# Exploring Dark Sector Portals with High Intensity Experiments

Brian Batell  Pittsburgh Particle Physics, Astrophysics, and Cosmology Center,
Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh,
Pennsylvania, USA  Nikita Blinov  Department of Physics and Astronomy,
University of Victoria, Victoria, British Columbia Canada  Christopher Hearty
University of British Columbia, Vancouver, British Columbia, Canada  Institute
of Particle Physics (Canada), Victoria, British Columbia, Canada  Robert
McGehee  Leinweber Center for Theoretical Physics, Department of Physics,
University of Michigan, Ann Arbor, Michigan, USA

###### Abstract

A broad program of searches at high intensity experiments during the coming
decade and beyond will sensitively probe new light mediator particles
interacting through the minimal renormalizable vector, Higgs, and neutrino
portals as well as higher-dimension axion-like particle portals. These portals
may link the visible and dark sectors and play a critical role in many
proposed solutions to some of the big open questions in particle physics and
cosmology. In this whitepaper, we survey the theoretical and experimental
progress, status, and prospects in the study of minimal dark sector portals.

###### pacs:

Submitted to the Proceedings of the US Community Study

on the Future of Particle Physics (Snowmass 2022)

###### Contents

  1. I Introduction
  2. II Experimental approaches
    1. II.1 $e^{+}e^{-}$ colliders
    2. II.2 Proton or electron beam dumps
    3. II.3 Electron beam fixed target experiments
    4. II.4 Large Hadron Collider
    5. II.5 Meson and lepton facilities
  3. III Minimal Portal Case Studies
    1. III.1 Vector Portal
    2. III.2 Higgs Portal
    3. III.3 Neutrino Portal
    4. III.4 ALP Portal
  4. IV Outlook

## Executive Summary

The 2021 Snowmass Rare and Precision Frontier RF6 Topical Group, Dark Sector
Studies at High Intensities, has solicited four Big Ideas white papers
surveying the theoretical motivations and the experimental opportunities in
the study of dark sectors. This white paper – Big Idea 2 – covers the physics
of minimal portal interactions, including the renormalizable vector, Higgs,
and neutrino portals, as well as minimal dimension-five, axion-like particle
(ALP) portals with photon or gluon couplings. The focus is on minimal
extensions of the Standard Model (SM) featuring a single new light mediator
particle coupled through one of these portals. This implies that both the
production of the mediator and its visible decay to SM particles occur due to
the portal interaction. As we will examine in detail, there are a rich variety
of exciting experimental opportunities to investigate the structure of the
dark sector by producing and detecting such unstable mediator particles. We
will review the current status and future prospects for exploring the minimal
portals and highlight the connections with some of the big open questions in
fundamental physics. Three other RF6 Big Ideas white papers cover the
complementary topics of dark matter production, rich and flavorful dark
sectors, and the experimental landscape for dark sector exploration at the
intensity frontier.

The paradigm of a dark sector comprised of new SM singlet dark particles
coupled to ordinary matter through a portal interaction is motivated on a
variety of grounds. Dark sectors can resolve some of the outstanding mysteries
in particle physics, including the dark matter puzzle, the dynamics underlying
neutrino masses, baryogenesis, the hierarchy problem, the strong CP problem,
and so forth. From a bottom up perspective, portals provide a systematic
effective field theory-based scheme for investigations of new light physics
with very weak interactions. The dark sector framework has proven to be a
versatile playground for exploring potential new physics explanations of an
array of experimental anomalies. Dark sector research has bloomed over the
past decade with the development of creative theoretical models, the
conception of novel phenomenological strategies, and the proposal and
implementation of innovative searches and novel experiments.

The detailed properties of the mediator, including its mass, spin, and pattern
of couplings to the visible sector, are of great interest from both
theoretical and phenomenological perspectives. From the theory side, the gauge
symmetries and field content of the SM impose tight constraints on the
possible nature of the mediator and its couplings. On the other hand, these
properties determine, to a significant extent, the possible phenomenological
avenues that can be pursued to probe the mediator. In this light, the
renormalizable vector, Higgs, and neutrino portals warrant special attention
owing to their uniqueness and economy. These portals offer minimal ways to
link gauge singlet scalar, fermion, or vector fields to the SM with sizable
couplings at low energies. Beyond these three portals, the mediation between
the visible and dark sectors can occur through higher-dimension portals. A
well motivated and often studied case is a light ALP, with e.g., couplings to
photons or gluons through dimension-five operators, whose mass is protected by
a shift symmetry. While we will explore the renormalizable portals and minimal
ALP portals here, it should, however, be emphasized that these are not the
only ways of coupling a mediator to the SM. Other well motivated and
phenomenologically distinctive possibilities will be examined in the other Big
Ideas white papers.

Dark sectors are being pursued on multiple experimental fronts with a diverse
set of search tactics. Electron and proton beam fixed target experiments with
sensitive detectors covering ${\cal O}$(meter - kilometer) baselines provide
excellent reach at low dark particle masses over a broad range of couplings.
Medium energy $e^{+}e^{-}$ colliders/meson factories provide powerful
sensitivity for moderate couplings both at low and intermediate masses.
Precision studies of meson and lepton decays, including those at pion, kaon,
$\eta^{(^{\prime})}$, and muon facilities, offer interesting and in some cases
unique coverage at low masses and small couplings. A diverse collection of
existing and planned experiments at the LHC will be able to probe extensive
regions of parameter space in a variety of dark sector models. Collectively,
these experiments will utilize a wide array of search strategies, including
bump-hunt searches for promptly decaying resonances, displaced vertex searches
for dark particles with moderate lifetimes, searches for long lived particle
decays to visible final states, and missing momentum searches in both
collisions and rare decays. These dedicated searches for dark sector particles
are complemented by a variety of other probes in astrophysics and cosmology,
precision measurements, and future energy frontier experiments.

The minimal portals feature prominently in a variety of proposed solutions to
the big questions in fundamental physics. These include a variety of motivated
dark matter scenarios with novel cosmology and phenomenology. One generic
example is secluded dark matter, in which heavier dark matter is thermally
produced in the early universe via its annihilation to lighter mediator
particles. Viable secluded DM models can be realized in any of the minimal
portals. The requirement of thermalization in secluded scenarios imposes a
lower bound on the portal coupling, offering an interesting target for high
intensity and astrophysical probes. A variety of other interesting dark matter
scenarios in which the mediator is the lightest dark sector state have been
proposed, many of which can be correlated with specific regions of parameter
space within the minimal portal models. The minimal portals may also play an
important role in solutions to puzzles motivated by naturalness
considerations. In particular, the Higgs portal is a critical ingredient in
the relaxion solution to the hierarchy problem, while the vector portal is
expected on general grounds and may have important consequences in the mirror
Twin Higgs model, which tackles the little hierarchy problem. The ALP portal,
and in particular the ALP-gluon interaction, is of course motivated by its
connection to the Strong CP problem. The neutrino portal is likely to offer an
explanation of the light SM neutrino masses and may also give rise to low-
scale leptogenesis mechanisms. Furthermore, a light scalar interacting via the
Higgs portal may also serve as the inflaton. This white paper will spotlight
the myriad connections between the minimal portal models and the potential
answers to the big questions in particle physics and cosmology.

