Non-perturbative running of the average momentum of non-singlet parton densities

We determine non-perturbatively the anomalous dimensions of the second mome nt of non-singlet parton densities from a continuum extrapolation of result s computed in quenched lattice simulations at different lattice spacings. W e use a Schrodinger functional scheme for the definition of the renormaliza tion constant of the relevant twist-2 operator. In the region of renormaliz ed couplings explored, we obtain a good description of our data in terms of a three-loop expression for the anomalous dimensions. The calculation can be used for exploring values of the coupling where a perturbative expansion of the anomalous dimensions is not valid a priori, Moreover, our results p rovide the non-perturbative renormalization constant that connects hadron m atrix elements on the lattice, renormalized at a low scale, with the experi mental results, renormalized at much higher energy scales, (C) 1999 Publish ed by Elsevier Science B.V.