71 2021 Posted with permission from the Annual Review of Nuclear and Particle
Science, Volume 71 © 2021 by Annual Reviews, http://www.annualreviews.org/

# Searches for dark photons at accelerators

Matt Graham  1 Christopher Hearty  2 and Mike Williams3,4 1SLAC National
Accelerator Laboratory, Stanford University, Stanford, CA 94309, USA
2University of British Columbia / IPP, Vancouver, Canada, V6T 1Z1
3Massachusetts Institute of Technology, Cambridge, MA 02139, USA  4Monash
University, Melbourne, Victoria 3168, Australia

###### Abstract

Dark matter particles may interact with other dark matter particles via a new
force mediated by a dark photon, $A^{\prime}$, which would be the dark-sector
analog to the ordinary photon of electromagnetism. The dark photon can obtain
a highly suppressed mixing-induced coupling to the electromagnetic current,
providing a portal through which dark photons can interact with ordinary
matter. This review focuses on $A^{\prime}$ scenarios that are potentially
accessible to accelerator-based experiments. We summarize the existing
constraints placed by such experiments on dark photons, highlight what could
be observed in the near future, and discuss the major experimental challenges
that must be overcome to improve sensitivities.

###### doi:

10.1146/annurev-nucl-110320-051823

###### keywords:

dark photons, dark matter, hidden sectors, non-minimal models, accelerators

††journal: Annual Review of Nuclear and Particle Science

###### Contents

  1. 1 INTRODUCTION
  2. 2 PHENOMENOLOGY
    1. 2.1 The Dark-Photon Portal
    2. 2.2 Dark-Photon Production
    3. 2.3 Dark-Photon Decays
    4. 2.4 Thermal Dark Matter Targets
    5. 2.5 Dark Matter Self-Interactions
  3. 3 SEARCH STRATEGIES
    1. 3.1 Visible Dark Photon Decays
      1. 3.1.1 Prompt Dark Photon Decays
      2. 3.1.2 Displaced Dark Photon Decays
    2. 3.2 Invisible Dark Photon Decays
      1. 3.2.1 Missing Mass
      2. 3.2.2 Direct Detection
  4. 4 SEARCHES FOR VISIBLE DARK PHOTONS
    1. 4.1 Searches in $e^{+}e^{-}$ Colliders
    2. 4.2 Searches in Hadron Colliders
    3. 4.3 Searches in Electron Beam Fixed Target Experiments
    4. 4.4 Searches in Electron Beam Dumps
    5. 4.5 Searches in Proton Beam Dumps
    6. 4.6 Searches in Meson and Lepton Decays
  5. 5 SEARCHES FOR INVISIBLE DARK PHOTONS
    1. 5.1 Searches at $e^{+}e^{-}$ Colliders
    2. 5.2 Searches at Electron Beam Dumps
    3. 5.3 Searches in Meson Decays
    4. 5.4 Searches for Dark Matter Produced in Proton Beam Dumps
  6. 6 RICH DARK SECTORS
    1. 6.1 Feeble Direct Couplings
    2. 6.2 Dark Supersymmetry
    3. 6.3 Strongly Interacting Dark Matter
    4. 6.4 Inelastic Dark Matter
  7. 7 SUMMARY & OUTLOOK
  8. A DESCRIPTION OF EXPERIMENTS
    1. A.1 Electron Beam Dumps
    2. A.2 Proton Beam Dumps
    3. A.3 $e^{+}e^{-}$ Colliders
    4. A.4 LHC Experiments
    5. A.5 Meson and Lepton Decay Experiments
    6. A.6 Electron Fixed Target Experiments

##  1 INTRODUCTION

It would be difficult to overstate the success of the Standard Model (SM) of
particle physics; however, the SM cannot be a complete theory of nature since,
e.g., it cannot explain dark matter. The existence of dark matter is firmly
established due to its gravitational interactions, but little is known about
the dynamics within the dark sector itself. An intriguing possibility is that
dark matter particles may interact with other dark matter particles via a new
dark force, similar to the electromagnetic force felt by ordinary matter. If
this is the case, then one expects there to be a dark photon, $A^{\prime}$,
that mediates this dark force, in analogy to the ordinary photon of
electromagnetism. This exciting possibility has motivated a dedicated
worldwide effort to search for dark photons and other dark sector particles
(see, e.g., Refs. [1, 2] for recent reviews).

In the standard dark sector paradigm, no SM particles are charged directly
under any dark-sector interactions and vice versa. Therefore, the dark photon
does not couple directly to SM particles; however, it can obtain a small
coupling to the electromagnetic (EM) current due to kinetic mixing between the
SM hypercharge and $A^{\prime}$ field strength tensors [3, 4, 5, 6, 7, 8, 9,
10]. This mixing-induced coupling, which is suppressed relative to that of the
photon by a factor labeled $\varepsilon$, provides a portal through which dark
photons can interact with SM particles: dark photons can be produced in the
lab, and they can decay into visible SM final states—though decays into
(nearly) invisible dark-sector final states are expected to be dominant if
kinematically allowed. One striking advantage of producing dark matter in the
lab is that it will be relativistic, which leads to accelerator-based
experiments having similar sensitivity to most types of dark matter particles.
This is in stark contrast to direct-detection experiments, which, e.g., have
much better sensitivity to scalars than fermions.

The minimal dark-photon model only has 3 unknown parameters: the strength of
the kinetic mixing, $\varepsilon$; the dark photon mass, $m_{A^{\prime}}$; and
the decay branching fraction of the dark photon into invisible dark-sector
final states, which is typically assumed to be either unity or zero
(corresponding to whether any invisible dark-sector final states are
kinematically allowed or not). This review focuses on the region of
$[m_{A^{\prime}},\varepsilon]$ parameter space accessible to accelerator-based
experiments, namely $m_{A^{\prime}}\gtrsim 1$ MeV and $\varepsilon\gtrsim
10^{-7}$ (see Ref. [2] for a summary of non-accelerator-based constraints on
dark photons). In addition, we concentrate on $A^{\prime}$ masses below the
electroweak scale, where dark photon phenomenology is markedly different than
supersymmetry and other scenarios that extend the SM.

Thus far, no accelerator-based dark-photon searches have found any evidence
for a signal. Therefore, we will focus on summarizing the constraints placed
by accelerator-based experiments on both visible and invisible dark photons.
In addition, this review will highlight what could be observed in the near
future, while also discussing the major experimental challenges that must be
overcome to improve sensitivities. Finally, other non-minimal models will be
discussed, where the coupling of the dark boson arises from a different
mechanism and/or where other dark-sector particles impact the observable dark-
boson phenomenology at accelerator-based experiments.

##  2 PHENOMENOLOGY

This section provides an overview of dark photon phenomenology, including both
the theoretical and astrophysical motivations for dark photons. In addition,
dark photon production and decay rates are discussed.

###  2.1 The Dark-Photon Portal

The minimal dark photon scenario involves a broken $U(1)^{\prime}$ gauge
symmetry in the dark sector whose field strength tensor,
$F^{\prime}_{\mu\nu}$, kinetically mixes with the SM hypercharge field
strength tensor, $B_{\mu\nu}$, via the operator
$F^{\prime}_{\mu\nu}B^{\mu\nu}$. After electroweak symmetry breaking, and with
the gauge boson kinetic terms diagonalized, the dark photon obtains a
suppressed coupling to the EM current, $J^{\mu}_{\rm EM}$, where the relevant
terms in the Lagrangian are

$\displaystyle\mathcal{L}_{\gamma A^{\prime}}\supset$
$\displaystyle-\frac{1}{4}F^{\prime}_{\mu\nu}F^{\prime\mu\nu}+\frac{1}{2}m^{2}_{A^{\prime}}A^{\prime\mu}A^{\prime}_{\mu}+\varepsilon\,e\,A^{\prime}_{\mu}J^{\mu}_{\rm
EM}+\mathcal{L}_{A^{\prime}\chi\chi}\,,$ (1)

where $\chi$ denotes the lightest dark-charged particle (presumably the dark
matter), and the form of the $A^{\prime}\chi\chi$ interaction is left
unspecified ($\chi$ could be a scalar, fermion, etc.). The minimal dark-photon
model only has 3 unknown parameters: $m_{A^{\prime}}$, $\varepsilon$, and the
$A^{\prime}\to\chi\bar{\chi}$ decay branching fraction, which as discussed
above, is taken to be either unity or zero depending on whether any invisible
dark-sector final states are kinematically allowed; i.e., depending on whether
$m_{A^{\prime}}>2m_{\chi}$. A model-dependent coupling to the weak $Z$ current
also exists, though this appears at
$\mathcal{O}(m^{2}_{A^{\prime}}/m^{2}_{Z})$ and is only relevant for
$m_{A^{\prime}}\gtrsim 10$ GeV. Furthermore, precision electroweak
measurements restrict the expanded mixing parameters to be roughly those of
Refs. [11, 12], leaving $\varepsilon$ as the only free mixing parameter.

In principle, the strength of the kinetic mixing is a priori unknown; however,
it is possible to define a target range of $\varepsilon$ to explore by
assuming that the mixing arises due to the quantum effects of high-mass
particles. For example, if a heavy particle does exist that carries both
hypercharge and dark charge, kinetic mixing could be generated at the one-loop
level as shown in Fig. 1. Alternatively, if both sectors are part of a larger
Grand Unified Theory (GUT) of nature, then the leading contribution to the
mixing arises at the two-loop order. Fully exploring this few-loop range of
kinetic-mixing strength, which roughly corresponds to
$10^{-6}\lesssim\varepsilon\lesssim 10^{-2}$ even if the relevant high-mass
particles are at the Planck scale, is an important milestone of dark-sector
physics, though values of $\varepsilon$ outside of this range could also
arise, e.g., if the mixing is nonperturbative.