The theoretical ideas and experimental approaches featured in this whitepaper
have important synergies and complementarity with other efforts across the
rare and precision, energy, cosmic, and neutrino frontiers. At the energy
frontier, the LHC and future high energy colliders will be able to probe
heavier mediators with larger couplings. Distinct experimental opportunities
are also available at the energy frontier, including e.g., exotic Higgs decays
and precision measurements of Higgs couplings and electroweak observables. At
the cosmic frontier, a suite of new direct detection experiments will directly
search for halo DM through its scattering, while an array of astrophysical
observations can indirectly search for signatures of DM annihilation. In
particular, these direct and indirect searches provide sensitivity to DM that
is heavier than the mediator and are therefore highly complementary to the
direct searches for the visibly decaying mediators at intensity frontier
experiments highlighted in this whitepaper. There is also an exciting
interplay with activities in the neutrino frontier. Dark sector mediators can
be sought at accelerator- and reactor-based neutrino experiments and have also
been invoked in a variety of potential BSM explanations for various
experimental anomalies in the neutrino sector (e.g., the MiniBooNE low energy
excess of electron like events). Within the RF6 topical group, two additional
big ideas whitepapers will cover various complementary aspects of the dark
sectors physics program. Big Idea 1 focuses on dark matter production and
covers invisible or semi-visible mediator decays to dark matter and search
strategies leveraging missing energy/momentum or DM re-scattering. Big Idea 3
explores rich and flavorful dark sectors, highlighting mediators with novel
flavor structure and more complex dark sectors, which may be anticipated in a
more complete models.

Figure 1:  Near-term and future opportunities to search for visibly decaying
massive dark photons interacting through the kinetic mixing vector portal
displayed in the dark photon mass $(m_{A^{\prime}})$ – kinetic mixing
$(\epsilon)$ parameter space. Constraints from past experiments (gray shaded
regions) and projected sensitivities from operating experiments and DUNE
(colored shaded regions), proposed near-term (pre-2032) experiments based in
the U.S. including Dark Matter New Initiatives (DMNI) supported experiments
(solid colored lines), proposed near-term (pre-2032) experiments based
internationally and having significant U.S. leadership (dashed colored lines),
proposed near-term (pre-2032) international projects (dotted colored lines),
and proposed future (post 2032) experiments (dotted gray lines) are shown; see
also Figure 3 for another version of this plot with all future experiments
labeled. Line coloring indicates the key experimental approach used
($e^{+}e^{-}$ collider, $pp$ collider, LHC LLP detector, electron fixed
target, proton fixed target, muon decay), highlighting one aspect of the
complementarity between different facilities/experiments. Collectively, these
experiments are poised to cover large regions of open dark photon and thermal
dark matter parameter space.  Figure 2:  Near-term and future opportunities to
search for visibly decaying massive dark scalars interacting through the Higgs
portal displayed in the scalar mass $(m_{S})$ – mixing angle $(\sin\theta)$
parameter space. Constraints from past experiments (gray shaded regions) and
projected sensitivities from operating experiments and DUNE (colored shaded
regions), proposed near-term (pre-2032) experiments based (solid colored
lines), proposed near-term (pre-2032) experiments based internationally and
having significant U.S. leadership (dashed colored lines), proposed near-term
(pre-2032) international projects (dotted colored lines), and proposed future
(post 2032) experiments (dotted gray lines) are shown; see also Figure 4 for
another version of this plot with all future experiments labeled. Line
coloring indicates the key experimental approach used ($e^{+}e^{-}$ collider,
$pp$ collider, LHC LLP detector, proton fixed target, kaon decay),
highlighting one aspect of the complementarity between different
facilities/experiments. Collectively, these experiments are poised to cover
large regions of open dark scalar and thermal dark matter parameter space.

As illustrative examples, Figs. 1 and 2 present the near-term and future
opportunities to probe the minimal vector portal and Higgs portal models,
respectively. Dark photons and Higgs portal scalars are well-motivated dark
sector benchmarks, may serve as a mediators to dark matter, and appear in a
variety of UV models addressing big open questions in particle physics. A
combination of operating, fully or partially funded, and proposed near term
and future experiments will be able to search for dark photons over a broad
range of currently unconstrained parameter space. As this example illustrates,
and as will be highlighted in this whitepaper with specific case studies,
there is great opportunity to explore vast uncharted parameter space and
investigate the structure of the dark sector during the next decade and
beyond.

The dark sector science program has developed significantly during the last
decade. Milestones in this trajectory can be seen in past community studies,
including the Dark Sectors 2016 Workshop Alexander  _et al._ (2016) and the US
Cosmic Visions New Ideas in Dark Matter 2017 Battaglieri  _et al._ (2017) and
the CERN Physics Beyond Colliders Beacham  _et al._ (2020). Furthermore, the
U.S. Department of Energy (DOE) Office of Science Dark Matter New Initiatives
(DMNI) Basic Research Needs (BRN) report Kolb  _et al._ (2019) has recently
highlighted the importance of MeV-GeV scale dark sector studies as a Priority
Research Direction: “Create and detect dark matter particles below the proton
mass and associated forces, leveraging DOE accelerators that produce beams of
energetic particles.” Already, the DMNI initiative is supporting CCM200 at Los
Alamos’ LANSCE proton beam and LDMX at SLAC’s LESA electron beamline.

Realizing the broad objectives of the dark sector science program, as
spotlighted by the three Big Ideas, necessitates efforts and investments in
several primary directions, including harnessing the potential of existing
large-scale multi-purpose detectors, supporting dedicated small-scale
experiments and facilities with high-intensity beams, and promoting advances
in dark sector theory and fostering the community of dark sector theorists.
Support for these projects and research activities will facilitate a broad and
high-impact dark sector physics program during the next decade, with US
scientists and institutions providing key leadership in this effort.

##  I Introduction

The SM of particle physics is an extraordinarily successful theory, correctly
describing familiar matter and forces down to length scales of at least
$10^{-18}$ m and playing an essential role in our understanding of the history
of the Universe. The spectacular successes of the SM are matched only by its
striking failures to provide answers to a handful of open questions raised by
both empirical observations and conceptual mysteries. What is dark matter?
What dynamics is responsible for neutrino masses? How is the matter-antimatter
asymmetry generated? What physics underlies the Higgs sector and sets the weak
scale? Why is CP conserved by the strong interactions? These and other
questions strongly motivate explorations of physics beyond the SM.

