facility and detector design are also important considerations that will
impact which and how backgrounds manifest. Modelling of detector performance
and simulations of background events will be critical in informing the design
of the experiment, deriving sensitivities, and ultimately in achieving final
science results [137].

###  VII.1 Underground Laboratories

Muons traversing detectors or surrounding materials will induce primary
backgrounds as well as secondary neutrons and cosmogenic backgrounds from
activation of materials [1018, 1019]. Dark matter detectors are thus deployed
in deep underground laboratories, where cosmic-ray muon backgrounds are
greatly reduced by the rock overburden [1020]. Nevertheless, for high-
sensitivity experiments, active muon shielding is still required in order to
tag remaining muon-related background events and reduce the muon-induced
background to a negligible level compared to other sources. Muon fluxes at the
typical underground laboratories range from 1 muon/m2/hour at the Laboratori
Nationali del Gran Sasso (LNGS, 3,100 meters water equivalent deep) [1018,
1021] to about 5 muons/m2/month at China’s Jinping underground laboratory
(CJPL, 6,720 meters water equivalent deep) [1022, 1023] (Figure 34).

Figure 34: Depth-dependent muon flux at various underground laboratories
(measured in “meters water equivalent” (m.w.e.). While the depth increases
from 620 m.w.e. to 6720 m.w.e, the muon flux decreases by more than four
orders of magnitude. The data points represent the following measurements:
CallioLab (Pyhäsalmi, Finland) at various depths [1024], LSC (Canfranc, Spain)
[1025] (with depth taken from [1026]), Soudan (Minnesota, USA) [1027], Kamioka
(Japan) [1028] (conversion from muon rate to flux based on simulations from
[1029]), Boulby (UK) at 1,100 m level (2850 m w.e.) [1030], LNGS (Gran Sasso,
Italy) [1031], SURF (South Dakota, USA) [1032] (depth taken from [1033]), LSM
(Modane, France) [1034], SNOLAB (Sudbury, Canada) [1035], and Jingping (China)
[1036].

There are a host of underground laboratories that can be considered as
location for the next-generation observatory discussed here. This includes the
laboratories hosting the current generation of liquid xenon detectors: LNGS
[1037] (location of XENONnT), CJPL [1038] (location of PandaX-4T) and SURF
[1039] (location of LZ). The Boulby Underground Laboratory has a similar muon
flux to LNGS with notably low radon levels [1040]. The Modane Underground
Laboratory [1041] includes a facility for radon-free air, and the entire
scientific campus of SNOLAB [1042] is equipped as a cleanroom with some of the
lowest available muon flux. Several of these laboratories entertain
feasibility studies for creating additional underground space for scientific
use. All in all, there is a favorable outlook that suitable underground space
can be made available for the next-generation liquid xenon observatory. While
radioactive and muon-induced backgrounds are dominated by the rock composition
and overburden, respectively, the varying geomagnetic field at different
latitudes has a (modest) impact on the science that can be done with
atmospheric neutrinos [771].

###  VII.2 Fiducialization

The dominant background component in liquid xenon detectors at a given energy
range has evolved with increasing detector size. In earlier detectors (e.g.
XENON100 [1043], LUX and PandaX-I/II), the gamma radiation from radioactive
contaminants of detector construction materials contributed significantly to
the electronic recoil background for dark matter searches in the keV energy
range. A fiducial volume selection is typically applied to reduce these
backgrounds, which predominantly appear towards the boundaries of the bulk
xenon: with larger detector masses and hence smaller surface-to-volume ratios,
fiducialization can preserve a higher proportion of the active volume for a
physics search. Gamma-induced electronic recoils will remain a significant
background for rare event searches at the MeV scale such as the
$0\nu\beta\beta$-decay of 136Xe (subsection IV.1, Figure 22).

Radioactive contaminants of detector materials are also the source of
radiogenic neutrons through spontaneous fission or $(\alpha,\mathrm{n})$
reactions. Fiducialization of the liquid xenon target is not quite as
effective for neutrons compared to gamma radiation. Therefore, current and
future liquid xenon detectors are equipped with dedicated neutron veto systems
for efficient mitigation of nuclear recoil background events.

###  VII.3 Material Selection

The selection of materials featuring the lowest contamination with radioactive
impurities is the most important strategy for background mitigation in current
and future liquid xenon experiments [1044, 1045]. Trace amounts of uranium and
thorium can be detected by means of highly sensitive gamma-spectrometers,
Inductively-Coupled Plasma Mass Spectrometry (ICPMS) measurements or neutron
activation analysis. Radon emanation rates are determined in dedicated setups
where the radon which is emanating from the sample accumulates in an ambient
carrier gas, before the radon activity in this sample gas is measured,
typically using proportional counters or electrostatic radon monitors [1045,
1046].

Various material samples are measured in intensive screening campaigns in
order to pre-select and built radiopure detector components which fit the
requirements for a next-generation liquid xenon experiment [89]. Once the
materials are selected, the screening measurements are used for background
modeling by means of simulation. Precise knowledge of emanation sources can
further be used to optimize the online purification systems.

###  VII.4 Intrinsic Background Mitigation

Sources of so-called intrinsic backgrounds are typically radioactive noble
gases which are homogeneously mixed within the liquid xenon target. Thus, any
type of shielding remains ineffective. Trace amounts of 85Kr that stay in the
xenon during its distillation from air will cause, if not removed, a low-
energy electronic recoil background from its beta decay. Due to the absence of
krypton sources within the detector, the 85Kr contamination is constant over
time and scales with the liquid xenon mass. 85Kr thus needs to be removed
through cryogenic separation of the xenon target, as pioneered by the XMASS
collaboration [122]. The purification of xenon from trace amounts of 85Kr has
been successfully demonstrated using both cryogenic distillation [122, 1047,
1048] and adsorption [1049, 1050] as separation techniques. Cryogenic
distillation in particular is appropriate to process large amount of xenon gas
before being filled into the experiment, but also an online krypton
purification at a running detector has been demonstrated. Starting with a Kr-
nat contamination of several ppm in commercial xenon, a purification to
$(360\pm 60)\,\mathrm{ppq}$ was achieved in XENON1T using the online krypton
purification [1051]. The lowest concentration to-date was measured in the
outlet of the XENON1T distillation system to be below $26\,\mathrm{ppq}$ (90%
CL) [1048], using an enhanced Rare Gas Mass Spectrometer (RGMS) with a
sensitivity of $8\,\mathrm{ppq}$ [1052]. This level is well below even the
requirements of a next-generation liquid xenon experiment.

