Lattice perturbation theory and Renormalisation

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Information on most properties of hadrons is derived from hadronic matrix elements of local operators which can be calculated in the framework of lattice QCD. To relate the lattice results to continuum quantities the renormalisation of the operators must be known. We concentrate on the perturbative renormalisation and will compare those results with non-perturbatively obtained renormalisation constants. We plan to derive the renormalisation factors as well as the improvement coefficients for two-quark operators with more than one covariant derivative in one-loop lattice perturbation theory. (Results for operators with a single covariant derivative have already been published.) This will allow us to compute the lowest few moments of the polarised and unpolarised nucleon structure functions. The renormalisation and improvement of four-quark operators will be investigated. The results are relevant for, e.g., higher twist effects in deep inelastic scattering and weak decays of heavy quarks. Techniques will be developed to include higher-loop contributions. A new renormalisation program is planned to be developed for the first moments of generalised parton distribution functions.