contents=  Submitted to the Proceedings of the US Community Study on the
Future of Particle Physics (Snowmass 2021) ,
scale=1,placement=top,opacity=1,color=black,position=3.25in,1.2in

# Report of the Topical Group on Wave Dark Matter
for Snowmass 2021

Conveners: Joerg Jaeckel  Institut für Theoretische Physik, Universität
Heidelberg, 69120 Heidelberg, Germany  Gray Rybka  Department of Physics,
University of Washington, Seattle WA 98195, USA  Lindley Winslow  Laboratory
for Nuclear Science, Massachusetts Institute of Technology, Cambridge MA
02139, USA

###### Abstract

There is a strong possibility that the particles making up the dark matter in
the Universe have a mass below 1 eV and in many important situations exhibit a
wave-like behavior. Amongst the candidates the axion stands out as
particularly well motivated but other possibilities such as axion-like
particles, light scalars and light vectors, should be seriously investigated
with both experiments and theory. Discovery of any of these dark matter
particles would be revolutionary. The wave-like nature opens special
opportunities to gain precise information on the particle properties a well as
astrophysical information on dark matter shortly after a first detection. To
achieve these goals requires continued strong support for the next generations
of axion experiments to probe significant axion parameter space this decade
and to realize the vision of a definitive axion search program in the next 20
years. This needs to be complemented by strong and flexible support for a
broad range of smaller experiments, sensitive to the full variety of wave-like
dark matter candidates. These have their own discovery potential but can also
be the test bed for future larger scale searches. Strong technological support
not only allows for the optimal realization of the current and near future
experiments but new technologies such as quantum measurement and control can
also provide the next evolutionary jump enabling a broader and deeper
sensitivity. Finally, a theory effort ranging from fundamental model building
over investigating phenomenological constraints to the conception of new
experimental techniques is a cornerstone of the current rapid developments in
the search for wave-like dark matter and should be strengthened to have a
solid foundation for the future.

###### Contents

  1. 1 Executive Summary
  2. 2 Introduction
  3. 3 Definitive Search Program for the QCD Axion
    1. 3.1 Axions in Particle Physics and Cosmology: Motivation and Role
    2. 3.2 Axion DM discovery: What can we learn? - Particle Physics
    3. 3.3 Axion DM discovery: What can we learn? - Cosmology and Astrophysics
    4. 3.4 Beyond QCD Axions: Axion-like particles - Motivation and Discovery
  4. 4 Wave-like DM scalars and vectors: A New Horizon
    1. 4.1 Scalars and Vectors in Particle Physics - Motivation
    2. 4.2 Scalar and Vector DM - Cosmology
    3. 4.3 Scalar and Vector DM - Detection and Discovery
  5. 5 QCD Axion Coverage
  6. 6 The Current Projects
    1. 6.1 ADMX-G2
    2. 6.2 DMNI Project: ADMX-EFR
    3. 6.3 DMNI Project: DMRadio-m3
    4. 6.4 Current Demonstrators and Future Projects
  7. 7 Importance of Small Projects
    1. 7.1 Demonstration-Scale Experiments
    2. 7.2 DMNI Process and Small Projects
    3. 7.3 Axion Facility
    4. 7.4 Work Force Development
  8. 8 Enabling Technologies
    1. 8.1 Quantum Measurement and Control
      1. 8.1.1 Moving Beyond the Standard Quantum Limit
      2. 8.1.2 Engineering Spin Ensembles
      3. 8.1.3 Atomic Clocks
    2. 8.2 Magnets
    3. 8.3 Resonant Systems
    4. 8.4 Cross-Disciplinary Collaborations
  9. 9 Strong Theory Program
    1. 9.1 Direct Impact on Experiments
    2. 9.2 Astrophysics, Cosmology and Phenomenology
    3. 9.3 New Theoretical Target Areas
  10. 10 Conclusions

##  1 Executive Summary

The search for dark matter (DM) is one of the great undertakings of particle
physics and cosmology. Dark matter is a critical ingredient in shaping the
structure of the universe we observe. Yet, we still do not know which new
particle it is made from. Candidates for dark matter can be roughly
categorized by their mass, with an incredible range from $\sim 10^{-20}$ eV to
above the Planck scale $\sim 10^{27}$ eV still being possible. When DM
candidates masses fall below 1 eV, their interactions become wave-like rather
than particle-like. The detection techniques are inherently different than
traditional particle detectors and they are intrinsically quantum in their
nature. Advances in quantum sensing and control along with the related
advancements in cryogenics and superconducting magnets have driven an
explosion of interests in these candidates.

The direct detection of any dark matter candidate would clearly be a
monumental step forward for both cosmology and particle physics and further
strengthen the connection between the two disciplines. But discovery of a
wave-like dark matter particle would bring with it an especially broad range
of opportunities. The nature of most experiments searching for wave-like dark
matter is such that there is a particularly small gap between what is needed
for a discovery and what is needed for precision measurements of properties
(e.g. the mass) of the dark matter particle as well as astrophysical
information (e.g. the local dark matter velocity distribution). A discovery
would start a revolution in particle physics as well as open the field of dark
matter astronomy.

Within wave-like dark matter, there is a broad sea of candidates anchored by
the highly-motivated QCD axion. An energetic and growing community focused on
the search for wave-like dark matter has put forward two goals:

  1. 1.

Execute a Definitive Search Program for the QCD Axion The QCD axion is the
theoretically most-studied and strongest motivated WLDM candidate. Decades of
experimental work along with advances in quantum measurement technologies has
put us in the unique position: this decade we can build a suite of experiments
that, together, are sensitive to the most plausible theoretical predictions of
QCD axion couplings at nominal dark matter densities. The community intends
moving from building technology demonstrators to building machines designed
for a discovery.

  2. 2.

Pursue a Theory and R&D program to elucidate the opportunities in
Scalar/Vector Dark Matter We are in the process of understanding how WLDM dark
matter candidates beyond the QCD axion can work. There are already
experimental techniques that promise to reach previously-unexplored parameters
for scalars and vectors. This Snowmass period we would like to see these
experimental techniques refined, and theoretical studies of new WLDM
candidates to inform the direction of developing experiments and help them
target the most interesting physics.

These goals are in-line with those outlined by the larger dark matter
community in the BRN for Dark Matter New Initiatives (DMNI) report.

