# Subproject A3: Efficient techniques for lattice perturbation theory

Project leader:

Prof. Dr. Ulrich Wolff, Institute of Physics, Humboldt-University of Berlin

Prof. Dr. Johann Kuehn, Institute of Theoretical Particle Physics,
Karlsruhe Institute of Technology (KIT)

In order to bring precision simulations such as those in project B2 into contact with continuum physics perturbative calculations on the lattice are necessary even though the the goal of the calculations itself is inherently non-perturbative. This concerns in particular the matching of different renormalization schemes at high energies and the calculation of improvement coefficients, which are needed to optimize the discretisation. Due to the reduced symmetries on the lattice perturbation theory is much more complicated than in the continuum where the powerful tool of dimensional regularization is available. Within the ALPHA collaboration two-loop calculations for the coupling have been performed, which on the lattice requires a considerable effort.

Obviously more perturbative results are needed in order to make optimal use of the expensive lattice simulations. We want to use the framework of the SFB to transfer methods of automated algebraic manipulation in perturbative calculations from the continuum to the lattice. While previous calculations by the ALPHA collaboration were done entirely 'by hand' we now aim at the development of a 'tool-box' to make these calculations more efficient. After reproducing the known results the goals are for example the coupling for the Iwasaki action or twisted mass QCD, the extension of one-loop calculations to the two-loop level as well as the calculation of new quantities.

Last Change: 16th June 2010