#
An Introduction to Particle Dark Matter^{ †}

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^{†}

## Abstract

**:**

## 1. Introduction

#### 1.1. Why Do We Need Dark Matter?

^{2}/kg

^{2}is Newton’s gravitational constant.

#### 1.2. Microscopic Features of Dark Matter

#### 1.2.1. Is Dark Matter Actually Dark?

#### 1.2.2. Is Dark Matter Collisionless?

#### 1.2.3. Is Dark Matter Classical?

#### 1.2.4. Is Dark Matter a Fluid?

**Mass:**- There are more than 90 orders of magnitude of mass range available for bosons; 70 for fermions.
**Interactions:**- A self-interaction is possible, if of the order at most of the strong interaction, so of the order of the MeV. It is in principle also possible to have interactions with ordinary Standard Model particles, as long as such interactions do not involve emission of photons, otherwise DM halos would shine and be visible. Particularly promising as DM candidates are massive particles that interact only via weak interactions, the so-called WIMPs (Weakly Interacting Massive Particle).
**Abundance:**- It has to be enough in order to satisfy the observational constraint ${\Omega}_{\mathrm{DM}}\approx 0.26$. As we shall see later, this is achieved naturally for WIMPs and such occurrence is usually referred to as the WIMP miracle.

#### 1.3. Observational Constraints on Dark Matter Interactions

## 2. Thermal Decoupling

#### 2.1. Thermal Relics

#### 2.1.1. Hot Thermal Relics

^{−2}is the Fermi coupling constant and ${T}_{\nu}$ is the neutrino thermal bath temperature. The freeze-out condition $\mathsf{\Gamma}=H$ gives us, using Equation (9):

#### 2.1.2. Cold Thermal Relics

#### 2.2. Boltzmann Equation

#### 2.3. Modified Expansion History and Relic Abundance: The Kination Example

#### 2.4. Dark Matter after Chemical Decoupling

## 3. Detectability of Particle Dark Matter

#### 3.1. Direct Detection

- Slowly decaying “primeval” nuclides such as Uranium, Thorium and Potassium-40, whose abundance is about ${10}^{-4}$ and half-life is $\approx {10}^{9}$ years;
- Rare, fast decaying trace elements like tritium and Carbon-14, whose abundance is about ${10}^{-8}$ and half-lives of the order of 10 years.

#### 3.2. Indirect Detection

- If DM particles belong to an SU(2) multiplet, then we expect well-defined combinations of $\overline{Z}Z$, $\overline{W}W$ final states;
- In Universal Extra Dimension (UED) theories [30], DM is the Kaluza-Klein KK-1 mode of hypercharged gauge boson, thus the scattering matrix element $\mathcal{M}$ is proportional to the fermion hypercharge ${Y}_{f}$, that is, ${\left|\mathcal{M}\right|}^{2}\propto {\left|{Y}_{f}\right|}^{4}$, and the preferred annihilation modes are the up quarks ${Y}_{{u}_{L}}=4/3$ and charged leptons ${Y}_{{e}_{R}}=2$.
- We expect a special selection rule, for example helicity suppression for Majorana fermion (analogous to charged pion decay):$${\left|\mathcal{M}\right|}^{2}\propto {m}_{f}^{2}.$$

- Very indirect. Looking for DM effects induced in astrophysical objects or in cosmological observations.
- Pretty indirect. Using probes that do not trace back to the annihilation event, since their trajectories are bent as the particles propagate. For example, cosmic rays.
- Not-so-indirect. Using neutrinos and gamma rays, which have the great added advantage of traveling in straight lines.

#### 3.2.1. Very Indirect Probes

- Solar Physics. It is possible that DM could affect Sun’s core temperature or the sound speed in its interior;
- Neutron Star Capture. DM can lead to Neutron star capture that eventually leads to the formation of black holes (notably e.g., in the context of asymmetric DM);
- Supernova and Stars, in which DM could be responsible for cooling processes;
- Protostars, for example WIMP-fueled population-III stars;
- Planets warming;
- Cosmological observation, where the DM content has strong implication for, for example Big Bang Nucleosynthesis or the Cosmic Microwave Background spectrum, also affecting the time of the recombination, or the structure formation process.

