90. Axions and Other Similar Particles

1

90. Axions and Other Similar Particles
Revised August 2023 by L. J Rosenberg (U. Washington), G. Rybka (U. Washington) and B. Safdi(UC Berkeley).

90.1 Introduction
In this section, we list coupling-strength and mass limits for light neutral scalar or pseudoscalarbosons that couple weakly to normal matter and radiation. Such bosons may arise from the spontaneous breaking of a global U(1) symmetry, resulting in a massless Nambu-Goldstone (NG) boson.
If there is a small explicit symmetry breaking, either already in the Lagrangian or due to quantum
effects such as anomalies, the boson acquires a mass and is called a pseudo-NG boson. Typicalexamples are axions (a) [1–4] and majorons [5, 6], associated, respectively, with a spontaneously
broken Peccei-Quinn PQ and lepton-number symmetry. Axions may also arise in extra dimension constructions as the zero-modes of higher-dimensional gauge fields compactified on internal
manifolds; in this case, the absence of a local contributions to the axion mass is due to the higherdimensional gauge symmetry [7, 8].
A common feature of these light bosons φ is that their coupling to Standard-Model particles issuppressed by the energy scale that characterizes the symmetry breaking, i.e., the decay constantf . For example, in models where the axion arises as a Goldstone boson, the interaction Lagrangianat energy scales below f is
L = f −1 J µ ∂µ φ ,(90.1)

where J µ is the Noether current of the spontaneously broken global symmetry. If f is very large,
these new particles interact very weakly. Detecting them would provide a window to physics far
beyond what can be probed at accelerators.
Axions are of particular interest because the PQ mechanism is a compelling scheme to preserve
CP -symmetry in QCD. Moreover, the cold dark matter (CDM) of the Universe may well consistof axions and they are searched for in dedicated experiments with a realistic chance of discovery.
Originally it was assumed
that the PQ scale fa was related to the electroweak symmetry√breaking scale vEW = ( 2GF )−1/2 = 246.22 GeV. However, the associated “standard” and “variant”
axions were quickly excluded—we refer to the Listings for detailed limits. Here we focus on “invisible
axions” with fa  vEW as the main possibility.
Axions have a characteristic two-photon vertex, inherited from their mixing with π 0 and η.
This coupling allows for the main search strategy based on axion-photon conversion in external
magnetic fields [9], an effect that also can be of astrophysical interest. While for axions the product“aγγ interaction strength × mass” is essentially fixed by the corresponding π 0 properties, one may
consider a more general class of axion-like particles (ALPs) where the two parameters (coupling andmass) are independent. A number of experiments explore this more general ALP parameter space.
ALPs populating the latter are predicted to arise generically, in addition to the axion, in low-energy
effective field theories emerging from string theory [7, 8, 10–16]. The latter may contain also very
light Abelian vector bosons under which the Standard-Model particles are not charged: so-called
hidden-sector photons, dark photons or paraphotons. They share a number of phenomenologicalfeatures with the axion and ALPs, notably the possibility of hidden photon-to-photon conversion
and of hidden photon dark matter [17–19]. Their physics cases and the current constraints arecompiled in Refs. [20–23].
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
31st May, 2024 10:12am

2

90. Axions and Other Similar Particles

90.2 Theory
90.2.1 Peccei-Quinn mechanism and axions
The QCD Lagrangian includes a CP -violating term LΘ = −Θ̄ (αs /8π) Gµνa G̃aµν , where −π ≤Θ̄ ≤ +π is the effective Θ parameter after diagonalizing quark masses, Gaµν is the color field strengthtensor, and G̃a,µν ≡ µνλρ Gaλρ /2, with ε0123 = 1, its dual. This term induces an electric dipole moment (EDM) of the neutron of strength dn = CEDM e Θ̄.
The coefficient CEDM is calculated−16
using QCD sum rules as CEDM = 2.4(1.0) × 10
cm [24], while lattice QCD computations find
CEDM = 1.48(14)(31) × 10−16 cm [25] including statistical and systematic uncertainties. Experimental upper bounds on the latter, |dn | < 1.8 × 10−26 e cm [26, 27], imply |Θ̄| . 10−10 even thoughΘ̄ = O(1) is otherwise completely satisfactory. Note that the proton has a similar EDM as theneutron, but it is less strongly constrained at present; this could change in the future [28]. Theppproton EDM may be written as dp = CEDMe Θ̄, with CEDM
= −3.8(11)(8) [25]. The opposite signsof the neutron and proton EDMs may be understood from the opposite signs of their magnetic
moments.
The spontaneously broken global PQ symmetry U(1)PQ was introduced to solve the“strong CP problem” [1, 2] of small Θ , the axion being the pseudo-NG boson of U(1)PQ [3, 4].
This symmetry is broken due to the axion’s anomalous triangle coupling to gluons,L=αs µνa aa− Θ̄G G̃µν ,fa
8π
(90.2)

where a is the axion field and fa the axion decay constant. Color anomaly factors have beenabsorbed in the normalization of fa which is defined by this Lagrangian. Thus normalized, fa isthe quantity that enters all low-energy phenomena [29]. Non-perturbative topological fluctuationsof the gluon fields in QCD induce a potential for a whose minimum is at a = Θ̄ fa , thereby cancelingthe Θ̄ term in the QCD Lagrangian and thus restoring CP symmetry.
The resulting axion mass, in units of the PQ scale fa , is identical to the square root of the topo√
logical susceptibility in QCD, ma fa = χ. The latter can be evaluated further [30, 31], exploiting
the chiral limit (masses of up and down quarks much smaller than the scale of QCD), yielding√
ma fa = χ ≈ fπ mπ , where mπ ≈ 135 MeV and fπ ≈ 92 MeV . In more detail one finds, by
including O(α) QED corrections and next-to-next-to-leading order (NNLO) corrections in chiralperturbation theory [32],!
109 GeVma = 5.691(51)meV .
(90.3)
fa
A direct calculation of the topological susceptibility via QCD lattice simulations finds almost thesame central value, albeit with an about five times larger error bar [33].
The QCD axion acquires a variety couplings to low-energy Standard Model observables, as we
discuss in detail in this review. The most model-independent couplings are those of the axion to
the neutron and proton EDM operators. While the axion removes the static neutron and proton
EDMs, displacements of the axion field a from its vacuum expectation value induce field-dependent
EDMs, which are characterized through the operatori
LaN γ = − gaN γ a Ψ N σµν γ5 ΨN F µν ,2(90.4)

with N = n, p for neutrons or protons, respectively. The coupling ganγ is related to CEDM byganγ = eCEDM /fa and similarly for gapγ . Direct probes of the axion-EDM operators are difficult,though by studying the thermal production of axions in the early universe one can broadly constrain,using Planck and Baryon Acoustic Oscillation (BAO) data, ma . 0.3 eV [34]. In the presence of an
oscillatory relic axion DM field, this operator induces an oscillating neutron EDM; this effect forms
31st May, 2024

90. Axions and Other Similar Particles

3

the basis of the CASPEr experiment [35,36] that is discussed more later in this review. Non-linearly
realized discrete-symmetries may be used to suppress the QCD axion mass below the prediction
in Eq. (90.3), in which case a variety of cosmological and terrestrial constraints on the operator in
Eq. (90.4) are also relevant [37–44]
Axions with fa  vEW evade almost all current experimental limits. One generic class ofmodels invokes “hadronic axions” where new heavy quarks carry U(1)PQ charges, leaving ordinary
quarks and leptons without tree-level axion couplings. The archetype is the KSVZ model [45, 46],
where in addition the heavy new quarks are electrically neutral. Another generic class of axion
models requires at least two Higgs doublets and ordinary quarks and leptons carry PQ charges, thearchetype being the DFSZ model [47, 48]; in this case the quarks and leptons may have tree-levelaxion couplings. All of these models contain at least one electroweak singlet scalar that acquires
a vacuum expectation value and thereby breaks the PQ symmetry. The KSVZ and DFSZ models
are frequently used as benchmark examples, but other models exist where both heavy quarks and
Higgs doublets carry PQ charges (see [49] for an extensive review). In supersymmetric models,the axion is part of a supermultiplet and thus inevitably accompanied by a spin-0 saxion and aspin-1/2 axino, which both also have couplings suppressed by fa and are expected to have large
masses due to supersymmetry breaking [50]. In extra-dimension constructions the axion emerges
from a higher-dimensional gauge field; the other components of the gauge field, however, tend tohave masses proportional to the Kaluza-Klein mass scale of the extra dimensions.
90.2.2 Model-dependent axion couplings
Although the generic axion interactions scale approximately with fπ /fa from the corresponding
π 0 couplings, there are non-negligible model-dependent factors and uncertainties. The axion’s
two-photon interaction plays a key role for many searches,
Laγγ = −gaγγ
a Fµν F̃ µν = gaγγ a E · B ,4(90.5)

where F is the electromagnetic field-strength tensor and F̃ µν ≡ µνλρ Fλρ /2, with ε0123 = 1, itsdual. The coupling constant is [51]gaγγ =

α
2πfa



E
E
− 1.92(4) = 0.203(3) − 0.39(1)
N
N






ma
,
GeV2

(90.6)

where E and N are the electromagnetic and color anomalies of the axial current associated withthe axion. In grand unified models, and notably for DFSZ [47, 48], E/N = 8/3, whereas for
KSVZ [45, 46] E/N = 0 if the electric charge of the new heavy quark is taken to vanish. In
general, a broad range of E/N values is possible [49, 52–54], as indicated by the diagonal yellow
band in Fig. 90.1, whose width is roughly determined by the boundary values E/N = 44/3 andE/N = 5/3, respectively. However, this band still does not exhaust all the possibilities. In fact,
there exist classes of QCD axion models whose photon couplings populate the entire still-allowed
region outside the yellow band in Fig. 90.1 [55–60], motivating axion search efforts over a wide
range of masses and couplings.
The two-photon decay width is
2 m3
gaγγ
a
≈ 1.1 × 10−24 s−1
Γa→γγ =
64 π



ma
eV

5

.

(90.7)The second expression uses Eq. (90.6) with E/N = 0. Axions decay faster than the age of the
Universe if ma & 20 eV.
31st May, 2024

90. Axions and Other Similar Particles

4
10−6
10−7
10−8

| gaγγ | [GeV−1]

10−9

10−10

MWD X-rays Neutron stars

K

10−18
10−19

MUSE

CAPP

ADMX

BASE

Z

SV

10−17

oT

10−16

Le

10−15

VIMOS

10−14

γ

QUAX

MWD

Polarisation

ORGAN

10−13

ADMX SLIC

10−12

RBF+UF

10−11

Z
FS

D

XMM-Newton
NuSTARINTEGRAL−12 −11 −10 0−9

10

10

10

1

−8

10

−7

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10

0

10

1

10

2

10

3

10

4

10

5

10

6

10

7

10

m a [eV]Figure 90.1: Exclusion plot for the ALP-photon coupling. Figure courtesy of Ciaran O’Hare[61], contains exclusions from refs. [62–168]. Constraints in red are from terrestrial experiments.
ABRA 10 cm, SHAFT, BASE, ADMX SLIC, ADMX, RBF+UF, CAPP, QUAX, and ORGAN
search for axion DM and assume the axion in 100% DM; CROWS. ALPS-I, OSQAR, PVLAS arelight-shining-through-walls experiments that are purely terrestrial, while CAST searches for axions
produced in the Sun with no DM assumption. Those shown in green are astrophysical but makeno assumption about axions being DM. See text for details regarding the orange band expectation
for the QCD axion and assumptions for blue high mass axion astrophysical limits.
The interaction with fermions f has derivative form and is invariant under a shift a → a + a0
as behooves a NG boson,
Cf
Laf f =∂µ a Ψ̄f γ µ γ5 Ψf .
(90.8)
2fa
Here, Ψf is the fermion field, mf its mass, and Cf a model-dependent coefficient. The dimensionless
2 /4π of a “finecombination gaf f ≡ Cf mf /fa plays the role of a Yukawa coupling and αaf f ≡ gaf
fstructure constant.” The often-used pseudoscalar form Laf f = −i (Cf mf /fa ) a Ψ̄f γ5 Ψf need not be
equivalent to the appropriate derivative structure, for example when two NG bosons are attached
to one fermion line as in axion emission by nucleon bremsstrahlung [169–171].
In hadronic axion models, Ce vanishes at tree level, but is then generated radiatively at one
loop [172, 173],





fa
Λχ
3α2 E
Ce '
log
−
1.92
log
,
(90.9)
4π 2 Nmeme
where Λχ ' 1 GeV is the chiral symmetry breaking scale. In the DFSZ model [47,48], the tree-level
coupling coefficient to electrons is [172]Ce =sin2 β,331st May, 2024

(90.10)90. Axions and Other Similar Particles

5

where tan β is the ratio of the vacuum expectation values of the two Higgs doublets giving masses
to the up- and down-type quarks, respectively: tan β = vu /vd . As a cautionary note, many of theoriginal axion references, such as [172], defined tan β = vd /vu , but the choice tan β = vu /vd adopted
here and in more modern axion works is a reflection of the choice taken in the two-Higgs-doublet
literature [174]. The resulting prediction for the axion-electron coupling, as a function of the axion
mass, for the KSVZ axion (E/N = 0), hadronic axions, with 5/3 ≤ E/N ≤ 44/3, and the DFSZ
axion is displayed in Fig. 90.2. For the DFSZ range we have taken into account the constraint
0.28 . tan β . 140 [175] arising from the requirement of perturbative unitarity of the Yukawa
couplings of Standard Model fermions.
For nucleons, Cp,n have been determined as [51]Cp = −0.47(3) + 0.88(3)Cu − 0.39(2)Cd − 0.038(5)Cs− 0.012(5)Cc − 0.009(2)Cb − 0.0035(4)Ct ,Cn = −0.02(3) + 0.88(3)Cd − 0.39(2)Cu − 0.038(5)Cs(90.11)− 0.012(5)Cc − 0.009(2)Cb − 0.0035(4)Ct ,in terms of the corresponding model-dependent quark couplings Cq , q = u, d, s, c, b, t. For hadronic
axions, the latter vanish at tree-level, which means that Cn is expected to be much smaller thanCp . In the DFSZ model, Cu = Cc = Ct = 13 cos2 β and Cd = Cs = Cb = 31 sin2 β, and Cp and Cn ,as functions of β,
Cp = −0.435 sin2 β + (−0.182 ± 0.025) ,(90.12)
Cn = 0.414 sin2 β + (−0.160 ± 0.025) .
The resulting prediction for the axion-neutron coupling, as a function of the axion mass, for the
KSVZ axion and the DFSZ axion is displayed in Fig. 90.3. Note, however, that these couplings
receive in-medium corrections, which may be important when considering compact stars [176].
The axion-pion interaction is given by the Lagrangian [173, 177]
Laπ =



Caπ
∂µ a π 0 π + ∂µ π − + π 0 π − ∂µ π + − 2π + π − ∂µ π 0 ,2fπ fawhere Caπ = 2(Cp −Cn )/(3gA ) and gA is the nucleon axial charge gA = 1.2723(23).
there are axion-pion-nucleon interactions of the form
LaπN =


CaπN∂µ a iπ + p̄γ µ n − iπ − n̄γ µ p ,2fπ fa(90.13)
Additionally,(90.14)√
where CaπN = (Cap − Can ) /( 2gA ).

90.3 Laboratory Searches
90.3.1 Light shining through walls
Searching for “invisible axions” is extremely challenging due to their extraordinarily feeble
coupling to normal matter and radiation. Currently, the most promising approaches rely on theaxion-two-photon interaction, allowing for axion-photon conversion in external electric or magnetic
fields [9]. For the Coulomb field of a charged particle, the conversion can be viewed as a scattering
process, γ + Ze ↔ Ze + a, called Primakoff effect [178]. In the other extreme of a macroscopic
field, usually a large-scale B-field, the momentum transfer is small, the interaction is coherent overa large distance, and the conversion can be viewed as an axion-photon oscillation phenomenon in
analogy to neutrino flavor oscillations [179].
Photons propagating through a transverse magnetic field, with incident Eγ and magnetic field B
parallel, may convert into axions. For m2a L/2ω  2π, where L is the length of the B field region and31st May, 2024

6

90. Axions and Other Similar Particles

ω the photon energy, the resultant axion beam is coherent with the incident photon beam and theconversion probability is Π ∼ (1/4)(gaγγ BL)2 . One such realization uses a laser beam propagating
down the bore of a superconducting dipole magnet (like, say, the bending magnets in high-energy
accelerators). If another magnet is in line with the first, but shielded by an optical barrier, thenphotons may be regenerated from the pure axion beam [180,181]. The overall probability is P (γ →A → γ) = Π 2 .
The first such Light-Shining-through-Walls (LSW) experiment was performed by the BFRT
(Brookhaven-Fermilab-Rochester-Trieste) collaboration. It utilized two magnets of length L =4.4 m and B = 3.7 T and found |gaγγ | < 6.7 × 10−7 GeV−1 at 95% CL for ma < 1 meV [182, 183].
More recently, several such experiments were performed (see Listings) [98, 101, 184–188]. The
current best limit, |gaγγ | < 3.5 × 10−8 GeV−1 at 95% CL for ma . 0.3 meV (see Fig. 90.1), hasbeen achieved by the OSQAR (Optical Search for QED Vacuum Birefringence, Axions, and Photon
Regeneration) experiment, which exploited two 9 T LHC dipole magnets and an 18.5 W continuous
wave laser emitting at the wavelength of 532 nm [101]. The ALPS I (Any Light Particle SearchI) experiment achieved a similar sensitivity [98], see Fig. 90.1. Some of these experiments havealso reported limits for scalar bosons where the photon Eγ must be chosen perpendicular to themagnetic field B.
The concept of resonantly enhanced photon regeneration may open unexplored regions of coupling strength [189–191]. In this scheme, both the production and detection magnets are within
Fabry-Perot optical cavities and actively locked in frequency. The γ → a → γ rate is enhanced bya factor FF 0 /π 2 relative to a single-pass experiment, where F and F 0 are the finesses of the twocavities. The resonant enhancement could be of order 10(10−12) , improving the gaγγ sensitivity by
10(2.5−3) . The experiment ALPS II (Any Light Particle Search II) is based on this concept andaims at an improvement of the current laboratory bound on gaγγ by a factor ∼ 103 [192]. ALPS II
began operations in 2023.
Resonantly enhanced photon regeneration has already been exploited in experiments searchingfor “radiowaves shining through a shielding” [193–196]. For ma . 10−5 eV, the upper bound on
gaγγ established by the CROWS (CERN Resonant Weakly Interacting sub-eV Particle Search)experiment [100] is slightly less stringent than the one set by OSQAR, see Fig. 90.1.
90.3.2 Photon polarization
An alternative to regenerating the lost photons is to use the beam itself to detect conversion: thepolarization of light propagating through a transverse B field undergoes dichroism and birefringence[197]. Dichroism: The Ek component, but not E⊥ , is depleted by axion production, causing a small
rotation of linearly polarized light. For m2a L/2ω  2π, the effect is independent of ma . For heavier
axions, it oscillates and diminishes as ma increases, and it vanishes for ma > ω. Birefringence:
This effect occurs because there is mixing of virtual axions in the Ek state, but not for E⊥ . Hence,linearly polarized light will develop elliptical polarization. Higher-order QED also induces vacuum
magnetic birefringence (VMB). A search for these effects was performed in the same dipole magnetsof the BFRT experiment mentioned before [198]. The dichroic rotation gave a stronger limit thanthe ellipticity rotation: |gaγγ | < 3.6 × 10−7 GeV−1 at 95% CL, for ma < 5 × 10−4 eV. The ellipticity
limits are better at higher masses, as they fall off smoothly and do not terminate at ma .
90.3.3 Long-range forces
New bosons would mediate new long-range forces, which are severely constrained by “fifth
force” experiments [199]. Those looking for new mass-spin couplings provide significant constraints
on pseudoscalar bosons [200–205], see for example in Fig. 90.3 the limit on the axion-neutron
coupling [206] from torsion balance tests of the gravitational inverse square law [207]. Presently,
the most restrictive limits are obtained from combining long-range force measurements with stellar
31st May, 2024

7

90. Axions and Other Similar Particles

cooling arguments [208, 209]. For the moment, any of these limits are far from realistic values
expected for the QCD axion. Still, these efforts provide constraints on more general low-massbosons.
In Ref. [210], a method was proposed that can extend the search for axion-mediated spin-dependent forces by several orders of magnitude. By combining techniques used in nuclear magnetic
resonance and short-distance tests of gravity, this method appears to be sensitive to the QCD
axion in the µeV – meV mass range, independent of the cosmic axion abundance, if axions havea CP -violating interaction with nuclei as large as the current experimental bound on the electric
dipole moment of the neutron allows. (Note that the CP -violation already present in the Standard
Model is sufficient for generating an axion-mediated force, though in this case the signal appears too
small to be detectable for the QCD axion in the foreseeable future [210].) The ARIADNE (Axion
Resonant InterAction DetectioN Experiment) is under development and employs this approach tosearch for axion-mediated spin-dependent short-range interactions between a hyper-polarized 3He sample and an unpolarized tungsten source mas [211]. The method relies on superconducting
magnetic shielding to screen the sample from ordinary magnetic field noise. Experimental tests
to demonstrate the requirements of ARIADNE, including characterization of the magnetic fieldbackgrounds, are under way [212, 213].

