Dark Matter and Particle Candidates

Roughly a quarter of the energy density of the universe is matter that neither emits nor absorbs light and clusters gravitationally, and it outweighs the ordinary baryonic matter by about five to one. Its existence is inferred entirely from gravity, at every scale from individual galaxies to the whole observable universe. None of the Standard Model particles fits: the only stable neutral one, the neutrino, is far too light and moves too fast to seed the observed structure. Dark matter is therefore the most direct empirical demand for physics beyond the Standard Model, and the leading candidates come from the extensions of the previous lessons.

The astrophysical evidence

Four independent observations, spanning very different scales, all point to the same missing mass.

• Galactic rotation curves. A star orbiting at radius $r$ in a galaxy moves at the circular speed set by the enclosed mass, $v(r)=\sqrt{GM(r)/r}$. Beyond the visible disk, where the luminous mass ends, Newtonian dynamics predicts a Keplerian falloff $v\propto r^{-1/2}$. Measured curves stay flat far past the light, which requires $M(r)\propto r$ — a halo of unseen mass extending well beyond the stars.
• Gravitational lensing. The bending of background light by galaxy clusters measures their total mass directly, independent of dynamics. Cluster masses from lensing exceed the luminous mass by the same factor. In merging clusters the lensing mass and the X-ray-emitting gas are spatially separated, showing the dominant mass is collisionless.
• The cosmic microwave background. The relative heights of the acoustic peaks in the temperature power spectrum fix the baryon and total matter densities separately. The fit gives a total matter density far above the baryon density.
• Structure formation. Ordinary matter could not have clumped into galaxies by today, because before recombination it was coupled to radiation and could not collapse. A collisionless component, free of radiation pressure, must have begun collapsing earlier to seed the observed structure.

The concordance fit to all of these gives the present energy budget of the universe:¹

so dark matter is about five times the baryon density and the visible matter is a twentieth of the whole.

The relic-abundance argument

The most compelling particle candidate follows from a thermal-freeze-out calculation. In the hot early universe a stable massive particle $\chi$ is kept in equilibrium with the plasma by annihilation $\chi \bar{\chi }\leftrightarrow f\bar{f}$. As the temperature drops below the mass, the equilibrium number density is Boltzmann-suppressed, $n_{\text{eq}}\propto e^{-m_{\chi }/T}$. When the expansion rate overtakes the annihilation rate, $H>n⟨\sigma v⟩$, annihilations stop and the comoving number freezes out at a fixed value. The surviving abundance is inversely proportional to the annihilation cross section,

A larger cross section keeps the particle in equilibrium longer, leaving fewer survivors; a smaller cross section freezes out earlier with more.

The striking fact is the value of the cross section that reproduces ${\Omega }_{\text{dm}}{h}^2\approx 0.12$. Setting the required $⟨\sigma v⟩\approx 3\times 10^{-26}{\text{cm}}^3{\text{s}}^{-1}$ and writing it as $⟨\sigma v⟩\sim {\alpha }^2/m_{\chi }^2$ gives a mass

the electroweak scale. A stable particle with weak-scale mass and weak-strength interactions automatically freezes out with about the observed dark-matter density. This coincidence, the WIMP miracle, ties dark matter to the same TeV scale that naturalness independently singles out.

Candidate particles

Several extensions supply a stable neutral particle.

• WIMPs. A weakly interacting massive particle, the generic freeze-out candidate. The lightest neutralino of a supersymmetric theory with conserved R-parity is the archetype: neutral, colorless, stable, and near the weak scale.
• Axions. A very light pseudoscalar, originally introduced to solve the strong-CP problem — the absence of CP violation in QCD. The axion couples feebly and, though light, is produced cold (non-thermally) and can carry the full dark-matter density.
• Sterile neutrinos. A right-handed neutrino that mixes weakly with the active neutrinos, with keV-scale mass. It is warm dark matter, intermediate between the cold WIMP and hot active neutrinos, and would decay slowly to an X-ray line.

The three candidates span some thirty orders of magnitude in mass and require entirely different detection strategies, so the search is broad rather than aimed at a single target.

Detection strategies

The same annihilation vertex $\chi \bar{\chi }\leftrightarrow f\bar{f}$ can be read in three directions.

• Direct detection. A dark-matter particle from the galactic halo scatters elastically off a nucleus in an underground detector, depositing a few keV of recoil energy. The signal is a tiny nuclear recoil above radioactive backgrounds, which is why the experiments run deep underground in ultrapure materials. Reading the vertex as $\chi N\to \chi N$.
• Indirect detection. Dark matter accumulated in dense regions — the galactic center, the Sun — annihilates to Standard Model particles, producing an excess of gamma rays, positrons, or neutrinos. Reading the vertex as $\chi \bar{\chi }\to f\bar{f}$.
• Collider production. A collider creates dark-matter pairs directly; they escape as missing momentum recoiling against a visible jet or photon. Reading the vertex as $f\bar{f}\to \chi \bar{\chi }$.

Current status

No detection has been confirmed. Direct-detection experiments using liquid xenon have pushed the spin-independent WIMP-nucleon cross-section limit below $10^{-47}{\text{cm}}^2$ for a $\sim 30$ GeV mass, cutting deep into the parameter space where a supersymmetric neutralino was expected, and approaching the neutrino floor where coherent solar-neutrino scattering becomes an irreducible background. Indirect searches constrain $⟨\sigma v⟩$ near the thermal value for low masses, and collider missing-momentum searches exclude simplified WIMP models up to the TeV scale.² The classic weak-scale WIMP is squeezed but not excluded, and attention has broadened to lighter and lighter candidates — sub-GeV dark matter and axions across a wide mass range. The identity of dark matter is the best established, and most stubborn, evidence that the Standard Model is incomplete.

Summary

Flat rotation curves ($v\propto r^{-1/2}$ predicted, flat observed), cluster lensing, the CMB acoustic peaks, and structure formation all demand about five times more matter than the baryons, non-luminous and collisionless. Thermal freeze-out gives a relic abundance ${\Omega }_{\chi }{h}^2\propto 1/⟨\sigma v⟩$, and the cross section that reproduces ${\Omega }_{\text{dm}}{h}^2\approx 0.12$ corresponds to a weak-scale mass — the WIMP miracle, with the supersymmetric neutralino as archetype and axions and sterile neutrinos as alternatives. Direct, indirect, and collider searches read the same annihilation vertex three ways; none has found dark matter, and the limits now cut into the natural WIMP region.³⁴