222Rn is not immanent in the xenon gas, but continuously emanates from
surfaces of detector materials. Due to its subsequent beta decays, radon is
the dominant background source in current liquid xenon detectors. A smaller
surface-to-volume ratio will naturally decrease the radon concentration in
next-generation liquid xenon detectors. However, further mitigation strategies
are needed to achieve a level of about $0.1\,\mathrm{\mu Bq/kg}$ that is
required in order to render radon-induced backgrounds sub-dominant versus the
irreducible contributions from neutrino signals. Once a new detector has been
built, its emanation rate of 222Rn is set and expected to be constant over the
lifetime of the experiment. A further suppression of the radon induced
background can be achieved through continuous purification of the xenon
target. The key for an efficient radon removal is a good separation technique
and a high purification flow which revolves the entire xenon target fast with
respect to the 3.8 d half-life of radon. Radon removal based on cryogenic
distillation has been successfully tested in large scale liquid xenon
experiments [1053] and will be used also in XENONnT. Radon purification
systems designed for small purification flows can also significantly reduce
the radon concentration in xenon. Since the dominating radon emanation sources
in an experiment are known from screening, dedicated purge flows towards the
radon removal system can prevent radon to enter the liquid xenon target
[1045].

Another intrinsic background source is the decay of 137Xe. It is naturally
created inside the xenon target through activation by muon-induced neutrons.
Thus, the 137Xe induced background strongly depends on the muon rate at the
experimental site.

###  VII.5 Isolated Light and Charge Signals and Accidental Coincidences

Due to the large electroluminiscence gain that is exploited in dual-phase
liquid xenon TPCs, even a single extracted electron can produce a detectable
S2 of tens of photoelectrons in size [1054, 1055, 1056, 484, 1057, 1058,
1059]. A standalone search with S2s (i.e. without requiring an accompanying S1
signal, see subsection III.2 on page III.2) can thus lower the energy
threshold, improving the reach to low-mass WIMPs, solar axions and solar
neutrinos, and other physics that have associated low-energy recoil signatures
[166]. However, this sensitivity to any process that can release even single
electrons from their shell brings in additional instrumental backgrounds.
Several sources of S2-only, single and few-electron backgrounds are known and
being further investigated [488, 489, 490, 485, 484, 486, 487, 1060, 482].
Photoionization backgrounds caused by large S2s die away within a maximum
drift time after the S2 [484]. Emission from metal surfaces would be evident
in specific locations that could be avoided with positional cuts. The most
impactful background appears to be S2s up to five electrons in size that
continue for times up to seconds after a large S2. The rates of these
correlated small S2s, which appear in the same location as a previous large
S2, decrease according to a power law with time after the large S2 [489, 488,
482]. This background can be mitigated with positional and temporal cuts after
large S2s.

Figure 35: Illustration of the accidental coincidence background distribution
from XENON1T in cS1 and log10(cS2b), with projections on each axis showing the
expected distribution within the entire analysis space (blue), and in the
reference region for 1.3 tonne fiducial volume. The reference region lies
between the nuclear recoil median and $-2\sigma$ quantile lines, marked by red
and black lines, respectively. Figure from Ref. [1061].

S1-only backgrounds also exist due to interactions in areas insensitive to the
charge channel. One such origin of lone S1 events is from outside of the main
drift field region of the TPC, notably below the cathode. Another origin is
from volumes where charges are depleted, or where electrons can not reach the
extraction region. Most notably this can be as a result of the field
configuration towards the edges of the detector [60]. Unrelated, isolated
S1-only and S2-only signals can be close enough in time to be mis-identified
as a single event. Such accidental coincidences of instrumental backgrounds
can thus mimic a physics interaction for a conventional search in S1-S2 phase
space. As both lone S1s and S2s are more likely to manifest at smaller signal
values, these accidental coincidence backgrounds are particularly problematic
for the WIMP search region of interest. The absolute incidence of such
accidental events should increase in a next-generation detector, as the
corresponding surfaces and volumes from which lone S1s and S2s can arise
become larger. However, their impact on the WIMP search will decrease with
increasing detector size, due to the favorable surface-to-volume ration.
Hence, combining a data-driven approach, as adopted for XENON1T (Figure 35),
with detailed detector simulations, should be sufficient to characterise this
background for a next-generation experiment.

###  VII.6 Monte-Carlo Simulation of Backgrounds

####  VII.6.1 Background Model

To construct a model of expected backgrounds, the activities and
normalizations found from material assays and physics estimates must be paired
with the corresponding detection efficiencies of the associated events. These
efficiencies are determined through Monte Carlo simulations of event
primaries, such as daughters from radioactive decay, within a realistic
representation of the experiment. Simulations are used to determine the energy
depositions from backgrounds within the detector, and in translating them into
observed signals.

A framework based on the GEANT4 toolkit [1062] allows for the tracking of
particles within a rendering of the detector geometry. Custom additions can
enhance the modelling of various physics processes and phenomena beyond the
standard physics lists available, as in the case of modelling neutron captures
on Gd using ANNRI [1063, 1064] or DICEBOX [1065] derived outcomes for an
improved veto assessment. Bespoke event generators enable the simulation and
study of more involved scenarios that are not well-captured in default GEANT4,
such as $(\alpha,\mathrm{n})$ reactions accompanied by a varying multiplicity
of gammas, or events from atmospheric muons which penetrate the laboratory
rock overburden [1066].

Analysis cuts can be applied to remove events with coincident scatters in veto
detectors, and restrict to an energy region of interest and/or a fiducial
volume. Persistent background counts can then be compared to those anticipated
from potential signals. This approach has been used in predicting the
background burden of many present-generation experiments, forming the basis of
WIMP sensitivity estimates for XENONnT [84], LZ [85] and PandaX-4T [83].

