Probing Candidates for Dark Matter: Evidence from WIMPs
and Axions
Hanqi Ruan
Zhejiang Wenzhou High School, Wenzhou, China
Keywords: Dark Matter, WIMPs, XENONnT, Fermi-LAT, Axion.
Abstract: As a matter of fact, dark matter makes a profound impact on the evolution and structure of the universe in
recent years. However, the exact composition of dark matter is still unknown, which remains unsolved and
puzzling issues for astrophysics and theoretical physics. To probe the components of dark matter, researchers
suppose candidates for dark matter, such as WIMPs and axions, correspond with the features of dark matter.
With this in mind, this study detailly analyze two most widely investigated dark natter candidates, i.e., WIMPs
and axions. To be specific, the theoretical framework as well as state-of-art detections scenarios are
demonstrated. According to the analysis and evaluations, detectors such as XENONnT for WIMPs as well as
ADMX for axions can shrink the parameter space to recognize the particles' range and give further definitions.
Overall, this analysis implicates the different probing circumstances and challenges in different particles,
introducing their regularity and compatibility.
1 INTRODUCTION
As one of the most advanced science topics, the
research for dark matter has experienced a process
that abounds with various explorations and
discoveries. From astronomical observations and
theoretical simulations to high-energy physical
experiments, all the stages have contributed valuable
insights into the composition of the universe. The
concept of dark matter dates back to the early 20th
century, when astronomers looked at galaxies and star
clusters and found inconsistencies between mass
estimates based on visible stars and observed
gravitational effects, suggesting an additional source
of mass. Fritz Zwicky is the first scholar to propose
that dark matter exists. In his in-depth study of the
Coma cluster, he used Verrier's theorem to analyze
the velocities of its members and found that the mass
estimated by the light emitted by the visible galaxies
alone was much lower than the actual mass needed to
sustain its motion, suggesting indirectly that dark
matter might exist. Specifically, he found that the
visible matter constituted only about 1% of the
required mass. Hence, Zwicky proposed a non-
luminous form of matter that could provide the
indispensable gravitational force to explain the high
velocities. Overall, the ground-breaking discovery
introduced that most of the universe's mass could be
invisible, challenging the prevailing notions of
cosmic structure (Fritz,1933). This breakthrough
leads to the concept of a flat spin curve that challenges
previous understanding that the distribution of
galactic matter and its gravitational pull decrease with
increasing radius. The unseen mass corresponded
with Zwicky’s concept of dark matter. Their work
made a difference in providing robust and
independent evidence for dark matter within
individual galaxies, reinforcing the necessity for a
new component in the cosmic mass inventory (Vera
et al., 1970). After that, with the numerical
simulations, Jerry Ostriker and Peebles studied the
stability of disk galaxies. They demonstrated that disk
galaxies without a meaningful number of non-
luminous masses would be dynamically unstable and
would not survive long without the gravitational
support of a substantial figure for dark matter
(Ostriker & Peebles, 1973).
Altogether, the early observations and
hypotheses about dark matter had a profound impact
on astronomy. They crucially influenced the
cognition of cosmic structure, galaxy formation, and
unified model, challenging existing models of the
universe and setting the stage for subsequent
researches. These pioneering efforts have revealed
the limits of visible matter in interpreting cosmic
282
Ruan, H.
Probing Candidates for Dark Matter: Evidence from WIMPs and Axions.
DOI: 10.5220/0013075000004601
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 1st International Conference on Innovations in Applied Mathematics, Physics and Astronomy (IAMPA 2024), pages 282-292
ISBN: 978-989-758-722-1
Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.
phenomena, meaning that it needs to extend beyond
visible entities to dark matter. These work challenges
traditional physics and opens up new avenues for
revealing the state and distribution of dark matter and
its impact on the evolution of the universe.
The theory of dark matter, accompanied by
technological advances, has moved from theoretical
speculation to the cornerstone of physics with
empirical support. After more than a century of
development, the theory has achieved remarkable
results and is seen as a central factor in explaining key
problems, scientists have not only made
breakthroughs in the proportion of dark matter, but
also deepened their understanding of the properties of
dark matter, further confirming the scientific and
accurate theory of dark matter. Recent studies have
mapped unprecedented precision for large-scale
structures by leveraging advanced observational
technologies. As data accumulate and analytical
techniques continue to evolve, the understanding of
dark matter will become more accurate. Power
spectrum is a tool to quantitatively describe the
intensity distribution of the density perturbation of
matter in the universe with the change of spatial scale.
In the dark matter power spectrum, oscillations at
specific wave numbers are hallmarks of baryon
acoustic oscillations (BAO). These sound waves
originate from the energy released by the formation
of hydrogen atoms in the early universe, and they
drive patterns of sound waves in the cosmic
background. As the universe expands, these sound
waves stretch, but their amplitude and phase
information is preserved. When these waves travel to
the time of formation of the cosmic microwave
background (CMB), they leave a unique mark in the
plasma environment, forming the "Doppler peak" or
"acoustic peak" in the CMB spectrum. This
phenomenon is an important prediction of the
standard cosmological model and has been verified
by observational data. With the further evolution of
the universe, these initial acoustic disturbances are
amplified and reflected in large-scale structures.
