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 1.4 Dark matter detection In this section, we describe the most popular methods to detect DM. 1.4.1 Direct detection The interaction of WIMP with the detector material can be classified into two categories: • Elastic and inelastic scattering: When WIMP interacts with the nucleus as a whole, it causes the nucleus to recoil, and the change in energy is of the order of KeV. It is elastic scattering, whereas in the inelastic case, the nucleus is excited and releases gamma photons (MeV). Therefore, the two events can be easily separated in the detector module. • Spin-dependent and spin-independent scattering: If DM’s spin couples with the spin contents of the nucleon, then such scattering events are called spin-dependent (SD) scattering; otherwise, spin-independent (SI) scattering. SI cross section is usually larger than SD due to coherence and therefore can be measured easily. Recoil events due to elastic scattering can be categorised as follows: • Vibration: Recoil nuclei can cause a vibration in the lattice by its movement, which can be detected as a rise in temperature by placing a highly sensitive thermometer • Ionization: An incident particle can ionize the atoms of the detector material, which creates free electrons in the material that can be detected by placing an electric field. • Excitation: Another possibility is that an incident particle excites the atom of the detector material, which spontaneously emits photons that can be collected in a photomultiplier tube and converted into an electric signal for analysis. The interesting quantity here is the scattering rate of DM particles to the nuclear target, which is given by Density profile The Standard Halo Model (SHM) [1] is the simplest model to describe the distribution of DM in our galaxy. It assumes that DM is distributed smoothly, homogeneously, and isotopically. If f(x,v) is the distribution function, then the DM density is given by In SHM, the distribution function f(x,v) is given by Here, 𝜌0 and 𝜎 are constants. 𝜓 is the potential field and related with 𝜌 via Poisson equation. Solving equations 1.8, 1.9, and 1.10, one can get. Similarly, the distribution function can be found, which is a well-known Maxwell-Boltzmann (MB) distribution, and the velocity is proportional to a constant 𝜎. Thus, SHM predicts pretty well the observed DM distribution. However, galaxies are always merging with some small or big astrophysical objects, which perturbs the galactic disk and distorts the current structure; therefore, the smooth isotropy assumption of the DM profile does not fit well. N-body simulations have shown a significantly different density profile from the MB distribution. Some popular DM density profiles are commonly used in studies, such as the NFW profile, Effective Interaction Any DM model can have the following effective interaction between DM (𝜒) and SM quarks (q), There are many experiments dedicated to direct searches, such as LUX [65], XENON1T [66], XENONnT [23, 24], LUX-ZEPLIN (LZ) [21, 22], etc. These searches have put very tight constraints on the DM-nucleon cross-section. However, the above-mentioned experiments are not sensitive to DM mass below a few GeV. In figure 1.5, the limit on DM - nucleon cross-section as a function of DM mass is shown. The strong bounds are by XENON1T. New limits from LZ [22] and XENONnT [24] have further put strong bounds on the DM-Nucleon scattering cross-section. These bounds get weaker at low masses due to the energy threshold of the experiments. The orange region is a neutrino background [29]. One can see that there is a very small parameter space left for searches in the GeV–TeV mass range. 1.4.2 Indirect detection 1.4.3 Dark matter at colliders Dark matter can be produced at colliders such as the LHC, which is the largest particle collider at CERN. DM can be searched here by using two different strategies. One can start searching for an ultraviolet (UV) complete model, e.g., SUSY or GUT (Grand Unified Theory), or search for a new physics signal that arises from an effective field theory (EFT) operator or extra-dimensional theory. However, no candidate for DM has been found. A DM candidate might exist at a much higher scale of energy than the LHC current run at 13 TeV. It is also possible that DM interacts very weakly with SM; therefore, it has not been produced with the current luminosity of the LHC [31, 70] This paper is available on arxiv under CC BY 4.0 DEED license. [1] See, note by M.Lisanti [32] 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 1.4 Dark matter