Excited state artefacts in calculations of hadron 3-point functions

High energy particle physics experiments, as presently conducted, e.g., at LHC, CERN, Geneva are among the most expensive human research efforts. At LHC protons are collided at very high energy resulting in the production of very many hadrons and a few rare particles, like the Higgs boson, the decay products of which one tries to identify reliably. For any such effort it is crucial to understand well the structure of protons and the interactions between its constituents, quarks and gluons. In addition, investigating hadron structure is also a prominent research area in its own right because QCD is one of the fundamental interactions of the standard model and its non-perturbative aspects are still only little understood. Lattice QCD has the potential to provide this information and in many aspects is complementary to direct experiments which can not address all aspects unambiguously. However, lattice QCD requires to take the combined limit of large volume, small lattice spacing, huge statistics and physical quark masses. The very substantial increase of computing power in recent years has allowed to reach the large volume and large statistics limit and in this project also the physical mass limit. (Other lattice collaborations addressing similar physics questions have reached the same limits in parallel, but this is not a problem, because one needs anyway independent confirmation with several lattice actions to be sure that the remaining artifacts are really under control.) The only limit which could not be reached so far is that of small enough lattice constants, see below. Let us note that there is a fundamental difference between lattice simulations which calculate known quantities, like masses, which are thus tests of QCD and the ideas of lattice QCD (which are already generally accepted) and lattice calculations for, e.g. Generalized Parton Distributions (GPDs), Transverse Momentum Parton distributions (TMDs), Double Distributions (DDs), Distribution Amplitudes (DAs) etc. all of which parameterize different well defined aspects of hadrons. These are in fact extremely complicated objects, which combine all difficulties of relativistic quantum field theory and extremely non-linear dynamics. They provide information which one either has not yet obtained or more often cannot obtain at all from experiment. Lattice simulations proceed in two steps. First configurations are generated and than physical observables are analyzed using these ensembles. In this case the ensemble generation took place on our home built computer QPACE. The LRZ projectspr85xi and pr86te concerned exclusively the physics analysis. (orig.)