90.4 Axions from Astrophysical Sources
90.4.1 Stellar energy-loss limits
Axions are produced in hot astrophysical plasmas, and can thus transport energy out of stars.
The coupling strength of these particles with normal matter and radiation is bounded by theconstraint that stellar lifetimes or energy-loss rates are not in conflict with observation [214, 215].
We begin this discussion with our Sun and concentrate first on the axion-photon coupling. In
the Sun axions are produced by the Primakoff process γ + Ze → Ze + a. Integrating this process
over a standard solar model yields the axion luminosity [216]2
La = g10
× 1.85 × 10−3 L ,(90.15)where g10 = |gaγγ | × 1010 GeV. The maximum of the spectrum is at 3.0 keV, the average at 4.2 keV,
2 × 3.75 × 1011 cm−2 s−1 . The solar photon luminosity is fixed,
and the number flux at Earth is g10
so energy losses due to the Primakoff process require enhanced nuclear energy production and thus
enhanced neutrino fluxes. The all-flavor measurements by SNO (Sudbury Neutrino Observatory),
together with a standard solar model, imply La . 0.10 L , corresponding to g10 . 7 [217], mildly
superseding a similar limit from helioseismology (sound speed, surface helium and convective radius)[218]. In Ref. [147], this limit was improved to g10 < 4.1 (at 3 σ), see Fig. 90.1, exploiting a
new statistical analysis that combined helioseismology and solar neutrino observations, including
theoretical and observational errors, and accounting for tensions between input parameters of solarmodels, in particular the solar element abundances. Going beyond the axion-photon coupling,
Ref. [217] considered also a non-zero axion-electron coupling and obtained the bound on the latter
displayed in Fig. 90.2.
A more restrictive limit derives from globular-cluster (GC) stars that allow for detailed tests ofstellar-evolution theory. The stars on the horizontal branch (HB) in the color-magnitude diagram
have reached helium burning with a core-averaged energy release of about 80 erg g−1 s−1 , compared
2 30 erg g−1 s−1 . The accelerated consumption of helium reduces
to Primakoff axion losses of g10
2 ). In contrast, the red giant (RG) branch stars are not
the HB lifetime by about 80/(80 + 30 g10
strongly affected by Primakoff losses, since unlike for the HB stars the plasma frequency in the
RG stellar cores is below the temperature. Thus, Primakoff production reduces the R-parameter,
31st May, 2024

90. Axions and Other Similar Particles

8
10−10

10−11

| gae |

10−12

10−13

(EM-an10−14

X-raysXENON1T

KS

omaly

VZ

XENONnTm a [eV]

free)

10−15
10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100

101

102

103

104

105

Figure 90.2: Exclusion plot for ALP-electron coupling as described in the text. Figure courtesy of
Ciaran O’Hare [61], contains data from refs. [168,217,219–228]. The hadronic QCD axion-electron
coupling arises at one loop and is given in Eq. (90.9); varying E/N between 5/3 and 44/3 gives
the indicated hadronic axion band. The KSVZ axion has E/N = 0, while the DFSZ axion-electron
coupling has the tree-level coupling given in Eq. (90.10) that depends on the unknown but boundedvalue of tan β (see text for details).
which is the number of observed HB branch stars to RG branch stars in a GC. Measurements of
the R-parameter in a large sample of 39 Galactic GCs
give a weak indication of non-standard losses which may be accounted by Primakoff-like axion
emission, if the photon coupling is in the range |gaγγ | = (2.9 ± 1.8) × 10−11 GeV−1 [122, 229]. Still,
the upper bound found in this analysis,|gaγγ | < 6.6 × 10−11 GeV−1 (95% CL),(90.16)

represents one of the strongest limits on gaγγ for a wide mass range. More recently, the R2 parameter has emerged as a potentially more sensitive probe of axions; the R2 -parameter is definedas the ratio of the asymptotic giant branch (AGB) stars to the HB stars in a GC. AGB stars havemore efficient Primakoff production than HB stars, meaning that R2 is expected to decrease forincreasing |gaγγ |. Ref. [123] used an R2 measurement based off of 48 GCs as observed by the Hubble
Space Telescope [230] to constrain|gaγγ | < 4.7 × 10−11 GeV−1 (95% CL) .

(90.17)The constraint above on gaγγ may be translated to fa > 4.8 × 107 GeV (ma < 0.12 eV) , using
E/N = 0 as in the KSVZ model, or to fa > 1.8 × 107 GeV (ma < 0.32 eV) , for the DFSZ axion
model, with E/N = 8/3, see Fig. 90.1.
31st May, 2024

990. Axions and Other Similar Particles

If axions couple directly to electrons, the dominant emission processes are atomic axio-recombination and axio-deexcitation, axio-bremsstrahlung in electron-ion or electron-electron collisions,and Compton scattering [231]. Stars in the RG branch of the color-magnitude diagram of GCs are
particularly sensitive to these processes: they would lead to an extension of the latter to larger
brightness. In fact, the tip of the RG branch (TRGB) – the brightest point of the RG branch –provides the currently most sensitive method to test the axion coupling to electrons. The strongest
bounds on it are derived from analyses of the TRGB in several GCs [232] and in the Galactic GC
ω Centauri [226]. The two analyses lead to very similar results,|gaee | < 1.48 × 10−13 (95% CL) and |gaee | < 1.3 × 10−13 (95% CL),(90.18)respectively, see Fig. 90.2. Reference [232] finds also a small hint for extra cooling, corresponding−13 , while Ref. [226] does not find any evidence for exotic cooling.
to |gaee | = 0.60+0..32−0.58 × 10
Bremsstrahlung is also efficient in white dwarfs (WDs), where the Primakoff and Compton
processes are suppressed by the large plasma frequency. A comparison of the predicted and observed
luminosity function of WDs can be used to put limits on |gaee | [233, 234]. An analysis based on
detailed WD cooling treatment and data on the WD luminosity function (WDLF) of the Galactic
disk found that electron couplings above |gaee | & 3 × 10−13 are disfavoured [235]. Lower couplings
cannot be discarded from the current knowledge of the WDLF of the Galactic disk [235–237]. These
probes may be improved by the Rubin Observatory Large Synoptic Survey Telescope (LSST), whichis expected to increase the sample of WDs in the Galactic halo to hundreds of thousands [238]. For
pulsationally unstable WDs (ZZ Ceti stars), the period decrease Ṗ /P is a measure of the cooling
speed. The corresponding observations of a handful pulsating WDs imply additional cooling thatcan be interpreted in terms of axion energy losses [239–243], though with axion-electron couplingvalues likely incompatible with other constraints [244].
Analogous constraints derive from neutron stars (NS) cooling. Broadly speaking, there are twoclasses of NS cooling searches for axions. One approach uses the proto-NS formed after SN 1987A toconstrain the axion luminosity produced during the first seconds of the proto-NS when the neutrino
luminosity is measured with terrestrial experiments. The second class of NS cooling constraints
consider older NSs, typically much older than ∼100 yr, and constrains the axion luminosity using
the surface temperature as measured with photons versus the age of NS as measured through e.g.
kinematic considerations. We begin with a discussion of the limits from SN 1987A.
Numerical simulations reveal that the energy-loss rate due to axions in a nuclear medium at thedensity 3 × 1014 g cm−3 and temperature 30 MeV should not exceed about 1 × 1019 erg g−1 s−1 tobe consistent with the neutrino signal observed from SN 1987A [256]. The energy-loss rate from
nucleon bremsstrahlung, N + N → N + N + a, is (CN /2fa )2 (T 4 /π 2 mN ) F . Here F is a numericalfactor that represents an integral over the dynamical spin-density structure function because axions
couple to the nucleon spin. For realistic conditions, even after considerable effort, one is limited
to a heuristic estimate leading to F ≈ 1 [215]. The SN 1987A limits are of particular interest for
hadronic axions where the bounds on |gaee | are moot. Using a proton fraction of 0.3, gann = 0,
F = 1, and T = 30 MeV, one finds fa > 4 × 108 GeV and ma < 16 meV [215]. A more detailed
numerical calculation [257] with state of the art SN models, again assuming gann = 0, found thata coupling larger than |gapp | & 6 × 10−10 , would shorten significantly the timescale of the neutrino
emission. This result is, not surprisingly, rather close to the estimate in Ref. [215]. Improving
the calculation of axion emission via nucleon-nucleon bremsstrahlung beyond the basic one-pionexchange approximation appears to loosen the bound [258,259]. The latter analysis finds a reductionof the axion emissivity by an order of magnitude if one takes into account the non-vanishing mass ofthe exchanged pion, the contribution from two-pion exchange, effective in-medium nucleon masses
31st May, 2024

90. Axions and Other Similar Particles

10
µHz

mHz

Hz

kHz

MHz

GHz

THz

10−1
10−2
10−3
10−4
10−5
10−6

| gan |

10−7
10−8
10−9

10−10
10−11
10−12
10−13
10−14
10−15
10−16

−22 −21 −20 −19 −18 −17 −16 −15 −14 −13 −12 −11 −10 0−9 0−8 0−7 0−6 0−5 0−4 0−3 0−2

10 10 10 10 10 10 10 10 10 10 10 10 10

1

1

1

1

1

1

1

1

m a [eV]Figure 90.3: Exclusion plot for ALP-neutron coupling as described in the text. Figure courtesyof Ciaran O’Hare [61], includes data from refs. [40, 42, 206, 245–255]. The hadronic axion model
prediction is given in Eq. (90.11) with vanishing quark couplings, while the DFSZ model prediction
depends on tan β as is found in Eq. (90.12), giving the shaded yellow region above. Note that fora fine-tuned value of tan β gan can be taken to zero. On the other hand, the neutron star coolingconstraints [254] also probe the axion-proton coupling gap at a comparable level (not shown), andboth gan and gap cannot simultaneously be taken to zero in the DFSZ model.
and multiple nucleon scattering, leading to the result [259]22gann+ 0.61 gapp
+ 0.53 gann gapp < 8.26 × 10−19 ,(90.19)which is consistent with the original estimate in [215]. This analysis, however, still neglects anothervery efficient mechanism for axion production in a SN: the pion production process, π − +p → a+n,also induced by the axion coupling to nucleons. Pion production was recognized long ago as being
competitive with nucleon bremsstrahlung [260–262]. However, only recently it was shown that thepion abundance in the early stages of a SN is much larger than previously expected [263]. It was
shown in Ref. [264] that pion induced processes dominate over bremsstrahlung and so strengthen
the bound on the axion-nucleon coupling. On the other hand, given the modeling uncertainties
and the sparse data from SN 1987A, the constraint on the axion-nucleon couplings from SN 1987A
should be considered more as indicative than as a sharp bound [257]. Furthermore, note that if
axions interact sufficiently strongly they are trapped. Only about three orders of magnitude in
gaN N , where N = n, p, or ma are excluded. For even larger couplings, the axion flux would havebeen negligible, yet it would have triggered additional events in the detectors, excluding a further
range [265].
Further bounds on the axion-nucleon coupling can be derived from observations of the cooling ofolder NSs. Recently, strong constraints were obtained by modeling the cooling of the “Magnificent
31st May, 2024

11

90. Axions and Other Similar Particles

Seven” (M7) NSs in the presence of axions [254]. Axion emission would accelerate NS cooling.
Thus, if the age and temperature of a NS are independently known, then by modeling axioninduced cooling in conjunction with the standard NS cooling mechanisms, in particular cooling via
neutrino emission from the bulk of the NS and thermal emission from the NS surface, one is able
to constrain the axion’s coupling strength. Ref. [254] used a sample of four of the M7 along withPSR J0659 to constrain ma < 16 meV for the KSVZ QCD axion at 95% CL and ma . 5 meV(ma . 30 meV) in the DFSZ scenario for asymptotically large (small) tan β. For axions that couple
exclusively to neutrons (protons) Ref. [254] constrains |gann | < 1.3 × 10−9 (|gapp | < 1.5 × 10−9 ),as illustrated in Fig. 90.3. The five NSs used in that work are unique in that their ages, allin the range 0.1 − 1 Myr, are known by kinematic measurements (e.g., tracing back to the SN
remnant), while their surface temperatures are measured in the X-ray band. Beyond statisticaluncertainties on these measurements, there are a number of confounding systematic uncertainties
that must be accounted for in NS cooling analyses, including uncertainties related to the core-surface temperature relation, which involves the chemical composition of the NS envelope. The NS
equation of state and the superfluid critical temperatures of the dense nuclear matter are also sourcesof uncertainty. Note that axions are predominantly produced by nuclear bremsstrahlung [266, 267]
except for temperatures near the superfluid critical temperature, when Cooper pair breaking andformation (PBF) processes may efficiently produce axions [268, 269]. Given the large densities it is
crucial to account for medium dependent couplings when computing the axion luminosities [270].
The young NS in the supernova remnant Cassiopeia A (Cas A) was previously though to strongly
constrain axions, at a level similar to the NS cooling bound described above, due to PBF axion
production [271]. This is because it was observed that Cas A was cooling rapidly, which may be
explained by neutrino cooling with neutron superfluidity and proton superconductivity [272, 273].
However, it is possible that the excessive cooling of Cas A is at least in part instrumental inorigin [274]. Fully accounting for uncertainties on both the NS properties and the data, constraints
from young NSs such as Cas A and the NS in the supernova remnant HESS J1731-347 [275] appear
to be sub-dominant compared to the limits from SN 1987A and the M7 [254].
Finally, let us note that if ma ∼ meV, SNe would lose a large fraction of their energy as axions.
This would lead to a diffuse SN axion background in the Universe with an energy density comparable
to the extra-galactic background light [276]. However, there is no apparent way of detecting it or
the axion burst from the next nearby SN. On the other hand, neutrino detectors such as IceCube,
Super-Kamiokande or a future mega-ton water Cherenkov detector will probe exactly the mass
region of interest by measuring the neutrino pulse duration of the next Galactic SN [257].
90.4.2 Searches for solar axions and ALPs
Instead of using stellar energy losses to derive axion limits, one can also search directly for thesefluxes, notably from the Sun. The main focus has been on ALPs with a two-photon vertex. They
are produced by the Primakoff process with a flux given by Eq. (90.15) and an average energy of
4.2 keV, and can be detected at Earth with the reverse process in a macroscopic B-field (“axion
helioscope”) [9]. In order to extend the sensitivity in mass towards larger values, one can endow thephoton with an effective mass in a gas, ωplas , and tune the mass to match the axion’s dispersion
relation (ωplas = ma ) [277].
An early implementation of these ideas used a conventional dipole magnet, with a conversion
volume of variable-pressure gas with a xenon proportional chamber as x-ray detector [278]. The
conversion magnet was fixed in orientation and collected data for about 1000 s/day. Axions were
excluded for |gaγγ | < 3.6 × 10−9 GeV−1 for ma < 0.03 eV, and |gaγγ | < 7.7 × 10−9 GeV−1 for
0.03 < ma < 0.11 eV at 95% CL.
Later, the Tokyo axion helioscope used a superconducting magnet on a tracking mount, viewing
31st May, 2024