Neutron stars also have emerged as critical natural
laboratories for studying dark matter. A recent
research by the University of Melbourne marks the
importance of neutron stars in capturing and
annihilation of dark matter. For the rapid energy
transfer, dark matter annihilation in neutron stars can
heat the stars rapidly, making the process remarkable
within days. In addition, the heating effect brings both
opportunities and challenges to the fields of
astronomical observation and cosmic exploration. It
bodes well for the discovery and confirmation of dark
matter through observations of stars or the structure
of the universe. Moreover, neutron stars also can
efficiently capture dark matter due to their high
density, accumulating these particles over time (Bell
et al., 2024). The main goal of the BREAD
experiment is to explore the dark matter in the
universe, focusing specifically on the mysterious
particle called the axion. The experiment uses a
wideband reflector to capture the weak radiation
signal generated by axion particles, thus effectively
improving the detection efficiency. This innovative
approach offers new opportunities to reveal the nature
of dark matter, such as axions and dark photons, by
using a broadband approach. This experiment
employs a coaxial dish antenna to capture photons
and improve the probability that axions change into
photons (Wang & Christina, 2023).
In spite of extensive research, the exact
composition of dark matter still needs to be
discovered. To give insights into the frontier research
and probe the composition, the paper elaborates on
the candidates for dark matter, WIMPs, axions. Also,
it provides compelling information about the other
types. The structure of this article goes like this: The
second part is about the details of dark matter,
including definitions, categories, and a series of
concepts and formulas. WIMPs and axions are
separately introduced in terms of their principles,
representative instruments, and current research in
Sec. 3 and Sec. 4. It also mentions the other types of
candidates in Sec. 5. The Sec. 6 is about the
limitations and prospects. Ultimately, Sec. 7 contains
a summary and conclusion.
2 DESCRIPTIONS OF DARK
MATTER
Because of its inability to emit, absorb, or reflect
light, dark matter cannot be detected by conventional
optical detection. Invisible as it is, dark matter's
influence in the universe is profound and significant,
affecting the motion of ordinary matter and light,
mainly through gravitational interaction. Scientists
have used sophisticated astronomical observations
and in-depth data analysis to confirm the existence of
dark matter, which is estimated to account for about
27% of the total mass of the universe. Dark matter is
a central topic in astronomy and cosmology, and its
existence can be inferred from indirect evidence is
mainly reflected in its significant gravitational effect.
Specifically, when measuring the velocities of stars at
the edges of galaxies, if dark matter does not
contribute, the predicted rotation rate based on the
Probing Candidates for Dark Matter: Evidence from WIMPs and Axions
283
distribution of visible matter will be lower than
observed. It reveals that the actual mass distribution
of galaxies is larger than the visible part, and this
extra, invisible mass is considered dark matter:
𝑣
𝑟
=
1
Here, V (r) represents the velocity of rotation at a
radius of r, which describes the linear velocity of a
planet or satellite around a star; G is Newton's
gravitational constant; and M (r) represents the total
mass of all visible matter within the radius r from the
center of the galaxy.
Based on Kepler's Third Law, when all the masses
are centered in a galaxy and form a center of mass,
objects in different orbits are gravitationally affected
by the center of mass. As the distance from the center
of the galaxy increases, the gravitational pull on the
object weakens and its rotation rate changes, showing
a decreasing trend with the increase of radius r:
𝑣
𝑟
∝
√
2
In the 1970s, Vera Rubin and her partners succeeded
in revealing the motion of gas layers in spiral galaxies
by observing 21-centimeter radio emission from
hydrogen atoms. At the time, it was widely believed
that the material distribution at the galaxy's edge
should decrease as the distance from the center
increases, and its rotation speed should decrease
accordingly. However, the actual observations were
unexpected, and the speed at which spiral galaxies
rotate did not follow this expected pattern. The
researchers have constructed mathematical models.
By doing so, scientists have successfully simulated a
complex system of mass distributions involving both
dark matter and ordinary matter, further confirming
the key role played by dark matter in maintaining the
stability of galaxy structure and determining its
dynamic behavior:
𝜌
𝑟
=
3
where 𝜌
and 𝑟
are constants. With the calculus
proving, this model helps maintain the flat rotation
curves that were observed at large radii by a
consistent gravitational pull from the dark matter
halo. Applying the galaxy rotation curves and dark
matter models, researchers can better understand the
mass distribution and dynamics of galaxies (Eistein,
1916).
Gravitational lensing plays an important role in
exploring the universe and verifying dark matter.