####  VII.6.2 Generation of S1 and S2 Signals

Figure 36: The light and charge yields for nuclear and electronic recoils, as
measured by various experiments and as modeled by the Noble Element Simulation
Technique (NEST) v2.3.5 [114]. The light (charge) yield is defined as the
number of photons (electrons) leaving the recoil site after electron-ion
recombination, per unit energy. For electronic recoils, NEST has two models
for $\beta$-induced and $\gamma$-induced recoils, respectively, and we show
the $\beta$ model. Correspondingly, we only show experimental measurements
from $\beta$ calibrations or low-energy line sources, which are observed to
fit the $\beta$ model better than the $\gamma$ model. The nuclear recoil data
points are from E. Dahl’s thesis [116], XENON1T [1061], XENON10 [115, 118,
1056, 1067], LUX Run 3 (WS2013) [1068], and dedicated xenon TPCs at Columbia
University [108], Case Western Reserve University [101], and Lawrence
Livermore National Lab [471]. The electronic recoil data points are from LUX
[1069, 1070, 1071, 1072], XENON100 [1073], PIXeY [1074], Xurich II [91], and a
paper by Doke et al. [103].

Generally, energy depositions are converted to observable S1s and S2s to
construct PDFs for background components and signal for likelihood-based
analysis [1075]. The microphysics behind the interactions of particles with
the active xenon is captured by the Noble Element Simulation Technique (NEST)
[112, 113, 1076, 107, 114]. NEST offers a comprehensive and mature framework
to simulate the atomic and nuclear physics of energy deposition and the
resulting detector response. Using world data from previous experiments
including LUX, XENON, PIXeY [1077, 490], neriX [1078, 1079], ZEPLIN-III [477],
and Xurich [1080, 91], the NEST collaboration has developed models for the
light and charge yields of various interactions. These models are semi-
empirical and reproduce calibration data from alphas, betas, gammas, nuclear
recoils, and exotic interactions like the two-step internal conversion of
${}^{\text{83m}}$Kr. The excellent agreement between the NEST models and data
can be seen in Figure 36. Physicists on a next-generation liquid xenon
experiment are thus able to take advantage of NEST to accurately simulate the
signals induced by both signals and backgrounds, including their S1, S2,
position, and pulse timing.

###  VII.7 Discrimination

Figure 37: Histograms for a flat electronic recoil spectrum and a nuclear
recoil spectrum as from a 50 GeV spin-independent WIMP, simulated for
different electric fields (using NEST 2.3.5). The top band for each plot is
the electronic recoil band, the bottom is the nuclear recoil band. Red lines
refer to the median for either band, and the white dotted lines delimit the
one-sigma region. Already-demonstrated discrimination is expected to be
sufficient for a next-generation detector.

The results of simulating events from a type of source, be it electronic or
nuclear recoils, are a list of S1 and S2 values for each event. Binning these
events into a 2D histogram will show how a given type of interaction looks
like in terms of the signals received. An example shown in Figure 37 is the
histogram of a 50 GeV spin-independent WIMP, which is lower in S2 than that of
electronic recoil events. This difference allows for distinction between these
two types of interactions and can be measured quantitatively in a few ways.
Leakage is the proportion of electronic recoil events per bin that lie below
the nuclear recoil median line; rejection is the percentage of background
events that are not in the region of interest given by $(1-\mathrm{leakage})$.
Various instrumental parameters affect the discrimination capability. For
example, the drift field affects the gap between the nuclear and electronic
recoil spectra, as does the $g1$ parameter which measures the S1 light yield
in the detector. As can be seen from Figure 37, even moderate drift fields
provide satisfactory discrimination. Discrimination is also affected by the
atomic structure of xenon, leading to increased leakage from neutrino and
Compton scatters on L-shell electrons due to the accompanying atomic de-
excitation via Auger electron cascades. This effect is still under study, but
available measurements indicate a reduction in rejection by a factor of
$6\times$ near the L-shell binding energy ($5.2\,\mathrm{keV}$) compared to
predictions from valence electronic recoils and $\beta$-decays [1081, 1082].
Including this effect for the solar neutrino-induced electronic recoil
background results in an 8% relative increase in leakage from 5.2–8 keV, for
50% nuclear recoil acceptance.

Importantly, already with the performance of running detectors, discrimination
between electronic and nuclear recoils in liquid xenon is sufficient to
achieve the various science goals presented in this review, whether they
pertain to WIMPs, neutrino-induced signals in both the electronic and nuclear
recoil band, or the search for neutrinoless double-beta decay. The accuracy of
these simulation results is confirmed in situ using dedicated calibration
sources, such as dissolved gamma line sources 83mKr [423], dissolved beta-
spectrum sources 220Rn [1083, 1084], TH3C [1070], as well as various neutron
sources [1085, 1086, 1068].

##  VIII Complementarity with Other Experimental Efforts

###  VIII.1 Crossing Symmetry for Freeze-Out Relic Particles

Production, decay and scattering of dark matter particles are often governed
by the same or similar interaction. Relic particles such as WIMPs are a
textbook example of this situation, where the production through freeze-out
from the thermal equilibrium in the early Universe creates the observed relic
density [1087, 2, 1088]. The three principal approaches to discover thermal
freeze-out relic particles correspond to the $s$\- or $t$-channel processes of
dark matter production or scattering, and the time-reversed process to
production, which might lead to annihilation of dark matter. This results in
the following detection channels, related through crossing symmetry [1089]
(see also Figure 38):

  1. 1.

Direct Detection: Direct detection of particle dark matter in the Galactic
halo in underground experiments as described here;

  2. 2.

Collider Production: Production of dark matter in the laboratory, usually
using high energy particle collisions;

  3. 3.

Indirect Detection: Detection of products of dark matter annihilating or
decaying in our local universe.

Figure 38: Based on the general idea of thermal relic particles (such as
WIMPs) interacting with the standard model, three detection techniques are
possible: production at colliders, scattering from a target material (direct
detection) and annihilation resulting in cosmic rays (indirect detection).

###  VIII.2 Dark Matter at Colliders

The electroweak energy scale is powerfully probed by the Large Hadron Collider
(LHC) at CERN [1090]. The freeze-out mechanism requires significant couplings
between the dark matter and the standard model, which further motivates
searches at a particle collider. Moreover, many ‘Beyond the Standard Model’
(BSM) theories in high energy physics require new particles at the electroweak
scale, which are either viable dark matter candidates or might couple to
particle dark matter. The most prominent example of such a theory that
connects naturally astrophysical and theoretical motivation is supersymmetry
(SUSY), which not only remedies many known problems of the Standard Model,
such as the hierarchy problem, but also provides an excellent dark matter
candidate [1091, 1092, 126, 320].