12

90. Axions and Other Similar Particles

the Sun continuously. They reported |gaγγ | < 6 × 10−10 GeV−1 for ma < 0.3 eV [279, 280]. This
experiment was recommissioned and a similar limit for masses around 1 eV was reported [281].
The most recent helioscope CAST (CERN Axion Solar Telescope) uses a decommissioned LHC
dipole magnet on a tracking mount. The hardware includes grazing-incidence x-ray optics withsolid-state x-ray detectors, as well as x-ray Micromegas position-sensitive gaseous detectors. Exploiting an IAXO (see below) pathfinder system, CAST has established the limit|gaγγ | < 6.6 × 10−11 GeV−1(95% CL),(90.20)for ma < 0.02 eV [99]. To cover larger masses, the magnet bores are filled with a gas at varying
pressure. The runs with 4 He cover masses up to about 0.4 eV [282], providing the high-masscomponent of the CAST limits shown in Fig. 90.1. To cover yet larger masses, 3 He was used toachieve a larger pressure at cryogenic temperatures. Limits up to 1.17 eV allowed CAST to “crossthe axion line” for the KSVZ model [283–285], see Fig. 90.1.
Sensitivity to significantly smaller values of gaγγ can be achieved with a next-generation axion helioscope with a much larger magnetic-field cross section. Realistic design options for this“International Axion Observatory” (IAXO) have been studied in some detail [286] and its physics
potential has been reviewed recently [287]. Such a next-generation axion helioscope may also push
the sensitivity in the product of couplings to photons and to electrons, gaγγ gaee , into a range beyond
stellar energy-loss limits and test the hypothesis that WD, RG, and HB cooling is dominated byaxion emission [288, 289]. As a first step towards IAXO, an intermediate experimental stage called
BabyIAXO is currently under preparation at DESY [290].
Direct detection experiments searching for dark matter (DM) consisting of weakly interacting
massive particles have also the capability to search for solar axions and ALPs. For low masses,
ma . 100 eV, the XENONnT experiment [291] has provided the most stringent bound among thoseexperiments on the axion-electron coupling constant,|gaee | < 1.9 × 10−12(90% CL),(90.21)

see Fig. 90.2, by exploiting the axio-electric effect in liquid xenon. Slightly less stringent limits wereset by PandaX-II [292] and by LUX [293]. However, this technique has not reached the sensitivityof energy-loss considerations in stars.
90.4.3 Conversion of astrophysical axion fluxes
Large-scale B fields exist in astrophysics that can induce axion-photon oscillations. In practicalcases, the strength of B is much smaller than in the laboratory, whereas the conversion region L
is much larger. Therefore, while the product BL can be large, realistic sensitivities are usually
restricted to very low-mass particles, far away from the “QCD axion band” in a plot like Fig. 90.1.
One example of this is SN 1987A, which would have emitted a burst of ALPs due to thePrimakoff production in its core. They would have partially converted into γ-rays in the Galactic
B-field. The lack of a gamma-ray signal in the GRS instrument of the SMM satellite in coincidencewith the observation of the neutrinos emitted from SN 1987A therefore provides a strong bound on
their coupling to photons [294, 295]. This bound has been revisited and the underlying physics has
been brought to the current state-of-the-art, as far as modeling of the supernova and the MilkyWay magnetic field are concerned, resulting in the limit [151, 152] |gaγγ | < 5.2 × 10−12 GeV−1 forma . 5 × 10−10 eV.
Reference [119] reports no evidence of a γ-ray burst in observations of extragalactic SNe with
the Fermi Large Area Telescope (LAT). Under the assumption that at least one SN was contained
within the LAT field of view, the authors derive an upper bound on the axion photon coupling
which is about a factor of 5 weaker than the one from SN 1987A, see Fig. 90.1.
31st May, 2024

13

90. Axions and Other Similar Particles

The cumulative emission of ALPs from all past core-collapse SNe would lead to a diffuse gammaray flux peaked at energies ∼ 50 − 100 MeV which can convert in the Galactic magnetic field into
photons. Using Fermi-LAT measurements of the diffuse γ-ray flux, Ref. [296] obtains a conservative
bound on the photon coupling, |gaγγ | < 5 × 10−10 GeV−1 , for ma . 10−11 eV, see see Fig. 90.1,
which can be decreased by nearly three orders of magnitude, if an ALP-nucleon coupling of maximal
phenomenologically allowed strength, |gaN N | ∼ 10−9 , is allowed.
Hot, young stars, such as Wolf-Rayet stars, efficiently produce ALPs with energies ∼ 10−100 keV
via the Primakoff effect. Large numbers of those stars are hosted by the Galactic Quintuplet andWesterlund 1 super star clusters (SSCs). The non-observation of hard X-rays originating fromaxion-photon conversion in the Galactic magnetic field in archival NuSTAR (Nuclear Spectroscopic
Telescope Array) data from these SSCs leads to a bound on the axion-photon coupling [159],|gaγγ | < 3.6 × 10−12 GeV−1 , for ma . 5 × 10−11 eV, see Fig. 90.1. A somewhat weaker bound in thesame mass range was established exploiting NuSTAR data on Betelgeuse [105].
A hard X-ray excess in data from the nearby M7 isolated NSs [297] may be explained by
ALPs produced in the cores of those stars and converted in the surrounding magnetic fields, with
|gaN N gaγγ | ∈ (2 × 10−21 , 10−18 ) GeV−1 , for ma . 10−5 eV [298]. The non-observation of an X-ray
excess from the magnetic WD RE J0317-853 [299] by Chandra yields the constraint |gaee gaγγ | .
1.3 × 10−25 GeV−1 , for ma  10−5 eV [128], which provides a non-trivial constraint on the ratio
gaee /gaN N for axion models explaining the M7 X-ray excess.
In addition to being produced in NS cores, axions may also be produced in NS magnetospheres.
In particular, it has recently been shown that axions could be copiously produced in the polar-cap
regions of NS magnetospheres due to time-varying, un-screened electric fields [145]. Those axions
could then convert to photons in the outer regions of the NS magnetosphere, leading to observable,
broadband radio flux. The absence of such radio flux sets competitive constraints on ALPs, as
indicated by the “pulsars” constraint in Fig. 90.1.
90.4.4 Conversion of astrophysical photon fluxes
Magnetically induced oscillations between photons and ALPs can modify the photon fluxes
from distant sources in various ways, featuring (i) frequency-dependent dimming, (ii) modified
polarization, and (iii) avoiding absorption by propagation in the form of axions. For example,
dimming of SNe Ia could influence the interpretation in terms of cosmic acceleration [300], although
it has become clear that photon-ALP conversion could only be a subdominant effect [301].
Polarization measurements are particularly powerful probes of photon-to-axion conversion since
only photons polarized parallel to astrophysical magnetic fields may convert into axions, meaningthat in the presence of large-scale ordered magnetic fields axions tend to leave distinct polarization
signatures in passing radiation. Searches for linear polarization from radio galaxies (see, e.g.,
Ref. [302]) and quasars [303] may approach in sensitivity |gaγγ | ∼ few × 10−13 GeV−1 , albeit withuncertainties related to the underlying modeling assumptions. Recently, robust limits at the level|gaγγ | ≤ 5.4 × 10−12 GeV−1 at 95% CL have been derived from optical polarization measurementsof nearby magnetic WDs [129] (see also [304]), see Fig. 90.1. The magnetic fields of magnetic
WDs may be well-measured through the Zeeman splitting of bound-bound transitions in the WD
atmospheres.
Remarkably, it appears that the Universe could be too transparent to TeV γ-rays that should beabsorbed by pair production on the extra-galactic background light [109,305–308]. The situation is
not conclusive at present [309–312], but the possible role of photon-ALP oscillations in TeV γ-ray
astronomy is tantalizing [313–315]. On the other hand, much of this parameter space is excludedby the previously-discussed WD polarization probes. Fortunately, the region in ALP parameter
space, gaγγ ∼ 10−12 − 10−10 GeV−1 for ma . 10−7 eV [316], required to explain the anomalous TeV
31st May, 2024

14

90. Axions and Other Similar Particles

transparency of the Universe, could be conceivably probed by the next generation of laboratory
experiments (ALPS II) and helioscopes (IAXO) mentioned above.
This parameter region can also be probed by searching for an irregular behavior of the gamma
ray spectrum of distant active galactic nuclei (AGN), expected to arise from photon-ALP mixing
in a limited energy range. In this type of studies, the uncertainty in the magnetic field around thesource needs to be taken into account. This typically leads to a range of limits on the ALP-photon
coupling that depend on the modeling assumptions. The H.E.S.S. collaboration has set a limit of|gaγγ | . 2.1 × 10−11 GeV−1 , for 1.5 × 10−8 eV . ma . 6.0 × 10−8 eV, from the non-observation of anirregular behavior of the spectrum of the AGN PKS 2155-304 [317]. The Fermi-LAT collaboration
has put an even more stringent limit on the ALP-photon coupling [118] from observations of the
gamma ray spectrum of NGC 1275, the central galaxy of the Perseus cluster, see Fig. 90.1. A
similar analysis has been carried out in Ref. [318], using Fermi-LAT data of PKS 2155-304, andin Ref. [131], using ARGO-YBJ and Fermi-LAT data of Mrk 421, see Fig. 90.1. However, these
constraints were obtained under certain theoretical assumptions about magnetic fields surrounding
the sources, not confirmed yet by direct astronomical observations in these particular directions;this introduces large systematic uncertainties in the reported constraints [319].
Evidence for spectral irregularities has been reported in Galactic sources, such as pulsars andsupernova remnants, and has been interpreted as hints for ALPs [320, 321] (see also discussion in
Ref. [322] and references therein). However, the inferred ALP parameters, |gaγγ | ∼ 10−10 GeV−1 ,ma ∼ neV, are in tension with the CAST helioscope bounds. Reference [322] updated the analysisof the pulsar signal region including astrophysical nuisance parameters and correctly deriving confidence intervals on ALP parameters by means of Monte Carlo simulations. The tension with the
CAST bounds can be evaded if environmental effects in matter, which would suppress the ALP
production in dense astrophysical plasmas like the solar interior, are invoked. If this explanation iscorrect, the claimed ALP signal would be in reach of the next-generation LSW experiment ALPSII. Other ways to make the CAST bound compatible with photon-ALP conversions in the lowdensity Galactic medium are invoking photon-ALP-dark photon oscillations [323] or the existenceof a number of ‘hidden’ ALPs [324].
At smaller masses, ma . 10−12 eV, galaxy clusters become highly efficient at interconverting
ALPs and photons at X-ray energies. Constraints on spectral irregularities in the spectra of luminous X-ray sources (Hydra A, M87, NGC 1275, NGC 3862, Seyfert galaxy 2E3140; taken by
Chandra and XMM-Newton) located in or behind galaxy clusters then lead to stringent upper limits on the ALP-photon coupling [110–112, 325–327], (for the limits exploiting spectra from Hydra
and M87 from Refs. [110] and [111], respectively, see Fig. 90.1). Reference [112] recently performed
the most sensitive x-ray searches for ALPs to date by employing Chandra’s High-Energy Transmission Gratings that allow for an unsurpassed spectral resolution. New observations of the AGN
NGC 1275 then led to the bound |gaγγ | < 8 × 10−13 GeV−1 at 99.7% C.L. for ultra-light ALPs, as
illustrated in Fig. 90.1. On the other hand, magnetic field modeling uncertainties in the clusters
may not be fully accounted for in these analyses [319].
90.4.5 Finite density effects for the QCD axion
If the QCD axion sector has a discrete, ZN , shift symmetry, its potential is much shallower, andits mass, in units of its decay constant, ma fa ' (3π)−1/4 N 3/4 2−N /2 mπ fπ , is smaller than the oneof the canonical QCD axion by an exponential factor ∝ 2−N /2 [57,58]. This opens up the parameter
space over which one should search for a QCD axion towards the left of the yellow canonical QCD
axion band in Fig. 90.1, Fig. 90.2, and Fig. 90.3. Novel bounds apply to this exceptionally light
QCD axion due to finite density effects [328–330]. In fact, in dense stellar media, the minimum of
the axion potential may be shifted to π. This has a number of phenomenological consequences that
31st May, 2024

15

90. Axions and Other Similar Particles

span from the modification of nuclear processes in stars due to θ = O(π) to modifications in theorbital decay of binary systems (and subsequently in the emitted gravitational waves). Recently
strong constraints have been set using the modification of the WD mass-radius relation due to suchaxions [331].
In fact, θ ∼ 1 in the solar core would lead to an increased proton-neutron mass difference,
which would prohibit the neutrino line corresponding to the 7 Be-7 Li mass difference observed by
Borexino [332].
Moreover, the fact that the position of the minimum of the axion potential depends on the
nuclear density of the medium may also source a long-range force between dense stars [328]. This
new long-range force sourced by the axion can be constrained by the measurement of the orbital
decay of double pulsar or NS-pulsar binaries [328]. The gravitational wave signal of NS-NS mergers
or black hole (BH) - NS mergers would also be modified by these axionic long-range forces [328,329].
There is also a corresponding bound [330] exploiting the gravitational waves observation fromthe binary NS inspiral GW170817 detected by LIGO (Laser Interferometer Gravitational-Wave
Observatory) and Virgo [333].
90.4.6 Superradiance of black holes
Light bosonic fields such as axions or ALPs can affect the dynamics and gravitational wave
emission of rapidly rotating astrophysical BHs through the superradiance mechanism. When theboson’s Compton wavelength is of order of the size of the BH’s ergoregion, they form gravitationalbound states around the BH. Their occupation number grows exponentially by extracting energy
and angular momentum from the black hole, forming a coherent axion or ALP bound state emitting
gravitational waves. When accretion cannot replenish the spin of the BH, superradiance dominates
the BH spin evolution; this is true for both supermassive and stellar mass BHs. The existenceof destabilizing light bosonic fields thus leads to exclusion regions in the mass versus spin plot ofrotating BHs. Stellar BH spin measurements exploiting well-studied binaries and two independent
techniques exclude a mass range – up to self-interaction caveats discussed below – 6 × 10−13 eV <ma < 2×10−11 eV at 2 σ, which for the axion excludes 3×1017 GeV < fa < 1×1019 GeV [12,334,335],
see Fig. 90.4. These bounds apply when gravitational interactions dominate over the axion selfinteraction, which is largely true for the QCD axion in this mass range. On the other hand,
Mehta et al. [336, 337] considered superradiance bounds for string theory ALPs with a quartic
self-coupling (of either sign) given by λ = m2a /fa2 , using the bosenova model of Ref. [335], andfound that for ma ∼ 10−12 eV the superradiant cloud, and thus the constraints, are destroyed for
fa . 1011 − 1012 GeV, depending precisely on the mass and the source.
Baryakhtar et al. [338] used a more advanced model for the effect of self-interactions on superradiant evolution, and a different (frequentist) statistical methodology, leading to more conservative
bounds from stellar mass BHs (region near 10−12 eV). In particular, Baryakhtar et al. [338] foundthat QCD axions are only excluded for ma . 6 × 10−12 M instead of the 2 × 10−11 M , as claimedin [336, 337]. Baryakhtar et al. [338] also vetoed supermassive BHs (SMBHs) with spins measured
at low significance, and thus found no ALP bounds in the SMBH region (near 10−18 eV); Mehta
et al. [336, 337, 339], in constrast, included SMBHs in a (quasi-)Bayesian analysis with a flat prioron the spin and found non-trivial constraints . In summary, it appears likely that the lower endof the QCD axion mass range is excluded by superradiance, with the requirement ma & 10−11 eV,
but the exact location of this limit is still debated. It is also too early to claim that ultra-light ALP
parameter space is excluded by SMBHs, though this may change with future work.
Long lasting, monochromatic gravitational wave signals, which can be distinguished from ordinary astrophysical sources by their clustering in a narrow frequency range, are expected to be
produced by axions or ALPs annihilating to gravitons. Gravitational waves could also be sourced
31st May, 2024

100

DFSZ

10−1

90. Axions and Other Similar Particles

16
10−2

10−3

10−2

10−1

Black hole spins

109

108

Models:

Lattice/χ( T ):Strings:
Strings+Walls:

π/6

10−8

10−7

π − 0.1 = |θi |

107

...

106

HI
= max GeV
(Isocurvature)

SMASH, 2016
Cogenesis, 2020
VISHν, 2022
Wantz, 2009
Berkowitz, 2015
Bonati, 2016
Borsanyi, 2016
Petreczky, 2016
Dine, 2017
Gorghetto, 2020Buschmann, 2021

Hot dark
matter+∆Neff

Kawasaki, 2012
Kawasaki, 2014
Fleury, 2015
Klaer, 2017
Buschmann, 2019
Kawasaki, 2014
Gorghetto, 2020

NDW > 1:10−13 10−12 10−11 10−10 10−9

π/2

10−6

10−5

10−4

QCD axion mass, m a [eV]

10−3

10−2

10−1

100

101

Figure 90.4: QCD axion mass predictions for obtaining the correct DM abundance assuming thePQ symmetry is and is not restored after inflation and, in the case the PQ symmetry is restored
after inflation, depending on the domain wall number N . Figure courtesy of Ciaran O’Hare [61],includes data from refs. [18, 33, 340–353]. The lower-end of the possible mass range is bounded
by BH superradiance constraints and the theoretical requirement that fa be below the Planckscale, while the upper end is bounded by the somewhat model-dependent NS cooling constraints(not shown), which exclude QCD axion masses above roughly ∼15-30 meV, depending on the UVcompletion. At even higher masses there are strong constraints from the production of DM in theearly universe, which behaves as hot DM and contributes to ∆Neff .
by axions/ALPs transitioning between energy levels of the effective gravitational atom.
Accordingly, the gravitational wave detector Advanced LIGO should be sensitive to the axion in thema . 10−10 eV region. LIGO measurements of BH spins in binary merger events could also provide
statistical evidence for the presence of an axion [354, 355]. Similar signatures could arise for supermassive and intermediate mass BHs for particles with masses . 10−15 eV. Gravitational waves fromsuch sources could be detected at lower-frequency observatories such as LISA (Laser InterferometerSpace Antenna). First attempts to use LIGO/Virgo data to search for monochromatic signaturesof axion superradiance were recently made in [356, 357].