On general grounds, the new dynamics addressing these questions could manifest
in several ways. First, if the new degrees of freedom are significantly
heavier than the weak scale, one can resort to searches for anomalous
phenomena or rare processes with precision measurements. Another possibility
involves new states charged under the SM gauge symmetries with masses near the
weak scale, which can be directly probed by experiments at the energy
frontier. Finally, there may be a dark sector (or hidden sector, etc.)
containing new SM gauge singlet states. The dark sector states may have masses
well below the weak scale and communicate weakly with the visible sector
through a portal interaction linking gauge invariant SM operators to a
mediator. Speculations regarding dark sectors have gained significant traction
over the last decade due to their possible connections with the big questions
mentioned above as well as their rich phenomenology.

The dark sector could be quite minimal, consisting of one or a few new states,
or it could be as rich as the SM, containing new dark forces, dark matter
states, and dark Higgs fields while exhibiting novel phenomena such as
confinement or spontaneous symmetry breaking. While it is important to examine
the theoretical and phenomenological implications of rich dark sectors,
including their potential role in addressing the big questions such as e.g.,
the dark matter puzzle, there is also merit in exploring the physics of
minimal portals, i.e., a single new mediator and portal coupling in isolation.
From a bottom-up effective field theory perspective, the portal concept
provides a natural point of departure for the systematic exploration of new
light weakly coupled physics. As is well-known, as a consequence of the SM
gauge symmetries and field content, there are just three options for
renormalizable portals: the vector portal, the scalar portal, and the neutrino
portal. At the dimension five level and higher, a variety of portal couplings
are allowed, including in particular the ALP-portal couplings to photons and
to gluons. ALPs may be naturally light as a consequence of a shift symmetry,
and these particular couplings are motivated by their appearance in solutions
to the Strong CP problem. Another clear motivation for considering minimal
portals is that the phenomenology of the mediator may naturally map on to more
complex dark sector models in the case that the mediator is the lightest new
state in the theory.

With this motivation, the scope of this 2021 Snowmass RF6 Big Idea 2 white
paper is on the physics of the mediator in the minimal vector, Higgs,
neutrino, and ALP portal models. These simple, well-motivated benchmark models
predict a rich variety of phenomena and motivate an expansive set of new
searches and dedicated experiments at the intensity frontier, complementing
other probes at the cosmic and energy frontiers. In these models, the single
portal coupling dictates both the production channels of the mediator in
collisions or rare decays of SM particles as well as its visible decay modes
to SM final states. Two other RF6 Big Ideas white papers cover the
complementary topics of dark matter production and rich and flavorful dark
sectors.

Next, in Section II, we survey the various experimental approaches available
and the specific existing or proposed experiments that can probe the minimal
portals. These include electron and proton beam fixed target experiments,
medium energy $e^{+}e^{-}$ colliders/meson factories, pion, kaon,
$\eta^{(^{\prime})}$, muon sources, and a variety of experiments at the LHC.

Following this, in Section III we introduce the minimal portal models,
describe their basic properties and interactions, discuss the future prospects
for probing these models at a diverse collection of experiments in the coming
years, and also highlight how these minimal portals may feature in more
complete dark sector models that address the big questions in fundamental
physics.

##  II Experimental approaches

The searches covered by this white paper involve a mediator decaying to a pair
of SM particles. The general search strategies depend on the mass of the
mediator and its couplings to the SM, which dictate its possible production
modes, decay channels, and lifetime.

Prompt decays, where the decay vertex is experimentally indistinguishable from
the production point, have large SM backgrounds, e.g.,
$\gamma^{*}\to\ell^{+}\ell^{-}$ for dilepton resonance signals. On an event-
by-event basis, these are indistinguishable from signal. Instead, a signal is
identified as a narrow peak on a smooth mass distribution from the SM
background. Sensitivity improves with better mass resolution and large data
sets. For long lifetimes, several to hundreds of meters in the laboratory,
large amounts of shielding can substantially reduce SM backgrounds. Given the
dependence of the lifetime on mass and coupling, these searches are
necessarily focused on low masses and small couplings. The boost of the
mediator in the laboratory frame, which plays a large role in determining the
range of relevant couplings, depends strongly on the energy of the beam used
to produce the mediator, as well as on the mediator mass.

Between these two cases, precision vertex detectors are used to distinguish
prompt SM backgrounds from displaced signals. A detailed understanding of the
location of detector materials is required to distinguish backgrounds from SM
particles interacting in the material. Searches in electron pair final states
are particularly affected by photon conversions. SM particles with comparable
lifetimes, such as $K^{0}_{s}$ mesons and $\Lambda$ baryons, are also a
consideration.

The different experiments that have produced results or projections can be
sorted into the following categories. Details on each experiment and facility
along with references are in the RF6 facilities white paper Ilten  _et al._
(2022).

###  II.1 $e^{+}e^{-}$ colliders

Experiments at $e^{+}e^{-}$ colliders can perform a wide range of searches for
different mediators, with either prompt or intermediate lifetimes. The
production mechanism can be either $e^{+}e^{-}$ annihilation, via coupling to
photons, or, for facilities operating at the $\Upsilon(4S)$ resonance, $B$
meson decay. Searches are enhanced by the large acceptance and nearly-hermetic
design of the detectors. Current facilities have modest center of mass
energies $\mathcal{O}(10)$ GeV, but future colliders could significantly
extend the mass reach.

Relevant experiments that have completed data collection include BaBar and
KLOE. BaBar collected 500 fb-1 of data at the PEP-II asymmetric $e^{+}e^{-}$
collider at SLAC from 1999–2008. KLOE operated at the DA$\Phi$NE collider from
2001–2006; the upgraded KLOE-2 collected data from 2014–2018. DA$\Phi$NE
operates at the $\phi$ resonance.

Belle II is currently collecting data at the SuperKEKB collider at KEK, in
Tsukuba, Japan. It is scheduled to record 50 ab-1 at the $\Upsilon(4S)$ over
the next decade. Proposed future colliders include the International Linear
Collider (ILC), the Future Circular Collider (FCC-ee), the Circular Electron-
Positron Collider (CEPC), and the Cool Copper Collider (C3).

###  II.2 Proton or electron beam dumps

Beam dump experiments look for the appearance of visible decay products in a
detector separated from the production target by sufficient shielding to
reduce SM backgrounds to manageable levels. They have very high intensities
and probe longer lifetimes, which gives them sensitivity to small couplings.
The typical mass reach is less than a few GeV$/c^{2}$.

The results of older electron beam dump experiments E141, E137, E774, KEK, and
Orsay have been recast into limits on dark photon production. The dark photon
is produced via bremsstrahlung, $eZ\to eZA^{\prime}$.

