Neutralino Dark Matter in
Supersymmetric Models
Chung Kao [Jung Gau]
University of Oklahoma
Norman Oklahoma
† Presented
at the National Central University, December 27, 2004.
Neutralino Dark Matter in
Supersymmetric Models
I.
The Search for Neutralino Dark Matter
with High Energy Neutrinos
• Minimal Supersymmetric Model
• Minimal Supergravity Model (mSUGRA)
• mSUGRA with Non-universal Higgs
Masses
II. Implications of New CMB Data for
Neutralino Dark Matter
Dark Matter in the Universe
• In 1933, Fritz Zwicky studided the
motions of distant galaxies and
estimated the total mass of a group of
galaxies by measuring their brightness.
When he used a different method to
compute the mass of the same cluster of
galaxies, he came up with a number that
was 400 times his original estimate!
• This discrepancy in the observed and computed masses is
now known as "the missing mass problem." In 1970's,
scientists began to realize that only large amounts of
hidden mass could explain many of their observations.
• Today, scientists are searching for dark matter not only to
explain the gravitational motions of galaxies, but also to
validate current theories about the universe.
MACHOs
• Massive Compact Halo Objects are non-luminous objects
that make up the halos around galaxies. MACHOs are
thought to be primarily brown dwarf stars and black holes.
• The existence of brown dwarfs was predicted by theories
that describe star formation.
• Black holes were predicted by Einstein's General Theory
of Relativity.
WIMPs
• Weakly Interactive
Massive Particles are
smaller than atoms.
• They have mass, but their
interactions are so weak
that they pass right
through ordinary matter.
•
Since each a WIMP has only a small amount of mass, there needs to
be a large number of them to make up the bulk of the missing
matter. That means that millions of WIMPs are passing through
ordinary matter--the Earth and you and me--every few seconds.
Composition of the Universe
WMAP best fit
WIMPs
I. The Search for Neutralino Dark
Matter with High Energy Neutrinos
• Stable weakly interacting massive particles
(WIMPs) are attractive cold dark matter candidates.
• The WIMPs in our galaxy halo can be
gravitationally trapped and accumulated by the Sun
and the Earth.
• They can annihilate into weak bosons and heavy
quarks which subsequently decay into neutrinos.
• The energetic muon neutrinos can be detected in
large ice or water detectors by the Cerenkov light.
Barger, Halzen, Hooper and Kao, Phys. Rev. D 65, 075022 (2002).
Jungman, Kamionkowski and Griest (1996); Silk, Olive and Srednicki (1985);
Ng, Olive and Srednicki (1986); Krauss, Srednicki and Wilczek (1986);
Gaisser, Steigman and Tilav (1986); Diehl, Kane, Kolda and Wells (1995);
Berezinsky et al. (1996); Nath and Arnowitt (1997); Bergstrom, Edsjo and Gondolo
(1998); Feng, Matchev and Wilczek (2001), Bertin, Nezri and Orloff (2002).
The Matter Density in the Universe
The matter and energy density of the
Universe (ρ) is often described in terms of a
relative density Ω = ρ/ρc, with
• ρc = 3 H02/(8πGN) ≅ 1.88 × 10−29 h2 g/cm3
= 1.1 × 10-5 h2 GeV/cm3,
= the critical density to close the Universe,
• H0 = the Hubble constant,
• h = H0/(100 km sec-1 Mpc-1), and
• GN = the Newton’s gravitational constant.
Evidence of Dark Matter
• Studies on clusters of galaxies and large scale
structure suggest that the matter density ΩM ≥ 0.2.
• The baryon density from Big-Bang Nucleosynthes is
Ωbh2 = 0.020 ±0.002.
• The matter density inferred from observations of
supernova, and the CMB data from BOOMERanG,
MAXIMA and DASI is ΩM = 0.3 ± 0.05.
• From WMAP and SDSS data, the best fit
parameters are: ΩM = 0.30 ± 0.04, h = 0.70 ± 0.04,
and ΩCDMh2 = 0.12 ± 0.01.
