SupersymmetricDark Matter

Minseok Cho

KAIST

December 07, 2019

1SUPERSYMMETRIC DARK MATTER

Table of Contents1. Dark Matter

2. Relic Abundance of WIMPs

3. Minimal Supersymmetric Standard Model (MSSM)

4. Detection of WIMPs

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Evidence for Existence of Dark MatterFritz Zwicky

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Coma Cluster

Evidence for Existence of Dark MatterRotation Curve of NGC 6503

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Vera Rubin

Nonbaryonic Dark MatterDensity parameter :

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open universe, expand forever

flat universe

close universe, halt expanding and recollapse

𝜌 =

Nonbaryonic Dark MatterTo explain abundance of Helium, Deuterium, and Lithium

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Measurements suggest

Bulk of dark matter is nonbaryonic

)

(WMAP, in LCDM model)

Candidates of Dark Matter1. Massive Compact Halo Objects (MACHOs)

◦ Neutron stars, brown dwarfs, black holes, etc.◦ EROS-2 researches gravitational microlensing effects. But not observed.

2. Hot dark matter◦ Neutrino

◦ N-body simulation was inconsistent.

3. Weakly Interacting Massive Particles (WIMPs)◦ Supersymmetry, extra dimension, little Higgs theory, etc.

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Relic Abundance of WIMPsRelic Abundance : how many particles remain from the early universe

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𝑛 =𝑔

2𝜋𝑓 𝑝 𝑑 𝑝

 

 

𝑛 ∝ 𝑇For 𝑇 ≫ 𝑚 ,

𝑛 ∝ 𝑔 𝑚 𝑇 2𝜋⁄⁄

exp − 𝑚 𝑇⁄For 𝑇 ≪ 𝑚 ,

But, the universe is not completely in thermal equilibrium

Relic Abundance of WIMPs

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𝜒�̅� ↔ 𝑥�̅�

Γ = 𝑛 𝜎𝑣

For 𝑇 ≫ 𝑚 ,

When Γ = 𝐻, 𝜒 stops to annihilate (freeze out)

𝜒 is abundant and annihilation is active

Annihilation rate :

Relic Abundance of WIMPs

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𝑛 𝑠⁄ = 𝑛 𝑠⁄ = Γ 𝜎𝑣 𝑠⁄ = 𝐻 𝜎𝑣 𝑠⁄

In freeze-out condition

Then

≃ 100 𝑚 𝑚 𝑔∗⁄

𝜎𝑣

Ω ℎ = 𝑚 𝑛 𝜌⁄ ≃ (3 × 10 cm s / 𝜎𝑣 )

Relic Abundance of WIMPs

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𝑑𝑛

𝑑𝑡+ 3𝐻𝑛 = − 𝜎𝑣 𝑛 − 𝑛

By the Boltzmann equation,

Larger cross section → smaller relic abundnace

Cross section of WIMPs 𝜎𝑣 ∼ 10 cm s

Minimal Supersymmetric Standard Model (MSSM)

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MSSM

= Standard model + Higgs doublet + SUSY partners

MSSM follows the gauge symmetry SU(3) × SU(2) × U(1)

R-parity : 𝑅 = −1

𝑅 = 1 for ordinary SM particles

𝑅 = −1 for superpartners

Minimal Supersymmetric Standard Model (MSSM)

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Annihilation Cross-section

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Detection of WIMPs1. Direct detection

◦ Very low cross section◦ Tiny deposited energy

20 - 400 GeV, 270 km/s WIMPs & 1 – 200 GeV nucleus

⇒ deposit 1 - 100 keV energy, 10-4 - 1 event per day per kilogram of matter

◦ Background cosmic raykeV - MeV cosmic ray in 100 events per day per kilogram

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Detection of WIMPs2. Observe energetic neutrinos from the Sun / Earth

Occasionally scattered↓

Smaller velocity than the escape velocity↓

Trapped in the sun↓

Additional scattering, settles to the core↓

Energetic neutrino from annihilation of WIMPs in the core

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