The enthusiasm for the QCD axion stems from its key role in solving the
Standard Model’s strong CP problem (one of the two severe fine tuning problems
of the Standard Model) while simultaneously being an excellent dark matter
candidate. The QCD axion encompasses two broad classes of models the KSVZ
axion which predicts additional quarks and the DFSZ axion which predicts an
expanded Higgs sector. Additional pseudo-scalars called Axion-Like-Particles
(ALPs) are a natural consequence of many candidates for fundamental extensions
of the Standard Model, in particular string theory.

Fundamental theories also motivate additional scalar and vector particles
which make excellent dark matter candidates. The rich phenomenology of these
candidates leads to a variety of detection mechanisms and constraints. Like
axions, the wave-like nature of the candidates demands experiments designed
around quantum techniques. A discovery of a new scalar or vector would
similarly drive a larger high energy physics program to understand the nature
of the new physics.

In support of these goals the community has put forward a road map for
discovery.

  1. 1.

Pursue the QCD Axion by Executing the Current Projects: The ADMX G2 effort
continues to scan exciting axion dark matter parameter space and the
experiments identified by the DMNI process DMRadio-m3 and ADMX-EFR are
prepared to start executing their project plans. These will probe some of the
presently most exciting mass ranges with excellent chance of discovery if the
axions make up dark matter.

  2. 2.

Pursue Wave-like Dark Matter with a Collection of Small-Scale Experiments The
wave-like nature of these candidates demands the full axion mas range be
explored by a collection of significantly different techniques. These
techniques vary in readiness level, but the entire range needs to be
comprehensively explored through some combination of them. The DOE DMNI
process is the right scale for many of these proposed experiments and was
effective at identifying those that were ready to proceed to full projects. In
addition, we should pursue opportunities to harness key US expertise for
International projects.

  3. 3.

Support Enabling Technologies and Cross-Disciplinary Collaborations: Many of
the proposed efforts share needs in ultra-sensitive quantum measurement and
quantum control, large, high-field magnets, spin ensembles, and sophisticated
resonant systems. These technologies overlap strongly with other HEP efforts
and synergies should be exploited both within HEP and beyond.

  4. 4.

Support Theory Beyond the QCD Axion: The QCD axion is an important benchmark
model, but not the only motivated one. Theoretical effort should be supported
to understand the role of scalars, vectors and ALPs in dark matter cosmology
and astrophysics.

The wave-like dark matter experiments enabled by technological advances
especially in quantum measurement and control are poised for a great
discovery. The US is a leader in this growing field and now is the time to
continue the momentum and move this program forward rapidly.

##  2 Introduction

The search for Dark Matter has been a main driver for High Energy Physics
(HEP) for several decades. Wave-like dark matter candidates have masses less
than 1 eV. In the local environment with a typical dark matter density
($\rho_{dm}\sim 0.45{\rm MeV}/{\rm cm}^{3}$), this corresponds to wavelengths
on the order $1\,{\rm km}(0.2\mu{\rm eV}/m)$ and large occupation numbers
$\sim 2\times 10^{34}(0.2\mu{\rm eV}/m)^{4}$. These candidates have been
relatively unexplored even though the highly motivated QCD axion is among
their number. The wave-like behavior itself has been the limiting factor
because it requires detection mechanisms that are significantly different than
traditional High Energy Physics (HEP) or WIMP direct detection experiments. It
also means that we have crossed the wave-particle divide and these experiments
are intrinsically quantum in their nature.

Advances in quantum measurement, control, and other enabling technologies
including large, high-field magnets, spin ensembles, and sophisticated
resonant systems have opened up a new candidates and parameter space to
explore. This has inspired a growing community to harness these advancements
for HEP and the search for Dark Matter. The community has embraced the
Snowmass process and submitted over 86 Letters of Interest and came together
to write two community white papers:

  * •

Axion Dark Matter [1]

  * •

New Horizons: Scalar and Vector Ultralight Dark Matter [2]

They form a complete report on all efforts, from the ongoing DOE Project
ADMX-G2 to demonstration-scale experiments to critical R&D on quantum sensing.

In this Cosmic Frontier topical group (CF2) report we will reiterate (drawing
heavily on the above mentioned white papers) the strong motivation for these
candidates and build the case for why the goals of this community to

  1. 1.

Execute a Definitive Search Program for the QCD Axion

  2. 2.

Pursue a Theory and R&D program to elucidate the opportunities in
Scalar/Vector Dark Matter

should resonate across high energy physics with a focus on the complementary
to the Energy, Rare & Precision Measurement, and other efforts on the Cosmic
Frontier. But there are further strong synergies with Instrumentation Frontier
and even with the Accelerator Frontier.

We will review the strong motivation of the QCD axion and highlights of its
role in both particle physics and cosmology in Sec. 3, and do the same for
scalars and vector wavelike dark matter in Sec. 4.

The current “big” projects are briefly discussed in Sec. 6, whereas the role
and importance of a diverse range of small projects is stressed in Sec. 7.
Both big and small projects will benefit from a wide range of enabling
technologies as well as a broad and vigorous theory program, Secs. 8 and 9. We
make our final conclusions in Sec. 10.

##  3 Definitive Search Program for the QCD Axion

Figure 1: (Left) Sensitivities of current and near future axion searches
(labelled outlines) compared to the couplings expected for the QCD axion
(yellow band) and already excluded areas (grey). Figure by A. Berlin. (Right)
Timeline for the experiments and possible common axion facility. Figure by L.
Winslow

###  3.1 Axions in Particle Physics and Cosmology: Motivation and Role

Axions take an outstanding role amongst the dark matter candidates as they are
motivated by an intrinsic problem of the Standard Model, the strong CP
problem, that exists independently from the need for DM. The strong CP is one
of two severe fine-tuning problems of the Standard Model (the other being the
smallness of the Higgs vacuum expectation value compared to the Planck scale).
To be consistent with constraints on the neutron electric dipole moment [3]
the CP violating dipole moment requires a tuning of 1 in $\sim 10^{10}$ of the
so-called $\theta$ angle. In contrast to other fine-tunings in the SM this
problem is unique as it cannot be addressed by anthropic reasoning. We could
almost certainly exist in a form very similar to our present one even for a
$\theta\sim 0.1$ [4].

