27. Dark Matter

1

27. Dark Matter
Revised August 2023 by L. Baudis (Zurich U.) and S. Profumo (UC Santa Cruz).

27.1 The case for dark matter
Modern cosmological models invariably include an electromagnetically close-to-neutral, nonbaryonic matter species with negligible velocity from the standpoint of structure formation, generically referred to as “cold dark matter” (CDM; see The Big-Bang Cosmology—Sec. 22 of thisReview). For the benchmark ΛCDM cosmology adopted in the Cosmological Parameters—Sec. 25of this Review, the DM accounts for 26.4% of the critical density in the universe, or 84.4% of thetotal matter density. The nature of only a small fraction, between at least 0.5% (given neutrino oscillations) and at most 1.6% (from combined cosmological constraints), of the non-baryonic matter
content of the universe is known: the three Standard Model neutrinos (see the Neutrino Masses,
Mixing, and Oscillations—Sec. 14 of this Review) ). The fundamental makeup of the large majorityof the DM is, as of yet, unknown.
Assuming the validity of General Relativity, DM is observed to be ubiquitous in gravitationally collapsed structures of size ranging from the smallest known galaxies [1] to galaxies of size
comparable to the Milky Way [2], to groups and clusters of galaxies [3]. The mass-to-light ratio isobserved to saturate at the largest collapsed scales to a value indicative, and close to, what inferredfrom other cosmological observations for the universe as a whole [4]. In such collapsed structures,the existence of DM is inferred directly using tracers of mass enclosed within a certain radiussuch as stellar velocity dispersion, rotation curves in axisymmetric systems, the virial theorem,
gravitational lensing, and measures of the amount of non-dark, i.e. baryonic, mass such as stellar
number counts and tracers of gas density such as X-ray emission [5]. The global DM abundance as
determined from cosmological probes is discussed in Sec. 22.
The picture of structure formation in modern cosmology heavily relies on, and can be considered
an independent and exceptionally strong motivation for, DM. Baryonic density fluctuations at CMB
decoupling are observed to be at most on the order of δρb /ρb |rec ≈ 10−5 ; since density perturbations
grow linearly with the scale factor in the linear regime, absent any other matter fluid, one would
predict thatδρb /ρb |today ≈δρb /ρb |rec≈ 10−2 ,arec(27.1)

at odds with the observed highly non-linear structures in the universe, δρb /ρb |obs  1. The presenceof a dominant non-relativistic (“cold”) pressure-less matter component decoupled from the thermalbath well before recombination allows instead for the prediction of a matter power spectrum inremarkable agreement with observations [6].
Assuming deviations of gravitational interactions on large scales from general relativity or fromits Newtonian limit, certain effects, attributed in the standard scenario to DM, can be explainedby modified gravity [7]. Usually such theories mimic the effects otherwise attributed to DM on alimited range of scales, but fail globally, and especially at the largest scales. Key issues that atpresent appear highly problematic in the framework of theories of modified gravity without DM
include (i) predicting the correct spectrum of density perturbations, (ii) predicting the observed
anisotropy power spectrum of the CMB, and (iii) explaining weak lensing and X-ray observationsof merging clusters such as 1E 0657-558 (the “Bullet” cluster) [8]. The inferred relative speed ofgravitational and electromagnetic radiation in GW170817 additionally excludes a significant swathof modified theories of gravity where the two speeds (of gravitational and electromagnetic waves)differ [9].
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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27. Dark Matter

27.2 Properties of dark matter candidates
Electric charge: The “darkness” of DM can be quantified based on constraints from the CMB
and large-scale structure: if the DM is charged, or “milli-charged” (for instance via a kinetic mixing
with a dark photon field, producing an effective suppressed coupling to the visible photon field), it
might impact the baryon-photon plasma during recombination; in turn, DM density fluctuations
can be suppressed by radiation pressure and photon diffusion, additionally altering the baryon
acoustic peak structure. [10] finds that the most stringent constraints stem from the requirementthat the DM be completely decoupled from the baryon-photon plasma at recombination, yielding
a maximal “milli-electric” charge, in units of the electron charge, of 3.5 × 10−7 (mDM /1 GeV)0.58
for mDM > 1 GeV, and of 4.0 × 10−7 (mDM /1 GeV)0.35 for mDM < 1 GeV. Limits also exist fromstructure formation on how optically dark and dissapationaless the DM should be.
Self-interactions: Observations of merging clusters [8] and of the ellipticity of certain galaxies as inferred from X-rays [11] constrain the level of DM-DM self interactions. The figure of
merit is the ratio of the DM-DM cross section and the DM mass [12] (see Ref. [13] for a review),
σDM−DM /mDM < 0.47 cm2 /g ' 0.84 barn/GeV at 95% C.L.. Assuming a velocity dependence in
σDM−DM , “self-interacting DM” has been advocated as a possible solution to certain possible smallscale structure issues in the standard non-collisional (σDM−DM ' 0) setup [13, 14] (see Sec. 27.4).
Mass: Lower Limits: Model-independent lower limits for very small DM masses are due
to quantum effects: for fermionic DM particles, the phase-space density f (~x, p~) is bounded fromabove due to Pauli’s exclusion principle, f < gh−3 , with g the number of internal degrees of
freedom and h Planck’s constant; observations of the velocity dispersion (or, equivalently, measuresof the enclosed mass) and physical density in dwarf galaxies, lead to a lower limit on fermionic DM
masses, sometimes known as the Tremaine-Gunn limit [15]. Using the Fornax dwarf, Ref. [16] finds
mF > 70 eV. More stringent limits can be drawn from Lyman-α observations, although such limits
depend on the thermal history of the DM. In the case of bosonic DM, the Compton wavelengthof an ultra-light species might erase small-scale structure, in conflict with CMB and large-scale
structure [17], Lyman-α observations [18,19], and measurements of high-redshift galaxy luminosity
functions and the Milky Way satellite luminosity function [20–22]: these observations indicate thatmB & 10−22 eV.
Mass: Upper Limits: General upper limits exist on the mass of the DM constituent from thestability against tidal disruption of structures immersed in DM halos, such as galactic disks andglobular clusters, and of individual small galaxies. The most stringent limits can be derived using
wide halo binaries [23] and the stability of the star cluster within Eridanus II [24]. Such limits
constrain an individual, point-like DM constituent, assuming it makes up 100% of the DM, to belighter than around 5 M . (Notice that the mass limits discussed here do not assume any specificproduction mechanism, and do not depend on the observed cosmological DM density).
Stability: The DM lifetime must be long compared to cosmological timescales [25].

27.3 Genesis of dark matter
The generation of DM in the early universe can proceed via thermal or non-thermal production,
or both, or it may result from a particle-antiparticle asymmetry.
Freeze-out: The process of chemical decoupling from the high-temperature, high-density thermal bath (freeze-out) as a paradigm for particle production in the early universe is both a predictive
and a successful one. The possibility that just like light elements, neutrinos, and CMB photons,
particle DM also originated from a thermal decoupling process has thus garnered significant attention.
A particle species chemically decouples when the rate Γ for the species’ number-changing processes drops below the Hubble rate H. Rough estimates for the abundance of relics can be ob31st May, 2024

3

27. Dark Matter

tained by (i) calculating the freeze-out (i.e. “decoupling”) temperature Tf.o. , corresponding toH(Tf.o. ) ∼ Γ (Tf.o. ), (ii) equating the comoving number density at freeze-out and today, eventually(iii) obtaining the physical density of relic particles today. This procedure assumes that entropy isconserved between Tf.o. and today, an assumption that could well be violated, especially for heavy
relics that decouple early, for instance by entropy injection episodes [26]. Notice also that thefreeze-out calculation strongly depends on the assumed background cosmology, and changes e.g. if
the early universe is not radiation-dominated around DM decoupling.
The calculation of the freeze-out relic abundance hinges on a Boltzmann equation relating the
Liouville operator to the collision operator acting on the phase space density. Under a variety ofsimplifying assumptions including homogeneity and isotropy, it is possible to reduce the relevant
equation for the number density n of a single species pair-annihilating with particles in the thermalbath via 2-to-2 processes todn− 3Hn = −hσvi n2 − n2eq ,(27.2)
dt
where hσvi is the thermally-averaged pair-annihilation cross section times relative velocity (seeRef. [27]), and neq is the equilibrium number density. Relics for which the freeze-out temperature
is much larger than the particle mass (and thus that freeze-out as ultra-reltivistic) are called hot
relics; if the opposite is true, the relic is instead considered cold.
A straightforward calculation shows that to leading order the frozen-out density of hot relics islinearly proportional to the relic particle mass. The comoving number density Y = n/s, where s isthe entropy density, for a hot relic is approximately given by its equilibrium value,
Yf.o. ' Yeq ' 0.278

geff
,
g∗s

(27.3)

where geff is the relic’s effective number of degrees of freedom, and g∗s is the number of entropic
relativistic degrees of freedom, both calculated at Tf.o. . The resulting relic abundance, assuming
an iso-entropic expansion, ismmYf.o. s0 h2',(27.4)Ωhot h2 =ρc93 eVwith s0 the entropy density today, and with the latter equality holding for the case of SM neutrinos,
with a freeze-out temperature around 1 MeV (which enters in the final relic abundance through thedegrees of freedom dependence on the right-hand-side of Eq. (27.3)).
For cold relics, the leading-order dependence of the relic abundance on the DM particle properties is an inverse proportionality relation to the pair-annihilation cross section,
xf.o.
Ωcold h2 ' 0.120

10−8 GeV−2
σDM+DM↔anything!