90.5 Cosmic Axions
90.5.1 Cosmic axion populations
There are two distinct populations of cosmic relic axion popoulations: a non-thermal one
behaving as CDM, and a thermal one comprising a HDM component, in analogy to massive
neutrinos. For ma . 0.01 eV, thermal axions are dominantly produced by processes involving
quarks and gluons [358, 359], while, for larger masses, the dominant thermalization process is
π + π ↔ π + a [173, 360, 361]. A number of evaluations exploiting cosmological precision data havefound restrictive constraints on a possible HDM fraction that translate into an upper bound on
the axion mass, ma . 1 eV, if a LO axion-pion chiral effective field theory (EFT) analysis of theaxion-pion thermalization rate is used [362–365]. Recently, it was found that the NLO contribution
exceeds the LO contributions for masses below ma . 1.2 (0.12/Caπ ) eV [366]. Therefore, in order
to assess the reach in sensitivity of future cosmological data sets, one has to improve the EFT description or to compute axion-pion scattering via lattice QCD techniques. Alternatively, recently
Ref. [367] used pion-pion scattering data to overcome the EFT description issues and found the
31st May, 2024

17

90. Axions and Other Similar Particles

constraint ma . 0.24 eV, see Fig. 90.4.
For ma & 10 eV, axions may decay faster than the age of the Universe (see Eq. (90.7)), dependingon the decay constant, which would remove the cosmic axion population while injecting photons.
If the axions were in thermal equilibrium in the early Universe, which depends on the inflationary
reheat temperature and assumptions about the pre-BBN cosmology [368,369], this excess radiation
provides additional limits on the axion- or ALP-photon coupling up to very large masses [368,369].
Such photons could contribute to the extragalactic background light (EBL), could ionize primordialhydrogen and thus contribute to the optical depth after recombination, or could spoil the agreementof big bang nucleosynthesis (BBN) with observations. The corresponding up-to-date bounds from
Refs. [166, 167] are displayed in Fig. 90.1. It has recently been shown that there is an irreducible
axion background [168] that arises from axion freeze-in before BBN; decays of that axion population
provide strong constraints on axions with masses above roughly 100 eV (see Fig. 90.1). For highenough decay constants, high-mass axions (ma & 10 eV) can account for the DM abundance throughthe misalignment mechanism, described in more detail below, though additional entropy dilution
or fine-tuning is needed to avoid overproducing the DM abundance [370] (see also [371] for heavy
axion production through lepton-flavor-violating decays). The decay of such high-mass axions tophoton pairs could leave narrow spectral features in e.g. optical or X-ray backgrounds [126, 138–
140, 161, 163, 372, 373] (see Fig. 90.1).
The main cosmological interest in axions at present derives from their possible role as CDM.
In addition to thermal processes, axions are abundantly produced by the misalignment (MIS)
mechanism [374–376]. The axion DM abundance crucially depends on the cosmological history.
Let us first consider the so called pre-inflationary PQ symmetry breaking scenario, in which the PQ
symmetry is broken before and during inflation and not restored afterwards. After the breakdownof the PQ symmetry, the axion field relaxes somewhere in the bottom of the “wine-bottle-bottom”
potential. Near the QCD epoch, topological fluctuations of the gluon fields such as instantons
explicitly break the PQ symmetry. This tilting of the “wine-bottle-bottom” drives the axion field
toward the CP -conserving minimum, thereby exciting coherent oscillations of the axion field that
ultimately represent a condensate of CDM. The fractional cosmic mass density in this homogeneous
field mode, created by the MIS mechanism, is [33, 377–379],
1.165
fa
F Θi2
9 × 1011 GeV
6 µeV 1.165≈ 0.12F Θi2 ,
ma

ΩaMIS h2 ≈ 0.12



(90.22)where h is the present-day Hubble expansion parameter in units of 100 km s−1 Mpc−1 , and −π ≤Θi ≤ π is the initial “misalignment angle” relative to the CP -conserving position attained in
the causally connected region which evolved into today’s observable Universe. F = F (Θi , fa )is a factor accounting for anharmonicities in the axion potential. For F Θi2 = O(1), ma shouldbe above ∼ 6 µeV in order that the cosmic axion density does not exceed the observed CDM
density, ΩCDM h2 = 0.12. However, much smaller axion masses (much higher PQ scales) are still
possible if entropy is diluted for example by the late decay of a scalar condensate (see for example[380] and references therein) or the initial value Θi just happens to be small enough in today’sobservable Universe (“anthropic axion window” [381]). In the latter cosmological scenario, however,quantum fluctuations of the axion field during inflation are expected to lead to isocurvature density
fluctuations which get imprinted to the temperature fluctuations of the CMB [382,383]. Their nonobservation puts severe constraints on the Hubble expansion rate HI during inflation [384–389],
31st May, 2024

18

90. Axions and Other Similar Particles

which read, in the simplest cosmological inflationary scenario,
HI . 5.7 × 108 GeV



5 neV
ma

0.4175,(90.23)

if axions represent all of DM. In Ref. [390] an alternative to the MIS mechanism was proposed: theso-called kinetic MIS mechanism. In this case, the axion field is assumed to have an initial velocity
which may be generated, e.g., by a hypothesized explicit breaking of the axion shift symmetry in theearly universe. The amount of QCD axion dark matter generated by the kinetic MIS mechanism
can fit the observed dark matter abundance for any fa . 1.5 × 1011 GeV, down to the minimum
value allowed by the SN 1987A constraint.
In the above prediction of the fractional cosmic mass density in axions, the exponent, 1.165,
arises from the non-trivial temperature dependence of the topological susceptibility χ(T ) = m2A (T )fA2
at temperatures slighty above the QCD quark-hadron phase transition. Lattice QCD calculations of
this exponent [33, 343,345, 391–393], but also Ref. [344], found it to be remarkably close to the prediction of the dilute instanton gas approximation [394] which was previously exploited. Therefore,
the state-of-the-art prediction of the axion mass relevant for DM for a fixed initial misalignment
angle Θi differs from the previous prediction by just a factor of order one.
In the post-inflationary PQ symmetry breaking scenario, on the other hand, Θi will take on
different values in different patches of the present Universe. The average contribution is [33,377–379]ΩaMIS h2 ≈ 0.1230 µeVma1.165.

(90.24)The decay of cosmic strings and domain walls gives rise to a further population of CDM axions,whose abundance suffers from significant uncertainties [341, 347–349, 378, 379, 395–403] which arise
from the difficulty in understanding the energy loss process of topological defects and the generated
axion spectrum in a quantitative way. In fact, in the present state-of-the-art it is still possible that
the CDM contribution from the decay of topological defects is subdominant [347] or overwhelmingly
large [348] in comparison to the one from the MIS mechanism. Correspondingly, the plausible rangeof axion masses providing all of CDM in scenarios with postinflationary PQ symmetry breaking is
still rather large, namely [347, 348]
ma ≈ 26 µeV − 0.5 meV,(90.25)for models with short-lived (requiring unit color anomaly N = 1) domain walls, such as the KSVZ
model. On the other hand, the most recent adaptive mesh refinement axion string simulations,which are able to evolve over larger dynamic ranges than static lattice simulations, suggest themass range ma ≈ 40 − 180 µeV [341]. For models with long-lived (N > 1) domain walls, such as
an accidental DFSZ model [404], where the PQ symmetry is broken by higher dimensional Planck
suppressed operators, the mass is predicted to be significantly higher [287, 349, 404–406],
ma ≈ (0.58 − 130) meV .

(90.26)

However, the upper part of the predicted range is in conflict with stellar energy-loss limits on theaxion. The pre- and post-inflationary mass predictions are summarized in Fig. 90.4.
In this post-inflationary PQ symmetry breakdown scenario, the spatial axion density variations
are large at the QCD transition, and they are not erased by free streaming. Gravitationally bound“axion miniclusters” form before and around matter-radiation equality [407–409]. A significant
fraction of CDM axions can reside in these bound objects [400, 410]. Remarkably, the minicluster
31st May, 2024

90. Axions and Other Similar Particles

19

fraction can be bounded by gravitational lensing [411–413], although more simulations are required
to understand whether miniclusters are dense enough and survive in sufficient quantities for lensing
bounds to apply.
The non-thermal production mechanisms attributed to axions are generic to light bosonic weaklyinteracting particles such as ALPs [18]. The relic abundance is set by the epoch when the axion
mass becomes significant, 3H(t) ≈ ma (t), and ALP field oscillations begin. For ALPs to contributeto the DM density this epoch must precede that of matter radiation equality. For a temperature
independent ALP mass this leads to the bound:−28

ma & 7 × 10

eV

Ωm h2
0.15

!1/2 

1 + zeq
3.4 × 103

3/2.

(90.27)

ALPs lighter than this bound are allowed if their cosmic energy density is small, but they arequite distinct from other forms of DM [414]. Ignoring anharmonicities in the ALP potential, andtaking the ALP mass to be temperature independent, the relic density in DM ALPs due to the
MIS mechanism is given by
ma
MIS 2
ΩALP
h =0.12
4.7 × 10−19 eV1/2 

fa
16
10 GeV

2

Ωm h2
0.15

!3/4 

1 + zeq
3.4 × 103

−3/4

Θi2 .

(90.28)An ALP decay constant near the GUT scale gives the correct relic abundance for ultralight ALPs
(ULAs) with mULA ≈ 10−19 eV [415, 416]. ULAs encompass the entire Earth in a single Compton
wavelength, and for large occupation numbers are modelled as a coherent classical field. The
2 ,coherence time is determined by the mass and virial velocity in the Milky Way, τcoh ∼ 1/mULA vvir
with the detailed properties described by a stochastic model with an approximately Rayleigh Jeans
distribution [417]. Natural models for ULAs can be found in string and M-theory compactifications[7, 8, 10–15], in field theory with accidental symmetries [418, 419], or new hidden strongly coupled
sectors [420, 421].
In addition to the gravitational potential energy, the ULA field also carries gradient energy.
On scales where the gradient energy is non-negligible, ULAs acquire an effective pressure and do
not behave as CDM. The gradient energy opposes gravitational collapse, leading to a Jeans scale
below which perturbations are stable [422]. The Jeans scale suppresses linear cosmological structureformation relative to CDM [423–425]. The Jeans scale at matter-radiation equality in the case that
ULAs make up all of CDM is:−1

kJ,eq = 8.7 Mpc



1 + zeq
3.4 × 103

−1/4

MIS
h2 ΩALP
0.12!1/4 

mULA
10−22 eV

1/2.

(90.29)On non-linear scales the gradient energy leads to the existence of a class of pseudo-solitons known
as oscillatons, or axion stars [426]. Axion stars are expected to form in all cosmological scenarios,and for all types of ALPs, including the QCD axion [427–429]. Some axion stars may explode into
radio photons, heating the interstellar medium [104].
Cosmological and astrophysical observations are consistent with the CDM model, and departures from it are only allowed on the scales of the smallest observed DM structures withM ∼ 106−8 M . The CMB power spectrum and galaxy auto-correlation power spectrum limit
the ULA mass to mULA & O(few) × 10−24 eV from linear theory of structure formation [414, 430].
Analytic models [431] and N -body simulations [432] for non-linear structures show that halo formation is suppressed in ULA models relative to CDM. This leads to constraints on the ULA massof mULA > 10−22 eV from observations of high-z galaxies [432–434], and mULA > 2 × 10−20 eV
31st May, 2024

20

90. Axions and Other Similar Particles

from the Lyman-alpha forest flux power spectrum [435]. Including the effects of anharmonicities on
structure formation with ALPs can weaken these bounds if the misalignment angle Θi ≈ π [436].
A comprehensive study of Milky Way satellites by the DES collaboration resulted in the boundmULA > 2.9 × 10−21 eV [437].
Cosmological simulations that treat gradient energy in the ULA field beyond the N -body approximation have just recently become available [427, 438–440], and show, among other things,
evidence for the formation of axion stars in the centres of ULA halos (various consequences ofaxion stars are considered in Refs. [441]). These central axion stars have been conjectured to play arole in the apparently cored density profiles of dwarf spheroidal galaxies, and other central galactic
regions [127, 427, 442–446]. However, the relationship between the halo mass and the axion starmass [447] leads to problems with this scenario in some galaxies [448–450]. It should be emphasisedthat many of the conclusions about the role of ULA axion stars in galactic dynamics are based on
use of simulation results that do not contain baryons and feedback could be important [451–453].
Inside DM halos the axion gradient energy causes coherence on the de Broglie wavelength andfluctuations on the coherence time [427, 454]. These fluctuations can be thought of as short-lived
quasiparticles and lead to relaxation processes that can be described statistically [416, 455] (thisrelaxation processes also leads to the gravitational condensation of axion stars [428]). The typicalrelaxation time is:10t ∼ 10mULA
years
10−22 eV

3 v
100 km s−1

2 

r
5 kpc

4

,

(90.30)where v and r are the velocity and radius of the orbit in the host DM halo.
Relaxation processes such as these are not observed in galaxies, though there are some circumstances where they may be desirable [416]. An absence of observed relaxation can be used
to set limits on the ULA mass. An absence of Milky Way disk thickening excludes mULA >0.6 × 10−22 eV [456], while stellar streams give the stronger bound mULA > 1.5 × 10−22 eV [457].
The survival of the old star cluster in Eridanus II [458] excludes the range of masses 10−21 eV .
mULA . 10−19 eV [459]. Recently Ref. [460] finds that ULA DM is excluded for mULA . 3 × 10−19
eV at 99% CL because such DM would kinematically heat the stars in the Segue I and Segue II
ultra-faint dwarf galaxies to a level inconsistent with their observed dynamics.
Finally, one should note that the beyond-CDM physics of ULAs (Jeans scale, relaxation, axion
star formation) of course also applies to the QCD axion on smaller length scales. This is of particularinterest inside axion miniclusters [407, 408, 428, 429].
90.5.2 Electron recoil searches
In a DM direct detection experiment, a DM ALP featuring a coupling to the electron canbe absorbed by the target material, leading to a mono-energetic electronic recoil signal peakedat ma . This mechanism allowed the EDELWEISS [461], PandaX [221], SuperCDMS [222] andXENON1T [462] collaborations to put the bounds on the axion-electron coupling displayed inFig. 90.2 in the keV mass range.
As discussed in the last sub-section, additionally dynamics
beyond the standard misalignment mechanism are needed to explain the axion DM abundance forkeV-scale axion masses (e.g., [370,371]). Moreover, such models are subject to stringent constraints
from axion decays to photons [370].
90.5.3 Telescope searches
The two-photon decay is extremely slow for axions with masses in the CDM regime, but could
be detectable for eV masses. The signature would be a quasi-monochromatic emission line fromgalaxies and galaxy clusters. The expected optical line intensity for DFSZ axions is similar to thecontinuum night emission. A search for optical line emission in two Abell clusters using spectra
31st May, 2024

21

90. Axions and Other Similar Particles

from the VIMOS (Visible Multi-Object Spectrograph) integral field unit at the Very Large Telescope(VLT) excludes axions and ALPs with a two photon coupling bigger than ∼ 5 × 10−12 GeV−1 in themass range between 4.5 and 5.5 eV [163], see Fig. 90.1. Spectral data on the dwarf spheroidal galaxy
Leo T from the Multi Unit Spectroscopic Explorer (MUSE) at the VLT improve these constraints
by more than an order of magnitude for ALP masses between 2.7 and 5.3 eV [162], see Fig. 90.1.
Very low-mass axions in halos produce a weak quasi-monochromatic radio line. Virial velocities
in undisrupted dwarf galaxies are very low, and the axion decay line would therefore be extremely
narrow. A search with the Haystack radio telescope on three nearby dwarf galaxies gave a limit|gaγγ | < 1.0 × 10−9 GeV−1 at 96% CL for 298 < ma < 363 µeV [161]. However, this combinationof ma and gaγγ does not exclude plausible axion models.
A monochromatic signal is also produced in the conversion of DM axions in the background ofslowly varying galactic B-fields [463]. The signal is, however, sensitive to magnetic field power on
the scale of the axion mass [464]. Present and future radio telescopes appear to be able to probe
ALP DM in the mass range 0.1 − 100 µeV for couplings gaγγ & 10−13 GeV−1 [464] – unfortunately
not reaching down to the benchmark QCD axion sensitivity.
Resonant conversion of QCD axion or ALP DM in NS magnetospheres may give a detectablesignal from individual NSs and populations of NSs for axion masses in the µeV range [465, 466].
Recent analyses of radio data in the frequency range 1-40 GHz from several NSs have found noevidence for a narrow peak predicted from this mechanism and therefore put bounds on the axion-photon coupling around 10−11 GeV−2 for ma ∼ 10 µeV [133–136], see Fig. 90.1. However, theselimits may still suffer from uncertainties because the line intensity is difficult to predict in detail inthe complicated environments of NSs [135, 467–470]. Still, next-generation radio telescopes such as
the Square Kilometer Array (SKA) may reach sensitivity to QCD axion-strength couplings [136].
Stimulated ALP decays in high radiation environments may be detectable, by e.g. the future SKA,
down to gaγγ & 10−11 GeV−1 , for masses between µeV and 0.1 meV [471]. Furthermore, in condensed
ALP dark matter structures such as ALP stars, a parametric instability may leadh to anRexponentiali
1/2
enhancement of the photon flux from ALP-photon conversion by a factor ∼ exp |gaγγ | dsρa (s) ,where the integral is along any photon trajectory through the ALP overdensity [472, 473].
Photon propagation on an ULA DM background can induce birefringence that can be comparedwith upper limits from the CMB [106, 141, 474] and may also be probed with other sources such aspulsars [475].
90.5.4 Microwave cavity experiments
Over a large part of the plausible ma range for CDM, Galactic halo axions may be detected bytheir resonant conversion into a quasi-monochromatic microwave signal in a high-Q electromagnetic
cavity permeated by a strong, static B field [9, 476, 477]. The cavity frequency is tunable, andthe signal is maximized when the cavity resonant frequency is the total axion energy, rest massplus kinetic energy, of ν = (ma /2π) [1 + O(10−6 )], the width above the rest mass representing theaxions’ virial distribution in the galaxy near Earth. The frequency spectrum may also containfiner structure from axions more recently fallen into the galactic potential and not yet completely
virialized [478, 479] or otherwise incompletely thermalized.
The feasibility of this technique was established in early experiments (RBF (Rochester-BrookhavenFlorida) and UF (University of Florida)) of relatively small sensitive volume, O(1 liter), with HFETbased microwave amplifiers, setting limits in the range 4.5 < ma < 16.3 µeV [91,95,482], but lacking
by 2–3 orders of magnitude the sensitivity required to detect realistic axions, see Fig. 90.5.
Later, the first generation of ADMX (B ∼ 8 T, V ∼ 200 liters) achieved sensitivity to KSVZ
axions, assuming they saturate the local DM density and are well virialized, over the mass range 1.9–
3.3 µeV [485]. Should halo axions have a significant narrow component not yet virialized, ADMX
31st May, 2024

90. Axions and Other Similar Particles

22

10−9

103

0
Frequency [MHz]

104

RADES

ORGAN

QUAX-aγ

HAYSTAC

HAYSTAC

CAPP

CAPP

CAPP

CAPP

10−14

TASEH CAPP

CAPP

10−13

GrAHal10−12CAST-CAPP

ADMX| gaγγ | [GeV−1]

10−11

ORGAN

10−10

E/ N

= 44/

3

KSVZ
DFSZ
E/ N

= 5/3

10−15
10−6

10−5

m a [eV]10−4

Figure 90.5: Exclusion plot for ALP-photon coupling with closeup on the parameter space of RF
cavity experiments as described in the text. This is a zoom-in of Fig. 90.1 that highlights regions
probed by axion DM direct detection experiments. In particular, note that all of the terrestrial
experiments shaded in red, except that of CAST, assume that the axion is 100% of the local DM.
Figure courtesy of Ciaran O’Hare [61], including data from Refs. [43, 64–68, 76, 78, 81–84, 86, 87, 91,
93, 99, 122, 123, 145, 216, 480–484]

was sensitive to DFSZ axions over the entire mass range [486]. The corresponding 90% CL exclusion
regions shown in Fig. 90.5 assume a local CDM density of 7.5 × 10−25 g cm−3 (450 MeV cm−3 ).
Somewhat later, the ADMX experiment commissioned an upgrade [64] that replaced the microwave HFET amplifiers by near-quantum-limited low-noise dc SQUID microwave amplifiers [487]and, more recently, with Josephson parametric amplifiers (related to the earlier dc SQUID amplifiers), also with noise near-quantum-limited [481]. With its large volume and low noise, ADMX
has achieved an unprecedented axion DM sensitivity in the mass range between 2.7 and 4.2 µeV[66–68, 480], down to the DFSZ benchmark axion-photon coupling over much of the range, seeFig. 90.5. This apparatus is also sensitive to certain other hypothetical light bosons, such as
hidden photons or chameleons, over a limited parameter space [18, 488, 489].
ADMX continues to scan at DFSZ sensitivity, and has since been joined by an array of haloscopes. One of the CAPP experiments has also achieved DFSZ sensitivity over a small range of
frequencies near 4.55 µeV [76]. A number of other experiments from the CAPP group have operated
at higher frequencies, many with KSVZ or near KSVZ sensitivity. [72–74,74,75] The HAYSTAC experiment also operates at or near KSVZ sensitivity and was the first to demonstrate near-quantum
limited noise using a Josephson parametric amplifier [82, 490], and demonstrated ‘state-squeezing’
31st May, 2024