This tuning problem is solved by the famous Peccei-Quinn mechanism [5, 6] that
is an important early example of solving a fine-tuning problem by dynamical
relaxation. The $\theta$-parameter is turned into a dynamical field that then
over the cosmological evolution relaxes to its potential minimum located at
the CP conserving value that ensures a vanishing electric dipole moment of the
neutron. The crucial observable consequence of $\theta$ being dynamical is
that its excitations correspond to particles, i.e.axions [7, 8]. An important
aspect of the PQ solution is that it still fully addresses the fine-tuning
problem. This is in contrast to proposed solutions of the electroweak
hierarchy problem, such as, e.g. supersymmetry, where experimental constraints
have led to the reemergence of a sizable amount of tuning (cf., e.g. [9, 10,
11]).

In the range $f_{a}\sim(10^{10}-10^{13})\,{\rm GeV}$ the misalignment
mechanism [12, 13, 14, 15, 16] provides a good way for axions to be the cold
dark matter in the Universe. This mechanism is an automatic consequence of the
dynamical relaxation of the $\theta$-angle. If the initial $\theta$-angle is
non-vanishing, this corresponds to a non-vanishing energy density. This energy
density is diluted by the cosmic expansion, reducing the $\theta$-angle to its
potential minimum at 0. It is straightforward to check that this energy
density behaves exactly as one would require for cold dark matter. Therefore
the axion is a natural dark matter candidate in the sense that unless tuning
of the initial value, or a strongly non-standard cosmology is applied it
inevitably yields an amount of dark matter roughly of the order of he observed
size111Additional contributions of a similar size may arise from topological
defects in the case that the final Peccei Quinn symmetry breaking happens
after inflation [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31,
32, 33, 34, 35, 36, 37]. These affect the argument only on a quantitative
level.. Moreover, this dark matter is automatically (very) cold, as required
by structure formation.

###  3.2 Axion DM discovery: What can we learn? - Particle Physics

The discovery of a new fundamental particle is in any case an enormous step
forward for physics. For the axion this would be especially true. The axion is
automatically connected to an energy scale $f_{a}\gtrsim 10^{7}\,{\rm GeV}$.
Thereby its pure existence gives a glimpse at fundamental physics at scales
more than 1000 times larger than those directly accessible at colliders such
as the LHC. But even beyond that, its nature as wave-like dark matter would
allow for high precision measurements soon after discovery that will give
important information both for fundamental particle physics (this subsection)
as well as astrophysics and cosmology (next subsection).

Let us briefly consider a few of the measurements that would be possible
relatively soon after an initial discovery, the insights that can be gained
from them, as well as their connection to other areas of particle physics.

The currently most sensitive axion dark matter search experiments use the
wave-like nature and in particular the intrinsically long coherence length of
the axion wave to achieve a resonance between the oscillations of the axions
with a frequency $m_{a}$ and suitable resonator, e.g. a cavity. In this way
the detection of axions is enhanced by a factor of the quality factor of the
resonator up to $Q\sim 1/v^{2}\sim 10^{6}$. Of course, this enhancement only
applies within the resonance width $\sim 1/Q$, i.e. a mass within a window
$\Delta m_{a}\sim m_{a}/Q$ around the known eigenfrequency of the resonator,
$\omega_{\rm res}=m_{a}$. Therefore, essentially the detection itself
automatically yields a measurement of the axion mass with an up to $10^{-6}$
precision.

For a standard QCD axion, measuring the mass immediately implies a measurement
of the corresponding axion decay constant, i.e. $f_{a}$, via the relation [7,
8, 38]222The precision in the expression being limited by the precision of the
underlying QCD/chiral perturbation calculation. Consequently, improvements in
the relevant QCD input could also make this more precise, giving also a first
example of the synergy between the two areas.,

$f_{a}\approx 10^{10}\,{\rm GeV}\left(\frac{0.6{\rm meV}}{m_{a}}\right).$ (1)

We would therefore get direct evidence for a new large energy scale in
particle physics. This could open connections to a wide range of fundamental
structures. For example, in string theories the axion scale $f_{a}$ is usually
directly linked to the string scale [39, 40, 41, 42, 43, 44, 45, 46, 47], but
its size is also suggestive of a scale suitable for the see-saw scale in
neutrino models as made explicit, e.g. in the SMASH model [48]. Measuring the
properties and couplings of the axion will give information on which option is
realized in nature, with significant implications for theoretical model
building.

A next step would be to actually demonstrate that the discovered dark matter
particle, seen, e.g., in an experiment targeting the axion photon coupling
(cf., e.g., the experiments discussed in Sec. 6), is indeed a QCD axion. To
achieve this requires establishing the defining gluon coupling. This could be
done by an experiment directly targeting this coupling, e.g. by searching for
an oscillating electric dipole moment of nuclei as done by CASPEr [49, 50].
Such a measurement would be strongly facilitated by already knowing the
precise mass of the axion, as this eliminates the need for scanning, speeding
up the experiment by a factor of up to $Q\sim 10^{6}$. Or, more importantly in
this case, allowing for a significant increase in the measurement time at the
given frequency, allowing an experiment that would otherwise not be sensitive
to a QCD axion to nevertheless make a detection.333For the same reason it is
likely that several experiments targeting the discovery coupling could confirm
the discovery relatively shortly after an initial discovery.

The photon coupling is usually determined by a the combination of a model
dependent electromagnetic anomaly plus a model independent contribution from
pion mixing [51, 52, 53]. A sufficiently precise determination may allow to
infer if the axion in question is a (sufficiently simple) DFSZ [54, 55] or
KSVZ [56, 57] type axion. Even assuming that the axion constitutes all of the
dark matter, the local axion density is at present not sufficiently well known
to make this distinction. However, this may be different if also a detection
in a helioscope [58] such as IAXO [59, 60] is achieved. Alternatively such a
distinction can be made if either IAXO or a direct detection experiment such
as QUAX [59, 60] measure a sizable coupling to electrons, which is expected
only in DSFZ type models. This would have crucial implications for collider
searches, as DFSZ models feature two Higgs doublets that typically should not
be too heavy. They would therefore be within reach of collider searches,
possibly even of the LHC.