detection In this section, we describe the most popular methods to detect DM. 1.4.1 Direct detection The interaction of WIMP with the detector material can be classified into two categories: • Elastic and inelastic scattering: When WIMP interacts with the nucleus as a whole, it causes the nucleus to recoil, and the change in energy is of the order of KeV. It is elastic scattering, whereas in the inelastic case, the nucleus is excited and releases gamma photons (MeV). Therefore, the two events can be easily separated in the detector module. • Spin-dependent and spin-independent scattering: If DM’s spin couples with the spin contents of the nucleon, then such scattering events are called spin-dependent (SD) scattering; otherwise, spin-independent (SI) scattering. SI cross section is usually larger than SD due to coherence and therefore can be measured easily. Recoil events due to elastic scattering can be categorised as follows: • Vibration: Recoil nuclei can cause a vibration in the lattice by its movement, which can be detected as a rise in temperature by placing a highly sensitive thermometer • Ionization: An incident particle can ionize the atoms of the detector material, which creates free electrons in the material that can be detected by placing an electric field. • Excitation: Another possibility is that an incident particle excites the atom of the detector material, which spontaneously emits photons that can be collected in a photomultiplier tube and converted into an electric signal for analysis. The interesting quantity here is the scattering rate of DM particles to the nuclear target, which is given by Density profile Density profile The Standard Halo Model (SHM) [1] is the simplest model to describe the distribution of DM in our galaxy. It assumes that DM is distributed smoothly, homogeneously, and isotopically. If f(x,v) is the distribution function, then the DM density is given by In SHM, the distribution function f(x,v) is given by Here, 𝜌0 and 𝜎 are constants. 𝜓 is the potential field and related with 𝜌 via Poisson equation. Solving equations 1.8, 1.9, and 1.10, one can get. Similarly, the distribution function can be found, which is a well-known Maxwell-Boltzmann (MB) distribution, and the velocity is proportional to a constant 𝜎. Thus, SHM predicts pretty well the observed DM distribution. However, galaxies are always merging with some small or big astrophysical objects, which perturbs the galactic disk and distorts the current structure; therefore, the smooth isotropy assumption of the DM profile does not fit well. N-body simulations have shown a significantly different density profile from the MB distribution. Some popular DM density profiles are commonly used in studies, such as the NFW profile, Effective Interaction Effective Interaction Any DM model can have the following effective interaction between DM (𝜒) and SM quarks (q), There are many experiments dedicated to direct searches, such as LUX [65], XENON1T [66], XENONnT [23, 24], LUX-ZEPLIN (LZ) [21, 22], etc. These searches have put very tight constraints on the DM-nucleon cross-section. However, the above-mentioned experiments are not sensitive to DM mass below a few GeV. In figure 1.5, the limit on DM - nucleon cross-section as a function of DM mass is shown. The strong bounds are by XENON1T. New limits from LZ [22] and XENONnT [24] have further put strong bounds on the DM-Nucleon scattering cross-section. These bounds get weaker at low masses due to the energy threshold of the experiments. The orange region is a neutrino background [29]. One can see that there is a very small parameter space left for searches in the GeV–TeV mass range. 1.4.2 Indirect detection 1.4.3 Dark matter at colliders Dark matter can be produced at colliders such as the LHC, which is the largest particle collider at CERN. DM can be searched here by using two different strategies. One can start searching for an ultraviolet (UV) complete model, e.g., SUSY or GUT (Grand Unified Theory), or search for a new physics signal that arises from an effective field theory (EFT) operator or extra-dimensional theory. However, no candidate for DM has been found. A DM candidate might exist at a much higher scale of energy than the LHC current run at 13 TeV. It is also possible that DM interacts very weakly with SM; therefore, it has not been produced with the current luminosity of the LHC [31, 70] 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 [1] See, note by M.Lisanti [32] 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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