23

90. Axions and Other Similar Particles

to increase scan speed by nearly a factor of 2. [83, 84] Other haloscopes operating at or near KSVZ
over narrow bands include TASEH [93] and QUAX-aγ [90]. The ORGAN experiment is the highest frequency haloscope, operating with a small cavity and sensitive to axion-like-particle masses
up to 67.1 µeV, though not yet with sensitivity to the KSVZ model. [86, 87] There are also a
number of other haloscopes sensitive to axion-like-particles with couplings above those predictedby KSVZ. [65, 81, 88, 89, 483] Fig. 90.5 shows the exclusions on axion-photon coupling from thesehaloscopes to date.
90.5.5 New concepts for axion DM direct detection
Other new concepts for searching for axion DM are also being investigated. “Plasma haloscopes” are under development by the ALPHA consortium [491]. This concept uses a metamaterial
consisting of a parallel-wire array, thereby inducing an effective photon mass which is tunable byadjusting wire separation, and sensitive to axion masses 35–400 µeV. Another detector concept
exploits the fact that a magnetized mirror would radiate photons in the background of axion DM,
which could be collected like in a dish antenna [492]. The proposed MADMAX experiment willplace a stack of dielectric layers in a magnetic field in order to resonantly enhance the photon
signal, aiming a sensitivity to probe the mass range 40 µeV . ma . 200 µeV [493, 494]. Opticaldielectric haloscopes with single photon signal detection have been proposed to search for axions in
the 50 meV – 10 eV mass range [495]. Other semi-resonant or nonresonant axion haloscope ideas
to read high mass axions that are based around similar principles but novel configurations include
BREAD [496] and CADEx [497].
Absorption of axions on molecular transitions can be sensitive to the axion pseudoscalar couplinggaN N to nucleons or the pseudoscalar coupling gaee to electrons in the 0.5 – 20 eV range [498]. It has
also been pointed out that the coupling induced by an axion field between photonic modes [96,499]
or atomic states [500] separated by an energy equal to the axion mass may be leveraged for axion
detection, though the implementation may be challenging. Certain magnetic topological insulators
are conjectured to contain axion-polaritons, quasiparticles composed of magnons and the electricfield, with magnetically tunable mass in the meV to eV range [501–503]. Axion dark matter leads
to resonant photon emission from such materials, which can be detected [504, 505].
In the intermediate mass region, neV . ma . 0.1 µeV, one may exploit a cooled LC circuit andprecision magnetometry to search for the oscillating electric current induced by DM axions in astrong magnetic field [506,507]. A number of small-scale pathfinder experiments have implemented
this approach: ABRACADABRA [62, 63] used a nonresonant configuration in a toroidal magnet
for a broadband search, ADMX-SLIC [70] used a resonant configuration in a solenoid magnet for anarrowband search, SHAFT [92] used a nonresonant configuration in a toroidal magnet enhancedwith a ferromagnetic core, BASE [80] used antiprotons in a Penning trap as the LC circuit, and
DANCE [508] used a laser interferometer. The exclusion limits from these experiments are shownin Fig. 90.1; none are yet sensitive to the QCD axion. Future work in this direction is expected tohave much more competitive limits [509, 510].
The oscillating Galactic DM axion field induces oscillating nuclear electric dipole moments(EDMs) [35],pdN (t) = gaN γ 2ρaDM cos(ma t)/ma ,(90.31)
where gaN γ is the coupling of the axion to the nucleon EDM operator, defined in Eq. (90.4). An
analysis of the ratio of spin-precession frequencies of stored ultracold neutrons and 199 Hg atoms
measured by neutron EDM experiments for an axion-induced oscillating neutron EDM revealed
no signal consistent with axion DM, excluding a sizeable region of parameter space in the mass
region 10−24 eV ≤ ma ≤ 10−17 eV [40], which surpass the limits on anomalous energy loss of
SN 1987A by more than seven orders of magnitude and are competitive with the ones from the
31st May, 2024

90. Axions and Other Similar Particles

24

requirement of successful BBN established in [38].1 In fact, the oscillating dark matter axion field
could increase the neutron-proton mass difference at neutron freeze-out and thus result in theunderproduction of 4 He during BBN. The oscillating EDMs cause also the precession of nuclear
spins in a nucleon spin polarized sample in the presence of an electric field. The resulting transverse
magnetization can be searched for by exploiting magnetic-resonance (MR) techniques, which aremost sensitive in the range of low oscillation frequencies corresponding to sub-neV axion masses.
The aim of the corresponding Cosmic Axion Spin Precession Experiment (CASPEr) [36] is toprobe axion DM in the anthropic window, fa & 1015 GeV (ma . neV), motivated from Grand
Unification [511–514]. There are two interactions probed through MR: the electric dipole coupling
as searched for by CASPEr-electric (with first result presented in [39]) and an interaction between
the axion field gradient and the nuclear spin, which is aimed for by CASPEr-Gradient. In themeantime, the latter has been explored through comagnetometry between a variety of nuclei: H12 C in CASPEr-ZULF [246, 247], Xe-Rb in NASDUCK [515], and K-3 He [251, 252]. The exclusions
from these searches are shown in Fig. 90.3. Sub-µeV ALP masses can also be probed by using thestorage ring EDM method proposed in Ref. [516] which exploits a combination of B and E-fields to
produce a resonance between the g − 2 spin precession frequency and the DM ALP field oscillation
frequency. This method, however, does not reach the sensitivity to probe the QCD axion prediction
for gaN γ . An eventually non-zero axion electron coupling gaee will lead to an electron spin precession
about the axion DM wind [517, 518]. The QUAX a-e experiment exploits MR inside a magnetizedmaterial [519]. Because of the higher Larmor frequency of the electron, it is sensitive in the classic
window. Its first run established the bound in the mass range 42.4 to 43.2 µeV [227], slightly better
than the solar ν bound, shown in Fig. 90.2.

90.6 Conclusions
There is a strengthening physics case for very weakly coupled light particles beyond the Standard Model. The elegant solution of the strong CP problem proposed by Peccei and Quinn yields
a particularly strong motivation for the axion. In many theoretically appealing ultraviolet completions of the Standard Model axions and ALPs occur automatically. Moreover, they are natural
CDM candidates. Perhaps the first hints of their existence have already been seen in the anomalous excessive cooling of stars and the anomalous transparency of the Universe for very high energy
gamma rays. Interestingly, a significant portion of previously unexplored, but phenomenologicallyvery interesting and theoretically very well motivated axion and ALP parameter space can be explored in the foreseeable future by a number of terrestrial experiments searching for axion/ALP
DM, for solar axions/ALPs, and for light apparently shining through a wall.

90.7 Acknowledgements
It is a pleasure to thank Masha Baryakhtar, Francesca Calore, Luca Di Luzio, Andrew Geraci,
Maurizio Giannotti, Igor Irastorza, David J.E. Marsh, Alessandro Mirizzi, Ciaran O’Hare, Georg
Raffelt, Ken’ichi Saikawa, Yannis Semertzidis, Guenter Sigl, Sergey Troitsky, and Lindley Winslow
for discussions, suggestions, and comments on this review. Particular thanks to Ciaran O’Hare formaintaining a publicly accessible collection of axion plots and providing updates to accommodate
this review [61].
References[1] R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977).
[2] R. D. Peccei and H. R. Quinn, Phys. Rev. D16, 1791 (1977).
[3] S. Weinberg, Phys. Rev. Lett. 40, 223 (1978).
1

These limits are still to the left of the canonical QCD axion line. However, as already mention in non-minimalmodels where the QCD axion is a mediator between strongly interacting hidden sectors enjoying a discrete, ZN , shift
symmetry, the QCD axion line can be shifted to the left in discrete steps, without any fine tuning [57, 58, 421].
31st May, 2024

25

90. Axions and Other Similar Particles[4] F. Wilczek, Phys. Rev. Lett. 40, 279 (1978).
[5] Y. Chikashige, R.N. Mohapatra, and R.D. Peccei, Phys. Lett. B98, 265 (1981).
[6] G. B. Gelmini and M. Roncadelli, Phys. Lett. 99B, 411 (1981).
[7] E. Witten, Phys. Lett. B 149, 351 (1984).
[8] P. Svrcek and E. Witten, JHEP 06, 051 (2006), [hep-th/0605206].
[9] P. Sikivie, Phys. Rev. Lett. 51, 1415 (1983) and Erratum ibid., 52, 695 (1984).
[10] J. P. Conlon, JHEP 05, 078 (2006), [hep-th/0602233].
[11] K.-S. Choi et al., Phys. Lett. B675, 381 (2009), [arXiv:0902.3070].
[12] A. Arvanitaki et al., Phys. Rev. D81, 123530 (2010), [arXiv:0905.4720].
[13] B. S. Acharya, K. Bobkov and P. Kumar, JHEP 11, 105 (2010), [arXiv:1004.5138].
[14] M. Cicoli, M. Goodsell and A. Ringwald, JHEP 10, 146 (2012), [arXiv:1206.0819].
[15] J. Halverson, C. Long and P. Nath, Phys. Rev. D96, 5, 056025 (2017), [arXiv:1703.07779].
[16] M. Demirtas et al., JHEP 04, 138 (2020), [arXiv:1808.01282].
[17] A. E. Nelson and J. Scholtz, Phys. Rev. D 84, 103501 (2011), [arXiv:1105.2812].
[18] P. Arias et al., JCAP 1206, 013 (2012), [arXiv:1201.5902].
[19] P. W. Graham, J. Mardon and S. Rajendran, Phys. Rev. D 93, 10, 103520 (2016),[arXiv:1504.02102].
[20] J. Jaeckel and A. Ringwald, Ann. Rev. Nucl. Part. Sci. 60, 405 (2010), [arXiv:1002.0329].
[21] A. Ringwald, Phys. Dark Univ. 1, 116 (2012), [arXiv:1210.5081].
[22] J. Jaeckel, Frascati Phys. Ser. 56, 172 (2012), [arXiv:1303.1821].
[23] A. Caputo et al., Phys. Rev. D 104, 9, 095029 (2021), [arXiv:2105.04565].
[24] M. Pospelov and A. Ritz, Nucl. Phys. B573, 177 (2000), [hep-ph/9908508].
[25] J. Liang et al. (2023), [arXiv:2301.04331].
[26] C. A. Baker et al., Phys. Rev. Lett. 97, 131801 (2006), [hep-ex/0602020].
[27] C. Abel et al. (nEDM), Phys. Rev. Lett. 124, 8, 081803 (2020), [arXiv:2001.11966].
[28] J. Alexander et al. (2022), [arXiv:2205.00830].
[29] H. Georgi, D. B. Kaplan and L. Randall, Phys. Lett. 169B, 73 (1986).
[30] R. J. Crewther, Phys. Lett. 70B, 349 (1977).
[31] P. Di Vecchia and G. Veneziano, Nucl. Phys. B171, 253 (1980).
[32] M. Gorghetto and G. Villadoro, JHEP 03, 033 (2019), [arXiv:1812.01008].
[33] S. Borsanyi et al., Nature 539, 7627, 69 (2016), [arXiv:1606.07494].
[34] L. Caloni et al., JCAP 09, 021 (2022), [arXiv:2205.01637].
[35] P. W. Graham and S. Rajendran, Phys. Rev. D88, 035023 (2013), [arXiv:1306.6088].
[36] D. Budker et al., Phys. Rev. X4, 2, 021030 (2014), [arXiv:1306.6089].
[37] I. Schulthess et al., Phys. Rev. Lett. 129, 19, 191801 (2022), [arXiv:2204.01454].
[38] K. Blum et al., Phys. Lett. B 737, 30 (2014), [arXiv:1401.6460].
[39] D. Aybas et al., Phys. Rev. Lett. 126, 14, 141802 (2021), [arXiv:2101.01241].
[40] C. Abel et al., Phys. Rev. X7, 4, 041034 (2017), [arXiv:1708.06367].
[41] T. S. Roussy et al., Phys. Rev. Lett. 126, 17, 171301 (2021), [arXiv:2006.15787].
31st May, 2024

26

90. Axions and Other Similar Particles[42] S. Karanth et al. (JEDI Collaboration), Phys. Rev. X 13, 031004 (2023), URL https://link.aps.org/doi/10.1103/PhysRevX.13.031004.
[43] X. Zhang et al., Phys. Rev. Lett. 130, 251002 (2023), URL https://link.aps.org/doi/
10.1103/PhysRevLett.130.251002.
[44] G. Lucente et al., Phys. Rev. D 105, 12, 123020 (2022), [arXiv:2203.15812].
[45] J. E. Kim, Phys. Rev. Lett. 43, 103 (1979).
[46] M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B166, 493 (1980).
[47] M. Dine, W. Fischler and M. Srednicki, Phys. Lett. 104B, 199 (1981).
[48] A. R. Zhitnitsky, Sov. J. Nucl. Phys. 31, 260 (1980), [Yad. Fiz.31,497(1980)].
[49] L. Di Luzio et al., Phys. Rept. 870, 1 (2020), [arXiv:2003.01100].
[50] J. E. Kim and G. Carosi, Rev. Mod. Phys. 82, 557 (2010), [arXiv:0807.3125].
[51] G. Grilli di Cortona et al., JHEP 01, 034 (2016), [arXiv:1511.02867].
[52] J. E. Kim, Phys. Rev. D58, 055006 (1998), [hep-ph/9802220].
[53] L. Di Luzio, F. Mescia and E. Nardi, Phys. Rev. Lett. 118, 3, 031801 (2017),[arXiv:1610.07593].
[54] L. Di Luzio, F. Mescia and E. Nardi, Phys. Rev. D 96, 7, 075003 (2017), [arXiv:1705.05370].
[55] M. Farina et al., JHEP 01, 095 (2017), [arXiv:1611.09855].
[56] P. Agrawal et al., JHEP 02, 006 (2018), [arXiv:1709.06085].
[57] A. Hook, Phys. Rev. Lett. 120, 26, 261802 (2018), [arXiv:1802.10093].
[58] L. Di Luzio et al., JHEP 05, 184 (2021), [arXiv:2102.00012].
[59] A. V. Sokolov and A. Ringwald, JHEP 06, 123 (2021), [arXiv:2104.02574].
[60] J. Diehl and E. Koutsangelas, Phys. Rev. D 107, 9, 095020 (2023), [arXiv:2302.04667].
[61] C. O’Hare, cajohare/AxionLimits: AxionLimits (2023), URL https://doi.org/10.5281/
zenodo.3932430.
[62] J. L. Ouellet et al. (ABRACADABRA), Phys. Rev. Lett. 122, 12, 121802 (2019),[arXiv:1810.12257].
[63] C. P. Salemi et al., Phys. Rev. Lett. 127, 8, 081801 (2021), [arXiv:2102.06722].
[64] S. J. Asztalos et al. (ADMX), Phys. Rev. Lett. 104, 041301 (2010), [arXiv:0910.5914].
[65] C. Boutan et al. (ADMX), Phys. Rev. Lett. 121, 26, 261302 (2018), [arXiv:1901.00920].
[66] N. Du et al. (ADMX), Phys. Rev. Lett. 120, 15, 151301 (2018), [arXiv:1804.05750].
[67] T. Braine et al. (ADMX), Phys. Rev. Lett. 124, 10, 101303 (2020), [arXiv:1910.08638].
[68] C. Bartram et al. (ADMX Collaboration), Phys. Rev. Lett. 127, 261803 (2021), URL https://link.aps.org/doi/10.1103/PhysRevLett.127.261803.
[69] C. Bartram et al., Review of Scientific Instruments 94, 4, 044703 (2023), ISSN 0034-6748,
URL https://doi.org/10.1063/5.0122907.
[70] N. Crisosto et al., Phys. Rev. Lett. 124, 24, 241101 (2020), [arXiv:1911.05772].
[71] S. Lee et al., Phys. Rev. Lett. 124, 10, 101802 (2020), [arXiv:2001.05102].
[72] J. Jeong et al., Phys. Rev. Lett. 125, 22, 221302 (2020), [arXiv:2008.10141].
[73] O. Kwon et al. (CAPP), Phys. Rev. Lett. 126, 19, 191802 (2021), [arXiv:2012.10764].
[74] Y. Lee et al., Phys. Rev. Lett. 128, 24, 241805 (2022), [arXiv:2206.08845].
31st May, 2024

