We investigate the nonperturbative renormalisation of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields. These include operators which are relevant to the calculation of moments of hadronic structure functions. The computations are based on Monte Carlo simulations using quenched Wilson fermions.

We describe the methods used to calculate the nucleon structure functions from quenched lattice QCD, and present some results for moments of the polarized and unpolarized structure functions.

Our previous calculation of the spin-dependent structure function g 2 is revisited. The interest in this structure function is to a great extent motivated by the fact that it receives contributions from twist-two as well as from twistthree operators already in leading order of 1/Q 2 thus offering the unique possibility of directly assessing higher-twist effects. In our former calculation the lattice operators were renormalized perturbatively and mixing with lowerdimensional operators was ignored. However, the twist-three operator which gives rise to the matrix element d 2 mixes non-perturbatively with an operator of lower dimension. Taking this effect into account leads to a considerably smaller value of d 2 , which is consistent with the experimental data.

A fully non-perturbative lattice determination of the up/down and strange quark masses is given for quenched QCD using both, O(a) improved Wilson fermions and ordinary Wilson fermions. For the strange quark mass with O(a) improved fermions we obtain m M S s (µ = 2 GeV) = 105(4) MeV, using the interquark force scale r 0 . Due to quenching problems fits are only possible for quark masses larger than the strange quark mass. If we extrapolate our fits to the up/down quark mass we find for the average mass m M S l (µ = 2 GeV) = 4.4(2) MeV.