###  3.3 Axion DM discovery: What can we learn? - Cosmology and Astrophysics

A crucial question for any dark matter candidate is whether it contributes all
or only a part of the dark matter. For an axion haloscope, the signal is
proportional to the product $\sim g^{2}_{a\gamma\gamma}\rho_{a}$ and so the
coupling and local density are degenerate with only a single detection.
Fortunately are at least two options to experimentally disentangle them. If a
haloscope detection can be combined with a search for a candidate in an
experiment that is independent of dark matter, e.g. the helioscope [58], IAXO
[59, 60], whose signal strength is $\sim g^{4}_{a\gamma\gamma}$ this can be
used to infer the local axion dark matter density $\rho_{a}$ which can then be
compared with the expected dark matter density $\rho_{\rm
CDM}\sim(300-450)\,{\rm MeV}/{\rm cm}^{3}$. If we also have a detection via
the gluon coupling/electric dipole moment, we can also use that in this case
the size of the coupling is uniquely related to the mass. Knowing the mass we
can therefore directly infer the local dark matter density from the strength
of the signal amplitude $\sim g_{agg}\sqrt{\rho_{a}}$. The precision with
which this comparison can be achieved in both cases also provides a nice
synergy to astrophysical observation and structure formation simulations that
give predictions for the local dark matter density. Moreover, precise
predictions for a relation between the axion gluon coupling and the resulting
oscillating electric dipole moment require theory input from QCD and nuclear
physics, giving another important synergy area.

Important astrophysical/cosmological information, in particular on the dark
matter distribution and therefore on small scale structure formation will be
available already shortly after an initial discovery. Resonant experiments
such as ADMX, ABRA and others (see Secs. 6 and 7) measure an amplitude of the
signal and are able to perform a high precision spectral analysis. Due to the
wave-like nature of axion dark matter this spectrum directly corresponds to
the energy spectrum of the axions converted in the detector. In that way we
can obtain a precise measurement of the kinetic energy, i.e. velocity squared,
distribution of axion in our location of the Galaxy. A $\Delta v^{2}\sim
10^{-9}$ resolution of the velocity squared distribution compared to a typical
$v^{2}\sim 10^{-6}$ is feasible in most discovery experiments without any
modification and within a very short timescale (cf. [61] for a high resolution
measurement done by ADMX within a data taking campaign). Observing daily and
annual modulations of the resulting spectrum can even give first information
on the full vectorial distribution [62]. This may be further enhanced by
exploiting the (small) intrinsic directionality of several of the detection
schemes (e.g., MADMAX [63], ADMX [64]).

Additional astrophysical information may be gleaned if IAXO is also able to
detect axions444For this axions do not need to be dark matter.. In this case
the axion may, e.g. also serve as a probe of the solar composition (e.g.
metalicity, elemental abundances) [65].

These examples demonstrate that discovery of wave-like axion dark matter would
open a new window of “dark astronomy”.

###  3.4 Beyond QCD Axions: Axion-like particles - Motivation and Discovery

While the axion is the most prominent wave-like dark matter candidate it is by
far not the only one. An important generalization are so-called axion-like
particles, loosely defined as particles sharing crucial features of the axion
(e.g. (pseudo-)scalar, low mass, weak couplings) but not solving the strong CP
problem. In field theory they can be imagined as pseudo-Nambu Goldstone bosons
arising from the spontaneous breaking of approximate global symmetries. In
string theory they can originate as the imaginary part of moduli fields [66,
40, 41, 42, 43, 44, 45, 46, 47, 67, 68]. Both are rather generic features of
extensions of the Standard Model and therefore we would them to be quite
common in many extensions of the Standard Model. Indeed, axion-like particles
could also arise in models for the flavor structure of the Standard Model
(they are then often also dubbed familons) [69] and in string theory there has
been plenty of discussion on the existence of axion-like particles including
the possibility to have a sizable number of them a so-called string axiverse
[41]. Similar to axions they can be wave-like dark matter via the misalignment
mechanism [12, 13, 14, 15, 16, 70].

The mass of axion-like particles is not determined by QCD effects as is the
case for QCD axions. Therefore, a much wider range is possible. Moreover, a
possible strong temperature dependence [70], an enlarged field range [71] or
coupling enhancing effects [72, 73, 74, 75, 76] may allow couplings to be much
stronger than that expected for the simplest QCD axions. This gives true
discovery potential also to experiments that do not (yet) reach the QCD axion
band.

As is the case for the QCD coupling to the Standard Model proceeds via higher
dimensional operators (typically derivative couplings). Therefore, as in the
case of the QCD axion a discovery would indicate a clear scale for new
physics. Any such discovery would therefore essentially give rise to a no-
loose theorem for experiments that explore this new scale with a broad reach.
Axion-like particles are often less constrained than QCD axions. In particular
the couplings could often still be stronger than those of QCD axions,
indicating a lower physics scale that could be within reach of other
experiments. Moreover, a stronger coupling could also put them into the reach
of other experiments, e.g. IAXO, that are independent of dark matter.

Most of the precise post-discovery measurements that could be performed with a
dark matter axion (see previous subsections) are likely to be also possible
with an axion-like particle. Therefore, an axion-like particles would open a
similar level of access to a wealth of information both on the underlying
fundamental particle physics model as well as new insights into astrophysics
and cosmology.

##  4 Wave-like DM scalars and vectors: A New Horizon

Figure 2: Overview of experimental techniques and the mass ranges they target,
for scalars (pink) and vector (green and blue). Figure taken and caption
adapted from [2].

While axions (and axion-like particles) are an important benchmark scenario
for wave-like dark matter they are far from the only well-motivated
candidates. As wave-like dark matter must be bosonic to avoid the Pauli
principle we in general have the possibility to have very light scalars or
vectors. Indeed they are amongst the simplest possible extensions of the
Standard Model, by a single scalar and by a simple U(1) gauge factor in the
case of vectors.

###  4.1 Scalars and Vectors in Particle Physics - Motivation

A central motivation for scalars and vectors is that they are the only bosonic
particles that can interact with the Standard Model via renormalizable
“portals”. For scalars ($\phi$) via the “Higgs-portal” [77, 78, 79, 80, 81]
$(\kappa\phi+\lambda\phi^{2})|H|^{2}$ and in the vector ($X_{\mu}$) case via
“kinetic mixing” [82, 83, 84] $\chi B_{\mu\nu}X^{\mu\nu}$ where $B_{\mu\nu}$
is the hypercharge field strength (at low energy it’s essentially the
electromagnetic field strength) and $X_{\mu\nu}$ that of the new vector field.
The portal interactions are special in that they are not suppressed by some
(very) high energy scale. As such they can be generated at a very high energy
scale while still leaving observable traces in low energy experiments.
However, due to the exceptional sensitivity of many low-energy experiments
searching for scalars and vectors, also additional interactions (that are
suppressed by a high energy scale) can be accessed.

