Direct Detection of WIMP Dark Matter

A Exam Presentation:
Direct Detection of WIMP Dark Matter
Christian Spethmann
May 1st , 2007
Outline
1 The WIMP Hypothesis
Evidence for Cold Dark Matter
Decoupling and Relic Density
Supersymmetric Dark Matter
Little Higgs Dark Matter
UED Dark Matter
2 Direct WIMP detection
Expected Signal and Challenges
Ionization Detectors
Scintillators
Cryogenic Detectors
3 The CDMS Experiment
Experimental Setup
Results from CDMS-II
Future Prospects
Gravitatating Dark Matter
On the scale of galaxies and galaxy clusters, predictions from
gravitational laws do not match observations:
• Rotation curves of galaxies do not match predictions from the
distribution of luminous matter:
v = const vs. v ∝ 1/r 2
• Intracluster gas emits energetic X-rays. Gas temperature ⇒
depth of potential well. Does not match visible mass.
• Gravitational lensing by galaxy clusters ⇒ size and mass of
cluster larger than observed galaxy distribution
Either laws of gravity have to be modified, or there is a huge amount
of unknown dark matter in the universe.
CMB Power Spectrum
Resonance patterns in the CMB power spectrum provide more
evidence for dark matter.
Dark Matter Density And Neutrino
Fraction
WMAP data: consistent with hot dark matter (ν’s) . . .
small scale structure formation ⇒ need cold dark matter
Relic Density: General Considerations
A particle species freezes out when the interaction rate drops below
the expansion rate of the universe, as given by the Hubble constant
H = Γ = nψ hσA v i
There are two qualitatively different cases:
• Tf & M: particle is relativistic at freeze-out and its equilibrium
density is comparable to the photon/entropy density
⇒ current relic density is still of order unity times current entropy
density (e.g. ν’s)
• Tf < M: equilibrium density is exponentially suppressed at
freeze-out temperature, relic density is correspondingly smaller
Numerical Solutions of the Boltzmann
Equation
Simplifying assumptions:
• Phase space distribution
functions are spatially
homogeneous and isotropic
• All particle species except
one are assumed to be in
thermal equilibrium
• T/CP invariance
• Maxwell-Boltzmann statistics
Larger interaction cross sections (with constant mass) correspond to
smaller relic densities today.
Estimate of WIMP Relic Density - Part
One
Assumptions:
• Energy-independent cross section
• Freeze-out temperature/mass ratio of mχ /Tf = 20
• Cross section of weak interaction strength
In the radiation era:
p
H = 1.66 g ∗ T 2 /mPl ,
s=
2π 2 ∗ 3
g T
45 S
g ∗ is the number of relativistic degrees of freedom, gS∗ is identical to
g ∗ when all particle species have a common temperature. Using the
freeze-out condition H = Γ = nψ hσA v i we find
nf
100
n0
=
≈
√
so
sf
mχ mPl g∗ hσA v i
Estimate of WIMP Relic Density - Part
Two
The cross section is roughly
hσA v i ≈
2
10−4
αw
≈
.
mχ2
mχ2
Using numerical values for the present entropy density (s0 ≈ 3000
cm−3 ) and critical density (ρc = 10−5 h2 GeV cm−3 ), we get
ωd =
106 mχ2
n0 mχ
3000 cm−3
√
=
≈ 0.1
ρc
10−5 GeV cm−3 g ∗ mPl
for mχ = 100 GeV and g ∗ ≈ 100. With all the approximations that
have been made, this result can of course only be taken seriously
within one or two orders of magnitude, but it still gives a strong case
for massive, weakly interacting dark matter particles.