When a massive object is in the middle of a light path,
it focuses the passing light gravitationally, bending or
even magnifying or shrinking the light from a distant
background. The gravitational field can change the
path of light, which may lead to the reconstruction of
distant galaxies, star clusters and even the structure of
the universe. The principle of gravitational lens effect
can be deduced and described by a set of precise
mathematical formulas, among which the deflection
angle formula is the most representative:
𝛼 =
4
where G is the gravitational constant proposed by
Newton, which describes the gravitational force
between objects; M is the mass of a lens object, which
determines the degree of bending of the lens to light;
c is the speed of light. The formula shows that the
deflection angle of light passing through the lens is
proportional to the lens mass and inversely
proportional to the distance. The lens equation,
combined with deflection angle, is widely used in
physics and astronomy to explain optical phenomena.
𝜃
⃗
𝑆 = 𝜃
⃗
−
𝑎⃗
5
where 𝜃
⃗
𝑆 is the actual position of the source, 𝜃
⃗
is the
observed position, 𝐷
is the distance between the
lens and the source, and 𝐷
is the distance from the
observer to the source. Moreover, the Einstein radius
𝜃
is also important to gravitational lensing. It is a
characteristic angular radius of the ring-like image
that is formed when the source, lens, and observers
are perfectly aligned:
𝜃
=
6
where 𝐷
epresents the distance between the observer
and the lens and affects the intensity of gravitational
lens effect. When light passes near a massive object,
it is bent by gravity, called gravitational lensing.
Einstein's radius describes the degree of bending.
Based on the abovementioned principles,
gravitational lensing has applications in mapping
dark matter, estimating cosmological parameters, and
detecting exoplanets and objects that do not emit light
(Mohan & Goswami, 2024). Polarization is an
attribute of electromagnetic wave, which describes
the directivity of electric vector. In CMB, due to the
fluctuation of density and the gravitational effect of
dark matter, microwave photons will be scattered in
the process of propagation, resulting in polarization
effect (Eisenstein et al., 2005). By measuring and
analyzing the CMB polarization accurately,
researchers can get the information of the early
universe, such as the distribution of matter, the
density of dark matter and the evolution of the
universe. Accurate measurement and analysis of
CMBs are essential for revealing the composition and
evolution of the universe. The researchers used radio
telescope facilities to make high-precision
observations of the CMB and constructed a
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284
temperature anisotropy and power spectrum. These
spectra describe the fluctuation characteristics of
CMB and can be transformed into cosmological
model parameters. For anisotropies, it can be
described by combining the Boltzmann equation with
fluid dynamics. The evolution of perturbations
reflects the influence of dark matter through the fluid
equations (Komatsu et al., 2009):
+ ∇⋅𝜈=0
7
+ ℋ𝜈 = −∇Φ
8
where 𝛿 is the density perturbation, 𝜈 is the velocity
field, ℋ is the Hubble parameter, and Φ is the
gravitational potential. For the CMB temperature
power spectrum 𝐶
, its relationship to cosmological
parameters can be obtained through linear
perturbation theory,
𝐶
=4𝜋∫𝑘
𝑃
𝑘
∆
𝑘
9
where 𝑃(𝑘) is the initial perturbation power
spectrum, and ∆
(𝑘) is the multipole coefficient. This
project intends to study the influence of microwave
background radiation (CMB) on the origin of the
universe by using the observed data of spectrum,
energy spectrum and polarization. By continually
improving observations and theoretical models, the
knowledge about dark matter will be more deeply
understood. The detailed cosmic composition charts
collected by the Planck Co-op reveal the distribution
of dark matter and dark energy in the universe. Fig. 1
shows the temperature power spectrum 𝐷
ℓ
,
highlighting the peaks and troughs that correspond to
different physical processes in the early universe. The
first peak at ℓ≈200 is influenced by the matter
content, including dark matter. The subsequent peak
reveals the abundance or ratio between dark matter
and ordinary matter, often reflected in the power
spectrum of cosmic microwave background radiation.
These early density perturbations leave unique
imprints on the CMB spectrum, containing
information on the ratio of dark matter to ordinary
matter (Planck Collaboration 2020).
Figure 1: The temperature power spectrum 𝐷
ℓ
(Planck
Collaboration 2020).
Combining the above-mentioned models and
observations and other attributes of dark matter,
researchers conclude three main properties of dark
matter. The gravitational effect from dark matter,
which is one of the main properties, has been
mentioned frequently in this paper. Generally
speaking, it provides gravitational forces to hold the
stars at the same velocity, whatever the distance they
are from the mass center, and helps the universe keep
in balance (Vera & Kent, 1970). Dark matter also has
a notable property of non-electromagnetic
interaction. Dark matter affects the fate of the
universe in its elusive form. It plays a transparent role
in the universe because of its weak interaction with
electromagnetic forces (Clowe, et al., 2006).
