Dark matter and cosmology

Indirect detection of neutralinos

Neutralinos as dark matter candidates

There is extensive astrophysical evidence that most of the matter in the universe is non-luminous. The matter content of the universe is normally described in terms of the density parameter $\Omega=\rho/\rho_c$ , where $\rho_c=3H_0^2/8\pi G$ is the critical density and H₀, often expressed in the dimensionless form $h=H_0/\mbox{100 km s}^{-1}\mbox{ Mpc}^{-1}$ , is the expansion rate.

Estimates of galactic halo masses from rotation curves and of the galactic number density give a value of $\Omega \ge 0.1$ , whereas the luminous matter in galaxies corresponds to $\Omega < 0.01$ . Studies of the dynamics of clusters and superclusters of galaxies increase the required value of $\Omega$ to around 0.2-0.3, and the popular inflationary paradigm generally requires $\Omega = 1$ (although this may include a contribution from a non-zero cosmological constant).

The density of baryonic matter is constrained by the abundances of the light elements to a range $0.008 \le \Omega_{\rm baryons}h^2 \le 0.024$ . With current measurements of h tending to lie in the range 0.6-0.7, this indicates that much of the dark matter required on the galactic scale and beyond must be non-baryonic. A prime candidate for non-baryonic dark matter is the Lightest Supersymmetric Particle (LSP).

Supersymmetry is a spontaneously broken symmetry between bosons and fermions, postulated as a natural mechanism for avoiding GUT-scale radiative corrections to the Higgs mass. The minimal supersymmetric model (MSSM) contains boson partners for every fermion, fermionic partners for all known bosons, and two Higgs doublets. In order to match the experimental limit on proton decay, it is generally assumed that a multiplicative quantum number called R-parity is conserved: R=+1 for ordinary particles and -1 for their supersymmetric partners. The natural consequence of this is that the lightest supersymmetric particle is stable, having no R-conserving decay mode.

The MSSM has numerous free parameters (105 from the most general soft-breaking terms in addition to the 19 parameters of the Standard Model, reducing to seven if we make a number of standard -- but not necessarily correct -- assumptions about masses and mixing angles), and the identity of the LSP is not unambiguous.

However, experimental limits rule out a charged LSP over a broad mass range, and it is therefore generally assumed that the LSP is the lightest of the four neutralinos, the mass eigenstates corresponding to the superpartners of the photon, the Z and the two neutral Higgs bosons. The mixing which generates the mass eigenstates depends on the choice of SUSY parameters: the LSP, $\chi$ , can be anything from a nearly pure B-ino to a nearly pure higgsino.

The mass of the LSP is constrained from below by non-detection in LEP2, and from above by the requirement that supersymmetry fulfil its role of maintaining the mass hierarchy between the GUT scale and the electroweak scale.

Neutralinos produced in the early universe will fall out of equilibrium when the annihilation rate, $\langle\sigma_A v\rangle n_\chi$ , falls below the expansion rate H. This condition leads to the estimate that

$\begin{displaymath}\Omega_\chi \simeq \frac{3\times 10^{-27}\mbox{ cm}^3\mbox{ s}^{-1}}{\langle\sigma_A v\rangle}, \end{displaymath}$

where $\langle\sigma_A v\rangle$ is the thermally averaged annihilation cross-section times the relative velocity. (Note that neutralinos are Majorana particles, $\bar\chi~=~\chi$ .) If the masses of SUSY particles are close to the electroweak scale, the annihilation cross-section is of order $\alpha^2/(100 \mbox{ GeV})^2 \sim 10^{-25}\mbox{ cm}^3\mbox{ s}^{-1}$ , indicating that $\Omega_\chi\sim 1$ is a realistic possibility. This heuristic argument is confirmed by detailed calculations, which indicate that a neutralino LSP has a cosmologically significant relic abundance over large regions of the MSSM parameter space.

Neutralino detection

If neutralinos make up a significant fraction of the Galactic dark halo, they will accumulate in the core of bodies such as the Earth or the Sun and in the Centre of our Galaxy. A neutralino passing through such a body has a small but non-zero probability of scattering off a nucleus therein, so that its velocity after scattering is less than the escape velocity. Once this happens, repeated passages through the body will generate additional scatters and the neutralino will sink relatively rapidly to the centre. Equilibrium will be reached when the gain of neutralinos from capture is balanced by the loss from annihilation, C = C_AN² where C is the capture rate, N is the number of captured neutralinos. The quantity C_A depends on the WIMP annihilation cross-section and the WIMP distribution.