27

90. Axions and Other Similar Particles[75] J. Kim et al., Phys. Rev. Lett. 130, 091602 (2023), URL https://link.aps.org/doi/10.
1103/PhysRevLett.130.091602.
[76] A. K. Yi et al., Phys. Rev. Lett. 130, 071002 (2023), URL https://link.aps.org/doi/10.
1103/PhysRevLett.130.071002.
[77] B. Yang et al. (2023), [arXiv:2308.09077].
[78] C. M. Adair et al., Nature Commun. 13, 1, 6180 (2022), [arXiv:2211.02902].
[79] Y. Oshima et al. (2023), [arXiv:2303.03594].
[80] J. A. Devlin et al., Phys. Rev. Lett. 126, 4, 041301 (2021), [arXiv:2101.11290].
[81] T. Grenet et al. (2021), [arXiv:2110.14406].
[82] L. Zhong et al. (HAYSTAC), Phys. Rev. D 97, 9, 092001 (2018), [arXiv:1803.03690].
[83] K. M. Backes et al. (HAYSTAC), Nature 590, 7845, 238 (2021), [arXiv:2008.01853].
[84] M. J. Jewell et al. (HAYSTAC) (2023), [arXiv:2301.09721].
[85] J. Heinze et al. (2023), [arXiv:2307.01365].
[86] B. T. McAllister et al., Phys. Dark Univ. 18, 67 (2017), [arXiv:1706.00209].
[87] A. P. Quiskamp et al., Sci. Adv. 8, 27, abq3765 (2022), [arXiv:2203.12152].
[88] D. Alesini et al., Phys. Rev. D 99, 10, 101101 (2019), [arXiv:1903.06547].
[89] D. Alesini et al., Phys. Rev. D 103, 10, 102004 (2021), [arXiv:2012.09498].
[90] D. Alesini et al., Phys. Rev. D 106, 5, 052007 (2022), [arXiv:2208.12670].
[91] S. De Panfilis et al., Phys. Rev. Lett. 59, 839 (1987).
[92] A. V. Gramolin et al., Nature Phys. 17, 1, 79 (2021), [arXiv:2003.03348].
[93] H. Chang et al. (TASEH), Phys. Rev. Lett. 129, 11, 111802 (2022), [arXiv:2205.05574].
[94] A. Arza et al., Phys. Rev. D 105, 9, 095007 (2022), [arXiv:2112.09620].
[95] C. Hagmann et al., Phys. Rev. D42, 1297 (1990).
[96] C. A. Thomson et al., Phys. Rev. Lett. 126, 8, 081803 (2021), [Erratum: Phys.Rev.Lett. 127,
019901 (2021)], [arXiv:1912.07751].
[97] C. A. Thomson et al., Phys. Rev. D 107, 112003 (2023), URL https://link.aps.org/doi/
10.1103/PhysRevD.107.112003.
[98] K. Ehret et al. (ALPS), Phys. Lett. B689, 149 (2010), [arXiv:1004.1313].
[99] V. Anastassopoulos et al. (CAST), Nature Phys. 13, 584 (2017), [arXiv:1705.02290].
[100] M. Betz et al., Phys. Rev. D88, 7, 075014 (2013), [arXiv:1310.8098].
[101] R. Ballou et al. (OSQAR), Phys. Rev. D92, 9, 092002 (2015), [arXiv:1506.08082].
[102] F. Della Valle et al., Eur. Phys. J. C76, 1, 24 (2016), [arXiv:1510.08052].
[103] Y. Kirita et al. (SAPPHIRES), JHEP 10, 176 (2022), [arXiv:2208.09880].
[104] M. Escudero et al. (2023), [arXiv:2302.10206].
[105] M. Xiao et al., Phys. Rev. Lett. 126, 3, 031101 (2021), [arXiv:2009.09059].
[106] P. A. R. Ade et al. (BICEP/Keck Collaboration), Phys. Rev. D 105, 022006 (2022), URL
https://link.aps.org/doi/10.1103/PhysRevD.105.022006.
[107] A. Keller et al., Astrophys. J. 927, 1, 71 (2022), [arXiv:2112.03439].
[108] M. H. Chan, Sci. Rep. 11, 20087 (2021), [arXiv:2109.11734].
[109] K. Kohri and H. Kodama, Phys. Rev. D96, 5, 051701 (2017), [arXiv:1704.05189].
31st May, 2024

28

90. Axions and Other Similar Particles[110] D. Wouters and P. Brun, Astrophys. J. 772, 44 (2013), [arXiv:1304.0989].
[111] M. C. D. Marsh et al., JCAP 1712, 12, 036 (2017), [arXiv:1703.07354].
[112] C. S. Reynolds et al., Astrophys. J. 890, 1, 59 (2020), [arXiv:1907.05475].
[113] J. S. Reynés et al., Mon. Not. Roy. Astron. Soc. 510, 1, 1264 (2021), [arXiv:2109.03261].
[114] F. Capozzi et al. (2023), [arXiv:2303.07426].
[115] H. Liu et al. (2023), [arXiv:2303.07370].
[116] B. Bolliet, J. Chluba and R. Battye, Mon. Not. Roy. Astron. Soc. 507, 3, 3148 (2021),[arXiv:2012.07292].
[117] M. A. Buen-Abad, J. Fan and C. Sun (2020), [arXiv:2011.05993].
[118] M. Ajello et al. (Fermi-LAT), Phys. Rev. Lett. 116, 16, 161101 (2016), [arXiv:1603.06978].
[119] M. Meyer and T. Petrushevska, Phys. Rev. Lett. 124, 23, 231101 (2020), [Erratum:
Phys.Rev.Lett. 125, 119901 (2020)], [arXiv:2006.06722].
[120] J. Davies, M. Meyer and G. Cotter (2022), [arXiv:2211.03414].
[121] J. L. Bernal et al. (2022), [arXiv:2208.13794].
[122] A. Ayala et al., Phys. Rev. Lett. 113, 19, 191302 (2014), [arXiv:1406.6053].
[123] M. J. Dolan, F. J. Hiskens and R. R. Volkas, JCAP 10, 096 (2022), [arXiv:2207.03102].
[124] S. Jacobsen, T. Linden and K. Freese (2022), [arXiv:2203.04332].
[125] A. Abramowski et al. (H.E.S.S.), Phys. Rev. D 88, 10, 102003 (2013), [arXiv:1311.3148].
[126] F. Calore et al., Mon. Not. Roy. Astron. Soc. 520, 3, 4167 (2023), [arXiv:2209.06299].
[127] D. Wadekar and G. R. Farrar, Phys. Rev. D 103, 123028 (2021), URL https://link.aps.
org/doi/10.1103/PhysRevD.103.123028.
[128] C. Dessert, A. J. Long and B. R. Safdi, Phys. Rev. Lett. 128, 071102 (2022), URL https://link.aps.org/doi/10.1103/PhysRevLett.128.071102.
[129] C. Dessert, D. Dunsky and B. R. Safdi, Phys. Rev. D 105, 10, 103034 (2022),[arXiv:2203.04319].
[130] M. M. Ivanov et al., JCAP 02, 059 (2019), [arXiv:1811.10997].
[131] H.-J. Li et al., Phys. Rev. D 103, 8, 083003 (2021), [arXiv:2008.09464].
[132] H.-J. Li, X.-J. Bi and P.-F. Yin, Chin. Phys. C 46, 8, 085105 (2022), [arXiv:2110.13636].
[133] J. W. Foster et al., Phys. Rev. Lett. 125, 17, 171301 (2020), [arXiv:2004.00011].
[134] J. Darling, Astrophys. J. Lett. 900, 2, L28 (2020), [arXiv:2008.11188].
[135] R. A. Battye et al., Phys. Rev. D 105, L021305 (2022), URL https://link.aps.org/doi/
10.1103/PhysRevD.105.L021305.
[136] J. W. Foster et al., Phys. Rev. Lett. 129, 25, 251102 (2022), [arXiv:2202.08274].
[137] R. A. Battye et al. (2023), [arXiv:2303.11792].
[138] K. Perez et al., Phys. Rev. D 95, 12, 123002 (2017), [arXiv:1609.00667].
[139] K. C. Y. Ng et al., Phys. Rev. D 99, 083005 (2019), [arXiv:1901.01262].
[140] B. M. Roach et al., Phys. Rev. D 107, 2, 023009 (2023), [arXiv:2207.04572].
[141] M. A. Fedderke, P. W. Graham and S. Rajendran, Phys. Rev. D100, 1, 015040 (2019),[arXiv:1903.02666].
[142] S. Adachi et al. (POLARBEAR Collaboration), Phys. Rev. D 108, 043017 (2023), URL
https://link.aps.org/doi/10.1103/PhysRevD.108.043017.
31st May, 2024

29

90. Axions and Other Similar Particles[143] A. Castillo et al., JCAP 06, 06, 014 (2022), [arXiv:2201.03422].
[144] T. Liu, X. Lou and J. Ren, Phys. Rev. Lett. 130, 121401 (2023), URL https://link.aps.
org/doi/10.1103/PhysRevLett.130.121401.
[145] D. Noordhuis et al. (2022), [arXiv:2209.09917].
[146] C. Severino and I. Lopes, The Astrophysical Journal 943, 2, 95 (2023), URL https://dx.
doi.org/10.3847/1538-4357/aca897.
[147] N. Vinyoles et al., JCAP 1510, 10, 015 (2015), [arXiv:1501.01639].
[148] N. H. Nguyen, E. H. Tanin and M. Kamionkowski (2023), [arXiv:2307.11216].
[149] J. Jaeckel, P. C. Malta and J. Redondo, Phys. Rev. D 98, 5, 055032 (2018),[arXiv:1702.02964].
[150] E. Müller et al. (2023), [arXiv:2304.01060].
[151] A. Payez et al., JCAP 1502, 02, 006 (2015), [arXiv:1410.3747].
[152] S. Hoof and L. Schulz, JCAP 03, 054 (2023), [arXiv:2212.09764].
[153] G. Lucente et al., JCAP 12, 008 (2020), [arXiv:2008.04918].
[154] A. Caputo, G. Raffelt and E. Vitagliano, Phys. Rev. D 105, 3, 035022 (2022),[arXiv:2109.03244].
[155] A. Caputo et al., Phys. Rev. Lett. 128, 22, 221103 (2022), [arXiv:2201.09890].
[156] M. Diamond et al., Phys. Rev. D 107, 10, 103029 (2023), [arXiv:2303.11395].
[157] W. DeRocco et al., Phys. Rev. Lett. 129, 10, 101101 (2022), [arXiv:2205.05700].
[158] C. Beaufort et al. (2023), [arXiv:2303.06968].
[159] C. Dessert, J. W. Foster and B. R. Safdi, Phys. Rev. Lett. 125, 26, 261102 (2020),[arXiv:2008.03305].
[160] K. R. Ferguson et al. (SPT-3G), Phys. Rev. D 106, 4, 042011 (2022), [arXiv:2203.16567].
[161] B. D. Blout et al., Astrophys. J. 546, 825 (2001), [arXiv:astro-ph/0006310].
[162] M. Regis et al., Phys. Lett. B 814, 136075 (2021), [arXiv:2009.01310].
[163] D. Grin et al., Phys. Rev. D 75, 105018 (2007), [arXiv:astro-ph/0611502].
[164] K. Nakayama and W. Yin, Phys. Rev. D 106, 10, 103505 (2022), [arXiv:2205.01079].
[165] P. Carenza, G. Lucente and E. Vitagliano (2023), [arXiv:2301.06560].
[166] D. Cadamuro and J. Redondo, JCAP 1202, 032 (2012), [arXiv:1110.2895].
[167] P. F. Depta, M. Hufnagel and K. Schmidt-Hoberg, JCAP 05, 009 (2020), [arXiv:2002.08370].
[168] K. Langhoff, N. J. Outmezguine and N. L. Rodd, Phys. Rev. Lett. 129, 24, 241101 (2022),[arXiv:2209.06216].
[169] G. Raffelt and D. Seckel, Phys. Rev. Lett. 60, 1793 (1988).
[170] M. Carena and R. D. Peccei, Phys. Rev. D40, 652 (1989).
[171] K. Choi, K. Kang and J. E. Kim, Phys. Rev. Lett. 62, 849 (1989).
[172] M. Srednicki, Nucl. Phys. B260, 689 (1985).
[173] S. Chang and K. Choi, Phys. Lett. B316, 51 (1993), [hep-ph/9306216].
[174] G. C. Branco et al., Phys. Rept. 516, 1 (2012), [arXiv:1106.0034].
[175] C.-Y. Chen and S. Dawson, Phys. Rev. D87, 055016 (2013), [arXiv:1301.0309].
[176] R. Balkin et al., JHEP 07, 221 (2020), [arXiv:2003.04903].
31st May, 2024

30

90. Axions and Other Similar Particles[177] K. Choi et al., JHEP 02, 143 (2022), [arXiv:2110.01972].
[178] D. A. Dicus et al., Phys. Rev. D18, 1829 (1978).
[179] G. Raffelt and L. Stodolsky, Phys. Rev. D37, 1237 (1988).
[180] A. A. Anselm, Yad. Fiz. 42, 1480 (1985).
[181] K. van Bibber et al., Phys. Rev. Lett. 59, 759 (1987).
[182] G. Ruoso et al., Z. Phys. C56, 505 (1992).
[183] R. Cameron et al., Phys. Rev. D47, 3707 (1993).
[184] M. Fouche et al., Phys. Rev. D78, 032013 (2008), [arXiv:0808.2800].
[185] P. Pugnat et al. (OSQAR), Phys. Rev. D78, 092003 (2008), [arXiv:0712.3362].
[186] A. S. Chou et al. (GammeV (T-969)), Phys. Rev. Lett. 100, 080402 (2008), [arXiv:0710.3783].
[187] A. Afanasev et al., Phys. Rev. Lett. 101, 120401 (2008), [arXiv:0806.2631].
[188] P. Pugnat et al. (OSQAR), Eur. Phys. J. C74, 8, 3027 (2014), [arXiv:1306.0443].
[189] F. Hoogeveen and T. Ziegenhagen, Nucl. Phys. B358, 3 (1991).
[190] P. Sikivie, D. B. Tanner and K. van Bibber, Phys. Rev. Lett. 98, 172002 (2007), [hepph/0701198].
[191] G. Mueller et al., Phys. Rev. D80, 072004 (2009), [arXiv:0907.5387].
[192] M. Diaz Ortiz et al., Physics of the Dark Universe 35, 100968 (2022), ISSN 2212-6864, URL
https://www.sciencedirect.com/science/article/pii/S2212686422000115.
[193] F. Hoogeveen, Phys. Lett. B288, 195 (1992).
[194] J. Jaeckel and A. Ringwald, Phys. Lett. B659, 509 (2008), [arXiv:0707.2063].
[195] F. Caspers, J. Jaeckel and A. Ringwald, JINST 4, P11013 (2009), [arXiv:0908.0759].
[196] R. Povey, J. Hartnett and M. Tobar, Phys. Rev. D82, 052003 (2010), [arXiv:1003.0964].
[197] L. Maiani, R. Petronzio and E. Zavattini, Phys. Lett. B175, 359 (1986).
[198] Y. Semertzidis et al., Phys. Rev. Lett. 64, 2988 (1990).
[199] E. Fischbach and C. Talmadge, Nature 356, 207 (1992).
[200] J. E. Moody and F. Wilczek, Phys. Rev. D30, 130 (1984).
[201] A. N. Youdin et al., Phys. Rev. Lett. 77, 2170 (1996).
[202] W.-T. Ni et al., Phys. Rev. Lett. 82, 2439 (1999).
[203] D. F. Phillips et al., Phys. Rev. D63, 111101 (2001), [arXiv:physics/0008230].
[204] B. R. Heckel et al., Phys. Rev. Lett. 97, 021603 (2006), [hep-ph/0606218].
[205] S. A. Hoedl et al., Phys. Rev. Lett. 106, 041801 (2011).
[206] E. G. Adelberger et al., Phys. Rev. Lett. 98, 131104 (2007), [hep-ph/0611223].
[207] D. J. Kapner et al., Phys. Rev. Lett. 98, 021101 (2007), [hep-ph/0611184].
[208] G. Raffelt, Phys. Rev. D86, 015001 (2012), [arXiv:1205.1776].
[209] C. A. J. O’Hare and E. Vitagliano, Phys. Rev. D 102, 11, 115026 (2020), [arXiv:2010.03889].
[210] A. Arvanitaki and A. A. Geraci, Phys. Rev. Lett. 113, 16, 161801 (2014), [arXiv:1403.1290].
[211] A. A. Geraci et al. (ARIADNE), Springer Proc. Phys. 211, 151 (2018), [arXiv:1710.05413].
[212] H. Fosbinder-Elkins et al. (2017), [arXiv:1710.08102].
[213] N. Aggarwal et al. (ARIADNE Collaboration), Phys. Rev. Res. 4, 013090 (2022), URL https://link.aps.org/doi/10.1103/PhysRevResearch.4.013090.
31st May, 2024

31

90. Axions and Other Similar Particles[214] M. S. Turner, Phys. Rept. 197, 67 (1990).
[215] G. G. Raffelt, Lect. Notes Phys. 741, 51 (2008), [,51(2006)], [hep-ph/0611350].
[216] S. Andriamonje et al. (CAST), JCAP 0704, 010 (2007), [hep-ex/0702006].
[217] P. Gondolo and G. G. Raffelt, Phys. Rev. D79, 107301 (2009), [arXiv:0807.2926].
[218] H. Schlattl, A. Weiss and G. Raffelt, Astropart. Phys. 10, 353 (1999), [hep-ph/9807476].
[219] P. Agnes et al. (DarkSide), Phys. Rev. Lett. 130, 10, 101002 (2023), [arXiv:2207.11968].
[220] M. Agostini et al. (GERDA), Phys. Rev. Lett. 125, 1, 011801 (2020), [arXiv:2005.14184].
[221] C. Fu et al. (PandaX), Phys. Rev. Lett. 119, 18, 181806 (2017), [arXiv:1707.07921].
[222] T. Aralis et al. (SuperCDMS), Phys. Rev. D 101, 5, 052008 (2020), [Erratum: Phys.Rev.D
103, 039901 (2021)], [arXiv:1911.11905].
[223] E. Aprile et al. (XENON), Phys. Rev. D 102, 7, 072004 (2020), [arXiv:2006.09721].
[224] E. Aprile et al. (XENON Collaboration), Phys. Rev. Lett. 129, 161805 (2022), URL https://link.aps.org/doi/10.1103/PhysRevLett.129.161805.
[225] K. Van Tilburg, Phys. Rev. D 104, 2, 023019 (2021), [arXiv:2006.12431].
[226] F. Capozzi and G. Raffelt, Phys. Rev. D 102, 8, 083007 (2020), [arXiv:2007.03694].
[227] N. Crescini et al. (QUAX), Phys. Rev. Lett. 124, 17, 171801 (2020), [arXiv:2001.08940].
[228] R. Z. Ferreira, M. C. D. Marsh and E. Müller, Phys. Rev. Lett. 128, 22, 221302 (2022),[arXiv:2202.08858].
[229] O. Straniero et al., in “Proceedings, 11th Patras Workshop on Axions, WIMPs and WISPs(Axion-WIMP 2015): Zaragoza, Spain, June 22-26, 2015,” 77–81 (2015).
[230] T. Constantino et al. .
[231] J. Redondo, Journal of Cosmology and Astroparticle Physics 2013, 12, 008 (2013).
[232] O. Straniero et al., Astron. Astrophys. 644, A166 (2020), [arXiv:2010.03833].
[233] G. G. Raffelt, Phys. Lett. 166B, 402 (1986).
[234] S. I. Blinnikov and N. V. Dunina-Barkovskaya, Mon. Not. Roy. Astron. Soc. 266, 289 (1994).
[235] M. M. Miller Bertolami et al., JCAP 1410, 10, 069 (2014), [arXiv:1406.7712].
[236] J. Isern et al., Astrophys. J. 682, L109 (2008), [arXiv:0806.2807].
[237] J. Isern et al., J. Phys. Conf. Ser. 172, 012005 (2009), [arXiv:0812.3043].
[238] A. Drlica-Wagner et al. (LSST Dark Matter Group) (2019), [arXiv:1902.01055].
[239] J. Isern et al., Astron. & Astrophys. 512, A86 (2010).
[240] A. H. Corsico et al., Mon. Not. Roy. Astron. Soc. 424, 2792 (2012), [arXiv:1205.6180].
[241] A. H. Corsico et al., JCAP 1212, 010 (2012), [arXiv:1211.3389].
[242] A. H. Córsico et al., The Astronomy and Astrophysics Review 27, 1, 7 (2019), URL https://doi.org/10.1007/s00159-019-0118-4.
[243] M. J. Dolan, F. J. Hiskens and R. R. Volkas, Journal of Cosmology and Astroparticle Physics
2021, 09, 010 (2021), URL https://doi.org/10.1088/1475-7516/2021/09/010.
[244] J. Isern, S. Torres and A. Rebassa-Mansergas, Front. Astron. Space Sci. 9, 815517 (2022),[arXiv:2202.02052].
[245] V. M. Mostepanenko and G. L. Klimchitskaya, Universe 6, 9, 147 (2020), [arXiv:2009.04517].
[246] T. Wu et al., Phys. Rev. Lett. 122, 19, 191302 (2019), [arXiv:1901.10843].
31st May, 2024

32

90. Axions and Other Similar Particles[247] A. Garcon et al., Sci. Adv. 5, 10, eaax4539 (2019), [arXiv:1902.04644].
[248] K. Wei et al. (2023), [arXiv:2306.08039].
[249] M. Jiang et al., Nature Phys. 17, 12, 1402 (2021), [arXiv:2102.01448].
[250] I. M. Bloch et al. (NASDUCK) (2022), [arXiv:2209.13588].
[251] I. M. Bloch et al., JHEP 01, 167 (2020), [arXiv:1907.03767].
[252] G. Vasilakis et al., Physical Review Letters 103, 26 (2009), ISSN 1079-7114, URL http://dx.doi.org/10.1103/PhysRevLett.103.261801.
[253] J. Lee et al., Phys. Rev. X 13, 011050 (2023), URL https://link.aps.org/doi/10.1103/
PhysRevX.13.011050.
[254] M. Buschmann et al., Phys. Rev. Lett. 128, 9, 091102 (2022), [arXiv:2111.09892].
[255] A. Bhusal, N. Houston and T. Li, Phys. Rev. Lett. 126, 9, 091601 (2021), [arXiv:2004.02733].
[256] G.G. Raffelt, Stars as Laboratories for Fundamental Physics, (Univ. of Chicago Press,
Chicago, 1996).
[257] T. Fischer et al., Phys. Rev. D94, 8, 085012 (2016), [arXiv:1605.08780].
[258] J. H. Chang, R. Essig and S. D. McDermott, JHEP 09, 051 (2018), [arXiv:1803.00993].
[259] P. Carenza et al., JCAP 10, 10, 016 (2019), [Erratum:[arXiv:1906.11844].

