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Particle physicists would like to believe that DM is a kind of
particles or many difference kinds of particles
These particles must have the following properties
 Electrically neutral
▪ No electromagnetic interactions (non-luminous)
 No strong interaction
▪ Otherwise, will see them already through the strong interaction process
with ordinary matter (like cosmic ray)
 Long life time
▪ Longer than the lifetime of the universe, otherwise would have disappeared
long ago
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Electroweak symmetry
breaking：Higgs particle
has not been found
Neutrino is a possible
candidate, but too light
curve
A new particle！
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Electron: lightest charged particle (charge conservation)
Proton: baryon number symmetry breaking interaction is
small.
Neutrinos: lightest fermion
Photon and graviton: cannot decay due to energy-momentum
conservation
What make the dark matter stable?
 Some symmetry which prevent its decay
 Or the decay interaction is very very weak
 MACHOS
 Primodial Black Holes
 Mirror Matter
 Axions (10-6 eV)
 WIMPs (weakly interacting massive particles), WIMPzillas
(1016 GeV)
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Consider a stable particle X, which interacts with SM particle
Y through,
, , when temp is much higher than Mx,
the creation and annihilation are equally efficient, therefore,
DM particle exist in large quantity along with SM particles.
As the temp drops below Mx, the creation becomes
exponentially suppressed. In the thermal equilibrium, the
number density is
if they remain in thermal eq. indefinitely, the nX will be
increasingly suppressed as the univer. cools, quickly becomes
irrel.
 To evade this fate,
 Particle-aniparticle asymmetry
 Hubble expansion to dilute the small annihilation rate
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The evolution of the particle density obeys the Boltzmann
equation
where hubble constant,
describes
the expansion, and
is the thermally averaged
annihilation cross section, multiplied by velocity.
 At very high T, due to large cross section, the density is given
by eq. density
 At small T, eq. density can be ignored, along with the entire
annihilation term, the density dilutes through hubble
expansion only. (comoving density remains constant)
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Temp. at which the
comoving density ceases to
decrease expon. is called
the freezout temp.
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c ~ 0.5, a, b is defined from
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The relic density of the
universe
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If X has a GeV-TeV scale mass and a roughly weak-scale
annihilation cross-section, xFO = 20-30, resulting relic
abundance.
From the DM density, one finds that
on the order to 3 x 10-26 cm3/s
 This is just consistent with the DM particle has weak
interaction cross section. Therefore apart from gravity, DM
shall have weak interactions.
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The annihilation cross section
and light
mass leads to an overall freeze-out temp on the order of few
MeV, the relic density is
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Since the SM neutrino mass is well below 9 eV, only a small
fraction of the dark matter could possibly be the SM
neutrinos.
Even if the neutrino mass were around 9eV , at the time of
freeze-out, the particle is relativistic, the large scale structure
of the universe will be much smoother than what has been
observed (Warm Dark Matter)
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The annihilation cross section becomes much larger, growing
with the square of mass up to the Z-pole,
, declining
with 1/m^2 above this. In this case, the free-out yields a cold
relic T – m/10, the abundance is given by,
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Therefore, if the relic density is explained by a heavy
neutrino, its mass must be either around 5GeV, or several
hundred GeV.
5GeV is ruled out by the LEP Z-width. The heavy one is
already excluded by the direct DM detection exp.
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A scenario in which the WIMP is unstable, decay to
gravitating stable particle.
This is a nightmare for DM search
Supersymmetry is motivated by the large scale discrepancy
between the electroweak symmetry breaking (240 GeV) and
Planck scale (1019 GeV). The symmetry ensures that the
quantum fluctuations at high-energy scale get cancelled
through symmetry.
 According to the symmetry, every fermion has a bosonic
partner (s-paticle) and every boson has a fermionic partner
(…inos)
 Supersymmetry breaking can happen at electroweak scale so
that so that all super-particles have masses around weak
scale. In this case, the weak scale is related to the SUSY
breaking.
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The lightest SUSY particle (LSP) is stable if R-parity is a good
symmetry
R = 1 for SM particles and R=-1 for
SUSY partners.
The identity for LSP depends on the details of SUSY breaking.
Only if it is electrically and color-neutral, LSP can be a DM
candidate
Four neutralinos (super-partner of the electrical neutral SM
particle):
 Gauginos for neutral gauge bosons (Z, gamma),
 Higgsinos for higgs bosons (h, H)
 three sneutrinos (spin-0),
 gravitino (spin, 3/2)
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In many respects, sneutrino is very similar to a fourth
generation neutrino. It can annihilate into SM fermions
through s-channel exchange of Z boson.
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It must be on the order of 500GeV to 1TeV to give rise the
right DM density.
It can scatter with ordinary matter through Z exchanges. The
resulting cross section is too large. Already rule out by direct
direction experiment.
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The lightest neutralino is a possible DM candidate. The mass
matrix is
M are the bino and wino masses, mu is the higgsino mass
parameter. This can be diagonalized to yield
the gaugino fraction and higgsino fraction are determined by
the mixing coefficients, which in term depend on SUSY breaking
scenarios.
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Assume gaugino masses evolve to a single value at GUT scale
m1/2, the neutralino has a small wino fraction but a bino like
if M1 is much less than mu, a higgsino like of M1 is much
bigger than mu.
To neutralino over-produce the DM density, therefore,
All scalar masses are set to m0 at GUT scale, three gaugino
masses are each set to m1/2.
 Blue region is where
the relic density is
Consistent with data.
 LEP chargino bound
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In the upper part, LSP is a
Mixed bino-higgsino type
There is also a viable
region close to lightest
stau LSP. There is also a
muon g-2 constraint.
Because of its weak gravity coupling, gravitino decouples
from the rest of the world very early, left with a huge quantity
(it must be very light to avoid over-closure).
 It can be diluted through inflation
 Gravitino will be regenerated through reheating process.
 If gravitino decays, its life time will be around M2pl/M3, which
could affect BBN.
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If gravitino is the lightest supersymmetric particle, it lives long
However, decay (to gravitino) of the next-to-the lightest
supersymmetric particles can affect BBN
This problem can be solve through small R-parity breaking
decays, which lead to a gravitino with lifetime much longer
than that of the universe.
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Superstring theories motivate space-time with extra
dimensions
Many popular scenarios
 Flat large extra dimension (millimeter scale)
 Randall-Sundrum scenario
 Universal extra dimension (UED) in which all SM fields are free to
propagate in the bulk
 …
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UED model assumes the extra dimension of size R ~TeV-1.
The excitation in the extra dimension has TeV scale mass and
can serve as a DM candidate.
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KK states arise from the excitations in the extra dimension
with masses
the additional mass is called xero mode mass.
 KK parity ensures that the extra dimensional excitation is
stable.
 DM candidates include the KK excitations of photon, Z, and
neutrinos, higgs boson, and graviton. The best possible
candidates are the first two types.