Motivations for SUSY and the MSSM
Motivations for SUSY are independent of cosmology:
• Hierarchy problem: sparticle loops stabilize Higgs mass
• β-functions: unification of gauge couplings
• String Theory: Need SUSY to include fermions
• Only non-trivial extension of Poincare group
The MSSM includes two Higgs supermultiplets Hu and Hd to produce
fermion masses from holomorphic superpotential. Neutral fermionic
superpartners mix, with mass matrix in the gauge eigenbasis
ψ 0 = (B̃, W̃ 0 , H̃d0 , H̃u0 ) given by


M1
0
−cβ sw mZ
sβ sw mZ

0
M2
cβ cw mZ
−sβ cw mZ 

MÑ = 
 −cβ sw mZ

cβ cw mZ
0
−µ
sβ sw mZ
−sβ cw mZ
−µ
0
Neutralino as Dark Matter Candidate
The lowest mass neutralino fits all requirements for a WIMP:
• Uncharged under U(1)QED and SU(3)C
• Interacts weakly with the standard model sector
• Stable: lightest particle with odd R-parity
Relevant interactions for cosmology:
• pair annihilation: determines relic density and chances of indirect
detection
• scattering off ordinary (baryonic) matter: determines chances for
direct detection, related to above by crossing symmetry
Non-relativistic nature of interaction:
⇒ Only the axial spin-spin interaction and the scalar interaction with
nuclei are relevant
Spin-Dependent Neutralino
Interactions
Effective Lagrangian for axial vector part of interaction:
L = dq χ̄γ µ γ5 χq̄γµ γ5 q
The coupling strength can be expressed in terms of fundamental
interactions and mixing coefficients. Main contributions to this
process: Z and squark exchange.
Wigner-Eckardt theorem:
Axial quark current can be replaced by the nuclear spin operator sNµ
when a matrix element between nucleon states is taken:
hN|q̄γ µ γ 5 q|Ni = 2sNµ λq
Spin-Dependent Neutralino
Interactions
Spin-dependent elastic neutralino cross section for scattering off an
atomic nucleus:
σ0axial 2
dσ
=
F (|q|)
2
d|q|
4mr2 v 2
• F (|q) is the nuclear form factor
• mr is the reduced nuclear/WIMP mass
• σ0axial = (32/π)GF2 mr2 Λ2 J(J + 1) is a “standard” cross section for
zero momentum transfer
1
[ap hSp i + an hSn i]
J
hSp i is the nuclear expectation value of the spin content of the proton
group hSn i the same for the neutron group.
⇒ Axial interaction strength is proportional to the nuclear spin J
Λ=
Spin-Independent Neutralino
Interactions
Scalar part of the interaction is enhanced
by the exchange of the
lightest Higgs boson:
• loop diagrams
coupling to gluons
• strange quark
component for
large tan β
Spin-Independent Neutralino
Interactions
Including nuclear effects, the differential cross section from scalar
interactions is:
σ0scalar 2
dσ
=
F (|q|)
d|q|2
4mr2 v 2
with the “standard” cross section
σ0scalar =
4mr2
2
[Zfp + (A − Z )fn ] ,
π
where fn and fp are the neutralino couplings to nucleons.
⇒ Scalar interaction strength ∝ A2 (for fn ≈ fp )
⇒ Dominates cross section for large nuclei
Neutralino/Proton Cross Sections
Neutralino-proton scattering cross sections depend on:
neutralino mass, dark matter density, muon g − 2
The Littlest Higgs Model
Little Higgs class of models:
• Relatively new idea to solve the hierarchy problem
• SM Higgs boson is a Pseudo-Goldstone boson
• Higgs mass is protected by collective symmetry breaking: picks
up only logarithmic contributions at one-loop order
Most studied model of this class: Littlest Higgs
• Global SU(5) symmetry is spontaneously broken to SO(5) at a
scale f ≈ 1 TeV
• Gauged subgroup of the global SO(5) is [SU(2) × U(1)]2 , broken
to the SM electroweak group SU(2) × U(1)
• Gauge sector includes four new heavy gauge bosons with
masses
M(WHa ) ≈ gf ,
g0f
M(BH ) ≈ √ ≈ 0.16f
5
T-Parity and the LTP
Electroweak precision measurements: ⇒ Z2 symmetry (“T-Parity”)
• The lightest T-odd particle (LTP) is stable
• The heavy gauge bosons are odd under this symmetry
• The model also includes new T-odd partners of all standard
model fermion doublets, as well as new heavy top singlet states
The heavy hypercharge boson (BH ) is expected to be the LTP and is
a viable dark matter candidate
• Couples to the SM sector via the Higgs
⇒ interaction is of weak strength
• Acceptable BH masses in the 100-300 GeV range
• It is possible to get correct relic abundances, independent of the
Higgs mass.
Spin-Independent Interactions of the
BH
Using an effective low-energy description and taking the chiral limit,
the spin-independent BH -nucleon interaction is found to be
σSI =
4πα2
mn4
1
,
729 cos4 θW mh4 (M + mn )2
where M is the LTP mass and mn is the nucleon mass. The total
spin-independent BH scattering cross section off a nucleus can be
found by substituting the total nuclear mass for mn .
