# 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

**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