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

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