Field-theoretical aspects of Brout-Englert-Higgs physics

• Applicant: Dr. René Sondenheimer
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2018 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 415504349

The discovery of the Higgs boson at the Large Hadron Collider confirmed our current picture of the interactions between the elementary building blocks of our Universe. The theoretical prediction as well as the experimental confirmation of the Higgs mechanism and the standard model of particle physics counts as a paradigm for the fruitful interplay between both. Despite the unprecedented achievement of the standard model in explaining the interactions between the currently known elementary particles, it has some shortcomings. For instance, it does not provide a reasonable explanation for neither the origin of dark matter nor the hierarchy of the coupling strengths and masses of the various particles. Furthermore, the standard model becomes inconsistent from a mathematical viewpoint at high energy scales due to the so-called triviality problem. Therefore, the standard model is only considered as an effective theory which has to be replaced by a more fundamental model. Also many of the proposed standard-model extensions rely on a generalized Higgs mechanism. Thus, a comprehensive understanding of this key ingredient in the formulation of these theories is mandatory. The objective of the project Field-theoretical aspects of Brout-Englert-Higgs physics is to obtain a deeper and thorough understanding of a consistent mathematical formulation as well as to uncover the resulting field-theoretical implications for the particle spectrum of the theory. In order to calculate the mass spectrum, various tools are available like perturbation theory, lattice simulations, or functional methods. In particular, same mass spectrum for the particles occurring in the standard model is obtained from the different methods. Moreover, Fröhlich, Morchio, and Strocchi developed a formalism which connects the results of the different methods in a surprising and nontrivial way and provide a proper gauge-invariant definition for the particle spectrum. However, it turns out that the situation is more involved for theories beyond the standard model. Recent lattice data show a mismatch between the particle spectrum predicted by perturbation theory and the one obtained from lattice simulations in a specific model. In order to get a more comprehensive understanding of such a possible mismatch, the method developed by Fröhlich, Morchio, and Strocchi shall be generalized and applied to various standard-model extensions for the first time. This will provide further constraints on existing models but will also offer new routes for model building. In addition, innovative and powerful renormalization group techniques will be used as a complementary tool to further examine the results. These allow for a continuous transition from microscopic quantum fluctuations to macroscopic observable degrees of freedom of a theory and thus will add another viewpoint on the mass spectrum.

• DFG Programme: Research Fellowships
• International Connection: Austria
• Host: Professor Dr. Axel Torsten Maas