,(27.5)

where x ≡ mDM /T . In turn, the freeze-out temperature is approximately given by the solution to
the equation√x · e−x = (mDM · MP · σDM+DM↔anything )−1 ,(27.6)
where MP ' 2.435 × 1018 GeV is the reduced Planck mass. As a result, Tf.o. ' mDM /xf.o. , with xf.o.
a number between 10 and 50, depending on the cross section, with only a logarithmic dependence
on the DM mass. Since for electroweak-scale cross sections and masses σDM+DM ' 10−8 GeV−2 ,“weakly-interacting massive particles”, or WIMPs have gained exceptional popularity. Notice thatEq. (27.5) bears, however, no connection to the weak scale [28], despite the relation being known
as “WIMP miracle”.
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427. Dark Matter

Numerous scenarios exist, including notably supersymmetry [29, 30] and models with universal
extra dimensions [31,32] where the relic abundance of the DM is controlled by processes involving aslightly heavier, unstable, co-annihilating species [33]. In this case the calculation of the abundanceof the stable species proceeds similarly to what outlined above, with an effective pair-annihilation
cross section that captures the effects of co-annihilation replacing the pair-annihilation cross section[30].
Freeze-in: Collisional processes can lead to the production of out-of-equilibrium particles that
progressively accumulate over cosmic time, a process sometimes called freeze-in. The abundance ofthe frozen-in particles produced at a given redshift depends on the product of the production ratetimes the Hubble time at that redshift. Freeze-in generally implies that the lightest observablesector particles decay to the DM with relatively long lifetimes, giving peculiar signals at colliders(see e.g. [34]). Gravitinos are an example of DM candidates possibly produced via a freeze-in type
scenario, albeit the portal coupling is in that case via a higher dimensional, Planck-suppressed
operator [35].
Cannibalization and other dark-sector number-changing processes: Thermal processes
can drive the abundance of the DM beyond simple 2-to-2 number-changing interactions. For instance, DM can “cannibalize” [36, 37] itself if n → 2 processes exist. In this case, a critical aspect
is whether or not the DM sector is in thermal contact with the Standard Model thermal bath.
If it is, n → 2 processes can drive the relic abundance, e.g. in the Strongly Interacting Massive
Particles (SIMP) scenario [38]. Models exist where the kinetic decoupling (i.e. the decoupling fromthe thermal equilibrium velocity distribution) of the two sectors drives the abundance of the DM(elastically decoupling relics, or ELDERs [39]). When the two sectors are not in thermal contact,n → 2 processes heat the DM sector dramatically, rapidly affecting the temperature ratio between
the visible and dark sectors [36, 38]. If the relevant cross sections are large enough, and the DM
mass light enough, significant effects can arise in structure formation [36].
Non-thermal production: DM production can proceed via processes out of thermal equilibrium (“non-thermal” production). These include DM production via the decay of a “mother”
particle [40, 41] (or of topological defects [42], moduli [43] etc.) to the DM, or production via
gravitational effects.
Asymmetric DM: An enticing alternative possibility for DM production is that of asymmetricDM [44, 45]: the relic DM abundance arises from an asymmetry between anti-DM and DM. Thisasymmetry may or may not be related to the baryon-antibaryon asymmetry. If it is, then dependingon the model and its thermal history, a relation exists between the mass of the DM and the proton
mass. A variety of proposals have been put forward where alternately baryogenesis is explained
from a DM sector asymmetry, or vice-versa (see e.g. Ref. [46] for a review).
Primordial Black Holes production: A qualitatively stand-alone class of DM candidates,
primordial black holes (PBHs), arises from entirely different mechanisms from what reviewed above.
PBHs are thought to originate from gravitational collapse of large density fluctuations in the early
universe [47, 48]. The over-densities could be produced in a variety of ways, such as topological defects like cosmic strings, necklaces or domain walls, curvature fluctuations from a periodof ultra-slow-roll, a sound speed “resonance” , an early phase of matter domination, or subhorizon phenomena including a phase transition and preheating.Albeit the calculation depends
on the details of gravitational
collapse, the formation
time is connected to the PBH mass via√

M = γMP BH ' 2 × 105 γ 1t s M , with γ ' (1/ 3)3 during radiation domination [49].
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527. Dark Matter

27.4 Density and velocity distribution of dark matter
27.4.1 Local density and velocity distribution
The density and distribution of DM in the Milky Way encipher relevant dynamical information
about our Galaxy, and are particularly important for direct and indirect detection experiments. The
local density (ρ0 ) is an average over a volume of a few hundred parsecs in the Solar neighbourhood.
To determine the local density from observations, two classes of methods are used [50]. So-called
local measures rely on the vertical motion of tracer stars in the vicinity of the Sun, while global
measures extrapolate ρ0 from the measured rotation curve, with additional assumptions about
the Galactic halo shape. Conversely, by comparing the extrapolated local density with the one
obtained from local measures, one can constrain the local shape of the Milky Way halo. A major
source of uncertainty on ρ0 is the contribution of baryons (stars, gas, stellar remnants) to the local
dynamical mass. For instance, the motion of tracer stars used in local measures is dictated by the
total potential generated by baryons and DM, and a robust baryonic census must be available toinfer the additional contribution from DM. Recent determinations from global methods lie in therange (0.2 − 0.6) GeV/cm3 , while new studies of the local DM density from Gaia satellite data yield(0.3 − 1.5) GeV/cm3 , depending on the type of stars used in the study.
Other observational quantities that enter in the phase space distribution of DM, and provide
constraints on mass models of the Milky Way are the local circular speed vc and the escape velocity
vesc . The local circular speed is measured by various methods, roughly divided into measurementsof the Sun’s velocity with respect to an object assumed to be at rest with respect to the Galactic
centre or direct measurements of the local radial force. These methods yield values of vc = (218 −
246) km/s. A recent estimate of the escape velocity, defined as the speed above which objects are
not gravitationally bound to our galaxy, is vesc =533+54−41 km/s [51] (see also the more recent estimate
in [52] of vesc =484.6+17.8
km/s,
which
is
not
in
tensionwith the value we use).
−7.4
The local velocity distribution of DM particles can not be measured directly at present, and ismostly derived from simulations. In general, experiments use the simplest, so-called Standard Halo
Model (SHM) for their data analysis. It assumes an isotropic, isothermal sphere of DM particles−2with a density profile of ρ(r)√ ∝ r , for which the velocity distribution is Maxwellian, with a velocity dispersion σv = vc / 2. This distribution, which formally extends to infinity, is truncatedat vesc [53]. Earlier high resolution, dark-matter-only simulations found velocity distributions thatmarkedly deviated from a Maxwell-Boltzmann distribution and in addition revealed components
above the dominant smooth distribution, including narrow spikes due to tidal streams. Recent hydrodynamical simulations of Milky Way-like galaxies including baryons, which have a non-negligible
effect on the DM distribution in the Solar neighbourhood, find velocity distributions that are indeed
close to Maxwellian, arguing that the SHM is a good approximation.
Ultimately the goal is to determine the velocity distribution from observations (for example bystudying the motion of stars that share the same kinematics as the DM), and the Gaia satellite
data offers a unique opportunity to study the various stellar populations. Recently it was revealed
that the local stellar halo has two components: a quasi-spherical, weakly rotating structure withmetal-poor stars, and a flattened, radially anisotropic structure of metal-rich stars, which arose due
to accretion of a large (1011−12 M ) dwarf galaxy around (8-10)×109 y ago [54]. The expectationis that the local DM halo shows a similar bimodal structure, and first velocity distributions of thetwo components - using the stellar populations as tracers - were inferred in [55]. In Ref. [56], an
updated halo model is introduced: it includes the anisotropic structure seen in the Gaia data andprovides an analytic expression for the velocity distribution. The value of the local DM density is
updated to (0.55 ± 0.17) GeV/cm3 , where the 30% error accounts for the systematics. The circularrotation and the escape speeds are updated to vc = (233 ± 3) km/s and vesc =528+24−25 km/s. The
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27. Dark Matter

former is in agreement with a new Bayesian estimation of the circular velocity using Gaia DR3, of
vc = (233 ± 7) km/s [57]. With Gaia DR3, new stellar streams are being discovered, some of theselikely originating from the disruption and merger of dwarf galaxies. The study of the velocities
of such streams will allow for increasingly improved constraints on both the DM subhalo density
profiles and the velocity distributions.
27.4.2 Small-scale challenges
The ΛCDM framework is tremendously successful at explaining the observed large-scale structures of the Universe (corresponding to distances ≥1 Mpc, the typical inter-galactic distance), as
well as the main properties of galaxies that form within DM haloes, see the comprehensive review
in Ref. [58]. The observed large-scale structure is consistent with point-like, cold DM particles thatinteract purely via the gravitational force. However, in the past decades, observations at scales
below ∼1 Mpc, where structure formation becomes strongly nonlinear, turned out more problematic to be described within the ΛCDM model. The main small-scale challenges are known as: themissing satellites problem, the cusp-core problem and the too-big-to-fail problem. Initially these issues, which are not all independent of one another, arose by comparing theoretical predictions fromdark-matter-only simulations to observation. While their most likely solutions are in dissipative,
baryonic physics (such gas cooling, star formation, supernovae feedback), see the recent reviews in
Ref. [59, 60], the small-scale problems could in addition call for a modification or an extension ofthe ΛCDM paradigm. Most importantly, the ever increasing amount of data on the satellites ofthe MW and M31 are used to constrain alternative DM models.
The missing satellites problem: High-resolution cosmological simulations of DM haloes
the size of the MW predict hundreds or thousands of subhaloes with masses that are in principle
large enough to allow for galaxy formation (> 107 M ). Yet less than ∼100 satellite galaxies with
masses down to ∼300 M are known to orbit our galaxy within 300 kpc. Galaxies in the field show
a similar under-abundance. One solution could be that galaxy formation becomes increasingly
inefficient as the halo mass drops, and thus the smallest DM haloes have naturally failed to form
galaxies. Progress in both observations and theoretical modeling of observable properties of dwarf
galaxies show that there is very scant evidence for a “missing satellite problem” [60]. Nonetheless,additional, related strong tensions remain, including the diversity of observed rotation curves [61]and the unexpected alignment of satellite planes, the latter issue possibly solved by high-precision
simulations tracking inflow along filaments of the cosmic web [62].
The cusp-core problem: The mass density profiles of DM haloes in ΛCDM simulations
rise steeply at small radii, ρ(r) ∝ r−γ , with γ ' 0.8 − 1.4. This is in contrast to the observed
density profiles of many low-mass galaxies (albeit not all), the rotation curves of which are best
fit with constant-density cores, γ ' 0 − 0.5. A related issue is that simulations predict more
DM than measured in the central regions of galaxies (also known as the central density problem).
A likely solution is that baryonic feedback modifies the structure of DM haloes. Hydrodynamic
simulations which include the effects of baryons on galaxy formation have shown that baryonicfeedback (e.g., supernova-driven blowouts) can erase the central cusps and produce core-like density
profiles. Surveys of satellites of hundreds of galaxies similar to the Milky Way, such as SAGA [63],will likely provide important observational information.
The too-big-to-fail problem: This problem is related to the fact that the dark matter halosof the largest observed Milky Way satellites are typically much smaller than those of the most
massive subhalos of simulated Milky Way-like halos. DM haloes of such masses are thought to
be too massive to have failed to form stars (hence the name of the problem), especially if lowermass subhaloes are capable of doing so. A similar issue is present in Andromeda and in fieldgalaxies outside the Local Group. Possible solutions include lowering the mass assumed for the
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27. Dark Matter

7

Milky Way host halo, or baryonic effects including tidal stripping and larger-than-expected innercores [60]. Other issues relate to the origin of ultra-faint galaxies, and the opposite problem of
dwarf galaxies with very little dark matter given their stellar mass; there exist proposed solutions
to both challenges, including the “bullet dwarf” scenario of Ref. [64].
The solutions that were briefly mentioned above do not require modifications to the ΛCDM
framework. Other solutions involve either modifications of linear theory predictions (via the natureof the DM particle, e.g., Warm DM - WDM) or modifications of nonlinear predictions (via DM
models that involve a self-interaction of DM particles - SIDM). WDM models postulate particles
with masses at the keV-scale, and the observed number of dark-matter-dominated satellites isused to set a lower limit on the number of subhaloes in the MW and thus a lower limit on theparticle’s mass [59]. Current constraints are in the range mW DM > (1.6 − 2.3) keV. Cosmologicalsimulations with SIDM find that σ/mSIDM '(0.5-10) cm2 /g can alleviate the cusp-core and too-bigto-fail problems, giving rise to DM cores in dwarf galaxies with sizes of (0.3-1.5) kpc [13]. Galaxy
clusters provide important constraints, and their large central DM densities prefer models with
σ/mDM .0.1 cm2 /g [65]. Thus, if SIDM is to solve the small-scale CDM problems and obey theconstraints observed on the scales of clusters, σ must depend on the velocity of the particle: itmust increase as the rms speed of the particle decreases from the scale of clusters (v ∼103 km/s)
to the scale of dwarf galaxies (v ∼10 km/s).