Therefore, indirect methods should be used for
detection and research. On the large scale, the
distribution forms a network structure, which affects
the formation and evolution of galaxies. It can be said
that dark matter is an integral part of cosmological
research, and its mysterious and unique nature
provides us with space to explore. It seems that the
dark form halos around galaxies to provide the
necessary gravitational pull to hold them together
(Navarro et al., 2016).
When discussing the evolution of the universe,
dark matter as a key and difficult to detect form of
matter, its classification and nature is particularly
important. This process is based on an in-depth
analysis of the velocity and interaction strength of the
dark matter elementary particles. In the Cold Dark
Matter (CDM) model, dark matter particles move
very slowly, much slower than the speed of light
(Navarro et al., 2016). In contrast, hot dark matter
(HDM) particles move at speeds close to the speed of
light, preventing them from coalescing rapidly and
keeping them relatively evenly distributed. Because
hot dark matter does not form density disturbances, it
does not contribute to the formation of galaxies and
clusters. However, they smooth the distribution of
matter at large scales, thus maintaining the uniformity
of the universe at large scales (White et al., 1983).
Warm dark matter (WDM) has a velocity that is
intermediate between those of CDM and HDM. The
moderate speed allows the medium-scale structures to
form, explaining some of the structural details that
CDM models struggle with (Colín, et al., 2000).
Dark matter is an important unsolved mystery in
cosmology and particle physics, and its exact
properties and modes of existence remain at the
forefront of scientific research. Although it cannot be
directly observed, scientists speculate through
indirect evidence such as gravitational effects that
dark matter accounts for about 85% of the total
Probing Candidates for Dark Matter: Evidence from WIMPs and Axions
285
material energy in the universe, and has a decisive
impact on astronomical phenomena such as cosmic
structure, galaxy evolution, and microwave
background radiation. The following parts of the
paper focus on the elaborations of the WIMPs,
axions, and other types.
3 SEARCHING FOR WIMPS
Weak-interaction massive particles (WIMPs) are
widely considered one of the main candidates for dark
matter. Here are properties of WIMPs that correspond
with the dark matter’s characteristics. First, WIMPs
are predicted to have masses in the range of giga-
electron volts to tera-electron volts, making them
significantly more massive than ordinary subatomic
particles such as protons and electrons. As the name
suggests, WIMPs interact primarily through the weak
nuclear force, which is one of the four fundamental
forces in nature, allowing WIMPs to pass through
ordinary matter without significant interaction that
makes them difficult to detect. Moreover, WIMPs are
stable on cosmological timescale. Scattering cross
section is a key physical quantity in particle physics
and cosmology, which quantifies the possibility of
interaction between WIMP and nucleon. It can be
complex, but a simplified version for spin-
independent interactions is:
𝜎≈
𝐺
𝜇
𝜋
𝑍
(
1 −4sin
𝜃
)
+
(
𝐴−𝑍
)
(
10
)
where 𝐺
is the Fermi constant that represents the
strength of the weak force, 𝜇 is the reduced mass of
the WIMP-nucleon system, given by 𝜇 = 𝑚
𝑚
/
(𝑚
+ 𝑚
), where 𝑚
is the WIMP mass and 𝑚
is
the nucleon mass, 𝑍 is the atomic number of the
nucleus and 𝐴 is the atomic mass number of the
nucleus. 𝜃
is the weak mixing angle, a parameter in
the electroweak theory (Lewin & Smith, 1996).
In addition to the scattering cross-section formula,
other formulas also make a difference in explaining
the principles of WIMPs. The thermal relic
abundance of WIMPs in the early universe is
determined by their interactions with Standard Model
particles. A typical formula for the relic abundance of
WIMPs is,
Ω
ℎ
≈
.×
√
∗
〈
〉
(
11
)
where Ω
ℎ
is the density parameter of WIMPs, and
𝑀
is the Planck mass. 𝑔
∗
is the adequate number of
relativistic degrees of freedom at the time of WIMPs
freeze-out,
〈
𝜎𝜈
〉
is the thermal average of the WIMP
annihilation cross-section times velocity (Griest &
Seckel, 1991). The formula for the annihilation cross
section describes WIMPs into Standard Model
particles, typically assuming WIMPs are spin-1/2
particles, which is,
〈
𝜎𝜈
〉
≈
(
12
)
where 𝑔 is the coupling constant. 𝑚
is the mass of
the WIMP (Bertone et al., 2024). Moreover, WIMPs
can be produced in proton-proton collisions at high-
energy accelerators. The production cross-section
formula depends on the specific WIMPs model. In the
Minimal Supersymmetric Standard Model (MSSM),
𝜎
(
𝑝𝑝 → 𝜒𝜒+X
)
≈
𝛼
𝑚
(
13
)
where 𝑎
is the strong interaction constant. 𝑚
is the
mass of the WIMP (Baer et al., 2015). The detections
of WIMPs can be categorized into three main
methods which are based on the theoretical properties
of WIMPs. Direct detection is one of the crucial
methods that aims to observe the scattering of WIMPs
off nuclei in a detector. When WIMP smashes into a
nucleus, it transfers some energy to the nucleus,
creating a backlash that can be detected and
measured. Nonetheless, the background noise from
cosmic rays and natural radioactivity can mimic
WIMP signals. Therefore, experiments are often
conducted deep underground to reduce these disturbs.