Figure 1:  Feynman diagrams depicting the generation of kinetic mixing at the
(left) 1-loop and (right) 2-loop levels.

###  2.2 Dark-Photon Production

Since dark photons couple to SM particles via the ordinary EM current,
suppressed by $\varepsilon$, they can be produced anywhere a virtual photon
with mass $m_{A^{\prime}}$ can be produced. The production mechanisms that
have been exploited by accelerator-based dark-photon searches can be
categorized as follows:

  * •

bremsstrahlung, $eZ\to eZA^{\prime}$ and $pZ\to pZA^{\prime}$, where an
incident electron or proton radiates a dark photon during an interaction with
a fixed nuclear target of charge $Z$;

  * •

annihilation, $e^{+}e^{-}\to A^{\prime}\gamma$, at an $e^{+}e^{-}$ collider;

  * •

Drell-Yan (DY), $q\bar{q}\to A^{\prime}$, where a quark and anti-quark
annihilate into a dark photon, which could occur at a hadron collider or when
a proton-beam is incident on a fixed nuclear target;

  * •

meson decays, e.g. $\pi^{0}\to A^{\prime}\gamma$ or $\eta\to
A^{\prime}\gamma$, for dark photons with $m_{A^{\prime}}<m_{\pi,\eta}$ at any
experiment where mesons are produced at high rates;

  * •

and $V\to A^{\prime}$ mixing, where $V=\omega,\rho,\phi$ denotes the QCD
vector mesons, which is important for $\mathcal{O}($GeV$)$-scale dark photons.

Proposed future searches largely exploit the same set of production mechanisms
(see Sec. 3). We note that other production mechanisms, e.g. secondary
positrons produced in beam dumps subsequently annihilating [13], are possible
though not considered in currently published constraints.

###  2.3 Dark-Photon Decays

Dark photons are expected to decay predominantly into invisible dark-sector
final states if kinematically allowed. If no such decays are allowed, e.g. if
$m_{A^{\prime}}<2m_{\chi}$, then the dark photon will decay into visible SM
final states, again due to its suppressed coupling to the EM current. The
partial decay widths of the dark photon into SM leptons are

$\displaystyle\Gamma_{A^{\prime}\to\ell^{+}\ell^{-}}=\tfrac{\varepsilon^{2}\alpha_{\rm
EM}}{3}m_{A^{\prime}}\left(1+2\tfrac{m^{2}_{\ell}}{m^{2}_{A^{\prime}}}\right)\sqrt{1-4\tfrac{m^{2}_{\ell}}{m^{2}_{A^{\prime}}}}\,,$
(2)

where $\ell=e,\mu,\tau$ and, of course, only decays into leptons for which
$m_{A^{\prime}}>2m_{\ell}$ are allowed. Decays into hadronic final states
cannot be calculated perturbatively for GeV-scale dark-photon masses; however,
since the dark photon couples to $J^{\mu}_{\rm EM}$, its hadronic decay width
can be extracted from the experimentally measured value of
$\mathcal{R}_{\mu}\equiv\sigma_{e^{+}e^{-}\to{\rm
hadrons}}/\sigma_{e^{+}e^{-}\to\mu^{+}\mu^{-}}$:

$\displaystyle\Gamma_{A^{\prime}\to{\rm
hadrons}}=\Gamma_{A^{\prime}\to\mu^{+}\mu^{-}}\mathcal{R}_{\mu}(m^{2}_{A^{\prime}})\,.$
(3)

Equation (3) automatically accounts for mixing with the QCD vector mesons, the
$\rho$, $\omega$, and $\phi$, along with all other nonperturbative QCD
effects. Figure 2 shows the branching fractions into $e^{+}e^{-}$,
$\mu^{+}\mu^{-}$, and to all hadronic final states for $m_{A^{\prime}}<2$ GeV.
At higher masses, $A^{\prime}\to q\bar{q}$ decays are easily calculable
perturbatively, making determining the branching fractions straightforward.
Finally, the dark photon lifetime, $\tau_{A^{\prime}}$, which is just
$\Gamma_{A^{\prime}}^{-1}$, clearly scales as
$[\varepsilon^{2}m_{A^{\prime}}]^{-1}$, i.e. the longevity of the dark photon
increases as its mass and kinetic-mixing strength decrease.

Figure 2:  From Ref. [14]: dark photon decay branching fractions for the
visible dark photon scenario for $m_{A^{\prime}}<2$ GeV. It is straightforward
to determine the decay rates into specific hadronic final states by replacing
the inclusive hadronic cross section in $\mathcal{R}_{\mu}$ with the relevant
exclusive cross sections.

###  2.4 Thermal Dark Matter Targets

Assuming that dark matter couples strongly enough to ordinary matter that
thermal equilibrium was reached in the early universe, there must be some
process that subsequently depleted the dark matter abundance. If
$m_{\chi}>m_{A^{\prime}}$, the purely dark-sector annihilation process
$\chi\bar{\chi}\to A^{\prime}A^{\prime}$ is kinematically allowed even at low
temperatures. Since this process does not depend on $\varepsilon$, we cannot
define a precise thermal target if this annihilation scenario is dominant.
However, if $m_{\chi}<m_{A^{\prime}}$, dark matter annihilation is via
$\chi\bar{\chi}\to A^{\prime*}\to f\bar{f}$, where $f$ denotes a charged SM
fermion. This process does depend on $\varepsilon$, which must be large
enough, and $m_{A^{\prime}}$ small enough, to achieve the required thermal
relic cross-section. It is standard to define the dimensionless interaction
strength $y$ such that

$\displaystyle\langle\sigma
v\rangle\propto\frac{\varepsilon^{2}\alpha_{D}m_{\chi}^{2}}{m_{A^{\prime}}^{4}}\equiv\frac{y}{m_{\chi}^{2}},$
(4)

where $\alpha_{D}$ is dark-sector fine-structure constant. Using this
convention, for any choice of dark matter mass a unique value of $y$ is
compatible with thermal freeze-out independently of the specific values of the
other parameters, in the limit $m_{\chi}\ll m_{A^{\prime}}$. In addition, for
any choice of $\alpha_{D}$ and the ratio $m_{A^{\prime}}/m_{\chi}$, we can
then determine the smallest value of $\varepsilon$ that is consistent with
thermal equilibrium in the early universe. For Dirac fermions, CMB data from
Planck [15] rule out $m_{\chi}\lesssim\mathcal{O}(10\,{\rm GeV})$. Therefore,
pseudo-Dirac fermions with a small mass splitting, Majorana fermions, and
scalars, which all have velocity suppressed annihilation cross sections, are
considered in this review.

###  2.5 Dark Matter Self-Interactions

Whether dark matter experiences any forces other than gravity, known as self-
interacting dark matter (SIDM), is a hotly debated topic in astrophysics. This
section provides a brief overview; the reader is encouraged to see Ref. [16]
for a thorough review. One motivation for SIDM is that the lightest dark
matter particle charged under a dark-sector interaction must be stable due to
charge conservation, consistent with the fact that dark matter particles have
survived for over 14 billion years to date. SIDM models also have observable
implications for astrophysical structure. For example, self-interactions could
explain several small-scale structure observations that appear to be in
tension with collisionless dark matter predictions, e.g. the so-called core-
cusp problem; however, at large scales, collisionless dark matter models have
been a great success. This can all be reconciled if dark matter self-
interactions are velocity dependent, which is expected if they are mediated by
a relatively light $\mathcal{O}($MeV–GeV$)$ mediator particle, e.g. a dark
photon. Indeed, simple dark-photon models can explain observations spanning a
large range of length scales, from dwarf galaxies to galaxy clusters. That
said, the interplay between baryonic interactions and dark matter, e.g. how
feedback from supernovae affect the dark matter density profile, is not fully
understood, and this non-linear dynamic may provide an alternative solution to
small-scale structure problems. Regardless, SIDM is well motivated and
searches for dark photons are of great interest to both the particle physics
and astrophysics communities.

##  3 SEARCH STRATEGIES

This section describes broadly the strategies experiments use to search for
dark photon decays into visible SM and (nearly) invisible dark-sector final
states. Since the signatures for these two decay paths are markedly different,
the experimental methods used to produce and detect the dark photon signatures
can also be quite different. Below we will summarize the experimental
strategies used to search for dark photons and the advantages and challenges
of each strategy.

###  3.1 Visible Dark Photon Decays

In scenarios where $A^{\prime}$ decays into invisible dark-sector final states
are kinematically forbidden, the dark photon will decay to visible SM final
states. If the kinetic mixing strength is
$\varepsilon\gtrsim\mathcal{O}(10^{-3})\times(10\,{\rm MeV}/m_{A^{\prime}})$,
the dark photon will decay promptly; i.e. at a point that is experimentally
indistinguishable from the production point. For smaller mixing strengths, the
dark photon decay point may be significantly displaced from the production
point. Both of these signatures are discussed below.