Another motivation for collider searches is the potential to study dark matter
in the laboratory. Collider production implies production of the mediator,
i.e. the force carrier that connects the dark sector with the visible sector
of the Standard Model. Hence, collider dark matter searches are in essence
searches for the mediator rather than dark matter. Most collider dark matter
searches assume maximal decay of the mediator into dark matter [197, 198].
This is in particular true for ’mono-X’ searches, where the main signature is
missing momentum in the transverse plane due to the dark matter particle
escaping the detector undetected. Constraints placed on the mediator masses
are typically about twice as strong as the constraints on the dark matter mass
itself. Other analyses attempt to place constraints on the nature of dark
matter by looking for deviations in the properties of known particles, for
example the Higgs boson, or to search for the mediator directly, such as in
dijet searches [1093]. Further complementarity stems from searches at
colliders for axion-like particles and dark photons, see e.g. [1094, 1095].

###  VIII.3 Indirect Dark Matter Searches

Dark matter annihilation and decay into standard model particles lead to
potential signatures in the Cosmic Microwave Background [1096, 1097, 526] and
astrophysical observables such as X-rays [1098, 1099, 1100], gamma rays [1101,
1102, 1103, 1104, 1105, 1106, 346, 1107, 1108, 1109, 1110, 1111, 1112, 1113,
1114, 1115, 1116, 1117, 1118, 1119, 1120, 1121, 1122, 1123, 1124, 1125, 1126,
1127], antiprotons [1128, 1129, 1130, 1131, 1132, 1133], positrons [1134,
1135, 337, 1136, 1137, 1138], neutrinos [1139, 1140, 1141, 1142, 1143, 1144,
1145, 1146, 1147, 1148, 1149, 1150], or other particles [1151, 1152, 1153,
1154, 1155, 1156, 1157, 1158, 1159, 1160, 1161]. Thermal relic dark matter
candidates are generically expected to have a thermally averaged annihilation
cross section $\langle\sigma v\rangle\simeq 2.2\times
10^{-26}\mathrm{cm}^{3}/\mathrm{s}$ [10, 131], though other production
mechanisms or annihilation channels are known to predict much smaller or
larger annihilation cross sections, e.g., Sommerfeld enhancement [1162, 300],
non-thermal/out-of-equilibrium production [1163, 1164, 1165, 1166], asymmetric
dark matter [1167, 1168, 1169, 592], co-annihilation [1170, 1171, 1172],
velocity-dependent annihilation, or non-standard cosmologies [1173, 1163,
1164, 1174, 1175, 1176, 1177, 1178, 1179]. The thermal relic cross section,
however, provides an important benchmark for indirect detection efforts. While
this leads to a characteristic signature of dark matter in the corresponding
cosmic ray spectrum [1101, 1104, 136], the topology, spectral shape and
strength of such a signal is rather model dependent and affected by
astrophysical foregrounds.

Since the annihilation rate of dark matter is proportional to the square of
the dark matter density at the location of annihilation, the brightest signals
are expected to come from dense structures. Present searches for annihilation
signatures aim at a variety of targets, with the Galactic center and local
spheroidal satellite galaxies (dSphs) of the Milky Way being among the most
prominent ones. The former is expected to be the brightest source in the sky
because of the large dark matter overdensity, but it also has the brightest
foregrounds and complex dynamics. The latter are the most extreme dark matter-
dominated galaxies known to us, but have a much lower J-factor [1180, 1181]
compared to the Galactic center (around $10^{17}-10^{19}\,\rm GeV^{2}cm^{-5}$
for dSphs and about $10^{22}\,\rm GeV^{2}cm^{-5}$ for the Galactic centre,
leading to a fainter potential signal.

In contrast, the flux of particles from decaying dark matter is only
proportional to a single power of density, so it is predicted to give rise to
less clumpy signals compared to those from annihilating dark matter.
Constraints on decaying dark matter come for example from isotropic gamma-ray
and neutrino observations [1146, 1124].

There is more than just phenomenological support for the hypothesis that dark
matter self-annihilates. $N$-body simulations suggest that dark matter halos,
in the absence of baryonic effects, follow a density profile which behaves
like $\rho\propto r^{-1}$ irrespective of initial conditions. This is referred
to as a Navarro-Frenk-White (NFW) profile [1182, 1183]. Measured profiles of
dwarf spheroidal galaxies appear to follow a shallower density profile
$\rho\propto r^{0}$. This disagreement is referred to as the ‘core-cusp-
problem’ and could possibly be resolved by co-annihilating or self-interacting
dark matter (subsection II.14).

###  VIII.4 Measurements of Standard Model Parameters

In some models of dark matter, the dark matter mass and nucleon-dark matter
scattering cross section are predicted or bounded as functions of standard
model parameters such as the top quark mass and the strong coupling constant.
In such scenarios, dark matter searches constrain the standard model
parameters, which can be precisely measured by future colliders [1184, 1185,
1186, 1187, 1188] and lattice QCD computations [1189].

For example, in a model that solves the strong CP problem by a space-time
parity symmetry [1190], the dark matter mass is proportional to the energy
scale at which the standard model Higgs quartic coupling vanishes
($10^{9}-10^{12}\,\mathrm{GeV}$), which is sensitive to the standard model
parameters. Dark matter couples to a massless dark photon and the dark matter-
nucleon scattering arises from unavoidable quantum corrections leading to
photon-dark photon mixing.

The resultant correlation between the dark matter signal rate and the standard
model parameters that determine the scale where the Higgs quartic coupling
vanishes is shown in Figure 39. Here, to estimate the projections for next-
generation experiments, we scale the limit from XENON1T according to the
projections in the high mass region shown in Figure 5. Another example is
sneutrino or higgsino dark matter in supersymmetric theories, where the dark
matter mass is predicted to be smaller than the scale at which the standard
model Higgs quartic coupling vanishes [1191]. Dark matter scatters with nuclei
via tree-level $Z$ boson exchange, generating signals detectable in a 1000
tonne-year exposure even for a dark matter mass as large as $10^{12}$ GeV.
Detection of or constraints on nucleon-dark matter scattering signals will
give an upper bound on the top quark mass and a lower bound on the strong
coupling constant.

Figure 39: The expected number of signals per tonne-year exposure as a
function of the top quark mass, $m_{t}$, and the strong coupling constant
evaluated at the $Z$ boson mass scale, $\alpha_{s}(m_{Z})$, in the model
described in [1190]. The signal count is inversely proportional to the
threshold energy $E_{\rm th}$. The thickness of each colored band corresponds
to $2\sigma$ uncertainty in the Higgs mass.