27.5 Dark matter models
Particle DM model building is deeply intertwined with the question of the nature of physics
beyond the Standard Model (BSM) of particle physics1 . Directions in this area have followed a few
strategies, including, but not limited to(1) pursuing DM candidates embedded in frameworks that include solutions to other open
issues in particle physics, for example WIMPs in connection with electroweak-scale new physics
that addresses the hierarchy problem, such as supersymmetry (see the Supersymmetry reviews
Sec. 88 and 88); axions in connection with frameworks that address the strong CP problem (seeAxions and Other Similar Particles—Sec. 90); sterile neutrinos in connection with the problem ofneutrino masses and mixing (see the Neutrino Masses, Mixing, and Oscillations—Sec. 14); or (2) ad
hoc, or bottom-up models built with the intent of addressing or explaining a putative experimental(e.g. particle physical anomalies) or observational (e.g. astronomical) signal.
WIMPs: The WIMP paradigm has been a preferred framework chiefly because it often arises
in beyond the Standard Model scenarios that address the hierarchy problem whilst also providing
a simple mechanism to explain the observed relic abundance via the “WIMP miracle” describedabove. Perhaps the most notable example of a framework containing a paradigmatic WIMP is theminimal supersymmetric extension to the Standard Model, if the lightest supersymmetric particle
is a neutralino (the mass eigenstate resulting from the mixing of the supersymmetric partners to
the Higgses and to the SU(2) and hypercharge gauge bosons, and, possibly, of additional singlet
scalars); purely SU(2) sneutrinos have long been ruled out by direct detection, but with suitable
mixing with “inert” (gauge-singlet) sneutrinos they can also play the role of WIMP candidates. For
more details see the the Supersymmetry—Sec. 88 and 89 in this Review. Other non-superysmmetric
WIMP models include models with a Higgs or Z (or Z 0 ) portal, universal extra dimensions [32],and other models with extra (warped or flat) dimensions, little Higgs theories, technicolor andcomposite Higgs theories, among others (see e.g. the review in [66]).
Axions and axion-like particles: Axions are an especially compelling example of a broad
category of DM candidates encompassing very light scalar or pseudoscalar fields. The QCD axion
provides a solution to the strong CP problem, and is at present a viable DM candidate (see Sec. 90
1

Notice that this includes the case of PBHs, as successful formation of the correct number density of PBHs
involves new ingredients beyond standard cosmology and particle physics
31st May, 2024

827. Dark Matterfor details on motivations, production mechanisms, and detection prospects for the QCD axion).
Ultra-light, bosonic DM generally implies the imprint of quantum effects on macroscopic scales(hence the name of wave or fuzzy DM). Specifically, some of the small-scale issues mentioned insec. 27.4 can be addressed if the de Broglie wavelength of the DM, of mass ma and velocity va ,λ~10−22 eV=' 1.9 kpc
2π
m a vama!

10 km/sva(27.7)

is comparable to the size of the smallest observed gravitationally collapsed structures, roughly, fora self-gravitating system of mass M , a scale r ' GM/v 2 . The typical expectation is the formationof a soliton-like core in the DM density profile of size λ, thus inversely proportional to the DM
mass, with an upper limit on the central density of aroundρs . 7 M /pc3

6 

ma



10−22 eV

M
9
10 M



(27.8)

for a halo of virial mass M . Additionally, wave DM predicts that halos lighter than around107 (ma /10−22 eV)−3/2 M should not exist [67], and that the number of halos in the local universe with a mass at or less 109 (ma /10−22 eV)−4/3 M [68] be significantly depleted, addressing inpart the too big to fail and missing satellite problems (see Sec. 27.4 above). Light bosonic DM isnecessarily produced non-thermally [69], and the connection with the visible sector need not, but
might, exist.
Dark photons: Light vector bosons such as a “dark photon” V with a mass below mV < 2me ,can be cosmologically stable (depending upon its kinetic mixing coupling with the visible photon)and be a viable DM candidate. Light dark photons can be produced in the early universe throughscattering or annihilation via processes such as γe± → V e± or e+ e− → V γ, or via resonant photondark photon conversion, or from a condensate seeded by inflationary perturbations [70], or from amisalignment mechanism similar to the one commonly invoked for axion production; constraints
on the parameter space stem from a combination of direct detection experiments, where the dark
photon is absorbed and leads to a large ionization signal, from stellar cooling constraints from theSun, horizontal branch stars, and red giants, and from CMB and the diffuse radiation from the
V → 3γ decay mode. More broadly, light dark (pseudo-)scalars and vectors can be best constrainedwith experiments that rely on their wave-like behaviour and/or on their possible “portal” with thevisible sector. A broad assortment of experiments is sensitive to the range of masses between 10−22
eV and 10−2 eV. Among these experimental efforts, the lowest masses are probed by torsion balanceexperiments [71, 72], atom interferometry [73], comagnetometers [74, 75], and even gravitational
wave detectors [76]; at increasing masses, if the light bosons couple electromagnetically, they cangenerate effective currents which are detectable with different apparata depending on the relevant,mass-dependent target frequency. The experimental portfolio includes the broadband axion search
ABRACADABRA [77, 78], the LC resonator DM Radio [79], lumped-element LC resonators [80],and cavity resonators such as HAYSTAC [81] and ADMX [82] .
Sterile Neutrinos: Sterile (gauge-singlet) neutrinos, assumed to share a Dirac mass termwith ordinary, SU(2)L -active neutrinos, have long been considered viable DM candidates [83]. The
mostly-sterile mass eigenstate participates in SU(2)L interactions via a mixing parameter θ  1
that controls much of the particle’s phenomenology. In particular, the sterile neutrino possesses aninverse-lifetime on the order of τ −1 ∼ G2F m5ν θ2 , forcing the mixing to not exceed−4

θ < 3.3 × 10

10 keVmν

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5(27.9)

9

27. Dark Matterin order for the lifetime to exceed the age of the universe. While the main decay channel is tothree active neutrinos, observationally the radiative decay mode to one neutrino plus a photon ismuch more relevant, giving rise to a quasi-monochromatic photon line at half the sterile neutrino
mass. A recent tentative signal at 3.5 keV was reported from stacked observations of clusters ofgalaxies, individual clusters [84,85], and the Galactic center [86] with both the XMM and Chandra
X-ray observatories. The signal however was not detected in a large sample of galaxies and groups ofgalaxies [87] and dwarf galaxies [88], and especially Draco [89], shedding strong doubts on its sterile
neutrino decay origin. Future observations with increased energy resolution might conclusively
pinpoint the origin of the 3.5 keV emission [90].
Models with rich dark sectors: The absence of any conclusive signals from DM as a particle
thus far motivates the hypothesis that the DM be charged under some new “hidden” dark-sector
force, an idea that dates back many decades [91], including in the guise of “mirror DM” (more recently in the context of “neutral naturalness”). Top-down motivation for hidden-sector DM comesfrom string theory [92], although TeV-scale BSM framework such as supersymmetry and composite Higgs models can also naturally accommodate hidden sectors [93]. Although no coupling of
the visible sector to the hidden sector need exist in principle, there are a few reasons to expect
it [94].The mass scale for hidden-sector DM is broader than, but overlapping with, that for WIMPs(this latter being limited to roughly between a few GeV and a few TeV). In particular, while somemotivation exists for electroweak-scale hidden sectors, light, sub-GeV hidden sectors have a strong
theoretical underpinning, and offer novel detection avenues and opportunities. The phenomenologyof hidden-sector DM depends primarily on the nature of the force and its force carrier. The mostwidely considered cases are (pseudo-)scalar and (axial-)vector mediators. Among the structures forthe mediators’ coupling to the visible sector, renormalizable “portals” include the H † H operator,
through Lagrangian terms of the type (µφ + λφ2 )H † H, coupling to the hypercharge field strength
B µν via kinetic mixing, 0 Bµν F 0µν , and the “neutrino” portal, yn LHN , where L is the lepton doublet of any generation, N is a right-handed neutrino, H is the SM Higgs doublet, and yn the Yukawa
coupling. Other possibilities are for instance a vector mediator directly coupled to SM fermionscharged under its corresponding symmetry [95], or a Z 0 associated to U(1)B−L .Additional possibilities, arising for instance from vector couplings to anomalous global symmetries of the SM like baryon
or lepton number, also exist [94]. The accelerator program necessary to probe hidden-sector DM
often involves small-scale colliders and fixed-target experiments, with experiments utilizing missing
energy and momentum offering the best sensitivity. Beam-dump experiments can test large rangesof DM-mediator couplings as long as mediators decay or scatter inside the detector (see e.g. therecent review [96]). Such experiments can also probe dark sectors with light vectors coupled tovisible matter besides gauge kinetic mixing: an instance are neutrino trident scattering used toplace bounds on e.g. Lµ − Lτ Z 0 gauge bosons. Being virtually unconstrained, the phenomenologyof dark sectors can be arbitrarily rich, with possibilities ranging from dark non-Abelian gauge interactions creating non-trivial self-interacting and/or particle number-changing dynamics, to modelsof “dynamical” DM, with multi-component, unstable DM candidates and a time-variable effective
total DM abundance and equation of state [97].

