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Quantum aspects of particle physics models with extended gauge symmetries
Sýkorová, Kateřina ; Malinský, Michal (advisor)
In this thesis, we study quantum aspects of the minimal renormalizable SO(10) Grand Unified Theory with the scalar sector consisting of 45 ⊕ 126 ⊕ 10C. It is an interesting candidate for a theory describing physics beyond the Standard model which has the potential to allow for proton lifetime prediction with Plank- scale-physics-induced theoretical uncertainties confined within the expected one- order-of-magnitude experimental proton lifetime improvement window. With the complete information about the numerical one-loop scalar mass spec- trum and analytical one-loop beta functions of all the dimensionless scalar cou- plings, we formulate consistency criteria that every viable region of the parameter space must satisfy; namely, we require the existence of a stable Standard-model- like vacuum, unification of gauge couplings and robustness of perturbative calcu- lations. Only narrow parameter space regions around symmetry breaking chains with SU(4)C × SU(2)L × U(1)R or SU(3)c × SU(2)L × SU(2)R × U(1)B−L intermedi- ate stages are demonstrated to be potentially realistic. Detailed analysis of the SO(10) Higgs model with 45⊕126 scalar sector indicates a preference for the for- mer option, mainly due to increased perturbative instability and phenomenologi- cally unsuitable values of energy scales predicted in the...
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Quantum aspects of particle physics models with extended gauge symmetries
Sýkorová, Kateřina ; Malinský, Michal (advisor) ; Beneš, Petr (referee) ; di Luzio, Luca (referee)
In this thesis, we study quantum aspects of the minimal renormalizable SO(10) Grand Unified Theory with the scalar sector consisting of 45 ⊕ 126 ⊕ 10C. It is an interesting candidate for a theory describing physics beyond the Standard model which has the potential to allow for proton lifetime prediction with Plank- scale-physics-induced theoretical uncertainties confined within the expected one- order-of-magnitude experimental proton lifetime improvement window. With the complete information about the numerical one-loop scalar mass spec- trum and analytical one-loop beta functions of all the dimensionless scalar cou- plings, we formulate consistency criteria that every viable region of the parameter space must satisfy; namely, we require the existence of a stable Standard-model- like vacuum, unification of gauge couplings and robustness of perturbative calcu- lations. Only narrow parameter space regions around symmetry breaking chains with SU(4)C × SU(2)L × U(1)R or SU(3)c × SU(2)L × SU(2)R × U(1)B−L intermedi- ate stages are demonstrated to be potentially realistic. Detailed analysis of the SO(10) Higgs model with 45⊕126 scalar sector indicates a preference for the for- mer option, mainly due to increased perturbative instability and phenomenologi- cally unsuitable values of energy scales predicted in the...
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Effects of a heavy scalar triplet in the primordial lepton asymmetry generation
Doležalová, Lenka ; Malinský, Michal (advisor) ; Susič, Vasja (referee)
The aim of this thesis is to study the possible effects of the heavy scalar triplet on the primordial baryon asymmetry generated in the Early universe. Such asymmetry is thought to be first generated in the lepton sector and then partially translated into baryon asymmetry by the sphaleron processes. We computed the CP asymmetry generated by the decay of the heavy right-handed neutrinos first in the sole type-I seesaw theory. Then we have set up the Boltz- mann equations for the evolution of the comoving number density of both the right-handed neutrinos and the lepton asymmetry, numerically solved the equa- tions and found the baryon asymmetry arising from the computed CP asym- metry. The scalar triplet was introduced into the model and the relevant CP asymmetry in the type-II seesaw was calculated. Part of the thesis concerns the term in the expression for the CP asymmetry generated in the right-handed neutrino decays which we called "the tail part". It does not appear in any lit- erature sources except one. Its significance was examined and we came to the conclusion that the effect of the tail part should not be neglected as it may be comparable to the effect of the scalar triplet in a certain regime. 1
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One-loop beta-functions of the scalar couplings in the minimal SO(10) Higgs model
Press, Pavel ; Malinský, Michal (advisor) ; Kolešová, Helena (referee)
This thesis is focused on the Minimal SO(10) Grand Unified Theory and, in particular, on the 45 ⊕ 126 Higgs sector. It has been shown that in the scalar spectrum of the model there are potentially tachyonic instabilities. However, these issues might be resolved by considering quantum effects at the 1-loop level. This entails the study of the second derivatives of the effective potential. In order to establish the stability of the results of this perurbative approach, it is necessary to evaluate the beta functions of the scalar couplings in the Higgs sector. This way one also addresses the questions regarding the Landau poles of the scalar couplings which tend to be around the unification scale. In this work, the running of the scalar couplings in 45 in the SO(10) Higgs model is evaluated using two approaches: direct summation of Feynman graphs and the effective potential method. 1
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Aspects of baryon and lepton number non-conservation in the Standard model of particle interactions and beyond
Hudec, Matěj ; Malinský, Michal (advisor) ; Kupčo, Alexander (referee) ; Nardecchia, Marco (referee)
This work is devoted to baryon and lepton number violation and flavour physics in theories beyond the Standard Model of particle interactions. First, the relations between the accidental and imposed symmetries are dis- cussed. For example, we argue that the Levi-Civita tensors in the color space may be understood as a unique spurion carrying the baryon number, and as such its absence in the Lagrangian of a specific model indicates baryon number conservation. Afterwards, the two minimal scenarios of quark-lepton unification are ana- lyzed in detail: the Minimal quark-lepton symmetry model and its extension by the inverse seesaw mechanism. We investigate if the observed anomalies in the B-meson decays could be to some extent accommodated within these models. Finally, possible low-energy effects of gauge leptoquarks are studied in the theory of quark-lepton unification and its simple extensions by vector-like leptons. Taking fully into account the freedom in the quark-lepton mixing, a catalogue of measurements currently forming the border of the excluded parameter space is found. We argue that, within the considered class of models, the gauge leptoquark can account for the discrepancies in the neutral-current B decays if and only if at least two extra generations of weak-isosinglet leptons exist. 1
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Witten's loop in simple extensions of the Standard Model of particle interactions
Miřátský, Václav ; Malinský, Michal (advisor) ; Smetana, Adam (referee)
The goal of this Master thesis is to demonstrate Witteńs mechanism in selected extensions of the Standard model based on the Pati-Salam gauge group. The purpose of this mechanism is to obtain an extremely large Majorana mass term for right-handed neutrinos at the two-loop level and consequently light physical masses of neutrinos using the type I see-saw mechanism. The existence of corresponding Feynman diagrams without any interactions of vector bosons is presented. While it is impossible to construct this type of corrections in minimal SO(10) or SU(5)xU(1) model in Pati-Salam model they may be even dominant. Subsequently, implications of possible partial gauge coupling unification or even embedding of the Pati-Salam group into a gauge group of "Great Unified Theory" are considered. At the end the possibility of unacceptably fast proton decay is inspected. The discussed models are concluded to be potentially realistic but only at the cost of predictivity, since completely unknown Yukawa couplings appear in numerous key relations. 1
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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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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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