###  VIII.5 Other Direct Dark Matter Searches

In the search for dark matter directly interacting with a laboratory target, a
host of synergistic detectors are required to overcome signal degeneracies,
particularly as experiments begin probing the neutrino fog. With different
technologies and targets, complimentary experiments can confirm potential dark
matter signatures and disentangle them from both neutrino-induced (CE$\nu$NS)
signals and instrumental backgrounds. Additionally, a large variety of
detectors can probe a wider dark matter mass range, as shown in Figure 40.
Target materials range from solid state crystals to dense liquids [137, 32].
Even within the context of liquid xenon TPCs, larger detectors are required
for dark matter nuclear scattering searches, but smaller detectors optimized
for single-electron signals might achieve better sensitivity to lower masses
and dark matter scattering with electrons [1192].

Figure 40: Spin-independent dark matter-nuclear scattering limits set by
leading direct detection experiments. Complementary experiments with different
targets are essential for breaking degeneracies between signals from CE$\nu$NS
and WIMP dark matter. Additionally, a variety of targets covers a wider range
of potential dark matter masses. Figure adopted from Ref. [552].

####  VIII.5.1 Solid State Detectors

Germanium detectors (HPGe detectors) are a well-understood target for dark
matter searches and have been used particularly by CoGeNT [48] and EDELWEISS
[51]. DAMIC [52] and SENSEI [54] are using silicon CCDs to look for dark
matter interactions, in particular through the electronic recoil channel.
SuperCDMS [49] measures both phonons and ionization in silicon and germanium
crystals cooled to millikelvin temperatures. CRESST [53] uses calcium
tungstate crystals at millikelvin temperatures to read both phonons and
scintillation. Sodium iodide is used by ANAIS [414], SABRE [51] as well as
DAMA/LIBRA [1013]. Depending on the target and readout, crystals have
different sensitivities to different dark matter interaction energies, but
largely overlap across dark matter masses in the GeV and sub-GeV range.

####  VIII.5.2 Liquid Target Detectors

The PICO experiment [64] uses Octafluoropropane in a bubble chamber to search
for dark matter-induced signals with a particularly strong sensitivity for
spin-dependent interactions. Piezo-electric sensors detect bubble formation in
the superheated target during an interaction, and cameras record the bubble
nucleation. Perhaps the most complementary experiments to liquid xenon TPCs
are liquid argon TPCs, such as DarkSide [59]. The operating principle is
identical to the detector described here, but the smaller atomic mass of argon
and its effect on collision kinematics makes Argon invaluable for breaking the
energy degeneracy of dark matter scatters and coherent elastic neutrino-
nucleus scatters, once observed in liquid xenon TPCs. While self-shielding of
external backgrounds is better in xenon, the ability to discriminate
electronic from nuclear recoils is better in argon. Taken together, the two
target elements provide a complementary approach to probing dark matter down
to the signal from atmospheric neutrinos.

###  VIII.6 Neutrinoless Double Beta Decay Experiments

Experimental searches for $0\nu\beta\beta$ decay [1193] span a variety of
isotopes, including 76Ge, 82Se, 100Mo, 130Te, 136Xe, and 150Nd. The choice of
isotope is driven by the Q-value of the $2\nu\beta\beta$ mode, the ability to
obtain high isotopic abundance, and compatibility with a suitable detection
technique. Detection techniques include semiconductor crystals, cryogenic
bolometers, time projection chambers, and organic and inorganic scintillators.
The choice of detection technique is a balance of the detector energy
resolution at the Q-value, the scalability of the technology to large masses,
and ability to achieve ultra low backgrounds. The leading experimental efforts
to date include MAJORANA [658], GERDA [1194], CUORE [1195], EXO-200 [659], and
KamLAND-Zen [654, 1196]. The next generation of $0\nu\beta\beta$ searches
includes LEGEND[1197], nEXO [666], NEXT [1198], CUPID [1199], KamLAND2-Zen
[1200], and SNO+ [1201]. Compared to the experiments using semiconductors and
bolometers, a next-generation liquid xenon detector will have significantly
larger isotopic mass, even with a natural abundance of 136Xe, but it will have
poorer energy resolution compared to other technologies. The ability to
fiducialize the detector means that the backgrounds from radiogenic sources
are significantly reduced. A next-generation liquid xenon dark matter detector
can have a $0\nu\beta\beta$ sensitivity comparable to those of the next
generation of dedicated $0\nu\beta\beta$ experiments (subsection IV.1).

###  VIII.7 CE$\nu$NS Experiments

The identification of neutrinos in dark matter experiments, in particular
through the CE$\nu$NS channel, will be complementary to terrestrial neutrino
experiments which operate in a similar energy regime. The COHERENT experiment
[1202] uses a stopped-pion source of neutrinos, generated by the Spallation
Neutron Source (SNS) at the Oak Ridge National Laboratory. Muon neutrinos with
energy $30\,\mathrm{MeV}$ are produced from charged pion decays, and
$\bar{\nu}_{\mu}$ and $\nu_{e}$ are produced with a Michel energy spectrum
from the subsequent decay of muons at rest. $\bar{\nu}_{\mu}$ and $\nu_{e}$
from muon decays are delayed relative to the $30\,\mathrm{MeV}$ $\nu_{\mu}$
neutrinos produced from the prompt pion decay. With characteristic energies of
tens of MeV, a large sample of the neutrino-nucleus interactions are coherent,
which together with the timing structure, permits a measurement of the
CE$\nu$NS process.

Using 14.6-kg CsI[Na] scintillator detectors, the COHERENT collaboration
announced the first detection of CE$\nu$NS in 2017 [743], with a best-fit
count of 134$\pm$22 CE$\nu$NS events, which is 77$\pm$16 percent of the
Standard Model prediction. From this initial detection, COHERENT was able to
constrain non-standard interactions in a regime of parameter space that had
not been possible to probe. In particular, the COHERENT data is sensitive to
u- and d-type non-standard interactions for flavor-diagonal muon components,
$\epsilon_{\mu\mu}$. The COHERENT detection also set new constraints on exotic
solutions to solar neutrino mixing, places novel constraints on new physics
that manifests through the neutrino sector (e.g. [1203]), constrains the
neutron form factor for CsI [1204], sterile neutrinos [1205, 1206], and the
$g-2$ anomaly [1207, 814, 815]. The collaboration has since also measured
CE$\nu$NS on Argon [1208].