27.6 Laboratory detection of dark matter
Laboratory searches for DM particles can be roughly classified in direct detection experiments,
axion searches (see Axions and Other Similar Particles—Sec. 90), and searches at accelerators andcolliders.
27.6.1 Searches at Accelerators and Colliders
Various searches for dark matter have been carried out by the CMS and ATLAS collaborations
at the LHC in pp collisions [98–102]. In general, these assume that dark matter particles escape
31st May, 2024

1027. Dark Matterthe detector without interacting leading to significant amounts of missing energy and momentum.
Searches for DM with the LHC and other colliders have targeted DM models that interact
with the SM via Higgs or Z boson exchange, effective field theories with heavy mediators, UVcomplete models such as supersymmetry, models with long-lived particles, and models with richdark sectors. The experimental program correspondingly includes searches for invisible-particle
production mediated by a SM boson, generic searches for invisible particles produced via newparticle mediators, and specific searches for complete models.
There are a variety of types of signals for DM, as noted by Ref. [98]:(a) the imbalance in the transverse momentum in an event due to the presence of DM particles,
produced together with one Standard Model particle,(b) a bump in the di-jet or di-lepton invariant mass distributions, or(c) an excess of events in the di-jet angular distribution, produced by a dark matter mediator.
No signal for DM has been observed in the LHC experiments so far. Instead, limits are set on
masses, couplings, and cross-sections. The latter can be compared, generally in a model-dependent
way, with direct detection experiments.
Searches strategies are designed to optimize signal-to-noise by selecting search-specific cuts:a model-independent instance is initial-state electromagnetic or strong-interaction radiation plus
missing transverse energy. Collider searches for DM inform, and are informed, by DM searches
through direct or indirect detection (see below), and, if possible, by the inferred thermal relic DM
abundance. The collider searches alone cannot prove that a discovery is of dark matter.
In the latter category, searches for DM with the LHC and other colliders have targeted DM
models that interact with the SM via Higgs or Z boson exchange, effective field theories withheavy mediators, UV-complete models such as supersymmetry, models with long-lived particles,
and models with rich dark sectors. The experimental program correspondingly includes searches forinvisible-particle production mediated by a SM boson, generic searches for invisible particles produced via new particle mediators, and specific searches for complete models. Searches strategies aredesigned to optimize signal-to-noise by selecting specific search-specific cuts: a model-independent
instance is initial-state electromagnetic or strong-interaction radiation plus missing transverse energy.
New fixed-target experiments are increasingly probing lighter, sub-GeV dark sectors; thermal, or
quasi-thermal relics (such as asymmetric, SIMP, ELDER DM models) provide sharp, largely modelindependent experimental targets in the case of direct annihilation to Standard Model particles;
even “secluded” annihilation to dark-sector particles can be probed with fixed-target experiments,
albeit with some model-dependent caveats. Accelerator searches provide unique ways to test light
DM models in that they present a lower dependence on the DM particle nature, that could e.g.
drive suppressed velocity-dependent direct detection cross sections, and on kinematic thresholds
that can similarly suppress rates with other search strategies; additionally, accelerator searches
offer opportunities to explore dark sectors in greater detail than other search strategies [94].
Experimental approaches to explore scenarios with a light DM χ and mediator A0 include (i)searches for missing mass in exclusive reactions such as e+ e− → γ(A0 χχ̄) or e− p → e− p(A0 χχ̄), (ii)missing momentum/energy, e.g. in fixed-target reactions such as eZ → eZ(A0 χχ̄), (iii) electron andproton beam dump, where the DM particle is detected from scattering in a downstream detector
after being produced in the beam dump, (iv) direct dark photon searches, when the mediatorcannot decay to the dark matter, mA0 < 2mχ . Current facilities actively probing the methods
listed above include APEX and HPS and JLab, MiniBooNE at Fermilab, NA64 at CERN, and
TREK at J-PARC. Future experiments that will eventually contribute to covering the mentioned
thermal targets include Belle-II at KEK, MAGIX at MESA, PADME at LNF, SHIP at CERN,VEPP3 at BINP, BDX at JLab, COHERENT at ORNL, DarkLight at JLab, LDMX at SLAC or
31st May, 2024

27. Dark Matter

11

JLab, MMAPS at Cornell, SBN at Fermilab, and SeaQuest [94].
27.6.2 Direct detection formalism
Direct detection experiments mostly aim to observe elastic or inelastic scatters of Galactic DM
particles with atomic nuclei, or with electrons in the detector material. Predicted event rates
assume a certain mass and scattering cross section, as well as a set of astrophysical parameters:
the local density ρ0 , the velocity distribution f (~v ), and the escape velocity vesc (see Sec. 27.4).
Table 27.1: Best constraints from direct detection experiments on the SI(at high >5 GeV and low < 5 GeV masses) and SD DM-nucleon couplings.
Experiment

TargetFiducial
Cross
DM
mass [kg] section [cm2 ] mass [GeV]Spin independent high mass (>5 GeV)LUX-ZEPLIN
Xe
5500
9.2 × 10−48
36
PandaX-4T
Xe
2670
3.8 × 10−47
40
XENONnTXe4180
2.6 × 10−47
30
SuperCDMSGe
12
1.0 × 10−44
46
DarkSide-50
Ar20
1.9 × 10−43
10DEAP-3600
Ar
2000
3.9 × 10−45
100Spin independent low mass (<5 GeV)LUX (Migdal)
Xe118
6.9 × 10−38
2
XENON1T (Migdal)
Xe1042
3 × 10−40
2
XENON1T (ionisation only)Xe1042
3.6 × 10−41
3
DarkSide-50 (ionisation only)Ar
20
1.4 × 10−42
2SuperCDMS (CDMSlite)Ge
0.6
2 × 10−40
2SuperCDMS (CDMSlite, Migdal)
Ge
0.6
6 × 10−38
2
CRESST
CaWO4 - O
0.024
1 × 10−39
2
CRESSTSi
0.0035
4.5 × 10−32
0.15
DAMIC
Si
0.3
1 × 10−40
4NEWS-GNe
0.3
1 × 10−38
2Spin dependent proton
PICO60C3 F8 - F
49
3.2 × 10−41
25
PandaX-4T
Xe
2670
1.7 × 10−40
40
LUX-ZEPLIN
Xe
5500
4.2 × 10−41
32
XENONnT
Xe
4180
1.4 × 10−40
30Spin dependent neutron
PandaX-4T
Xe
2670
5.8 × 10−42
40
LUX-ZEPLIN
Xe
5500
1.5 × 10−42
30
XENONnT
Xe
4180
4.3 × 10−42
30

Ref.

[103]
[104]
[105]
[106]
[107]
[108]
[109]
[110]
[111]
[107]
[112]
[113]
[114]
[115]
[116]
[117]
[118]
[119]
[103]
[105]
[119]
[103]
[105]

Interactions with atomic nuclei: For DM scattering off nuclei, the differential scattering
rate R as a function of nuclear recoil energy ER is
ρ0dR(ER , t)
= NT
dER
mDM

Z

vf (~v + ~vE (t))
v>vmindσ(ER , v) 3
d v,
dER

(27.10)where NT is the number of target nuclei, mDM is the mass of the DM particles, v = |~v | is the speedof the particle in the experiment’s rest frame, f (~v +~vE (t)) is the velocity distribution in the Earth’s
frame, vmin is the minimum speed of the DM particles that can cause a recoil energy ER and σ isthe scattering cross section on the nucleus [29, 120]. For elastic scattering, the minimum velocity
is vmin = (mN ER /2m2r )1/2 , with mN being the mass of the nucleus, and mr = (mN mDM )/(mN +mDM ) the reduced mass of the nucleus-DM system. In case of inelastic scattering, the minimum
31st May, 2024

1227. Dark Matter

speed becomes vmin = (mN ER /2m2r )1/2 + E ∗ /(2mN ER )1/2 , with the nuclear excitation energy E ∗ ,for part of the kinetic energy of the incoming particle will be spent on exciting the nucleus. The
prompt de-excitation energy, if observed in addition to the nuclear recoil energy, will boost theregion-of-interest to higher energies [121].
If one assumes the standard, leading order spin-independent (SI) and spin-dependent (SD)interactions, which couple to the charge/mass and spin of the nucleus, respectively, the differential
cross-section is proportional to the inverse squared speed of the DM particle, dσ/dER ∝ v −2 , andthe dependence on the velocity distribution can be expressed as:f (~v + ~vE (t)) 3
d v.
v
v>vminZg(vmin , t) =(27.11)This functions allows for the comparison of various experimental results independently of the underlying velocity distribution [122], for a given DM mass. The time-integrated differential crosssection is the sum of the SI and SD contributions:dσ(ER , v)
mN  SI 2
SD 2
=
σ
F
(E
)
+
σ
F
(E
)
,
R
R
0
SI
0
SD
dER
2m2r v 2(27.12)where F 2 (ER ) are the nuclear form factors and σ0 the cross-sections in the limit of zero momentum
transfer. Since the incoming particle velocity is v/c ∼ 10−3 , the nuclear recoil energy is at mosttens of keV (much smaller than typical nuclear binding energies per nucleon), and the momentum
transfer q = (2mN ER )1/2 ∼ O(10 − 100) MeV. This implies that 1/q can be of the same orderas nuclear radii R ∼ A1/3 fm, and that nuclei are not point-like from the perspective of a DM
particle. The cross sections will thus involve nuclear form factors. These were calculated in [123]and [124] for the SI and SD case, respectively, for specific target nuclei, while the cross sections areoften expressed in terms of single-nucleon cross sections and effective couplings of the DM particle
to protons and neutrons. In the SI case, all the nucleons in the nucleus contribute coherently tothe cross-section (under the assumption of isospin independence in the DM couplings). Dominantsources of uncertainty are the nucleon sigma terms, especially for Higgs-dominated interactions,where the couplings are proportional to the quark masses. An overview is presented in Ref. [125].
For SD scattering, the nuclear spin contents due to the protons and neutrons must be considered.
The interactions of DM particles with nuclei can be treated in a non-relativistic effective field
theory (NR-EFT) approach, which considers more general DM scenarios based on the lowest-order,
four-field operators that describe the couplings to nucleons. These operators, which correspond todifferent types of interactions between the DM and quark fields, can be momentum- and velocitydependent, and might be leading when momentum-independent interactions are suppressed, oreven vanish in the limit of zero momentum [126, 127]. In Ref. [127, 128] all 15 operators (arisingfrom 20 possible bilinear combinations between the DM and nucleon fields) which obey Galileaninvariance, T -symmetry and are Hermitian are written out up to quadratic order in q, and thenuclear response functions evaluated in shell-model calculations for DM targets made of F, Na, Ge,
I and Xe isotopes. The connection to particle physics within the context of simplified DM models ismade in Ref. [129,130], where the simplified models assume a single DM particle with one mediator
which couples it to quarks. More recently the DM-nucleus scattering was also analysed in theframework of chiral effective field theory (Ch-EFT), a low-energy effective theory of QCD, whichallows for a consistent derivation of the nuclear responses beyond the leading-order expressions [131,132]. Ch-EFT preserves the QCD symmetries, and predicts DM couplings to two nucleons (e.g.,when the hypothetical particle couples to a virtual pion exchanged between the nucleons). It also
provides a power counting that suggests a hierarchy of the various NR-EFT operators, which is
31st May, 2024

