as the one proposed here [269, 270, 271, 272, 273, 274, 275, 276, 277, 278,
279, 280, 281, 282, 283, 284, 285].

###  II.11 Electroweak Multiplet Dark Matter

One particularly simple case among WIMP candidates is the dark matter particle
as the lightest member of an electroweak multiplet. This is in essence the
original WIMP model, sometimes also called the “minimal dark matter” scenario
[286, 287, 288]. Where ”WIMP” refers to particles interacting through the Weak
force, this WIMP is the same an as electroweak multiplet, by definition. The
interaction between the dark matter and the Standard Model particles are
therefore mediated by the Standard Model gauge bosons and the Higgs boson,
without the need to introduce additional mediators. Since the interactions are
governed by the Standard Model gauge invariance, this is a very predictive
scenario and serves as an example of a simple and elegant WIMP dark matter
model that is still largely unexplored by experimental searches.

In this model, the fermionic multiplets only have gauge interactions at the
renormalizable level. In general, we could consider multiplets $(1,n,Y)$ under
the Standard Model gauge group SU(3)${}_{\rm C}\times$SU(2)${}_{\rm
L}\times$U(1)Y. The mass scale of the electroweak multiplet is set by a
vector-like mass parameter. After electroweak symmetry breaking, the mass
spectrum of the multiplet is not exactly degenerate. Minimally, the degeneracy
will be lifted by electroweak loop corrections [289, 290, 286, 287, 291, 292].
For a large multiplet $n>7$, the Landau pole will be about one order of
magnitude above the mass of electroweak multiplet [293], which makes the model
contrived; conversely, new physics below the scale of the Landau pole may lead
to an asymptotically safe scenario [294]. Ultimately, perturbative unitarity
of the annihilation cross section provides a limit of $n<14$ [295, 292].

Figure 12: Expected spin-independent scattering cross-section for Majorana
multiplets (red) and for real scalar multiplets (blue), assuming the Higgs
portal coupling $\lambda H=0$). Vertical errors correspond to LQCD
uncertainties on the elastic cross-section, horizontal errors indicate
uncertainties from the determination of the WIMP freeze out mass. The next-
generation experiment discussed here will fully probe these classes of highly
motivated WIMP dark matter models. Figure adopted from [292].

Sommerfeld enhancement [296, 297, 298, 299, 300, 301] and bound state effects
[302, 303, 304, 305, 306] need to be included in accurate calculations of
predictions. Target masses of the electroweak multiplet dark matter are in the
range of 1 to 30 TeV [288, 307, 305] for $n<7$, but can approach the unitarity
bound for larger multiplets, which saturates at $n=13$ [295, 292]. These
masses are beyond the reach of the Large Hadron Collider [308, 309, 310, 311]
and would require one of the proposed future high energy colliders [312, 313,
314, 292]. In contrast, the direct detection of the electroweak multiplet dark
matter is through 1-loop processes involving the Standard Model W, Z, and
Higgs bosons. The spin-independent cross sections have been computed to be
around $10^{-47}\,\mathrm{cm^{2}}$ for the Majorana triplet (wino) [315] and
$10^{-48}\,\mathrm{cm^{2}}$ for the Dirac doublet (Higgsino) [316]. The other
cases are expected to be within the same order [295]. As shown in Figure 12,
this level of spin-independent cross section is well within the reach of the
next-generation liquid xenon detector discussed here [317, 318, 292]. To avoid
confusion, note that the LZ line in [292] corresponds to the sensitivity from
the LZ Design Reports [319, 94] instead of the goals shown Ref. [85].

###  II.12 Implications for Supersymmetry

One classic WIMP dark matter model is the lightest supersymmetric partner
(LSP). Supersymmetric models, such as the Minimal Supersymmetric Standard
Model (MSSM), with an exact R-parity, predicts that a stable electrically
neutral LSP could be a cold dark matter candidate [126]. There are three
possibilities for a stable neutral LSP: sneutrino, gravitino and neutralino.
Among them, the most attractive scenario for direct detection is neutralino
dark matter. For a general review on supersymmetry and its low-energy
phenomenology, see [320].

In the MSSM, two neutral higgsinos and two neutral gauginos could mix with
each other after electroweak symmetry breaking to form four mass eigenstates
called neutralinos. Current direct detection is sensitive to the scattering of
WIMPs off nuclei through tree-level Higgs exchange. Thus, existing data has
ruled out a significant part of the parameter space of the “well-tempered”
neutralino scenario [321], in which the LSP is a mixed neutralino (e.g., mixed
bino and higgsino) with the right thermal relic abundance and couplings to the
nucleus through the Higgs boson.

Yet, there are large regions of parameter space unprobed by current
experiments. In the MSSM, the reason is that for an LSP that is predominantly
a bino, there is a general reduction of the spin-independent direct detection
cross section for negative values of the higgsino mass parameter $\mu$. This
reduction is induced by a decrease of the coupling of the bino to the Higgs
boson [322], as well as by a destructive interference between the
contributions of the standard Higgs with the ones of non-standard Higgs bosons
[323, 324]. The same happens in other minimal supersymmetric extensions, like
the NMSSM, but for a singlino dark matter candidate, the reduction occurs for
positive values of $\mu$ [325]. Moreover, there are regions of parameter
space, called blind spots, in which the scattering amplitude is drastically
reduced [322, 323, 325, 326]. The precise parameter space associated with
these blind spots is slightly modified by loop corrections [327]. Quite
generally, for the appropriate signs of $\mu$, the spin-independent scattering
cross section can easily be below $10^{-47}\,\mathrm{cm^{2}}$ [325, 328, 329,
330]. This range of cross sections are out of the reach of current
experimental searches but can be probed by next generation direct detection
experiments like the one discussed here.

In addition to the well-tempered neutralino at the blind spot, nearly pure
wino or higgsino dark matter can scatter off nuclei elastically at one-loop
level with a small cross section [331, 205]. The pure wino scenario has been
strongly constrained by indirect detection of gamma rays from the Galactic
center [332, 333] and local spheroidal satellite galaxies [334, 335], although
the former is subject to large uncertainty from the dark matter profile. The
spin-independent pure wino-nucleon cross section is around $2\times
10^{-47}\,\mathrm{cm^{2}}$ [315], which can be probed by next-generation
direct detection experiments. The elastic scattering cross section of the
higgsino is found to be below $10^{-48}\,\mathrm{cm^{2}}$ with a large
theoretical uncertainty [316]. Depending on the mass splitting between neutral
higgsinos, the inelastic scattering of higgsino dark matter could be
potentially probed with such a future experiment [241].

It is also possible that dark matter could have multiple components such as a
combination of very light QCD axions and neutralinos in a supersymmetric
theory that solves the strong CP problem [336]. In this scenario, direct
detection experiments probe the dark matter fraction of the WIMP times its
scattering cross section. The next-generation experiment is thus also
motivated as pushing its sensitivity to lower cross section enhances the
sensitivity to smaller fractions of dark matter in a multi-component scenario
[337, 338, 339, 340, 341, 342].

###  II.13 Inelastic Dark Matter

Inelastic Dark Matter (iDM) was originally proposed [237] to resolve the
tension between results published by the DAMA/LIBRA collaboration [343, 344,
345] and other direct and indirect observations [346, 347, 348]. Multiple
particle candidates have since been proposed as inelastic dark matter [300,
349], mostly motivated by the measured DAMA/LIBRA spectrum and the constraints
for other experiments. Although ultimately this model failed given later
exclusions from XENON100 [350], inelastic dark matter has sparked significant
theory development and has remained as an interesting and well-studied family
of dark matter models. A common feature is a dark matter particle that
scatters off Standard Model particles through an excited state of the dark
matter particle itself. The mass difference of the excited state $\delta$
imposes a threshold on the energy transfer of the interaction, below which
interactions are suppressed. This threshold on the energy transfer Enr limits
the population of dark matter that can interact with a given target to those
with a minimum velocity $\beta_{\rm min}$ expressed by

$\beta_{\rm min}=\sqrt{\frac{1}{2M_{N}E_{\rm nr}}}\left(\frac{M_{N}E_{\rm
nr}}{\mu}+\delta\right)$ (2)

where $M_{N}$ is the nucleus mass and $\mu$ is the reduced mass of the dark
matter and target particles. Enforcing this constraint alters the spectrum of
the expected interaction and can result in peaked recoil spectra [237, 40],
strong dependencies on the particular target material [351], or halo
distributions with differing high velocity behavior [352]. Note that number-
changing interactions that involve multiple dark matter and one standard model
particle (Co-SIMPs) lead to similar effects, since rest mass is converted to
kinetic energy [353]. Calculating this spectrum for a given detector can be
done in a model-independent way; software packages have been developed [354]
to perform these calculations in a consistent manner. Dedicated searches for
inelastic dark matter are thus required and have been carried out in XENON100
[174], PandaX-II [355], and LUX [356].

###  II.14 Self-Interacting Dark Matter

Figure 13: Predicted event rates at a xenon-based experiment for a self-
interacting dark matter model with a light mediator (solid red), a model with
three times the mediator mass (dashed magenta), and the vanilla WIMP model
with contact interaction (dotted green). The spectra are normalized to have
the same number of total events within the signal range. See [357] for
details.

Self-interacting dark matter (SIDM) [358, 359] is a leading candidate that can
resolve both long-standing and more recent tensions between small-scale
structure observations and prevailing cold dark matter predictions, see [360]
for a review. SIDM phenomenology is also expected if the dark matter is
composite (subsection III.10) or arises from a Mirror World scenario
(subsection III.11). Dark matter self-interactions, analogous to the nuclear
interactions, can thermalize the inner Galactic halo in the presence of the
stellar component and tie dark matter and baryon distributions in accord with
observations [361, 362, 363, 364]. In many particle physics realizations of
SIDM, there exists a light force carrier that mediates dark matter self-
interactions [365, 366, 367, 368, 369, 370, 371, 372, 373]. When the mediator
couples to Standard Model particles, it may generate dark matter signals in
direct detection experiments [374]. For a typical SIDM model, the mediator
mass is comparable to or less than the momentum transfer in nuclear recoils.
Compared to WIMPs with a contact interaction, the SIDM signal spectrum is then
more peaked towards low recoil energies [357, 375], see Figure 13. Thus the
detection of such a spectrum can be an indication of the self-scattering
nature of dark matter. Even a null result can put a stringent constraint on
the coupling constant between the two sectors. Recently, the PandaX-II
collaboration analyzed their data based on an SIDM model with a dark photon
mediator and derived an upper bound of $\sim 10^{-10}$ [376, 377] on the
kinematic mixing parameter between the dark and visible photons. Limits from
liquid xenon experiments set the strongest constraints also on light SIDM
models [378]. The next-generation liquid xenon experiment discussed in this
review will further test SIDM models, and dark matter models with a light
mediator in general.

###  II.15 Leptophilic Interactions

While past efforts in direct dark matter detection have mostly focused on WIMP
couplings to nucleons, it is also possible that dark matter would couple
preferentially to leptons. Such “leptophilic” dark matter candidates have been
discussed extensively in the context of the cosmic ray positron excess
observed by PAMELA [379] and AMS-02 [380], as well as the bright
$511\,\mathrm{keV}$ X-ray signal from the Galactic Center [381], and the high-
energy cosmic ray electron data from DAMPE [382]. Leptophilic dark matter is
easily realized in concrete models. This is the case, for instance, if dark
matter interactions with the Standard Model particles are mediated by a new
gauge boson that couples predominantly to leptons [383, 384]. Another example
are dark matter interactions mediated by new scalar particles carrying lepton
number, such as the sleptons in supersymmetric models [385, 386, 387, 388,
389].

Even if the tree-level interactions of dark matter are leptophilic, couplings
to nucleons can be induced at loop level. In that case the WIMP–nucleon
scattering is the more promising detection channel, despite loop-suppression,
as long as the WIMP is much heavier than the electron [390, 391, 388, 392,
393, 384, 394, 395, 396]. The reason for this is the more favorable
kinematics: the scattering of a heavy WIMP ($\gg\mathrm{MeV}$) on an electron
leads to a very small momentum transfer, mostly invisible to a typical direct
detection experiment.

However, there are scenarios in which WIMP couplings to nucleons are absent
even at the loop level. This can happen for instance if WIMP–lepton
interactions are mediated by a new axial vector boson. In this case, the
dominant direct detection signal is dark matter scattering on electrons [390,
397, 395], and searches for this process have been carried out by many
experiments, including XENON100 [398, 399, 400] and LUX [401]. Scattering on
electrons is particularly efficient for sub-GeV dark matter [402], making it
the primary detection channel in that mass range.