####  3.1.1 Prompt Dark Photon Decays

Searches for prompt visible $A^{\prime}$ decays exploit the fact that the
natural width of the dark photon is negligible compared to the mass resolution
of any experiment. Therefore, such decays will produce a peaking resonant
structure, or bump, in the invariant mass spectrum of the decay products,
whereas the backgrounds to these searches predominantly produce spectra
without sharp features. Experiments typically focus on the $e^{+}e^{-}$ or
$\mu^{+}\mu^{-}$ decay channels, since these final states have substantial
branching fractions and are the easiest to identify and trigger on. The
backgrounds for these final states largely arise from
$\gamma^{*}\to\ell^{+}\ell^{-}$ processes, which are experimentally
indistinguishable from the signal making them irreducible. In addition, since
dark photons couple to the EM current, the expected $A^{\prime}$ yield is
related to the observed $\gamma^{*}\to\ell^{+}\ell^{-}$ yield in a small
$\pm\Delta m$ window around $m_{A^{\prime}}$ by
$n(A^{\prime}\to\ell^{+}\ell^{-})=\varepsilon^{2}n(\gamma^{*}\to\ell^{+}\ell^{-})\mathcal{F}(m_{A^{\prime}})/2\Delta
m$, where $\mathcal{F}$ is a known mass-dependent function [17]. Most
experiments also have other background sources, including misidentified
particles and leptons produced in weak decays, that also decrease the
sensitivity of the analysis. Many past, existing, and future experiments
either have or plan to search for prompt dark photon decays. The keys to
improving sensitivity include increasing the luminosity and improving the mass
resolution, which would decrease the effective background yields, both of
which are extremely challenging to substantially improve upon.

####  3.1.2 Displaced Dark Photon Decays

Searches for dark photon decay points that are significantly displaced from
the production point are able to highly suppress, or even eliminate, the
prompt $\gamma^{*}\to\ell^{+}\ell^{-}$ backgrounds. Since the dark photon
lifetime scales as $[\varepsilon^{2}m_{A^{\prime}}]^{-1}$, it is only possible
to exploit this displaced-decay signature for small masses and kinetic-mixing
strengths. In addition, low-mass dark photons can be highly boosted resulting
in $A^{\prime}$ flight distances up to $\mathcal{O}(100\,{\rm m})$ for
sufficiently small values of $\varepsilon$. In such cases, backgrounds can be
highly suppressed by inserting shielding material between the production point
and instrumented decay region, a strategy employed by so-called beam-dump
experiments. For intermediate $A^{\prime}$ lifetimes, where
$c\tau_{A^{\prime}}$ is $\mathcal{O}({\rm mm})$ or less, resolving the
$A^{\prime}$ decay point as displaced requires installing a high-precision
vertex detector as close as possible to the production point. The boost
imparted to the $A^{\prime}$ is also important to ensuring that its decay is
significantly displaced from the production point. The primary background in
these searches for intermediate-lifetime dark photons are SM photons that
convert to $\ell^{+}\ell^{-}$ in the vertex detector itself, though via
precision in situ spatial mapping of the detector material, these backgrounds
can be highly suppressed by rejecting dilepton vertices that are consistent
with locations occupied by material (see, e.g., Ref. [18]). This intermediate-
lifetime area is the focus of much ongoing experimental effort. The keys to
improving sensitivity again include increasing luminosities, along with either
decreasing the length of the required shielding in beam-dump experiments or
improving the vertex resolution at other experiments. These are challenging
given the suite of high-quality experiments already performed.

###  3.2 Invisible Dark Photon Decays

If $m_{A^{\prime}}>2m_{\chi}$, where $\chi$ again denotes the lightest dark-
charged particle, the dark photon will predominantly undergo the (nearly)
invisible $A^{\prime}\to\chi\bar{\chi}$ decay. We can search for these types
of decays in two ways: by looking for an excess of events with a consistent
invariant mass formed from the imbalance of observed energy and momentum, the
missing mass; or by looking for the incredibly rare interactions of the dark-
sector $\chi$ particles in a detector downstream of the $A^{\prime}$ decay
point, referred to as direct detection. We will address both of these classes
below.

####  3.2.1 Missing Mass

Experiments that employ the missing-mass method attempt to detect and measure
all visible final state particles in each individual interaction, searching
for events with an imbalance of energy and momentum. It is important to avoid
final states with substantial SM backgrounds from processes that produce
neutrinos, as these can mimic a signal. Clearly these experiments must also
have a precisely determined initial state, which is achieved either using
information from the accelerator or by measuring the energy and momentum of
some produced initial state directly. For example, the initial state could
consist of two beam particles at a collider, or one beam particle striking a
stationary, or fixed, target particle. Eliminating losses of particles or
energy due to gaps in the detector acceptance or the lack of containment of
secondary particles is the key to reducing backgrounds, and hence, achieving
good sensitivity in these experiments. Therefore, these detectors must have
extensive and hermetic tracking and EM and hadronic calorimetric systems in
order to minimize losses. Assuming these losses are minimized, the predominant
backgrounds arise from photo-nuclear effects in the calorimeter systems.
Increasing the luminosity while maintaining excellent background suppression
is extremely challenging.

####  3.2.2 Direct Detection

It is also possible to search for the rare interactions of the dark-sector
$\chi$ particles in a detector placed downstream of the $A^{\prime}$ decay
point (making the term invisible somewhat of a misnomer). For these
experiments, the dark photon is produced in the usual ways, and then
subsequently produces the $\chi$ particles in $A^{\prime}\to\chi\bar{\chi}$
decays. These $\chi$ particles are then detected via their scattering off of
the electrons and nuclei in a downstream detector. This scattering involves
the $\chi$ particle emitting a dark photon which interacts with the detector
particles via its coupling to the EM current, leading to a detectable energy
transfer. This emission of a dark photon and its coupling to the detector
particle leads to an addition suppression factor of
$\alpha_{D}\varepsilon^{2}$, such that rates in direct-detection experiments
scale as $\alpha_{D}\varepsilon^{4}$ (compared to $\varepsilon^{2}$ for other
types of experiments).

Due to the substantial suppression factor, direct-detection experiments must
be capable of producing a huge number of dark photons, and employ a large
active detector mass while maintaining small background rates. Beam-dump
experiments are ideal for the upstream component, given their high intensities
and low backgrounds. The large-mass downstream detectors must have sensitivity
to low energy transfers, since the recoils of their electrons (protons) are at
most $\mathcal{O}(100\,(10)\,{\rm MeV})$ using existing and near-future beams.
Short-baseline neutrino experiments (or near detectors at long baselines) are
well suited to performing these searches; however, one obvious drawback is
that they are designed to maximize the neutrino rate in the downstream
detector, which sources a large background for $\chi$ searches. To overcome
this, the MiniBooNE experiment ran with a dedicated direct-detection
configuration and achieved good results, see Sec. 5. Another drawback of
neutrino experiments is that they typically use proton beams, which by design,
produce substantial neutrino backgrounds. Future dedicated direct-detection
experiments propose using electron beams instead, which would greatly reduce
the backgrounds.

##  4 SEARCHES FOR VISIBLE DARK PHOTONS

The current constraints on visible $A^{\prime}$ decays in the
$[m_{A^{\prime}},\varepsilon]$ plane are presented in Fig. 3. The few-loop
$\varepsilon$ region is excluded in the low-mass $m_{A^{\prime}}\lesssim 20$
MeV region. For intermediate masses, $0.02\lesssim m_{A^{\prime}}\lesssim 0.5$
GeV, there is a gap in the current coverage of roughly
$10^{-5}\lesssim\varepsilon\lesssim 10^{-3}$. Above 0.5 GeV, existing results
only require $\varepsilon\lesssim 10^{-3}$. Projections of the sensitivity
expected in the next 5 years from many experiments are shown in Fig. 4.
Assuming these are realized, the entire intermediate-mass few-loop region
could be explored in the near future; however, there are currently no known
viable ways to explore the $m_{A^{\prime}}\gtrsim 1$ GeV and
$\varepsilon\lesssim 10^{-4}$ region. This section summarizes the landscape of
searches for visible $A^{\prime}$ decays. More details on each experiment are
provided in Appendix A.

Figure 3:  From Ref. [14] made using Ref. [19]: Constraints on visible
$A^{\prime}$ decays from electron beam dumps, proton beam dumps, $e^{+}e^{-}$
colliders, $pp$ collisions, meson decays, and electron on fixed target
experiments. The constraint derived from $(g-2)_{e}$ is shown in grey [20,
21]. The gaps in the prompt limits correspond to regions near the masses of
the QCD vector mesons.  Figure 4:  Same as Fig. 3 but with all existing
constraints shown in grey, and proposed future sensitivities in the next 5
years shown as lines (using the same experiment-type color scheme as Fig. 3).
Only published projections are shown, which for example, does not include a
Run 3 update from CMS or the sensitivity of an inclusive $A^{\prime}\to
e^{+}e^{-}$ search at LHCb.

###  4.1 Searches in $e^{+}e^{-}$ Colliders

At $e^{+}e^{-}$ colliders, the predominant production mode for dark photons is
$e^{+}e^{-}\to A^{\prime}\gamma$, where one photon in the SM annihilation
process is replaced with a dark photon. Thus far, searches at $e^{+}e^{-}$
colliders [22, 23, 24, 25] have looked for prompt $A^{\prime}$ decays in the
$e^{+}e^{-}$, $\mu^{+}\mu^{-}$, and $\pi^{+}\pi^{-}$ final states. The
background for these searches is dominated by the irreducible
$e^{+}e^{-}\to\ell^{+}\ell^{-}\gamma$ continuum. In addition, there are
sizable peaks in the background spectrum due to vector meson decays ($\omega$,
$\phi$, J/$\psi$, $\psi(2S)$, $\Upsilon$, etc.); these peak regions are
removed from consideration during the searches. For the $A^{\prime}\to
e^{+}e^{-}$ decay, there is also background from photon conversions in the
detector material, which can be highly suppressed by rejecting $e^{+}e^{-}$
vertices that are inconsistent with originating from the primary beam-beam
interaction point; however, at low $e^{+}e^{-}$ invariant masses, where the
opening angle between the leptons is small, some of this conversion background
remains.

