Dark Matter Part II What it could be and what it could do
Theories of Dark Matter What makes a good dark matter candidate? Charge/color neutral (doesn't have to be though) Heavy We know KE ~ kev CDM ~ GeV or heavier Non-baryonic Fall out of larger theory Natural production mechanism e.g. WIMP miracle More theories than you can count! Let's discuss a few of them 2
Old News: MACHOs Massive Compact Halo Objects Jupiter-like planets, brown dwarf stars Extra normal matter that doesn't emit light But MACHOs are baryons! Doesn't this disagree with WMAP? MACHO searches were conducted about the same time that the CMB measurements were made Look for MACHOs via gravitational lensing Micro-lensing of starlight from within the milky way Look for brightening of star as MACHO passes in front of it Galactic survey to look for MACHOs in the milky way Some MACHOs were found Not enough to constitute DM Consistent with WMAP result that DM is non-baryonic! 3
Sterile Neutrinos We know about 3 types of neutrinos Could there be a fourth type? The full answer will be discussed in neutrino lectures Short answer, yes, but it must be sterile! Doesn't participate in weak interactions Only accessible via oscillations Usually heavy (~ kev) Not quite cold, but warm DM candidate 4
Axions Remember CP violation? C = charge congugation P = parity (invert coordinates, like looking in mirror) CP symmetry means that under inversion of charge and parity, physics is unchanged Does an electron behave the same as a positron when viewed in a mirror? CP violation: processes which do not obey this symmetry CP violation observed in weak interactions Never observed in strong interactions But remember Noether's theorem: Symmetry Conserved quantity No such symmetry in strong interaction Strong CP problem Add axial symmetry to strong interaction Resulting particle is the axion Would solve strong CP problem Could also be DM Huge parameter space for axion coupling and mass Subset gives correct DM density ADMX Experiment Search for axion dark matter No discovery yet Not ruled out either 5
WIMPs Recall the WIMP Miracle Weak-scale cross section gives correct abundance Many, many theories give WIMPs Extensions to the SM often have new physics just beyond our reach Electroweak scale New particles and new interactions New forces or extensions of existing ones Natural framework for CDM Heavy (e.g. cold) particles Scaling of WIMP miracle: Relic density roughly scales with Smaller cross section but larger mass gives same relic density 6
SUSY Remember our old friend SUSY Doubling of SM Fermion Boson symmetry Lightest SUSY Particle (LSP) Naturally neutral Neutralino: SUSY is by far the most popular framework for physics beyond the SM, and DM A lot of flexibility Answers many shortcomings of SM By no means the only possibility for WIMP DM 7
Composite Dark Matter DM could be composite Made up of constituent particles Like baryons consist of quarks One example: DM consists of 4 fundamental particles Each carries both weak and electrical charge But the DM particle is electrically neutral Couples through Z, H exchange Many other models: Different numbers of constituents Different properties EM, weak, strong interactions New interactions Always globally neutral (like neutron) Come from adding a new symmetry to SM 8
Mirror Dark Matter Mirror copy of normal particle physics All known particles have a copy in the mirror sector Same physics in the mirror sector as normal sector The two sectors are connected by a photon mixing Consistent with WIMP miracle High density allows freezeout as with other WIMPs Mixing is small (ε ~ 10-9) Characteristics: More dynamic physics available in DM halos Bullet cluster and non-bullet cluster like collisions Dominantly an EM interaction But strongly suppressed by ε 9
Compact Dimensions: Kaluza Klein Particles Compact extra dimension Periodic boundary Think of a loop Compact, ~ TeV-1 (10-21 m) Quantized excitations Shows up as effective mass ~ TeV particles In Kaluza Klein theory, the lowest mode is stable Invoke a symmetry to protect KK number Orthogonality: New dimension (w) orthogonal to x, y, z Welcome to the fourth dimension 10
WIMP Miracle and DM Detection The WIMP Miracle predicts three types of interactions DM annihilation DM production DM scattering We look for all three experimentally! 11
