QCD lattice simulations with 2+1 flavours (when two quark flavours are mass degenerate) typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass and then the up-down quark mass to its respective physical value. Here we discuss an alternative method of tuning the quark masses, in which the singlet quark mass is kept fixed. Using group theory the possible quark mass polynomials for a Taylor expansion about the flavour symmetric line are found, first for the general 1 + 1 + 1 flavour case and then for the 2 + 1 flavour case. This ensures that the kaon always has mass less than the physical kaon mass. This method of tuning quark masses then enables highly constrained polynomial fits to be used in the extrapolation of hadron masses to their physical values. Numerical results for the 2 + 1 flavour case confirm the usefulness of this expansion and an extrapolation to the physical pion mass gives hadron mass values to within a few percent of their experimental values. Singlet quantities remain constant which allows the lattice spacing to be determined from hadron masses (without necessarily being at the physical point). Furthermore an extension of this programme to include partially quenched results is given.

We describe a high statistics quenched lattice QCD calculation of the moments of the polarized deep-inelastic structure functions g 1 and g 2 of the proton and neutron.Speaker at the workshop

We calculate the lower moments of the deep-inelastic structure functions of the and the meson on the lattice. Of particular interest to us are the spin-dependent structure functions of the . The calculations are done with Wilson fermions and for three values of the quark mass, so that we can perform an extrapolation to the chiral limit. ͓S0556-2821͑97͒04315-4͔PACS number͑s͒: 12.38. Gc, 13.88.ϩe, 14.40.Aq, 14.40.Cswhere ϭp•q, and r , s , t , u are kinematical tensors ͓7͔ constructed from the momentum transfer q and the polarization vector ⑀. The latter satisfies ⑀•pϭ0, ⑀ 2 ϭϪm 2 , and s ϭ Ϫiwith m being the hadron mass. Here ⑀ is the completely antisymmetric tensor with ⑀ 0123 ϭϪ1. The structure functions F 1 , F 2 , g 1 , and g 2 play the same role as for a spin-1 2 target. In the parton model, the structure PHYSICAL

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.