Field-theoretical aspects of Brout-Englert-Higgs physics
Final Report Abstract
The objective of this DFG research fellowship was to obtain a deeper and thorough understanding of a consistent field-theoretical formulation of theories with a Brout-Englert Higgs mechanism. The Brout-Englert-Higgs mechanism is a central ingredient in the theoretical formulation of the standard model of particle physics. Its most famous prediction is the existence of the Higgs boson which was discovered at the Large Hadron Collider in 2012. Further, the Brout-Englert-Higgs mechanism also plays a crucial role in many extensions of the standard model aiming to solve unanswered fundamental questions in physics. For instance, grand unified theories are such a standard model extension trying to unify three fundamental forces of nature, namely electromagnetism, the weak nuclear force, and the strong nuclear force into one single force at high energies, and predict further Higgs particles. In order to make adequate predictions for experiments, the properties of the particle spectra of such theories have to be calculated carefully. Surprisingly, different methods can provide different results for the mass spectrum of a given theory with a Brout-Englert-Higgs mechanism. This circumstance can be traced back to the fact that the Brout-Englert-Higgs mechanism is often associated with a symmetry reduction in the physical system. However, this point of view is questioned by field-theoretical ambiguities which actually forbid gauge symmetry breaking on mathematical grounds. For the standard model, all computational methods predict the same spectrum but for theories with a different gauge symmetry, lattice simulations find a qualitatively different spectrum from the standard perspective of gauge symmetry breaking and performing perturbative expansions. In a seminal work, a formalism was developed that connects the results of the different methods in a surprising and nontrivial way within the standard model and provided a proper gauge-invariant definition of the particle spectrum. Here, we generalized this method to standard model extensions with arbitrary gauge symmetries in a systematic fashion for the first time. The main result of this project can be summarized as a rethinking of the Brout-Englert-Higgs mechanism in terms of a duality relation connecting the particle spectra of different gauge theories. We did a systematic study of different gauge theories with scalar fields in different representations and worked out the mappings of particles in different theories in detail. The advantage of this duality is given by the fact that albeit it might be difficult to compute the properties of a particle in one theory, it might be easier to perform the calculations for the dual particle in another model. By this, we were able to derive novel constraints on proposed standard model extensions and to rule out classes of grand unified theories. In addition, we investigated potential phenomenological implications from this new view point for the standard model. We were able to demonstrate that properties as masses and decay widths of the particles remain the same by this approach which is in accordance to the current successful description of experimental observations. However, small quantum fluctuations can be altered which might have impact on future collider physics. This is important because any deviation from the conventional viewpoint could be misinterpreted as potential new physics beyond the standard model while being just normal but nontrivial standard model effects that have to be investigated in more detail.
Publications
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Scheme dependence of asymptotically free solutions. Eur. Phys. J., C79(6):463
Holger Gies, René Sondenheimer, Alessandro Ugolotti, and Luca Zambelli.
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Analytical relations for the bound state spectrum of gauge theories with a Brout-Englert-Higgs mechanism. Phys. Rev. D, 101(5):056006
René Sondenheimer
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Gauge-invariant description of the Higgs resonance and its phenomenological implications. Phys. Rev. D, 102:113001
Axel Maas and René Sondenheimer
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Testing the mechanism of lepton compositeness. SciPost Phys., 10:062
Vincenzo Afferrante, Axel Maas, René Sondenheimer, and Pascal Törek.