As shown in Fig. 3, the BaBar experiment at SLAC has produced the most
stringent limits on visibly decaying dark photons in the 1–10 GeV mass region,
and also for 0.1–0.2 GeV masses in the prompt regime [22]. BaBar ran from
1999–2008 at center-of-mass collision energies in the range 10.3–10.5 GeV. In
addition, Fig. 4 shows that the Belle II experiment, which recently started
taking data and runs at a similar center-of-mass energy as BaBar, is expected
to be sensitive to $\varepsilon$ values that are about 3 times smaller than
BaBar [26]. Looking further down the road, a Future Circular Collider could
produce world-leading sensitivity up to higher masses [27, 28, 29]. These
results and projections demonstrate that $e^{+}e^{-}$ colliders are powerful
probes of prompt visible dark photon decays.

###  4.2 Searches in Hadron Colliders

At the LHC, the predominant production modes for dark photons depend on
$m_{A^{\prime}}$: meson decays, e.g., $\pi^{0}\to A^{\prime}\gamma$ and
$\eta\to A^{\prime}\gamma$, for $m_{A^{\prime}}\lesssim 0.5$ GeV; $A^{\prime}$
mixing with the $\rho$, $\omega$, and $\phi$ mesons for $0.5\lesssim
m_{A^{\prime}}\lesssim 1$ GeV; and Drell-Yan, $q\bar{q}\to A^{\prime}$, for
larger masses. Thus far, searches at the LHC have looked for both prompt (LHCb
and CMS) and displaced (LHCb) $A^{\prime}\to\mu^{+}\mu^{-}$ decays, with plans
to also search for $A^{\prime}\to e^{+}e^{-}$ decays at LHCb. The background
for the prompt searches is dominated by the irreducible SM Drell-Yan
continuum, leptons produced in heavy-flavor decays, and hadrons misidentified
as leptons. The sizable peaks due to QCD vector meson decays are removed from
consideration during the searches. The background in the search for displaced
$A^{\prime}$ decays is dominated by: photon conversions, which can be highly
suppressed by rejecting dilepton vertices that are consistent with originating
from locations occupied by detector material; leptons produced in heavy-flavor
decays, though these are only important for $A^{\prime}$ lifetimes
$\mathcal{O}({\rm ps})$; and $K_{S}\to\pi^{+}\pi^{-}$ decays, where both pions
are misidentified as leptons, for $0.35\lesssim m_{A^{\prime}}\lesssim 0.5$
GeV.

Figure 3 shows that the LHCb [30, 31] and CMS [32] experiments have produced
the most stringent limits on visibly decaying dark photons for
$m_{A^{\prime}}>10$ GeV. In addition, LHCb has produced world-leading
constraints for $2m_{\mu}\lesssim m_{A^{\prime}}\lesssim 0.5$ GeV from both
its prompt and displaced searches, the latter being the only search to achieve
sensitivity using a displaced-vertex signature. This is made possible by its
high-precision vertex detector and flexible trigger system. Figure 4 shows
that LHCb is expected to greatly enhance its sensitivity in the next 5 years,
specifically with its upgrade for LHC Run 3 [33, 17]. LHCb also plans to
perform inclusive searches for $A^{\prime}\to e^{+}e^{-}$ decays, using both
current and future data, which should explore the mass gap between its
published projections, and CMS expects to substantially improve on its
sensitivity in the high-mass region as well, though no published projections
exist for either of these searches. These results demonstrate that LHC
experiments are powerful probes of both prompt and displaced visible
$A^{\prime}$ decays.

Several new experiments have been proposed recently that will search for dark
photons produced in LHC proton-proton collisions using new detector packages
dedicated to long-lived $A^{\prime}$ scenarios. For example, FASER [34] is
being installed in an LHC service tunnel positioned 480 m downstream from the
ATLAS interaction point. FASER plans to start collecting data in LHC Run 3 and
expects to provide the $A^{\prime}$ sensitivity [35] shown in Fig. 4. An
upgrade, FASER2, has been proposed, that would increase the luminosity by a
factor of 20, greatly increasing the $A^{\prime}$ sensitivity. Similar
experiments like MATHUSLA [36] and Codex-b [37] could also come online in the
next decade.

###  4.3 Searches in Electron Beam Fixed Target Experiments

Fixed-target experiments send a high-current electron beam through a thin,
high-$Z$ target (or assembly of targets) and detect the products with a
downstream, forward detector. Production of dark photons is via a radiative
$A^{\prime}$ recoiling against the target nucleus, i.e. via the $eZ\to
eZA^{\prime}$ bremsstrahlung process [10, 38]. These radiative dark photons
are largely produced in the forward region with close to the beam energy,
leading to decay leptons that are boosted in the forward direction and carry
(on average) half of the beam energy. There is a large background from QED
trident events, of which the radiative part is irreducible. As discussed in
Sec. 3.1.1, since $A^{\prime}$ production is proportional to the SM
$\gamma^{*}\to e^{+}e^{-}$ yield, these experiments are normalized using the
observed number of radiative events. Therefore, the total integrated
luminosity, which typically has large uncertainties in this type of
experiment, does not need to be determined.

The A1 (Mainz Microtron) [39] and APEX (JLAB) [40, 41] experiments both
utilized movable, low-angle, high-resolution spectrometers to search for
prompt $A^{\prime}\to e^{+}e^{-}$ decays. The HPS experiment (JLAB) instead
uses a silicon vertex tracker inside of a magnetic field near the target which
enables searching for both prompt and displaced $A^{\prime}$ decays [42, 43].
Figure 3 shows that experiments in this category do not currently provide
world-leading sensitivity to dark photons; however, both APEX and HPS have
further running planned in the near future, and expect to expand their reach
into unexplored regions of $A^{\prime}$ parameter space (see Fig. 4). Similar
experiments have been proposed for running further into the future [44, 45,
46, 47].

###  4.4 Searches in Electron Beam Dumps

Data from the electron beam dump experiments E141, E137, E774, KEK, and Orsay
[48, 49, 50, 51, 52], which ran during the 1980s, have been recast [10, 53] to
place constraints on displaced visible $A^{\prime}\to e^{+}e^{-}$ decays.
These experiments exploit the same $eZ\to eZA^{\prime}$ bremsstrahlung
production process as the experiments in the previous subsection. A major
difference, however, is that they all employed shielding after their beam-dump
targets to absorb SM particles. Each experiment employed an EM calorimeter
placed downstream of its substantial shielding. The length of the shielding
sets a hard lower limit on the $A^{\prime}$ flight distance in the lab frame.
Since the $A^{\prime}$ lifetime scales as
$[\varepsilon^{2}m_{A^{\prime}}]^{-1}$, beam-dump experiments provide
sensitivity to wedge-shape regions of dark-photon parameter space. There is
also one experiment in this category that is currently running: NA64 uses a
100 GeV electron beam derived from the CERN SPS proton beam incident on an
active target upstream of an EM calorimeter to enable searches for dark photon
decays to $e^{+}e^{-}$ [54]. Figure 3 shows that electron beam dump
experiments provide world-leading constraints on dark photons in the low-mass
region. Future experiments have also been proposed; see, e.g., Ref. [55].

###  4.5 Searches in Proton Beam Dumps

Data from previously run proton beam dump experiments have also been used to
place limits on $A^{\prime}\to e^{+}e^{-}$ decays. The experimental setups
were similar to those in the previous subsection; however, the use of a proton
beam results in more possible production processes to consider. Thus far,
limits have been set by the following experiments: $\nu$-CAL I [56, 57], using
$\pi^{0}\to A^{\prime}\gamma$ decays [58] and proton bremsstrahlung [59];
CHARM [60], using $\eta^{(\prime)}\to A^{\prime}\gamma$ decays [61]; and NOMAD
[62] and PS191 [63] using $\pi^{0}\to A^{\prime}\gamma$ decays [64]. Figure 3
shows that these limits are largely comparable to those obtained from electron
beam dumps, exceeding them at higher masses. In the near future, two
variations of the SeaQuest experiment, dubbed SpinQuest and DarkQuest, will
use the 120 GeV main injector proton beam at Fermilab incident on a beam dump
to search for $A^{\prime}\to\mu^{+}\mu^{-}$ and $A^{\prime}\to e^{+}e^{-}$
decays [65, 66]. As can be seen in Fig. 4, this will greatly enhance the
sensitivity compared to that of the older proton beam dumps. Further into the
future, proposed experiments like SHiP could provide even greater enhancements
[67].

###  4.6 Searches in Meson and Lepton Decays

While meson-decay processes contribute to the production of dark photons at
hadron colliders and proton beam dumps, experiments like NA48/2, located at
the CERN SPS, exclusively exploit such decays. Specifically, NA48/2 searched
for $\pi^{0}\to A^{\prime}\gamma$ followed by prompt $A^{\prime}\to
e^{+}e^{-}$ decays using $\pi^{0}$ mesons produced in $K^{+}\to\pi^{+}\pi^{0}$
decays [68]. Figure 3 shows that the NA48/2 constraints are world leading for
prompt decays in the 10–100 MeV mass region. Soon, the Mu3e experiment located
at the Paul Scherrer Institute expects to provide the first dark-photon
sensitivity in lepton decays using stopped muons [69]. Figure 4 shows that
Mu3e could be sensitive to currently unexplored parameter space soon. Future
experiments that exploit other meson decays are also being considered; see,
e.g., Ref. [70].