27. Dark Matter13

however approximate given that the couplings between the DM and the Standard Model fields are
not known. The generalized SI structure factors for spin-1/2 and spin-0 DM particles and various
isotopes of F, Si, Ar, Ge and Xe employed in direct detection experiments are provided in Ref. [132].
Scattering off bound electrons and absorption: For DM particle masses below the GeVscale, most searches for DM-nucleus scattering rapidly lose sensitivity, due to energy thresholds
around a few 100 eV - few keV. As an example, a light DM particle with a mass of 100 MeV andv ∝ 10−3 c will induce a nuclear recoil energy of about 0.5 eV in a target made of argon. Anotherstrategy is to search for DM scattering off bound electrons, allowing for all of the kinetic energy(50 eV in the above case) to be transferred to the material [133]. The leading possibilities areionisation, excitation, and molecular dissociation processes, which typically require energies of (110) eV, and thus allow to probe scattering of DM particles with masses down to the O(MeV) range.
For a bound electron with binding energy EB DM particle masses of mDM ≥ 250 keV × EB /1 eV
can in principle be probed. The signal depends on the material, and can consist of one or more electrons (in semiconductors, noble liquids, graphene), one or more photons (in scintillators) or phonons(in superconductors and superfluids) and quasiparticles (in superconductors). As an example, thedifferential event rate for ionization in atoms is given by:dRion
ρ0 dhσion vi= NT,
d ln ERmDM d ln ER(27.13)where ER is the recoil energy transferred to the electron, hσion vi is the thermally averaged ionization
cross section and NT is the number of target atoms per unit mass. The cross-section is related to
the non relativistic DM-electron elastic scattering cross-section (σe ):
dRion
6.2
=
d ln ERA

ρ0
0.4 GeV cm−3



σe
−40
10 cm2



10 MeVmDM

×dhσion vi/d ln ER events
10−3 σekg d(27.14)

Predicted differential rates in various materials (He, Ar, Ge, Xe) and for different particle
masses are shown in [133], together with cross section sensitivities as a function of mass andexpected background rates from neutrinos. More recently, rates of electronic transitions induced
by DM-electron scattering on Xe, Si and Ge for spin 0, spin 1/2, and spin 1 DM models were
calculated in [134]. The code EXCEED-DM (extended calculation of electronic excitations for direct
detection of dark matter) can compute DM-electron interaction rates with inputs from a variety of
ab initio electronic structure calculations [135].
Two classes of DM candidates, axion-like-particles (ALPs) and dark (or hidden) photons (seeSec. 27.5), can be absorbed in a target material by interactions with bound electrons via theaxioelectric effect, which is analogous to the photoelectric effect: a boson is absorbed by a boundelectron, which is then ejected from the atom [70, 136, 137]. The dark photon arises in extensionsof the SM by a new massive or massless U(1)’ field, coupled to the SM U(1)Y via a kinetic mixing
term κ, see Sec. 27.5. The absorption cross-section of a massive, NR particle mV with couplinge0 = eκ to electrons is (in natural units, and for energies EV  me )α0σabs =
α



EV
2me

2

σpe ,

(27.15)where σpe is the photoelectric cross-section, and an analogue to the electromagnetic fine structure
constant α is introduced, α0 = (eκ)2 /4π. The rate per atom isR'ρ0× κ2 σpe .
mV31st May, 2024

(27.16)

14

27. Dark Matter

Since the kinetic energy of the dark photon is negligible compared to its rest energy, a monoenergetic peak at its mass is expected in the spectrum of a direct detection experiment. Dark
photons with a thermally generated abundance are excluded by direct detection experiments [70],however non-thermal mechanisms (e.g., via perturbations during inflation) could create the relicabundance, see Section 27.3.
Similarly to axions, ALPs arise in the spontaneous breaking of a global symmetry, and are
phenomenologically described by a mass ma and a decay constant fa . Unlike for QCD axions,however, there is no strict relation between ma and fa . The coupling strength to electrons withmass me is parameterised by gae = 2me /fa , and the absorption cross section of a particle withincoming velocity va is related to the cross-section for the photoelectric effect as
2
3Ea2
3gae
σabs va 'σ=pe
4παfa2
4πα



Ea
2me

2

σpe .

(27.17)

As in the case of the dark photon, the signature is a mono-energetic peak at the mass of theparticle, broadened by the energy resolution of the detector. Constraints on the couplings of ALPs
and dark photons to electrons from direct detection experiments in ma and mV mass ranges from∼ (1 − 104 ) eV were derived in Ref. [138, 139], and compared to indirect limits from anomalousenergy losses in the Sun, in red-giant and horizontal-branch stars. For a detailed discussion ofaxion and ALP searches, we refer to the Axion review.
27.6.3 Current and future direct detection technologies
Direct detection experiments aim to observe the small (keV-scale and below) and rare (fewer
than ∼1 event/(kg y)) signals which are induced by DM particle scatters in a detector, mostly in theform of ionisation, scintillation or lattice vibrations. A majority of experiments detects more than
one signal, which allows to distinguish between scattering off of electrons (electronic recoils, ER)
and off of atomic nuclei (nuclear recoils, NR). A 3D position resolution is required to define central
detector regions (or fiducial volumes) with low background rates from surrounding materials, andthe distinction between single- versus multiple-scatters rejects a significant fraction of backgrounds,
given that DM will scatter at most once. We refer to [140, 141] for recent reviews of the field.
Specific signatures: For NRs, the shape of the differential recoil spectrum is exponentiallyfalling with recoil energy, and depends on the mass of the particle and on the nuclear mass. Unless
mDM  mN , mDM can in principle be determined from the measured recoil spectrum, wheremultiple targets will provide tighter constraints [142]. The Earth’s motion through the MW induces
a seasonal variation of the total event rate and a forward-backward asymmetry in a directionalsignal [143, 144]. The annual modulation is due to the Earth’s motion in the Galactic rest frame,
which is a superposition of the Earth’s rotation around the Sun and the Sun’s rotation aroundthe Galactic center. Since the Earth’s orbital speed is much smaller than the Sun’s speed, theexpected amplitude of the modulation is ' 5%. In the SHM, the period is one year, and the phaseis 150 d (June 2), when both speeds add up maximally. This expectation is modified for different
DM distributions, e.g. in the case of sub-structures such as clumps and streams [145, 146] anda DM disc [147]. In addition, the modulation changes phase at a specific recoil energy (known
as crossing-energy) [148], which depends on the DM and nuclear mass, allowing to in principle
determine mDM if low energy thresholds can be achieved. A powerful signature is provided by
the ability to detect the axis and direction of the recoiling nucleus. Since the DM flux in thelaboratory frame is peaked in the direction of motion of the Sun towards the constellation Cygnus,
the recoil spectrum is peaked in the opposite direction. The observation of such a dipole feature
would provide a ’smoking-gun’ evidence for DM, where the forward-backward rates can differ by afactor of ∼10, depending on the energy threshold. Ref. [149] provides a review of the theoreticalframework and of the discovery reach of directional detectors.
31st May, 2024

27. Dark Matter

15

Backgrounds, including neutrinos: Early direct detection experiments employing lowbackground Ge spectrometers featured background levels around 2 events/(kg d keV), while thelatest generation of liquid Xe experiments reduced this noise by almost five orders of magnitude, to
4×10−5 events/(kg d keV). In liquid xenon detectors, the measured ER spectra at low energies arefor the first time dominated by solar pp neutrino interactions, second-order weak decays, as well as
214 Pb β-decays from radon mixed with the xenon. Other backgrounds are due to the radioactivityof detector components, followed by cosmic muons and their secondaries such as fast neutrons. The
cosmic and environmental radiation are suppressed by going deep underground and surrounding theexperiments with appropriate shielding structures (mainly large water Cherenkov detectors for thecurrent and next-generation detectors). Activation of materials via cosmic-ray interactions produce
long-lived radio-nuclides (e.g., 39 Ar, 60 Co, 68 Ge, 32 Si, etc), while long-lived, human-made isotopes(85 Kr, 137 Cs, etc) can mix with detector materials or generate surface backgrounds. For details, werefer to Section 36.6 of this Review.

10 38
10 40

CDMSlite (2018)

10 2

DAMIC (2020)

10 4

CRESST (2019)10 42 DarkSide-50 (2023)
10 44

10 6

017)
SuperCDMS (2019)
DEAP-3600 (2
10 8
)
1
2
0
PandaX-4T (2XENONnT (2023)
10

XENON1T (2020)

10 46
10 48
10 50

10

LZ (2023)

Neutrino coherent scattering

100

SI WIMP-nucleoncross section [pb]

SI WIMP-nucleon cross section [cm2]

100

101

WIMP Mass [GeV/c2]

10 12
102

10 14
103

Figure 27.1: Upper limits on the SI DM-nucleon cross section as a function of DM mass.
The final backgrounds are due to the irreducible neutrino flux from the Sun, the atmosphere andthe diffuse supernovae background [150]. Solar pp-neutrinos start dominating the electronic recoil
background due to elastic neutrino-electron scatters, at a level of ∼ (10 − 25) events/(t y) below
energies of ∼100 keV, while coherent elastic neutrino-nucleus scatters (CEνNS) from 8 B solar neutrinos will induce up to ∼ 103 events/(t y) for high-A targets, at nuclear recoil energies below ∼few
keV. Nuclear recoils from atmospheric neutrinos and the diffuse supernovae neutrino backgroundwill yield event rates in the range (1 − 5) events/(100 t y), depending on the detector material. In
general, 8 B and atmospheric neutrinos will impact light (≤ 6 GeV) and heavy (100 GeV and above)
DM searches for cross sections on nucleons below ∼ 10−45 cm2 and ∼ 10−49 cm2 , respectively. The
precise cross-sections where neutrinos constitute a dominant background strongly depend on thesystematic uncertainties on the neutrino flux normalisation for each source [151]. For very low
energy thresholds to nuclear recoils, e.g. 10-30 eV in Ge and Si detectors, CEνNS due to the 7 Be
neutrino flux become relevant for exposures of ∼50 kg y [152]. For DM searches with electron re31st May, 2024

