Table of Links Acknowledgements 1 Introduction to thesis 1.1 History and Evidence 1.2 Facts on dark matter 1.3 Candidates to dark matter 1.4 Dark matter detection 1.5 Outline of the thesis 2 Dark matter through ALP portal and 2.1 Introduction 2.2 Model 2.3 Existing constraints on ALP parameter space 2.4 Dark matter analysis 2.5 Summary 3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction 3.2 Model 3.3 Theoretical and experimental constraints 3.4 Phenomenology of dark matter 3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻 3.6 Summary 4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction 4.2 Model 4.3 Theoretical and experimental constraints 4.4 Dark Matter analysis 4.5 Summary 5 Summary Appendices A Standard model B Friedmann equations C Type I seasaw mechanism D Feynman diagrams in two-component DM model Bibliography 3.3 Theoretical and experimental constraints We discuss different constraints on the model parameters such as𝑈(1)𝑋 gauge coupling and scalar mixing angle. To estimate the constraints we consider vacuum stability, perturbative unitarity, and collider searches of BSM Higgs and 𝑍′ boson respectively. 3.3.1 Vacuum Stability The above scalar potential must be bounded from below. To determine the conditions for 𝑉(𝐻, Φ, 𝜒) to be bounded from below, we need to check the following symmetric matrix which comes from the quadratic part of the potential, Requiring such a matrix to be positive-definite, we obtain the following conditions, 3.3.2 Higgs Invisible decay Hence the total invisible decay width of SM Higgs boson ℎ1 is given a Accordingly, the invisible branching ratio for ℎ1 is given b 3.3.4 Bounds on the mixing parameter between physical mass eigenstates This paper is available on arxiv under CC BY 4.0 DEED license. Author:
(1) Shivam Gola, The Institute of Mathematical Sciences, Chennai. Table of Links Acknowledgements Acknowledgements 1 Introduction to thesis 1 Introduction to thesis 1.1 History and Evidence 1.1 History and Evidence 1.2 Facts on dark matter 1.2 Facts on dark matter 1.3 Candidates to dark matter 1.3 Candidates to dark matter 1.4 Dark matter detection 1.4 Dark matter detection 1.5 Outline of the thesis 1.5 Outline of the thesis 2 Dark matter through ALP portal and 2.1 Introduction 2 Dark matter through ALP portal and 2.1 Introduction 2.2 Model 2.2 Model 2.3 Existing constraints on ALP parameter space 2.3 Existing constraints on ALP parameter space 2.4 Dark matter analysis 2.4 Dark matter analysis 2.5 Summary 2.5 Summary 3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction 3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction 3.2 Model 3.2 Model 3.3 Theoretical and experimental constraints 3.3 Theoretical and experimental constraints 3.4 Phenomenology of dark matter 3.4 Phenomenology of dark matter 3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻 3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻 3.6 Summary 3.6 Summary 4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction 4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction 4.2 Model 4.2 Model 4.3 Theoretical and experimental constraints 4.3 Theoretical and experimental constraints 4.4 Dark Matter analysis 4.4 Dark Matter analysis 4.5 Summary 4.5 Summary 5 Summary 5 Summary Appendices Appendices A Standard model A Standard model B Friedmann equations B Friedmann equations C Type I seasaw mechanism C Type I seasaw mechanism D Feynman diagrams in two-component DM model D Feynman diagrams in two-component DM model Bibliography Bibliography 3.3 Theoretical and experimental constraints We discuss different constraints on the model parameters such as𝑈(1)𝑋 gauge coupling and scalar mixing angle. To estimate the constraints we consider vacuum stability, perturbative unitarity, and collider searches of BSM Higgs and 𝑍′ boson respectively. 3.3.1 Vacuum Stability The above scalar potential must be bounded from below. To determine the conditions for 𝑉(𝐻, Φ, 𝜒) to be bounded from below, we need to check the following symmetric matrix which comes from the quadratic part of the potential, Requiring such a matrix to be positive-definite, we obtain the following conditions, 3.3.2 Higgs Invisible decay Hence the total invisible decay width of SM Higgs boson ℎ1 is given a Accordingly, the invisible branching ratio for ℎ1 is given b 3.3.4 Bounds on the mixing parameter between physical mass eigenstates This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv Author: (1) Shivam Gola, The Institute of Mathematical Sciences, Chennai. Author: Author: (1) Shivam Gola, The Institute of Mathematical Sciences, Chennai.

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Theoretical and Experimental Constraints: Discussing Different Constraints on the Model Parameters

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