##  5 SEARCHES FOR INVISIBLE DARK PHOTONS

The current constraints on invisible $A^{\prime}\to\chi\bar{\chi}$ decays are
summarized in Fig. 5. These results were obtained by looking for an excess of
events with a consistent missing invariant mass, formed from the imbalance of
observed energy and momentum. In this section, we will first discuss how these
results were obtained, and the near-term prospects for improvement. Then, in
Sec. 5.4 we will discuss the alternative strategy of direct detection of the
incredibly rare interactions of the dark-sector $\chi$ particles in a detector
downstream of the $A^{\prime}$ decay point. Figure 5 shows that existing
constraints exclude otherwise viable thermal dark matter scenarios, e.g. EM-
like values of $\alpha_{D}$. Furthermore, even pessimistic scenarios with a
large $\alpha_{D}$ and small $m_{A^{\prime}}/m_{\chi}$ ratio will be
accessible in the near future.

Figure 5:  Updated from Ref. [14] using Ref. [19]: Constraints and proposed
sensitivity within the next 5 years on invisible $A^{\prime}$ decays. The
color scheme is the same as in Fig. 3. The (solid and dashed black lines)
thermal targets for different dark matter scenarios are also shown [71].

###  5.1 Searches at $e^{+}e^{-}$ Colliders

As discussed above, the predominant production mode for dark photons in these
experiments is $e^{+}e^{-}\to A^{\prime}\gamma$, where one photon in the SM
annihilation process is replaced with a dark photon. For the case where the
$A^{\prime}$ decays invisibly, the visible final state is a single photon with
a substantial imbalance in momentum and energy compared to the initial
$e^{+}e^{-}$ beams. The dominant backgrounds are $e^{+}e^{-}\to\gamma\gamma$,
where one photon is not detected, $e^{+}e^{-}\to\gamma\gamma\gamma$, with one
photon out of acceptance and another undetected, and $e^{+}e^{-}\to
e^{+}e^{-}\gamma$, radiative Bhabha scattering where both leptons are out of
acceptance. The $e^{+}e^{-}\to\gamma\gamma$ background mimics a low-mass
$A^{\prime}$ signal. In the BaBar experiment, the primary cause of not
detecting a photon was azimuthal gaps in the calorimeter crystals [72]. This
was highly suppressed by looking for subsequent interactions of the photon in
the muon system, and by disfavoring missing momenta that are consistent with
the locations of these calorimeter gaps. The $e^{+}e^{-}\to\gamma\gamma\gamma$
background is dominant at intermediate masses, while the radiative Bhabha
background is irreducible and dominant for $m_{A^{\prime}}\gtrsim 4$ GeV.

Figure 5 shows that the BaBar constraints on invisible $A^{\prime}$ decays are
world leading in the 0.2–8 GeV mass region [72]. The structure in the BaBar
constraints at higher masses is due to the fact that its singe-photon-trigger
data was collected at several center-of-mass energies, corresponding to the
$\Upsilon(2S)$, $\Upsilon(3S)$, and $\Upsilon(4S)$ masses, and with two
different energy thresholds for the detected SM photon. Belle II projections
[73] indicate that competitive sensitivity with BaBar can be achieved with
almost 5 times less data. There are two aspects of the Belle II calorimeter
design that enhance its sensitivity to invisible dark photons: larger solid
angle coverage due to both a larger calorimeter and a smaller beam-energy
asymmetry; and the crystals in the central (barrel) part of the calorimeter
are tilted so that gaps between crystals do not align with the interaction
point. We note that the projections in Fig. 5 are for only $\approx 0.04\%$ of
the full planned Belle II data sample; extrapolations to the full sample
require studies of the systematic uncertainties in photon detection
probabilities. The KLOE2 experiment has also recorded a data set with a single
photon trigger at a much smaller center-of-mass energy than BaBar and Belle
II, though sensitivity projections are not yet available. Finally, for masses
larger than 10 GeV, mono-photon data from the DELPHI experiment at LEP [74,
75], which was recast as a search for invisible dark photon decays in Ref.
[76], provides the strongest constraints.

###  5.2 Searches at Electron Beam Dumps

The aforementioned NA64 experiment, discussed in Sec. 4, is also able to
search for invisible $A^{\prime}$ decays. Dark photons would be produced via
hard bremsstrahlung from its 100 GeV electron beam interacting in an active
target, an EM calorimeter. The subsequent $A^{\prime}\to\chi\bar{\chi}$ decay
would carry off substantial energy, resulting in an energy deposition in the
EM calorimeter well below the beam energy. The vast majority of SM events with
small EM energy deposited in the calorimeter involve the production of
hadrons, which deposit substantial energy in the hadronic calorimeter located
further downstream. After rejecting events with activity in the hadronic
calorimeter, the largest surviving background is due to electro-production of
a hadron in the beam line prior to the beam electron reaching the EM
calorimeter, where the hadron misses the hadronic calorimeter. These NA64
limits are the most stringent available for $m_{A^{\prime}}<0.2$ GeV [77]. If
the analysis remains background free, the limits on $\varepsilon$ will improve
as the square root of the number of electrons on target. Projections for the
full data sample are also shown in Fig. 5, while further improvements from
running with a muon beam are also possible [78].

LDMX is a proposed electron beam fixed target experiment that would search for
the invisible decay of dark photons [71]. In addition to EM and hadronic
calorimetry, the detector includes tracking in a magnetic field before and
after the thin target, enabling measurements of both missing momentum and
missing energy. This additional information provides better rejection of rare
backgrounds than energy measurements alone. LDMX expects to provide good
coverage of the most pessimistic relic density targets for dark photon masses
up to hundreds of MeV. Various sites are under consideration, including a
proposed new beam line derived from the LCLS beam at SLAC.

BDX is a proposed experiment to be located in a new underground experimental
hall downstream of the JLAB Hall A beam dump [79]. It will use a homogeneous
CsI(Tl) calorimeter to detect $\chi$ particles scattering off of electrons.
BDX expects to probe unexplored parameter space for dark photon masses up to
several hundred MeV.

###  5.3 Searches in Meson Decays

The NA62 experiment has exploited its large sample of charged kaons and its
hermetic photon coverage to search for invisible dark photons produced in
$\pi^{0}\to\gamma A^{\prime}$ decays. The $\pi^{0}$ mesons are produced in
$K^{+}\to\pi^{+}\pi^{0}$ decays, where the four-momenta derived from that of
the $K^{+}$ and $\pi^{+}$ must be consistent with a $\pi^{0}$. Dark photon
candidates are the subset of these events that contain only a single detected
photon. To suppress backgrounds from photon conversions, the only hit in a
scintillator upstream of the EM calorimeter must be from the $\pi^{+}$. The
dominant remaining background is $K^{+}\to\pi^{+}\pi^{0}(\gamma)$ where one of
the $\pi^{0}\to\gamma\gamma$ photons is lost due to a photonuclear reaction or
conversion. The resulting limits [80], which are shown in Fig. 5, are
comparable to NA64, but not world leading; however, we note that these results
used only about 1% of the full NA62 data sample. Finally, as noted in Ref.
[81], the proposed KLEVER experiment [82] may be able to probe invisible
decays of dark photons with masses in the 100–200 MeV range in conjunction
with its study of the rare decay $K_{L}\to\pi^{0}\nu\bar{\nu}$.

###  5.4 Searches for Dark Matter Produced in Proton Beam Dumps

Figure 6:  Constraints on the invisible $A^{\prime}\to\chi\bar{\chi}$ scenario
in the $[m_{\chi},y]$ plane for pessimistic values of $\alpha_{D}$ and the
$m_{A^{\prime}}/m_{\chi}$ ratio. All of the results from Fig. 5 also apply
here. In addition, searches for dark photons produced in proton beam dumps
with the subsequent scattering of $\chi$ particles detected downstream are
shown using the same proton beam dump color scheme as before. The direct
detection constraints from CRESST II [83], CRESST III [84], and XENON1T [85]
only apply for the elastic scalar dark matter case and have sizable
uncertainties [86, 87]. Otherwise, direct detection experiments have much
worse sensitivity than accelerator searches, since $\chi$ particles produced
at accelerators are relativistic. As in Fig. 5, less pessimistic values of
dark-sector parameters are already excluded.

An alternative strategy for detecting $A^{\prime}\to\chi\bar{\chi}$ decays is
to detect the incredibly rare interactions of the dark-sector $\chi$ particles
in a detector downstream of the $A^{\prime}$ decay point. Given how unlikely
such interactions are, direct-detection experiments must be capable of
producing a huge number of dark photons, and employ a large active detector
mass while maintaining small background rates. Proton beam dumps placed
upstream of neutrino detectors are well suited to performing these searches.
Dark photons are predominantly produced at proton beam dumps via $\pi^{0}$ and
$\eta$ decays, along with proton bremsstrahlung. The $\chi$ particles can be
detected through neutral-current-like processes, $e\chi\to e\chi$, $N\chi\to
N\chi$, or if the $\chi$ beam is energetic enough, scattering off of nucleons
can also create pions. Charged-current quasi-elastic neutrino scattering,
which has no analog involving dark matter interactions, can be used to
normalize the neutrino flux.

