Meson electroproduction and resonances in the BSE formalism

Based on functional approaches to the theory of the Strong Interaction, Quantum Chromodynamics, the production process of elementary particles in the reaction of an electron with a nucleon will be studied. The aim is to understand how the relevant scattering amplitudes are related to the spectrum of hadrons, the strongly-interacting elementary particles. Related experiments are performed in sever- al laboratories in Europe, the USA and China. The outcome of these experiments is undoubtedly de- termined by the underlying theory, Quantum Chromodynamics. However, the properties of the Strong Interaction, which dominate in these processes, prevented until now first-principle calculations. Within this project it is planned to develop the missing necessary theoretical and computational framework to study the interplay between hadron structure and these so-called electroproduction scattering ampli- tudes. In view of the fact that quark models predicted always more states then found in experiments (a fact which goes under the name of the ``missing resonances problem) such studies are timely and highly interesting. The theoretical framework to be used in this project is a combination of non-linear and linear integral equations which are valid in all Quantum Field Theories, that is, theories describing elementary parti- cle physics. These equations describe the correlations of elementary fields as well as the bound states of a theory. They have proven to be a very powerful tool for the investigation of the phenomenology of elementary particles and are, for this reason, actively studied by several groups around the world. Building on existing results for hadrons in a well-studied approximation to the above mentioned inte- gral equations the electroproduction amplitudes will be calculated. As these calculations are very likely not solving the ``missing resonances problem this project is intended to contribute significantly to the development of superior approximation schemes. It is planned to take the necessary steps to make the calculation of hadron properties from the dynamics of the underlying theory only, i.e., without the need for model input, possible. By detailed comparison of the obtained results to experiments and in collaboration with other theoretical and experimental groups a significant contribution to the resolution of the ``missing resonances problem and therefore for our understanding of elementary particles might be provided.

Meson electroproduction is an experimental method to study the properties of a class of particles called hadrons. Among hadrons, the most relevant for our everyday lives are the proton and the neutron. Hadrons split in two large families called mesons and baryons, protons and neutrons being members of the latter. In the most basic description of them, mesons are formed by two elementary particles, namely a quark and an antiquark, whilst baryons are formed by three quarks. Quarks and antiquarks are bound together by gluons and the way the formation of those bound states works and what their properties are is determined, in principle, by the theory of the Strong Interaction, Quantum Chromodynamics (QCD). The theory is so complicated that since its invention in the 70s many different approximation schemes have been developed in order to study its implications. In this project we used a particular approximation scheme based on a system of equations called Bethe-Salpeter (BSE) and Dyson-Schwinger (DSE) equations, which form a combination of non-linear and linear integral equations which are valid in all Quantum Field Theories, that is, theories describing elementary particle physics. One of the goals of the project was the calculation, from QCD and using DSEs and BSEs, of the electromagnetic properties of the proton and neutron, but also of some of their excited states (which form the so-called baryon octet and baryon decuplet). What these properties describe is the way a photon (the carrier of the electromagnetic force) interacts with hadrons and are therefore crucial for the study of meson electroproduction since in those processes baryon excitations are generated by scattering electrons off protons or neutrons, with electrons and baryons interacting only electromagnetically. The results of these investigations have been published in peer-reviewed international journals and presented at several national and international conferences. Another major goal of this project was to study the influence on hadron properties of so-called non-valence quark effects. By valence quarks we refer to the pair quark-antiquark or the three quarks that we described above as those forming the bound state. However, it is known that, due to the strong interaction, pairs of quarks and antiquarks are continuosly formed inside hadrons and these are called non-valence quarks. Their presence impacts, among other things, the hadron's electromagnetic properties since a photon interacting with a hadron can do so by interacting with the valence quarks individually but also with the non-valence ones. We have successfully, for the first time in the DSE/BSE approach, included those non-valence contributions in our calculations of electromagnetic properties. This is a ground-breaking step towards a realistic calculation of hadron properties from the QCD theory.