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Effects of additional scalar decaplet in the RG evolution of the running gauge couplings in the minimal SO(10) grand unified theory
Press, Pavel ; Malinský, Michal (advisor) ; Sousa da Fonseca, Renato Miguel (referee)
Effects of additional scalar decaplet in the RG evolution of the running gauge couplings in the minimal SO(10) grand unified theory Pavel Press Abstract We begin the thesis with the fundamentals of Lie groups and algebras. Then we introduce basic concepts regarding classical field theory and gauge theory. We formulate the Goldstone theorem and with it we describe the Higgs mechanism. We quantize the classical fields and outline the calculations within the quantum field theory. Using the renormalization procedure we derive the equations for the running coupling of a general gauge theory. We calculate the running gauge couplings in the Standard model and motivate theories beyond it. In particular, we will study the Grand Unified Theories. We discuss a specific Higgs sector with a 45 ⊕ 126 Higgs field. In order to have a more realistic theory we add a scalar Higgs decaplet and study its effects on the running couplings. Finally we discuss the implications of the decaplet for the proton decay. Keywords Quantum field theory, gauge field theory, running couplings, grand unification, proton decay 1
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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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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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