16

27. Dark Mattercoils via DM-electron scattering and dark photon or ALP absorption, solar neutrinos will also limit
the sensitivity to DM masses in the range ∼(1-103 ) MeV and ∼(1-103 ) eV, respectively, for large
exposures ∼1 t y, as shown in Ref. [153].
Solid-state cryogenic detectors: Current experiments using the bolometric technique (seeSection 36.5 of this Review), together with either charge or light readout, are SuperCDMS (Si,Ge) at Soudan (until 2015) and SNOLAB (in construction), EDELWEISS (Ge) at the Laboratoire Souterrain de Modane (LSM) and CRESST (CaWO4 , Al2 O3 , Si, LiAlO2 ) at the Laboratori
Nazionali del Gran Sasso (LNGS). These experiments are optimised for low-mass DM searches, andcan probe WIMP masses down to ∼0.03 GeV. CRESST operated a 0.35-g thin wafer Si detector
and reached a 10-eV energy threshold, probing DM masses in the range (115–500) MeV, improving
existing limits by up to a factor 20 for masses below 160 MeV. CDMSlite operated detectors at
higher bias voltages to amplify the phonon signals produced by drifting charges and thus haveaccess to light DM around 1.5 GeV. A reanalysis of the CDMSlite data using the Migdal effectallowed to exclude new parameter space for WIMP-nucleon cross-sections down to 30 MeV [113].
The goal at SNOLAB is to probe the (0.05–5) GeV region down to cross sections of ∼ 10−44 cm2 .
Much smaller, gram-scale versions of cryogenic detectors can have single-charge resolution and thusprobe low-mass DM via inelastic electron recoils. A SuperCDMS single-charge sensitive Si detector
placed upper limits on DM interacting with electrons for masses between (0.5–104 ) MeV, as well as
on dark photon kinetic mixing for dark photon masses in the range (1.5–40) eV. With Ge crystals
operated at Soudan, SuperCDMS constrained dark photons and ALPs in the mass range 40 eV to
500 keV.
Germanium ionisation detectors operated at 77 K can reach sub-keV energy thresholds and low
backgrounds, but lack the ability to distinguish electronic from nuclear recoils. The CDEX-10
experiment at the China Jinping Underground Laboratory (CJPL) uses p-type, point-contact Ge
detectors operated in liquid nitrogen to probe DM masses down to 3 GeV. It also reported constraints on the kinetic mixing of dark photons in the mass range (0.1–4.0) keV. The 0νββ-decay
experiments Majorana Demonstrator and GERDA have obtained constraints on the couplings of
ALPs and dark photons to electrons, with masses between (6-100) keV and (60-1000) keV, respectively. The Majorana Demonstrator improved laboratory constraints on solar axion masses between(1.2–100) eV, setting limits on the axion-photons coupling of gaγ < 1.45 × 10−9 GeV−1 (95% CL).
Noble liquids: Liquid argon (LAr) and liquid xenon (LXe) are employed as DM targets,
while R&D on liquid helium is ongoing. We refer to Ref. [154] for a review of the liquid noble
gas detector technology in low-energy physics, as well to Section 36.4 of this Review. At present
the best constraints on DM-nucleus interactions come from multi-tonne experiments using xenon:
the LZ experiment at SURF, PandaX-4T at CJPL and XENONnT at LNGS. These experiments
probe particle masses down to ∼6 GeV (when using both light and charge signals) and the SI DMnucleon cross section down to 9.2×10−48 cm2 (at 36 GeV). LAr experiments employ pulse shapediscrimination (PSD) that allows for distinguishing between ER and NR events, at the expense ofhigher energy thresholds than in LXe. The DarkSide-50 TPC at LNGS (until 2019) sets a minimum
upper limit on the SI, DM-nucleon cross-section of 6×10−43 cm2 at 10 GeV, while the single-phase
experiment DEAP-3600 at SNOLAB constrains the SI cross-section to values below 3.9×10−45 cm2
at 100 GeV.
In noble liquids, sub-GeV DM particles can be searched for by observing inelastic, ER processes
following a low-energy nuclear recoil: excitation and ionisation of the recoiling atom (the hypothetical Migdal effect) and a bremsstrahlung photon [155]. As an example, LUX and XENON1T constrained DM particle masses between (0.3–5) GeV via bremsstrahlung photons and Migdal electrons.
Even lower masses are accessible when using the amplified, charge signal only, at the expense of giving up discrimination between ERs and NRs. XENON1T probed particle masses down to 60 MeV,
31st May, 2024

17

27. Dark Matter

while DarkSide-50 published constraints on WIMP masses as low as 40 MeV. DM masses at the
MeV-scale can also be probed by exploiting the scattering off electrons. PandaX-4T presented light
DM searches with ionisation signals, with NR and ER energy thresholds of 0.77 keV and 0.07 keV,obtaining leading constraints in the mass range 40 MeV–100 GeV and 100 MeV–10 GeV for a heavy
and light mediator, respectively [156]. DarkSide-50 set limits in the mass range (16 − 56) MeV andabove 80 MeV for a heavy and light mediator, respectively [157]. Noble liquids TPCs also search forsolar axions, galactic ALPs and dark photons. XENONnT set upper limits on the axion-electron
coupling of 2×10−12 in the mass range (10−6 –1) eV for solar axions, and probes couplings between(1 − 2)×10−14 in the mass range (1–10) keV for galactic ALPs [158]. DarkSide-50 probes ALP
masses down to 0.03 keV with couplings in the range 10−13 − 10−14 [157].
The next generation of liquefied noble gas detectors are in construction (DarkSide-20k) or at thedesign and R&D stage (Argo, DARWIN/XLZD, PandaX-xT). These will increase the sensitivity tovarious DM candidates by 1-2 orders of magnitude, with the ultimate goal of exploring the experimentally accessible parameter space, until the backgrounds from neutrinos will start dominating
the event rates.
Room temperature scintillators: Several large DM experiments using high-purity NaI(Tl)crystals are acquiring data in various underground laboratories. Of these, DAMA/LIBRA at LNGS
has the highest mass, 250 kg, and the largest exposure: 1.33 t y with an energy threshold of 1 keV
and 2.46 t y with an energy threshold of 2 keV. It is the only experiment in the field that reported
an annually modulated event rate with a statistical significance of 12.9 σ C.L. (20 annual cycles),with a modulation amplitude around 0.02 events/(kg d keV) in the energy region (1-4) keV. Thesefindings were interpreted as due to DM interactions via nuclear or electronic recoils. The ANAIS
experiment at Canfranc operates 112.5 kg of NaI(Tl) scintillators with an energy threshold of 1 keV
and a background rate of 3.6 events/(kg d keV) in the (1-6) keV region. A blind analysis of 3 y of data,
for an exposure of 314 kg y is consistent with an absence of modulation at 3.3 σ. The COSINE100 experiment, located at the Yangyang Underground Laboratory in Korea, operates 106 kg of
NaI(Tl) crystals in a liquid scintillator, with an energy threshold of keV and a background rate of
3.6 events/(kg d keV). Results from a 173 kg y exposure in the (1-6) keV energy range are consistent,
at 68.3%C.L., with both the null hypothesis and DAMA/LIBRA’s best fit value in the same energy
range. A larger exposure and a reduced energy threshold are required to test DAMA/LIBRA for 3 σcoverage. COSINE-200, under construction at the new, deeper underground laboratory Yemilab,
will be a larger experiment with reduced backgrounds. The SABRE experiment plans to operate a
total of 50 kg of NaI(Tl) crystals, focussing on reaching a background level of 0.1 events/(kg d keV),
an order of magnitude below DAMA/LIBRA. Twin detectors will be installed at LNGS and at
the Stawell Underground Physics Laboratory in the Southern hemisphere. While a DM-induced
signal is expected to have the same phase in both hemispheres, seasonal or site-related effects
would show different amplitudes and phases in the twin detectors. The COSINUS experiment,
under construction at LNGS, will use NaI crystals operated as cryogenic scintillating calorimeters
to differentiate between nuclear and electronic recoils based on the observation of phonon and lightsignals. The first phase aims for an exposure of 100 kg d, while the second phase aims to achieve,with 1000 kg d, a fully model-independent cross-check of a NR origin of the DAMA/LIBRA signal.
Room temperature ionisation detectors: Silicon charged-coupled devices (CCDs) are employed for low-mass DM searches, as well as for hidden photon searches in the eV-mass range. Ionisation events induced in bulk silicon of high-resistivity, fully depleted CCDs are observed with charge
resolutions around 1-2 e− and extremely low leakage currents, at the level of few e− mm−2 d−1 .
The position of an energy deposit is reconstructed in 3 dimensions and the particle type (electron,
neutron, muon, α-particles, etc) is reconstructed based on the recorded track pattern.
The DAMIC experiment at SNOLAB yielded new constraints on DM-electron scattering, and31st May, 2024

18

27. Dark Matteron the hidden-photon kinetic mixing parameter in the mass range (1-30) eV with an exposure of
7.6 kg d and on low-mass WIMPs with an exposure of 11 kg d. The SENSEI projects employs theskipper technology to achieve single-electron sensitivity. A run with a 2 g detector in the MINOS
cavern at Fermilab yielded world-leading constraints on DM-electron scattering for a large rangeof sub-GeV dark matter masses. The skipper technology is also employed in the next stage of the
DAMIC programme, DAMIC-M at LSM, which plans for a kg-size mass. The goal is to achievethresholds of 2-3 electrons and to probe the DM-nucleon cross-section down to few×10−43 cm2around 2-3 GeV and the DM-electron cross section down to 2×10−41 cm2 at 10 MeV mass. DAMICM has operated first CCDs at LSM and achieved constraints on sub-GeV DM particles interactingwith electrons in the mass range (0.53-1000) MeV, for an exposure of 85.23 g d.
The NEWS-G collaboration operates spherical proportional counters filled with a noble gas.
Advantages of this technology are the low intrinsic electronic noise and a high amplification gain,
allowing for low energy thresholds down to single-electron detection, and the possibility to use
different light targets (He, Ne, etc). A 60 cm diameter chamber operated at LSM with a gas mixtureof Ne + CH4 (0.7%) at 3.1 bar, excluded SI, WIMP-nucleon cross sections above 4.4×10−37 cm2
at 0.5 GeV after an exposure of 9.6 kg d with an energy threshold ∼100 eV. The next iteration, a140-cm sphere detector made of very low radioactivity copper (few µBq/kg of 238 U and 232 Th) has
been installed at SNOLAB in 2021. The detector has recently started to acquire physics data, witha predicted background level of (5 ± 2) events/(kg keV d) for sub-keV events.
Superheated liquid detectors: Investigation of the spin-dependent interaction channel calls
for target nuclei with uneven total angular momentum. A particularly favourable candidate is 19 F,
the spin of which is carried mostly by the unpaired proton, yielding a cross-section which is almosta factor of ten higher than of other employed nuclei with spin (e.g., 23 Na, 73 Ge, 127 I, 129 Xe, 131 Xe).
Fluorine is part of the target of experiments using superheated liquids, such as the ones operated
by the PICO collaboration. A search in the PICO-60 C3 F6 bubble chamber at SNOLAB with an
exposure of 1404 kg d and an energy threshold of 2.45 keV, yielded the most stringent constraint on
the DM-proton SD cross-section at 3.2×10−41 cm2 for a 25 GeV particle mass. In construction at
SNOLAB is PICO-500, a detector with 250 l of superheated freon (C3 F8 ) contained between twoquartz jars inside a pressure vessel filled with mineral oil, itself inside a tank of ultra-pure water.
Directional detectors: Detectors capable of measuring the direction of the recoiling nucleus
would unequivocally confirm the Galactic origin of a signal and could probe the region below theneutrino floor [159, 160]. Because nuclear recoils have a range which is about 10 times smaller
than the one of Compton recoils of the same energy, gaseous detectors have an excellent intrinsic
background rejection if they can measure the range of events precisely. Several directional detectors
are presently in operation, where a 1 m3 detector has a typical mass of a few 100 g and can measure
the sense of an incoming nuclear recoil above a few tens of keV. Cygnus is a proto-collaboration
which coordinates the R&D efforts for gas based TPCs with 1 keV threshold. One of these is
CYGNO, an experiment that aims to build a 1-m drift length gaseous TPC filled with a He:CF4
60:40 gas mixture at atmospheric pressure and room temperature at LNGS.
A new technique is based on fine-grained nuclear emulsions (solid-state detectors with silver
halide crystals uniformly dispersed in a gelatine film, where each crystal works as a sensor forcharged particles), as proposed by the NEWSdm collaboration. These act as target and nanometrictracking device, and the expected NR tracks are sub-µm in size. Due to the small crystal size andlarger number density, a superior spatial resolution compared to gaseous detectors is obtained.
Simulations show that to reach the neutrino floor, exposures of 10 t y and 100 t y are required if a
30 nm and 50 nm threshold for detecting the track length is reached. This requires further R&D,
since current emulsions allow for 100 nm tracking and target masses are around 1 kg, with 10 kg y
exposures planned. A proposed approach for the directional detection of sub-GeV DM is to use
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27. Dark Matter