#### 3.2.2. Pretty Indirect Probes

^{3}He, for which the relevant process is:

- There is no excess of antiprotons, so DM should be leptophilic, which is possible but not generic;
- There is no observed secondary radiation due to bremsstrahlung or inverse Compton scattering;
- A very large pair annihilation rate is required for thermal production, which leads to unseen gamma-ray or radio emission, that is:$$\langle \sigma v\rangle \approx {10}^{-24}\frac{{\mathrm{cm}}^{3}}{\mathrm{s}}\xb7{\left(\frac{{m}_{\chi}}{100\phantom{\rule{0.277778em}{0ex}}\mathrm{GeV}}\right)}^{1.5}.$$

#### 3.2.3. Not-So-Indirect Probes

^{2}. With equilibration, the flux of neutrinos of flavour f only depends on the capture rate and is:

- Dwarf Spheroidal Galaxies
- Draco, $J\approx {10}^{19}$ GeV
^{2}/cm^{5}± a factor 1.5; - Ursa Minor, $J\approx {10}^{19}$ GeV
^{2}/cm^{5}± a factor 1.5; - Segue, $J\approx {10}^{29}$ GeV
^{2}/cm^{5}± a factor 3.

- Local Milky-Way like galaxies
- M31, $J\approx {10}^{19}$ GeV
^{2}/cm^{5}.

- Local clusters of galaxies
- Fornax, $J\approx {10}^{18}$ GeV
^{2}/cm^{5}; - Coma, $J\approx {10}^{17}$ GeV
^{2}/cm^{5}; - Bullet, $J\approx {10}^{14}$ GeV
^{2}/cm^{5}.

- Galactic center
- ${0.1}^{\circ}$, $J\approx {10}^{22-25}$ GeV
^{2}/cm^{5}; - ${1}^{\circ}$, $J\approx {10}^{22-24}$ GeV
^{2}/cm^{5}.

#### 3.2.4. The Galactic Center Excess

#### 3.2.5. Collider Production of Dark Matter Particles

**Top-down:**pick a model and scan the parameter space (e.g., supersymmetry or unified theories).**Bottom-up:**use some effective field theory (EFT) or simplified models to sketch of how DM could manifest itself at colliders.

#### 3.2.6. Axions and Axions Searches

#### 3.2.7. Sterile Neutrinos and the 3.5 keV Line Puzzle

- SU(2)
_{L}gauge singlet but have a small mixing angle with active neutrinos; - Cosmologically viable candidates of DM [53];
- not stable because they decay via mixing with active neutrinos.

- Plasma temperature;
- Relative elemental abundances.

**Theorem.**

- It is a new indirect detection channel;
- it has an unmistakable signature, free of background;
- Is a good model, in the sense that it is economic, with a natural UV completion and a thermal relic DM.

- Its line shape, for example geometric average of thermal DM velocities, can be resolved by for example the Hitomi/astro-h satellite;
- It has unique morphology
- It has unique target-dependence
- Lines could appear anywhere in the spectrum, from eV, to UV, to X-ray.

## 4. Dark Matter Bestiarium

#### 4.1. Gravitinos

#### 4.2. WIMPzillas and Super-Heavy Dark Matter Candidates

- The DM particle is never in thermal equilibrium;
- The particle mass is comparable to the inflaton mass say ${M}_{\varphi}$;
- The particle lifetime is much longer than the age of the universe.

#### 4.3. Self-Interacting Dark Matter

#### 4.4. Asymmetric Dark Matter

#### 4.5. Minimality

#### 4.6. Dark Photons

## 5. Conclusions

## Funding

## Conflicts of Interest

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1. | This is not the case in the so-called Asymmetric WIMPs models, see, for example, Reference [17]. |

2. | Note that this bound is not valid in presence of Sommerfeld enhancements annihilation, see, for example, Reference [19]. |

3. | Note that when dealing with annihilation this formula provides the freeze-out temperature, whereas when dealing with elastic scattering this formula provides the kinetic decoupling temperature. |

4. | |

5. | |

6. | The interested reader might try to run a simulation with PITHIA, http://home.thep.lu.se/Pythia/. |

7. | William of Occam, c. 1286–1347. |

8. | Quoted in Reference [65], Section 2.5.1, The psychology of astronomers and astrophysicists. |

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Profumo, S.; Giani, L.; Piattella, O.F.
An Introduction to Particle Dark Matter. *Universe* **2019**, *5*, 213.
https://doi.org/10.3390/universe5100213

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Profumo S, Giani L, Piattella OF.
An Introduction to Particle Dark Matter. *Universe*. 2019; 5(10):213.
https://doi.org/10.3390/universe5100213

**Chicago/Turabian Style**

Profumo, Stefano, Leonardo Giani, and Oliver F. Piattella.
2019. "An Introduction to Particle Dark Matter" *Universe* 5, no. 10: 213.
https://doi.org/10.3390/universe5100213