The Phenomenology of Dark Matter Explained

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

3.4 Phenomenology of dark matter

• The relic density coming from Planck satellite data [49]

The total relic abundance of DM in our model is given by the sum of the scalar (𝜒) and fermion (𝑁3) relic abundances:

Only for solutions falling exactly within the band given in Eq. (3.31) the totality of the DM can be explained by 𝜒 and 𝑁3.

• Direct detection cross-section of DM scattering of nucleon set by various experiments such as XENON1T [66], LUX [65] and PandaX-II [174]

We implemented the model in the SARAH package [175] to calculate all the vertices, mass matrices, tadpole equations etc. The thermal cross sections and DM relic abundance are determined using micrOMEGAS-5.0.8 [176]. Even though the model introduces new free parameters, not all of them are important to DM analysis. For example, self-quartic coupling 𝜆𝜒 does not play any role in DM phenomenology. Hence we choose to fix 𝜆𝜒 = 0.1 in our analysis. The remaining free parameters relevant for DM analysis can be chosen as:

In the next sections, we will study how the DM phenomenology of this model depends on the free parameters and to do that we choose the following benchmark points which are allowed from all the above-mentioned constraints:

Table 3.2: The cubic couplings of the DM scalar and fermion.

3.4.1 Relic density

Table 3.3: The quartic couplings of the DM scalar.

Figure 3.3: The conversion channels which contribute to the two-component DM scenario.

Figure 3.4: Relic density of scalar (right) and fermion (right) DM as a function of DM mass for one DM candidate. Here, we set the parameter space as BP given in Eq. (3.34). Blue and red lines stand for 𝜆 = 0.01 and 0.1.

which we can be utilized to compute the relic density of both the components,

3.4.2 Direct detection

The direct detection study of our DM candidates 𝜒𝑅 and 𝑁3 are done here. The current experimental constraints on the DM direct detection assume the existence of only one DM candidate. As in our model, two-component DM candidates are predicted, and the contribution of each candidate to the direct detection cross-section should be rescaled by the fraction contributing to the total relic density. Hence it is convenient to define the fraction of the mass density of 𝑖th DM in the case of multi-component DM [156,157,178,179]

The upper limit on the direct detection now can be recast as

Figure 3.7: The tree-level 𝜒-nuclei scattering Feynman diagrams mediated by Higgs, 𝑍, and 𝑍′.

The above formula in Eq. (3.40) is an extension of the expression corresponding to the singlet scalar DM case [180]. The relative negative sign between the ℎ1 and ℎ2 contributions arises in our considered model as the couplings get modified according to Eq. (3.42). Due to the presence of the two different channels, depending on the parameter space, we can have destructive interference between these two channels, and direct detection can be very small.

Figure 3.8: The tree-level 𝑁3-nuclei scattering Feynman diagrams mediated by Higgs, 𝑍, and 𝑍

Figure 3.9: The spin-independent DM-nucleon scattering cross section with respect to the DM mass is plotted here. The left and right panels stand for scalar and fermionic DM cases. The light-red shaded region denotes the excluded region coming from the XENON1T experiment [18]. The light-orange region corresponds to the “neutrino floor” coming from coherent elastic neutrino scattering [19]. We have also shown various projected sensitivities coming from experiments such as PandaX-4t [20], LUX-ZEPLIN(LZ) [21,22], XENONnT [23, 24], DarkSide-20k [25], DARWIN [26] and ARGO [27].

Table 3.4: Benchmark points where both relic abundance and direct detection limit for two-component DM are satisfied.