2. Outline Find a signal, have champagne Calculating the (relic) density
Signal of what?
Is it the dark matter?
Calculating the (relic) density
What we need from colliders, detectors, and theory
Calculating the wimp mass from dark matter data alone
A General method to place bounds on the relic density of the LSP given any available knowledge of the MSSM
Summary and outlook

3. A WIMP is Discovered
A wimp discovery has enormous implications for particle physics
May be the first observation of supersymmetry
Unprecedented triumph of astroparticle physics
Could possibly (hopefully) explain the dark matter mystery
What is its relevance to cosmology?
There is no reason to suspect that dark matter is entirely composed of a single particle

4. No-Lose Theorem vs. Our Ability to Win
'No lose theorem': we may be able to directly detect a very small wimp component of the dark matter.
Therefore, we will not know the cosmological relevance of a wimp until we know its relic density
[Dūda, Gelmini, Gondolo, Edsjö, Silk, etc.]
wimp is the dark matter
wimp is the dark matter
wimp only a small piece of the dark matter
~reach of experiments tomorrow
(?)
~reach of experiments tomorrow
(?)
(each point corresponds to a general MSSM consistent with all current data)
emphasized by BCK in hep-th/

5. Local and Relic Density
We will assume that it is sufficient to know the local density of a wimp to deduce its relic density:
The local density of 'dark matter', dm~0.3 GeV/cm3, is known independent of cosmological data: this is known by the velocities of stars near the sun
This agrees roughly with dmh2~0.1 and so
Therefore, if the wimp density is ~0.3 GeV/cm3, we will conclude that almost all of the dark matter is made of 
This introduces subtleties about the halo
If the halo is clumpy, then the ambient density—not in clumps—may be less than 0.3 GeV/cm3
This can be determined from direct detection data alone
It will be easy to see if the wimp density fluctuates in time
If the sun is located in a dark matter stream (e.g. Sgr) or caustic
May only be corrected with DRIFT or other directional dark matter experiments
For this work, we will assume the halo is isothermal

6. Deducing the Local Density
Detection rates are proportional to the local density of wimps:
Unknown parameters:
halo model
nuclear physics
unknown physics
(the particle physics of )

7. Density Calculation Prerequisites
Particle identification:
Without any quantum numbers, it is not possible to distinguish between the LSP, lightest Kaluza-Klein particle, wimpzillas, etc.
The only way (so far) to identify the wimp is to determine its mass from direct detection alone and then observe this particle at colliders
The wimp mass:
Calculable from direct detection alone (at least two methods)
Annual modulation crossing energy (robust, if applicable)
Kinematical consistency constraints (work in progress)
Single detector if sensitive to spin-dependent interactions
Multiple detectors required if nuclei have no spin (or nuclear physics unknown)
Maybe calculable at colliders (at least for most reasonable wimps)
May not be easy: If the wimp is the LSP, for example, it is not clear that there exists any way to determine its mass (model independently) at the LHC better than ~20-30%
If you assume mSUGRA (which you aren't allowed to do), then the LSP mass could be determined to about 10% with 1 year of high-luminosity data

8. Density Calculation Prerequisites
Interaction parameters:
These cannot be determined from any dark matter experiment alone
Requires detailed knowledge of the wimp couplings to quarks and gluons
For example, if the wimp is the neutralino, then you must have
Spin-dependent: squark masses & mixing, tanb, and content of the neutralino
Spin-independent: squark masses & mixing, higgs masses, tanb, and content of the neutralino
May require years of collider data (if possible at all)
However, we can estimate these given partial data and (even current) parameter limits
Halo model
All analysis may be plagued by caustics or dark matter streams until experiments like DRIFT determine the isotropy of the local halo
Could introduce (large) errors in the relic density calculation and
Some halo models may preclude mass estimates (e.g. no annual modulation crossing)

9. Determining the Wimp Mass
Recall that the annual modulation amplitude changes sign at some particular energy
Notice that there is always some point at which there is no annual modulation
this is the 'crossing energy'

10. Determining the Wimp Mass
This crossing energy directly determines the wimp mass!
~2 keV resolution on crossing energy corresponds to ~10 GeV resolution on the wimp mass
Notice the clear functional dependence

11. Determining the Wimp Mass
However, this fails for detectors composed of several different-mass elements

12. Consistency Function Mass Calculation
Notice that  f 2p,n and a2p,n are constants.
For each independent set of data, we can compute these constants independently for given the mass.
Define a consistency function
where i,j represent a minimal set of data used to compute the constants using the assumed value for m
Clearly, (m) should have a minimum at the true mass. (Independent determinations of the constants should agree)

13. Alternative Method for the Mass
If we plot the 'kinematical consistency function' (m), we see
*Note: this algorithm does not take into account uncertainties in the data

14. Using Multiple Experiments
If we know the wimp mass and halo profile, then given measurements
at different energies
from different detector materials,
we can solve for

15. Wimp Interaction Parameters
We can generally solve for
an upper bound on any single parameter is equivalent to a lower bound for the density
a lower bound on any single parameter is equivalent to an upper bound for the density
Easier to estimate one of the parameters than all 4
Multiple density estimates are relatively independent

16. LSP Interaction Bounds
For the most general MSSM, given bounds on tanb and a lower bound on the lightest squark mass, one obtains an upper bound for ap,n:
(some subtleties exist about scaling quark to nucleon interactions, see our coming paper for details)
where the expression is maximized relative to the 6 unknown, bounded parameters
It is clear how this type of approach can be iteratively improved given more specific data and bounds
Note: the expression above is greatly simplified for less general MSSMs (e.g. mSUGRA, GMSB, or AMSB)

17. LSP Relic Density Lower Bound
Using the upper bound for ap,n, we get a lower bound on 
a perfect density estimate
The bound is robust: for no model does it overestimate the density
Bound calculated for 6050 randomly generated (physically allowable) MSSMs

18. Summary and Outlook
One cannot compute the relic density of wimps from direct detection alone
Given collider data and bounds, one can (at least) estimate the local neutralino density
It is possible to learn about the wimp from direct detection alone (e.g. its mass, scaled couplings, etc.)
These are powerful tests for colliders and the MSSM
The only way to identify the wimp
Data from multiple detector materials greatly simplifies and strengthens our ability to compute the density

19. MSSMs with ~Same Signals and Different
Models with the very similar direct and indirect detection signals but different relic densities (many are easy to find)
m(GeV)
m2(GeV)
mA(GeV)
tanb
m0(GeV)
At/m0
Ab/m0
Model A
412.1
372.7
337.4
23.3
435.5
0.0707
Model B
463.4
371.1
428.1
18.4
593.8
0.4366
h2
Ge signal
(20 keV)
(cpd/kg-keV)
NaI signal
(5 keV) (cpd/kg-keV)
Muon flux
(muons/yr-km2) m
lightest squark mass
(GeV)
lightest higgs mass
Model A
0.0449
4.2x10-5
1.4x10-5
3.6
185.3
384.2
105.7
Model B
0.1228
3.6x10-5
1.2x10-5
3.7
184.1
562.9
109.4
Notice that the lighter squark mass gives a larger coupling—hence, a stronger signal.
This also gives a hint about the importance of knowing the lightest squark mass: GeV difference corresponds to a factor of 3 in the local density calculation