2. Outline Evidence for dark matter
Dark matter candidates: WIMPs, the LSP
Direct and indirect detection methods
Determining the relic density from signals
What information about the wimp is required?
A method to compute a wimp mass from dark matter experiments alone
If the wimp is the LSP,
What collider data is required
What we can learn about the MSSM without colliders
Summary and outlook

3. Evidence for Dark Matter
1933: Fritz Zwicky studies
the coma cluster
Finds nearly 90% of the mass
'spherically distributed.'
In the 1970s, more rotation curves were measured. The problem was found to be universal.
Rotation curve for M33 (from astro-ph/ )

4. Dark Matter: Not a Problem!
Plenty of candidates.
Astronomy:
'Jupiters,' white dwarfs, black holes…
Neutrinos?
Particle Physics:
The axion
Weakly interacting massive particles (WIMPs):
the LSP, right-handed neutrinos, CHAMPs, self-interacting dark matter (SIDM), wimpzillas, the lightest Kaluza-Klein particle, superweakly interacting massive particles (superWIMPs)…

5. Why WIMPs? Plenty of candidates.
Almost any extension of the Standard Model of particle physics introduces massive particles that interact only weakly (otherwise we would have seen them already)
How many wimps were produced in the big bang?
estimate of the thermal production in early universe; 'freeze out'
This gives
weak scale:

6. How to Observe a WIMP Direct detection Indirect detection
(DAMA, ZEPLIN, DRIFT, EDELWEISS, CDMS, ANAIS, CASPAR, CRESST, CUORE, GENIUS, HDMS, IGEX, LIBRA, MACHe3, Majorana, NAIAD, ORPHEUS, Picasso, ROSEBUD, UKDMC, &etc).
Indirect detection
Neutrinos from the sun/earth
(AMANDA, ANTARES, IceCube, MACRO, Super-Kamiokande, Nestor, BAIKAL, DUMAND, &etc)
Antimatter excess/cosmic rays
(AMS, BESS, CAPRICE, GLAST, IMAX, NINA, PAMELA, &etc)

7. No-Lose Theorem vs. Our Ability to Win
What is the cosmological relevance of discovering a wimp?
No lose theorem: we can directly detect very small wimp components of the dark matter in some models.
Therefore, we will not know the cosmological significance of a discovered wimp until we know its relic density
[Dūda, Gelmini, Gondolo, Edsjö, Silk, etc.]

8. Direct Detection Rates
Signal rate for wimp-scattering at energy Q
Given the halo model, wimp mass, and signals
at different energies
from different detector materials,
we can solve for

9. What if we Don't Know the Mass?
Notice that fp,n and ap,n are constants.
For each independent (minimal) set of data, we can compute these constants if the mass were known.
Let us define the consistency function
where i,j represent a minimal set of data used to compute the constants using the assumed value for m

10. Weighing a WIMP
Clearly, (m) should have a minimum at the true mass. (Independent determinations of the constants should agree)
(m) as a function of m for ATLAS SUSY point 2

11. Measuring the Density
Therefore, direct detection experiments can be used to determine
Notice that we must have a model which tells us fp, fn, ap, or an before we can determine !
(This isn't helped with indirect data for similar reasons)

12. Supersymmetry and the LSP
In R-parity conserving supersymmetric standard models, the lightest super particle (LSP) will be stable: an excellent dark matter candidate!
For most models within current constraints, the LSP is the lightest mass eigenstate of the neutralino:
In the basis we have,
So the LSP is

13. LSP Interaction Parameters
Recall that we must compute fp, fn, ap, or an in order to measure 
To tree-level, these correspond to the following

14. LSP Interaction Parameters
For up quarks in a general (soft) MSSM,

15. LSP Relic Density Calculation
We see that the axial-vector ('spin-dependent') parameters depend on:
LSP mass (1)
All squark masses and mixing phases to u, d, s (36)
Gaugino and higgsino content of the Neutralino (8)
tan (1)
Total: 46 (real) parameters
Why wait for colliders? Can't we do better than this?

16. LSP Relic Density Bounds
One can compute bounds on the density by simply over- or under-estimating the interaction parameters
For example, one can use a lower bound on the lightest squark mass and modest bounds for tan to arrive at
This has only 6 free, real, bounded parameters and is completely independent of SUSY-breaking

17. LSP Relic Density Bounds
Using the upper bound on ap,n, one arrives at a lower bound on the relic density:
Upper bound:
work in progress
Bound calculated for 6050 randomly generated (physically allowable) MSSMs

18. Summer Research Advancements
My research with Gordon Kane this summer:
Developed a general algorithm to compute the mass of an arbitrary WIMP from direct detection data alone
Proved the requirement of model input to measure the density (this also applies to indirect detection scenarios mentioned briefly)
For the MSSM,
Developed a robust method to compute a lower bound on the relic density from limited collider data or current bounds
Investigated many ways to explore the MSSM parameter space with dark matter experiments
This information can be used to complement and make predictions for the LHC and Tevatron
More to come…

19. Work in Progress
Making the mass calculation robust (non-ideal data and handling non-unique solutions)
Getting an upper bound on the density from weak model input
Observing halo irregularities (lumpiness, streams, triaxial components, &etc)
Learning about the MSSM from dark matter direct detection data
Comparing ap,n and fp,n should give insight and place bounds on
Higgs/squark masses, tan, neutralino content, …?

20. Summary and Outlook BUT,
Dark matter ~ 83% of the matter in the universe
We can hope to detect wimps soon if they exist
Dozens of experimental groups are competing to be the first to make discovery. (Some already have claims).
BUT,
Even if wimps are discovered, we cannot address their cosmological relevance until we know their density.
Therefore, we must determine the density of any wimps observed before we can begin to understand dark matter.

21. Acknowledgements Research in collaboration with Gordon Kane
Special thanks to
Homer Neal, Jean Krisch, & Jeremy Birnholtz
Steve Goldfarb
University of Michigan Physics Summer REU Program
Research supported by

22. Support Slides Evidence for the energy budget of the universe
More direct detection rate analysis
Obtaining nucleon interaction parameters from quark interaction parameters
An 'Antonio Pich' supersymmetric standard model particle table

23. The Dark Side of the Universe
How do we know what's in the universe?
Cosmic microwave background
Flatness of the universe
Rotation curves of galaxies
Big bang nucleosynthesis
X-ray spectra from galaxy clusters
Weak gravitational lensing
Large scale structure formation
Type 1a supernovae data …

24. Direct Detection Rates
Signal rate is given by
A function of
model input
nuclear physics
depends on wimp mass
depends on detector nucleus

25. LSP Interaction Parameters
We scale these quark 'cross sections' to nucleon interaction parameters by

26. Supersymmetric Standard Model
A symmetry between bosons and fermions
Based on A. Pich's CERN summer student lectures 2004