Results from proton beam dump experiments have also been recast as dark photon
or scalar limits. $\nu-$CAL I uses proton bremsstrahlung and $\pi^{0}$ decay;
CHARM, NOMAD, and PS191 all rely on $\pi^{0}$ decay.

DarkQuest, an upgrade of the existing SeaQuest/SpinQuest experiment, will use
120 GeV protons from the Fermilab main injector to search for dark photons and
scalars. Production mechanisms include Drell-Yan, meson decay, and proton
bremsstrahlung. Two proposals would use 400 GeV protons extracted from the
CERN SPS. SHiP will search for a wide range of feebly interacting particles.
SHADOWS, a somewhat smaller facility, will be located off-axis adjacent to
NA62. Both will use sets of dipole magnets to sweep away muons and other
charged particle backgrounds.

###  II.3 Electron beam fixed target experiments

Electron beam fixed target experiments produce dark photons or scalars in
bremsstrahlung and search for the subsequent decay to $e^{+}e^{-}$. For prompt
decays, the search is for a narrow peak on a large background from
$\gamma^{*}\to e^{+}e^{-}$.

The HPS experiment at JLAB looks for displaced decays using a high-resolution
silicon vertex tracker. Data has been collected at a beam energy of 4.55 GeV;
additional data sets will be collected with beam energies as high as 6 GeV.

NA64 is a fixed target experiment using a 100–150 GeV electron beam from the
CERN SPS to search for a variety of dark sector particles in both visible and
invisible modes. It features an active target separated from a deep
calorimeter by a decay volume and veto and tracking elements.

###  II.4 Large Hadron Collider

Dark sector particles are produced in proton-proton collisions via meson
decay, dark photon mixing with $\rho$, $\omega$, and $\phi$ mesons, or Drell-
Yan ($q\bar{q}$ annihilation). LHCb and CMS have searched for dark photons
decaying to muon pairs. LHCb uses both prompt and displaced vertices, and
intends to add the $e^{+}e^{-}$ final state.

FASER is located 480 m downstream of the ATLAS collision point. It exploits
the large cross section in the forward direction and the large boost of light
particles to search for long-lived dark particles. It will collect first data
starting summer 2022. MoEDEL-MAPP, located 100 m from the LHCb interaction
point, will search for minicharged and other feebly-interacting particles
starting in 2023. Other proposed long-lived particle experiments at the LHC
include CODEX-b and MATHUSLA. Both are at wide angles, giving it access to
production in the decay of heavier particles. The proposed Forward Physics
Facility Anchordoqui  _et al._ (2022); Feng  _et al._ (2022) would house a
variety of experiments sensitive to new physics, including FASER2, an upgrade
of FASER.

###  II.5 Meson and lepton facilities

Dark sector mediators can be produced in rare decays of Kaon or eta mesons, or
of muons. Searches exploit the large data sets available, and the narrow width
of the mother particle. NA48/2 has searched for prompt decay of dark photons
to $e^{+}e^{-}$ in $\pi^{0}$ decay. The NA62 experiment plans a wide range of
searches, including prompt and displaced electron pairs, muon pairs, and
photon pairs, and searches for long-lived mediators via missing mass
techniques.

REDTOP is a proposed very-high statistics $\eta$ and $\eta^{\prime}$ facility
that would be sensitive to a variety of dark sector particles through searches
in lepton pair final states.

Mu3e, located at the Paul Scherrer Institute (PSI), is principally a search
for the (forbidden) decay $\mu^{+}\to e^{+}e^{-}e^{+}$, but will also have
sensitivity to dark photon decays to $e^{+}e^{-}$. Also located at PSI is
PIONEER. It will primarily study lepton flavor universality in charged pion
decay, but will also have sensitivity to heavy neutral leptons.

##  III Minimal Portal Case Studies

We now turn our attention to minimal portal models, including the vector
portal, Higgs portal, neutrino portal, and ALP portal with photon or gluon
couplings. We discuss the interactions of the mediator with the SM and its
essential properties concerning its production, decay, and lifetime that enter
into phenomenological considerations. We then consider the current status and
constraints on the mass-coupling parameter space in each model, and also
highlight the future prospects at a variety of existing or proposed
experiments. Finally, we discuss how these minimal portals, within the context
of more complete dark sector models, may play a role in addressing the
outstanding questions in particle physics.

###  III.1 Vector Portal

Figure 3: Minimal vector portal model. Existing constraints (gray shaded
region) and future experimental projections (colored contours) are shown in
the $m_{A^{\prime}}-\epsilon$ plane. The existing bounds are from Refs.
Blümlein and Brunner (2011, 2014); Tsai  _et al._ (2021); Bjorken  _et al._
(2009); Andreas  _et al._ (2012); Bjorken  _et al._ (1988); Bross  _et al._
(1991); Riordan  _et al._ (1987); Davier and Nguyen Ngoc (1989); Banerjee  _et
al._ (2020); Batley  _et al._ (2015); Merkel  _et al._ (2014); Abrahamyan  _et
al._ (2011); Anastasi  _et al._ (2018); Aaij  _et al._ (2018, 2020); Ablikim
_et al._ (2017); Lees  _et al._ (2014); Sirunyan  _et al._ (2020); Curtin  _et
al._ (2015). Also shown are projections from a number of existing and proposed
future experiments, including DUNE Berryman  _et al._ (2020), Belle II
Altmannshofer  _et al._ (2019); Ferber  _et al._ (2022), LHCb Craik  _et al._
(2022), FASER and FASER2 Feng  _et al._ (2018a); Ariga  _et al._ (2019), HPS
Baltzell  _et al._ (2022), NA62-Dump Beacham  _et al._ (2020), LDMX Berlin
_et al._ (2019), DarkQuest Berlin  _et al._ (2018), APEX Essig  _et al._
(2011), Mu3e Echenard  _et al._ (2015), DarkLight Pachal (2019), FACET Cerci
_et al._ (2021), REDTOP Elam  _et al._ (2022), MUonE Galon  _et al._ (2022),
SHiP Ahdida  _et al._ (2021), and a muon beam dump experiment Cesarotti  _et
al._ (2022).

We will first consider the vector portal, which couples a new dark $U(1)$
gauge boson $A^{\prime}_{\mu}$, commonly referred to as a dark photon, to the
hypercharge gauge boson via the kinetic mixing operator,

${\cal
L}\supset\frac{\epsilon}{2\cos\theta_{W}}F^{\prime}_{\mu\nu}\,B^{\mu\nu}.$ (1)

Here $F^{\prime}_{\mu\nu}$ ($B_{\mu\nu}$) is the dark photon (hypercharge)
field strength tensor, $\epsilon$ is the kinetic mixing parameter, and
$\theta_{W}$ is the weak mixing angle. The kinetic mixing operator, Eq. (1),
is allowed at the renormalizable level by all symmetries of the theory, may be
generated radiatively Holdom (1986), or have important connections to UV
physics, and a broad range of values for $\epsilon$ are well motivated
theoretically Holdom (1986); Dienes  _et al._ (1997); Arkani-Hamed and Weiner
(2008); Koren and McGehee (2020); Gherghetta  _et al._ (2019). We assume here
that the dark photon obtains a mass $m_{A^{\prime}}$ via a dark Higgs or
Stueckelberg mechanism, such that the minimal vector portal parameter space is
$(m_{A^{\prime}},\epsilon)$.