The LSND experiment produced a huge sample of $\pi^{0}$ decays by impinging a
low-energy proton beam onto a fixed target. Any subsequent
$A^{\prime}\to\chi\bar{\chi}$ decays would produce low-energy $\chi$ particles
only capable of transferring a visible amount of energy to electrons, thus
only $e\chi\to e\chi$ scattering was considered in the reinterpretation of its
results [88]. Figure 6 shows that the LSND limits are competitive with those
obtained from searches for invisible $A^{\prime}$ decays.

The MiniBooNE experiment could produce $\chi$ particles with sufficient energy
to produce visible scatters off of both electrons and nucleons; however, the
electron-scattering analysis still provides better sensitivity in the minimal
model [89] (the nucleon-scattering analysis is more sensitive to leptophobic
models, where the $e\chi$ coupling is highly suppressed). The dominant
background is due to neutral-current neutrino scattering events. Figure 6
shows that the MiniBooNE limits are also competitive with those obtained from
searches for invisible $A^{\prime}$ decays.

The COHERENT experiment plans to search for dark matter scattering at low
momentum transfer, $Q^{2}<(50\,\mathrm{MeV})^{2}$, where the $\chi$ particles
can interact coherently with an entire nucleus in the detector, producing a
several keV nuclear recoil [90]. Neutrinos, which are produced by charged pion
decays at rest, will produce a similar signal by design. A major difference is
that the dark matter signal is prompt (coincident with the 600 ns long beam
bunch), whereas the neutrino signal has both a prompt component and a
component delayed by the muon lifetime. The recoil energy spectra are also
somewhat different. As can be seen in Fig. 6, COHERENT expects to probe some
unexplored parameter space soon.

Figure 6 shows that the thermal targets for accelerator-based experiments have
minimal dependence on the nature of the dark matter particles. This is because
dark matter produced at accelerators is relativistic, and due to the fact that
the strength of the $A^{\prime}$ interactions with SM particles are fixed at
thermal freeze-out. Conversely, the rate of non-relativistic relic dark-matter
scattering in direct-detection experiments varies by $\approx 20$ orders of
magnitude between the elastic scalar and pseudo-Dirac scenarios considered
here. Therefore, as can be seen in Fig. 6, accelerator-based experiments can
probe nearly all thermal scenarios in this mass regime in the next 5 years,
with future efforts fully covering these targets [79, 91, 92, 71]. Near-future
direct-detection experiments will only be able to explore the elastic scalar
case. That said, while discovery of $A^{\prime}$ and/or $\chi$ particles at an
accelerator would undoubtedly be Nobel worthy, these may not be part of the
sector that constitutes the majority of the dark matter in the universe.
Further study would be needed considering astrophysical, cosmological, direct
and indirect detection data sets, which demonstrates the complementarity
inherent in understanding the nature of dark matter.

##  6 RICH DARK SECTORS

The minimal dark photon model described in Sec. 2 is not the only dark-sector
option. The strongest connection to the dark sector may not arise via kinetic
mixing. Furthermore, the dark sector could be populated by other types of
particles that have phenomenological implications. Indeed, studying non-
minimal dark sectors is a major challenge due to the wide array of viable
dark-sector models. This section briefly discusses a few examples of rich dark
sectors.

###  6.1 Feeble Direct Couplings

The dark-photon portal described in Sec. 2.1 is not the only way to connect
the light and dark sectors. The SM fields could be charged directly under the
gauge interaction of the dark sector, resulting in very different couplings
cf. a kinetically mixed dark photon. For example, $B\\!-\\!L$ interactions
would also result in a coupling of the $A^{\prime}$ to neutrinos. While this
alters the results of Sec. 2, a data-driven approach similar to that described
above for the dark photon can be used for $B\\!-\\!L$ and any other vector-
boson model to determine the production and decay rates [14]. Furthermore,
dark-photon searches provide serendipitous discovery potential for $B\\!-\\!L$
bosons, as well as many other types of new particles [14, 93, 94, 95]. Figure
7 shows the constraints placed on the $B\\!-\\!L$ model from both dark-photon
searches and from neutrino-scattering measurements. If the $B\\!-\\!L$ boson
mass $m_{B-L}$ is below the weak scale, its associated gauge coupling must be
tiny.

Figure 7:  Updated from Ref. [14] using Ref. [19]: Constraints derived on
$B\\!-\\!L$ decays to SM final states using the same experimental color scheme
as in Fig. 3. The (orange) invisible constraints also apply to $B\\!-\\!L$ due
to its coupling to neutrinos. The grey constraints are from the neutrino-
scattering experiments Borexino [96, 97], Texono [98, 99], CHARM-II [98, 100],
COHERENT [101].

The $B\\!-\\!L$ model is popular because, exceptionally, it is an anomaly-free
global symmetry (assuming only the existence of three right-handed neutrinos).
This is important because classical symmetries can be broken through quantum-
mechanical triangle anomalies, which must be canceled to obtain a valid
quantum field theory. Gauging an anomalous current requires introducing new
chiral fermions with electroweak charges to cancel the anomalies. Such models
must then address the fact that these fermions have not been observed, neither
directly, e.g. at the LHC, nor indirectly, via the enhanced couplings they
produce in the low-energy theory between the $A^{\prime}$ and the $W$ and $Z$
bosons, e.g. which enhance the $A^{\prime}$ production rate in penguin decays.
See Ref. [102] for detailed discussion on this topic.

###  6.2 Dark Supersymmetry

Supersymmetric models can also produce hidden sectors at low energy scales,
which is often called dark SUSY (see, e.g., Ref. [9]). In these models, the
coupling of the dark photon to SM particles typically still arises via the
same kinetic mixing term as in the minimal dark photon model; therefore, the
$A^{\prime}$ decays and lifetime are still given by Sec. 2.3. However, the
fact that the dark sector is connected via SUSY to the SM gives rise to
additional production mechanisms, e.g., involving decays of the Higgs boson. A
standard benchmark case involves the Higgs decaying into the two lightest non-
dark neutralinos, followed by each of these decaying into the dark matter
particle (presumably a dark neutralino) and a dark photon. The dark matter
particles are undetected while the two dark photons each decay as shown in
Fig. 2, though in practice only the $A^{\prime}\to\mu^{+}\mu^{-}$ decays are
used. The detector signature is, thus, two isolated (possibly displaced) pairs
of high-$p_{\rm T}$ muons (the large transverse momentum imparted by the large
Higgs mass). Both ATLAS [103, 104, 105] and CMS [106] have searched for these
types of processes. Together, they have ruled out almost all of the
$\epsilon\gtrsim 10^{-7}$ parameter space for $2\,m_{\mu}\lesssim
m_{A^{\prime}}<9$ GeV, under the assumption that $\mathcal{B}(H\to
2\,A^{\prime}+X)\gtrsim 1\%$.

###  6.3 Strongly Interacting Dark Matter

The low-energy phenomenology of the dark sector could be dominated by a
strongly coupled interaction, similar to QCD, along with the force mediated by
the dark photon (with all SM particles uncharged under both interactions, and
the $A^{\prime}$ coupled to the SM via kinetic mixing). The dark matter in
such a scenario would then be the pseudo-Nambu-Goldstone bosons of a
spontaneously broken chiral symmetry, i.e. the dark pions of the strongly
coupled interaction, which are stable; see, e.g., Ref. [107]. As in QCD, the
dark vector mesons will also be important phenomenologically, e.g., they will
mix with the dark photon analogously to $\rho$–$\gamma$ mixing, coupling the
dark photon to the dark pions. These vector mesons can produce striking
signals at accelerators in most of the cosmologically favored parameter space,
where they are naturally long-lived resulting in missing energy from the dark
pions produced along with displaced vertices of SM particles if they decay
within the detector. Dark pion masses from roughly 10 MeV to $\mathcal{O}({\rm
GeV})$ are cosmologically allowed. The strongest constraints come from the
invisible $A^{\prime}$ searches discussed in Sec. 5, where the dark vector
meson must decay outside of the detector, and from visible $A^{\prime}$
searches at beam-dump experiments, where the dark vector meson must decay
after the shielding but otherwise within the detector, and from a recent
search performed by LHCb [108]. Future searches at colliders and fixed-target
experiments that look for the displaced vertex signature, whose topology is
markedly different from that of an $A^{\prime}$ decay due to the missing
energy and since the $A^{\prime}$ can be off shell, can greatly improve the
discovery potential for this class of dark-sector models [109].

###  6.4 Inelastic Dark Matter

Another interesting area under study is dark sectors that contain unstable but
long-lived particles. For example, inelastic dark matter models that contain
two nearly mass-degenerate states, $\chi_{1}$ and $\chi_{2}$ with
$m_{2}>m_{1}$, which are coupled off-diagonally to the dark photon leading to
the processes $\chi_{1}\chi_{2}\to A^{\prime*}\to{\rm SM}$ and
$\chi_{2}\to\chi_{1}A^{\prime(*)}\to\chi_{1}+{\rm SM}$, where the $A^{\prime}$
again couples to the SM via kinetic mixing. (N.b., such a scenario is natural
in the strongly coupled class of dark-matter models discussed in the previous
section.) Since the heavier $\chi_{2}$ state is unstable, dark matter
annihilations essentially stop once the $\chi_{2}$ population has died off,
which avoids the otherwise stringent bounds due to CMB anisotropies (assuming
the mass splitting provides sufficient phase space to keep the $\chi_{2}$
lifetime short enough). Furthermore, constraints from direct detection
experiments are severely weakened, since inelastic scatters are kinematically
suppressed by the mass splitting and elastic scatters are loop suppressed.
Therefore, the only way to test this scenario is at accelerator experiments,
where $\chi_{2}\chi_{1}$ pair production is mediated by a possibly off-shell
dark photon. The characteristic $\chi_{2}$ decay length is comparable to that
of a typical charged-particle tracking (sub)system, resulting in an
experimental signature of a displaced $A^{\prime(*)}\to{\rm SM}$ vertex and
missing energy if $\chi_{2}$ decays in the detector, and only missing energy
otherwise. The best existing constraints come from the invisible $A^{\prime}$
searches discussed in Sec. 5, and this scenario will also benefit from
improved invisible searches. In addition, dedicated searches that include the
displaced vertex signature are planned that will greatly improve the
sensitivity at higher masses; see, e.g., Refs. [110, 111].