WIMP Scattering Let's start with a few assumptions: Cold Dark Matter exists and consists of SUSY WIMPs with m ~ 100 GeV The WIMP miracle tells us DM should interact with normal matter! Our galaxy is immersed in a WIMP halo with density ~ 0.3 GeV/cm3 The WIMP velocity distribution is roughly understood (details later) WIMPs and matter have weak scale interaction How do we determine the interaction rate in a WIMP detector? We can follow general scattering theory New physics only shows up in the cross section (in most cases) We can ignore the details, and calculate the rate for a given cross section 12
Scattering Theory In quantum mechanics, you will study scattering theory Probability (or rate) of interaction In general, it can be written in this form Two things to deal with: Velocity integral Differential cross section R = scattering rate ρ0 = 0.3 GeV/cm3 is the local dark matter density mx and mn are the WIMP and Nucleon masses respectively v is the WIMP speed f(v) is the 1D WIMP speed distribution S is the elastic WIMP-nucleon cross section q is the momentum transfer 13
Some Useful Substitutions Reduced mass: Energy transferred: At low momentum transfer: σ0 is the cross section at zero momentum transfer F2(Q) is the nuclear form factor Integrating over all possible velocities, the differential rate can be written as: Three terms to deal with: Velocity integral Cross section Form factor 14
Details of the Velocity Minimum velocity: bound by kinematics Two cases for maximum velocity: Simple model: vmax = Realistic model: vmax = vesc WIMPs greater than vesc are not gravitationally bound Different measurements exist for the escape velocity in the Milky Way 496 < vesc < 655 km/s Earth-Sun motion: The sun moves around the galactic center at v0 = 220 km/s The earth moves with or against the sun motion Annual modulation of relative WIMP velocity distribution 15
Simplest Model: Ignore vesc and vearth Maxwellian distribution: Velocity integral: What does this mean for the WIMP scattering rate? Consider F2(Q) = 1 (true for light WIMPs): General feature: Exponential Energy Spectrum! This is a global feature, all additional terms only modify this slightly 16
More Realistic Model: Include Earth-Sun Motion Recall: The 1D Boltzmann distribution has two terms (derivable from 3D distribution) With this form and still ignoring the escape velocity, the velocity integral is: General feature: Exponential Energy Spectrum! This is a global feature, all additional terms only modify this slightly 17
The Full Solution Re-evaluating the previous integral with finite vesc And the differential rate can be written as: vmin is a function of Q ve is a function of cos(t) 18
Features of the Velocity Integral Exponential behavior predicts high rate at low recoil energy Experiments must be sensitive to few kev Earth-Sun motion creates modulation in rate Modulation in total number of events May ultimately allow for probing our own DM Halo Escape velocity truncates rate at high E More complicated velocity distributions can be considered (streamers, motion or structure in Halo, etc) 19
Form Factor Describes how a wave overlaps with nuclear structure How much nuclear structure do you see Recall the DeBroglie wavelength Long wavelength sees nucleus as one blob Short wavelength resolves nuclear sub-structure 20
Computing the Form Factor The nuclear form factor is the Fourier transform of the matter density in the nucleus Need to know matter density inside nucleus Nuclear physics Many different form factors used Most agree to a large extent 21
Example of Form Factor Woods-Saxon form factor Treat the nucleus as a hard, uniform sphere, but with blurry edges j1(x) is a spherical bessel function q is the momentum transfer R1 is related to the nuclear radius R s is the skin depth of the nuclear edge 22
Features of the Form Factor Suppresses high momentum exchange Poles at certain momentum exchange: Destructive interference Form factor 0 Rate 0 Goes to 1 as q goes to 0 No effect when no resolution of nuclear structure! 23
Cross Section The cross section at zero momentum transfer is: # protons # neutrons Proton coupling Neutron coupling Let's make an assumption: fp = fn Maybe that's not too crazy, we're looking for SUSY WIMPs Ignoring form factor effects, the rate should scale with A2 19 24
The Final Event Rate Plugging in all the numbers, one gets a differential rate for each WIMP mass, cross section and target material Features of this plot: Differential Rate Unit (dru) Events / kg / kev / day A2 dependence Heavy target is better (at low E) Form factor large nucleus has pole at low E Incredibly low rate! (few events / year) experimental challenge Mχ = 100 GeV, σ = 10-44 cm2 25