The liquid noble gas detector is a standard
detector for probing WIMPs, such as XENONnT,
LUX-ZEPLIN, and PandaX, using liquid xenon or
argon to detect scintillation and ionization produced
by nuclear recoils. XENONnT, as one of the frontier
detectors, currently improves sensitivity to WIMPs-
nucleon elastic scattering cross section to detect. The
process of the XENONnT experiment includes a
series of detections. Initially, when particles interact
with the liquid xenon target, they cause a primary
scintillation light (S1 signal). This light is detected by
photomultiplier tubes (PMTs) within the liquid
xenon. Simultaneously, the interaction also generates
ionization electrons, which drift towards the gas
phase above the liquid xenon due to the work of an
electric field, creating a secondary scintillation light
(S2 signal). Then, the S1 and S2 signals detected in
the Time Project Chamber (TPC) are analyzed for
their time distribution. The S1 signal occurs almost
immediately, while the S2 signal is delayed as it
involves the drift of electrons. Meanwhile,
Cherenkov light signals detected in neutron veto
(NV) are also analyzed. The NV detects signals with
a typical delay of around 200 microseconds, which
helps differentiate between neutron events and
potential WIMP signals.
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Subsequently, by analyzing the spatial and
temporal distribution of the signals, the experiment
can effectively suppress background noise, such as
the noises from neutrons and 𝛾 photons, ensuring the
accuracy of the detected signals. Ultimately,
combining S1 and S2 signals allows for accurate
three-dimensional reconstruction of events, with the
potential signal regions hidden during initial analysis
to maintain objectivity, determining their position and
energy within the detector. Fig. 2 illustrates how the
experiment distinguishes between different event
types using time and spatial correlations, ultimately
aiming to identify potential dark matter with high
sensitivity. The top left graph shows the time
distribution of S1 signals that are generated by
scintillation light when particle deposits are detected
in the TPC. As for the data, the peak amplitude is
approximately 0.4 𝑃𝐸/𝑛𝑠, and most S1 signals fall
within the first 100-150 𝑛𝑠, indicating the prompt
scintillation light caused by the initial energy
deposition. The bottom left graph describes the time
distribution of S2 signals produced by ionization
electrons drifting to the gas phase above the liquid
xenon, generating a second scintillation light.
According to the graph, the primary S2 signal appears
around 5-6 𝜇𝑠 with an amplitude of around 0.4
𝑃𝐸/𝑛𝑠, and the alternative S2 signals are visible at
around 2-3 𝜇𝑠 and 10-12 𝜇𝑠, representing secondary
interactions or reflections. Seen from Fig. 2, all of the
data is combined in the bottom graph. The right panel
displays the spatial and temporal distribution of
signals detected in both the NV and the TPC. The
color scale presents the intensity and location of the
signals (XENON Collaboration, 2024).
This study will focus on the generation rate of
nuclear reactions for WIMP particles that do not
depend on rotation, specifically in relation to the data
shown in the black line and the results of the LZ
experiment (preprint, in purple), the PandaX-4T
experiment (in red) and the XENON1T experiment
(in blue). Altogether, the result from XENONnT
represents a significant step forward in the search for
WIMPs. Seen from Fig. 3, the experiment improves
sensitivity, particularly in the mid-mass range,
positioning it as a leading project in the field of dark
matter research (XENON Cillaboration, 2020).
An indirect detection experiment plays a vital role
in detecting the WIMPs. It looks for the annihilation
or decay products of WIMPs, such as high-energy
gamma rays, antiprotons, antideuterons, and
neutrinos. The principle is that WIMPs cluster in the
galactic halo, annihilate or decay, and produce high-
energy particles.
The Fermi LAT is a high-precision instrument
designed to detect high-energy gamma rays. It
observes high-energy gamma-ray radiation in areas
such as the center of the Milky Way Galaxy and
implements experimental restrictions on WIMP
annihilation. The core component of the instrument is
the LAT, which integrates a precision target chamber
composed of a multilayer silicon strip detector and a
tungsten layer. When gamma-ray photons interact
with tungsten, electron-positron pairs are generated,
and these secondary particles trigger a detector to
record their trajectory as they travel through the zone.
By accurately measuring the motion paths and energy
losses of these secondary particles, scientists can
accurately reconstruct the initial energy and direction
of incident gamma rays.
Figure 2: An overview of a signal detection and analysis
process (XENON Collaboration, 2024).