Nuclear reactors have been purposed as a copious source of electron anti-
neutrinos. The characteristic neutrino energy is $\lesssim 1$ MeV; as such,
the coherence condition for the recoil is largely preserved over the entire
reactor energy regime. The primary difficulty in detecting CE$\nu$NS using
reactors is that detectors have not been able to achieve the low threshold
required to identify the CE$\nu$NS nuclear recoil signal. With further
improvements in detector technology, several experiments are poised to
identify CE$\nu$NS at reactors [1209, 1210, 986, 1211, 1212, 1213, 1214,
1215]. The two-phase noble gas detection technique is very promising for this
purpose [1215, 1216], and currently the RED-100 detector (with $\sim
160\,\mathrm{kg}$ of active liquid xenon) is being tested at the Kalinin NPP
site. This is the first CE$\nu$NS experiment using a two-phase emission
technique, and other experiments, such as NUXE with liquid xenon and CHILLAX
with xenon-doped liquid argon, are currently being developed.

###  VIII.8 Solar Neutrino Experiments

Direct real-time measurements of solar neutrinos have been observed for the
first time by the Borexino experiment [1217, 751, 761]. A next-generation
liquid xenon experiments can offer complementary measurements when detecting
solar neutrinos through elastic neutrino-electron scattering (subsection V.2).
Neutrinos that contribute to the signal are generated from the $pp$-reaction
chain, produced from the electron-capture decay of beryllium-7, and emitted in
the carbon, nitrogen, oxygen (CNO) fusion cycle. The measurement of CNO
neutrinos in liquid xenon-based detectors is limited by the presence of the
two-electron spectrum arising from the $2\nu\beta\beta$-decay of 136Xe.
Depletion of 136Xe by at least a factor of 100 relative to its natural
abundance would be necessary to detect the CNO solar neutrino component in the
next-generation xenon-based detector [754].

###  VIII.9 Gravitational Wave Searches

Liquid xenon-based detectors can be utilized to look for neutrinos and gamma-
rays released in association with gravitational waves emitted during
cataclysmic cosmic events. Such “simultaneous” observation is related then to
supernova detection and multi-messenger astrophysics, as discussed in
subsection V.4.

###  VIII.10 Xenon in Medical Physics

The great advantages of using liquid xenon for medical imaging have been
noticed already back in the 1970s [1218, 1219]. Its fast primary scintillation
and sufficiently large ionization yield make it especially attractive for
Positron Emission Tomography (PET). The two-phase emission detector with
condensed xenon as working medium has been tested in the 1980s as a high-
quality gamma-camera for nuclear medicine [1220]. The 1990s saw compressed
xenon gas being proposed for very effective, collimator-less SPECT systems
[1221, 1222, 1223]. The first liquid xenon detector prototypes for PET scans
were built and tested around the same time [1224, 1225, 1226]. Further
developments of liquid xenon detectors for PET came recently [1227, 1228,
1229, 1230]. In a PET scan, patients are injected with small amounts of
chemicals, such as sugar, where molecules have had common stable carbon atoms
replaced with positron-emitting isotopes. Position-electron annihilation in
the electron shells of atoms in the body leads to back-to-back 511 keV
$\gamma$-rays. Cancerous tumors will preferentially absorb more sugar than
other parts of the body due to higher rates of metabolic activity [1231].
Liquid xenon is being explored due to its advantageous spatial, temporal, and
energy resolutions. Already, PETALO is a full-body PET scanner using the S1
signals in liquid xenon to achieve a high resolution image with reduced
patient radioactivity exposure [1232]. Many of the developments in liquid
xenon detector technology for particle physics thus directly benefit other
scientific disciplines, such as medicine, as evidenced here.

Xenon in its gaseous form has also come into use as an alternate anesthetic
with minimal dangerous side-effects [1233]. Xenon anesthesia results in a more
stable blood pressure, a lower heart rate, and faster emergence from
anesthesia than other conventional methods, despite a higher risk of nausea
[1234]. Most oddly and uniquely, there are some studies that suggest it is
useful for treating Traumatic Brain Injuries and Post-Traumatic Stress
Disorder (PTSD) [1235, 1236]. While in the United States these claims have not
been evaluated by the Food and Drug Administration (FDA), in Russia, the
inhalation of xenon is used for selective “deletion” of traumatic memories,
associated with negative emotions [1236]. All this serves to illustrate the
extreme versatility of the element. The study of xenon for particle physics
may thus have side-effects spilling over into numerous other fields that seem
entirely unrelated.

###  VIII.11 Liquid Xenon TPCs for Nuclear Security

The neutron is the gold-standard calibration particle of choice for any WIMP
detector, since it is supposed to emulate the nuclear recoil generated by dark
matter WIMPs. This implies that a WIMP dark matter detector is also an
outstanding neutron detector. Liquid xenon TPCs stationed at seaports and
airports can allow for non-intrusive inspection (NII) of fissionable materials
in cargo, by detecting gamma rays and fast neutrons emitted spontaneously or
by stimulation from nuclear materials [1237]. The ability of discriminating
between nuclear and electronic recoils allows to better discriminate against
activation from other backgrounds. This holds true even through shielding,
given the low $\sim$keV energy thresholds achieved recently for dark matter
searches.

Another homeland security application is monitoring of nuclear reactors at
power plants for fuel rod theft, which could change the outgoing neutrino (and
not just neutron) flux, or rod type replacement, which could change the
balance of uranium and plutonium amounts. This concept has been explored by
the Nucifer Experiment [1238] with a scintillating liquid. Liquid xenon could
be ideal for detecting the resulting change in the rate of CE$\nu$NS, already
discussed in detail above. Liquid xenon is being considered for detecting
CE$\nu$NS by the RED [1215] and NUXE [1216] collaborations.

###  VIII.12 Data-Intensive and Computational Sciences

All of the aforementioned scientific deliverables require the development of
cyber-infrastructure such as algorithms, methods, and tools, for the wider
benefit of data-intensive sciences. Years of substantial improvements in dark
matter detectors means that the field launched into the realm of petabyte data
science. The computational science pursued in this field includes, but is not
limited to: how ultra-low-energy simulations are performed, including relevant
microphysics (subsection I.6); how event reconstruction can be performed with
the aid of e.g. machine learning [1239]; and how high-throughput/high-level
triggers can be deployed on such non-collider experiments.