##  7 SUMMARY & OUTLOOK

[SUMMARY POINTS]

  1. 1.

Dark matter particles may interact with other dark matter particles via a new
force mediated by a dark photon, which would be the dark-sector analog to the
photon.

  2. 2.

The $A^{\prime}$ can obtain a highly suppressed mixing-induced coupling to the
EM current, providing a portal through which dark photons can interact with
ordinary matter.

  3. 3.

The minimal dark-photon model only has 3 unknown parameters: the strength of
the kinetic mixing, $\varepsilon$; the dark photon mass, $m_{A^{\prime}}$; and
the decay branching fraction of the dark photon into invisible dark-sector
final states, which would be either (nearly) unity or zero (corresponding to
whether any invisible dark-sector final states are kinematically allowed or
not).

  4. 4.

Great progress has been made recently in exploring the $A^{\prime}$ parameter
space. However, well-motivated scenarios, including the $0.02\lesssim
m_{A^{\prime}}\lesssim 0.5$ GeV and $10^{-5}\lesssim\varepsilon\lesssim
10^{-3}$ region in the visible $A^{\prime}$ case, and thermal targets for
large $\alpha_{D}$ in the invisible case, remain unexplored.

  5. 5.

One striking advantage of producing dark matter in the lab is that it will be
relativistic, which leads to accelerator-based experiments having similar
sensitivity to most types of dark matter particles. This is in stark contrast
to direct-detection experiments, which, e.g., will only be able to explore
thermal targets for the elastic scalar case in the near future. That said, an
accelerator-based discovery may not be what constitutes the majority of the
dark matter in the universe. Further study would be needed considering
astrophysical, cosmological, direct and indirect detection data sets, which
demonstrates the complementarity inherent in understanding the nature of dark
matter.

[FUTURE ISSUES]

  1. 1.

For visible dark photons, the entire few-loop $\varepsilon$ region could be
explored in the near future for $m_{A^{\prime}}\lesssim 0.5$ GeV; however,
there are currently no known viable ways to explore the $m_{A^{\prime}}\gtrsim
1$ GeV and $\varepsilon\lesssim 10^{-4}$ region. Will any future experiments
manage to probe this space?

  2. 2.

For invisible dark photons, existing constraints already exclude many
otherwise viable thermal dark matter scenarios. Even pessimistic scenarios
will be accessible in the near future. Can well-defined targets be defined for
dark matter scenarios that do not involve thermal equilibrium in the early
universe?

  3. 3.

Dark matter self-interactions could explain several small-scale structure
anomalies; however, the interplay between baryonic interactions and dark
matter is not fully understood, and this may provide an alternative solution.
Can enough progress be made in these calculations to enable defining
accelerator-based $A^{\prime}$ targets motivated by small-scale structure?

  4. 4.

The minimal $A^{\prime}$ scenario is not the only option. Studying non-minimal
dark sectors is a major challenge due to the wide array of viable models.
Dark-photon searches provide serendipitous discovery potential for many other,
but not all, types of new particles. How can we maximize our exploration
capabilities? Are we missing other well-defined targets similar to thermal
dark matter for these models?

## DISCLOSURE STATEMENT

MW is a member of the LHCb collaboration. CH is a member of the BaBar and
Belle II collaborations. MG is a member of the BaBar, HPS, LDMX, and DarkQuest
collaborations.

## ACKNOWLEDGMENTS

We thank Gordan Krnjaic for providing several of the exclusion regions in Fig.
6. All other constraints were obtained from Ref. [19]. The authors were
supported by the following grants: MG by the U.S. Department of Energy under
Contract No. DE-AC02-76SF00515, CH by Natural Sciences and Engineering
Research Council of Canada, and MW by NSF grant PHY-1912836.

##  Appendix A DESCRIPTION OF EXPERIMENTS

This appendix discusses a selected set of experiments that have and/or will
search for dark photons. They are organized by dark-photon production method,
or the first method used in cases where there are more than one. Proposals for
future searches are only included here if they expect to produce results
within the next five years.

###  A.1 Electron Beam Dumps

NA64: published results [112, 54] and future projections [78] for both visible
displaced $A^{\prime}\to e^{+}e^{-}$ decays and invisible
$A^{\prime}\to\chi\bar{\chi}$ decays. NA64 uses a 100 GeV $e^{-}$ beam derived
from the CERN SPS proton beam incident on an active (calorimeter) target to
search for invisible dark photon decays by a missing energy technique. The
$e^{-}$ momentum is measured by a micromegas tracking station upstream of, and
micromegas, GEM, and straw tube tracking downstream of a pair of dipole
magnets. Synchrotron radiation emitted by electrons in the magnetic field is
used to tag electrons and strongly suppress pion contamination. A hermetic
shashlik-type EM calorimeter is followed by a hadronic calorimeter to provide
good energy containment for SM particle interactions. In an alternative
configuration, an active target is added upstream of the EM calorimeter to
enable searches for dark photon decays to $e^{+}e^{-}$.

E141, E137, E774, KEK, Orsay: Data from these older electron beam-dump
experiments [48, 49, 50, 51, 52] have been recast [10, 53] to place
constraints on visible $A^{\prime}\to e^{+}e^{-}$ decays. Each experiment
employed an EM calorimeter placed downstream of substantial shielding, with
thicknesses in the range 0.12–179 m. The decay-region lengths were in the
range 2–204 m.

###  A.2 Proton Beam Dumps

SpinQuest: future projections [65, 66] for displaced visible
$A^{\prime}\to\mu^{+}\mu^{-}$ decays. SpinQuest (E1039), the successor to the
SeaQuest experiment, will use Drell-Yan dimuon pairs produced in polarized
targets to study the intrinsic spin of the nucleus. It uses the 120 GeV main
injector proton beam at Fermilab. Hadrons are suppressed by an absorber and
beam dump located between the target and the spectrometer. The spectrometer
uses multiple tracking stages, with two magnets and an additional absorber
before the final tracking stage. The addition of two scintillator hodoscopes
enables triggers on muon pairs from the decay of dark photons produced in the
beam dump. The experiment will collect data for two years. Following this run,
an electromagnetic calorimeter will be added to allow searches for dark
photons in the $e^{+}e^{-}$ final state. This configuration of the detector
will be known as DarkQuest, and will start data taking in 2023 [67].

CHARM, NOMAD, PS191, $\nu$-CAL I: Data from these older proton beam-dump
experiments [56, 57, 60, 62, 63] have been recast [58, 59, 61, 64] to place
constraints on visible $A^{\prime}\to e^{+}e^{-}$ decays. Each experiment
employed an EM calorimeter placed downstream of substantial shielding, with
thicknesses in the range 64–835 m. The decay-region lengths were in the range
7–23 m.

LSND: published search for direct detection of $\chi$ particles [88]. The LSND
experiment, which was located at Los Alamos and ran from 1993 to 1998,
produced a huge sample of $\pi^{0}$ decays by impinging an 800 MeV proton beam
onto a fixed target, which was either water or a high-$Z$ material [113]. The
detector consisted of a tank filled with 167 tons of mineral oil doped with
organic scintillator material, and an array of 1220 photomultiplier tubes that
detected the Cherenkov radiation emitted when particles scattered in the tank.

MiniBooNE: published search for direct detection of $\chi$ particles [89]. The
MiniBooNE experiment was located in the 8 GeV BNB proton beam line at
Fermilab. After the completion of its original neutrino physics program, the
experiment undertook a special one-year run (2013–2014) in which the beam
bypassed the neutrino target to directly strike its beam dump. This
configuration strongly suppressed the $\nu$ flux in the MiniBooNE detector 490
m downstream, enabling a search for dark matter produced in
$A^{\prime}\to\chi\bar{\chi}$ decays, where the dark photons would have been
created in the beam dump. MiniBooNE consisted of 818 tons of mineral oil in a
12.2 m-diameter tank, optically divided into an inner signal volume and an
outer veto region, each viewed by separate sets of photomultiplier tubes.

COHERENT: projections for direct detection of $\chi$ particles. COHERENT is a
set of detectors located 20–30 meters from the Spallation Neutron Source at
Oak Ridge National Laboratory, in a low-neutron flux area dubbed neutrino
alley. The high power 1 GeV proton beam strikes a mercury target to produce a
large number of neutrinos through charged pion decay at rest. The six detector
technologies include a 22 kg liquid argon scintillation detector, whose
performance is the basis of their dark matter studies, and a sodium-doped CsI
crystal, which provided the first observation of coherent elastic neutrino-
nucleus scattering [114].