Scattering on electrons is also the most efficient channel for dark matter
capture in the Sun [390, 403, 404]. Therefore, if dark matter annihilates into
a final state including high-energy neutrinos, searches for these neutrinos
from the Sun leads to highly competitive and complementary limits. On the
collider side, strong limits on leptophilic dark matter are obtained from LEP
data [405]. Future lepton collider would lead to further improvements [406,
407, 408]. Progress with these experiments will be complementary to advances
from the experiment proposed here.

###  II.16 Modulation Searches

As the Earth revolves around the Sun, a sinusoidal annual modulation should be
observable in the dark matter flux hitting direct detection experiments
underground [36, 409], with details depending on the phase space distribution
of the halo [410, 411]. The DAMA/LIBRA collaboration upholds a long-standing
claimed observation of an annually modulating event rate [345] with a
statistical significance in excess of 9$\sigma$. However, most interpretations
of this signal in terms of WIMPs have been ruled out by numerous other
experiments. A substantial level of particle model fine-tuning is now required
to reconcile the DAMA/LIBRA observation with other null results [38, 412].
Moreover, experiments such as ANAIS [413, 414], COSINE-100 [415, 416] and
SABRE [417] attempt to replicate DAMA/LIBRA with an identical sodium iodide
target but have not found any evidence of modulation.

A next-generation liquid xenon experiment will be robustly constructed using
long-term infrastructure that is made to last multiple years or even decades.
Combined with the extremely low background and large target mass, a next-
generation experiment may be the ideal experiment to perform an annual
modulation search. An annual modulation analysis thus is an integral part of
the primary dark matter data analysis, with a sensitivity enhanced by the long
data taking time spanning many annual cycles.

A diurnal modulation is guaranteed for most dark matter candidates due to the
varying speed of the Earth relative to the dark matter wind as the Earth
rotates, though this will be around two orders of magnitude smaller than the
annual modulation. However, if dark matter interacts more strongly inside the
Earth, then there may be a much larger diurnal modulation effect as the
Earth’s “shadow” eclipses the dark matter wind from the perspective of an
experiment [418, 419, 420, 421]. Such shadowing effect also provides
additional sensitivity to cosmic-ray boosted dark matter (CRDM) with mass
lower than around 1 GeV [422]. Many models within the scope of a future xenon
experiment will exhibit such a modulation (section III).

Experimentally, the challenge for detecting diurnal modulations remains to
understand sub-1% variations in detector parameters on a daily basis rather
than from weekly or monthly calibrations. In a massive next-generation
detector, spatial variation of quantities such as light collection
efficiencies may be inherently greater, but there is no reason to assume that
temporal variation will be worse than in contemporary detectors. These
experiments can teach us how to better control variation, through existing
logging of temperature and pressure data as function of time, and excellent
handles for temporal systematic uncertainties [94, 61], especially when
coupled to frequent calibrations using fast-decaying radioisotopes such as
${}^{83\textrm{m}}$Kr [423, 424].

###  II.17 Confronting the Neutrino Fog

As the size and sensitivity of direct detection experiments improves, the
detectable signal of dark matter will become so small that it will reach a
level similar to the strength of the coherent elastic neutrino-nucleus
scattering signal of astrophysical neutrinos [159, 425, 149]. While there is a
substantial science case for the detection of astrophysical neutrinos in their
own right (section V), for dark matter searches they are a critical
background.

When searching for a signal that is mimicked by a background, discovery is
only possible when an excess in events is larger than the expected statistical
fluctuations and systematic uncertainties of that background. For the neutrino
background, the systematic uncertainties on the flux normalizations dominate,
which range from 1%–50%. Many of the particle models discussed here will
eventually be limited in some way by the neutrino background, in both the
electronic [426, 427] and nuclear recoil channels [149, 428, 429, 430, 431].
This background is often referred to as the “neutrino floor”, or more
accurately, the “neutrino fog”, as it represents a gradual worsening of
sensitivity and a dependence on the systematics of the neutrino flux. Various
definitions of this neutrino fog have been put forward [432]. Just like any
generic limit on dark matter, the shape of a neutrino fog is dependent on
nuclear [433], astrophysical [157] and particle model [429, 430, 243] inputs
for the dark matter signal. Given non-standard neutrino-nucleus interactions,
these could be further modified [434, 435] and even raised by several orders
of magnitude [436].

Unlike many other backgrounds, neutrinos cannot be shielded, so they must be
dealt with statistically, or by searching for some discriminating features.
Techniques that have been discussed in the past include exploiting the
differing annual modulation signatures [437], or the complementarity between
different target nuclei [438]. However, only direction-dependence provides
enough of a discriminant to fully subtract the background [439, 440, 441, 442,
443], but measuring this in any large-scale experiment is extremely
challenging.

Figure 14: Spin-independent discovery limits at $m_{\chi}=100$ GeV as a
function of the expected number of atmospheric CE$\nu$NS events $N$, and the
fractional uncertainty on the atmospheric neutrino flux, $\delta\Phi_{\rm
Atm}/\Phi_{\rm Atm}$ from Ref. [157]. Three scaling regimes as a function of
$N$ are shown with dashed lines: 1) “background-free” $\sigma\sim N^{-1}$, 2)
Poissonian $\sigma\sim N^{-1/2}$, and 3) Saturation
$\sigma\sim\sqrt{(1+\delta\Phi^{2}N)/N}$. The bottom panels in each case show
the logarithmic scaling exponent defined as: $n_{\rm
DL}\equiv\textrm{d}\ln\sigma_{\rm DL}/\textrm{d}\ln N$. This figure shows the
importance of the neutrino flux systematic uncertainty in extending the dark
matter physics reach below the neutrino fog.

Fortunately for the next-generation xenon experiment, extending the dark
matter physics reach below the neutrino fog will be facilitated by
complementary measurements made by neutrino experiments. Taking the example of
standard WIMP-nucleon cross sections, the most important backgrounds will be
8B solar neutrinos for WIMP masses below $\sim$10 GeV/$c^{2}$, and atmospheric
neutrinos above that. The 8B flux is measured at the 2% level from Solar
neutrino data [444]. The atmospheric flux on the other hand, is difficult to
measure and to theoretically predict at the relevant sub-100 MeV energies, so
it still has a $\sim$20% uncertainty (subsection V.3 and [150]). Any reduction
in these uncertainties will, in effect, “lower” the neutrino fog. Indeed,
gradual improvements in neutrino flux measurements are expected independent of
the experiment under discussion here. For example, experiments like SNO+
[445], JUNO [446] and DUNE [447, 448] will be either operating or under
construction over a similar timescale to the next-generation xenon experiment.

In Figure 14 we show how the minimum discoverable spin-independent cross
section for a $100\,\mathrm{GeV}$ WIMP evolves with increasing exposure in a
xenon experiment. The brief plateau in the discovery limit is the impact of
the atmospheric neutrino background. However, in the limit of high statistics,
the number of observed background events will eventually be large enough to
account for the finite uncertainty. At this point, the discovery limit breaks
past the neutrino fog and smaller cross sections can be accessed. Comparing
the different lines, we see clearly the importance of the systematic
uncertainty. A future improvement down to $\sim$4% would be enough to extend
the reach of a 1000 tonne-year xenon experiment almost an order of magnitude
into the neutrino fog at high masses [449]. This is where much of the
remaining supersymmetric WIMP candidates [450, 451, 331, 452], as well as many
alternative WIMP models [273, 453, 454] lie.

##  III Broadening the Dark Matter Reach

Liquid xenon experiments have already demonstrated that they are versatile
detectors with significant sensitivity to a variety of non-WIMP dark matter
models. Traditionally, WIMPs are searched-for using analyses that exploit the
electronic/nuclear recoil discrimination capability of liquid xenon and
achieve the lowest nuclear recoil background of any dark matter direct
detection technology. To broaden this reach, a number of different analyses
and technologies are available as presented in this section. This in turn
enables liquid xenon experiments to achieve competitive sensitivity to a
number of dark matter models that are also described here. In particular,
subsections III.1–III.5 describe dedicated analyses and technologies to lower
the energy threshold of liquid xenon TPCs. Subsections III.6–III.9 describe
models that especially profit from such lower thresholds, and subsections
III.8–III.12 models where the signal can be in the electronic recoil band.
Subsections III.13 and III.14 describe two models that require dedicated
analyses to increase the reach of liquid xenon TPCs to complex interactions
and up to Planck mass dark matter, respectively.

With the WIMP model being probed extensively by experiment, the community is
in parallel starting to work on detector concepts that can probe dark matter
over a much wider mass range [455], in particular covering thermal relic
particles in the $\mathrm{MeV/c^{2}}-\mathrm{GeV/c^{2}}$ mass range [402, 456,
457, 458, 459, 455]. Searches in this lower mass range were pioneered with
liquid xenon detectors [460]. While many experiments optimized for very low-
energy recoils now exist [461, 462, 463, 464, 465], liquid argon [466, 467]
and xenon [468, 469, 166] TPCs still remain the leading technologies even for
sub-GeV masses. There is thus significant interest in achieving the lowest-
possible energy threshold in a next-generation liquid xenon detector.

Figure 15: Maximum recoil energy transferred in elastic dark matter
interactions to a xenon nucleus (blue) or in inelastic dark matter
interactions to an electron (green). Currently-achieved energy thresholds are
indicated for both the traditional S1$+$S2 analysis [82, 470] as well as a
S2-only analysis [166]. The ultimate thresholds for an ideal detector are also
shown ($13.7\,\mathrm{eV}$ for inelastic scatters [105] and
$0.3\,\mathrm{keV}$ for elastic nuclear recoils [471]).

Figure 15 visualizes the relevant dark matter scattering kinematics. For a
maximum-velocity dark matter particle
($v=v_{\mathrm{esc}}+v_{\mathrm{Earth}}$) and a head-on dark matter-nucleus
collision, it shows the maximum recoil energy for either elastic scatters
resulting in a nuclear xenon recoil, or inelastic scatters resulting in
electronic recoils. For a given energy threshold, this translate into a
minimum mass for the dark matter particle to be able to leave a signal in the
xenon target. As can be seen, lowering the threshold increases the dark matter
mass range that the detector is sensitive to. Further, inelastic scatters as
discussed below can be used to probe drastically lighter dark matter
candidates (see e.g. Ref. [472]).

###  III.1 Double Photoelectron Emission

In the traditional analysis where both primary scintillation (S1) and
ionization (S2) signals are read out, the energy threshold of two-phase liquid
xenon TPCs is set by the smallest scintillation signal that can be confidently
discriminated from background sources. Typically, dark matter experiments
require an $n$-fold coincidence of PMTs within a short time window for a pulse
to be classified as an S1. The optimal value of $n$ (typically in the range
2–4) is a compromise between signal efficiency and the rejection of fake S1
pulses, caused by random coincidences of PMT dark counts [473].

This methodology makes no attempt to otherwise discriminate dark count
background pulses from actual photon-induced pulses. However, it is known
that, for some PMT photocathodes, the energy of the liquid xenon scintillation
photons (175 nm or 7 eV [474]) is enough to produce two photoelectrons on the
PMT photocathode a fraction of the time, resulting in pulses that are on
average twice as large as a single photoelectron pulse.

Figure 16: Superposition of single photon pulse area spectra of a R11410 PMT
for different wavelengths. Each spectrum is normalized by the integral in the
region between 50–120 mV ns in order to show the effect more clearly. Figure
from Ref. [475].

This so-called Double Photoelectron Emission (DPE) effect can therefore be
exploited to increase the signal efficiency beyond the standard $n$-fold
optimisation, provided that the DPE fraction and efficiency gain can be
properly calibrated. This requires the precise determination of the PMT DPE
probability, which depends strongly on the wavelength of the impinging light,
as well as on the composition and thickness of the photocathode. For the
widely-used Hamamatsu R11410 PMT model, a wavelength scan was performed with
single photons down to the VUV range on one unit [475] (see Figure 16). The
inter-PMT variability due to the photocathode manufacturing process has also
been measured at low temperature with a batch of 35 R11410-22 PMTs [476].
Measuring the DPE probability is also crucial for pulse area calibration. A
pulse area in ‘photoelectrons’ does not represent the number of photon hits
detected, but can be understood and calibrated if the DPE probability is
known. Experiments have reported average values of their PMT DPE probability
of around $\sim$10–20% given liquid xenon scintillation light [477, 478].

Figure 17: 90% CL upper limits on the spin-independent WIMP-nucleon cross
section obtained using the single-photon population producing Double
Photoelectron Emission in the LUX 2013 WIMP search. The observed limit with a
0.3 keV NR energy cut-off is shown in solid black, with 1$\sigma$ and
2$\sigma$ sensitivity bands shown in green and yellow. The dashed black line
is derived from the same analysis but with a model cut-off at 1.1 keV. Both of
these results correspond to the NEST v.2.0.0 model. The upper limit using a
0.3 keV NR energy cut-off with the newer NEST v.2.0.1 model is shown using a
dotted black line. Also shown are other results current at the time, namely
from the LUX 2013 search [479] (gray), the LUX complete exposure [60] (red),
DarkSide-50 [466] (green), PandaX-II [62] (blue), PICO60 [64] (lilac) and
CDMSLite [461] (purple). Figure from Ref. [478].