This effort requires computational science developments, which can benefit
other scientific efforts at both small and large scales. For small scales,
there has been an explosion in the number of experiments in recent years.
Examples of advancements in this field that are broadly impactful to those
having to harness their data are integrating smaller efforts into existing
infrastructure using frameworks such as GAUDI [1240]; data management systems
such as OSG [1241]; and demonstrating the effectiveness of columnar compilers
in tackling data-intensive applications in high-level descriptive languages.
For large scales, overcoming computational science hurdles with novel
technologies means serving as a test bed for technologies for Big Science
projects such as the HEP Software Project [1242]. Therefore, achieving our
physical science goals requires novel computational science and cyber-
infrastructure development.

##  IX Research Community Priority

The need for a next-generation liquid xenon TPC is strongly acknowledged
throughout the international particle physics community. Studies towards a
large-scale liquid xenon dark matter detector started already in 2009 within
the EU-ASPERA program, which eventually led to the DARWIN project. The support
for DARWIN was strongly recommended in the 2011 update of the ASPERA roadmap
[1243]. During the “Snowmass” process to plan research priorities in 2013,
U.S. particle physicists concluded that the discovery goal of liquid xenon
dark matter detectors must be to “search for WIMPs over a wide mass range (1
GeV to 100 TeV)… until we encounter the coherent neutrino scattering signal
that will arise from solar, atmospheric and supernova neutrinos.” [1244]. In
2017, the Astro Particle Physics European Consortium (APPEC) devised a
European Strategy, which aimed to converge “with its global partners” on the
realization of at least one “ultimate Dark Matter detector based on xenon”
[1245].

The Division of Particles and Fields of the American Physical Society defined
the next step for the detection of WIMPs to be “to partner with Europe and
Asia on one large international generation-3 detector” [1246] and they note
that detector R&D looks promising for “the scaling up of liquid
noble…detectors to cover the WIMP mass range to the coherent neutrino floor”
[1247]. The Chinese community also endorses a next generation deep underground
xenon observatory as one of the top priorities in particle astrophysics
[1248]. The APPEC Dark Matter Report states that underground dark matter
programs with the sensitivity to reach down to the “neutrino floor at the
shortest possible timescale” should receive enhanced support [1249]. Clearly,
the main goal is to search for dark matter, but it is understood that such
ultimate detector will have other important implications for astrophysics and
the quest for the nature of neutrinos. This present paper is a response to the
global support for a next-generation liquid xenon TPC, as evidenced here.
Progress is also made in assembling a strong global liquid xenon detector
community, evidenced for example by the signing in 2020 of a joint Memorandum
of Understanding between the members of the LZ and XENON collaborations.

###  IX.1 Dark Matter

In the past two decades, the goal of liquid xenon TPCs has been to detect
theorized elastic scatters of WIMP dark matter off xenon nuclei. In addition
to WIMPs, these detectors have sensitivity to a large host of well-motivated
dark matter candidates, as outlined in this work. About 10 different xenon-
based dark matter detectors were built over the years, increasing the xenon
target mass by almost three orders of magnitude, reducing the electronic
recoil background by about four orders of magnitude and improving the
sensitivity to WIMP dark matter by more than a factor 1000. After the
pioneering work by ZEPLIN-II/III and XENON10, XENON100, LUX and PandaX managed
to build a suite of detectors with world-leading sensitivity. XENON1T was the
first TPC with a target above the tonne-scale. The current generation of
detectors, XENONnT [84], LUX-ZEPLIN (LZ) [85], and PandaX-4T [83], feature
multi-tonne liquid xenon targets. Despite a lack of definitive signal so far,
these detectors are clear leaders in sensitivity to WIMPs and other physics
channels, and scale reliably in mass [82]. It is for these reasons that a
next-generation liquid xenon TPC is of such high interest to the international
physics community.

The Update of the European Strategy for Particle Physics (ESPP) from 2020
points out that the search for dark matter is a crucial part of the search for
new physics and that experiments that offer “potential high-impact” should be
supported [1250]. The APPEC Report on the Direct Detection of Dark Matter
(2021) states that “the search for dark matter with the aim of detecting a
direct signal of dark matter particle interactions with a detector should be
given top priority in astroparticle physics, and in all particle physics”
[1249]. Already in 2014, the U.S. Particle Physics Project Prioritization
Panel (P5) highlighted the identification of the new physics of dark matter as
one of the five science drivers for all of particle physics and recommended
that U.S. funding agencies “support one or more third-generation (G3) direct
detection experiments…[with] a globally complementary program and increased
international partnership in G3 experiments” [1251]. Consolidation of the
world-wide xenon community already took place when the members of the ZEPLIN
collaboration joined LUX, and XMASS teamed up with XENON. Another important
step towards the realization of this next-generation detector happened in
2021, when the scientists from the XENON/DARWIN and LUX-ZEPLIN collaborations
agreed to join forces towards the realization of this observatory.

The German [1252], Swiss [1253] and Dutch [1254] particle physics communities
likewise identified the multi-tonne liquid xenon observatory DARWIN of
particular interest for their national strategy roadmaps and support R&D
towards this goal via national funding programs. Other countries are strong
members of the XENON experiment and it is expected that its follow-up project
(e.g. DARWIN) will also be supported. The U.K.’s Particle Astrophysics roadmap
also stresses the importance of a xenon-based next-generation (”G3”)
observatory, explicitly recommending R&D towards this detector as the highest
priority in dark matter. Relevant R&D is also supported through multiple
European Research Council (ERC) grants.

###  IX.2 Neutrinoless Double Beta Decay

Understanding the physics of neutrino mass is another important science driver
for particle physics identified by the U.S. P5 and APPEC, which noted the
importance of neutrinoless double beta decay searches in that context [1251,
1245]. Such experiments are also a top priority in the 2015 US Long Range Plan
for Nuclear Science [1255], with one of the four main recommendations being
the construction of a massive detector. The European APPEC double beta report
(2019) states that ”the search for neutrinoless double beta decay is a top
priority in particle and astroparticle physics” and acknowledges that the
$0\nu\beta\beta$ sensitivity of a next generation _dark matter_ detector opens
up an exciting scenario [1256]. Similar statements of support for neutrinoless
double beta decay detection, especially in dark matter detectors, can be found
in UK [1257], Russian [1258], CERN/European [1259], and Chinese [1260]
particle and nuclear physics priority planning documents. The APPEC Dark
Matter Report states on this topic that “the potential of dark matter
detectors to search for rare nuclear decays has been demonstrated
spectacularly when XENON1T observed for the first time double electron capture
on 124Xe [718]” [1249].

