Chiral symmetry properties of hadron spectra

Quantum-Chromo-Dynamics (QCD) is at present considered to be the fundamental theory of quark and gluons, the building blocks of all hadrons, which make up almost all of the known matter. The theory ought to explain two important experimentally observed features: permanent confinement of the building blocks and chiral symmetry breaking. Confinement means, that quarks and gluons cannot be observed as free particles. Chiral symmetry is a symmetry for the theory in the limit of vanishing quark masses. The real quark masses are not exactly vanishing but small and the chiral symmetry appears to be broken spontaneously. This breaking is responsible for the existence of the light pi-mesons. Starting from the fundamental QCD Lagrangian there are two theoretical paths to compute the properties of hadrons. The traditional path is a perturbative expansion. However, the mentioned issues cannot be derived with this method. One has to follow a non-perturbative approach. The only such approach satisfying further conditions (like gauge invariance) is the formulation of the theory on a space-time lattice and the quantization as a path integral with help of computer methods. This approach allows us to determine the spectrum of hadrons from basic principles. However, computing numbers is on one hand restricted in its range of applicability due to the enormous demand on computer resources. On the other hand it does not necessarily improve the physical "understanding" of the phenomena observed. Such an understanding leads to the modelling of the physics by approximate, but efficient concepts. Such a model based on confining potentials and Goldstone boson exchange for baryons has explained a significant level ordering interchange of excited baryons. Another idea suggests the effective restoration of chiral symmetry for high-lying hadrons. We want to carefully study the hadron spectrum (mesons and baryon excited states) from ab initio lattice computations in order to identify these effects and better understand the underlying mechanisms.

We have computed the masses and properties of hadrons and excitations of hadrons with new methods and using super-computer resources. In particular we have progressed in our understanding of the role of the elusive chiral symmetry of Quantumchromodynamics (QCD). QCD is at present considered to be the fundamental theory of quark and gluons, the building blocks of all hadrons, which make up almost all of the known matter. The theory ought to explain two important experimentally observed features: permanent confinement of the building blocks and chiral symmetry breaking. Confinement means that quarks and gluons cannot be observed as free particles. Chiral symmetry is a symmetry for the theory in the limit of vanishing quark masses. The real quark masses are not exactly vanishing but small and the chiral symmetry appears to be broken spontaneously. This breaking is responsible for the existence of the light pi-mesons (Pions). In the project we have employed the formulation of the theory on a space-time grid. The quantization can then be done via a high-dimensional integral with help of computer methods, so-called Monte Carlo methods. This approach allows us to determine the spectrum of hadrons from basic principles. New techniques allowed us to study not only the ground states (like the Proton and the Pion) but also excitations of higher mass. Computing numbers is on one hand restricted in its range of applicability due to the enormous demand on computer resources. On the other hand it does not necessarily improve the physical "understanding" of the phenomena observed. Such an understanding leads to the modelling of the physics by approximate, but efficient concepts. Our ab initio lattice computations allowed us to better understand the underlying mechanisms and the relevance of models that try to approximately describe certain intriguing features like the effective restoration of chiral symmetry for high-lying hadrons.