two-dimensional materials such as monolayer graphene [161], from which the DM particle can eject
electrons. Their energy and direction, correlated with the direction of the incoming DM, can bemeasured for instance with the proposed PTOLEMY experiment.
New techniques: To probe light (sub-GeV) DM particles, either via scatters off electrons or
via couplings to phonons, new techniques beyond the ones discussed above are proposed. The DM
particle mass that can be accessed in DM-electron scattering in noble liquids and semiconductors
is limited by the minimum ionisation/excitation energy and the size of the band gap, respectively(at the ∼eV-scale). To reach lower energy thresholds, materials with smaller band gaps for electron excitations (∼meV), such as superconductors and superfluids, as well as Dirac materials were
proposed [162]. These would in principle allow for the detection of keV-scale DM. Other ideas todetect keV-MeV scale DM are to observe NRs in superfluid He, via collective excitation modes in
the fluid [163], as realised in HeRALD and DELight, or based on the breaking of chemical bonds
between atoms [164].
Even lighter DM, with masses in the meV-eV range, could be detected via absorption on a
conduction electron in a superconductor, followed by the emission of an athermal phonon [165].
Another proposed target for light DM are polar materials (for example GaAs, sapphire), which
are especially sensitive for scattering through an ultralight dark photon, via excitation of single
optical phonons [166]. If an anisotropic crystal such as sapphire is employed, a daily modulationinteraction rate could be established [167]. A new class of detectors for bosonic DM, based onresonant absorption onto a gas of small polyatomic molecules, is proposed in [168]. The DM would
effectively act as a laser that resonantly excites transitions in molecules when its mass closely
matches the transition energy. While DM with SI couplings can efficiently excite phonons, it
has been shown in [169] that if DM couples to the electron spin, magnon excitations (quanta ofcollective spin wave excitations) in materials with magnetic dipole order may also offer a promisingdetection avenue. Yet another approach for sub-GeV DM is to employ superconducting nanowires
as both target and sensor, and first bounds on DM-electron interactions were placed from a 4.3 ng
tungsten-silicide prototype with a 0.8 eV energy threshold and an exposure of 8.8 × 10−14 kg y [170].
The detection of light DM via collective excitations in condensed matter systems and othermethods is a rapidly evolving field, and a growing area of research at the interface of DM physics,
condensed matter and materials science. We refer to Ref. [171, 172] for discussions of some of thesenew directions and models. Critical challenges are to detect these very small energy depositions,and to reliably asses the background noise.
Table 27.1 summarises the most stringent constraints on the DM-nucleon SI and SD crosssections, and Figure 27.1 shows the best constraints for SI couplings in the cross-section versus DM
mass parameter space, above masses of 0.3 GeV.

27.7 Astrophysical detection of dark matter
DM as a microscopic constituent can have measurable, macroscopic effects on astrophysicalsystems. Indirect DM detection refers to the search for the annihilation or decay debris from DM
particles, resulting in detectable species, including especially gamma rays, neutrinos, and antimatterparticles. The production rate of such particles depends on (i) the annihilation (or decay) rate (ii)the density of pairs (respectively, of individual particles) in the region of interest, and (iii) the
number of final-state particles produced in one annihilation (decay) event. In formulae, the rate
for production of a final state particle f per unit volume from DM annihilation can be cast as

ΓfA = cρ2DM
hσviNfA ,m2DM

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(27.18)

27. Dark Matter20

where hσvi indicates the thermally-averaged cross section for DM annihilation times relative velocity[27], calculated at the appropriate temperature, ρDM is the physical density of DM, and NfA is thenumber of final state particles f produced in one individual annihilation event. The constant c
depends on whether the DM is its on antiparticle, in which case c = 1/2, or if there is a mixture of
DM particles and antiparticles (in case there is no asymmetry, c = 1/4). The analog for decay is
ΓfD =

ρDM 1
N D,
mDM τDM f(27.19)with the same conventions for the symbols, and where τDM is the DM’s lifetime.

10−23

Excluded by CMB
hσvi (cm3 s−1 )10−24

Abazijian+ (2015)
Daylan+ (2014)
Calore+ (2014)

HESS

10−25

Relic Density Steigman+

10−26

CTA
6 year dSph 95% UL
gNFW GC 95% UL
NFW GC 95% UL

10−27

101

102

103

104

mχ (GeV)Figure 27.2: Upper limits and projected sensitivity from CTA on the pair-annihilation rate versus
the DM mass from gamma-ray and CMB observations (figure courtesy of Logan Morrison).
Gamma Rays: DM annihilation to virtually any final state produces gamma rays: emission processes include the dominant two-photon decay mode of neutral pions resulting from thehadronization of strongly-interacting final states; final state radiation; and internal bremsstrahlung,the latter two including, possibly, the emission of massive gauge or Higgs bosons subsequently producing photons via their decay products. Similarly, neutrinos are produced from charged pion
decay and from radiative processes. The flux of gamma rays and neutrinos is calculated integrating
the rate Γf per steradian (simply meaning, for isotropic emission, Γf /(4π)) along the line of sightwithin the appropriate angular region (the differential flux is obtained in the same way by simply
replacing Nf with the differential flux at production, at the appropriate redshift in the case ofcosmologically distant sources),ZZΓf(27.20)
φf =
dΩ
dl .
4π
∆Ω
l.o.s.
It is customary to factor out, in the expression for the rate, a particle physics factor, depending
upon the DM particle mass and its annihilation or decay rate, and an astrophysical factor, which
only depends on the observational target. The latter is sometimes denoted with J∆Ω (ψ) with ψ
31st May, 2024

27. Dark Matter21

indicating the direction of the line of sight. Although different conventions are in use, a common
choice is to defineZ
ZJ∆Ω (ψ) =ρ2DM (l, Ω) dldΩ.
(27.21)∆Ω l.o.s.(ψ)

For a target with uniform density ρ and radius r at a distance d  r, such that the target is entirely
within the solid angle ∆Ω,
4πr3 ρ̄2DM
J'.
(27.22)3d2
Searches for gamma-ray emission from DM annihilation have focused on targets chosen basedon a variety of considerations, primarily intended to maximize signal to noise. Nearby dwarf
spheroidal galaxies contain very small amounts of gas, and do not host any significant astrophysicalbackground at gamma-ray or X-ray frequencies, and are thus an optimal target choice for DM
searches. An accurate determination of the DM density profile in these objects results in somewhat
large systematics when deriving constraints from the non-observation of emission from DM; future
optical surveys will help pinpoint with greater accuracy stellar kinematics and thus reduce such
uncertainty; a second target is the inner region of the Milky Way: while nearby and potentiallyhosting a large density of DM, the Galactic center region is however very bright at almost any
wavelength, making the extraction of a signal highly problematic; nearby clusters of galaxies arealso known to host significant astrophysical emission, but are potentially ideally suited to constrain
DM decay. Finally, putative nearby DM clumps are also a possible source of a bright DM signal(albeit from an unknown direction), as is the annihilation of DM in all halos at all redshifts.
DM annihilation and decay can lead to striking spectral features. Since the process happens
typically at very low particle velocities, if the DM pair-annihilates e.g. to two photons or twoneutrinos, the final-state particles will be nearly monoenergetic, with an energy close to the DM
particle mass and a width proportional to the DM velocity in units of c (if a γγ line is present
electroweak symmetry also implies a Zγ line, if kinematically allowed). No astrophysical processes
are known to produce lines at gamma-ray or neutrino energies in the GeV and above (with, perhaps,
the possible exception of cold pulsar winds [173]) making this channel virtually background-free. At
lower energy, lines are expected from radiative decay modes of candidates such as sterile neutrinos(see Sec. 27.5).DM annihilation or decay can lead to additional spectral features besides lines. These
include (one or more) “boxes” [174], produced by boosted final states decaying to monochromatic
photons (such as e.g. neutral pions), or combinations thereof. Processes occurring at higher redshift
can distort these spectral features by smearing them to lower energies. Neglecting gamma-ray
attenuation, the flux of gamma rays from all redshift can be cast asdNγc(Eγ ) =
dEγ
8πZ

hσviρDM (z)dz
H(z)(1 + z)3 m2DM



dNγ
dE 0



.