###  IX.3 Neutrinos

Recently, the observed phenomenon of coherent elastic neutrino-nucleus
scattering [743] has made large dark matter detectors, such as the one
discussed here, particularly desirable for studying neutrinos. Such a detector
would be invaluable to the field of astrophysics for measuring Galactic
supernovae neutrinos of all flavors. A next-generation liquid xenon detector
would be able to probe multiple solar, atmospheric and supernova neutrino
signals, which are invaluable measurements in their own right. The US Nuclear
Physics community, in the 2015 Long Range Plan for Nuclear Science (LRP)
[1255], notes that measuring the CNO cycle and addressing the “metallicity
problem” in the Sun — both accessible to this detector technology — are the
next big challenges in solar neutrino research.

Taken together, the experiment discussed here addresses a number of high-
priority science issues. Spanning across (astro-)particle physics,
astrophysics, and nuclear physics, such a detector will significantly advance
fundamental science on a variety of fronts.

##  X Summary

The compelling and versatile science case for a next-generation liquid xenon
experiment, combined with its mature technology and minimal technological
risk, renders such a detector a paramount facility for the next decade of
particle physics, nuclear physics, and astrophysics. This detector will be
sensitive to many types of dark matter interactions. Probing the remaining,
well-motivated parameter space for spin-independent WIMP scattering down to
the neutrino fog will be a milestone in the quest to unravel the nature of
dark matter. With its xenon target, this detector will have unprecedented
sensitivity to a variety of dark matter models, including spin-dependent
couplings, axion-like particles, dark photons, and sterile neutrinos. With the
help of optimized analyses, it covers dark matter masses ranging from kilo-
electronvolts all the way up to the Planck mass. This next-generation
experiment will therefore have significant and lasting impact on dark matter
physics.

Simultaneously, such a next-generation liquid xenon experiment will be a
competitive experiment in the search for neutrinoless double-beta decay, using
a very cost-effective natural xenon target. It will therefore directly address
one of the most pressing problems of nuclear physics. Isotopic separation of
the natural xenon target can be used to further this sensitivity, or to enable
a direct measurement of solar CNO neutrinos.

Furthermore, this next-generation experiment will be a true observatory for a
number of relevant physics. Examples include a precision measurement of the
Solar pp neutrino flux, a measurement of the Solar metallicity through boron-8
neutrinos, as well as a first measurement of atmospheric neutrinos in the
mega-electronvolt energy range. This detector also has the chance to observe
neutrinos from a Galactic supernova in a complementary, flavor-independent
channel, if such an event were to occur in the lifetime of the experiment.

Finally, this detector provides the opportunity to search for a host of
signatures from physics beyond the standard model of particle physics. No
other technology is capable of probing this many different signals, spanning
areas from cosmology to nuclear physics, particle physics, and solar
astrophysics.

##  XI Acknowledgements

This work has been supported by the US National Science Foundation (NSF,
grants PHYS-1719271, PHYS-2112796, PHYS-2112801, PHYS-2112802, PHYS-2112803,
PHYS-2112851, PHYS-2137911); by the Department of Energy (DOE), Office of
Science (grants DE-AC02-05CH11231, DE-AC02-07CH11359, DE-AC02-76SF00515, DE-
AC52-07NA27344, DE-FG02-00ER41132, DE-FG02-10ER46709, DE-NA0003180, DE-
SC0006605, DE-SC0008475, DE-SC0009999, DE-SC0010010, DE-SC0010072, DE-
SC0010813, DE-SC0011640, DE-SC0011702, DE-SC0012161, DOE-SC0012447, DE-
SC0012704, DE-SC0013542, DE-SC0014223, DE-SC0015535, DE-SC0015708, DE-
SC0018982, DE-SC0019066, DE-SC0020216, UW PRJ82AJ); by the U.K. Science &
Technology Facilities Council (grants ST/M003655/1, ST/M003981/1,
ST/M003744/1, ST/M003639/1, ST/M003604/1, ST/R003181/1, ST/M003469/1); by the
German Research Foundation (DFG) (grants KO 4820/4-1, EXC-2118, 279384907 (SFB
1245)); by the Max Planck Gesellschaft; by the Dutch Research Council (NWO);
by the Swiss National Science Foundation (grants PCEFP2_181117,
200020-188716); by the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (grants 742789,
101020842); by the Portuguese Foundation for Science and Technology (FCT)
(grants PTDC/FIS-PAR/28567/2017); by the Institute for Basic Science, Korea
(grant IBS-R016-D1); by the Australian Research Council through the ARC Centre
of Excellence for Dark Matter Particle Physics, CE200100008; and by the Marie
Skodowska-Curie grant agreement No 860881. BvK acknowledges support from Emmy
Noether Grant No. 420484612; AM et al. acknowledge additional support from the
STFC Boulby Underground Laboratory in the U.K., the GridPP [1261, 1262] and
IRIS Collaborations, in particular at Imperial College London and additional
support by the University College London (UCL) Cosmoparticle Initiative. This
research used resources of the National Energy Research Scientific Computing
Center, a DOE Office of Science User Facility supported by the Office of
Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
The University of Edinburgh is a charitable body, registered in Scotland, with
the registration number SC005336. PK and SB from the National Research
Foundation of Korea (NRF) grants NRF-2018R1A2A3075605 and NRF-2019R1A2C3005009
and by KIAS Individual Grant No. PG021403; RC from an individual research
grant from the Swedish Research Council (Dnr 2018-05029); RC and TE from the
Knut and Alice Wallenberg project Light Dark Matter (Dnr KAW 2019.0080 and
2019.0080); PB and SS from the Dr. Raja Ramanna Fellowship program of the
Department of Atomic Energy (DAE), Government of India. RB acknowledges ISF
and the Pazy foundation. Finally, RFL acknowledges support from the Purdue
University Department of Physics and Astronomy and from the Purdue Research
Foundation without which this paper could not have been realized.

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