DARK MATTER AND DIRECT SEARCHES David G. Cerdeo (2) Freeze out of - - PowerPoint PPT Presentation

DARK MATTER AND DIRECT SEARCHES

David G. Cerdeño

(2) Freeze out of massive particles (WIMPs)

Contents

• Freeze-out of massive species
• The collisional operator
• Argument for WIMPs

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• Important special cases
• Coannihilation
• Resonant annihilation
• List of Dark Matter candidates

Freeze-out of massive species

• The collisional operator
• The WIMP “miracle”

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How is Particle Dark Matter produced?

time Temperature Today t~13.6 Gyr T~3K Thermal equilibrium Due to the expansion of the Universe DM particles fall out of equilibrium and cannot annihilate any more. A Relic Density of DM is

• btained

which remains constant. The number density, n, of DM decreases with T. time

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time Temperature Today t~13.6 Gyr T~3K Thermal equilibrium Due to the expansion of the Universe DM particles fall out of equilibrium and cannot annihilate any more. A Relic Density of DM is

• btained

which remains constant. The number density, n, of DM decreases with T. time How much dark matter remains depends on its interaction rate A particle with stronger interactions keeps in equilibrium for longer… … and is more diluted

How is Particle Dark Matter produced?

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time Temperature Today t~13.6 Gyr T~3K Thermal equilibrium Due to the expansion of the Universe DM particles fall out of equilibrium and cannot annihilate any more. A Relic Density of DM is

• btained

which remains constant. The number density, n, of DM decreases with T. time How much dark matter remains depends on its interaction rate Particles with very weak interactions decouple earlier, having a larger relic density

How is Particle Dark Matter produced?

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time

How is Particle Dark Matter produced?

Non-relativistic when they decoupled from the thermal plasma

• The resulting WIMP relic density

is naturally of order 0.1 when the annihilation cross section is of “weak scale”

σ ~ 10-9 GeV

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The WIMP “miracle”

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The WIMP “miracle”

• Very different scales conjure up to lead to the electroweak scale

The relic abundance can be written as In terms of very different scales CMB Temperature Hubble parameter Planck scale Where the result turns out to be

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The WIMP “miracle”

• Very different scales conjure up to lead to the electroweak scale

A typical electroweak scale cross section for a non-relativistic particle WIMP WIMP f f _ MX Notice that this implies (non-relativistic particle) Imposing

(Griest, Kamionkowski '90)

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Special cases

• The low-temperature expansion for the annihilation cross section

is not valid in some cases: Resonant annihilation Thresholds Coannihilations with other particles close in mass

(Gondolo, Gelmini '91) (Griest, Seckel '91)

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Special cases

• Resonant annihilation:

WIMP WIMP f f _ MX

σ

s = (2 mWIMP)2 (2 mWIMP)2=(mX) 2 The resonant increase in the cross section implies a sharp decrease in the relic abundance. General expression for thermal average of annihilation cross section

(Gondolo, Gelmini '91)

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Special cases

• Coannihilations

(Griest, Seckel '91)

In principle, the evolution of all coupled species should be taken into account when determining the WIMP density, evolution and decoupling. In particular, particles which carry the same quantum number that protects the decay of DM (R-parity, KK-parity, T-parity) contribute to the abundance of the lightest one. In practice, the Boltzmann suppresssion of the equilibrium density implies that the abundance of all other exotic particles is suppressed and can be ignored. EXCEPTION: if there is a heavy exotic particle with approximately the same mass as the DM.

f eq=e

−E T

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Special cases

• Resonant annihilation

(Griest, Seckel '91)

The annihilation cross section is significantly increased in the pole of the propagator. As a consequence, the relic density decreases rapidly. Thermal motion allows resonant annihilation when

f eq=e

−E T This is not possible for

m W= m A 2

m W mA 2 m W mA 2

Dark matter candidates

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• Conditions
• A brief list of “usual suspects”

Conditions for Dark Matter candidates

1) Correct relic abundance

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Remember that the different production mechanisms rely on a given “thermal history”of our Universe. WIMPs are successful candidates if thermally produced and if there was no subsequent reheating or entropy injection. From unitarity of the S matrix we know that Which leads to an upper bound on the WIMP mass

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However....

• Not applicable to non-thermal candidates (for which the relic abundance is

calculated differently, such as decays of heavier particles) (e.g., gravitinos and axinos)

• Non-standard Cosmology, e.g.,

The presence of scalar fields in the Early Universes may induce a period of a much higher expansion rate. WIMPs decouple earlier and have a much larger relic abundance (by several orders of magnitude).