Spin-Dependent Interactions of the BH
The total spin-dependent elastic scattering cross section is then
found to be
2

X
mN2
16πα2 Ỹ 4
M2
σSD =
JN (JN + 1) 
λq  ,
3 cos4 θW (M + mN )2 (M 2 − M̃ 2 )2
q=u,d,s
where M̃ is the heavy quark/lepton mass scale. The contribution from
the quark vector current is found to be suppressed in the
non-relativistic limit and can be neglected.
Universal Extra Dimensions
In this class of models, SM fields also propagate in one or more
compactified extra dimensions
• This introduces a tower of Kaluza-Klein modes for all particles
• Momentum conservation in the extra dimension(s) is broken by
loop corrections and by the orbifold compactification
• The remaining Z2 symmetry is called Kaluza-Klein (KK) Parity
• The lightest KK-odd particle (LKP) is stable (B (1) )
For the nth level KK mode with one extra dimension, the neutral
(n)
gauge boson mass matrix in the (B (n) , W3 ) basis is given by
!
1
n2
1 2 2
2
2
+
g
v
+
δM
g
g
v
1
2
2
1
4 1
4
R
,
1
n2
2
+ 41 g22 v 2 + δM22
4 g1 g2 v
R2
Cosmological Constraints on the LKP
Mass
Relic density calculations (not including coannihilation effects) favor
an LKP mass of 1-1.5 TeV
LKP Scattering Cross Sections
Elastic spin-dependent (blue) and spin-independent (red) proton-LKP
cross sections for different KK particle masses and different values of
r = (mq (1) − mB (1) )/mB (1) .
Elastic and Inelastic Scattering
We now look at the experimental possibilities for direct detection of
dark matter:
• Inelastic scattering
• The WIMP will produce an excited nuclear or electronic state or
ionize the atom
• Backgrounds: cosmic ray muons, neutrinos, and high energy
electrons and photons from natural radioactivity
• Impossible to isolate and identify WIMP events
• Elastic scattering
• The WIMP exchanges momentum with the nucleus as a whole,
producing an observable recoil
• Backgrounds: neutrons from radiactive sources
• Easier to identify as a WIMP interaction
The Expected Recoil Signal
Why is Dark Matter so difficult to detect?
• WIMP distribution: % = 0.3 GeV/cm3 , hv i = 270 km/s
• Predicted scattering event rate: 10−6 to 10 events/(kg day).
• Recoil energy of tens of keV’s for a 100 GeV WIMP.
• Background event distribution has same shape as signal
Annular Modulation/Detector Types
Fortunately, the WIMP recoil spectrum has two features which can be
used to distinguish it from background:
• Annular modulation of the signal strength of vEarth /vSun ≈ 0.07
• Forward-backward asymmetry of O(1), but requires directional
information
Three different secondary effects from nuclear recoils can be used to
construct direct WIMP detectors:
• Ionization (electrons)
• Scintillation (light)
• Heat energy (phonons)
The first generation of WIMP detectors was sensitive to just one of
those effects, while some newer detectors are able to look for two out
of the three effects to increase background rejection rates.
Ge/Si Diode Experiments
The first Dark Matter experiments we originally built to seach for
neutrinoless 2β-decay. Dedicated dark matter detectors include
COSME, IGEX, the Heidelberg/Moscow experiment, HDMS, and the
proposed GENIUS and GENEON detectors.
Advantages of using Germanium as the detector material:
• High radiopurity
• Low energy thresholds (≈ 2.5keV)
• Good energy resolution (1 keV at 300 keV)
• Quenching factor (nuclear/e ionization efficiency) of ≈ 25%
Main disadvantage: no way to distinguish signal from background
(except anti-coincidence to veto against multiple scattering, as done
by HDMS).
Germanium detectors can be build with the natural isotope mix, with
enriched 73 Ge (I=9/2) or with enriched 76 Ge (I=0).
The DRIFT detector series
The DRIFT detector series can measure directional information.
A gas target has to be used because the ranges of recoil nuclei in
solids and liquids are very short (≈ 10 nm). The low target mass of a
gas detector is compensated by background rejection rates of 99.9 %
(at 6 keV).
NaI Crystal Detectors
Experiments using NaI-crystal scintillators have been build by
UKDMC and the DAMA collaboration. Detectors of this type have less
energy resolution and a higher threshold then Germanium. Their
advantages are
• Building detectors with large masses to increase the total
sensitivity is easier
• NaI Scintillators are a well understood and widely used
technology in nuclear experiments (510 Lab)
• NaI is sensitive to both scalar and axial interactions, because
both elements naturally have nonzero nuclear spin: J(23 Na)=3/2,
J(127 I)=5/7.