Figure 3: The cross-section of WIMPs (XENON
Collaboration, 2024).
Probing Candidates for Dark Matter: Evidence from WIMPs and Axions
287
In terms of technical specifications, the Fermi
LAT showed excellent performance indicators. It
covers a wide range of energies, from 20 to 300
billion electron volts. In terms of field of view, the
Fermi LAT has a wide field of view of about 2.4
spherical degrees, meaning it can scan and cover the
entire sky every three hours. As the observed energy
increases, the angular resolution is also excellent, at
about 3.5 degrees at 100 megavolts and about 0.15
degrees at 10 billion. The telescope shown here is an
exquisitely designed and massive telescope that
measures 1.8 meters long, 1.8 meters wide and 0.72
meters high. The telescope was designed to operate at
650 watts, taking full account of the power
requirements. In addition, the telescope weighs an
astonishing 2,789 kilograms (Atwood et al., 2009).
Figure 4: A sketch of the Fermi LAT (Atwood et al.,
2009).
Recent observations by Fermi-LAT have focused
on dwarf galaxies, which are considered ideal targets
for dark matter searches due to their high dark matter
content and low gamma-ray background. The latest
analysis shows no significant gamma-ray signals by
the 12 years of data, further constraining the
parameter space for WIMP mass and interaction
rates. This includes constraints that consider
electromagnetic cascades (in solid blue lines) and not
electromagnetic cascades (in dashed blue lines). For
comparison, these constraints are also compared with
the constraints of VERITAS (expressed in dotted
lines), MAGIC (expressed in dotted lines) and
HAWC (also expressed in dotted lines) and the
correction of the J coefficient (see section 5 for
details). In addition, the diagrams contain thermal
cross-sections (up to m` 200 TeV, in red lines) and
partial wave unity limits from nearby dSphs (in gray
dotted lines) (Song et al., 2024). In the accelerator
detection experiments, high-energy proton-proton
collisions may produce WIMPs so detectors can
identify WIMPs by observing missing energy and
momentum. The paper just gives a brief about this
detector (seen from Fig. 5).
Figure 5: The upper 95% confidence level (CL) for
the annihilation cross section of the 𝑏𝑏
(shown on the
left) and μ
+
μ
-
(shown on the right) channels of Draco
is shown (Song et al., 2024).
4 SEARCHING FOR AXIONS
Axions is a hypothetical particle proposed in the
theory of quantum color dynamics (QCD) to solve the
problem of CP breaking. Axions are also considered
an ideal candidate for dark matter, given their weak
interaction and small mass. The interaction of axion
with photons is the main task for axions to make a
difference, according to which can be described by
the effective Lagrangian,
ℒ
= 𝑔
𝑎Ε⋅Β
(
14
)
where 𝑔
is the axion-photon coupling constant, 𝑎
is the axion field, and Ε and Β are the electric and
magnetic fields. Understanding the mass formula and
the axion-photon conversion rate is meaningful for
both theoretical and experimental studies. For the
axion mass formula, it relates the mass of the axion to
fundamental constants and parameters in QCD,
𝑚
=
√
(
15
)
where 𝑚
is the axion mass, 𝑧 is the quark mass ratio,
𝑓
is the pion decay constant, 𝑚
is the pion mass,
and 𝑓
is the axion decay constant (Steven, 1978).
The conversion rate of axions to photons in a
magnetic field can be described by the Primakoff
effect. The differential flux of axions converting into
photons is given by:
∝𝑔
Β
𝑉
(
16
)
where Β is the magnetic field strength, 𝑉 is the
volume of the interaction region, 𝑞 is the momentum
transfer, and 𝐿 is the path length of the magnetic field.
The conversion rate formula is essential to calculate
the expected signal in axion detection experiments.
The experimenters can design setups such as
magnetic field strength and cavity dimensions to
maximize the chances of detecting axions. Besides,
the formula also helps in setting limits on the axion-
IAMPA 2024 - International Conference on Innovations in Applied Mathematics, Physics and Astronomy
288
photon coupling constant from non-detections,
thereby refining the parameter space for axion
searches (Pierre, 1983).
Through persistent improvements in detection
methods and equipment, researchers have made
significant progress in detecting axions and exploring
their potential as dark matter candidates. The resonant
cavity is an important method to detect axions, such
as ADMX, CAST, APLS II. It is a process that axions
in a strong magnetic field convert into microwave
photons that can be enhanced using a resonant cavity,
providing signals for probes in the magnetic field.
Axion dark matter experiment (ADMX) is a
representation of resonant cavity experiments. The
main equipment needed in the experiment are high-
quality factor resonant cavities, strong magnets, and
cryogenic detectors, which are composed together for
measurements and detections. Seen from Fig. 6, the
two primary measurements used in the ADMX are
transmission measurement and reflection
measurement, which are used to determine the
resonant frequency 𝜔
of the resonant cavity
(ADMX Collaboration, 2024).
