Particle Theory Group
Institute for Theoretical Physics
University of Leipzig
Perturbative QCD lattice calculations
Our group has initiated a program to calculate the hadronic structure functions on a lattice. The numerical simulations to compute the forward nucleon matrix elements are done on the parallel computer Quadrics. In order to extract the physical content of these computations one has to calculate the renormalization or Z-factors. This can be done non-perturbatively or perturbatively. The perturbative calculations are performed in Leipzig.
We have calculated the Z-factors for the first, second and third moments of the quark operators occuring in the corresponding operator product expansion in one-loop approximation on a hypercubic lattice based on the Wilson action in quenched form. To this aim we have developed a symbolic code written in Mathematica. Taking the symbolic Feynman rules for a specific operator as input it computes analytically its lattice and continuum matrix elements between quark states.
In order to reduce the dependence of the results on the lattice spacing (a) so-called improved actions have been proposed. We have recalculated the Z-factors for the local scalar, pseudo scalar, vector, axial vector and tensor (h1) currents in the scheme of the Sheikholeslami-Wohlert action accompanied with rotations of the quark fields. The mass independent renormalization scheme has been exploited and the corresponding improvement coefficients have been computed.