Project Area A: Perturbative Methods and Lattice Simulation in Quantum Field Theory

Perturbation Theory and Lattice Simulation are the fundamental current methods for the treatment of relativistic quantum field theories, in particular of the Standard Model of particle physics. Both methods rely to a large extent on using powerful computers with extensive storage space. The issues and questions addressed in these frameworks are, however, motivated by questions arising from current physics problems. Project Area A is devoted to the conceptual development of these two methods, which is either of intrinsic interest or of particular relevance to the applications treated in Project Areas B and C. To some extent the projects within Area A are also intertwined. For example, the development of computer algebra systems within A2 is essential for the success of A1, conversely the direction of research within A2 is strongly motivated by the physics questions arising in A1. There is also a strong link between projects A1 and A4, since in A4 results from perturbation theory are directly used to describe and interprete non-perturbative simulation data.

Important preparatory work, mainly multi-loop calculations within QCD, is being done within A1 for investigations on deep-inelastic scattering (B3) or for top production close to threshold (C3). Project A3 has provided efficient techniques for lattice perturbation theory and its results have been used also in project C1. The development of chirally improved twisted mass and chiral invariant overlap fermions within lattice QCD in project A4 is crucial to reach physically realistic situations and address questions where chiral symmetry plays an important role. The development of strategies for the automated evaluation of multi-parton cross sections in one-loop approximation, performed in the new project A5 reflects the increasing importance of LHC physics and provides the automated tools that can be employed by projects emphasising phenomenology at hadron colliders (B1, B5, C4). These considerations have motivated the following four projects:

A1 Multi-Loop Calculations and Computer-Algebraic Techniques in Quantum Field Theory
A2 Parallelization of Algebraic Program Systems
A3 Efficient Techniques for Lattice Perturbation Theory --- terminated
A4 Chirally Invariant and Twisted Mass Formulations of QCD on the Lattice
A5 Automated NLO/NLL Monte Carlo programs for the LHC --- new

Project A1 aims at developing concepts and computer algebra programs to evaluate multi-loop amplitudes and at applying the results to particle phenomenology. Methods and results are mainly directed towards QCD, some of them, however, are also of interest for electroweak interactions. Finally, predictions for certain anomalous dimensions as obtained with integrability methods and AdS/CFT correspondence will be checked with these methods in a completely different perturbative framework. These calculations are frequently motivated by phenomenological considerations some of which are integrated into this project.

The main focus of project A2 is the continued development of ParFORM and TFORM, the parallel versions of FORM designed to handle huge algebraic expressions. In particular, the combination of the two different parallelisation concepts is considered. This will help to handle computer-algebra programs of ever increasing complexity, exploiting at the same time the increasing availability of multi-core hardware. In addition we develop in this project efficient programs for the reduction to master integrals and the numerical evaluation of Feynman integrals.

The development of efficient techniques for lattice perturbation theory in project A3 has provided useful tools for the automated generation and numerical evaluation of the huge sums that appear in this context. Within the CRC/TR these results have been used in project C1.

Project A4 is concerned with investigations of twisted mass Wilson fermions and chirally invariant overlap fermions on the lattice. It is aimed to work both at zero and at non-vanishing temperature. The computations will be performed with the inclusion of a mass-degenerate up and down quark doublet as well as a mass-split strange and charm quark. All quark masses are tuned close to or at their physical values thus reaching fully realistic lattice calculations. The evaluation of correlators both in a perturbative framework in A1 and in lattice simulations in A4 gives useful insights into the structure of QCD and allows the determination of quantities like quark masses or condensates. There is also a very close link to project B3. For example A4 provides all necessary configurations with maximally twisted mass fermions on which moments of parton distribution functions (the target of B3) can be computed.

The goal of project A5 is the automated calculation of multi-parton LHC cross sections at next-to-leading order, including the summation of next-to leading logarithmic corrections through combination with parton showers. The results will be required for the interpretation of experimental measurements at the Large Hadron Collider. The automated tools developed within A5 can be employed by all projects which address the phenomenology of LHC collider processes, in particular projects B1, B5 and C4.

Last change: 8th June 2011