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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 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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