Bennett et al., astro-ph/0302207; Spergel et al., astro-ph/0302209;
Tegmark et al. [SDSS Collaboration], astro-ph/0310723.
Weakly Interacting Massive Particles
• The critical density of the Universe is closely related to
the weak scale if WIMPs (χ) make major contributions
to the present matter density of the Universe.
• The WIMP annihilation cross section is approximately
σ ∼ α2/mχ2,
from dimensional analysis, and their relative density is
Ωχ h2 ~ 3 × 10−27 cm3 s−1/<σv>
<σv> ∼ 1 × 10−19 cm3 s−1 (α2/mχ2 ) [mχ in GeV]
where α is the fine-structure constant (α ∼ 10−2) .
• For Ωχ∼1, we have mχ∼mw .
Scherrer and Turner (1985).
Weakly Interacting Massive Particles
The time evolution of the number density (n) of WIMPs
is described by the Boltzmann equation
dn/dt = −3Hn −<σv> (n2−nE2)
where
• H = the Hubble expansion rate,
• <σv> = the thermally averaged cross section (σ)
times velocity (v),
• nE = the number density at thermal equilibrium.
The Neutralino Dark Matter
A supersymmetry (SUSY) between fermions and bosons
provides an elegant explanation for light Higgs bosons.
• Quantum corrections with large couplings between
top quark and Higgs bosons at the grand unified scale
can spontaneously break the electroweak symmetry.
• With particle mass spectra of minimal supersymmetry
and MZ≤ MSUSY ≤ a few TeV, the strong and the
electroweak couplings meet at MGUT ≈2 × 1016 GeV.
• If R-parity is conserved, the lightest SUSY particle
can be a good candidate for cold dark matter.
Muon Neutrinos from WIMP Annihilation
To estimate the indirect detection rate for a generic
WIMP dark matter, we make the following assumptions:
• the WIMPs contribute to most of the measured halo
density and their flux is
φχ= nχ vχ ≅ (ρχ/mχ) vχ ≅ (1.2 × 107/mχ ) cm−2 s−1,
• the WIMP-nucleon cross section is approximately σ(χ
N) ≡ σDA ≅ (GFmN2)2 /mW2 = 6 × 10−42 cm2,
• the WIMP annihilate about 10% into neutrinos
from χχ→ W+W− or QQ where Q is a heavy quark.
*In this section, the galactic WIMP density ρχ = 0.4 GeV/cm3 and vχ= 300 km/s.
The Indirect Detection Rate
The indirect detection rate for neutrinos from WIMP
annihilation in the Sun can be estimated by determining:
(i). the capture cross section in the Sun
σSUN = f (nNuceons)(σElastic Scattering) = f (1.2 ×1057) σDA,
where f ~ 1-10 is a focusing factor given by the ratio of
kinetic and potential energy of the WIMP near the Sun;
(ii). the WIMP flux from the Sun which is given by
φSUN = φχ σSUN /4πd2
where d = 1 A.U. = 1.5 × 1013 cm;
The Indirect Detection Rate
(iii). the neutrino flux obtained with the branching
ratio: φν = (0.1) φSUN = (3 × 10−5)/mχ cm−2 s−1;
(iv). The probability to detect the neutrino, that is
P = NAσνRµ = 2 × 10−13 mχ2, with
NA = Avogadro number = 6.0 × 1023,
σν = σ(ν+N→µ+X) = 0.5 × 10−38 Eν (GeV) cm2,
R = muon range = 500 cm Eµ (GeV);
(v). the number of events from the Sun per unit area
detected by a neutrino telescope is
dNID/dA = 1.8 × 10−6 mχ (year−1 m−2).
J. Ahrens et al., astro-ph/0202370
High Energy Neutrino Telescopes
The process of detecting neutrinos by looking for
neutrino-induced muons is
νµ + N → µ + X, where
N is a nucleon in the material surrounding the detector.
• The detector has an effective volume that is the
product of the detector area and the muon range in
rock (Rµ). The muon range increases with energy.
• The AMANDA has an effective area of 104-105 m2.
The ANTARES has an effective area of 0.1 km2.
The effective area of the ICECUBE is about 1 km2.