The LUX experiment exploited this DPE to lower the coincidence condition from
two PMTs to just a single PMT with an S1 pulse consistent with DPE [478]
(Figure 17). In general, an experiment may lower its $n$-fold condition by
requiring that a subset of PMT hits are consistent with DPE. A PMT with a low
dark count rate and high DPE probability might enhance the low-energy reach of
a next-generation dark matter experiment with a straightforward extension of
the analysis [480].

###  III.2 Charge-Only Analysis

Interactions from WIMP candidates below $\sim\mathrm{GeV/c^{2}}$ would produce
scintillation (S1) signals close to or below the typical low-energy threshold
of liquid xenon TPCs. This loss of efficiency can be bypassed by removing the
requirement that the S1 signal be detected at all, and leveraging the inherent
gain in the S2 signal [481, 466, 166, 480, 482, 483]. Relaxing the requirement
of an observed S1 allows events which resulted in even a single extracted
electron to be analyzed. This increased sensitivity to low-mass dark matter
candidates comes at the expense of recoiling particle discrimination (usually
from the S2/S1 ratio) and accurate determination of the z-coordinate (usually
from the delay between the S1 and S2 signals). While sometimes these analyses
still make use of S1 pulses to reject background events, when they do not
require an S1 to be present, they are commonly referred to as ‘charge-only’ or
‘S2-only’ analyses.

Thus far, charge-only analyses have been background-limited due to large
single- and few-electron backgrounds, which have yet to be reliably quantified
and mitigated [484, 485, 486, 487, 488, 489, 490, 482, 483]. The extended
drift volume of a next-generation detector may be subject to stronger electron
lifetime effects, but will also provide improved identification of S2s
originating from the bottom of the detector because of increased electron
diffusion (resulting in wider S2 pulses). Additionally, xenon contamination
from out-gassing or surface detachment of impurities will benefit from the
relative scaling of volume and surface area. Despite being background limited,
charge-only analyses have been used to set leading limits on dark matter
interaction rates, see Figure 18. The sensitivity of liquid xenon TPCs to
signals at the level of single electrons results in leading sensitivity to
sub-GeV WIMPs as well as other particle models. Specifically, charge-only
analyses are especially good for detecting electronic recoil signals, as their
S1 is much smaller than for a nuclear recoil of the same S2 size. A charge-
only analysis in a next-generation detector will further improve this
sensitivity over the current generation of xenon TPCs (see also Figure 15).

Figure 18: Shown are 90% confidence level upper limits (black lines with gray
shading above) on spin-independent dark matter-nucleus scattering with the
dark matter mass, $m_{\chi}$, on the horizontal axis. The thick black line is
the result from the XENON1T charge-only analysis. Other results are shown from
XENON1T in blue [82], LUX in orange [60], PandaX-II in magenta [376],
DarkSide-50 in green [466], XENON100 in turquoise [481, 123]. Dotted lines
show the XENON1T limit when assuming the $Q_{y}$ from NEST v2.0.1 [491] cut
off below 0.3 keV. Figure taken from Ref. [166].

###  III.3 General Dark Matter-Induced Atomic Responses

A dark matter particle with mass in the MeV–GeV range can deposit enough
energy in the collision with an electron in a xenon atom to ionise the target
and produce a detectable S2 signal in a TPC detector [390, 402]. This charge-
only analysis has mainly been performed with models where the interaction
between dark matter and electrons is mediated by a new hypothetical force
carrier such as the dark photon [467, 166, 482]. To avoid confusion, here the
dark photon acts as force carrier, as opposed to the analysis described in
subsubsection III.8.1, where the dark photon itself is the dark matter
candidate. In this framework, the total ionisation rate for a given xenon
orbital can be expressed in terms of a single target-dependent ionisation form
factor, which is a function of the initial and final state electron wave
functions [390, 402].

Xenon detectors can also probe more complex models, such as those where the
amplitude for dark matter scattering by a free electron, $\mathcal{M}$,
depends on the initial electron momentum [492]. These include models where
dark matter couples to electrons via magnetic dipole or anapole interactions.
By expanding $\mathcal{M}$ using effective theory methods similar to the ones
previously discussed in the context of dark matter-nucleon interactions (see
subsubsection II.5.1), reference [492] found that the most general form for
the total ionisation rate of a given xenon orbital is a linear combination of
four target-dependent atomic responses, which are defined in terms of initial
and final state electron wave function overlap integrals. Assuming that dark
matter is made of fermions with mass in the MeV-GeV range and interactions
dominated by electromagnetic moments of higher order, such as the electric and
magnetic dipoles or the anapole moment, reference [493] showed that liquid
xenon TPCs can shed light on whether dark matter is a Dirac or Majorana
particle. By using Monte Carlo simulations and a non-trivial extension of the
likelihood ratio test to the case where one of the hypotheses lies on the
boundary of the parameter space, only about $45-610$ signal events are
required to reject Majorana dark matter in favour of Dirac dark matter at 3
sigma confidence level.

###  III.4 Migdal Effect and Bremsstrahlung

Figure 19: Limits on the spin-independent light mediator dark matter-nucleon
interaction cross section at 90% confidence level using signal models from the
Migdal effect and Bremsstrahlung in the XENON1T experiment with the S1-S2 data
(blue contours and lines) and charge-only data (black contours and lines). The
solid and dashed (dotted) lines represent the lower boundaries (also referred
to as upper limits) and Midgal (Bremsstrahlung) upper boundaries of the
excluded parameter regions. Green and yellow shaded regions give the 1 and
2$\sigma$ sensitivity contours for upper limits derived using the S1-S2 data,
respectively. The upper limits on the spin-independent dark matter-nucleon
interaction cross sections from LUX [469] and XENON1T charge-only (elastic
nuclear recoil results) [166] are also shown. Figure taken from Ref. [494].
Figure 20: Spin-independent sensitivity for the electronic recoil-inducing
Migdal effect for the case of a heavy scalar mediator. The S1-S2 sensitivity
(black, solid) and the charge-only sensitivity (violet, solid) are shown. The
charge-only analysis improves the sensitivity by more than two orders of
magnitude with respect to the standard S1-S2 analysis (red, solid).
Experimental limits from similar analyses in LUX (blue, solid) [469], XENON1T
(green, solid) [166] and CDEX (gray, solid) [495] are also shown.

The progressive loss of the scintillation (S1) response with decreasing
nuclear recoil energy impedes the ability of liquid xenon TPCs to reach
sensitivity for sub-GeV dark matter masses. However, the standard dark matter-
nucleus interaction can also induce an inelastic atomic scattering signal. The
Migdal effect [496] predicts the ionization of the atom with some (small)
probability due to the sudden nuclear acceleration caused by the dark matter
collision, resulting in excitation and ionization processes from the electrons
[497]. Since electronic recoils produce a more detectable signal than nuclear
recoils, this channel enables liquid xenon detectors to reach dark matter
masses of order $\sim 100\,\mathrm{MeV/c^{2}}$ [498, 469, 494, 499], see
Figure 19. The sensitivity of liquid xenon detectors to sub-GeV dark matter
achieved using the Migdal effect is competitive with other detectors that are
dedicated to searches of light dark matter [465, 53, 55]. Figure 20 shows a
conservative projected Migdal sensitivity for a next-generation detector
assuming LZ detector parameters with an extended exposure of 300 tonne-years,
equivalent to e.g. a 56 tonne fiducial mass and 5.4 live-years. However, the
Migdal effect has not yet been observed directly in dark matter targets. A
dedicated calibration could be performed using a low-energy neutron beam
[500]. This could provide a direct test of the theoretical predictions of the
Migdal effect.

Similar to the Migdal effect, nuclear Bremsstrahlung searches leverage the
fact that in liquid xenon at low energies, electronic recoils produce a
stronger signal than nuclear recoils [472]. Bremsstrahlung searches consider
the emission of a photon from the recoiling atomic nucleus. In the atomic
picture this can be viewed as the dipole emission of a photon from a xenon
atom that has been polarized in the dark matter-nucleus scattering. In xenon,
the emission of the Bremsstrahlung photon is more heavily suppressed compared
to the Migdal effect and hence results in a weaker signal for all interaction
types [501]. The theoretical motivation and event rates for Bremsstrahlung
have been derived in [472] and searches using liquid xenon detectors have been
published in [469, 63, 502].

###  III.5 Hydrogen Doping

Kinematically, the large xenon nucleus (average mass 122 GeV/$c^{2}$) is not
well suited for an efficient transfer of energy from Galactic dark matter with
mass $\lesssim$1 GeV/$c^{2}$. As a result, nearly all of the resulting xenon
nuclear recoils fall below the energy threshold for detection. A possible
solution for enhancing the sub-GeV sensitivity of liquid xenon TPCs is to
dissolve a lighter species in the liquid xenon bulk [503]. In this
configuration, the lighter nucleus becomes the dark matter target, and the
xenon becomes the sensing medium.

This strategy exploits two of the primary advantages of the liquid xenon
medium. First, the high atomic number and density of liquid xenon provides
excellent self-shielding of external backgrounds from the central volume of
the detector. Such a suppression would not be possible in a similarly-sized
detector comprised of the light species alone. Second, the high yield of
detectable quanta (electrons and photons) resulting from low-energy particle
interactions makes xenon an ideal sensor for the recoiling light nuclei.

Having the lightest nucleus of any element, hydrogen is kinematically the best
candidate species for detecting interactions from sub-GeV dark matter and
astrophysical neutrinos [504]. The lone proton comprising hydrogen’s nucleus
additionally provides unique sensitivity to the spin-dependent dark matter
coupling to protons. Likewise, doping the xenon target with deuterium would
provide similar sensitivity to the neutron-only couplings. There are still
significant open questions concerning the actual feasibility of adding H2 to a
liquid xenon TPC. Drifting electrons in the detector’s gas space will be
cooled down by the hydrogen and therefore the electric field strength needed
to extract quasi-free electrons out of the liquid and into the gas space will
be increased [505]. Furthermore, the light yield of xenon electroluminescence
will be suppressed. Molecular species within the liquid space are also known
to quench the S1 light production. S1 as well as ionization signals for H2
mole fractions up to $5.7\,$% have been observed in a 26 atm gaseous xenon TPC
from 241Am $5.5\,$MeV alpha particles [506], although there is a reported loss
of about half of the S1 and electron signals for an H2 mole fraction of
$1.1\,$%. To broaden the understanding of the exact properties of such an
H2-doped liquid xenon TPC, further measurements are in progress. Helium is
also a viable option as the light mass target species, as it would not have
the signal quenching properties of H2, but its spin-dependent sensitivity
would be comparatively poor. Introduction of helium into the detector might
not be suitable if PMTs are used as a photosensor due to its ability to
diffuse into and degrade the PMT vacuum. However, helium could be considered
as a dopant if silicon photomultipliers (SiPMs) are used to detect light
signals instead of PMTs.

###  III.6 Upscattered Dark Matter

The sensitivity reach of liquid xenon detectors for sub-GeV dark matter is
significantly enhanced if some dark matter particles receive a kinematic boost
from up-scattering with cosmic rays [507, 508, 509, 431, 510, 511, 512]. This
process, often denoted Cosmic Ray Dark Matter (CRDM), will create a small
population of fast or even relativistic dark matter particles. This in turn
provides sensitivity to liquid xenon experiments to dark matter with masses
several orders of magnitude below 1 GeV. Cosmic ray up-scattered dark matter
is only a fraction of the Galactic dark matter population, with an abundance
and flux that depends on the dark matter-cosmic ray scattering cross section,
the local dark matter density, and the local interstellar spectrum of cosmic
rays. Relatively large cross section values of e.g. $\sigma_{\chi N}\gtrsim
10^{-31}{\rm{cm}}^{2}$ for $m_{\chi}=1$ GeV are required to have a notable
impact on the sensitivity of a typical liquid xenon detector. For spin-
independent interactions, liquid xenon experiments are competitive with and
complementary to existing neutrino experiments [507, 509, 422], which have
sensitivity in a similar region of parameter space. Additionally, cosmic-ray
upscattering extends the sensitivity of liquid xenon detectors to inelastic
dark matter models with mass splittings up to $\sim 100$ MeV [513].

Another upscattering mechanism extending the sensitivity of liquid xenon
detectors to dark matter masses down to keV scales is a process called “solar
reflection” [514, 515, 516, 517, 518]. This is based on the observation that
scatterings on thermal electrons and nuclei within the Sun can accelerate
light dark matter particles. This could give rise to an observable flux of
highly energetic particles in a liquid xenon TPC detector.