(Catena, Fornengo, Masiero, Pietroni, Rosati, '04)

Changes in the cosmology also affect the calculation of relic abundance for non-thermal dark matter. E.g., quintessence-motivated kination models.

(Gómez, Lola, Pallis, Rodríguez-Quintero '08)

Late entropy production which dilutes the DM density

(Abazajian,Koushiappas '06)

E.g., decay of heavy sterile neutrinos

(Asaka, Shaposnikov, Kusenko '06) See, e.g., (Giudice, Kolb, Riotto '01)

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However.... Late (out of equilibrim) decay of semistable particles induce an injection of entropy.

(Kolb, Turner Chapt.5)

The only constraint to be considered is not to spoil BBN predictions

T R5 MeV

There are various possibilities depending on whether TR is smaller or larger than the DM freeze out temperature and on whether the decay produces more DM particles.

T RT f

No change in the predicted dark matter thermal relic

• abundance. Chemical equilibrium is restored.

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• Thermal production without chemical equilibrium
• Non-thermal production without chemical equilibrium

Production of DM is suppressed

• Thermal production with chemical equilibrium

X cdm ~ 〈 v〉 10

−16 GeV −2

100GeV m X 

5



T R GeV

7



10 gx

3/2

X∝T R

3 T f T f new −4cdm

The particle freezes out before the reheating with a too large relic density and is then diluted. The particle freezes out before the reheating with a too large relic density and is then diluted.

X cdm ~2×10

6b

m mX T R MeV

• Non-thermal production with chemical equilibrium

X~ T f T R cdm

The particle freezes out before the reheating with a too large relic density and is then diluted.

T RT f

Conditions for Dark Matter candidates

2) Non-relativistic at the epoch of structure formation (a.k.a. cold)

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Relativistic (hot) dark matter (with a large free-streaming length) damp the power spectrum of density fluctuations at large scales (for neutrinos this corresponds to the scale of superclusters) Also, hot dark matter predict a top-down hierarchy in structure formation (small structures forming by fragmentation of larger ones). Observation show that galaxies are older than superclusters. For cold dark matter only fluctuations smaller than the Earth scale are

• suppressed. N-body simulations also support this kind of DM for structure

formation. However, N-body simulations usually predict many more satellites of galaxies than are observed... Solutions include strongly interacting DM or warm dark matter with masses around 1 keV.

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Numerical simulations with warm dark matter show the reduction in the number

• f subhaloes.

Structure of a DM distribution in a simulated halo comparable to the Milky Way. Left) Halo formed assuming that DM is made of cold, massive particles. Right) The same halo simulated from same initial cosmological parameters and resolution, but assuming that DM is made of warm, light particles with rest mass = 3 keV

Conditions for Dark Matter candidates

3) Neutral (.... or not)

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Charged stable (DM) particles could bind to nuclei, forming exotic isotopes that would have shown in searches for this kind of atoms. However, this need not be the case if the DM is very heavy. Charged Massive Particles (CHAMPS), could be viable with masses of 1- 1000 TeV.

(de Rújula, Glashow, Sarid '90)

4) Consistency with BBN constraints Crucial in the case of particles with non-thermal production due to late decays of massive particles. E.g., the gravitino or the axino. (MORE ON THIS LATER...) 5) Stellar evolution Important to particles with very small masses that could be produced in the interior of stars and excape, leading to energy losses, modifying stellar evolution.

Neutrinos

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• Light neutrinos are “hot” dark matter, known to contribute very little but also

excluded from structure formation. However: what about massive sterile neutrinos? (i.e., cold)

HOT COLD HOT COLD

A heavy neutrino can have the correct relic abundance!

Neutrinos

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• Light neutrinos are “hot” dark matter, known to contribute very little but also

excluded from structure formation. Direct detection experiments exclude the window GeV < mν < TeV DM searches at Homestake (Ahlen et al. '87) If sterile neutrinos were the DM they would have been observed at direct detection experiments.

Axions

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• Spin 0 pseudo-Goldstone bosons associated to the spontaneous breaking of a

global U(1) Peccei-Quinn symmetry, postulated to solve the strong-CP problem.