The capture rate C depends on the local halo mass density $\rho_\chi$ , the velocity dispersion of neutralinos in the halo $\bar v$ , and the elastic scattering cross-section, which depends on the mass of the neutralino and on the effective volume and chemical composition of the Sun or Earth. Representative values of $\rho_\chi$ and $\bar v$ are 0.3 GeV cm^-3 and 270 km s^-1 respectively.

Neutrinos from neutralino annihilation

Neutralinos annihilate into a fermion-antifermion pair or into various two-body combinations of W, Z and Higgs bosons. Direct decay into neutrinos is zero in the non-relativistic limit, but decays into c, b and t quarks, $\tau$ leptons, Z, W and Higgs can all produce a significant flux of high-energy neutrinos (light quarks and muon pairs do not contribute, as they are stopped before they decay). The typical neutrino energy produced is thus around one-half to one-third of the neutralino mass, with a broad spectrum whose detailed features depend on the branching ratios into the different channels (which in turn depend on the neutralino composition--gaugino vs higgsino--as well as its mass) and are modified, especially in the Sun, by hadronisation and stopping of c and b quarks, and stopping, absorption and possibly oscillation of neutrinos.

Since both the neutrino-nucleon cross-section and the range of the produced muon scale with the neutrino energy, the resulting muon rate is approximately proportional to $E_\nu^2\mbox{ d}N_\nu/\mbox{d}E_\nu$ , indicating that this method of neutralino detection is most likely to be competitive for higher mass neutralinos.

The expected muon flux depends on the neutralino mass and the assumed MSSM parameters.

The Sun is a point-like source of neutrinos from neutralino annihilation, but the Earth is not, especially for lower mass neutralinos. Despite the smearing produced by measuring the muon flux rather than the neutrinos, a detector with good angular resolution would be able to use the observed angular distribution to constrain the neutralino mass.

Indirect detection explores a region of parameter space which is somewhat different from that investigated by direct techniques, although there is also considerable overlap. Indirect detection is particularly useful when the axial coupling of the neutralino dominates, as axially-coupled neutralinos are captured in the Sun due to their interaction with hydrogen. Detection of neutralinos by both direct and indirect techniques would provide information on neutralino couplings and MSSM parameters, as would indirect detection of signals from both the Sun and the Earth.

Relic sources

In recent years, the Fly's Eye atmospheric fluorescence detector and the AGASA air shower array have convincingly detected cosmic rays with energies exceeding 5x10¹⁹ eV -- the Greisen-Zatsepin-Kuz'min (GZK) cutoff set by interactions on the 2.7 K black body cosmic microwave background.

These ultra high-energy cosmic rays (UHECR) constitute a population distinct from those at lower energies ( <5x10¹⁸ eV), in having a flatter spectrum. The depth in the atmosphere at which the shower reaches its maximum suggests a correlated change in the composition from iron nuclei to protons between 10¹⁸ and 10¹⁹ eV.

The lack of any detectable anisotropy argues against a local origin in the Galactic disc where the presumed sources of low energy cosmic rays reside. However, there are no potential extra-galactic sources such as active galaxies near enough (within 50 Mpc) to evade the GZK cutoff. Thus the origin of the UHECR is a major puzzle for standard physics and astrophysics.

An exciting possibility is that UHECRs result from the decay of massive particles, rather than being accelerated up from low energies. The most popular models in this context are based on the annihilation or collapse of topological defects (TDs) such as cosmic strings or monopoles formed in the early universe.

A more recent suggestion is that UHECRs arise from the decays of metastable relics with masses exceeding 10²¹ eV which constitute a fraction of the dark matter. Such particles can be naturally produced with a cosmologically-interesting abundance during re-heating following inflation. A lifetime exceeding the age of the universe is natural if they have only gravitational interactions, e.g. if they are `cryptons' -- bound states from the hidden sector of string theory. This interpretation also naturally accounts for the required mass.

The essential point is that whatever process creates the UHECRs, it is exceedingly likely that there is a concomitant production of very high energy neutrinos. Measurement of the neutrino flux will, at the very least, provide important clues as to the origin of UHECRs and may even provide dramatic evidence for new physics.