Final Report Summary - PRECISION LATTICEQCD (Precision lattice QCD calculations) It is estimated the human body is made up of about 100 trillions cells, and it is about the same number of atoms which make up a cell. For long time it was thought atoms are the smallest indivisible building block of matter, though since Rutherford's experiments we know atoms have a rich inner structure, too. Today we know of 114 different (confirmed) chemical elements, and that an atom is more or less empty and concentrates all its mass at the centre, the nucleus. If one looks at a much smaller scale, one finds the nucleus has a substructure itself. It consists of protons and neutrons, held together by the nuclear force. This force is a residuum of the strong interaction, which is so strong that equally charged protons are held together at a few femtometres. As part of the Standard Model of particle physics, Quantum Chromodynamics (QCD) is the theory which describes this interaction. QCD is a quantum field theory with quarks and gluons as their elementary degrees of freedom, and, in QCD terms, protons and neutrons are hadrons which are bound states of strongly interacting quarks and gluons. At large energies QCD is asymptotically free and so perturbative calculations are applicable. This has allowed for many theoretical predictions which have all successfully been confronted with experiment. Outside of the perturbative regime, however, QCD becomes very complex and theoretical predictions are highly non-trivial to obtain. A theoretical framework that can provide nonperturbative estimates for many quantities is lattice QCD. It is a discretised version of QCD in Euclidean space-time (the lattice), whose input parameters are only those of QCD, the strong coupling and the quark masses at some energy scale. That is, no model assumptions are in place. The identifying feature of lattice QCD is that it allows to perform Monte Carlo (MC) calculations, like, for instance, of hadron masses or moments of structure functions. Such numerical calculations are fully nonperturbative and all systematic uncertainties can be controlled by taking the limits of vanishing lattice spacing, infinite volume and physical quark masses. In recent years, lattice QCD has become sufficiently mature to provide estimates for quantities of immediate relevance for experimental programs, where these are either not accessible or difficult to measure. It has been the main objective of this research project to use this progress to further unveil the structure of hadrons and to provide precision measurements of the strong coupling constant. This project has been thus a welcome add-on to the existing collaborative research centre on Lattice Hadron Physics of the University of Regensburg and Wuppertal. Its research objectives and those of the centre are complementary, in particular on hadron structure functions, and has allowed the researcher to pursue his research together with his students (PhD and master) independently of the centre. Due to the complementary nature there was also plenty of fruitful interactions among the local lattice QCD and the researcher in charge of this project. This project was of great help to integrate the researcher into the existing group.From the beginning of the project, lattice data has been produced using computing time on different parallel supercomputing systems. There is now a large set of data for the strong coupling constant in the Minimal MOM scheme for different numbers (Nf) of fermion flavors, as well as data for moments of various baryon distribution amplitudes (DAs), and also data for moments of nucleon generalised parton distributions (GPDs). This project also introduced a new method into the field to treat hypercubic lattice artifacts, which are inherent to many lattice observables. This new approach has been successfully tested within the project and will now be further investigated as part of a new project for the renormalization of hadronic operators.Part of the data has been published already in peer-reviewed journals with a high impact. Further results will be appear in due time.Lattice QCD as a research field has a high international profile and European research groups have always been among the groups working at the so-called "precision frontier". The research of this project profits from recent progress done in the field and will be of great asset for the European physics community. Furthermore, this project is run with the active participation of students, who have to master state-of-the-art computational methods to perform these advanced numerical studies. These skills are of great potential value also for the European industry which commonly attracts a large fraction of those students.
