Baryon-Photon interactions in a covariant Faddeev approach

The main objective of this proposal is to develop further an understanding of the nucleon structure and shape by investigating electromagnetic interactions of baryons within an approach based on the underlying theory of quarks, i.e. Quantum Chromodynamics (QCD). The electromagnetic transition of the Delta baryon to the nucleon is sensitive to the shape of the nucleon. Accordingly, this transition has been studied in a number of models as well as in QCD lattice calculations with the aim to relate the violaton of spherical symmetry to the quark substructure of the nucleon. Hereby it has been noted that issues such as confinement, dynamical chiral symmetry breaking and the formation of highly relativistic bound states are important. Exactly these issues can be understood from and related to the properties of the non-perturbative propagators of QCD. On the other hand, these propagators have been used to describe the nucleons` quark core within a Poincare-covariant Faddeev approach. Based on the recently obtained results within this approach the proposed investigations aim at deepening the understanding of the nucleon be getting more insight into the structure and the shape of the Delta. If these studies support the recently obtained results then, in addition, mesonic (especially pionic) effects will be included in subsequent calculations. It has to be emphasized here that in two important respects the proposed investigations differ from most quark model studies of the nucleon. First, the resulting nucleon state is a four-momentum eigenstate. This is simply due to the fact that Poincare covariance has been respected in every step. Second, there are no parameters adjusted to any observable. Starting with non-perturbative quark propagators this is simply not necessary. Especially, one inherits the scale generated by dimensional transmutation when non-perturbatively renor- malizing QCD. Observables to be calculated include baryon masses, radii, magnetic moments and elastic as well as transition form factors. Comparing these quantities to experimental and lattice data as a function of the current quark mass will allow on the one hand to understand the quality of the approach and on the other hand the role of explicit and dynamical chiral symmetry breaking in the quark substructure of baryons.

This project furnished important contributions to the understanding of the structure and form of nucleons. For this the electromagnetic interactions of baryons have been investigated in an approach based on the theory of Strong Interactions, i.e. Quantum Chromodynamics (QCD). The electromagnetic transition of the Delta baryon to the nucleon which is sensitive to the shape of the nucleon has been studied in a relativistic Faddeev approach. This allowed definitive conclusions on the deviation of nucleons and Delta baryons from the spherically symmetric form and on the relation of this violation of spherical symmetry to the quark substructure of the nucleon.The Strong Interaction is described by QCD and determines the behavior of a class of particles called hadrons. To these belong also the building blocks of atomic nuclei, the nucleons (protons and neutrons). Both nucleons are the lightest in a sub-class of hadrons which are named baryons. The essential characteristic of baryons is that their structure is dominantly given by three quarks. However, their actual structure is far more complicated and is the subject of many experimental and theoretical investigations. Especially the electromagnetic transition of the Delta baryon to the nucleon has been studied in a number of models and computer simulations in lattice QCD with the aim to understand the observed violation of spherical symmetry in terms of the quark substructure of the nucleon. It became evident that phenomena as quark confinement, dynamical mass generation (by breaking of chiral symmetry) and the formation of highly relativistic bound states are important in this respect. Based on these results the ``quark core of baryons was described in a Poincaré covariant Faddeev approach (i.e. with the help of a relativistic three-body equation). The calculated observables include baryon masses and radii, magnetic moments and elastic as well as transition form factors. Comparing these quantities to experimental and lattice QCD data as function of the quark masses did allow conclusions on the form of baryons as well as a deepened understanding of the role of explicit and dynamical chiral symmetry breaking in the quark substructure of baryons.