Dark photons that are significantly lighter than the $Z$ boson dominantly
couple in the physical basis to electrically charged particles with
interaction strength suppressed by $\epsilon$. As such, dark photons will
decay democratically to all kinematically accessible electrically charged
particles. The dark photon decay length scales parametrically as
$c\tau_{A^{\prime}}\sim(\epsilon^{2}m_{A^{\prime}})^{-1}$, and may be prompt
for moderate kinetic mixing strength ($\epsilon\gtrsim{\cal O}(10^{-3})$) or
displaced/ macroscopic for smaller values of $\epsilon$. As it couples with
similar strength to both charged leptons and quarks, there are a variety of
promising experimental venues for dark photon searches in high intensity
facilities utilizing hadrons, electrons, and muons. In particular, dark
photons can be copiously produced and probed through their visible decays at
high-luminosity $e^{+}e^{-}$ colliders, electron and proton beam fixed target
experiments (employing bump hunt, displaced vertex, and LLP decay searches),
meson factories, and the LHC. Figure 3 displays the current bounds and future
sensitivity projections from a variety of experiments in the
$m_{A^{\prime}}-\epsilon$ parameter space.

Visibly-decaying dark photons detectable at near-future experiments are
motivated by many solutions to the big questions including the nature of DM.
For secluded DM models in which DM annihilates to lighter dark-sector states
Pospelov  _et al._ (2008); Arkani-Hamed  _et al._ (2009), the requirement of
thermal equilibrium for freeze-out predicts one such target Evans  _et al._
(2018). In Forbidden Dark Matter scenarios, DM instead annihilates to heavier
states, such as visibly-decaying dark photons with masses and kinetic mixings
in range of future searches D’Agnolo and Ruderman (2015). Going to heavier
dark photons motivates _Not_ Forbidden Dark Matter, where the mediator is too
heavy to permit even suppressed $2\to 2$ annihilations, so $3\to 2$
annihilations determine the DM relic abundance. Again, using the vector portal
is a natural simple choice and some of the viable parameter space which
reproduces the relic abundance will be probed at future experiments Cline  _et
al._ (2017). Resonant Dark Matter models consider the possibility of
resonantly enhancing DM annihilations through the vector portal to evade
cosmological constraints. Interestingly, smaller tuning of the resonance
results in a more predictive target for dark photon searches Bernreuther  _et
al._ (2021). The resonance may not be in the vector portal itself, but rather
in DM self interactions to alleviate small-scale structure issues. The
resulting Resonant Self-Interacting Dark Matter may still use the vector
portal for entropy transfer and again, less fine tuning motivates a narrower
region for future dark photon searches to probe Tsai  _et al._ (2022). Some
Strongly Interacting Massive Particle scenarios, in which $3\to 2$ self
annihilations set the DM relic abundance, also use the vector portal to
transfer excess entropy out of the dark sector. The resulting viable parameter
space which explains the DM relic abundance while evading all other
constraints can be quite predictive in the $m_{A^{\prime}}-\epsilon$ plane and
may be imminently probed Choi  _et al._ (2017).

The vector portal has also been present in answers to the naturalness and
baryon asymmetry questions. For example, the Mirror Twin Higgs paradigm always
contains the vector portal since it proposes a copy of the SM matter and gauge
content to solve the little hierarchy problem Chacko  _et al._ (2006). One
such model alleviates otherwise-expected cosmological tensions and provides an
imminently-testable, well-motivated benchmark for many future searches due to
naturalness considerations Harigaya  _et al._ (2020). Another realizes a
Strongly Interacting Massive Particle DM scenario within the Mirror Twin Higgs
framework and predicts visibly-decaying “twin” photons in the process Hochberg
_et al._ (2019). As for the baryon asymmetry, one model provides an
explanation and a simultaneous asymmetric dark matter candidate using a dark
sector similar to the Mirror Twin Higgs. It thus has a vector portal which
must efficiently transfer entropy prior to BBN and, due to the precisely
predicted ratio between SM and dark baryon asymmetries, requires $10\text{
MeV}\lesssim m_{A^{\prime}}\lesssim 300\text{ MeV}$, which will be probed by
many visibly-decaying dark photon searches Hall  _et al._ (2019).

###  III.2 Higgs Portal

Figure 4: Minimal Higgs portal model. Existing constraints (gray shaded
region) and future experimental projections (colored contours) are shown in
the $m_{S}-\sin\theta$ plane. The existing bounds are from Refs. Frugiuele
_et al._ (2018); Aaij  _et al._ (2015, 2017); Athanassopoulos  _et al._
(1998); Aguilar-Arevalo  _et al._ (2001); Foroughi-Abari and Ritz (2020);
Bernardi  _et al._ (1986, 1988); Gorbunov  _et al._ (2021); Abratenko  _et
al._ (2021); Bergsma  _et al._ (1985a); Winkler (2019); Egana-Ugrinovic  _et
al._ (2020); Goudzovski  _et al._ (2022); Artamonov  _et al._ (2008, 2009);
Cortina Gil  _et al._ (2021a, b, c). Also shown are projections from a number
of existing and proposed future experiments, including ICARUS Batell  _et al._
(2019), DUNE Berryman  _et al._ (2020), Belle II Kachanovich  _et al._ (2020);
Filimonova  _et al._ (2020), LHCb Craik  _et al._ (2022), CMS Evans  _et al._
(2021), DarkQuest Batell  _et al._ (2021); Berlin  _et al._ (2018), FASER and
FASER2 Feng  _et al._ (2018b), MoEDAL-MAPP Pinfold (2021); Staelens (2022),
CODEXb Aielli  _et al._ (2022), MATHUSLA Curtin  _et al._ (2019), NA62-Dump
Beacham  _et al._ (2020), SHADOWS Lanfranchi (2022), HIKE Lanfranchi (2022),
and SHiP Alekhin  _et al._ (2016).