Figure 6: The transmission measurement detects the
signal transmission from the weak port to the
principal port of the cavity and then the data input in
the network
analyzer
(left panel). The reflection
measurement probes the signal reflected back from
the major port of the cavity (right panel), and then the
network analyzer displays the spectrum of the
reflected signal, including the dip that also designates
the cavity’s resonant frequency 𝜔
.
The transmission measurement and reflection
measurement can confirm the resonant frequency to
maximize the sensitivity of the detection system to
axion signals, probing the frequency at which axions
exist. After the measurements and further
amplications, the data can be analyzed and plotted to
show the limits of axion-photon coupling constants at
different axion masses. Fig. 7 includes the results
from different models, such as Maxwellian and N-
body models, as well as theoretical predictions
(KSVZ and DFSZ models). According to the graph,
the exclusion limits based on the Maxwellian model
are higher than the ones based on the N-body model
at the same axion mass, while the fluctuations are
similar. Areas above the red and blue curves are
parameter spaces where axions have not been
detected, helping to define the mass and coupling
ranges that are inconsistent with the presence of
axions under current experimental conditions.
Overall, the Fig. 7 provides a summary of current
experimental capabilities and limitations
Figure 7: The chart shows the exclusion limits on the
axion-photon coupling
constant
𝑔
as a function of
axion mass (ADMX Collaboration, 2024).
Solar axion telescopes such as the CERN axion
solar telescope (CAST) also provide support for
detecting axions. CAST uses strong magnets to
capture and detect axions from the sun, which convert
into X-rays. CAST uses a superconducting magnet to
create a strong magnetic field through which solar
axions can pass. The strong magnetic field also does
convert work, and then specialized X-ray detectors at
the ends of the magnets detect those photons.
Moreover, the sunrise and sunset systems precisely
align the magnet with the sun during sunrise and
sunset, tracking it for about 1.5 hours each session.
The converted X-ray photons are then detected by X-
ray detectors, allowing researchers to analyze the data
for axion signals as shown in Fig. 8 (CAST
Collboration, 2017).
Probing Candidates for Dark Matter: Evidence from WIMPs and Axions
289
Figure 8: The flow chart for axions production.
(CAST Collboration, 2017).
Based on the data collected from 2012 to 2015, CAST
found no evidence of solar axion but set the most
stringent limits yet on the axion-photon coupling
constant 𝑔
, which excludes a significant portion of
the parameter space that is predicted by theoretical
models. Seen from Fig. 9, the refined exclusion limits
help narrow down the possible parameter space for
axions (CAST Collboration, 2017).
Figure 9: The
parameter
space for axions and axion-
like particles (ALPs), showing the range of the latest
constraints on the axion-photon coupling
constant 𝑔
.
Currently, optical cavities and lasers are used to
detect axions. It probes the axion-photon conversion
by applying intense lasers and high-reflectivity
optical cavities. The Any Light Particle Search II
experiment (ALPS II) is a representation of this kind
of detection. ALPS II aims to achieve a sensitivity to
the axion-photon coupling constant that is several
orders of magnitude better than current limits. The
experimental setups are superconducting dipole
magnets to form the strong magnetic fields for the
conversion, a high-power laser that generates the
required input power, two 106-meter long optical
cavities with a light-tight wall between them to block
any direct light, a half-wave plate, and a detector, as
presented in Fig. 10.
Figure 10: The flow chart illustrates the setups of the
ALPS II experiment,
which
is designed to search for
axion-like particles (ALPs) using a light-shining-
through-a-wall (LSW) approach (Diaz et al., 2020).
During the detection, initially, the laser generates
a high-intensity beam. Then, the half-wave plate
adjusts the polarization of the laser beam to optimize
the interaction within the magnetic field. For the most
important part, the strong magnetic field in the
production cavity prompts the photons from the laser
beam to transfer into axion-like particles and
facilitates ALPs conversion back into the
regeneration cavity. Ultimately, the detector detects
the regenerated photons, indicating the presence of
ALPs (Diaz et al., 2020). The TES (Transition et al.)
detection system, which is a highly sensitive
calorimeter operated at cryogenic temperatures, plays
a vital role in the ALPS II experiment by providing
empathetic photon detection capabilities. The pulse
exhibits a more profound and sharper voltage drop in
1.165 eV, and the pulse shows a shallower and
broader voltage drop in 0.583 eV, meaning the
detection captures a higher energy photon in 1.165 eV
and a lower energy photon in 0.583 eV. Hence, to
verify the linearity of the TES system, the pulse
shapes maintain a positive correlation with the
intensities. By comparing the detection results for
photons of different energies, researchers can
demonstrate that the TES system detects high-energy
and has a higher sensitivity. Besides, researchers can
optimize data analysis methods by analysing the data
of the TES systems (Christina et al., 2024).