• Barger, Halzen, Hooper and Kao, Phys. Rev. D65, 075022 (2002).
Antarctic Muon and Neutrino Detector Array
(AMANDA)
Astronomy with a Neutrino Telescope and Abyss
environmental RESearch (ANTARES)
The Background and Detector Threshold
• For indirect detection, the background event rate is
determined by the flux of atmospheric neutrinos in
the detector coming from a pixel around the Sun.
• For large mχ, Eµ ≈ mχ/4 > 100 GeV, the number of
background events in a 104 m2 detector is about 102/Eµ
(TeV) and the pixel size is determined by the angle
between muon and neutrino ∼ 1.2o/√[Eµ(TeV)].
• The typical energy thresholds for high energy neutrino
telescopes are in the rage of 25 GeV to 100 GeV.
The Background and Detector Threshold
Eµ (GeV)
10
N(BG)
in 104 m2
in 2π
3200
N(pixels)
of solar
size in 2π
140
N(BG)/year
per 104 m2
per pixel
23
100
1060
1.4 × 103
0.8
1000
110
1.4 × 104
8 × 10−3
The Background and Detector Threshold
For large mχ, the signal to the background ratio is
(NS/NB )ID = (dNID/dA)/(dNB/dA) > 7.2 × 10−6 mχ3
mχ(GeV)
50
500
2000
Indirect Events
/104 m2/year
NS/NB
2.3 × 101
2 × 102
1.7 × 102
>1
> 102
> 104
Relic Density of the Lightest Neutralino
In significant portions of the parameter space in most
SUSY models, the lightest neutralino (χ1) is the LSP
and the favored cold dark matter particle.
The relic density at the present temperature (T0) is
Ωχh2 = ρ(T0)/(8.0992 ×10−47 GeV4), where
ρ(T0) ≅ 1.66 × (1/MPl) (Tχ/Tγ)3 Tγ3 √(g*)/(∫〈σv〉dx)
with Tχ/Tγ being the ratio of the neutralino
temperature to the microwave background temperature.
V. Barger and C. Kao, (1998);
V. Barger and C. Kao, Phys. Lett. B518, 117 (2001);
V. Barger, C. Kao, P. Langacker and H.S. Lee, to appear in Phys. Lett. B (2004).
Summary for the MSSM
In most SUSY models, the lightest neutralino (χ01) is
the preferred SUSY particle dark matter and it is a
mixture of gauginos and higgsinos,
χ0
~
1
~3
~0
~0
= z11 B + z12 W + z13 H 1 + z14 H 2.
The gaugino fraction can be defined as
fG = z112 +z122
and the higgsino fraction can be defined as
fH = z132 + z142.
The lightest neutralino is more gaugino-like for µ > M2
and gauginos annihilate mostly into fermions; while it
becomes more higgisino-like for M2 > µ and the
higgsinos annihilate dominantly into gauge bosons.
A Grand Unified Theory
• At a range of 10−29
cm, the world may
be a simple place
with just one
important force.
• In 1973, Georgi
and Glashow
proposed a unified
theory based on a
SU(5) symmetry.
Supersymmetric Unification
With the mass spectra
of MSSM particles,
the renormalization
group evolution is
consistent with
MGUT ∼ 2 ×1016 GeV
and an effective
SUSY mass scale in
the range
MZ < MSUSY < 2 TeV.
The Minimal Supergravity Model
In the minimal supergravity model, it is assumed that
SUSY is broken in a hidden sector with SUSY
breaking communicated to the observable sector
through gravitation interactions, leading naturally to a
(i) common scalar mass (m0), (ii) a common gaugino
mass(m1/2), (iii) a common trilinear coupling (A0), and
(iv) a bilinear coupling (B0),
at the GUT scale (MGUT 2× 1016 GeV).
Through minimization of the Higgs potential, the B
parameter and magnitude of the superpotential Higgs
mixing parameter (µ)are related to tanβ and MZ.
