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Quantum chromodynamics (QCD) is the quantum field theory of quarks and gluons. There are two properties of QCD which are fundamental for a microscopic description of matter: 'confinement' and 'dynamical mass generation'. Confinement implies that free quarks and gluons cannot be observed in nature. Instead, they are constituents of bound states ('hadrons') as for example protons and neutrons. Inside hadrons quarks and gluons interact strongly. The dynamics of this interaction generates the constituent masses of quarks. This mechanism accounts for 99 percent of all mass observed in our daily life. Contributions from a variety of theoretical and experimental approaches are necessary to understand the origins of confinement and quark-mass generation. Within a nonperturbative functional integral framework we are working in several research fields related to this challenge.

Firstly, we study the dynamics of the strong interaction and the resulting spectrum and properties of hadrons. On the one hand, this includes 'ordinary' hadrons, i.e., baryons with three quarks and mesons with a quark-antiquark pair. On the other hand we are particularly interested in 'exotic' hadrons (glueballs, hybrids, and four-quark states) which do not fit into this picture. The study of the structure and dynamics of these states is a hot topic in contemporary hadron physics both in theory and experiment. Theoretical predictions are related to international experiments at BESIII, Belle II, LHCb, GlueX/JLab and the planned PANDA experiment at FAIR/GSI. For reviews including the work of our group see Refs. [1, 2].

Secondly, we work on our understanding of the electromagnetic structure and decays of hadrons and leptons. Photons very efficiently probe the internal structure of composite hadrons as well as the structure of elementary particles such as the muon. We are particularly interested in the low-energy behavior of form factors that reveal the meson-cloud aspects of hadrons as well as the light-by-light scattering contribution to the anomalous magnetic moment of the muon. Our efforts are related to international experiments at Fermilab (Muon g–2), JLab, HADES and the planned PANDA experiment at FAIR/GSI. Again, see Ref. [1] for a review.

Thirdly, the properties of the strong interaction at nonzero temperature and density are of tremendous interest. When heated or compressed, strong matter undergoes several phase transitions which are explored in international experiments at RHIC/BNL, ALICE/LHC, HADES and the planned CBM experiment at FAIR/GSI. In particular the fundamental properties of QCD, dynamical mass generation, and confinement change in highly nontrivial ways. We are investigating these transitions, the associated fluctuations, and the properties of hadrons in medium. The question whether a critical endpoint exists in the phase diagram of QCD is of utmost interest. For a review including the work of our group see Ref. [3].

[1] G. Eichmann, H. Sanchis-Alepuz, R. Williams, R. Alkofer, and C. S. Fischer
     Prog. Part. Nucl. Phys. 91 (2016) 1, arXiv: 1606.09602 [hep-ph]

[2] G. Eichmann, C. S. Fischer, W. Heupel, N. Santowsky, and P. C. Wallbott
     accepted for publication in Few-Body Syst., arXiv: 2008.10240 [hep-ph]

[3] C. S. Fischer
     Prog. Part. Nucl. Phys. 105 (2019) 1, arXiv: 1810.12938 [hep-ph]