1. Supersymmetric Dark Matter
Shufang Su • U. of Arizona
K. Olive, astro-ph/

2. Composition of the Universe-
We know how much, but no idea what it is.
» 0.7
Dark Energy
, quintenssence,…
» 0.02 baryon
Non-baryonic
dark matter
Baryonic dark matter (lum» 0.003)
 Hot dark matter: Neutrino
 Cold dark matter
WIMP
axions
 Other possibilities
self-annihilating DM
self-interacting DM
warm DM
fuzzy CDM …
S. Su Dark Matter

3. WIMP CDM requirements  Stable lifetime ¸ 10 Gyr  Non-baryonic
 Neutral: color (strong interaction) and electric
strong upper limits on the abundance of anomalously
heavy isotopes
 Cold: non-relativistic
 Yield correct density WIMP
weak interacting:  » 0.01, mW » 100 GeV
  » 0.1
S. Su Dark Matter

4. Not for cosmology observations
Standard Model - I II
III
Quarks u c t d s b
SM is a very successful theoretical framework that describes all experimental observations to date
Leptons e   e  
Not for cosmology observations
Dark Matter
Cosmology constant
Baryon asymmetry …
Gauge boson
(force carrier) 
W§,Z g
electro
-magnetic
» 0.01
weak
» 0.03
strong
» 0.1
=g2/4
Higgs H
S. Su Dark Matter

5. Standard Model No good candidates for CDM in SM I II III Quarks u c t- I II
III
Quarks u c t d s b
CDM requirements
 Stable
Leptons e   e  
 Non-baryonic
 Neutral
 Cold
 Correct density
Gauge boson
(force carrier) 
W§,Z g
Higgs H
No good candidates for CDM in SM
S. Su Dark Matter

6. Supersymmetry  SM is an effective theory below some energy scale -
 SM is an effective theory below some energy scale 
Hierarchy problem: MEW100 GeV , Mplank 1019 GeV ?
Naturalness problem: mass of a fundamental scalar (like Higgs) receive huge quantum corrections:
(mH2)physical  (mH2)  (100 GeV)2 H
- 2 H
-(1019 GeV)2
precise cancellation
up to 1034 order
(1019 GeV)2
 Supersymmetry
SM particle superpartner
Spin differ by 1/2
Naturalness  ms-particle » O( ) GeV
S. Su Dark Matter

7. Gauge Coupling Unification- SM
SUSY
S. Su Dark Matter

8. Minimal Supersymmetric Standard Model (MSSM)-
Spin differ by 1/2
SM particle superpartner
Squarks u c t d s b
CDM requirements
 Stable
sleptons e   e  
 Non-baryonic
 Neutral
 Cold
m > 45 GeV
Gauginos B0
W§,W0 g
 Correct density
weak interaction
Higgsino
(Hu+,Hu0) , (Hd0, Hd-)
S. Su Dark Matter

9. MSSM DM Candidates Possible DM candidates  Stable ?-
Possible DM candidates
sneutrino 
neutralino (B0,W0,Hd0,Hu0) ! i0 ~ ~ ~ ~ ~
 Stable ?
General MSSM, including B,L-violating operators -
dangerous  introduce proton decay p ! K+
R-parity SM particle: even + superparticle: odd -
no proton decay
lightest supersymmetric particle (LSP) stable
LSP  SM particle, LSP  super particle
Good candidate of DM: could be  or 10 d u P K+ ~ s - 
odd ~
S. Su Dark Matter

10. Sneutrino Dark Matter rapid annihilation, hAvi large- ~  Z
/l/q ~  
/l ~ 
W/Z f
rapid annihilation, hAvi large
light sneutrino: GeV  low abundance
heavy sneutrino: 550 – 2300 GeV  0.1    1
disfavored on theoretical ground
excluded by nuclear recoil direct detection: m ¸ 20 TeV ~
Sneutrino CDM in MSSM is excluded
S. Su Dark Matter

11. Neutralino ~ ~ ~ ~ B0, W0, Hd0, Hu0 Properties fermion neutral- ~ ~ ~ ~
B0, W0, Hd0, Hu0
Superpartner of
gauge bosons
Superpartner of
Higgs bosons
Properties
fermion
neutral
heavy: m > 45 GeV
(B0, W0, Hd0, Hu0)  neutralinos i0, i=1…4 mass eigenstates
Interactions: weak interacting / gauge coupling ~ ~ ~ ~ f  ~ H 
W,Z 
S. Su Dark Matter

12. Lightest Neutralino CDM-
Now let us focus on neutralino as a candidate for CDM
Neutralino mass matrix
Input parameter: M1, M2, , tan
i0=i B0+ i W0+i Hd0 +i Hu0 , m1 m2  m3  m4 , 1 being LSP ~
For small mixing: mZ ¿ M1, M2, 
M1< M2, ||: B0 Bino-LSP
M2< M1, ||: W0 Wino-LSP
||< M1, M2: Hu0 § Hd0 Higgsino-LSP ~
S. Su Dark Matter

