evidence for and observational bounds on dark...

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−=


• 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


• 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=


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.


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.


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.


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.

evidence for and observational bounds on dark...

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