5 SEARCHING FOR OTHER
TYPES
Besides WIMPs and axions, there are also some other
competitive candidates for dark matter. Dark photons
are hypothetical particles similar to photons but
associated with dark matter, which interact weakly
with ordinary photons through a mixing mechanism.
The mixing term is,
ℒ
= −
𝐹
𝐹
(
17
)
where 𝐹
is the electromagnetic field tensor of the
ordinary photon, 𝐹
is the electromagnetic field
tensor of the dark photon, and 𝜖 is the mixing
parameter. Experiments look for weak interactions
between ordinary matter and dark matter as detections
IAMPA 2024 - International Conference on Innovations in Applied Mathematics, Physics and Astronomy
290
(Abazajian et al., 2012). Sterile neutrinos are also
dark matter candidates assembled interacting only
through gravity, not the weak nuclear force. The
masses of sterile neutrinos are generally heavier than
ordinary neutrinos. The mass term is,
ℒ
=
1
2
𝑚
𝑣̅
𝑣
(
18
)
where 𝑚
is the sterile neutrino mass, and 𝑣
is the
sterile neutrino field. Indirect detection through
neutrino oscillation experiments and cosmic
microwave background are used to analyze sterile
neutrino experiments (Abazajian et al. 2012).
Primordial black holes (PBHs) are black holes that
formed in the early universe, shortly after the Big
Bang, which are dark matter candidates. This study
discusses the role of sterile neutrinos in cosmology
and astrophysics, including their implications for dark
matter and structure formation in the universe.
The mass of a single PBH is from less than a solar
mass to several hundred times the solar mass. The
mass can probably described as,
𝛽
(
𝑀
)
~
(
)
exp
−
(
)
(
19
)
where 𝛽
(
𝑀
)
is the probability of forming a PBH of
mass 𝑀, 𝜎
(
𝑀
)
is the density fluctuation at the mass
scale, and 𝛿
is the critical density contrast. The
experiments use gravitational wave observations and
microlensing effects to detect (Carr, et al., 2016).
6 LIMITATIONS AND
PROSPECTS
In spite of research such as WIMPs, axions, and
sterile neutrinos have made significant progress in
probing the dark matter candidates, they are still
facing several challenges. For WIMPs, despite
extensive searches, those experiments have yet to
observe conclusive WIMP signals, so the interaction
cross-sections they probed may still be above or
below the sensitivity threshold. On the other hand,
WIMPs span a broad range of possible masses and
cross-sections, which makes it easier to rule out
WIMPs entirely with significant experimental
advancements. However, future experiments such as
XENONnT aim to achieve greater sensitivity and
lower background levels, potentially enabling the
detection of lower interaction cross sections
(XENON Collaboration, 2024).
Axions also face some limitations. For one thing,
axions couple very weakly to photons and other
particles, making them challenging to detect with
existing technology. For another, the possible mass
range for axions is vast, from micro-electron volts to
millie-electron volts, which requires different
detection strategies for different mass ranges. As the
future prospects are high, haloscopes like ADMX are
improving sensitivity to axions within specific mass
ranges. The upgrades and new research also aim to
cover broader mass ranges and increase detection
potential. Moreover, laboratory searches are
developing new techniques involving high-precision
magnetometers and resonant cavities to detect axions
(ADMX Collaboration, 2024).
Besides, sterile neutrinos cover a broad range of
masses and mixing angles, but current experiments
could be more extensive in their ability to explore the
entire space, and it is indirect in obtaining the data.
Thus, in future research, scientists expect they can
explore the parameter space more comprehensively,
and cosmological surveys can improve precision,
which provides tighter constraints on sterile neutrino
properties (Abazajian et al. 2012).
While the current research has faced several
challenges, experimental sensitivity, technologies for
observations, and theoretical modeling provide
opportunities for overcoming this limitation. Probing
for dark matter candidates is crucial for human beings
to get insights into the truths of the universe.
7 CONCLUSIONS
Probing candidates for dark matter is the frontier
mission for understanding the composition of dark
matter. WIMPs and axions, as the most representative
candidates for dark matter, lead researchers to focus
on more specific data, aiming to correspond with the
attributes of dark matter as the initial description in
this paper. In spite of significant efforts, the
detections of these candidates have been challenging
due to their weak interactions or extensive parameter
space. Advanced detection techniques and next-
generation experiments such as XENONnT for
WIMPs and ADMX for axions continue to push the
boundaries of the knowledge. Further advancements
in detector sensitivity, observational technology, and
theoretical modeling will hold promise for
overcoming current limitations. The continuing
research not only deepens the understanding of dark
matter but also propels the field of particle physics
and cosmology forward, enhancing the grasp of the
fundamental nature of the universe. By probing and
understanding dark matter, one can obtain insights
into the structure and evolution of the universe,
agitating the study of dark matter to go ahead.
Probing Candidates for Dark Matter: Evidence from WIMPs and Axions
291
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