.05, 4.20$.
Subtraction of ${\cal O}(a^2)$ terms is carried out by performing the
perturbative evaluation of these operators at 1-loop and up to ${\cal O}(a^2)$.
The renormalization conditions are defined in the RI$'$-MOM scheme, for both
perturbative and non-perturbative results. The renormalization factors,
obtained for different values of the renormalization scale, are evolved
perturbatively to a reference scale set by the inverse of the lattice spacing.
In addition, they are translated to ${\bar{\rm MS}}$ at 2 GeV using 3-loop
perturbative results for the conversion factors.

High Energy Physics - Lattice;High Energy Physics - Phenomenology