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Pseudo-Goldstone bosons in grand unified theories
Jarkovská, Kateřina ; Malinský, Michal (advisor) ; Beneš, Petr (referee)
The minimal renormalizable SO(10) Higgs model with the unified gauge sym- metry broken down by the adjoint representation 45S is known to suffer from tachyonic instabilities along all potentially realistic symmetry breaking chains. Few years ago, this issue has been identified as a mere relic of the tree-level cal- culations and the radiative corrections to the masses of the pair of the "most dangerous" pseudo-Goldstone scalars transforming as (8, 1, 0) and (1, 3, 0) with respect to the SU(3)c × SU(2)L × U(1)Y Standard model gauge group were com- puted. Remarkably enough, it turns out that in the minimal potentially realistic renormalizable realization of the model - consisting of 45S ⊕ 126S scalar and 45G gauge fields - there is third pseudo-Goldstone scalar, a full singlet with respect to the Standard model gauge group that, until recently, happened to escape the community's attention. In this thesis we computed the one-loop corrections to its mass employing two different methods within the effective potential approach. In both cases we reduced the complexity of our calculations by decomposition into the Standard model irreducible representations. In the end, we cross-checked the resulting formulae in four distinct symmetry breaking limits in which the pseudo- Goldstone mass was degenerated with those of...
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Aspects of renormalization of spontaneously broken gauge theories
Hudec, Matěj ; Malinský, Michal (advisor) ; Beneš, Petr (referee)
In this thesis, we use the Coleman-Weinberg effective potential for computing the radiative corrections to scalar masses in six simple models of the quantum field theory. We probe, for example, the theory of two scalar fields, simple generalizations of the Abelian Higgs model or some classic extensions of the Standard Model. A common feature of all the theories considered is the existence of (at least) two mass scales different in order of magnitude. Being motivated by the hierarchy problem, we study mainly the sensitivity of light scalar masses on the radiative corrections induced by the heavy fields in relevant Feynman loops. We demonstrate that while the masses of scalars with zero VEV obtain corrections proportional to the masses of the heavy fields, in theories with the spontaneous symmetry breakdown is the Higgs mass always governed by the corresponding ordering parameter, i.e., by its vacuum expectation value. For the Standard Model, understood as an effective field theory, this implies that the Higgs boson mass is as stable with respect to the effects of possible new physics on very high energies as the masses of the leptons, quarks, W and Z bosons. Powered by TCPDF (www.tcpdf.org)
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Quantum aspects of grand unified theories
Gráf, Lukáš ; Malinský, Michal (advisor) ; Smetana, Adam (referee)
In this thesis we focus on Grand Unified Theories based on the SO(10) gauge group and, in particular, on the viability of the minimal nonsupersymmetric SO(10) models. Technically, this amounts to a detailed assessment of their vac- uum stability and related (non-)tachyonicity of their scalar spectrum. It turns out that the one-loop scalar mass corrections are important for elimination of the tachyonic behaviour of certain pseudo-Goldstone bosons. In this work these issues are briefly reviewed and two distinct methods for the calculation of the critical radiative corrections are discussed. More specifically, besides the revision of the effective potential approach to the 45 ⊕ 16 Higgs model also the standard perturbative theory method is employed for this purpose. The latter approach is particularly suitable for the more realistic 45 ⊕ 126 Higgs model since it appears to be practically impossible to construct the corresponding effective potential in that case. Consequently, diagrammatic methods are used to calculate the SO(10)- invariant leading scalar quantum correction to the problematic pseudo-Goldstone masses in the 45 ⊕ 126 model. 1
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