JCAP 05, E01 (2020)],[260] M. S. Turner, Phys. Rev. D 45, 1066 (1992).
[261] G. Raffelt and D. Seckel, Phys. Rev. D 52, 1780 (1995), [arXiv:astro-ph/9312019].
[262] W. Keil et al., Phys. Rev. D 56, 2419 (1997), [arXiv:astro-ph/9612222].
[263] B. Fore and S. Reddy, Phys. Rev. C 101, 3, 035809 (2020), [arXiv:1911.02632].
[264] P. Carenza et al., Phys. Rev. Lett. 126, 7, 071102 (2021), [arXiv:2010.02943].
[265] J. Engel, D. Seckel and A. C. Hayes, Phys. Rev. Lett. 65, 960 (1990).
[266] N. Iwamoto, Phys. Rev. Lett. 53, 1198 (1984).
[267] N. Iwamoto, Phys. Rev. D 64, 043002 (2001).
[268] A. Sedrakian, Phys. Rev. D93, 6, 065044 (2016), [arXiv:1512.07828].
[269] J. Keller and A. Sedrakian, Nucl. Phys. A897, 62 (2013), [arXiv:1205.6940].
[270] T. Fischer, Astron. Astrophys. 593, A103 (2016), [arXiv:1608.05004].
[271] K. Hamaguchi et al., Phys. Rev. D98, 10, 103015 (2018), [arXiv:1806.07151].
[272] D. Page et al., Phys. Rev. Lett. 106, 081101 (2011), [arXiv:1011.6142].
[273] P. S. Shternin et al., Mon. Not. Roy. Astron. Soc. 412, L108 (2011), [arXiv:1012.0045].
[274] B. Posselt and G. G. Pavlov, Astrophys. J. 864, 2, 135 (2018), [arXiv:1808.00531].
[275] M. V. Beznogov et al., Phys. Rev. C98, 3, 035802 (2018), [arXiv:1806.07991].
[276] G. G. Raffelt, J. Redondo and N. Viaux Maira, Phys. Rev. D84, 103008 (2011),[arXiv:1110.6397].
[277] K. van Bibber et al., Phys. Rev. D39, 2089 (1989).
[278] D. M. Lazarus et al., Phys. Rev. Lett. 69, 2333 (1992).
[279] S. Moriyama et al., Phys. Lett. B434, 147 (1998), [hep-ex/9805026].
[280] Y. Inoue et al., Phys. Lett. B536, 18 (2002), [arXiv:astro-ph/0204388].
[281] Y. Inoue et al., Phys. Lett. B668, 93 (2008), [arXiv:0806.2230].
31st May, 2024

33

90. Axions and Other Similar Particles[282] E. Arik et al. (CAST), JCAP 0902, 008 (2009), [arXiv:0810.4482].
[283] S. Aune et al. (CAST), Phys. Rev. Lett. 107, 261302 (2011), [arXiv:1106.3919].
[284] M. Arik et al. (CAST), Phys. Rev. Lett. 112, 9, 091302 (2014), [arXiv:1307.1985].
[285] M. Arik et al. (CAST), Phys. Rev. D92, 2, 021101 (2015), [arXiv:1503.00610].
[286] E. Armengaud et al., JINST 9, T05002 (2014), [arXiv:1401.3233].
[287] E. Armengaud et al. (IAXO), JCAP 1906, 06, 047 (2019), [arXiv:1904.09155].
[288] M. Giannotti et al., JCAP 1710, 10, 010 (2017), [arXiv:1708.02111].
[289] K. Barth et al., JCAP 1305, 010 (2013), [arXiv:1302.6283].
[290] A. Abeln et al. (BabyIAXO), JCAP 2105, 05, 137 (2021), [arXiv:2010.12076].
[291] E. Aprile et al. (XENON), Phys. Rev. Lett. 129, 16, 161805 (2022), [arXiv:2207.11330].
[292] X. Zhou et al., Chinese Physics Letters 38, 10, 109902 (2021), URL https://dx.doi.org/
10.1088/0256-307X/38/10/109902.
[293] D. S. Akerib et al. (LUX), Phys. Rev. Lett. 118, 26, 261301 (2017), [arXiv:1704.02297].
[294] J. W. Brockway, E. D. Carlson and G. G. Raffelt, Phys. Lett. B383, 439 (1996), [arXiv:astroph/9605197].
[295] J. A. Grifols, E. Masso and R. Toldra, Phys. Rev. Lett. 77, 2372 (1996), [arXiv:astroph/9606028].
[296] F. Calore et al., Phys. Rev. D 102, 12, 123005 (2020), [arXiv:2008.11741].
[297] C. Dessert, J. W. Foster and B. R. Safdi, Astrophys. J. 904, 1, 42 (2020), [arXiv:1910.02956].
[298] M. Buschmann et al., Phys. Rev. Lett. 126, 2, 021102 (2021), [arXiv:1910.04164].
[299] C. Dessert, A. J. Long and B. R. Safdi, Phys. Rev. Lett. 123, 6, 061104 (2019),[arXiv:1903.05088].
[300] C. Csaki, N. Kaloper and J. Terning, Phys. Rev. Lett. 88, 161302 (2002), [hep-ph/0111311].
[301] A. Mirizzi, G.G. Raffelt, and P.D. Serpico, Lect. Notes Phys. 741, 115 (2008).
[302] D. Horns et al., Phys. Rev. D85, 085021 (2012), [arXiv:1203.2184].
[303] A. Payez, J. R. Cudell and D. Hutsemekers, JCAP 1207, 041 (2012), [arXiv:1204.6187].
[304] R. Gill and J. S. Heyl, Phys. Rev. D84, 085001 (2011), [arXiv:1105.2083].
[305] A. Dominguez, M. A. Sanchez-Conde and F. Prada,[arXiv:1106.1860].

JCAP 1111,

020 (2011),[306] W. Essey and A. Kusenko, Astrophys. J. 751, L11 (2012), [arXiv:1111.0815].
[307] D. Horns and M. Meyer, JCAP 1202, 033 (2012), [arXiv:1201.4711].
[308] G. I. Rubtsov and S. V. Troitsky, JETP Lett. 100, 6, 355 (2014), [Pisma Zh. Eksp. Teor.
Fiz.100,no.6,397(2014)], [arXiv:1406.0239].
[309] D. A. Sanchez, S. Fegan and B. Giebels, Astron. Astrophys. 554, A75 (2013),[arXiv:1303.5923].
[310] J. Biteau and D. A. Williams, Astrophys. J. 812, 1, 60 (2015), [arXiv:1502.04166].
[311] A. Domínguez and M. Ajello, Astrophys. J. 813, 2, L34 (2015), [arXiv:1510.07913].
[312] A. Korochkin, G. Rubtsov and S. Troitsky, JCAP 12, 002 (2019), [arXiv:1810.03443].
[313] A. De Angelis, G. Galanti and M. Roncadelli, Phys. Rev. D84, 105030 (2011), [Erratum:
Phys. Rev.D87,no.10,109903(2013)], [arXiv:1106.1132].
[314] M. Simet, D. Hooper and P. D. Serpico, Phys. Rev. D77, 063001 (2008), [arXiv:0712.2825].
31st May, 2024

34

90. Axions and Other Similar Particles[315] M. A. Sanchez-Conde et al., Phys. Rev. D79, 123511 (2009), [arXiv:0905.3270].
[316] M. Meyer, D. Horns and M. Raue, Phys. Rev. D87, 3, 035027 (2013), [arXiv:1302.1208].
[317] A. Abramowski et al. (H.E.S.S.), Phys. Rev. D88, 10, 102003 (2013), [arXiv:1311.3148].
[318] C. Zhang et al., Phys. Rev. D97, 6, 063009 (2018), [arXiv:1802.08420].
[319] M. Libanov and S. Troitsky, Phys. Lett. B 802, 135252 (2020), [arXiv:1908.03084].
[320] Z.-Q. Xia et al., Phys. Rev. D97, 6, 063003 (2018), [arXiv:1801.01646].
[321] J. Majumdar, F. Calore and D. Horns, JCAP 1804, 04, 048 (2018), [arXiv:1801.08813].
[322] G. A. Pallathadka et al. (2020), [arXiv:2008.08100].
[323] K. Choi et al., Phys. Rev. D 101, 4, 043007 (2020), [arXiv:1806.09508].
[324] F. Chadha-Day (2021), [arXiv:2107.12813].
[325] M. Berg et al., Astrophys. J. 847, 2, 101 (2017), [arXiv:1605.01043].
[326] J. P. Conlon et al., JCAP 1707, 07, 005 (2017), [arXiv:1704.05256].
[327] L. Chen and J. P. Conlon, Mon. Not. Roy. Astron. Soc. 479, 2, 2243 (2018),[arXiv:1712.08313].
[328] A. Hook and J. Huang, JHEP 06, 036 (2018), [arXiv:1708.08464].
[329] J. Huang et al., Phys. Rev. D 99, 6, 063013 (2019), [arXiv:1807.02133].
[330] J. Zhang et al. (2021), [arXiv:2105.13963].
[331] R. Balkin et al. (2022), [arXiv:2211.02661].
[332] G. Bellini et al. (Borexino), Phys. Rev. D 89, 11, 112007 (2014), [arXiv:1308.0443].
[333] B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. Lett. 119, 16, 161101 (2017),[arXiv:1710.05832].
[334] A. Arvanitaki and S. Dubovsky, Phys. Rev. D83, 044026 (2011), [arXiv:1004.3558].
[335] A. Arvanitaki, M. Baryakhtar and X. Huang, Phys. Rev. D91, 8, 084011 (2015),[arXiv:1411.2263].
[336] V. M. Mehta et al. (2020), [arXiv:2011.08693].
[337] V. M. Mehta et al., JCAP 07, 033 (2021), [arXiv:2103.06812].
[338] M. Baryakhtar et al., Phys. Rev. D 103, 9, 095019 (2021), [arXiv:2011.11646].
[339] M. J. Stott (2020), [arXiv:2009.07206].
[340] G. Ballesteros et al., Phys. Rev. Lett. 118, 071802 (2017), URL https://link.aps.org/
doi/10.1103/PhysRevLett.118.071802.
[341] M. Buschmann et al., Nature Commun. 13, 1, 1049 (2022), [arXiv:2108.05368].
[342] C. Bonati et al., JHEP 03, 155 (2016), [arXiv:1512.06746].
[343] E. Berkowitz, M. I. Buchoff and E. Rinaldi, Phys. Rev. D92, 3, 034507 (2015),[arXiv:1505.07455].
[344] M. Dine et al., Phys. Rev. D96, 9, 095001 (2017), [arXiv:1705.00676].
[345] P. Petreczky, H.-P. Schadler and S. Sharma, Phys. Lett. B762, 498 (2016), [arXiv:1606.03145].
[346] L. Fleury and G. D. Moore, Journal of Cosmology and Astroparticle Physics 2016, 01, 004(2016), URL https://dx.doi.org/10.1088/1475-7516/2016/01/004.
[347] V. B. Klaer and G. D. Moore, JCAP 1711, 11, 049 (2017), [arXiv:1708.07521].
[348] M. Gorghetto, E. Hardy and G. Villadoro, SciPost Phys. 10, 050 (2021), [arXiv:2007.04990].
31st May, 2024

35

90. Axions and Other Similar Particles[349] M. Kawasaki, K. Saikawa and T. Sekiguchi, Phys. Rev. D91, 6, 065014 (2015),[arXiv:1412.0789].
[350] R. T. Co, L. J. Hall and K. Harigaya, Journal of High Energy Physics 2021, 1, 172 (2021),
ISSN 1029-8479, URL https://doi.org/10.1007/JHEP01(2021)172.
[351] N. Blinov et al., Phys. Rev. D 100, 015049 (2019), URL https://link.aps.org/doi/10.
1103/PhysRevD.100.015049.
[352] C. A. J. O’Hare et al., Phys. Rev. D 105, 055025 (2022), URL https://link.aps.org/doi/
10.1103/PhysRevD.105.055025.
[353] L. D. Luzio et al., Journal of Cosmology and Astroparticle Physics 2021, 10, 001 (2021),
URL https://dx.doi.org/10.1088/1475-7516/2021/10/001.
[354] A. Arvanitaki et al., Phys. Rev. D95, 4, 043001 (2017), [arXiv:1604.03958].
[355] K. K. Y. Ng et al., Phys. Rev. D 103, 6, 063010 (2021), [arXiv:1908.02312].
[356] C. Palomba et al., Phys. Rev. Lett. 123, 171101 (2019), [arXiv:1909.08854].
[357] L. Sun, R. Brito and M. Isi, Phys. Rev. D 101, 6, 063020 (2020), [Erratum: Phys.Rev.D 102,
089902 (2020)], [arXiv:1909.11267].
[358] E. Masso, F. Rota and G. Zsembinszki, Phys. Rev. D 66, 023004 (2002), [hep-ph/0203221].
[359] P. Graf and F. D. Steffen, Phys. Rev. D 83, 075011 (2011), [arXiv:1008.4528].
[360] Z. G. Berezhiani, A. S. Sakharov and M. Y. Khlopov, Sov. J. Nucl. Phys. 55, 1063 (1992).
[361] S. Hannestad, A. Mirizzi and G. Raffelt, JCAP 07, 002 (2005), [hep-ph/0504059].
[362] S. Hannestad et al., JCAP 08, 001 (2010), [arXiv:1004.0695].
[363] M. Archidiacono et al., JCAP 10, 020 (2013), [arXiv:1307.0615].
[364] E. Di Valentino et al., Phys. Lett. B 752, 182 (2016), [arXiv:1507.08665].
[365] W. Giarè et al., Mon. Not. Roy. Astron. Soc. 505, 2, 2703 (2021), [arXiv:2011.14704].
[366] L. Di Luzio, G. Martinelli and G. Piazza, Phys. Rev. Lett. 126, 24, 241801 (2021),[arXiv:2101.10330].
[367] A. Notari, F. Rompineve and G. Villadoro, Phys. Rev. Lett. 131, 1, 011004 (2023),[arXiv:2211.03799].
[368] E. Masso and R. Toldra, Phys. Rev. D 52, 1755 (1995), [hep-ph/9503293].
[369] E. Masso and R. Toldra, Phys. Rev. D55, 7967 (1997), [hep-ph/9702275].
[370] J. W. Foster et al., JHEP 12, 119 (2022), [arXiv:2208.10504].
[371] P. Panci et al., Phys. Lett. B 841, 137919 (2023), [arXiv:2209.03371].
[372] E. Todarello et al. (2023), [arXiv:2307.07403].
[373] J. W. Foster et al., Phys. Rev. Lett. 127, 5, 051101 (2021), [arXiv:2102.02207].
[374] J. Preskill, M. B. Wise and F. Wilczek, Phys. Lett. B120, 127 (1983).
[375] L. F. Abbott and P. Sikivie, Phys. Lett. B120, 133 (1983).
[376] M. Dine and W. Fischler, Phys. Lett. B120, 137 (1983).
[377] K. J. Bae, J.-H. Huh and J. E. Kim, JCAP 0809, 005 (2008), [arXiv:0806.0497].
[378] O. Wantz and E. P. S. Shellard, Phys. Rev. D82, 123508 (2010), [arXiv:0910.1066].
[379] G. Ballesteros et al., JCAP 1708, 08, 001 (2017), [arXiv:1610.01639].
[380] R. T. Co, F. D’Eramo and L. J. Hall, Phys. Rev. D 94, 7, 075001 (2016), [arXiv:1603.04439].
[381] M. Tegmark et al., Phys. Rev. D73, 023505 (2006), [arXiv:astro-ph/0511774].
31st May, 2024