Scalars and vectors are also abundant in extensions of the Standard Model
based on string theory. Indeed, string theory usually features plenty of
scalars in the form of moduli (the real part), and brane constructions of the
Standard Model generically contain extra U(1) gauge factors giving rise to
vector bosons (cf., e.g., [66, 40, 41, 42, 43, 44, 45, 46, 47, 67, 68, 85, 86,
87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98]).

Scalars also feature in models to address the hierarchy problem (e.g. the
relaxion [99]) (synergy with theory), and may also play a role in dark energy
(e.g. quintessence [100, 101]) giving a synergy with CF4-6.

It is noteworthy that very light scalars and vectors can often be tested to an
amazing precision, often at a level that is at or even below gravitational
strength (see [2] for a wide variety of examples). This gives access to truly
fundamental effects at the highest imaginable energy scales.

###  4.2 Scalar and Vector DM - Cosmology

For both types of particles their role as wave-like dark matter is supported
by the existence of suitable production mechanisms that can generate
sufficient amounts to explain the full observed dark matter abundance. The
mechanisms include the misalignment mechanism [12, 13, 14, 15, 16, 102, 70]
already discussed in the case of axions, but there are also mechanisms that
are based on resonant/tachyonic decays [103, 104, 105, 106, 107], inflationary
and gravitational production [108] as well as the decay of topological
configurations such as strings [109]. Notably, the production mechanism,
clumpy vs non clumpy or for vectors the type of polarization can also impact
the required search strategies [70, 108, 110, 111, 112].

###  4.3 Scalar and Vector DM - Detection and Discovery

From the experimental side the search for scalars and vectors is driven from
two directions. One is that experiments searching for axions are often also
directly sensitive to vectors555There is also some sensitivity to certain
types of scalars and more might be achievable with adapted configurations
[113]. (indeed the search is often simpler, e.g. by not requiring a
superstrong magnetic field to be present). A second equally important driver
are a wide diversity of ultra-precise measurements using an amazing range of
experimental techniques and technologies ranging from atomic physics
measurements, atomic clocks, ultrasensitive mechanical sensing, optical and
atom interferometry to observations of the cosmic microwave background and
black holes (e.g. via gravitational waves). All these often employ and further
develop cutting edge technologies such as, in particular also quantum
technologies.

As in the case of axions, opportunities go far beyond the discovery of a new
particle and dark matter. Indeed in most cases the post-discovery measurements
discussed above for the case of axions are based on the wave-like nature and
can also be done in the case of scalars and vectors. Therefore, in this case,
too, unprecedented information on particle physics as well as cosmology would
be within reach.

##  5 QCD Axion Coverage

One of our goals for the wavelike dark matter community is to “execute a
definitive search for the QCD axion”. We will define a ‘definitive search’ as
sensitivity to QCD axions with DFSZ coupling if they make up the majority of
our local dark matter density. We believe this is achievable, but it should be
noted that it is not exhaustive; as describe in Sec. 9 it is conceivable that
axions have smaller couplings or make up a minority fraction of the local dark
matter density. In the event of no discovery, such considerations can be
addressed in the next Snowmass period.

Achieving this goal is not tenable by any one experiment. Different energy
scales require different technologies. The applicability of current ant future
projects over the QCD axion mass range is shown in Fig. 3.

Figure 3: Axion mass ranges explored by different experiments. Running
experiments are shown in green. The proposals based on the axion-photon
coupling are shown in red, those targeting other couplings in blue. Figure
taken and caption adapted from [1].

Here we have divided coverage into existing limits, current ongoing
experiments, and future projects. The relevant QCD axion masses are bounded
from above by stellar astrophysics, and from below by the non-observation of
axion superradiance effects on black hole spins. A beachhead into the QCD
axion couplings in the $\mu$eV has already been established by the ADMX G-2,
HAYSTAC, and CAPP cavity haloscopes, demonstrating their effectiveness.
Experiments currently funded will expand this explored region as described in
Sec. 6. A complete exploration of the QCD axion mass range will require
supporting R&D to establish a suite of experiments in the near future as
described in Sec. 7.

##  6 The Current Projects

###  6.1 ADMX-G2

The ADMX program has led the axion community for many decades. The current
stage of the program ADMX-G2 has been running since 2015. It is the first
experiment to reach the sensitivity to search for QCD axions at typical DFSZ
coupling making up the bulk of the local dark matter density [114]. The
experiment is built around a large (8.5 Tesla) high inductance (540 Henry)
NbTi Superconducting Solenoid magnet with a 60 cm inner diameter and a height
of 112 cm. The induced axion signal the couples to a cavity and is readout
with quantum amplifiers. It has performed three runs ([114], [115], [116]).
Each run used slightly different cavity geometries to provide sensitivity to
increasing frequencies. The quantum amplifier technology has been key. Run 1A
used a Microstrip SQUID Amplifier but subsequent runs used Josephson
Parametric Amplifiers (JPAs) for amplification. The final run will combine 4
frequency locked cavities coherently to take advantage of the axions coherent
signal to make up for the volume lost by operating a single cavity. This is
scheduled to complete its scan as the DMNI project ADMX-EFR completes its
construction and commissioning, as indicated in Figure 1. ADMX-G2 will have
succeeded in search approximately two octaves of parameter space from 2$\mu$eV
to 8$\mu$eV. Figure 3 shows in green the current the ADMX-G2 accomplishments
and the current status of demonstrator-scale experiments HAYSTAC and CAPP
which are now probing QCD axions at near-KSVZ sensitivity.

###  6.2 DMNI Project: ADMX-EFR

The ADMX collaboration aims to push to the higher frequency range of 2–4 GHz
with the Extended Frequency Range (EFR) experiment. The goal is to achieve
DFSZ sensitivity across this frequency range, which corresponds to an axion-
mass range of 8.3–16.5 $\mu\mathrm{eV}$. ADMX plans to overcome the
sensitivity loss due to the decreasing volume of the cavity operating an array
of eighteen cavities. Further sensitivity improvements come from increased
magnetic field strength from an existing 9.4 T MRI magnet, increased quality
factor by coating cavities with superconducting films or low-loss dielectrics
and finally reduced amplifier noise enabled by squeezed state amplifiers or
single photon counting techniques that evade the Standard Quantum Limit. The
experiment is ready to make great inroads into critical parameter space as
soon as the DMNI projects are given the green light. The ideal funding
scenario would have the run start in 2024 completing 2027.

