Monte Carlo Study with chirally improved fermion actions

Quantum-Chromo-Dynamics (QCD) is the quantum field theory of quark and gluons and explains the confinement of these objects into hadrons. These hadrons, the nuclei baryons and the mesons, make up 99.98% of known matter. A deeper understanding of how QCD works is therefore of fundamental importance for our basic knowledge of elementary forces and particles. Although the theory itself is simple to formulate, its implications are extremely difficult to derive. They require the quantization of the gluon and quark fields which involves integration over infinitely many degrees of freedom, a formidable task, technically similar to the precise calculation of critical indices in phase transitions. A controlled approximation is to substitute continuous space-time by a grid: lattice quantum field theory. Originally a formal concept to allow regularization of the path integral quantization of fields, it has developed into a powerful tool to study QCD in ab initio calculations. Although formulated by K. Wilson already in the 70-ies only recently one has made an essential step forward in understanding the symmetries of the quark sector in the lattice formulation. The so-called chiral symmetry relates left-handed and right-handed quarks and is (better: its spontaneous breaking is) an important aspect of QCD. Newly developed formulations of the lattice quarks allow us now studies that take into account these aspects in a substantially better way. In the project we concentrate on computer calculations on large scale computers that lead to ab initio determination of hadronic properties. Since the new formulation allows to take into account chiral symmetry we can study the region of small quark masses, closer to experiment and to the chiral limit than in other approaches.

99.98% of the observable matter in the universe is made out of atoms, and almost all matter there is concentrated in the atomic nuclei in form of protons and neutrons. These particles are called hadrons and in the last century experiments have shown, that there is a large zoo of hadrons (mesons and baryons). All hadrons themselves are built out of quarks and gluons, which however cannot be observed as free particles. Quantum-Chromo-Dynamics (QCD) is the quantum field theory of quark and gluons and explains the confinement of these objects into hadrons. A deeper understanding of how QCD works is therefore of fundamental importance for our basic knowledge of elementary forces and particles. Although the theory itself is simple to formulate, its implications are extremely difficult to derive. They require the quantization of the gluon and quark fields which involves integration over infinitely many degrees of freedom, a formidable task, technically similar to the precise calculation of critical properties in phase transitions. A controlled approximation is to substitute continuous space-time by a grid: lattice quantum field theory. Originally a formal concept to allow regularization of the path integral quantization of fields, it has developed into a powerful tool to study QCD in ab initio calculations. Although formulated by Kenneth Wilson already in the 70- ies only recently one has made an essential step forward in understanding the symmetries of the quark sector in the lattice formulation. The so-called chiral symmetry relates left-handed and right-handed quarks and is (better: its spontaneous breaking is) an important aspect of QCD. Newly developed formulations of the lattice quarks allow us now studies that take into account these aspects in a substantially better way. In the project we concentrate on computer calculations on large scale computers that lead to ab initio determination of hadronic properties like masses or decay constants. Since the new formulation allows us to take into account chiral symmetry we could study the region of small quark masses, closer to experiment than in other approaches. Important first steps to a complete consideration of dynamical quarks, i.e. vacuum fluctuations of quarks and gluons, were done.