36

90. Axions and Other Similar Particles[382] A. D. Linde, Phys. Lett. 158B, 375 (1985).
[383] D. Seckel and M. S. Turner, Phys. Rev. D32, 3178 (1985).
[384] M. Beltran, J. Garcia-Bellido and J. Lesgourgues, Phys. Rev. D75, 103507 (2007), [hepph/0606107].
[385] M. P. Hertzberg, M. Tegmark and F. Wilczek, Phys. Rev. D78, 083507 (2008),[arXiv:0807.1726].
[386] J. Hamann et al., JCAP 0906, 022 (2009), [arXiv:0904.0647].
[387] P. A. R. Ade et al. (Planck), Astron. Astrophys. 571, A22 (2014), [arXiv:1303.5082].
[388] P. A. R. Ade et al. (Planck), Astron. Astrophys. 594, A20 (2016), [arXiv:1502.02114].
[389] B. Bolliet, J. Chluba and R. Battye, Monthly Notices of the Royal Astronomical Society 507,
3, 3148 (2021), ISSN 0035-8711, URL https://doi.org/10.1093/mnras/stab1997.
[390] R. T. Co, L. J. Hall and K. Harigaya, Phys. Rev. Lett. 124, 25, 251802 (2020),[arXiv:1910.14152].
[391] S. Borsanyi et al., Phys. Lett. B752, 175 (2016), [arXiv:1508.06917].
[392] R. Kitano and N. Yamada, JHEP 10, 136 (2015), [arXiv:1506.00370].
[393] Y. Taniguchi et al., Phys. Rev. D95, 5, 054502 (2017), [arXiv:1611.02411].
[394] R. D. Pisarski and L. G. Yaffe, Phys. Lett. 97B, 110 (1980).
[395] S. Chang, C. Hagmann and P. Sikivie, Phys. Rev. D59, 023505 (1999), [hep-ph/9807374].
[396] C. Hagmann, S. Chang and P. Sikivie, Phys. Rev. D63, 125018 (2001), [hep-ph/0012361].
[397] T. Hiramatsu et al., Phys. Rev. D83, 123531 (2011), [arXiv:1012.5502].
[398] T. Hiramatsu et al., Phys. Rev. D85, 105020 (2012), [Erratum: Phys. Rev.D86,089902(2012)],[arXiv:1202.5851].
[399] M. Gorghetto, E. Hardy and G. Villadoro, JHEP 07, 151 (2018), [arXiv:1806.04677].
[400] M. Buschmann, J. W. Foster and B. R. Safdi, Phys. Rev. Lett. 124, 16, 161103 (2020),[arXiv:1906.00967].
[401] M. Hindmarsh et al., Phys. Rev. Lett. 124, 2, 021301 (2020), [arXiv:1908.03522].
[402] M. Dine et al., Journal of Cosmology and Astroparticle Physics 2021, 11, 041 (2021), URL
https://dx.doi.org/10.1088/1475-7516/2021/11/041.
[403] M. Hindmarsh et al., Phys. Rev. D 103, 10, 103534 (2021), [arXiv:2102.07723].
[404] A. Ringwald and K. Saikawa, Phys. Rev. D93, 8, 085031 (2016), [Addendum: Phys.
Rev.D94,no.4,049908(2016)], [arXiv:1512.06436].
[405] T. Hiramatsu et al., JCAP 1301, 001 (2013), [arXiv:1207.3166].
[406] K. A. Beyer and S. Sarkar, SciPost Phys. 15, 003 (2023), [arXiv:2211.14635].
[407] C. J. Hogan and M. J. Rees, Phys. Lett. B205, 228 (1988).
[408] E. W. Kolb and I. I. Tkachev, Phys. Rev. Lett. 71, 3051 (1993), [hep-ph/9303313].
[409] B. Eggemeier et al., Phys. Rev. Lett. 125, 4, 041301 (2020), [arXiv:1911.09417].
[410] A. Vaquero, J. Redondo and J. Stadler, Journal of Cosmology and Astroparticle Physics
2019, 04, 012 (2019), URL https://dx.doi.org/10.1088/1475-7516/2019/04/012.
[411] E. W. Kolb and I. I. Tkachev, Astrophys. J. 460, L25 (1996), [arXiv:astro-ph/9510043].
[412] M. Fairbairn, D. J. E. Marsh and J. Quevillon, Phys. Rev. Lett. 119, 2, 021101 (2017),[arXiv:1701.04787].
31st May, 2024

37

90. Axions and Other Similar Particles[413] A. Katz et al., JCAP 1812, 005 (2018), [arXiv:1807.11495].
[414] R. Hlozek et al., Phys. Rev. D91, 10, 103512 (2015), [arXiv:1410.2896].
[415] D. J. E. Marsh, Phys. Rept. 643, 1 (2016), [arXiv:1510.07633].
[416] L. Hui et al., Phys. Rev. D95, 4, 043541 (2017), [arXiv:1610.08297].
[417] G. P. Centers et al., Nature Communications 12, 1, 7321 (2021), ISSN 2041-1723, URL
https://doi.org/10.1038/s41467-021-27632-7.
[418] A. G. Dias et al., JHEP 06, 037 (2014), [arXiv:1403.5760].
[419] J. E. Kim and D. J. E. Marsh, Phys. Rev. D93, 2, 025027 (2016), [arXiv:1510.01701].
[420] H. Davoudiasl and C. W. Murphy,[arXiv:1701.01136].

Phys. Rev. Lett. 118,

14,141801 (2017),[421] L. Di Luzio et al., JCAP 10, 001 (2021), [arXiv:2102.01082].
[422] M. Khlopov, B. A. Malomed and I. B. Zeldovich, Mon. Not. Roy. Astron. Soc. 215, 575(1985).
[423] W. Hu, R. Barkana and A. Gruzinov, Phys. Rev. Lett. 85, 1158 (2000), [arXiv:astroph/0003365].
[424] L. Amendola and R. Barbieri, Phys. Lett. B642, 192 (2006), [hep-ph/0509257].
[425] D. J. E. Marsh and P. G. Ferreira, Phys. Rev. D82, 103528 (2010), [arXiv:1009.3501].
[426] E. Seidel and W. M. Suen, Phys. Rev. Lett. 66, 1659 (1991).
[427] H.-Y. Schive, T. Chiueh and T. Broadhurst, Nature Phys. 10, 496 (2014), [arXiv:1406.6586].
[428] D. G. Levkov, A. G. Panin and I. I. Tkachev, Phys. Rev. Lett. 121, 15, 151301 (2018),[arXiv:1804.05857].
[429] B. Eggemeier and J. C. Niemeyer, Phys. Rev. D 100, 6, 063528 (2019), [arXiv:1906.01348].
[430] R. Hlozek, D. J. E. Marsh and D. Grin, Mon. Not. Roy. Astron. Soc. 476, 3, 3063 (2018),[arXiv:1708.05681].
[431] D. J. E. Marsh and J. Silk, Mon. Not. Roy. Astron. Soc. 437, 3, 2652 (2014),[arXiv:1307.1705].
[432] H.-Y. Schive et al., Astrophys. J. 818, 1, 89 (2016), [arXiv:1508.04621].
[433] B. Bozek et al., Mon. Not. Roy. Astron. Soc. 450, 1, 209 (2015), [arXiv:1409.3544].
[434] P. S. Corasaniti et al., Phys. Rev. D95, 8, 083512 (2017), [arXiv:1611.05892].
[435] K. K. Rogers and H. V. Peiris, Phys. Rev. Lett. 126, 7, 071302 (2021), [arXiv:2007.12705].
[436] H.-Y. Schive and T. Chiueh, Mon. Not. Roy. Astron. Soc. 473, 1, L36 (2018),[arXiv:1706.03723].
[437] E. O. Nadler et al. (DES), Phys. Rev. Lett. 126, 091101 (2021), [arXiv:2008.00022].
[438] B. Schwabe, J. C. Niemeyer and J. F. Engels, Phys. Rev. D94, 4, 043513 (2016),[arXiv:1606.05151].
[439] J. Veltmaat and J. C. Niemeyer, Phys. Rev. D94, 12, 123523 (2016), [arXiv:1608.00802].
[440] P. Mocz et al., Mon. Not. Roy. Astron. Soc. 471, 4, 4559 (2017), [arXiv:1705.05845].
[441] D. G. Levkov, A. G. Panin and I. I. Tkachev, Phys. Rev. Lett. 118, 011301 (2017); T. Helfer
et al., JCAP 1703, 03, 055 (2017), [arXiv:1609.04724]; J. Eby et al., Journal of HighEnergy Physics 2018, 1, 66 (2018), ISSN 1029-8479, URL https://doi.org/10.1007/
JHEP01(2018)066.
31st May, 2024

38

90. Axions and Other Similar Particles[442] D. J. E. Marsh and A.-R. Pop, Mon. Not. Roy. Astron. Soc. 451, 3, 2479 (2015),[arXiv:1502.03456].
[443] S.-R. Chen, H.-Y. Schive and T. Chiueh, Mon. Not. Roy. Astron. Soc. 468, 2, 1338 (2017),[arXiv:1606.09030].
[444] A. X. González-Morales et al., Mon. Not. Roy. Astron. Soc. 472, 2, 1346 (2017),[arXiv:1609.05856].
[445] I. De Martino et al., Phys. Dark Univ. 28, 100503 (2020), [arXiv:1807.08153].
[446] T. Broadhurst et al., Phys. Rev. D 101, 8, 083012 (2020), [arXiv:1902.10488].
[447] H.-Y. Schive et al., Phys. Rev. Lett. 113, 26, 261302 (2014), [arXiv:1407.7762].
[448] V. H. Robles, J. S. Bullock and M. Boylan-Kolchin, Mon. Not. Roy. Astron. Soc. 483, 1, 289(2019), [arXiv:1807.06018].
[449] V. Desjacques and A. Nusser, Monthly Notices of the Royal Astronomical Society 488, 4,4497 (2019), ISSN 0035-8711, URL https://doi.org/10.1093/mnras/stz1978.
[450] M. Safarzadeh and D. N. Spergel, The Astrophysical Journal 893, 1, 21 (2020), URL https://dx.doi.org/10.3847/1538-4357/ab7db2.
[451] A. Pontzen and F. Governato, Nature 506, 171 (2014), [arXiv:1402.1764].
[452] P. Mocz et al., Phys. Rev. Lett. 123, 14, 141301 (2019), [arXiv:1910.01653].
[453] J. Veltmaat, B. Schwabe and J. C. Niemeyer, Phys. Rev. D 101, 8, 083518 (2020),[arXiv:1911.09614].
[454] J. Veltmaat, J. C. Niemeyer and B. Schwabe, Phys. Rev. D98, 4, 043509 (2018),[arXiv:1804.09647].
[455] B. Bar-Or, J.-B. Fouvry and S. Tremaine, Astrophys. J. 871, 1, 28 (2019), [arXiv:1809.07673].
[456] B. V. Church, P. Mocz and J. P. Ostriker, MNRAS 485, 2861 (2019), [arXiv:1809.04744].
[457] N. C. Amorisco and A. Loeb (2018), [arXiv:1808.00464].
[458] T. S. Li et al. (DES), Astrophys. J. 838, 1, 8 (2017), [arXiv:1611.05052].
[459] D. J. E. Marsh and J. C. Niemeyer, Phys. Rev. Lett. 123, 5, 051103 (2019),[arXiv:1810.08543].
[460] N. Dalal and A. Kravtsov, Phys. Rev. D 106, 6, 063517 (2022), [arXiv:2203.05750].
[461] E. Armengaud et al. (EDELWEISS), Phys. Rev. D 98, 8, 082004 (2018), [arXiv:1808.02340].
[462] E. Aprile et al. (XENON), Phys. Rev. Lett. 123, 25, 251801 (2019), [arXiv:1907.11485].
[463] K. Kelley and P. J. Quinn, Astrophys. J. 845, 1, L4 (2017), [arXiv:1708.01399].
[464] G. Sigl, Phys. Rev. D96, 10, 103014 (2017), [arXiv:1708.08908].
[465] A. Hook et al., Phys. Rev. Lett. 121, 24, 241102 (2018), [arXiv:1804.03145].
[466] B. R. Safdi, Z. Sun and A. Y. Chen, Phys. Rev. D 99, 12, 123021 (2019), [arXiv:1811.01020].
[467] S. J. Witte et al. (2021), [arXiv:2104.07670].
[468] R. A. Battye et al., Journal of High Energy Physics 2021, 9, 105 (2021), ISSN 1029-8479,
URL https://doi.org/10.1007/JHEP09(2021)105.
[469] A. J. Millar et al. (2021), [arXiv:2107.07399].
[470] J. I. McDonald, B. Garbrecht and P. Millington (2023), [arXiv:2307.11812].
[471] A. Caputo et al., JCAP 1903, 03, 027 (2019), [arXiv:1811.08436].
[472] P. Carenza, A. Mirizzi and G. Sigl, Phys. Rev. D 101, 10, 103016 (2020), [arXiv:1911.07838].
31st May, 2024

39

90. Axions and Other Similar Particles[473] D. G. Levkov, A. G. Panin and I. I. Tkachev, Phys. Rev. D 102, 2, 023501 (2020),[arXiv:2004.05179].
[474] T. Fujita et al., Phys. Rev. D 103, 4, 043509 (2021), [arXiv:2011.11894].
[475] T. Liu, G. Smoot and Y. Zhao (2019), [arXiv:1901.10981].
[476] P. Sikivie, Phys. Rev. D32, 2988 (1985), [Erratum: Phys. Rev.D36,974(1987)].
[477] R. Bradley et al., Rev. Mod. Phys. 75, 777 (2003).
[478] P. Sikivie and J. R. Ipser, Phys. Lett. B291, 288 (1992).
[479] P. Sikivie, I. I. Tkachev and Y. Wang, Phys. Rev. Lett. 75, 2911 (1995), [arXiv:astroph/9504052].
[480] C. Bartram et al. (ADMX), Phys. Rev. D 103, 3, 032002 (2021), [arXiv:2010.06183].
[481] R. Khatiwada et al., Review of Scientific Instruments 92, 12, 124502 (2021), ISSN 0034-6748,
URL https://doi.org/10.1063/5.0037857.
[482] W. Wuensch et al., Phys. Rev. D40, 3153 (1989).
[483] A. A. Melcón et al. (CAST), JHEP 21, 075 (2020), [arXiv:2104.13798].
[484] B. T. McAllister et al., Annalen der Physik n/a, n/a, 2200622 (2022), URL https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.202200622.
[485] S. J. Asztalos et al. (ADMX), Phys. Rev. D69, 011101 (2004), [arXiv:astro-ph/0310042].
[486] L. Duffy et al., Phys. Rev. Lett. 95, 091304 (2005), [arXiv:astro-ph/0505237]; J. Hoskins
et al., Phys. Rev. D84, 121302 (2011), [arXiv:1109.4128].
[487] S. J. Asztalos et al. (ADMX), Nucl. Instrum. Meth. A656, 39 (2011), [arXiv:1105.4203].
[488] G. Rybka et al. (ADMX), Phys. Rev. Lett. 105, 051801 (2010), [arXiv:1004.5160].
[489] A. Wagner et al. (ADMX), Phys. Rev. Lett. 105, 171801 (2010), [arXiv:1007.3766].
[490] B. M. Brubaker et al., Phys. Rev. Lett. 118, 6, 061302 (2017), [arXiv:1610.02580].
[491] A. J. Millar et al. (Endorsers), Phys. Rev. D 107, 055013 (2023), URL https://link.aps.
org/doi/10.1103/PhysRevD.107.055013.
[492] D. Horns et al., JCAP 1304, 016 (2013), [arXiv:1212.2970].
[493] A. Caldwell et al. (MADMAX Working Group), Phys. Rev. Lett. 118, 9, 091801 (2017),[arXiv:1611.05865].
[494] P. Brun et al. (MADMAX), Eur. Phys. J. C79, 3, 186 (2019), [arXiv:1901.07401].
[495] M. Baryakhtar, J. Huang and R. Lasenby, Phys. Rev. D98, 3, 035006 (2018),[arXiv:1803.11455].
[496] J. Liu et al. (BREAD Collaboration), Phys. Rev. Lett. 128, 131801 (2022), URL https://link.aps.org/doi/10.1103/PhysRevLett.128.131801.
[497] B. Aja et al., Journal of Cosmology and Astroparticle Physics 2022, 11, 044 (2022), URL
https://dx.doi.org/10.1088/1475-7516/2022/11/044.
[498] A. Arvanitaki, S. Dimopoulos and K. Van Tilburg, Phys. Rev. X8, 4, 041001 (2018),[arXiv:1709.05354].
[499] A. Berlin et al., JHEP 07, 07, 088 (2020), [arXiv:1912.11048].
[500] P. Sikivie, Phys. Rev. Lett. 113, 20, 201301 (2014), [Erratum: Phys.Rev.Lett. 125, 029901(2020)], [arXiv:1409.2806].
[501] R. Li et al., Nature Phys. 6, 284 (2010), [arXiv:0908.1537].
31st May, 2024

40

90. Axions and Other Similar Particles[502] K. Ishiwata, Phys. Rev. D 104, 1, 016004 (2021), [arXiv:2103.02848].
[503] L. Cao et al., Phys. Rev. B 104, 054421 (2021), URL https://link.aps.org/doi/10.1103/
PhysRevB.104.054421.
[504] D. J. E. Marsh et al., Phys. Rev. Lett. 123, 12, 121601 (2019), [arXiv:1807.08810].
[505] J. Schütte-Engel et al., JCAP 08, 066 (2021), [arXiv:2102.05366].
[506] P. Sikivie, N. Sullivan, and D. B. Tanner, Phys. Rev. Lett. 112, 131301 (2014).
[507] Y. Kahn, B. R. Safdi and J. Thaler, Phys. Rev. Lett. 117, 14, 141801 (2016),[arXiv:1602.01086].
[508] Y. Oshima et al., Phys. Rev. D 108, 072005 (2023), URL https://link.aps.org/doi/10.
1103/PhysRevD.108.072005.
[509] L. Brouwer et al. (DMRadio), Phys. Rev. D 106, 10, 103008 (2022), [arXiv:2204.13781].
[510] L. Brouwer et al. (DMRadio), Phys. Rev. D 106, 11, 112003 (2022), [arXiv:2203.11246].
[511] M. B. Wise, H. Georgi and S. L. Glashow, Phys. Rev. Lett. 47, 402 (1981).
[512] A. Ernst, A. Ringwald and C. Tamarit, JHEP 02, 103 (2018), [arXiv:1801.04906].
[513] L. Di Luzio, A. Ringwald and C. Tamarit, Phys. Rev. D98, 9, 095011 (2018),[arXiv:1807.09769].
[514] P. F. Pérez, C. Murgui and A. D. Plascencia, Journal of High Energy Physics 2019, 11, 93(2019), ISSN 1029-8479, URL https://doi.org/10.1007/JHEP11(2019)093.
[515] I. M. Bloch et al. (NASDUCK) (2021), [arXiv:2105.04603].
[516] S. P. Chang et al., Phys. Rev. D99, 8, 083002 (2019), [arXiv:1710.05271].
[517] L. Krauss et al., Phys. Rev. Lett. 55, 1797 (1985).
[518] R. Barbieri et al., Phys. Lett. B 226, 357 (1989).
[519] R. Barbieri et al., Phys. Dark Univ. 15, 135 (2017), [arXiv:1606.02201].

31st May, 2024