###  6.3 DMNI Project: DMRadio-m3

The DMRadio-m3 experiment aims to search for the QCD axion over the mass range
$20\,\mathrm{neV}\lesssim m_{a}\lesssim 800\,\mathrm{neV}$, achieving DFSZ
sensitivity over the range $120\,\mathrm{neV}\lesssim m_{a}\lesssim
800\,\mathrm{neV}$ with a 5 year total scan time. This mass range begins to
probe the top of the GUT-scale QCD axion masses, in addition to testing a wide
swath of interesting ALP parameter space. In this mass and frequency range (30
MHz to 200 MHz), the axion signal starts behaving like a current, so the
experiment can started to be modelled as lumped element circuit components,
hence these experiments are referred as the lumped element experiments in
comparison to the cavity experiments like ADMX. Like ADMX-EFR, DMRadio-m3 is
ready to search a wide complementary parameter space. In the ideal funding
scenario, construction starts in 2024 with the physics data taking from
2026-2031.

###  6.4 Current Demonstrators and Future Projects

As will be described in Section 7, the nature of wave dark matter detection
requires an evolution of techniques as a function of frequency and candidate.
For axion physics we outline in Figure 1 many of the efforts that are
demonstrating many of the key technologies and techniques outlined in Section
8 that will be critical for the definitive search for the axion. We highlight
in blue the techniques that are pursuing the measurements of the alternative
couplings which will be particularly critical in the event of a detection.

##  7 Importance of Small Projects

The wave-like nature of candidates in the sub-1 eV mass range leads to
detection mechanisms that are inherently quantum and require detection schemes
that are very different than standard particle detectors. The wave-like nature
also demands experiments optimized for the frequency range of interest. Much
intuition can be gleamed from our understanding of the detection of
electromagnetic radiation, the techniques for measuring radio waves are very
different than visible light. For this reason the search for wave-like dark
matter demands a suite of experiments not one monolithic detector. This suite
of experiments requires a strong program of experiments at different scales
from R&D, see Section 8 to demonstrators to Small Projects.

###  7.1 Demonstration-Scale Experiments

The current suite of experiments has a healthy mix of experiments. Having a
range of demonstration-scale experiment has been key and in light of the huge
mass/coupling range that needs to be tackled it will be very important to also
have strong support for new initiatives at this level. In axions,
demonstration-scale Experiments on the order of $\sim$$100k to $\sim$$1M such
as ABRACADABRA, DMRadio-Pathfinder, ADMX-SLIC, ADMX-Orpheus, ADMX-Sidecar and
HAYSTAC provided key results that proved readiness to move to full projects.
These were funded as a combination of Foundation money and grants to
individual institutions. Support of demonstrators continues to be key part of
the pipeline, establishing new approaches and technologies. We highlight
experiments like CASPEr to measure the nuclear couplings and HAYSTAC which
continue to innovate in quantum sensor readout. A variety experiments in
scalar/vector that will move from table-top R&D to demonstrators and we should
be poised to embrace these opportunities.

###  7.2 DMNI Process and Small Projects

In 2018, the dark matter community came together to write a Basic Research
Needs Report (BRN) for Dark Matter New Initiattives (DMNI). This outlined
general goals for the field. This was followed by a DOE funding call to
provide funds for the development of project execution plans for full
proposals. The selected experiments,DMRadio-m3 and ADMX-EFR, were described in
Section 6.

The current DMNI experiments are ready to progress to construction and will
commence operations in the next five years. To keep an active pipeline, a new
DMNI call for proposals to prepare projects should come concurrently with the
current experiment proceeding to construction.

###  7.3 Axion Facility

For axion experiments, much of the infrastructure to host experiments could be
common. This includes electromagnetic shielding, cryogenic systems and low
noise warm electronics with well-characterized grounding schemes. This
infrastructure may be appropriate for scalar/vector searches depending on the
details of the detection technique. The magnet is the cost-driver for many of
the experiments. It may also be possible for the experiments in the $>$ GHz
regime to share one smaller bore high-field magnet while in the $<$ MHz regime
share a large magnet with slightly more modest fields. The community is
interested in coming together to produce a conceptual design for 1-2 such
facilities in support of future small projects.

Indeed in Germany and South Korea efforts for a consolidation are already
underway with the plan to house three experiments at DESY (ALPS-II, IAXO and
MADMAX) as well as the construction of a whole suite of dark matter
experiments at CAPP. In both cases experiments strongly benefit from existing
and expanding expertise and infrastructure in particular with regards to
magnets and cryogenics.

Having such a facility at hand could significantly speed up (and reduce costs)
further development as well as construction of experiments and help to achieve
a leading role for the US program.

###  7.4 Work Force Development

Demonstrator-Scale experiments and Small Projects are incredibly good for
training the next generation of experimentalists. In such experiments,
students and postdocs get experience in all aspects of the experiment. The
training of instrumentalists has been highlighted as a strategic need for the
field. Wave dark matter experiments are particularly valuable training grounds
since the enabling technologies including quantum sensing and control, as
described in Section 8, have been identified as national priorities. For these
reason, wave dark matter experiments are particularly critical as drivers for
work force development.

##  8 Enabling Technologies

The small projects described in Section 7 are enabled by a strong R&D program.
In this section, we highlight the technologies that are at the heart of
searches for wave-like dark matter. This is not exhaustive as many new
techniques are constantly emerging beyond the horizon of axions, ALPs, scalars
and vectors summarized in Figures 1, 2, 3. We emphasize that these are very
much interdisciplinary activities involving cross frontier topics such as
magnet and cavity development, but also groups that may classically be atomic
physicists who bring key experience in quantum control and measurement.

###  8.1 Quantum Measurement and Control

By definition the search for wave-like dark matter sits at the transition from
particles behaving like particles and them behaving like waves, therefore the
detection techniques are inherently quantum and quantum measurement and
control is a key enabling technology. This directly aligns with recent
national initiatives to increase investment in quantum technology and build
the quantum workforce of the future.