###  III.7 Dark Matter Annihilation Products

In several models of so-called “neutrino portal” dark matter, Galactic dark
matter self-annihilates into neutrinos [519, 520, 521, 522, 523]. These in
turn may be detected at direct detection experiments with high rates via
coherent elastic neutrino-nucleus scattering (see subsubsection V.1.1). A
next-generation liquid xenon detector would be sensitive to the flux of these
neutrinos for dark matter mass (respective neutrino energy) of
$[0.01-1]\,\mathrm{GeV/c^{2}}$ [524]. The sensitivity to this neutrino flux
would complement neutrino detectors such as Super-Kamiokande. Similarly, dark
matter that annihilates to a second component of nucleophilic, “boosted” dark
matter could also be discovered. A next-generation liquid xenon TPC will be
sensitive to the effective baryonic coupling of thermal boosted dark matter
that is as low as the weak interaction [524].

Alternatively, dark matter may annihilate or decay within the target volume of
future liquid xenon detectors [525]. Considering deposited energies up to a
few MeV, the relevant final states include annihilation into $\gamma\gamma$
and $e^{-}e^{+}$, and decays into $\gamma\gamma$, $\gamma\nu$ and
$e^{-}e^{+}$. Although the sensitivity obtained is not as high as the current
limits from cosmological considerations [526] and X-ray measurements [527],
this is a complementary approach in a well-understood background environment
and free of the large uncertainties typically present in indirect detection
experiments.

###  III.8 FIMPs and Super-WIMPs

Broad classes of non-WIMP dark matter candidates are Feebly Interacting
Massive Particles (FIMPs), which are produced by the thermal freeze-in
mechanism [528, 529], as well as Super Weakly Interacting Massive Particles
(super-WIMPs), which are produced by the decay of a freeze out-produced state
to a lighter state which is secluded from the Standard Model [530]. Both
classes share the feature that they couple to Standard Model particles with
cross sections far smaller than the Weak scale. These include fermions such as
sterile neutrinos [531] and gravitinos, both of which only couple to the
Standard Model gravitationally and thus are impossible to observe in a typical
direct detection experiment. However, both multi-GeV bosonic and fermionic
FIMPs and keV-scale bosonic FIMPs or super-WIMPs can couple to light Standard
Model particles in such way to be observed with low-background experiments
[532, 533, 534]. We note here that dark sectors with non-trivial dynamics, for
instance an early universe thermal phase transition, allow freeze-in
production of dark matter in the mass range $10\,\mathrm{keV/c^{2}}\lesssim
m\lesssim 100\,\mathrm{MeV/c^{2}}$ with relatively large scattering cross
section with nucleons and/or electrons, which blurrs the distinction between
FIMPs and WIMPs [535]. In the following, we give two examples of possible keV-
scale candidates, namely dark photons and axion-like particles, and discuss
related signals.

####  III.8.1 Dark Photons

Dark photons, more properly dark $Z^{\prime}$ vector bosons, are a possible
FIMP or super-WIMP candidate if they are stable over cosmological time scales
[532], and even if unstable, they can act as the mediator of dark
matter–Standard Model interactions [456]. Like axions, they are well motivated
in many UV constructions, and have the advantage over some other candidates of
having a mass which is naturally protected from large corrections. In addition
to production related to the usual thermal freeze-in or freeze-out, there is
also an attractive universal inflationary fluctuation mechanism that gives the
observed relic density depending only on the vector-boson mass and
inflationary scale [536]. A well-studied interaction of dark photons with the
Standard Model is via kinetic mixing [537] with hypercharge, and thus with
both the Standard Model photon and the Z-boson [538, 539]. As a consequence,
dark photons can be absorbed in a detector with a cross section proportional
to the photoelectric cross section. The expected signal is therefore a mono-
energetic electronic recoil peak at the dark photon mass. Direct detection
experiments have set competitive constraints on kinetic mixing parameter
$\kappa$ of dark photons, in a mass range from several to hundreds of keV
[540, 166, 470]. A next-generation detector such as the one discussed here
will have improved sensitivity to this mixing parameter $\kappa$. Further,
dedicated low-energy calibrations, for example using 37Ar diluted in the
liquid xenon, will help to improve the search in the keV mass range and reduce
the relevant detector-specific systematics to negligible levels for a
discovery experiment. Using a low-energy charge-only analysis (subsection
III.2), the sensitive mass range can be extended to the sub-keV level, see
e.g. [541]. In addition, XENON1T data already results in the current-best
limits on the solar emission of dark photons for some masses [542]. These
channels offer significant room for improvement with a next-generation
detector.

####  III.8.2 Axions and Axion-Like Particles

The QCD axion is a pseudoscalar Nambu-Goldstone boson originally proposed as a
solution to the strong CP problem of QCD [543, 544, 545]. The QCD axion is
also an excellent dark matter candidate [546, 547, 548, 549, 550]: As they
acquire their mass via non-perturbative QCD effects, they are stable on
cosmological timescales. Further, QCD axions offer a variety of well-motivated
production mechanisms. They couple to the Standard Model very weakly, with
couplings suppressed by a high energy scale $f_{a}$. In terms of this unknown
(but constrained) scale, QCD axions are predicted to have a mass $m_{a}\simeq
5.7\mu{\rm eV}(10^{12}{\rm GeV}/f_{a})$ [551]. The strict lower bound
$f_{a}\gtrsim{\rm few}\times 10^{7}{\rm GeV}$ (see [552]) arising from
astrophysical constraints [553, 554, 555, 556, 557] and the solar axion
helioscope CAST [558] implies that QCD axion dark matter is beyond the reach
of detectors like the one discussed here, and requires dedicated experiments.
However, axions produced in the Sun would have thermal spectra with keV
energies, and could be detected with a xenon TPC as discussed in subsection
VI.1.

Axion-like particles (ALPs) are a generalization of the QCD axion in that they
share many of the same properties, except that the strict relationship between
the mass and the scale $f_{a}$ is relaxed and that the various possible
couplings of ALPs to the Standard Model vary over greater ranges than the QCD
axion. In particular ALPs can be both much lighter than the QCD axion or much
heavier. These particles do not solve the strong CP problem, but nevertheless
are good dark matter candidates and can show up abundantly in theories for
physics beyond the Standard Model, in particular String Theory [559, 560, 561,
562, 563]. In a similar way to dark photons, ALPs can be detected via an
analogous process to the photoelectric effect [564]. For dark matter ALPs, the
resulting signal is again a mono-energetic spectrum of electronic recoils at
the ALP mass, with an event rate proportional to the square of the
dimensionless axion-electron coupling $g_{ae}$.

Due to their ultra-low electronic recoil background levels, liquid xenon TPCs
have placed the strongest constraints to date on keV ALP dark matter [565,
566, 567, 568, 569, 166, 470, 570, 482, 541]. Next-generation detectors
including the one discussed here will continue to set world-leading
constraints [1].

####  III.8.3 Solar Axions, Dark Matter, and Baryon Asymmetry

As discussed in subsection VI.1, a liquid xenon TPC can detect the QCD axion
and axion-like particles from the Sun for sufficiently large couplings of the
axion with electrons or photons. Such relatively large couplings correspond to
a small decay constant, $f_{a}$, of the axion. In this case, the cosmological
abundance of axions produced by conventional mechanisms [547, 548, 546, 571]
is too small for the axion to explain the observed dark matter. However, the
axion abundance can be large enough to be dark matter in the various scenarios
proposed in [572, 573, 574, 575, 576, 577, 578], with couplings that are
sufficiently large to be detected in the proposed detector.

In one such cosmological scenario for example [577], a non-zero field velocity
delays the onset of field oscillations, enhancing the axion abundance relative
to the conventional misalignment mechanism. For axion-like particles, this
field velocity can simultaneously explain the baryon asymmetry of the universe
[579]. Fitting the ratio of dark matter to baryon abundances predicts the
axion coupling in terms of its mass $m_{a}$

$g_{a\gamma}\simeq 2\times 10^{-11}c_{\gamma}~{}{\rm
GeV}^{-1}\left(\frac{m_{a}}{\rm meV}\right)^{1/2},$ (3)

where $c_{\gamma}$ is a model-dependent constant of order unity. For any axion
mass, this is much larger than the photon coupling of the QCD axion. A next-
generation liquid xenon TPC with a 1000 ton-year exposure can probe this
coupling down to $g_{a\gamma}\sim 3\times 10^{-11}{\rm GeV}^{-1}$ [580],
corresponding to $m_{a}\sim$ meV.

###  III.9 Asymmetric Dark Matter

Asymmetric Dark Matter (ADM) is one of the most motivated non-WIMP dark matter
candidate. Similar to the physics that sets the Standard Model cosmic baryon
abundance, Asymmetric Dark Matter posits that the dark matter relic density is
determined by a dark-sector particle-antiparticle asymmetry associated to a
new conserved quantity. In the most attractive scenarios where the Standard
Model is linked to the dark sector by connector interactions with non-trivial
Standard Model global quantum numbers, this dark asymmetry may be thought of
as dark “baryon” or “lepton” number, though more complicated cases involving,
e.g. flavor are also possible [581, 582, 583, 584, 585, 586, 587, 588, 589,
590, 591, 592]. Then, similarly to protons and baryon number, the lightest
symmetry-carrying state in the dark sector is cosmologically stable. Unlike
WIMPs, this dark matter particle is necessarily non-self-conjugate. If
$\eta_{B}$ and $\eta_{dm}$ are, respectively, the baryon and dark matter
asymmetries, and if like for baryons and anti-baryons the process of particle-
antiparticle annihilation is efficient in the dark sector, then the ratio of
the dark matter to the baryon densities is given by

$\frac{\Omega_{dm}}{\Omega_{B}}=\left|\frac{\eta_{dm}}{\eta_{B}}\right|\frac{m_{dm}}{m_{B}}~{}.$
(4)

Here, $m_{dm}$ is the mass of the lightest asymmetry-carrying dark matter
particle.

In many beyond the Standard Model theories, the asymmetries are naturally
equal and opposite, up to a computable coefficient which is of order $\sim 1$.
Thus, in this case we have an explanation of why the observed baryon and dark
matter densities are so close, $\Omega_{dm}\simeq 5\Omega_{B}$, if
$m_{dm}\sim{\rm few}~{}{\rm GeV}/c^{2}$. This strongly motivates searches for
dark matter particles in the $\sim 1-10~{}{\rm GeV}/c^{2}$ mass range. Though
less minimal, this mass range can be extended in more involved models with an
$\eta_{dm}/\eta_{B}$ ratio much different than 1. Since the freeze-out
mechanism is no longer setting the dark matter density, the scattering cross
section of the dark matter with the Standard Model can be smaller (or larger)
than that for WIMPs. Moreover, it is noteworthy that independently-motivated
theories, such as those based on “neutral naturalness” Twin Higgs [593] or
composite Higgs explanations of the LHC-data driven little hierarchy problem
for the Weak Scale also give non-self-conjugate dark-sector states at the
$1-10{\rm GeV}/c^{2}$ scale [594, 595, 371, 596].

In theories such as Twin Higgs the leading interactions of the individual ADM
particles with the Standard Model are due to Higgs-portal and/or kinetic
mixing with hypercharge, so often the direct-detection phenomenology is
similar to the case of WIMPs with these interactions, though without a
necessary link to a crossed-channel freeze-out process. In other cases the
leading higher-dimensional interaction of the individual ADM particles arises
from the “connector” interaction that determines the relation between
$\eta_{dm}$ and $\eta_{B}$ [597, 598, 599, 368, 600], or can sometimes be
related to a freeze-out process involving heavier states [601].

###  III.10 Composite Dark Matter

Similar to the very rich set of cosmologically stable composite states that
exist in the Standard Model sector, all or part of the dark matter density
might be in the form of bound states of individual dark matter particles. This
is a natural possibility, especially in asymmetric dark matter case, if the
dark matter is part of a dark sector as is in turn often so in explicit
constructions of physics beyond the Standard Model, or if the dark matter is
self interacting. These composites may be strongly-bound “dark nuclei” or
“dark nuggets” [602, 603, 604, 605, 240, 606, 607] of possibly extremely large
dark nucleon number, or they could be “dark atoms” [608, 609, 371] made of
dissimilar stable dark matter particles, or they could be weakly bound two-
body “dark-onium” states of identical or conjugate particles [302, 610, 611,
612]. Q-balls [613] can also be thought of as a form of composite state
carrying a conserved quantum number, the Q-ball description sometimes applying
to bound states of bosonic dark matter particles.