Next, we turn to the Higgs portal, which couples the gauge invariant Higgs
mass operator $H^{\dagger}H$ to a new gauge singlet scalar particle $S$. There
are two allowed renormalizable couplings in general,

$-{\cal L}\supset(A\,S+\lambda\,S^{2})\,H^{\dagger}H.$ (2)

where $A$ has dimensions of energy and $\lambda$ is dimensionless. If $A$ is
non-vanishing, or even if $A=0$ and the scalar potential leads to a vacuum
expectation value for $S$, the dark scalar will acquire a small mass mixing
with the Higgs boson. The phenomenology of the Higgs portal is thus broadly
described by two parameters: the physical mass $m_{S}$ of the dark scalar and
the scalar-Higgs mixing angle $\theta$. The dark scalar inherits the
interactions of the Higgs to SM particles, with a coupling suppressed by
$\sin\theta$. As such it may be abundantly produced through flavor-changing
meson decays, e.g. $K\rightarrow\pi S$, $B\rightarrow KS$, etc, and
furthermore will dominantly decay to the heaviest kinematically accessible
final states. For $m_{S}<2m_{\mu}$, the scalar decays to dielectrons with a
naturally long lifetime, and is probed in beam dump experiments, dedicated LLP
LHC detectors, and in rare kaon decays with missing energy. At higher masses
above the dimuon threshold, the dark scalar may additionaly be sought in
experiments studying rare $B$ meson decays. Figure 4 displays the current
experimental bounds and expected reach from a variety of experiments in the
dark scalar parameter space. It is important to note that there may be
additional signatures in models with a sizable $hSS$ trilinear coupling (e.g.,
exotic Higgs boson decays); see e.g., Refs. Beacham  _et al._ (2020);
Frugiuele  _et al._ (2018) for further studies of this possibility.

The Higgs portal is also motivated by simple solutions to many of the big
questions, including the nature of DM. It appears in predictive models of
secluded DM Pospelov  _et al._ (2008) as well as light thermal DM Krnjaic
(2016). Some such secluded DM models can produce exciting targets for future
experiments due to thermal equilibrium requirements Evans  _et al._ (2018), as
can models of SIMP DM in which the Higgs portal is an important necessity
again Choi  _et al._ (2017). The Higgs portal also naturally appears in
solutions to the electroweak hierarchy problem. The relaxion, a scalar which
dynamically reduces the mass of the Higgs during inflation, may naturally mix
with the Higgs at near-detectable levels Flacke  _et al._ (2017); Frugiuele
_et al._ (2018). Another light, cosmologically-evolving scalar is the inflaton
itself, which may also mix with the Higgs and lead to interesting signals
Bezrukov and Gorbunov (2010).

###  III.3 Neutrino Portal

The neutrino portal refers to the coupling of the gauge invariant operator
$LH$ formed of the lepton and Higgs doublets to a gauge singlet fermion $N$,

$\mathcal{L}\supset-y^{\alpha}L_{\alpha}HN+{\rm h.c.},$ (3)

where $y^{\alpha}$ is a Yukawa coupling with $\alpha=e,\,\mu,\,\tau$. We refer
to $N$ as a heavy neutral lepton (HNL). Following electroweak symmetry
breaking, the HNLs mix with the SM neutrinos, inheriting interactions with the
electroweak bosons, with a coupling strength suppressed by the mixing angles.
Due to its gauge singlet nature, a Majorana mass term for $N$ may be present
in the theory, in which case $N$ will be a Majorana particle. It is also
possible to formulate models with Dirac or pseudo-Dirac HNLs. For the purposes
of characterizing experimental sensitivities, we will follow the common
convention of considering a single HNL that dominantly mixes with a specific
neutrino flavor, i.e., dominant electron-, muon-, or tau- flavor mixing. The
phenomenology is then characterized by the HNL mass, $m_{N}$, and mixing
angle, denoted by $|U_{e}|^{2}$, $|U_{\mu}|^{2}$, $|U_{\tau}|^{2}$,
respectively, for the three mixing scenarios.

Much like SM neutrinos, HNLs are readily produced through weak interaction
decays, such as muon, pion, kaon, $D$ meson, tau lepton, and $B$ meson decays.
HNLs also decay through the weak interactions and typically feature a wide
variety of visible/semi-visible decay modes involving charged leptons,
hadrons, and/or neutrinos. HNLs can thus be probed at a variety of
experiments, including in dedicated pion or kaon decay experiments, beam dump
experiments, and with a variety of experiments at the LHC. Figures 5 and 6
summarize the current bounds and future experimental sensitivities for the
electron-dominance and tau-lepton-dominance scenarios, respectively.

HNLs are particularly well motivated given their likely connection with the
generation of neutrino masses through the seesaw mechanisms Minkowski (1977);
Yanagida (1979); Gell-Mann  _et al._ (1979); Glashow (1980); Mohapatra and
Senjanovic (1980); Schechter and Valle (1980). In addition to this broad
motivation from the observation of neutrino masses, the neutrino portal could
help explain the baryon asymmetry Asaka and Shaposhnikov (2005) through the
ARS leptogenesis mechanism Akhmedov  _et al._ (1998) and dark matter via a
light keV-scale sterile neutrino Boyarsky  _et al._ (2019). It has also been
motivated by models of secluded DM Pospelov  _et al._ (2008). It also exists
in extensions of the SM which copy the SM itself, as in twin Higgs solutions
to the little hierarchy problem. In order to achieve a consistent cosmology
for some such models, the neutrino portal is necessary with masses and mixings
of the sterile neutrinos detectable at near-future experiments Chacko  _et
al._ (2017).

Further discussion of the theoretical motivations and experimental prospects
for HNLs can be found in the recent Snowmass whitepaper Abdullahi  _et al._
(2022).

Figure 5:  Neutrino portal with electron mixing dominance. Existing
constraints (gray shaded region) and future experimental projections (colored
contours) are shown in the $m_{N}-|U_{e}|^{2}$ plane. The existing bounds are
from Refs. Bryman and Shrock (2019); Aguilar-Arevalo  _et al._ (2018); Cortina
Gil  _et al._ (2020); Abe  _et al._ (2019); Bernardi  _et al._ (1986, 1988);
Bergsma  _et al._ (1986); Liventsev  _et al._ (2013); Abreu  _et al._ (1997);
Tumasyan  _et al._ (2022); Aad  _et al._ (2019); Sabti  _et al._ (2020). Also
shown are projections from a number of existing and proposed future
experiments, including DUNE Berryman  _et al._ (2020); Ballett  _et al._
(2020); Coloma  _et al._ (2021), NA62 Cortina Gil  _et al._ (2020), NA62-dump
Beacham  _et al._ (2020), FASER2 Kling and Trojanowski (2018); Feng  _et al._
(2022), FASER2 Kling and Trojanowski (2018); Feng  _et al._ (2022), CODEX-b
Aielli  _et al._ (2020, 2022), MATHUSLA Curtin  _et al._ (2019); Alpigiani
_et al._ (2020), SHADOWS Baldini  _et al._ (2021), and SHiP Ahdida  _et al._
(2019).  Figure 6:  Neutrino portal with tau mixing dominance. Existing
constraints (gray shaded region) and future experimental projections (colored
contours) are shown in the $m_{N}-|U_{\tau}|^{2}$ plane. The existing bounds
are from Refs. Abreu  _et al._ (1997); Boiarska  _et al._ (2021); Bergsma  _et
al._ (1986); Sabti  _et al._ (2020). Also shown are projections from a number
of existing and proposed future experiments, including DUNE Berryman  _et al._
(2020); Ballett  _et al._ (2020); Coloma  _et al._ (2021), DarkQuest Batell
_et al._ (2021); Berlin  _et al._ (2018), NA62 Cortina Gil  _et al._ (2020),
NA62-dump Beacham  _et al._ (2020), FASER2 Kling and Trojanowski (2018); Feng
_et al._ (2022), MATHUSLA Curtin  _et al._ (2019); Alpigiani  _et al._ (2020),
CODEX-b Aielli  _et al._ (2020, 2022), SHADOWS Baldini  _et al._ (2021), and
SHiP Ahdida  _et al._ (2019).