####  8.1.1 Moving Beyond the Standard Quantum Limit

Figure 4: Principles of beyond the standard quantum limit amplification.
(Left) The goal is to push the quantum noise out of the experimental
observable. (Right) The source of quantum noise changes as a function of
frequency and therefore the techniques change. Figure by L. Winslow with A.
Chou and K. Irwin

For the detection of wave-like dark matter, the experiment ultimately couples
to an electromagnetic sensor. As the temperature of the experiment is reduced
below a few hundred milli-kelvin, the sensitivity of the experiment is
dominated by quantum noise rather than thermal noise. To improve sensitivity,
the sensor needs to push beyond this standard quantum limit. This is achieved
by pushing the noise out of the signal being measured as indicated in Figure
4. The details of how to achieve this are frequency dependent. Below about 1
GHz, the noise is quantum back action and the corresponding techniques is back
action evasion using devices such at quantum upconverters. Above 1 GHz the
statistics of the photons dominates and techniques such as quantum squeezing
can be used to evade the standard quantum limit. Quantum squeezing was
successfully demonstrated by the HAYSTAC collaboration to achieve a quantum
advantage gain of about 2.5. Single photon counting promises an even larger
quantum advantage [117] and a superconducting qubit-based single photon
detector was recently used in a dark photon search using a fixed frequency
cavity [118]. These devices must be coupled with high Q resonators or cavities
($Q>5\times 10^{5}$).

####  8.1.2 Engineering Spin Ensembles

Quantum engineering of spin ensembles are used in experiments searching for
all types of wave-like dark matter. These include experiments such as CASPEr
which can search for EDM and gradient interactions induced by both axions and
scalar dark matter candidates [119]. The goal is to observe spin ensemble
dynamics at the level of spin projection noise and then use spin squeezing and
more generally spin ensemble correlations to further increase sensitivity. The
spin ensemble is ultimately coupled to an electromagnetic sensor so the
techniques developed above will find application here. The other key R&D
activity is engineering to optimize the materials that host these spin
ensembles to increase the sensitivity to the EDM and gradient interactions of
ultra-light dark matter [120].

####  8.1.3 Atomic Clocks

There are many novel and interesting techniques in development for the search
for scalar and vector dark matter, see Figure 2. We highlight here atomic
clocks as due to its broad application. In the last $\sim 15$ years, optical
atomic clocks have improved by more than three orders of magnitude in
precision,reaching a fractional frequency precision below 10-18 [121]. The
interaction of scalar dark matter can lead to the oscillation of fundamental
constants such as the fine-structure constant $\alpha$ or proton-to-electron
mass ratio. If these vary in space or time then atomic, molecular or nuclear
will vary as will the clock frequencies that use them. Such an oscillation
signal would be detectable with atomic clocks for a large range of DM masses
($m\lesssim 10^{-13}$ eV) and interaction strengths. Clock DM searches are
naturally broadband, with mass range depending on the total measurement time
and specifics of the clock operation protocols (see [122] for details). A
multidisciplinary team is needed to continue to develop atomic clocks as a
tool for dark matter searches.

###  8.2 Magnets

Magnets are at the heart of all axion experiments and can be used in some
searches for scalar-type dark matter. Advances in superconducting materials
for the construction of magnets are enabling larger, higher-field magnets. The
development of production and quality of rare-earth barium copper oxide
(REBCO) tapes is particularly promising and harnesses key technology that
overlaps with other industries including fusion power.

The DMNI experiments are based on conventional large magnet technology based
on Nb3Sn and/or NbTi technology. To move to higher masses, 30–50 $\mu$eV
range, it is proposed to design a high-temperature superconducting (HTS)
insert to create a maximum central magnetic field strength of 32 T over a 15
cm diameter. The National High Magnetic Field Laboratory (MagLab) has been
developing higher field REBCO inserts with current designs reaching a maximum
field of 45 T [123] and future designs aiming for even higher field strengths
across smaller bore diameters. To move to smaller axion masses, proposals like
DMRadio-GUT [124] require more modest fields but large volumes and large
bores. More complicated geometries may be advantageous in some measurements.
Advances in HTS technology and the corresponding cryogenics are critical for
the entire field.

R&D efforts in this area will allow for the development of cost-effective
large-volume high-field magnet designs that will benefit many axion detection
experiments and beyond. We seek to establish a framework by which experiments
can create optimized magnetic field profiles based on the individual
experimental needs, minimizing signal losses/leakage while still maximizing
the science potential of axion searches in the highest possible magnetic
field. We are interested in partnering with experts at national labs and
industry in order to design, construct and then successfully implement these
next generation of magnets for use in the search for wave-like dark matter.

###  8.3 Resonant Systems

The detection of wave-like dark matter often relies on resonant readout to
amplify the wave-like signal. Cavities with sophisticated geometry and tuning
mechanisms have long been used to allow scanning across frequencies
corresponding to axion masses greater than 1 $\mu$-eV. The move to higher
frequency and masses results in smaller cavity volumes and lower quality
factors for ordinary metals. The move to higher frequency requires cavities to
leverage new ideas from both accelerators and quantum information sciences
[125].

For axion searches below 1 $\mu$-eV, the transition to a lumped element
detection model requires the development of high quality factor resonant
circuits that allow tuning at cryogenic temperatures. The fundamental limits
on the quality factors of such circuits is a subject of active research.

Resonant systems are not unique to axion searches. In particular, dark photon
searches rely on similar resonant circuit and cavity readouts. This is
fundamental R&D which is important for wave dark matter searches but will find
application in related fields including accelerator development.

###  8.4 Cross-Disciplinary Collaborations

A strong R&D program grows from harnessing technological advancements for
application in particle detectors. This process needs expertise from a broad
range of disciplines. The technologies that are needed for wave dark matter
searches range from novel materials to fabrication of complex devices. A
particular need in the search for wave-like dark matter are interdisciplinary
collaborations with experts in quantum measurement and control. Nurturing
broad cross-disciplinary collaborations is key to a strong program searching
for wave dark matter and high energy physics more broadly.

##  9 Strong Theory Program

###  9.1 Direct Impact on Experiments

A strong collaboration between theory and experiment is one of the hallmarks
of the wave-like dark matter community. It’s also at the heart of the current
and rapid development of the area. This interaction goes far deeper than
theorists proposing models that are than tested in experiments or
experimentalists providing data that is then used to constrain models. Indeed
theorists often conceptualize the experiments 666Of course there are also very
nice examples of this in the wider dark matter community, e.g. [126] for WIMP
detection. For a wider appreciation of the fruitful interaction between theory
and experiment see also the TF09 white paper [127]. and then often closely
collaborate in the following stages.

An early, perhaps the earliest example of the strength of this interaction is
the seminal paper by Pierre Sikivie [58] that outlined the two main approaches
to axion searches that are still pursued today, the axion helioscope and the
axion haloscope, and which followed quickly upon the realization that axions
are a good dark matter candidate [12, 13, 14]. This resulted amongst other
things in today’s ADMX collaboration with which Pierre Sikivie is still
connected, cf, e.g. [116].