(27.23)E 0 =Eγ (1+z)

While the calculation of the differential spectrum of gamma rays from a given final state f ,dNγf /dEγ , is carried out using numerical tools, such as Pythia [175] that reproduce hadronizationand particle decay for masses well above a few GeV, in the sub-GeV range gamma-ray production
follows primarily from meson decay and radiative processes well outside the range of applicabilityof the Altarelli-Parisi splitting function. The MeV gamma-ray range will soon be probed withforthcoming satellites [176]. Recently a code that provides the expected gamma-ray spectrum for
sub-GeV DM, Hazma, has become available [177].
Observations with the Fermi Large Area Telescope (LAT) and with ground-based facilities such
as HESS, VERITAS, MAGIC, and HAWC have provided an unprecedented picture of the gammaray sky ideally suited to look for a signal from DM annihilation or decay for DM particles from a few
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27. Dark Matter

GeV mass up to several TeV. The LAT has provided some of the most stringent constraints to-dateon DM pair-annihilation for a variety of annihilation final states, chiefly from stacked observationsof nearby satellite dwarf spheroidal galaxies [178]. Excesses of gamma rays over the expected diffuse
and point-source background have been claimed, most importantly from the direction of the inner
Galaxy, where a signal from DM annihilation might be especially bright [179, 180]. The nature ofthis excess is quite controversial: while the morphology and spectrum fall within what expected
for a standard WIMP with a mass of a few tens of GeV [181], unresolved point sources, including
especially an (expected) population of millisecond pulsars (MSPs) have been advocated as a possible
plausible counterpart [182]. Statistical methods to discriminate between DM and MSPs have beenutilized [183, 184], but recent studies indicate that such results might not be conclusive [185].
Large uncertainties in the Galactic diffuse background emission model are additionally known toexist, and possible plague the morphological and spectral information [186, 187].Other notablepotential gamma-ray excesses include a diffuse emission from the Andromeda galaxy (M31) [188–190], possibly in excess of what expected from cosmic-ray models [191]; and a diffuse emission at
511 keV energy in the inner Galaxy from Integral-SPI observations [192]; such emission has known
astrophysical counterparts [193], as well as several proposed DM explanations (e.g. [194]).
While DM annihilation and decay typically occurs at low velocities, the possibility of “boosted”
DM has also been considered [195]. In this case, the DM particle might dominantly pair-annihilate
to a lighter dark species, which does interact with Standard Model particle, and could be detectedwith neutrino telescopes or direct detection experiments. Future facilities that promise to widen
the reach of gamma-ray searches for DM include especially the Cherenkov Telescope Array (CTA),
see fig. 27.2.
Neutrinos: DM can be captured in celestial bodies in significant amounts, depending on
the DM scattering cross section off of nucleons, the DM mass, and the DM flux incident on thecelestial body of interest. For DM masses at or around the GeV scale, evaporation from thecelestial body plays an important role [196]. If enough DM accumulates, DM annihilation inside
the celestial body can then lead to the production of Standard Model particles. Such particles
can heat up the body, if they lose most of their energy before escaping. Utilizing models for heatproduction in planets, or stellar interior models in the case of stars, constraints can be put on
DM particle properties. Of note are constraints from anomalous warming of cold planets such as
Uranus [197], alterations to the stellar structure or the Sun’s seismic activity [198], and anomalous
Earth heat flow [199]. Alternately, DM annihilation in celestial bodies can result in the productionof particles that can escape the body. Within the Standard Model, the only such instance isannihilation to neutrinos, but, similarly to the boosted DM case the DM can annihilate to a (stable
or unstable) dark-sector particles, whose decay or interactions can be detected on Earth [200, 201].
For direct annihilation to neutrinos, given the lower limit on the DM mass from evaporation, thetypical neutrino energies usually exceed the energy of neutrinos from the Sun, the best target forthis type of searches, making this a virtually background-free DM search. Significant neutrino
fluxes can only be achieved, however, if near-equilibration is reached between the capture andannihilation rates. In turn, this requires large-enough DM-nucleon scattering cross sections, to-datevery close to the limits from direct detection (see sec. 27.6). Only spin-dependent cross section,and capture in the Sun usually provide large-enough neutrino fluxes. IceCube and ANTARES
searches for an anomalous flux of high-energy neutrinos from the Sun yielded null results, which canbe interpreted as constraints on spin-dependent nucleon-DM interactions under the assumption ofequilibration and of specific annihilation final states [202,203]. Lower-threshold detectors, including
DeepCore [204] and PINGU [205], can produce interesting limits on lower-mass DM candidates
above the evaporation threshold.
Cosmic-ray Antimatter: Stable charged particles produced by decays of products of, or
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27. Dark Matterdirectly from DM annihilation or decay, populate the cosmic radiation and are a prime target forindirect DM searches. To maximize signal to noise, searches focus on relatively rare particle species,
such as positrons, antiprotons, and antinuclei. While in certain models the production of particles
and antiparticles is not symmetric [206], generally DM annihilation or decay produces as many
particles as antiparticles in the final state. Charged particles produced by DM propagate and lose
energy prior to reaching detectors. The transport of charged particles is customarily carried out
in the context of diffusion models such as the Galactic “leaky box” setup, see e.g. [207]. While
progress in constraining the uncertain propagation and energy-loss processes has been steady withimproved data from new detectors such as PAMELA [208] and AMS-02 [209], the calculation of
the particle flux at Earth from that at production suffers from significant uncertainties [207].
An excess of high-energy positrons over the standard secondary production from inelastic
cosmic-ray interactions has been firmly established by several experiments, most recently and withthe highest statistics by AMS-02 [210]. The excess has been ascribed to DM annihilation, althoughstrong constraints from the non-observation of corresponding anomalies in other channels, suchas antiprotons and gamma rays, and the peculiar spectral shape, force DM models to be quite
convoluted (see e.g. [211]). Alternately, excess primary positrons can be produced in the magnetosphere of nearby pulsars [212, 213]. This latter explanation was questioned in [214] in connection
with the detection of a TeV halo around two candidate pulsars, leading to the determination ofa highly suppressed diffusion coefficient within the pulsar nebula; with such low diffusion coefficient, positrons from the pulsars would not contribute significantly to the flux at Earth; Ref. [215],
however, showed that likely the diffusion coefficient is not constant, and that if it increases outside the nebula, as expected from other cosmic-ray measurements, pulsars can still be consideredas the counterpart to the positron excess. Other explanations for the excess, albeit somewhat
controversial, and increasingly constrained by data, also exist [216, 217].
The antiproton spectrum in the cosmic radiation as measured by AMS-02 [209] also exhibits
features that might be considered as excess flux between 10 and 20 GeV, and energies above 100
GeV [218], which have been interpreted as possible signal of DM annihilation; more realistically,
however, systematic uncertainties in the antiproton production cross section, in cosmic-ray transport, reacceleration at high energy and, at low energy, solar modulation make it extremely difficult
to assess the robustness of the excesses [219, 220].
Antinuclei such as anti-deuterium and anti-helium could also form as a result of DM annihilation or decay. While baryon number conservation forces the typical kinetic energy of antinuclei
produced in inelastic cosmic-ray processes to large values, antinuclei arising from hadronizationof DM-initiated jets have low energy, offering optimal signal-to-noise when a low-energy cut on
the antinucleus kinetic energy is used [221–225]. Specific detector designs have been developed tosingle out low-energy cosmic-ray antinuclei (e.g. E < 0.25 GeV/nucleon in the case of the General
Antiparticle Spectrometer, or GAPS [226]). The detection of even a single antinucleus would haveconsiderable importance as a possible sign of new physics [227].
Multi-wavelength studies: Electrons and positrons from DM lose energy quite efficiently,
radiating at a variety of wavelengths. This secondary radiative emission presents spectral and morphological features that might provide an important additional indirect detection channel. The
most efficient energy loss mechanisms for high-energy electrons and positrons are inverse Compton(IC) up-scattering of background photons, and synchrotron radiation in the presence of magnetic
fields. Depending on the DM mass, the emitted light from synchrotron peaks at MHz-GHz frequencies, while the IC emission at X-ray to gamma-ray frequencies, depending on the energy of the
background radiation, typically ranging from CMB photons up to starlight photons [228–230]. The
calculation of the secondary emission from DM entails both solving the transport of the electronsand positrons from DM, and for the radiative emission; codes exist that perform these calculations
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27. Dark Matterfor certain astrophysical environments [231–233], with diffusion playing an increasingly critical rolein smaller and smaller structures such as dwarf galaxies [229]. It has been demonstrated that forlarge magnetic fields and for certain final states, the synchrotron emission is more constraining
than the gamma-ray emission [234].
Stellar Physics: Microscopic properties of the DM can meaningfully alter, and thus be constrained by, several astrophysical environments, from planets and stars, up to the universe as awhole. DM particles light enough to be produced in collisional processes inside stars, with typically temperatures in the keV, or supernovae, with energy scales in the MeV, lead to an additionalenergy-loss mechanism, if capable of escaping the system. If this is the case, the increased neededenergy output would also result in an increased neutrino flux, leading to constraints on the masses
and couplings of the DM, see e.g. [235] for a comprehensive review. DM annihilation can even have
fueled early stages of stellar evolution, perhaps with measurable consequences [236]. DM capturein neutron stars could lead to the collapse of the star into black holes; the existence of neutronstars in DM-rich environments can thus be used to constrain the mass and interaction cross sectionof DM with nucleons [237] and even relatively light, but stable, primordial black holes [238].
Cosmology: Energy injection from DM processes in the early universe, as well as the contribution of DM to the effective relativistic degrees of freedom, are severely constrained from dataon Big Bang Nucleosynthesis (see Sec. 24 in this Review) and on the energy and anisotropy power
spectrum of the CMB (see Sec. 29). Codes exist that perform the calculation of the constraints onparticle DM models [177, 239].
PBH Detection: Macroscopic DM candidates can gravitationally perturb structure and compromise the stability of, for instance, globular clusters such as Eridanus II [24], and/or disrupt
wide binaries [240]. This constrains the maximal mass of a macroscopic DM candidate to notmuch more than 5 M [240] (see also [24]). In the specific case or primordial black holes, strong
constraints also stem from the acceleration of charged particles around and after recombination,with significant effects on the CMB [241], albeit a lively debate exists over the accretion efficiency
around such objects at high redshift [242,243]. Whether or not PBH in the solar-mass range can be
100% of the DM is therefore disputed at present. Other effects produced by macroscopic, massive
DM candidates are the microlensing of stars [244, 245] and quasars [246], femtolensing of gammaray bursts [247], and neutron star capture [238]. It is important to note that recently constraints
from both microlensing and femtolensing have been corrected after the realization of important
finite-size source and wave effects [245, 248, 249], leaving a substantial window, at PBH masses
1017 . MBH /g . 1021 where PBH can be 100% of the DM. Light black holes, MBH . 1017 g,
are also constrained by the non-detection of products of evaporation [250]; future MeV gamma-ray
detectors are slated to significantly improve such constraints and to enable the direct detection of
Hawking radiation [251]. If evaporation shuts down at or near the Planck scale, Planck-scale relic
PBH are generally expected to carry electric charge and to be detectable with direct detection andneutrino experiments, or with paleo-detectors [252].
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