Spectroscopy of SU(3) gauge-scalar theories

Elementary scalars interacting with gauge bosons are abundant in particle physics. If these theories exhibit a Brout-Englert-Higgs effect, analytical predictions exists for their spectrum. Recently, it was found using numerical simulations that conventional analytical methods may be insufficient for some of these theories. Fortunately, recently developed advanced analytical tools seem to be capable to do so. However, these advanced methods have only been tested for some cases, where qualitative differences appear. And also in these case, the numerical simulations have only covered a subset of possibilities and systematic error sources. Therefore, the aim of this project is to improve this situation. To this end, two different types of scalars will be simulated. The spectrum of observable particles, which may deviate from those of the elementary ones, will be obtained. The two theories are on the one hand one of the already tested ones, but aiming at a much wider range of possibilities and systematic reliability. The second theory has not been investigated so far at all, and genuine new results can be expected. The advantage is that large parts of the simulation codes can be shared between both theories, giving rise to many synergies in code development and analysis strategies. In total, two independent goals are pursued. The first is that the spectrum of both theories should be established in a reliable way from the simulations. The second is to check the analytical predictions, and thus test whether the new methods are indeed reliable, especially as the predictions for these two theories differ qualitatively between the conventional and the new approach.

This project has opened up a fascinating view on Brout-Englert-Higgs physics in so-called grand-unified theories. These are theories aimed at unifying the fundamental forces of nature and would, e.g., explain why the hydrogen atom is electrically neutral. This is so far an unexplained feature of nature, but essentially for chemistry and biology to work in a way which sustains human life. There have been three major outcomes. Two are related to this idea that all the fundamental forces are obtained from a common origin. One result is structural and one is about the observed particles. The structural aspect cleared how such theories can be realized. Before the project, it was not yet clear how such theories can find a unique realization. There had been two options. One would be a mixture of all possible realizations, and one would have been a selection of one realization. The results of large-scale simulations prefer strongly that one is selected, and how this selection takes place. Concerning the observed particles, there already existed hints from previous investigations that the actual observable particles strongly differ from those which are usually expected. Again, numerical simulations have confirmed this outcome, and require to rethink how a unification of forces can be possible at all. Especially, unexpected particles have shown up, which need an explanation. Such an explanation appears possible with a scenario, the so-called Fröhlich-Morchio-Strocchi approach, which is in agreement with the obtained results from simulations, in contrast to previous ideas. It is also this approach which is the center of the third result. Originally undertaken as a preliminary test of methods, it showed that consistency of the theory requires that even within the standard model of particle physics genuine new observations may be possible at the experiments at CERN. Confirming these observations would shift our understanding of particle physics tremendously. This will be investigated in follow-up studies, and eventually be compared to experiments.