The Minimal Supergravity Model
The gaugino masses at the weak scale have the
following relations:
(i) M1/α1 = M2/α2 =M3/α3,
(ii) M1 ≅ 0.4 m1/2, M2 ≅ 0.8 m1/2, M3 ≅ 2.7m1/2.
We impose the following theoretical requirements:
(i) radiative electroweak symmetry breaking,
(ii) the correct vacuum for EWSB obtained,
(iii) lightest neutralino as the lightest SUSY particle.
Barger and Kao (1998)
The mSUGRA Model
Most relevant parameters: m1/2, m0 and tanβ.
In most of the mSUGRA parameter space, χ01 is a
gaugino (bino). For m0 ≤ 100 GeV or m0 ≥ 1000 GeV,
χ01 can have a large higgsino fraction.
For tanβ ≥ 35, the indirect detection rate of the
neutralino dark matter can become very significant in
a large region of the parameter space.
Recent studies on Ωχh2 in the mSUGRA model :
V. Barger and C. Kao, Phys. Rev. D57, 3131 (1998); Phys. Lett. B518, 94
(2001). J. Ellis, K.A. Olive, Y. Santoso, and V.C. Spanos (2003);
H. Baer, C. Balazs and A. Belyaev (2002); R. Arowitt and B. Dutta (2002);
L. Roszkowski, R. Ruiz de Austri and T. Nihei (2001);
A. Djouadi, M. Drees and J.L. Kneur (2001).
Summary for the mSUGRA Model
• In large portions of the MSSM parameter space with
tanβ ≥ 10, the indirect detection rate is predicted to be
greater than 10 events/km2/year. However, the indirect
search for neutralino annihilation may be difficult for
tanβ ≤ 10 or mχ ≤ 200 GeV.
•The indirect search for the mSUGRA neutralino dark
matter will be challenging. Only several years of
observation with a square kilometer detector will likely
lead to a discovery.
Minimal Supergravity Model
with Non-universal Higgs Masses
• The mSUGRA model with non-universal boundary
conditions for Higgs boson masses and tanβ ≥ 35 give
more interesting rates. mHi(GUT) = (1+δi) m0, i = 1, 2.
• SUSY neutralino dark matter with mχ ≥ 200 GeV
offers great promise for indirect detection experiments.
Together with direct detection experiments of
neutralino dark matter and collider experiments, highenergy neutrino telescopes will be able to survey large
regions of parameter space beyond present experiments.
II. Implications of New CMB Data
for Neutralino Dark Matter
• Recent precision mapping of the Cosmic
Microwave Background (CMB) anisotropy implies
that the cold dark matter (CDM) density should be
ΩCDMh2 = 0.1126 ± 0.0081 (WMAP)
= 0.12 ± 0.01 (SSDS+WMAP)
• A more recent analysis suggests that
ΩCDMh2 = 0.122 ± 0.018
Spergel et al. (2003); Tegmark et al. (2003); Fosalba and Szapudi (2004);
Barger and Kao (2001);
Ellis,Olive,Santoso, Spanos (2003); Baer and Balazs (2003),
Chattopadhyay, Corsetti, Nath (2003); Lahanas, Mavromatos, Nanopoulos (2003);
Wang and Yang (2004).
Δaµ
=(23.9±
10.0)
Barger and Kao (2001)
Implications from the CMB data
Neutralino Dark Matter in a
Supersymmetric U(1)’ Model
Neutralino Dark Matter in a
Supersymmetric U(1)’ Model
Direct Direction of Neutralinos
• In the mSUGRA model, the χ-nucleon
scattering cross-section depends strongly on
the values of tanβ and mχ;
it increases with tanβ but decreases with mχ.
• The expected event rate in a 73Ge detector for
mχ = 120 GeV and tanβ = 35
is about 0.015 events/kg-day.
Baer, Balazs, Belyaev and O'Farrill (2003); Ellis, Ferstl, Olive, and Santoso
(2003); Drees, Kim, Kobayashi, and Nojiri (2000); Gabrielli, Khalil, Munoz,
and Torrente-Lujan (2000); Jungman, Kamionkowski and Griest (1996).
Direct versus Indirect Detections
Bertin, Nezri, and Orloff (2002).