Evidence For and Observational Bounds on Dark Matter
• Doppler Shift of spectral lines from galaxies in galactic clusters indicate 400 times more binding
energy than can be accounted for by luminous mass!
Virial Theorem tells us that for a gravitationally bound N-body system in thermal equilibrium,
Kinetic Energy and Potential Energy are related by:
First such conclusion by Fritz Zwicky in 1933 followed by several other studies.
PEKE 2−=
Evidence For and Observational Bounds on Dark Matter
• Rotational Curves. Of galaxies in galactic clusters and of stars in individual galaxies.
Newtonian gravity from a central mass distribution gives a velocity distribution:
Nearly flat velocity profile observed is far from M=constant.
We are immersed in a halo of density profile , or, M ~ r!
Lower bound set:
r
rMv
)(=
21~)( rrρ
1.0>ΩDM
Evidence For and Observational Bounds on Dark Matter
• Gravitational Lensing Studies
• Detailed N-body simulations of galactic structure.
Converge to a value for local dark matter density in our solar system
323.0 cmcGeVDM =ρ
Candidates for Dark Matter
Conditions
• They must be stable on cosmological time-scales or else they would’ve decayed by now.
• They must interact very weakly or not at all with electromagnetism.
• They must have relic density comparable to
Candidates
Primordial black holes?
Axions?
Weakly Interacting Massive Particles?
o Heavy Neutrinos?
o Sneutrinos?
o Neutralinos?
Two observational bounds on masses and cross sections.
Low mass would thermalise at relativistic velocities which would wash out structure formation.
Cross section is inversely related to present relic density.
323.0 cmcGeVDM =ρ
v
pbh
WIMP
WIMP σ1.02 ≅Ω
Candidates for Dark Mattero Heavy Neutrinos?
We know they have mass. But would be relativistic and constitute Hot Dark Matter. If density
is what is expected, it would wash out structure formation in the universe. Upto 45 GeV is
excluded by LEP. Heavier neutrinos “unnatural”. What would keep it stable?
o Sneutrinos?
Have large interaction cross sections. Insignificant relic density.
o Neutralinos?
Possible. They have the correct thermal relic density for most values in parameter space.
They are a mixture of a bino, a wino and two neutral higgsinos which have same quantum
numbers. Undetermined parameters of mixing: M1, M2, µ, tan β. Mass matrix given by
the diagonalisation of MN where:
( )
−−
−−
−
=
=
0cossinsinsin
0coscossincos
cossincoscos0
sinsinsincos0
,
~~~~
2
1
~
000
µθβθβµθβθβ
θβθβθβθβ
ψ
WZWZ
WZWZ
WZWZ
WZWZ
N
ud
mm
mm
mmM
mmM
M
and
HHWB
..2
1~_ ccMLN
T
massneutralino +−=∆ ψψ
Direct Detection of Neutralinos
( ) ∫+=
velocityescape
recoilforvelocitynucleusWIMP
nucleusWIMP
recoil
dvv
vfqF
mm
m
dE
dR_
__min_
20 )()(
2
ρσ
The predicted collision rate with respect to nuclei in detector is given above.
σ0 is the total cross section of the WIMP-nucleus interaction, ρWIMP is the density of WIMPs,
mWIMP and mnucleus are the masses of the WIMP and nucleus respectively, F2(q) is a nuclear form
factor dependent on the momentum transferred from the WIMP to the partons q, and f(v) is the
distribution of WIMP velocities in the halo. Of these the mass and interaction cross section are
unknown and hence scattering rates as a function of energy are drawn as contours in the WIMP
mass-cross section plane.
Neutralino-nucleus cross section has spin dependent part and spin independent part. Nuclei
without spin like Ge interact with spin-independent coupling while nuclei with spin like I127
interact with both.
( )( )
dvevkT
mdvvf kT
vm
DM
DM
DM
22
23
24
−=
ππρ
The velocity distribution of neutrinos can
be written as a Maxwellian f(v) with rms
speed v. The temperature T is related to the
gravitational potential at the region of
space we are concerned about.
k
mT
gravityWIMPΦ=
Direct Detection of Neutralinos
The cross section normalized to a nucleon for a range of neutralino models within MSSM
and MSUGRA is shown in Figure 2. The pink area is bino dominated while the green
bounded area is higgsino dominated. Both spin dependent and independent parts are used.
