Conformality, Spontaneous Symmetry Breaking and Mass Hierarchies

Who: Matin Mojaza (CP3-Origins)
When: Monday, June 2, 2014

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Matin Mojaza‘s advisor was Francesco Sannino. Co-advisor was Claudio Pica.


Gauge theories with scalar fields are generically plagued with different types of ‘instabilities’ at the quantum level. Some of these are also present in the current standard model of particle interactions, where the origin of mass is explained through the existence of a scalar field: The Higgs-field. Due to the issues with the Higgs-field the search for alternative descriptions of the origin of mass and the recently discovered Higgs-particle has received and still receives a lot of attention. It is the hope that a resolution will simultaneously explain, or provide clues about other puzzles of Nature, such as the occurrence of dark matter in the Universe.

In this work the problems arising in quantized scalar field theory are carefully treated and discussed. The phase diagram of gauge theories is outlined and the concept of the scalar conformal window is introduced, as a counterpart to the conformal window known from the phase diagram of purely fermionic gauge theories. Theories within a conformal window share the property of exhibiting conformal invariance at long-distances. The phenomenological interest in such theories relies in the fact that a replacement of the Higgs-sector of the standard model with a near-conformal sector might be able to resolve the issues of the Higgs-field. Opposed to the familiar fermionic conformal window, the entire scalar conformal window is well-defined within perturbation theory. The machinery developed here to delineate the scalar phase diagram is in particular used to study conformal phase transitions and the associated near-conformal dynamics in certain models. An interesting aspect is that supersymmetry can with some fine-tuning be realized as an emergent phenomenon in several of the exhibited examples.

Our ultimate goal of understanding new aspects of quantum field theory is to construct viable novel models of Nature. Based on our studies, a new idea is proposed as a resolution to the naturalness issue of the Higgs-field, dubbed perturbative natural conformality (PNC). In PNC extensions of the standard model the electroweak vacuum is generated by the Coleman-Weinberg mechanism and at the same time the naturalness issue is delayed to higher scales by the Veltman condition. Through a search for viable PNC models, one candidate model is found that passes the quite strict PNC test, and at the same time predicts the observed Higgs-boson mass. This PNC model is surprisingly simple; it requires the existence of another scalar boson with a mass of around 541 GeV, also predicted by the PNC criteria, which must couple to the Higgs-field and an unspecified new fermionic sector.

The PhD thesis is available as a PDF file.