As well as implications for cosmological and indirect detection observations,
such composite states typically give rise to a wide variety of new or modified
signatures in direct detection experiments. One of the most studied cases is
that of large dark nuclei in which case the recoil spectrum is modified by a
characteristic quasi-universal dark sector form factor [240, 614, 615, 616].
Since there is often an $N^{2}$ ($N\gg 1$) dark nucleon number coherent
enhancement in the direct detection scattering cross-section which is not
present in the collider production of (pairs of) individual dark matter
particles, the usual collider bounds on direct detection cross sections can be
much weakened [240]. In addition since many of these composite states have low
lying single particle or collective excitations of parametrically small energy
splitting above the ground state, leading to a very rich set of possible
inelastic signatures depending on the exact model (subsection II.13). It is
also possible to have an enhanced diurnal modulation signal as a consequence
of the dissipative dynamics that is naturally associated with such composite
dark matter states [617].

###  III.11 Mirror Dark Matter

Closely related to both asymmetric and composite dark matter is the idea of
Mirror Dark Matter [618, 619, 620, 621]. This is the intriguing idea that an
exact copy of the Standard Model in the dark sector is invoked with an
unbroken symmetry between the two. Like some other asymmetric and composite
dark matter models, Mirror Dark Matter can generate signatures both in nuclear
recoils similar to those expected from $\sim 7\,\mathrm{GeV}/c^{2}$ WIMPs with
a cross section around $10^{-44}\,\mathrm{cm^{2}}$, as well as in electronic
recoils [622, 623, 624]. The strongest direct detection constraint on the
kinetic mixing currently comes from LUX [625], with a factor of $\sim$2 better
projected sensitivity for the current-generation detectors [541]. Mirror dark
matter as a hypothesis is potentially entirely falsifiable by the next-
generation liquid xenon experiment discussed here [626].

###  III.12 Luminous Dark Matter

It is possible to construct models where the dominant signal of the dark
matter originates from photons. These photons could be observed in direct
detection experiments as a monoenergetic line produced by dark matter decay
from an excited state [627, 628]. The excited state could be populated through
upscattering in or near the detector (and have short lifetimes $\sim 1\,\mu
s$) or in the Earth (lifetimes $\sim(1-10)$ s). For this scenario to work, the
elastic cross section needs to be small relative to the inelastic cross
section. A simple way to achieve this is with a magnetic dipole operator which
couples two distinct Majorana fermions that have a small, keV-order mass
splitting. Such “Luminous dark matter” was first proposed as a potential
explanation of the DAMA/LIBRA modulation [627] and has since been used to
explain the recent XENON1T excess [629]. While the former scenario is now
strongly constrained, the latter scenario will be confirmed or ruled out by a
next-generation liquid xenon experiment.

###  III.13 Magnetic Inelastic Dark Matter

A natural scenario where dark matter dominantly scatters off nuclei through an
inelastic transition in the dark sector (subsection II.13) is the case of a
magnetic dipole interaction [630]. This model relies on the fact that
fermionic dipole operators vanish for Majorana fermions. Thus, if a dark
matter Dirac fermion state is split into two nearly degenerate Majorana
fermions, an elastic dipole transition is forbidden, leaving the leading dark
matter interaction to be an inelastic magnetic dipole transition. Many
examples of dark matter models that can realize this scenario have been
studied, see e.g. [631, 632, 633, 634].

For magnetic inelastic dark matter, the sensitivity of a direct detection
experiment is modified by both the kinematic constraints of inelastic
transitions and by the dependence on the charge and magnetic dipole moment of
the target nuclei [630]. Depending on the dark matter mass splitting and the
size of the dipole moment, the excited dark matter state can also decay in the
detector, thus yielding both a nuclear recoil from the initial scatter and an
electronic recoil from the decay shortly thereafter. Searching for the photons
produced by this decay can be an additional handle on uncovering such a
scenario [635, 628]. A dedicated search has been performed by XENON100 [636],
with the proposed experiment providing significantly improved sensitivity not
only due to the lower background and longer exposure, but also due to the
larger size of the detector which translates into a sensitivity to longer
decay times.

###  III.14 Dark Matter around the Planck Mass

Figure 21: Per-nucleon spin-independent scattering cross sections and dark
matter masses that can be probed by liquid xenon dark matter detectors via
dedicated searches for multi-scatter signals. For cross sections above
$\sigma_{\rm MIMP}$ (horizontal green lines) one expects dark matter to
scatter multiple times in the detector while transiting. The maximum mass
reachable (vertical green lines) is limited by the total integrated flux of
dark matter in the detector over the run-time of the experiment. Masses up to
and beyond the Planck mass $\simeq 10^{19}\,\mathrm{GeV/c^{2}}$ may be probed
with a next-generation detector. Only smaller cross-sections and smaller
masses are probed by the standard single-scatter analyses (blue lines). Figure
taken from Ref. [141].

The observed local dark matter mass density could be made up of few but very
massive dark matter particles with masses around the Planck mass $\simeq
10^{19}\,\mathrm{GeV/c^{2}}$, as opposed to numerous lighter particles. Super-
massive species are motivated by supersymmetric and grand unified theories
[637], or production by Hawking evaporation of early universe primordial black
holes [638, 639]. In extensions of the WIMP scenario, with two thermal relics,
one of which has a finite lifetime, super-massive dark matter particles with
stronger interactions than typical electroweak WIMPs are naturally expected
[640], and provide excellent targets. The detection of any such particles
could help determine parameters of the early universe such as inflation [641],
or an epoch of early matter domination [642, 640] leading to efficient
primordial black hole production. Their existence could also imply new light
mediators beyond the Standard Model [643].

Due to the small number density, the flux of these particles through a given
detector would be very low, and thus any detection would both imply and
require a very high scattering cross section, such that almost all particles
impinging on the detector prompt a signal. When the cross section becomes high
enough that these particles would interact more than once in the detector,
discovery requires a dedicated analysis looking for multiple-scatter events.
Such events are typically discarded in WIMP-like dark matter analyses, leaving
many orders of magnitude of unexplored parameter space, see Figure 21. In this
multiple scattering regime, a next-generation liquid xenon experiment would be
capable of probing dark matter masses up to and beyond the Planck mass $\simeq
10^{19}$ GeV [141], in a complementary way to the range that could be probed
using dedicated neutrino experiments [644, 645, 646]. A dedicated search using
the DEAP-3600 liquid argon detector has already been published [647]. Clusters
of dark matter formed through self-attraction [603, 614, 648], such as “dark
blobs” or “dark nuggets” [603, 240, 615, 616] could exist at these high masses
and create tracks if they have sufficiently large cross-sections.

##  IV Double Beta Processes

###  IV.1 Neutrinoless Double Beta Decay of 136Xe

Among the main intellectual challenges facing the nuclear and particle physics
communities today are the neutrino-mass generation mechanism, the absolute
neutrino-mass scale, and the neutrino-mass spectrum. One of the best ways to
address these fundamental questions is to search for neutrinoless double beta
decay ($0\nu\beta\beta$) [649, 650, 651, 652]. The observation of this rare
nuclear decay process, forbidden in the Standard Model, would imply that the
lepton number is violated by two units and confirm the Majorana nature of the
neutrinos. It would also provide invaluable information about the dominance of
matter over antimatter in the universe, because two matter
particles—electrons—are emitted in the decay without the balance of the
corresponding antiparticles. Double beta decay can occur in the two xenon
isotopes 134Xe [653] and 136Xe, with the latter offering a larger sensitivity
to the $0\nu\beta\beta$ half-life ($T^{0\nu}_{1/2}$). The best experimental
constraint on the 136Xe $0\nu\beta\beta$ half-life, $T^{0\nu}_{1/2}>1.07\times
10^{26}\,\mathrm{years}$ (90% CL), is set by the KamLAND-Zen collaboration
using 136Xe dissolved in a liquid scintillator [654]. Among double-beta
experiments, only 76Ge, 82Se, 100Mo and 130Te offer $0\nu\beta\beta$ half-life
limits comparable to 136Xe [655, 656, 657, 658, 659, 660]. The EXO-200
collaboration demonstrated that better energy resolution and background
rejection can be achieved with a liquid xenon TPC [661], and the PandaX-II
collaboration conducted a first search using a dual-phase natural xenon
detector [662]. XENON1T recently demonstrated that energy resolutions below
$\sigma/\mu=1$% at $Q_{\beta\beta}$ can be achieved in liquid xenon TPCs used
for dark matter searches [102].

Figure 22: Predicted background spectrum around the $0\nu\beta\beta$ energy
region of interest (ROI) for a proposed next-generation dark matter
experiment. Rates are averaged over a fiducial volume (FV) containing
$5000\,\mathrm{kg}$ of liquid xenon with natural isotopic abundance. Bands
indicate $\pm~{}1\sigma$ uncertainties. The orange line represents a
hypothetical signal corresponding to $T_{1/2}=2\times
10^{27}\,\mathrm{years}$. Figure from Ref. [663].

A next-generation liquid xenon detector will contain multiple tonnes of the
136Xe isotope, either at the natural abundance of 8.9%, or, as a possible
upgrade, using enriched xenon. Given a TPC design optimized for WIMP searches,
a detector instrumenting $\sim 40,000\,\mathrm{kg}$ of non-enriched xenon can
already improve the sensitivity to $0\nu\beta\beta$ decay by more than one
order of magnitude over current limits, without any interference with its
primary dark matter science goal. Taking advantage of the excellent self-
shielding of liquid xenon, the material-induced gamma ray background can be
suppressed below the total intrinsic background rate (subsection VII.2).
Figure 22 shows the relevant sources of background with a hypothetical
$0\nu\beta\beta$ signal for the innermost $5000\,\mathrm{kg}$ of natural xenon
in the TPC of a proposed next-generation detector [663]. The background from
material-induced gamma rays will be further reduced in more massive detectors
than the one simulated in Figure 22.

Figure 23: Efficiency of $0\nu\beta\beta$ signal acceptance and background
rejection as a function of the minimum distance for individual reconstruction
of energy depositions. The three signal lines (blue) compare different energy
and angular distributions for the $0\nu\beta\beta$ signal based on a back-to-
back electron emission, a mass mixing (MM) mechanism and a right-handed
current (RHC) model. The background rejection efficiency is shown for
$\gamma$s (red) and electrons (green) with
$E=Q_{\beta\beta}=2457.8\,\mathrm{keV}$. The vertical line (gray) corresponds
to the value assumed here. Bands indicate $\pm~{}2\sigma$ uncertainties [663].
Figure 24: Predicted median $T_{1/2}^{0\nu}$ sensitivity at 90% CL as a
function of the exposure time for a next generation TPC detector containing
$40\text{\,}\mathrm{t}$ of liquid xenon with natural isotopic abundance. The
band indicates the sensitivity range between a baseline radio purity scenario
at a depth of $3500\text{\,}\mathrm{m}$ water equivalent to a scenario with
neutrino dominated background. Sensitivity projections for future 136Xe
$0\nu\beta\beta$ experiments [663, 664, 665, 666, 667] are shown for
comparison. Figure based on the one in [663].

Selecting ultra-low background materials for construction can further reduce
the material contribution as well as the background rate from 222Rn, which
emanates from material surfaces into the target volume. A sufficiently deep
laboratory suppresses cosmogenic background sources, such as the in-situ
activation of 136Xe by muon-induced neutrons (producing 137Xe) [668, 669],
down to the limit set by electron scattering of solar 8B neutrinos. Optimizing
the detector design for an improved spatial resolution would allow to further
exploit background rejection, based on the different topology of background
and signal events caused by bremsstrahlung radiation, as shown in Figure 23.
Combining these measures, the experimental sensitivity can be further enhanced
to make a next-generation dark matter detector competitive to dedicated next-
generation, tonne-scale $0\nu\beta\beta$ experiments, as shown in Figure 24.
Naturally, a larger target mass would allow further gains in self-shielding
and even more competitive sensitivity to rival the next generation of
dedicated experiments. Isotopic enrichment in 136Xe would further improve this
sensitivity, as it linearly increases the signal, although this also increases
the background rate from the two-neutrino double beta decay ($2\nu\beta\beta$)
of 136Xe and $\beta$-decay of 137Xe.

In addition, there exist mechanisms of $0\nu\beta\beta$ decay where the
lepton-number violation necessary for the decay is due to a lepton-number
violating mechanism other than the standard scenario of exchange of light
neutrinos. A large fraction of these models can be tested using an effective
field theory approach [670, 671, 672, 673, 674, 675, 676, 677, 678, 679] which
in the case of chiral EFT also provides a hierarchy for the relevant nuclear
matrix elements [680, 681, 682, 683, 684, 685, 686, 687, 688, 689], along
similar lines as described in subsection II.5 for dark matter. These
theoretical models can thus be used as a low-energy test of new physics
phenomena that complements high-energy searches at accelerators.

