Moments of parton evolution probabilities on the lattice within the Schroedinger functional scheme

We define, within the Schroedinger functional scheme (SF), the matrix elements of the twist-2 operators corresponding to the first two moments of non-singlet parton densities. We perform a lattice one-loop calculation that fixes the relation between the SF scheme and other common schemes and shows the main source of lattice artefacts. This calculation sets the basis for a numerical evaluation of the non-perturbative running of parton densities.