13. MSSM Parameters Interactions involve the whole set of MSSM parameters-
Interactions involve the whole set of MSSM parameters
> 100 new parameters (SM: 19 parameters)
other experimental constraints
LSP
Simplest assumption (unification)
CMSSM (constrained MSSM) m0
M1/2 A0
tan
sign 
GUT scale
||,b replaced by mZ, tan
common scalar mass
common gaugino mass
common trilinear scalar
Low energy
MSSM
parameters 
S. Su Dark Matter

14. Relic Density Thermal relic density Decoupling: >H =nhvi ¼ H-
Thermal relic density
Decoupling:
=nhvi ¼ H
>H
 ! X+Y
early time
n ¼ neq
late time
(n/s)today » (n/s)decoupling
at freeze-out
T » m/20
<H
n/s
Approximately, relic / 1/hvi
S. Su Dark Matter

15. Neutralino Relic Density (I)-
10 f ~
10 + W
t-channel
(dominate)
absent for B0 ~ ~
10
Z,H
/l/q
s-channel
Important near pole
m » mZ,H/2 ~
10
Relic Density: =hAvi n » H
<v> = a+bx+…
x=T/m
Special cases:
Co-annihilation: mLSP ¼ mNLSP
Annihilation near a pole: e.g. m » mZ,H/2
S. Su Dark Matter

16. Neutralino Relic Density (II)-
No EWSB
0.1  h2  0.3
m » mA.H/2
CMSSM
Focus point
m=mZ,h/2
Co-annihilation 10-l ~
bulk
stau LSP
S. Su Dark Matter

17. Phenomenological Constraints-
Other constraints
Higgs mass
mh > GeV
b ! s  : » 10-4
exclude small m1/2
important for  <0
muon g-2
th-exp=(26 § 16)£ 10-10 b s 
muon g-2
me=99GeV ~
m= mZ,h/2 region
already excluded
b ! s 
S. Su Dark Matter

18. Bulk region and -l coannihilation region~ -
m » m
+X ! +Y in equilibrium
 decays into  eventually
Co-annihilation:, ,  ~
co-annihilation mh
bulk
if ignore co-annihilation
hvi » 1/m2,  / m/hvi
 upper bound on m
mB » 200 GeV ~
S. Su Dark Matter

19. hvi » 1/(4m2 – mA,H2)2 too big
Funnel-Like Region - ~
10
A,H
/l/q
Large tan : m » mA,H/2
A,H: heavy Higgses
SM: h0
MSSM: h0,H0,A,H§
 / 1/hvi
hvi » 1/(4m2 – mA,H2)2 too big 
 too small
S. Su Dark Matter

20. Focus Point Region (100 GeV)2 conventional wisdom focus point-
(100 GeV)2
conventional wisdom
focus point
naturalness  m0, M1/2, ||  TeV
m0 a few TeV , natural
m0 term negligible
m0 term not negligible
|| À M1
|| » M1
DM Bino-like: 10 ¼ B0
DM Bino-Higgsino mixture
Co-annihilation, funnel and focus point regions are very fine-tuned
Highly depend on the other input parameters ~
S. Su Dark Matter

21. Direct Detection of DM -
Direct detection via neutralino-nucleon scattering
DM low velocity, non-relativistic
Spin-dependent:  i  q i q
Mspin / pq h Spi/ JN + nq h Sni/ JN
Spin-independent:   q mq q / mW
Mscalar / Z fp+ (A-Z) fn -
Bino DM: no diagram 1
require small m0
Bino-Higgsino DM
large m0 detectable ,Z
/ 1/mq2 ~
S. Su Dark Matter

22. Neutralino-Nucleon Scattering (II)
2 £ pb  SI  6 £ 10-8 pb
2 £ 10-7 pb  SD  pb
S. Su Dark Matter

23. DAMA and CDMS -
CDMS
DAMA
DAMA finds signal in annual modulation as earth passes through WIMP wind
CDMS and Edelweiss excludes much of the favored region
Edelweiss
NUHM
CMSSM
pb = cm2
S. Su Dark Matter

24. Indirect Detection -
DM annihilation products from the Sun, Earth, galaxy
require hard annihilation products (not good for Bino DM)
 from the core of the Earth and Sun
e+ from the local solar neighborhood
 from the Galactic center  
Under-ice, underwater neutrino telescopes
Anti-matter/ anti-particle experiments
Atmospheric Cherenkov telescopes, space-based  ray detectors
S. Su Dark Matter

25. Comparison of pre-LHC SUSY Searches
DM searches are complementary to collider searches
When combined, entire cosmologically attractive region will be explored before LHC ( » 2007 )
S. Su Dark Matter

26. Conclusion DM is the one of the strongest phenomenological-
DM is the one of the strongest phenomenological
motivation for new physics
Fruitful interplay of particle physics, cosmology,
and astrophysics
A fascinating time: we know how much,
but have no idea what it is
Many, many experiments
MSSM neutralino LSP is a good candidate for CDM
In SUSY, DM searches are promising, highly
complementary to collider searches
S. Su Dark Matter