Besides the search for $0\nu\beta\beta$ decay, precision measurements of the
$2\nu\beta\beta$ decay can reduce the experimental uncertainty on the
$2\nu\beta\beta$ nuclear matrix element [690] and constrain the underlying
nuclear theories [691, 692, 652]. This is especially relevant regarding
$0\nu\beta\beta$ decay, because predictions of nuclear matrix elements
disagree by a factor three or more, severely limiting the interpretation of
current limits and the physics reach of future searches, for instance in terms
of neutrino masses [692, 652]. The nuclear many-body methods used to calculate
$0\nu\beta\beta$ nuclear matrix elements are generally the same that are also
used to obtain the nuclear structure factors in subsection II.6. The nuclear
shell model among other more phenomenological approaches yields most
predictions [693, 694, 695, 696, 697, 698, 699, 700, 678, 701], complemented
by recent ab initio studies [702, 703, 704, 689]. A precise $2\nu\beta\beta$
spectrum shape measurement can provide insights towards reliable
$0\nu\beta\beta$ nuclear matrix element calculations [705]. In addition,
precision measurements of $2\nu\beta\beta$ decay can also be used to probe new
physics. For example, right-handed lepton currents affect the angular and
energy distributions of the decay [706], MeV-scale sterile neutrinos can be
searched for through kinks in the $2\nu\beta\beta$ spectrum [707, 708], and
neutrino self-interactions can leave an imprint on the spectrum as well [709].
Because lepton number is not necessarily violated in $2\nu\beta\beta$ decay,
this is independent of the neutrino nature and can be used to constrain or
pinpoint properties of both Majorana and Dirac neutrinos.

###  IV.2 Double Electron Capture on 124Xe

Similar to double beta decay, double electron capture is a second order Weak
Interaction process [710, 711] with extremely long half-lives. Two electrons
are captured from the atomic shell and two protons are converted into
neutrons. In the Standard Model decay, two neutrinos carrying virtually the
total Q-value are emitted and leave the active volume undetected ($2\nu$ECEC).
The measurable signal is constituted by the atomic de-excitation cascade of
X-rays and Auger electrons that occurs when the vacancies of the captured
electrons are refilled. In a liquid xenon detector, this cascade is measured
as a single resolvable signal at $64.3\,\mathrm{keV}$ for the double K-capture
[712] as the most likely case [713]. The half-life of this decay is of great
interest with regard to nuclear matrix element calculations, as it provides a
benchmark point from the proton-rich side of the nuclide chart [714, 715,
716]. A precise measurement would help to narrow down uncertainties, which in
turn have implications on the neutrino mass scale derived from
$0\nu\beta\beta$ as discussed in subsection IV.1.

Following hints in XMASS [717], the half-life of the 124Xe double K-capture
has recently been measured by XENON1T [718]. At
$T_{1/2}^{2\nu\text{KK}}=(1.8\pm 0.5_{\text{stat}}\pm 0.1_{\text{sys}})\times
10^{22}\,\mathrm{years}$, it agrees with recent theoretical predictions [714,
715, 716]. For comparison, this is about one order of magnitude slower than
the $2\nu\beta\beta$ decay of 136Xe due to the small overlap of the K-electron
with the nucleus. Assuming a natural isotopic abundance similar to XENON1T, a
next-generation experiment would record on the order of 10,000 events in its
full exposure. This will allow a precision measurement of the double K-capture
half-life to the percent level. Additionally, an observation of the KL-capture
and LL-capture would be within reach [713]. Their measurement would help to
decouple the nuclear matrix element from phase-space factors.

Beyond the Standard Model, the double electron capture on 124Xe without
neutrino emission ($0\nu$ECEC) can complement $0\nu\beta\beta$ in addressing
fundamental questions about the mass and nature of the neutrino [719, 720]. To
conserve energy and momentum, $0\nu$ECEC is possible if the 124Xe decay
populates an excited state of the 124Te daughter nucleus, so that the final
energy matches the initial one. This scenario would allow a resonant
enhancement of this channel, which would be needed to provide accessible half-
lives [721]. A suitable daughter state exists, but current measurements of the
Q-value indicate only an approximate match of the 124Te level, two-hole
energy, and Q-value that would only provide a minor enhancement [712]. If this
decay is realized, the experimental signature contains multiple $\gamma$-rays
emitted in a cascade, so coincidence techniques could increase experimental
sensitivity [722].

###  IV.3 Other Double-Beta Processes

The 124Xe $Q$-value of 2857 keV also allows second-order decays involving
positrons [723]. Examples are the as-yet unobserved Standard Model
$2\nu$EC$\beta^{+}$ and $2\nu\beta^{+}\beta^{+}$ decays, as well as the
hypothetical $0\nu$EC$\beta^{+}$ and $0\nu\beta^{+}\beta^{+}$ decays. The
decay $2\nu$EC$\beta^{+}$ is predicted to have a half-live one order of
magnitude above that of $2\nu$ECEC [724]. Exploiting the coincidence signature
of the positron annihilation and the atomic de-excitation cascade, this decay
could already be within reach of LZ and XENONnT [725, 722] and be a sure
signal in the next-generation detector. The $2\nu\beta^{+}\beta^{+}$ decay is
expected to be several orders of magnitude slower [724]. It exhibits a unique
signature with five point-like ionization clusters, located in the same plane
with the central vertex [726].

On the neutrinoless side, $0\nu$EC$\beta^{+}$ would be favoured in the absence
of resonance enhancement for $0\nu$ECEC, even though the decay rate is
expected to be suppressed by about three orders of magnitude with respect to
the $0\nu\beta\beta$ decay of 136Xe [727, 724, 728, 729]. Here, the current
lower limits on the half-lives are on the order of $10^{21}$ years [730, 731,
732]. These would be accessible to a large extent in a next-generation liquid
xenon experiment when exploiting the coincidence signature of the atomic
relaxation, the mono-energetic positron, and the two subsequent back-to-back
$\gamma$-rays. Moreover, limits on half-lives of neutrinoless second-order
weak decays in 124Xe could complement $0\nu\beta\beta$ searches in 136Xe and
other nuclei and help to identify the decay mechanism [733, 734, 735, 722].
These channels provide an exciting avenue for the next-generation detector
discussed here to complement ongoing searches for double-weak processes.

##  V Neutrinos for Astrophysics

Many sources of astrophysical neutrinos exist [736, 737], and those in the
relevant energy range for xenon experiments are shown in Figure 25 [738].
Overall, the flux is dominated by pp solar neutrinos, which will be the
leading source of low-energy electronic recoils. Atmospheric neutrinos have
the highest energy and can induce sizable nuclear recoils of tens of keV
through Coherent Elastic Neutrino-Nucleus Scattering; their measurement is a
goal of the next-generation liquid xenon experiment. A prominent source is 8B
solar neutrinos as they lie in a sweet spot: their energy is high enough that
nuclear recoils are visible in dedicated xenon TPCs, while their flux is so
large that a first measurement can be achieved already with the currently-
running generation of liquid xenon experiments.

Figure 25: Astrophysical neutrino fluxes span many orders of magnitude in flux
and energy. This explains the different exposures and energy thresholds
required to measure them. Figure adopted from Ref. [738].

A next-generation detector will make important advances in neutrino
astrophysics, covering low-energy realms that are out of the reach of
experiments such as Hyper-K [739] or DUNE [740]. This section outlines the
scientific scope of the next-generation detector, including solar,
atmospheric, and supernova neutrinos, and discusses the unique interaction
channels that this detector will be sensitive to.

###  V.1 Neutrino Interactions

Neutrinos can interact with liquid xenon through Charged Current (CC) and/or
Neutral Current (NC) interactions to produce detectable electronic and nuclear
recoils. The neutrino-induced rate is

$\frac{{\rm d}R}{{\rm
d}T_{R}}=\mathcal{N}\times\int_{E_{\nu}^{min}}{\phi\left(E_{\nu}\right)\times\frac{{\rm
d}\sigma(E_{\nu},T_{R})}{{\rm d}T_{R}}{\rm d}E_{\nu}}$ (5)

where $\mathcal{N}$ is the number of target nuclei or electrons per unit of
mass of detector material (for nuclear and electronic recoils, respectively),
$\phi\left(E_{\nu}\right)$ is the neutrino flux as a function of the neutrino
energy as shown in Figure 25 [738], and $E_{\nu}^{min}$ is the minimum
neutrino energy required to generate a recoil at an energy $T_{R}$. For a
nuclear recoil, in the limit where $m_{N}\gg E_{\nu}$, the minimum energy is
given by

$E_{\nu}^{min}=\sqrt{\frac{m_{N}T_{R}}{2}},$ (6)

whereas in the case of an electronic recoil, it is given by

$E_{\nu}^{min}=\frac{1}{2}\left(T_{R}+\sqrt{T_{R}\left(T_{R}+2m_{e}\right)}\;\right)$
(7)

The differential cross section depends on the nature of the interaction. In
the next two sections, we discuss Coherent Elastic Neutrino-Nucleus Scattering
and the Electroweak interaction, which constitute the major contributions to
the potential detectable signal for liquid xenon detectors.

####  V.1.1 Coherent Elastic Neutrino-Nucleus Scattering

In the Standard Model, elastic neutrino-nucleon scattering proceeds only
through neutral current interaction with the exchange of a $Z$-boson. The
resulting differential neutrino-nucleus cross section as a function of the
nuclear recoil energy $T_{R}$ and the incoming neutrino energy $E_{\nu}$ is

$\displaystyle\frac{{\rm d}\sigma(E_{\nu},T_{R})}{{\rm d}T_{R}}$
$\displaystyle=\frac{G^{2}_{f}}{\pi}m_{N}\left(Zg_{v}^{p}+Ng_{v}^{n}\right)^{2}$
$\displaystyle\times\left(1-\frac{m_{N}T_{R}}{2E^{2}_{\nu}}\right)F^{2}(T_{R}),$
(8)

where $m_{N}$ is the target nucleus mass, $G_{f}$ is the Fermi coupling
constant, $N$ the number of neutrons, $Z$ the number of protons,
$g_{v}^{n}=-1/2$, and $g_{v}^{p}=1/2-2\sin^{2}\theta_{w}$, where $\theta_{w}$
the Weak mixing angle. Because $\sin^{2}{\theta_{w}}\simeq 0.23$, the cross
section scales roughly with the number of neutrons squared. The nuclear form
factor $F(T_{R})$ describes the loss of coherence due to the internal
structure of the nucleus. For momentum transfers less than the inverse of the
size of the nucleus, the coherence condition is largely satisfied and
$F(T_{R})\rightarrow 1$. In lieu of experimental data on the neutron
distribution in the nucleus, a typical parameterization is the Helm form
factor [219] that is also commonly used for WIMP direct detection [741, 152].
Note that Eq. (V.1.1) gives the leading form of the cross section, keeping
only the coherently enhanced part of the vector interaction; Ref. [742] has
the complete expressions.

Figure 26: Nuclear recoil event rates from astrophysical neutrinos via
CE$\nu$NS. 8B solar neutrinos are expected to be measured first in the
currently-running generation of experiments. The detector proposed here
targets a precision measurement of that flux, and a first measurement of the
atmospheric neutrino flux.

In effect, this Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS) [743]
increases the cross section for heavy nuclei such as xenon, while pushing the
recoil energy spectrum to small energies of keV or less. Given the excellent
performance of liquid xenon detectors at such low energies, this channel thus
opens the possibility to detect neutrinos from astrophysical sources with a
target mass that is modest in comparison to other neutrino detectors, see
Figure 26. In addition to providing the possibility to measure some
astrophysical neutrino sources for the first time, the fact that this
interaction is flavor-independent provides complementary information for
sources that have been measured by other neutrino detectors [744, 745].

####  V.1.2 Electroweak Interaction

The neutrino-electron electroweak interaction proceeds through both Charged
Current ($W$-boson exchange) and Neutral Current ($Z$-boson exchange)
interactions. In the free electron approximation, the resulting differential
neutrino-electron cross section as a function of the electronic recoil energy
$T_{R}$ and the incoming neutrino energy $E_{\nu}$ is

$\displaystyle\frac{{\rm d}\sigma(E_{\nu},T_{R})}{{\rm d}T_{R}}$
$\displaystyle=\frac{G^{2}_{f}m_{e}}{2\pi}\Bigg{[}\left(g_{v}+g_{a}\right)^{2}+\left(g_{a}^{2}-g_{\nu}^{2}\right)\frac{m_{e}T_{R}}{E_{\nu}^{2}}$
$\displaystyle+\left(g_{v}-g_{a}\right)^{2}\left(1-\frac{T_{R}}{E_{\nu}}\right)^{2}\Bigg{]},$
(9)

where $m_{e}$ is the electron mass, $G_{f}$ is the Fermi coupling constant,
$g_{v}=2\sin^{2}{\theta_{w}}-1/2$ and $g_{a}=1/2$ are respectively the
vectorial and axial coupling, and $\theta_{w}$ is the weak mixing angle. In
the context of $\nu_{e}+e\rightarrow\nu_{e}+e$ scattering, the interference
coming from the addition of the charge current leads to a shift in axial and
vectorial couplings such as: $g_{v}\rightarrow g_{v}+1$ and $g_{a}\rightarrow
g_{a}+1$. This is then contributing to enhance the
$\nu_{e}+e\rightarrow\nu_{e}+e$ scattering cross section with respect to the
$\nu_{\tau,\mu}+e\rightarrow\nu_{\tau,\mu}+e$ cross section by about one order
of magnitude. Further, neutrino oscillations also are an important factor that
needs to be taken into account to properly calculate neutrino-induced event
rates.

