OutlineFind a signal, have champagneSignal of what?Is it the dark matter?Calculating the (relic) density What we need from colliders, detectors, and theoryCalculating the wimp mass from dark matter data aloneA General method to place bounds on the relic density of the LSP given any available knowledge of the MSSMSummary and outlook

A WIMP is DiscoveredA wimp discovery has enormous implications for particle physicsMay be the first observation of supersymmetryUnprecedented triumph of astroparticle physicsCould possibly (hopefully) explain the dark matter mysteryWhat is its relevance to cosmology?There is no reason to suspect that dark matter is entirely composed of a single particle

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[Dda, Gelmini, Gondolo, Edsj, Silk, etc.] wimp is the dark matterwimp is the dark matter~reach of experiments tomorrow (?)~reach of experiments tomorrow (?)emphasized by BCK in hep-th/0005158(each point corresponds to a general MSSM consistent with all current data)

Local and Relic DensityWe 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 sunThis agrees roughly with dmh2~0.1 and soTherefore, 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 haloIf the halo is clumpy, then the ambient densitynot in clumpsmay be less than 0.3 GeV/cm3This can be determined from direct detection data aloneIt will be easy to see if the wimp density fluctuates in timeIf the sun is located in a dark matter stream (e.g. Sgr) or causticMay only be corrected with DRIFT or other directional dark matter experimentsFor this work, we will assume the halo is isothermal

Deducing the Local DensityDetection rates are proportional to the local density of wimps:

Unknown parameters:(the particle physics of )unknown physics

Density Calculation PrerequisitesParticle 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 collidersThe 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 interactionsMultiple 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

Density Calculation PrerequisitesInteraction parameters:These cannot be determined from any dark matter experiment aloneRequires detailed knowledge of the wimp couplings to quarks and gluonsFor example, if the wimp is the neutralino, then you must haveSpin-dependent: squark masses & mixing, tanb, and content of the neutralinoSpin-independent: squark masses & mixing, higgs masses, tanb, and content of the neutralinoMay require years of collider data (if possible at all)However, we can estimate these given partial data and (even current) parameter limitsHalo modelAll analysis may be plagued by caustics or dark matter streams until experiments like DRIFT determine the isotropy of the local haloCould introduce (large) errors in the relic density calculation andSome halo models may preclude mass estimates (e.g. no annual modulation crossing)

Determining the Wimp MassRecall that the annual modulation amplitude changes sign at some particular energyNotice that there is always some point at which there is no annual modulationthis is the 'crossing energy'

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

Determining the Wimp MassHowever, this fails for detectors composed of several different-mass elements

Consistency Function Mass CalculationNotice 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)

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

Using Multiple ExperimentsIf we know the wimp mass and halo profile, then given measurements at different energiesfrom different detector materials,we can solve for

Wimp Interaction ParametersWe can generally solve for

an upper bound on any single parameter is equivalent to a lower bound for the densitya lower bound on any single parameter is equivalent to an upper bound for the densityEasier to estimate one of the parameters than all 4Multiple density estimates are relatively independent

LSP Interaction BoundsFor 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 parametersIt is clear how this type of approach can be iteratively improved given more specific data and boundsNote: the expression above is greatly simplified for less general MSSMs (e.g. mSUGRA, GMSB, or AMSB)

LSP Relic Density Lower BoundUsing the upper bound for ap,n, we get a lower bound on

Bound calculated for 6050 randomly generated (physically allowable) MSSMsThe bound is robust: for no model does it overestimate the densitya perfect density estimate

Summary and OutlookOne cannot compute the relic density of wimps from direct detection aloneGiven collider data and bounds, one can (at least) estimate the local neutralino densityIt 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 MSSMThe only way to identify the wimpData from multiple detector materials greatly simplifies and strengthens our ability to compute the density

MSSMs with ~Same Signals and DifferentModels with the very similar direct and indirect detection signals but different relic densities (many are easy to find)Notice that the lighter squark mass gives a larger couplinghence, a stronger signal. This also gives a hint about the importance of knowing the lightest squark mass: 180 GeV difference corresponds to a factor of 3 in the local density calculation

m(GeV)m2(GeV)mA(GeV)tanbm0(GeV)At/m0Ab/m0Model A412.1372.7337.423.3435.5-0.01190.0707Model B463.4371.1428.118.4593.8-0.18440.4366

h2Ge signal(20 keV)(cpd/kg-keV)NaI signal(5 keV) (cpd/kg-keV)Muon flux(muons/yr-km2)mlightest squark mass(GeV)lightest higgs mass(GeV)Model A0.04494.2x10-51.4x10-53.6185.3384.2105.7Model B0.12283.6x10-51.2x10-53.7184.1562.9109.4