More recent examples of this fruitful collaboration are experiments such as
CASPEr, DMRadio, MADMAX, IAXO and ALPHA that arose from theoretical concepts
and direct collaboration with experiments [58, 128, 129, 49, 50, 130, 131,
132, 59, 60, 133]. Similarly strong interactions exist not only for axions,
but also for scalar and vector DM, cf. [134, 135, 136] for some examples and
[2] for many more.

###  9.2 Astrophysics, Cosmology and Phenomenology

An important aspect of theoretical support for experiments is also to identify
areas that are already excluded by other means as well as, more positively,
detect areas that are especially promising because other experiments or
observations have found hints that point into the respective area.

This requires development of meaningful “benchmark scenarios” as well as the
interpretation of a wide range of data from experiments and observation
against these benchmarks.

A further, particularly important aspect for the very weakly coupled particles
that are the subject of the wave-like dark matter community are astrophysical
and cosmological observations. Due to their weak couplings stars in a broad
range of evolutionary stages are outstanding probes of these particles and
provide the best constraints (see the famous book [137] as well as the
discussion in [1] where more references can be found) as well as intriguing
hints (cf., e.g., [138, 139]). Also the propagation of photons through the
cosmic medium, featuring magnetic fields, but also a plasma of charged
particles as well as various types of photons (cosmic microwave photons, extra
galactic background light etc.) is modified in the presence of axions and
similar particles and therefore can provide powerful constraints but also
intriguing hints, e.g. [140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150,
151] (see also [1] for more details and references). Further progress will, of
course, arise from the complementarity with new data from existing as well as
future cosmic ray observatories such as HESS [146], Fermi-LAT [147], CTA
[152], LHAASO [153] but also from new telescopes such as the newly active
James Webb telescope [154] or the Vera Rubin Observatory [155], see, again,
[1] for an in depth discussion and references.

Cosmology, too, can provide powerful constraints. For example, the first
papers on the misalignment can be interpreted as a cosmological constraint on
the parameter space as certain parameter regions may produce too much dark
matter inconsistent with observations [12, 13, 14]. Famously, the lower
boundary on the mass of wave-like dark matter candidates $\sim 10^{-22}\,{\rm
eV}$ also arises from their impact on cosmological structure formation [156,
43]. In particular for low masses CMB polarization measurements can also be a
tool to probe axion and ALP dark matter, see [157] as well as [158] for a more
recent study.

An improved theoretical understanding of the cosmological production of dark
matter may also give crucial information on where as well as how to search for
dark matter. For example in a scenario where the last Peccei-Quinn symmetry
breaking happens after inflation (so-called post inflationary scenario), the
dark matter density is a definite function of the axion mass. Comparing with
the rather precisely observed (average) density would allow to get a precise
prediction for the axion mass. However, this determination is currently
precluded by the insufficient understanding of the production that receives
possibly significant contributions from topological defects [17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37] in
addition to the misalignment production. The same scenario also suggests that
dark matter may be inhomogeneously distributed on very small (e.g. solar
system sized) scales, e.g. featuring miniclusters [159, 160]. This has direct
impact on the experiments (searching in resonant vs broadband mode) [161] but
also opens the potential for synergies with astrophysical observation such as
gravitational lensing [162, 163, 164, 165] (see however also [166]). To bring
this to fruition improvements in the quantitative understanding of the
formation (cf., e.g., [167, 162, 163, 165, 168, 161, 169, 170, 171]) as well
as the survival of these structures [172, 173, 174, 175] would be welcome.

###  9.3 New Theoretical Target Areas

Last but definitely not least, fundamental theory research can first of all be
the original motivation for new (wave-like or other) dark matter candidates.
It can open entirely new or previously overlooked areas of parameter space. It
provides a framework to understand and interpret experimental results and
makes and highlights meaningful connections to other areas of particle
physics. Let us look at a few examples of this role in the following.

The first example is clearly the QCD axion itself [5, 6, 7, 8]. Motivated by a
theoretical finetuning problem of the SM (strong CP problem) it led to
concrete predictions that were soon tested and excluded. This then gave rise
to the advent of “invisible” axion models [56, 57, 54, 55]. As already
mentioned, measurement of an axion electron coupling would point to a DFSZ
model and therefore an extended Higgs sector that can be tested at the LHC or
a future collider, thereby making a connection that would not be possible
without a more complete theory model.

A recent example is the widening of parameter space for QCD axion models.
Whereas the original models predicted a strict relation between the axion mass
and the coupling to gluons (and also an order of magnitude relation to that
with photons) recent theory efforts [176, 177, 178, 179, 180, 181, 182, 183,
184, 185, 186, 187, 188, 189, 190] (see also [191, 192, 193, 194] for some
older works) have led to the realization that a wider range of possibilities
exist, albeit at the price of some model complications. Similarly the relation
to the photon coupling was significantly widened [195, 72, 73, 74, 75, 76].
These motivates new experimental searches with a broad range of techniques.

On the more theoretical side, string theory provides significant motivation
for light (pseudo-)scalars [66, 40, 41, 42, 43, 44, 45, 46, 47, 67, 68, 196]
as well as vectors [86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98]. The
former often arise as moduli that feature a scalar and a pseudoscalar
“axionic” component.

String theory models also provides a strong connection to cosmology and the
corresponding observations. An example is the prediction of a significant
amount of axionic dark radiation arising from moduli decays [197, 198, 199,
200, 201]. This provides constraints but can be consistent with observations
[196] but is also a potential observable in cosmological observations as well
as experiments such as IAXO [202]. Moreover, string theory also opens the
opportunity to build more complete models that also include to inflation,
again providing a connection to new observables [196] such as dark radiation
constraints from future CMB experiments, e.g. CMB-S4 [203].

##  10 Conclusions

While wavelike dark matter candidates (such as the QCD axion) have always been
well-motivated, the last decade has seen explosive growth in both enthusiasm
for WLDM models and search techniques, and fortuitous alignment between the
enabling technologies for those searches and the strategic needs of the US
quantum workforce. In the coming decade, the WLDM community endorses
supporting a strong program of experiments at different scales and R&D in key
enabling technologies. The goal of this program is to enable a discovery of
wavelike dark matter which will revolutionize our understanding of the
universe and our place in it.

## Acknowledgements

JJ is grateful for support from the EU ITN HIDDEN (No 860881). The conveners
thank the Department of Energy and National Science Foundation for their
support of the US axion dark matter community.

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