(Peccei-Quinn ' 77; Weinberg '78;Wilczek '78; Kim '79)

The axion coupling constant is constrained Supernovae overcooling (SN1987) Not overclosing the Universe Axions with a mass of order m a=10

−5eV

can reproduce the correct relic density Very weakly interacting, can only be detected through conversion into photons in large magnets (e.g., CAST experiment)

Axions

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• Axion searches are already starting

probing the parameter space of axion models

• Figs. From (J.E. Kim '08)

They have, however, not yet probed into the region interesting for Dark matter

• Nb. searches with microwave cavities

(not shown) are probing smaller values for the axion mass.

Comment on non-thermal candidates

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time

Reheating Nucleosynthesis

3He, 4He, D, Li

Thermal Production Non-Thermal Production Photons, charged leptons…

?

NLSP freezes out

Comment on non-thermal candidates

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• Gravitino production mechanisms
• Thermal production

Through scattering processes and an annihilation with (s)particles during thermal expansion of the Early Universe.

• Non-thermal production

Through late decays of the NLSP (normally staus or neutralinos)

χ  G γ

 τ  G Z τ ,  G ντW

χ  G Z ,  Gh ,  G H ,  G A

 τ  G τ

Note that

NLSP NTP G ~

Ω < Ω

The gravitino can be a good dark matter candidate in regions where

1

NLSP >

Ω

(Bolz, Buchmüller, Plümacher 98) (see, e.g,. Feng et al. 03, 04)

• Gravitino production mechanisms

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+

The total relic density may become too large, especially for large reheating temperatures (essential for thermal leptogenesis)

Gravitino dark matter

• Constraints from Big Bang Nucleosynthesis

Late decays of the NLSP can generate highly energetic electromagnetic and hadronic fluxes which may alter significantly the abundances

• f light elements (thus spoiling the success of

Big Bang Nucleosynthesis).

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NLSP decays into gravitinos typically after Big Bang Nucleosynthesis. Energy released into EM and HAD showers Branching Ratios Energy of the sleptons… Yield of NLSP

Gravitino dark matter

• Constraints from Big Bang Nucleosynthesis

Neutralino NLSP:

χ  G γ

Dominant channel (in the CMSSM the neutralino is almost a purely bino). Contributes to Electromagnetic fluxes.

χ  G Z ,  Gh ,  G H ,  G A

Allowed above kinematic thresholds. Contributes to Hadronic fluxes. Below the kinematic thresholds, three body decays, which contribute to Hadronic fluxes need to be considered.

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Gravitino dark matter

• Constraints from Big Bang Nucleosynthesis

Stau NLSP: Dominant channel. Contributes mainly to Electromagnetic fluxes. Three-body decays give contributions to Hadronic fluxes.

 τ  G τ  τ  G Z τ ,  G ντW

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Gravitino dark matter

• In the CMSSM

Regions of the parameter space appear where the gravitino is a good dark matter candidate

Correct relic density from only NTP Correct relic density with TP (D.G.C., K.Choi, K.Jedamzik, L.Roszkowski, R.Ruiz de Austri ´05)

Gravitino dark matter

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• In the CMSSM

Neutralino NLSP excluded by BBN. Only part of those with stau NLSP are left. Non-thermal production not sufficient. Contributions from thermal prod. are necessary.

As long as TR≤109 GeV sizable regions are found with correct Ω

Gravitino dark matter

(D.G.C., K.Choi, K.Jedamzik, L.Roszkowski, R.Ruiz de Austri ´05)

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• In the CMSSM

Neutralino NLSP excluded by BBN. Only part of those with stau NLSP are left.

Gravitino dark matter

(See Steffen '08 and references therein)

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Constraints on the abundance of 7Li have recently pushed the BBN constraints to heavier supersymmetric masses

• In the CMSSM

In the remaining regions the Fermi vacuum is metastable. The global minimum breaks charge and/or colour.

UFB UFB

Gravitino dark matter

Neutralino NLSP excluded by BBN. Only part of those with stau NLSP are left. Non-thermal production not sufficient. Contributions from thermal prod. are necessary.

(D.G.C., K.Choi, K.Jedamzik, L.Roszkowski, R.Ruiz de Austri ´05)

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• Very light gravitinos and constraint on TR

(D.G.C., K.Choi, K.Jedamzik, L.Roszkowski, R.Ruiz de Austri ´05) For very light neutralinos non-Thermal Production is negligible

1 m m

NLSP G ~

<<

Thermal Production proportional to

G ~ R

m T

(BBN) (mG>100 keV)

Gravitino dark matter