• NaI-crystal scintillators offer the ability to distinguish between
WIMP and electron/photon scattering events from pulse height
and decay time constant analysis
DAMA signal oscillation
The DAMA NaI experiment claims to have observed a dark matter
signal with annular modulation, consistent with a 60 GeV WIMP.
• Same parameter space has been explored by CDMS and
Edelweiss
• Observed modulation signal from DAMA is difficult to reconcile
with the exclusion limits of those experiments.
Xe Ionization Detectors
A different kind of scintillation detector uses Xenon as the detector
material. Detectors of this kind have a liquid and a gas phase:
• A recoil event occurs in the
liquid phase
• It produces light and
ionization
• The ions drift into the gas
phase and produce
secondary scintillation
• Nuclear recoils have weaker
secondary signal
Xenin has the right atomic weight
to acquire large recoil momentum,
and can be separated into isotopes with zero and non-zero spin.
This detector design is used by the
ZEPLIN dark matter experiments.
Cryogenic Detectors
Cryogenic detectors directly measure the total amount of energy
deposited by a WIMP scattering event:
• At low temperatures, the specific heat of a crystaline target
varies as T 3
• At 20 mK, a 1 kg detector could theoretically achieve 100 eV
resolution
• In practice the resolution is limited by the efficiency of the
thermalization process
Experiments that use this approach are
• CRESST: CaWO4 target crystal, superconducting W
thermometer, scintillation signal is independently measured
• EDELWEISS: Germanium detector, neutron transmutation doped
(NTD) Ge thermistors, ionization signal is also measured
• CDMS: see next section
Signal Discrimination at EDELWEISS
Surface electron scattering produces less ionization then bulk events
and makes background rejection more difficult.
The CDMS detector
Cryogenic Dark Matter Search:
• Si and Ge semiconductor targets
• Operating temperature: 50 mK
• ZIP elements: cylindrical, 1 cm thick, 3 in diameter
Phonon Energy Readout System
The energy deposited by a WIMP interaction is measured through the
following chain of events:
• WIMP scattering causes nuclear recoil
• Phonons are created in the Ge/Si crystal, propagate to aluminum
• Phonons split Cooper pairs in Al and create quasiparticles, those
diffuse to W strips
• Tungsten is close to transition temperature. Quasiparticles
generate heat and produce large change in resistivity.
• W strips are inductively coupled to SQUIDs
Ionization is simultaneously measured by collecting charge carriers
with an electrode on the opposite side of the ZIP detector.
Event Discrimination at CDMS
Rejection of surface scattering events at CDMS:
• Near-surface events produce faster propagating photons
• Faster signal rise times can be used to discriminate events
Radiation Shielding at CDMS
• Location at Soudan Mine
(780 m rock, 2090 mwe)
reduces muon flux by
factor of 5 × 104
• muon veto system, 40
paddles of 5 cm thick
plastic scintillators
• 22.5 cm of Pb and 50 cm
polyehylene against
photons and neutrons
• Use of archaeological lead
CDMS Results: Spin-Independent
interaction
• Results start to exclude SUSY parameter space
• DAMA oscillation still consistent with small WIMP masses
• Si offers better kinematics for small WIMP masses
CDMS Results: Spin-Dependent
interaction
Left: pure neutron coupling, Right: pure proton coupling
Symbols represent limits from other experiments: CRESST (x),
PICASSO (), NAIAD (o), ZEPLIN (∆), SuperKamiokande (*)
Upscaling of current experiments
Several new detectors with a target mass of ≈ 1 ton are planned for
the next decade. All of those are basically upscaled versions of
current experiments, e.g.:
• CRESST/EDELWEISS ⇒ EURECA
• DAMA/NaI ⇒ LIBRA
• CDMS ⇒ SuperCDMS
Because of the larger target mass, lower detection limits can only be
reached by reducing the background:
• Improvements in radiopurity of detector materials
• Better shielding, deeper underground sites
• Improved background rejection algorithms
The future of CDMS
The grey regions represent a general MSSM scan(light), mSUGRA
(medium) and gµ − 2 consistent SUSY models
• SuperCDMS A: 25 kg, completed by 2011
• SuperCDMS B: 150 kg
• SuperCDMS C: 1000 kg