###  III.4 ALP Portal

ALPs are parity-odd scalars that can arise as (pseudo-) Nambu-Goldstone bosons
of spontaneously broken global symmetries or as compactifications of higher-
dimensional gauge fields. These theoretical features ensure that ALPs can be
very light compared to the scale of fundamental dynamics that generates them
(e.g., the Peccei-Quinn breaking scale or the Planck scale). The QCD axion is
the specific realization of the ALP that interacts with QCD (and gets its mass
only from QCD effects which fix the mass as a function of the ALP coupling)
and provides one of the most compelling explanations for the strong CP problem
Peccei and Quinn (1977a, b); Wilczek (1978); Weinberg (1978). Here we consider
the more general ALPs where the mass and coupling to SM particles are
independent parameters. From an effective field theory point of view, ALPs
couple to the SM through dimension five operators, suggesting that ALPs can be
some of the first messengers of UV physics. As such, they also provide a
compelling portal to dark sectors that require interactions with the SM Batell
_et al._ (2009), such as certain models of DM (see, e.g., Ref. Hochberg  _et
al._ (2018)).111For much lighter masses and weaker couplings than considered
here, ALPs provide viable DM candidates themselves Abbott and Sikivie (1983);
Dine and Fischler (1983); Preskill  _et al._ (1983); Arias  _et al._ (2012).
It is therefore important to search broadly for the interactions of ALPs with
SM particles.

ALP interactions depend strongly on the UV physics from which they arise. As a
result, there is a wide variety of dimension five operators that can be
manifest at experimental energies. Here we focus on two simple, minimal
examples that capture a broad (but incomplete) range of possible production
and decay modes. We will consider models where the ALP couples dominantly to
photons or to gluons just above the QCD scale; the corresponding interactions
are given by

$\mathcal{L}\supset
c_{\gamma\gamma}\frac{\alpha}{4\pi}\frac{a}{f}F_{\mu\nu}\widetilde{F}^{\mu\nu}+c_{GG}\frac{\alpha_{s}}{4\pi}\frac{a}{f}G_{\mu\nu}^{a}\widetilde{G}^{a,\,\mu\nu},$
(4)

where $a$ is the ALP field, $F$ ($G$) are the electromagnetic (gluon) field-
strength tensors, and we take only one of $c_{\gamma\gamma}/f$ or $c_{GG}/f$
to be non-zero at a time (these coupling constants have inverse mass
dimension). In the gluon-coupled case, QCD confinement generates interactions
of the ALP with hadrons, including mixing with pseudo-scalar mesons, which in
turn couple to photons. Thus, in both the photon- _and_ gluon-coupled ALP
scenarios, the ALP interacts with photons. This enables a very broad search
strategy for ALPs of both kinds in precision-frontier experiments. ALPs are
produced in collisions of SM particles via their couplings to photons or
hadrons and travel a macroscopic distance before decaying into pairs of
photons (in the gluon-coupled case, non-photon decay modes are also
available). In Figs. 7 and 8, we show existing constraints and projections for
future searches in the photon- or gluon-coupled ALP models, respectively.

Figure 7: _Photon-coupled ALPs._ Existing constraints (gray) and projected
sensitivities (colored lines) of various experiments to the photon-coupled
ALP. The constraints are obtained from Refs. Dolan  _et al._ (2017); Döbrich
_et al._ (2019); Jaeckel and Spannowsky (2016); Abudinén  _et al._ (2020);
Aloni  _et al._ (2019a); Lucente  _et al._ (2020); Ertas and Kahlhoefer
(2020). We show the sensitivities of phase 1 and 2 of DarkQuest Berlin  _et
al._ (2018); Blinov  _et al._ (2022); Apyan  _et al._ (2022); phase 1 and 2 of
LDMX (visible search mode) Berlin  _et al._ (2019); PIP2-BD Toups  _et al._
(2022); phase 1 and 2 of FASER Feng  _et al._ (2018c); Ariga  _et al._ (2019);
NA62 Döbrich  _et al._ (2019); NA64 Dusaev  _et al._ (2020); phase 0 of LUXE-
NPOD Bai  _et al._ (2021); Belle II Dolan  _et al._ (2017); a reanalysis of
existing PrimEx data Aloni  _et al._ (2019a); DUNE Brdar  _et al._ (2021); and
ILC beam dump Sakaki and Ueda (2021). Figure 8: _Gluon-coupled ALPs._ Existing
constraints (gray) and projected sensitivities (colored lines) of various
experiments to the gluon-coupled ALP. The existing constraints are from Refs.
Ahn  _et al._ (2019); Cortina Gil  _et al._ (2021a); Lazzeroni  _et al._
(2014); Aad  _et al._ (2021); Blumlein  _et al._ (1991, 1992); Bergsma  _et
al._ (1985b); Altmannshofer  _et al._ (2020); Aguilar-Arevalo  _et al._
(2018); Pocanic  _et al._ (2004); Adhikari  _et al._ (2022); Abudinén  _et
al._ (2020); Jaeckel and Spannowsky (2016); Ertas and Kahlhoefer (2020). We
show the projected sensitivities of phase 1 and 2 of DarkQuest Blinov  _et
al._ (2022); Apyan  _et al._ (2022); phase 1 and 2 of FASER Ariga  _et al._
(2019); Feng  _et al._ (2022); CODEX-b Aielli  _et al._ (2020); REDTOP Beacham
_et al._ (2020); MATHUSLA Chou  _et al._ (2017); Beacham  _et al._ (2020);
DUNE Kelly  _et al._ (2021); LHCb Craik  _et al._ (2022) and HL-LHC Track
Trigger Hook  _et al._ (2020); Kelly  _et al._ (2021). We emphasize that these
projections and sensitivities are for an ALP model where the gluon coupling is
the only relevant interaction at low energies; if the interaction is instead
defined at a high scale (like a TeV), renormalization group evolution
generates a multitude of other interactions leading to additional constraints
and discovery opportunities Bauer  _et al._ (2021a); Chakraborty  _et al._
(2021).