Low-energy electronic recoil starts to deviate from the simple free electron
approximation below a few tens of keV. Therefore, it is important to include
corrections for the stepping of atomic shells and atomic binding. This has
been included into the calculation by using the Relativistic Random Phase
Approximation (RRPA) as presented in [148]. The inclusion of these atomic
effects result in a reduction of the neutrino-induced electronic recoil event
rate below $\sim 5$ keV. Importantly, this reduces the neutrino background in
the $[2-10]\,\mathrm{keV}$ energy range by $\sim$22%. Figure 27 shows the
electronic recoil event rate for different neutrino flux contributions. The
wavy features in the energy spectra are due to the stepping of atomic shells,
smoothed by detector resolution effects.

###  V.2 Solar Neutrinos

Experimental studies of solar neutrinos date back to over half of a century
ago [746]. The primary goal of these experiments is to measure the different
components of the solar neutrino flux, in order to provide an understanding of
the physics of the solar interior. Many different types of solar neutrino
experiments were operated, and they have evolved in their size and scientific
scope since the original experiments [747]. The combination of all solar
neutrino data with terrestrial experiments that study neutrinos in the same
energy range has led to the LMA-MSW solution to neutrino flavor transformation
from the Sun to the Earth [748]. With this solution, at low energies $\lesssim
5\,\mathrm{MeV}$, vacuum oscillations describe the neutrino flavor
transformation, and the electron neutrino survival probability is $\gtrsim
50\%$. At energies $\gtrsim 5\,\mathrm{MeV}$, matter-induced transformations
describe the flavor transformation, with a corresponding survival probability
of $\gtrsim 1/3$.

However, in spite of all the theoretical and experimental progress in the
field of solar neutrino physics over the past several decades, there are still
outstanding questions that surround some of the data. For example, three
experiments (Super-Kamiokande [749], SNO [750], and Borexino [751]) that are
sensitive to electronic recoils from neutrino-electron elastic scattering find
that, at electronic recoil energies of a few MeV, the data are $\sim 2\sigma$
discrepant relative to the prediction of the best-fitting LMA-MSA solution. In
addition, the recent measurement of the solar mass-squared difference from
solar neutrino data, in particular from the day-night Super-Kamiokande data
[749], is discrepant at the $\sim 2\sigma$ level relative to that measured by
KamLAND [752]. Non-standard interactions provide a possible solution to this
discrepancy [753].

Figure 27: Electronic recoil scattering rates from solar neutrinos. The step-
wise decrease in event rate towards low energies corresponds to the energy
levels of electrons in the xenon atom. Figure from Ref. [754].

Another outstanding question relates to the measured neutrino flux, and how it
is able to inform the physics of the solar interior. There is a long-standing
problem with standard solar models (SSMs) and predictions of the abundances of
heavy elements, or metals, in the Sun. Older abundance calculations [755]
relied on many simplifying assumptions, but nevertheless fit solar observables
well, in particular helioseismology data. More recent calculations however
[756], while more sophisticated in construction, were ultimately worse fits to
the data [756, 757, 758, 759]. These calculations are referred to as high-Z
and low-Z models respectively, according to their relative predicted
metallicities. Their disagreement is known as the solar abundance problem
[760], and has not yet been resolved. A global analysis of all solar neutrino
fluxes remains inconclusive [444]. A step towards resolving this problem will
be to accurately measure the flux of solar neutrinos from the CNO nuclear
fusion cycle, first achieved by Borexino [761], which is possible with the
experiment discussed here (subsubsection V.2.4).

####  V.2.1 Boron-8 Solar Neutrinos (NR)

Combined with the neutrino-electron scattering data from SNO, Super-Kamiokande
and Borexino, precision measurements of 8B neutrino induced CE$\nu$NS in a
next-generation liquid xenon detector will constrain the $\nu_{e}$ survival
probability in the 5–15 MeV range. A significant deficit from the theoretical
prediction can be interpreted as evidence of active-to-sterile neutrino
oscillation [156]. A next-generation liquid xenon detector will provide an
independent measurement of the neutral current component of the solar 8B
neutrino flux, with an expected event rate of $\sim 90$ events per tonne-year
[1], measured to be right in between that predicted by the low and high
metallicity Standard Solar Model [762, 751, 473].

####  V.2.2 Hep Solar Neutrinos (NR)

A future next-generation detector may detect neutrinos from the minor branch
of the pp chain that generates the most energetic neutrinos via the reaction
3He + p $\rightarrow^{4}$He + e- \+ $\nu_{e}$. Along with 8B neutrinos,
neutrinos from this hep reaction also undergo adiabatic conversion in the
solar interior. Neutrinos from the hep reaction have not been directly
identified in solar neutrino experiments; the best upper bound from the SNO
experiment is $\sim 4$ times greater than the SSM prediction [763].

####  V.2.3 pp Solar Neutrinos (ER)

The possibility to use liquid xenon as a low-energy solar neutrino detector by
means of $\nu+e$ scattering was suggested in [764] but only now is becoming a
realistic measurement. A next-generation liquid xenon detector will provide a
new, high-precision observation of the electronic recoil energy spectrum
induced by elastic scattering of pp neutrinos, see Figure 27. This, in turn,
will improve measurements of the Sun’s (neutrino) luminosity. The pp neutrino
flux was first indirectly identified as a component of the Gallium data, and
Borexino was the first experiment to make a measurement of the spectral energy
distribution of electronic recoil events induced by pp neutrinos [765]. The
Borexino measurement uncertainty on this component is now down to $\lesssim
10\%$ [751]. Further improving upon the measurement of this component will
better constrain the “neutrino luminosity” of the Sun because pp neutrinos
account for 86% of all solar neutrino emission [766]. Projections for a next-
generation xenon experiment indicate that the pp neutrino flux can be measured
to 0.15% uncertainty with 300 tonne-years of exposure. Combined with a 1%
measurement of the next-largest component, 7Be, such a detector could
ultimately achieve 0.2% uncertainty in the neutrino-inferred solar luminosity
[767]. This will also have the important consequence of constraining
alternative sources of energy production in the solar interior [754].

####  V.2.4 CNO Neutrinos (ER)

The flux of CNO neutrinos from the Sun makes up less than 1% of the Sun’s
total neutrino luminosity but is sensitively dependent on the solar
metallicity, with higher metallicity models predicting a higher CNO component.
A precise measurement of the CNO flux would provide the necessary information
to discriminate between the low and high-Z calculations, thereby resolving the
solar abundance problem directly. The very first measurement of CNO neutrinos
was achieved recently by Borexino [761], though with insufficient statistics
to yet conclusively resolve the abundance problem.

Due to the small CNO luminosity fraction, measuring the CNO flux in a xenon
TPC will require large experimental exposures and well controlled backgrounds.
A next-generation liquid xenon detector would be capable of measuring the 13N
and 15O fluxes individually (20-25%) even in the presence of the
$2\nu\beta\beta$ decay background from 136Xe [767]. Significant improvements
to the precision of these measurements can be achieved through depletion of
the natural xenon target from the 136Xe isotope [754], while negating the
possibility of a $0\nu\beta\beta$ search (subsection IV.1). Hence, both a
natural xenon target and a 136Xe-depleted target provide exciting physics
opportunities for a next-generation liquid xenon detector.

####  V.2.5 Neutrino Capture on Xenon-131 and Xenon-136

Solar neutrinos may also be observed through the neutrino capture process on
xenon: $\nu_{e}+\,^{A}_{54}\textrm{Xe}\to\,^{A}_{55}\textrm{Cs}^{(*)}+e^{-}$
[768]. The isotopes 131Xe and 136Xe have sufficiently low reaction thresholds
of $Q=355$ keV and $Q=90.3$ keV for capture of all solar neutrino species. The
prompt electron gives an electronic recoil with an energy that is offset from
that of the captured neutrino as $E_{e}=E_{\nu}-Q-E_{\rm ex}$, where $E_{\rm
ex}$ is the excitation energy of the resulting Cs nucleus.

The possibility of tagging neutrino capture events which populate excited
states in the product Cs nuclei has been explored in [769]. The emission of
$\gamma$-rays and/or conversion electrons during relaxation of the excited
nuclear state in conjunction with the primary fast electron provides
opportunities for background rejection.

An especially high suppression of background can be achieved if a delayed
coincidence signature in the Cs de-excitation could be exploited. The product
isotopes 131Cs and 136Cs are unstable with half-lives 9.7 d and 13.0 d,
respectively. Detection of the corresponding electron-capture and
$\beta$-decay signatures which occur long after the initial capture event may
also be possible. With abundances of 21.2% and 8.9%, one expects 0.6 and 0.7
neutrino capture events per tonne of natural Xe per year on 131Xe and 136Xe,
respectively [769].

###  V.3 Atmospheric Neutrinos (NR)

The collisions of cosmic rays in the atmosphere produce neutrinos over a wide
range of energies. A precise determination of this atmospheric neutrino flux
depends on several factors, including the cosmic-ray flux at the top of the
Earth’s atmosphere, the propagation of cosmic rays through the atmosphere, and
the decay of the mesons and muons as they propagate though the atmosphere to
Earth’s surface. Since the flavors of neutrinos that are produced in the
decays are known, theoretical models accurately predict the ratio of the
flavor components of neutrinos across all energies. However, the
normalizations of the fluxes differ depending upon the theoretical input.

Figure 28: The differential fluxes of atmospheric neutrinos that are
accessible by various experiments, normalized such that the area under the
curves is equal to unity. The flux accessible to a next-generation xenon
experiment (labeled G3 LXe) is shown in blue, and reaches much lower in energy
than Super-Kamiokande currently does (shown as solid violet). Figure from Ref.
[150].

While the atmospheric neutrino flux for energies $\gtrsim 1\,\mathrm{GeV}$ has
been well studied by the aforementioned experiments, the low-energy flux of
atmospheric neutrinos, $\lesssim 100\,\mathrm{MeV}$, is difficult to both
model and measure [770]. The resulting energy spectrum of neutrinos
corresponds to that from muon and pion decay at rest, but the absolute
normalization of the flux is less well constrained, due to uncertainties that
arise from several uncertain physical processes. A next-generation dark matter
detector will measure this neutrino flux at so-far unexplored low energy, see
Figure 28. The flux at these energies is impacted by the geomagnetic field and
modulated by the solar cycle, but the corresponding effects, namely a larger
modulation at higher latitudes but an overall smaller flux at lower latitudes
[771] will be challenging to discern, given the low interaction rates. In
fact, measuring atmospheric neutrinos will require an exposure of order 700
tonne-years [150], thus providing a benchmark target exposure for a next-
generation liquid xenon observatory.

###  V.4 Supernova Neutrinos (NR)

The next supernova event in the Milky Way or in nearby galaxies will provide
unprecedented information on the physics of neutrino propagation from the
supernova core [772, 773]. For example, large water Cherenkov detectors such
as Super-Kamiokande will measure thousands of events, mostly through the
charged-current inverse beta decay channel, and hundreds of events through
various other elastic and inelastic channels [774, 775, 776]. Dark matter
detectors can play an important role in supernova neutrino astrophysics
through their sensitivity to supernova neutrinos via coherent elastic
scattering, yielding complementary information for example on the nature of
stellar collapse and the explosion energy of the supernova [777, 778].

####  V.4.1 Galactic Supernova Neutrinos

Current and future liquid xenon dark matter detectors are uniquely sensitive
to neutrinos of all flavors through CE$\nu$NS [779, 780], whether from core-
collapse (Type II) [781, 782] or thermonuclear runaway fusion (Type Ia) [783].
This provides a calorimetric measurement of the explosion energy going into
neutrinos, independent of oscillation effects [782]. The physics available
with the statistics collected by a next-generation liquid xenon detector would
complement that of larger, dedicated neutrino observatories: in a next-
generation detector, there are of order 100 expected events from a core-
collapse supernova within 10 kpc of Earth [782].