###  A.3 $e^{+}e^{-}$ Colliders

KLOE: published results for prompt visible $A^{\prime}$ decays to the
$e^{+}e^{-}$, $\mu^{+}\mu^{-}$, and $\pi^{+}\pi^{-}$ final states [24, 25];
and future projections for invisible $A^{\prime}\to\chi\bar{\chi}$ decays. The
KLOE experiment is located at the DA$\Phi$NE $e^{+}e^{-}$ collider at the
Frascati National Laboratory. DA$\Phi$NE operates at the $\phi$ meson
resonance, enabling precision studies of the neutral kaon system. The original
detector configuration, which collected 2.5 fb-1 between 2001–2006, included a
large drift chamber and a lead/scintillating-fiber EM calorimeter within a 0.5
T solenoidal magnetic field. KLOE-2, which collected an additional 5.5 fb-1
between 2014 and 2018, added a cylindrical GEM vertex tracker. KLOE-2 included
a trigger for single photon events, which will enable searching for invisible
dark photon decays.

BaBar: published searches for prompt visible decays to the $e^{+}e^{-}$ and
$\mu^{+}\mu^{-}$ final states [22], and for invisible
$A^{\prime}\to\chi\bar{\chi}$ decays [72]. The primary focus of the BaBar
experiment was the study of CP violation in the $B$ meson system. It was
located at the PEP-II asymmetric $e^{+}e^{-}$ collider at SLAC, and collected
500 fb-1 of data at and near the $\Upsilon(4S)$ resonance between 1999 and
2008. It was a general purpose collider detector, with a silicon strip vertex
tracker, a drift chamber, charged hadron particle identification using the
DIRC technique, a CsI(Tl) crystal EM calorimeter, and a muon-identification
system. The BaBar search for visible $A^{\prime}$ decays used the full data
set. The search for invisible decays, however, used only the 2008 data,
approximately 10% of the total, as this was the only data set that included
the necessary single-photon trigger.

Belle II: future projections for prompt visible decays to the $e^{+}e^{-}$ and
$\mu^{+}\mu^{-}$ final states [26], and for invisible
$A^{\prime}\to\chi\bar{\chi}$ decays [73]. Belle II is located at the
SuperKEKB asymmetric $e^{+}e^{-}$ collider at the KEK laboratory, which
operates at energies near the $\Upsilon(4S)$. Using the nanobeam technique,
the target peak luminosity is $40\times$ larger than the original KEKB
collider. The primary physics goal of Belle II is to search for new physics
through a wide range of measurements that are sensitive to the presence of
heavy virtual particles, and that can be precisely predicted in the SM. These
could include CP violation and other asymmetries, rare decays, or forbidden
decays. Belle II will also search for the direct production of new light
particles. Data taking started in 2019, and is expected to continue through
2026.

LEP: published results from the DELPHI experiment [74, 75] were recast as
limits on invisible $A^{\prime}$ decays in Ref. [76]. LEP produced
$e^{+}e^{-}$ collisions from 1989–2000. When it first started operating, it
ran at the $Z$ pole, but after a few upgrades it eventually reached
$\sqrt{s}=209$ GeV. DELPHI was a general-purpose detector and one of the four
main LEP detectors. Its mono-photon data set was used to place limits on
invisible $A^{\prime}$ decays.

###  A.4 LHC Experiments

LHCb: published results [30, 31] and future projections [17] for both prompt
and displaced visible $A^{\prime}\to\mu^{+}\mu^{-}$ decays, along with future
projections for both prompt and displaced $A^{\prime}\to e^{+}e^{-}$ decays,
where the $A^{\prime}$ is produced in the decays of charm mesons [33]. LHCb is
a general purpose detector in the forward region, located at the LHC at CERN.
It studies heavy flavor physics, including CP violation, rare decays, and new
phenomena such as lepton universality violation. LHCb employs real-time
calibration, alignment, and physics analysis. During long shutdown 2
(2018–2021) LHCb is moving to a triggerless readout system, in which the full
detector information is read out every LHC collision; a data rate of 40 Tb/s.
The instantaneous luminosity will increase by a factor of 5, and when combined
with the detector upgrades, will greatly increase the sensitivity for many
physics channels, including dark photon decays.

CMS: published results for prompt visible $A^{\prime}\to\mu^{+}\mu^{-}$ decays
[32]. CMS is a large, general purpose detector located at the CERN Large
Hadron Collider, which features a 4 T solenoid magnet. CMS has a broad physics
program with particular focus on searches for new physics in high transverse
momentum processes. The highlight to date has been the discovery, along with
ATLAS experiment, of the Higgs boson. The experiment is preparing a number of
upgrades to deal with high luminosity LHC running, scheduled to begin in 2026.

FASER: future projections [35] for visible displaced $A^{\prime}$ decays to
the $e^{+}e^{-}$, $\mu^{+}\mu^{-}$, and $\pi^{+}\pi^{-}$ final states. FASER
[34] will search for long-lived light particles produced in $pp$ collisions at
the LHC. It will be located directly on the beam collision axis 480 m from the
ATLAS interaction point. The detector consists of a scintillator veto,
followed by a 1.5 m decay volume, a 2 m long spectrometer, and a shashlik-
style EM calorimeter. The spectrometer has three silicon-strip tracking
stations, with three 0.6 T permanent magnet dipoles. Background rates, as
confirmed by 2018 emulsion measurements, will be low, and are dominated by
high-momentum muons. Data taking will start in 2022.

###  A.5 Meson and Lepton Decay Experiments

NA48/2: published results on $\pi^{0}\to\gamma A^{\prime}$ decays followed by
visible prompt $A^{\prime}\to e^{+}e^{-}$ decays [68]. NA48/2 undertook a wide
range of studies of charged kaon properties, including direct CP violation,
using data collected in 2003 and 2004 at the CERN SPS. The experiment used
simultaneous $K^{+}$ and $K^{-}$ beams produced from a 400 GeV proton beam.
The NA48/2 apparatus included a 114 m long decay volume, two sets of drift
chambers separated by a dipole magnet, a scintillator hodoscope for timing, a
LKr EM calorimeter, a hadronic calorimeter, and a muon system.

NA62: published results [80] and future projections for invisible $A^{\prime}$
decays, where the dark photons are produced in $\pi^{0}$ decays; and future
projections for visible displaced decays to the $e^{+}e^{-}$ and
$\mu^{+}\mu^{-}$ final states. NA62 is the successor to NA48/2. Its goal is to
reconstruct 80 of the ultra-rare decay $K^{+}\to\pi^{+}\nu\bar{\nu}$ with low
background to extract a measurement of $|V_{td}|$ and to search for deviations
from SM expectations. Kaons in a 75 GeV hadron beam are identified using
Cherenkov radiation before decaying in flight. A magnetic spectrometer and
ring-imaging Cherenkov detector characterize the decay products. The apparatus
includes a muon veto, and hermetic photon detection out to wide angles. The
nominal detector configuration uses tagged $\pi^{0}$ mesons produced in
$K^{+}\to\pi^{+}\pi^{0}$ decays to search for invisible dark photon decays. An
alternative beam dump mode configuration, would use the 400 GeV proton beam
incident on an upstream beam dump to search for visible decays of long-lived
dark photons.

Mu3e: future projections for prompt visible $A^{\prime}\to e^{+}e^{-}$ decays,
where the dark photons are produced in muon decays [69]. Mu3e will search for
the lepton-flavor-violating process $\mu^{+}\to e^{+}e^{-}e^{+}$ at the Paul
Scherrer Institute. Using a beam of $10^{8}$ $\mu$/s stopping in the target,
Mu3e will achieve a single event sensitivity of $2\times 10^{-15}$ in 350
data-taking days. The detector consists of a thin pixel tracker in a 1 T
magnetic field, with scintillating fibers and tiles giving timing resolution
of $\mathcal{O}(100\,{\rm ps})$. Studies are under way for a new high-
intensity muon beam line that could improve sensitivity by a factor of 20.

###  A.6 Electron Fixed Target Experiments

A1: published results on prompt visible $A^{\prime}\to e^{+}e^{-}$ decays
[39]. The A1 experiment was located at the Mainz Microtron (MAMI). It searched
for dark photon decays to $e^{+}e^{-}$ produced by electron Bremsstrahlung,
with 180–855 MeV electron beams incident on a thin tantalum target. The
apparatus includes a pair of high-resolution spectrometers consisting of four
layers of drift chambers, scintillators for timing, and gas Cherenkov
detectors to distinguish electrons from pions. The spectrometers were set to
their minimum opening angle, with kinematic acceptance adjusted by changing
the beam energy.

APEX: published results and future projections for prompt visible
$A^{\prime}\to e^{+}e^{-}$ decays [41]. APEX is located in Jefferson
Laboratory Hall A. It searches for dark photons produced in electron
Bremsstrahlung in a thin tantalum target. Two septum magnets direct the
outgoing $e^{+}$ and $e^{-}$ into the two arms of the HRS high-resolution
spectrometer. Each spectrometer contains two drift chambers, a timing
hodoscope, and gas Cherenkov and lead-glass calorimetry for electron
identification. Data with a 2.2 GeV beam energy were recorded in 2019.
Additional runs at 1.1 GeV, 3.3 GeV, and 4.4 GeV are planned.

HPS: published results [43] and future projections for prompt visible
$A^{\prime}\to e^{+}e^{-}$ decays, along with future projections for displaced
decays. HPS searches for dark photons produced by electron Bremsstrahlung on a
thin tungsten target [42]. It is located in Jefferson Laboratory Hall B. The
apparatus is a magnetic spectrometer with two sets of silicon microstrip
trackers located 0.5 mm from the beam plane. A lead tungstate scintillating
crystal calorimeter provides particle identification and triggering
capability. HPS had engineering runs in 2015 at 1.056 GeV beam energy and in
2016 at 2.3 GeV. The first physics run was at 4.56 GeV in 2019. Additional
beam energies are planned for future runs.

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