Direct Detection of Neutralinos
Expected Characteristics of the Recoil Signal
• A characteristic but featureless recoil spectrum depending on target nuclear mass and spin.
• Events distributed uniformly throughout the detector.
• An expected annual modulation in both the event rate and the recoil spectrum since the Earth’s
orbital velocity adds and subtracts from the Solar System orbital velocity in the galaxy.
• An expected daily modulation in the scattering rate due to WIMPs because of the Earth
shadowing the incident flux from the direction of orbital motion.
• A daily and annual modulation in direction corresponding to the angle subtended by the earth’s
surface at the experiment site and the velocity of revolution around the Sun.
Characteristics of an Ideal Detector
• Energy threshold < 1 keV
• Good energy resolution to see daily and annual modulations in the recoil signal.
• High ability to discriminate between nuclear recoil and background events.
• Low radiation background around the site of the experiment. To protect against cosmic ray
induced backgrounds, experiments are done underground. Cross sections calculated in MSSM
models predict interaction rates of at most 1 event per kg per day, much lower than usual
radioactive backgrounds.
• Large quantities of detector material to ensure a sufficiently high WIMP count rate.
• Stable operation for a number of years.
Direct Detection of Neutralinos
Ionisation Detectors
Germanium ionization type detectors were among the first to be used in direct searches. A germanium
nucleus is roughly of the same mass as the estimated WIMP mass and hence is the most suitable
candidate for detecting a nuclear recoil event. COSME and TWIN were two experiments that used it.
Freshly fined or enriched germanium is preferred to decrease cosmogenic backgrounds. No significant
signals were seen.
Solid Scintillation Detectors
Either a solid crystal or liquid scintillator is used. NaI has been the most effective. The non-zero nuclear
spin of both Na and I make them more sensitive to axial coupling. They are also cheaper and hence
easier to make massive detectors out of than germanium.
Cryogenic Phonon Detectors
Most of the energy imparted to the nucleus of a crystalline target ultimately end up as phonons in the
crystal lattice. We know from Debye’s Law that the specific heat capacity of a crystal at low
temperatures goes as T3. Hence to observe a large change in temperature due to phonons, we must keep
the crystal cold. At a temperature of 20 mK, a 1 kg detector could achieve 100 eV of resolution with a
correspondingly low threshold. After the phonons thermalise, one can estimate the rise in temperature
as 10-7 K per keV for a 1 kg detector.
Direct Detection of Neutralinos
A compilation of various direct search
experiments on the left.
The upper bounds of spin-independent cross
sections with respect to mWIMP from some
experiments shown below.
Bounds on Collider Physics Set by Direct Searches
Direct dark matter searches offer limits on the free parameters of SUSY in searches at the LHC.
Here I give an example of such a study limiting the free parameters of the MSSM by V.A. Bednyakov.
Experimental bounds on MSSM free parameters:
LSP-nucleus interaction rate calculated while randomly
picking a point in this parameter region of the MSSM.
If it violated experimental bound, the parameter set
was discarded.
GeVMGeVM
GeVMGeVMGeVMGeVM
GeVMGeVMGeVM
HH
tqe
70,79
85,210,70,43
127,76,45,99,65
0
03,2,112
~~~~
~~~
≥≥
≥≥≥>
≥≥≥
±
++
ν
χχχ
262
3
2
3
222
2
1
10,,,10
100060
50tan1
2,,2
11
GeVmmmmGeV
GeVMGeV
TeVaMTeV
TeVMTeV
LQLQ
A
t
<<
<<
<<
<<−
<<−
β
µ
Bounds on Collider Physics Set by Direct Searches
The interaction rate integrated over recoil
energies versus LSP mass from this study.
The scatter points on the cross section-mass
plot represent the LSP-nucleus cross sections
while scanning across the MSSM parameter
space. The lines represent the lower limit
reaches of direct dark matter search
experiments, some of which are currently in
operation. By excluding points on the MSSM
parameter space using direct searches like
DAMA, HDMS and GENIUS, one can narrow
down on the possible range of supersymmetry
parameters and hence signal channels at the
LHC.