Glueball properties in a Dyson-Schwinger approach

The proposed project aims at the calculation of glueball properties from first principles. Glueballs are hypothetical particles predicted by the theory of Strong Interactions, called Quantum Chromodynamics (QCD), which are, in a first approximation, bound states of gluons only. These particles have not yet been identified experimentally despite intense corresponding efforts. Future experiments such as GlueX at Jefferson Laboratory or PANDA at GSI aim to study exotic hadron spectroscopy and thus will shed light on this issue. Any quantum field theory, and therefore also QCD, can be described by Dyson-Schwinger equations (DSEs), which are an infinite set of coupled integral equations for the Green`s functions of the theory. Both, the off- and on-shell behavior of particles, are encoded in Green`s functions. Restricting to the case when particles form a bound state, the corresponding DSE reduces to a Bethe-Salpeter equation (BSE). This equation depends on other Green`s functions which fulfill in turn respective DSEs. This framework constitutes the BSE/DSE approach which is used to calculate bound-state properties in quantum field theory. This approach has been extensively used to calculate meson and baryon properties. In particular, the major part of the applicant`s PhD thesis consisted on studying the spectrum and electromagnetic properties of spin-3/2 baryons in this framework. In this thesis, a first step in the calculation of glueballs in the BSE/DSE approach was taken by proposing a BSE for a two-gluon bound state. The current project is based on this result. In the 24 months in Gießen (Germany) the goal is to solve the two-gluon BSE and in this way obtain the low-lying glueball spectrum. Several models for the undetermined but required Green`s functions will be used, with the intention to study the model dependence of the results. The importance of terms neglected in the above-mentioned equation will also be studied. The group of Prof. Fischer in Gießen has experience on glueball calculations in this approach as well as connections with GSI/FAIR, where experiments aiming at glueball detection are planned. The research during the return phase in Graz will be focused on the mixing of glueballs with mesons and comparison with experimental results as Prof. Alkofer`s group is one of the leading ones in the field of meson and baryon studies using BSE/DSEs.

Most of the matter content of the Universe is composed of baryons. Baryons are composite particles, formed by three elementary particles called quarks and bound together by the strong interaction. The strong interaction is mediated by other elementary particles called gluons, so that one usually says that the three quarks in a baryon are held together by the gluons. This system is at first sight analogous to an atomic system, where protons with positive charge and electrons with negative charge are bound together by the electromagnetic interaction. At the fundamental level, the electromagnetic interaction is described by particles called photons, which do not carry any electric charge themselves. It is here where a difference between the electromagnetic and the strong interaction appears. Whilst an electromagnetically bound system formed by photons only cannot exist, since they carry no electric charge, gluons carry a strong-interaction charge (called colour charge) and therefore it is possible that bound states formed by gluons only exist. These hypothetical particles are called glueballs.This project aimed at the calculation of glueball properties from first principles, that is, using the theory of strong interactions. This theory is called Quantum Chromodynamics (QCD).More specifically, the goal was to be able to calculate the masses of such bound states of gluons and some of their basic properties. Note that these particles have not yet been identified experimentally despite intense corresponding efforts. Future experiments such as GlueX at Jefferson Laboratory or PANDA at GSI aim, among other things, to study the properties of those exotic particles. But for the moment, any theoretical predictions, such as the ones provided by this project, are of tremendous value for the scientific community.The main result of the project has been a successful calculation of the lightest glueball particles (the so-called scalar and pseudoscalar glueballs). The results obtained are in very good agreement with those obtained using different methods, which increases our confidence in the method. Note also that due to quantum effects, glueballs will necessarily mix with other particles as, for example mesons (which are particles formed by one quark and its antiparticle) and, therefore, any theoretical method must be able to account for this. Progress in this direction has been made too and published in several high-impact journals, and will be continued thanks to a newly-funded FWF project.