It is important to note that low-energy interactions of the gluon-coupled ALP
are still somewhat uncertain because they involve strongly-coupled physics of
QCD below the confinement scale. Several theoretical and data-driven models
have been proposed Aloni  _et al._ (2019b); Bauer  _et al._ (2021b, c). In
particular, Refs. Bauer  _et al._ (2021b, c) emphasized that many existing
hadronic ALP calculations suffer from certain theoretical inconsistencies that
can significantly impact the interpretation of experimental results. While it
is unlikely that these issues lead to qualitative changes of the various
experimental constraints and projections discussed below, it will be important
to resolve this theoretical issue in the future.

As mentioned above, the ALP interactions are sensitive to their UV origin; we
specialized to two models that are minimal at low energies, featuring only a
single defining coupling just above the QCD scale. A different approach to
studying the ALP model is to begin with a UV complete model at a high scale
(say, a TeV) and integrate out heavy physics and then evolve the resulting
interactions to experimental scales Bauer  _et al._ (2021a). This procedure
generically produces many additional interactions in addition to the gluon and
photon couplings in Eq. 4. These other interactions can provide additional
constraints Bauer  _et al._ (2021a) and discovery opportunities Chakraborty
_et al._ (2021) – see, e.g., Ref. Bauer  _et al._ (2021a) for a comprehensive
discussion.

With these caveats in mind, in Fig. 7 we show the existing constraints and
projections for the photon-coupled ALP model. The constraints, shaded in gray,
come from old beam dump experiments (E137 and E141 Dolan  _et al._ (2017),
CHARM and $\nu$CAL Döbrich  _et al._ (2019)); colliders (LEP Jaeckel and
Spannowsky (2016), BaBar Dolan  _et al._ (2017) and Belle II Abudinén  _et
al._ (2020)); the photon beam experiment PrimEx Aloni  _et al._ (2019a);
supernova 1987A Lucente  _et al._ (2020) and big bang nucleosynthesis Ertas
and Kahlhoefer (2020).222We show the least stringent constraint derived by
allowing $\Delta N_{\mathrm{eff}}$ and neutrino chemical potential to vary. We
also show the projected sensitivities for the following experiments: phase 1
and 2 of DarkQuest Berlin  _et al._ (2018); Blinov  _et al._ (2022); Apyan
_et al._ (2022), PIP2-BD Toups  _et al._ (2022), phase 1 and 2 of FASER Feng
_et al._ (2018c); Ariga  _et al._ (2019); phase 1 and 2 of LDMX (search for
visible energy depositions in the HCAL) Berlin  _et al._ (2019), NA62 Döbrich
_et al._ (2019); NA64 Dusaev  _et al._ (2020); phase 0 of LUXE-NPOD Bai  _et
al._ (2021); Belle II Dolan  _et al._ (2017); a reanalysis of existing PrimEx
data Aloni  _et al._ (2019a); DUNE Brdar  _et al._ (2021) and the ILC beam
dump Sakaki and Ueda (2021).

In Fig. 8 we show the existing constraints and future projections for the
gluon-coupled ALP scenario. The constraints, shaded in gray, come from KOTO
Ahn  _et al._ (2019); NA62 Cortina Gil  _et al._ (2021a); Lazzeroni  _et al._
(2014); ATLAS Aad  _et al._ (2021); $\nu$CAL Blumlein  _et al._ (1991, 1992)
and CHARM Bergsma  _et al._ (1985b); PIENU and PIBETA Altmannshofer  _et al._
(2020); Aguilar-Arevalo  _et al._ (2018); Pocanic  _et al._ (2004); GlueX
Adhikari  _et al._ (2022); recasts of the photon-only bounds from Belle II
Abudinén  _et al._ (2020) and LEP Jaeckel and Spannowsky (2016); and supernova
1987A Ertas and Kahlhoefer (2020). We also show the projected sensitivities of
phase 1 and 2 of DarkQuest Blinov  _et al._ (2022); Apyan  _et al._ (2022);
phase 1 and 2 of FASER Ariga  _et al._ (2019); Feng  _et al._ (2022); CODEX-b
Aielli  _et al._ (2020); REDTOP Beacham  _et al._ (2020); MATHUSLA Chou  _et
al._ (2017); Beacham  _et al._ (2020); DUNE Kelly  _et al._ (2021); LHCb Craik
_et al._ (2022); and HL-LHC Track Trigger Hook  _et al._ (2020); Kelly  _et
al._ (2021).

The coupling of ALPs to photons is predicted at near-detectable levels in many
proposed answers to the big questions. A special, pion-phobic ALP which has
predictive couplings to photons may be the long sought-after QCD axion Alves
and Weiner (2018). Such a QCD axion could even help explain some nuclear de-
excitation anomalies in ^8Be and ^4He Alves (2021). A heavier QCD axion may
instead ammeliorate the “axion quality problem” of traditional QCD axion
models, with a finite parameter space that will continue to be explored by
future ALP searches Hook  _et al._ (2020).

ALPs also appear in solutions to other outstanding big questions besides the
Strong CP problem, the original motivation for QCD axions. For example,
coupling ALPs to both photons and dark-sector particles can provide a portal
from DM to the SM. This ALP portal may provide the requisite thermalization
between the SM and dark sectors during freeze-out in a SIMP DM model Hochberg
_et al._ (2018), with almost the entire viable parameter space observable in
ALP searches at near-future experiments. If instead semi-annihilations of DM
to ALPs set the relic abundance, the distinct parameter space which reproduces
the measured DM abundance still predicts some benchmarks detectable at future
ALP searches Kamada  _et al._ (2017).

##  IV Outlook

The minimal portals featured in this whitepaper are of intrinsic theoretical
interest, constituting an essential ingredient in a variety of motivated dark
sector theories that address some of the basic mysteries in particle physics
and cosmology. Intensity frontier experiments have great potential to explore
the renormalizable vector, Higgs, and neutrino portals, as well as the minimal
ALP-gluon and ALP-photon portals, in the coming years. A variety of
experimental facilities and detection strategies are required to probe the
broadest range of mediator masses and portal couplings. These studies form a
core part of a broader dark sector science program that also covers searches
for dark matter production and rich dark sectors. Achieving the ambitious
goals of this program necessitates investment in a variety of facilities and
experiments, as well as support for theory research. Building on an already
distinguished dark sector research tradition, there is great opportunity for
U.S. scientists and institutions to provide key leadership in this enterprise
over the next decade and beyond.

## Acknowledgements

B. B. is supported by U.S. Department of Energy (DOE) Grant DE–SC0007914 and
by PITT PACC. N. B. was supported in part by NSERC, Canada. C. H. is supported
by the Natural Sciences and Engineering Research Council of Canada and Compute
Canada. R. M. is supported in part by the DoE grant DE-SC0007859.

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