CE$\nu$NS is the primary detection interaction from galactic neutrinos in
liquid xenon detectors, but charge current reactions are also possible. A
supernova within 10 kpc could produce a handful of charge current interactions
in a next-generation detector, particularly interacting with the 136Xe isotope
[784, 785]. Even the large water Cherenkov veto volumes that typically
surround these detectors may record notable supernova neutrino event rates
[786].

Also possible are inelastic charged current interactions of the supernova
electron neutrinos with the xenon nuclei. Such interactions, while creating an
electron in the final state, leave the post-interaction target nucleus in an
excited state. Its subsequent de-excitation produces, among other particles,
gamma rays and neutrons [787, 788]. The electron and the de-excitation gamma
rays give rise to electronic recoils. On the other hand, neutrino-induced
neutrons ($\nu$I$n$) from the de-excitation of the final state nucleus can
create, through their multiple scattering on the xenon nuclei, additional
xenon nuclear recoil events. The rate of $\nu$I$n$ nuclear recoil events is
generally low compared to CE$\nu$NS nuclear recoils. However, it may still be
possible to identify these $\nu$I$n$ nuclear recoil events using the
capability of large liquid xenon detectors to tag neutrons which undergo
multiple scatterings, both within the TPC and using the external neutron veto
detector. Detection and identification of both electronic and nuclear recoils
from supernova $\nu_{e}$ charged current interactions, together with the
nuclear recoil events from neutral current CE$\nu$NS, may thus provide an
additional probe of the distribution of the total supernova explosion energy
going into different neutrino flavors.

Observations of astrophysical neutrinos are complementary to terrestrial
experiments which are sensitive to MeV-scale neutrinos [774]. The recent
detection of CE$\nu$NS has provided novel bounds on new physics, for example
in the form of kinetic mixing, hidden sector models, flavor models, and
sterile neutrinos [743]. Future measurements of supernova neutrinos at dark
matter detection experiments can improve on this sensitivity [789], providing
further information on new physics models (see also section VI).

####  V.4.2 Pre-Supernova Neutrinos

Figure 29: For a next-generation liquid xenon dark matter experiment with an
assumed target mass of 50 tonnes, the expected number of pre-supernova
neutrinos above the detection threshold is shown as function of time until the
core collapse, for two different stellar masses at a distance of 200 pc.
Figure from Ref. [790].

In the event of a near-Earth ($d<$ kpc) core-collapse supernova, future liquid
xenon detectors will also be sensitive to neutrinos of all flavors that are
emitted by a massive star in its silicon-burning stage, a few hours prior to
core collapse [791, 792]. Due to lower stellar temperatures before collapse,
these “pre-supernova” neutrinos are $\mathcal{O}$(10) softer than supernova
neutrinos, and therefore require low thresholds for detection [793]. Figure 29
indicates that a next-generation liquid xenon experiment operating at 0.1 keV
energy threshold would detect, in a 12 hour window prior to collapse,
$\mathcal{O}$(100) pre-supernova neutrinos from a massive star 200 pc away,
e.g. Betelgeuse [790]. Such a detection would constitute the first measurement
of the final stages of stellar evolution, and provide a valuable warning
before the explosion. Pre-Supernova neutrinos can also help constrain dark
photon, axion, and ALPs parameters [794, 795, 796].

####  V.4.3 Supernova Early Warning System

In order to be optimally prepared for the next supernova, the Supernova Early
Warning System (SNEWS) was developed [797]. SNEWS is an inter-experiment
network to prepare and provide an early warning for Galactic supernovae: in
contrast to the optical signal, neutrinos basically free-stream from the
collapsing star and thus reach Earth minutes, hours or even days before the
optical counterpart becomes visible. Therefore, by detecting supernova
neutrinos, an early alert can be sent to astronomers to facilitate early
observations of the Supernova [798]. SNEWS is in the process of being revamped
and amplified to SNEWS2.0 which will have a larger physics reach [799, 800].
The next-generation detector discussed here will be able to contribute to this
network.

####  V.4.4 Diffuse Supernova Neutrinos

In addition to the yield from a Galactic supernova event, an exciting prospect
is the detection of the diffuse supernova neutrino background (DSNB) [801,
802, 803], i.e. the neutrinos emitted from past supernovae occurring across
the universe. Modern predictions put this flux at approximately
$6\,\mathrm{cm^{-2}}\,\mathrm{s}^{-1}$ [804] for neutrino energies above 17.3
MeV, including contributions from all neutrino flavors. In addition to being a
probe on supernova physics, the diffuse supernova neutrino background is an
independent probe of the local core-collapse supernova and cosmic star
formation rate [801, 805]. Although this signal has not yet been directly
detected, there are strong upper bounds on the $\bar{\nu}_{e}$ component of
the flux from Super-Kamiokande [806]. The best predictions for the flux of all
flavors, with an expected event rate of $\sim 0.05$ events per tonne-year,
implies that liquid xenon dark matter detectors with exposures $\sim 1000$
tonne-year may have discovery potential to this signal above known backgrounds
[425, 807]. Besides, these detectors might be the only ones capable of probing
the non-electron component of the DSNB, thanks to their excellent sensitivity.

###  V.5 Terrestrial Antineutrinos (ER)

The Earth is a rich source of antineutrinos with energies in the MeV range,
due to radioactive decays in Earth’s crust and interior [801]. A signal from
these geoneutrinos has been measured at Kamland [808] and Borexino [809].
Coherent neutrino interactions with xenon will produce recoil energies that
are likely below experimental thresholds. However, depending on exposure time,
mass, and other backgrounds, several neutrino-electron scattering events may
be detectable in a next-generation xenon detector.

###  V.6 Other Neutrino Physics

####  V.6.1 Measuring the Weinberg Angle

The solar pp flux is very strongly determined by the luminosity constraint on
the total neutrino flux, to a precision of $\sim 0.4$% [444]. The dependence
of the neutrino-electron cross section on the Weinberg (weak) angle
$\sin^{2}\theta_{W}$ thus allows for an independent measurement of this
quantity, at energies far below the reach of colliders. Precision
determinations of $\sin^{2}\theta_{W}$ must be made by running LEP
measurements (at $\sim$100 GeV) down to lower energies. At present, the
lowest-energy determination of $\sin^{2}\theta_{W}$ remains above the MeV
scale [810]. Electronic recoils from pp neutrinos yield an exchanged momentum
on the order of $\sim$ keV, so a detection of the pp flux via electronic
recoils in next-generation xenon experiments will cover new and uncharted
territory. The next-generation xenon detector discussed here would be able to
constrain $\sin^{2}\theta_{W}$ with (4–5)% precision [767] even without any
additional constraints from other experiments. Alternatively, using the solar
luminosity condition, a liquid xenon experiment with a 200 tonne-year exposure
can already yield a measurement of $\sin^{2}\theta_{W}$ with a precision of
1.5% at the keV scale [811]. This is complementary to measurements using
CE$\nu$NS of pion-decay neutrinos as achieved by the COHERENT collaboration
[812]. Applying the Relativistic Random Phase Approximation correction (see
subsubsection V.1.2 and [148]), the expected electronic recoil rate from solar
pp neutrinos is $\sim 90$ counts per 1000 tonne-day in the (0–15) keV energy
range (or 780 counts per 1000 tonne-day in the full energy range). Hence, a
150 tonne-year exposure can reduce the statistical uncertainty in the
measurement of $\sin^{2}\theta_{W}$ down to 1.4% for the energy transfer in
the range of (0–15) keVee.

A deviation of $\sin^{2}\theta_{W}$ from the computed value at low energies
would be an indication of new physics. For example, a new light gauge boson
could lead to a different value at low momentum $Q^{2}$. Figure 30 shows an
example of the variation that could be produced by a 50 MeV
$Z^{\prime}$-mediator, with a coupling in the range required to simultaneously
explain the muon $(g-2)_{\mu}$ anomaly [813, 814, 815].

Figure 30: Running of the Weinberg angle $\sin^{2}\theta_{W}$ as a function of
momentum scale $Q^{2}$, along with measured values. A deviation from Standard
Model predictions (black line) could indicate the presence of new physics
effects. The green band indicates the effect of a new $Z^{\prime}$ with
$m_{Z^{\prime}}=50\,\textrm{MeV}$, where the width of the band is determined
by the strength of the kinetic mixing parameter with $U(1)_{Y}$. An
$\mathcal{O}$(tonne-year) xenon dark matter observatory can extend the reach
of these measurements down to the keV scale, significantly to the left of this
plot, via the measurement of the pp solar neutrino flux. Figure from Ref.
[813].

####  V.6.2 Electron-Type Neutrino Survival Probability

The total electron-neutrino scattering rate receives neutral-current
contributions from all three flavors, but charge-current contributions only
from the electron-type neutrino. Consequently, a high-statistics observation
of solar pp neutrinos enables a liquid xenon experiment to directly measure
the oscillation probability of the electron-type neutrinos emitted from the
Sun in an energy range that is not accessible to any other experiment. Figure
31 shows that with an exposure of 300 tonnes-years, a liquid xenon detector
would measure the low-energy survival probability to 3–4% [767]. Such a
measurement would serve as a test of the MSW-LMA (Mikheyev-Smirnov-Wolfenstein
Large Mixing Angle) solution of neutrino oscillation and a probe of exotic
neutrino properties and non-standard interactions. This can also be used to
perform a solar-neutrino-only measurement of the magnitude of the $U_{e3}$
entry of the neutrino mixing matrix, to search for very light sterile
neutrinos in currently unexplored regions of parameter space, and one can
extend the sensitivity to the hypothesis that neutrinos are pseudo-Dirac
fermions by an order of magnitude [816].

Figure 31: The $\nu_{e}$ survival probability versus neutrino energy, assuming
the high-Z SSM. Dots represent the solar measurements of pp (green), 7Be
(blue), pep (orange), and 8B (red) from Borexino. The upward (downward)
triangle shows a measurement of 7Be (8B) from KamLAND (SNO). The open point
indicates that a next-generation liquid xenon experiment could enhance the
precision of the $\nu_{e}$ survival probability to 0.02 below 200 keV, using
solar pp neutrino events. The pink band represents the 1$\sigma$ prediction of
the MSW-LMA solution. Figure from Ref. [767].

####  V.6.3 Searching for New Physics of Neutrinos

A next-generation liquid xenon detector will also be a powerful tool to search
for new physics of neutrinos via elastic neutrino-electron scattering. An
extensively-studied scenario of new physics of neutrinos is the so-called non-
standard interaction (NSI) [817], which might play a potentially important
role in future long-baseline experiments such as DUNE [818]. In addition,
there has also been rising interest in new interactions mediated by light
mediators [819, 820, 821, 822]. A next-generation liquid xenon detector can
significantly improve the sensitivity to sterile neutrino mixing parameters,
particularly if solar neutrino detection via elastic neutrino-electron
scattering (pp component) and the CE$\nu$NS channel (8B component) is combined
with reactor neutrino data from JUNO [823]. Notably, the correlation of the
mixing angles $\sin^{2}\theta_{12}$ and $\sin^{2}\theta_{14}$ can be broken by
a combined analysis of these complementary data sets.

It has been shown that when combined with a radioactive source, a multi-tonne-
scale liquid xenon detector can significantly improve current bounds on
leptonic NSIs [824] and light mediators, thanks to the high electron density
in liquid xenon. In addition, xenon nuclei lie in a range where radiative
corrections are particularly sensitive to new weak isospin conserving
processes from new physics and are insensitive to isospin violating processes
[825]. Considering solar neutrinos as the source, since the Borexino
experiment has demonstrated excellent sensitivities to such new interactions
[826, 827], especially to $\nu_{\tau}$ interactions, it is expected that a
next-generation liquid xenon detector will be superior in searching for new
physics of neutrinos [828].

##  VI Additional Physics Channels

At the time of writing, an excess of electronic recoil events below
$7\,\mathrm{keV}$ has been reported by XENON1T [470]. With a statistical
significance of about 3 $\sigma$, this excess has received enormous interest
from the community [829, 830, 831, 832, 833, 834, 542, 835, 836, 837, 838,
839, 840, 820, 841, 842, 843, 844, 845, 846, 847, 848, 849, 629, 850, 851,
852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866,
867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881,
580, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895,
896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910,
911, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 821,
925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939,
940, 941, 353, 942, 943, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953,
954, 570, 955, 956, 957]. We refrain here from discussing whether one or the
other explanation is more likely and instead mention the various explanations
in the respective sections of this review.

###  VI.1 Solar Axions

Originally postulated to resolve the strong CP problem in QCD [543, 544, 545],
axions have emerged as a suitable non-baryonic dark matter candidate [546,
547, 548, 958, 959]. As such, there has been a growing interest in the last
few decades to search for axion particles in general, and for axion dark
matter in particular [960, 961, 962, 963, 562, 964, 965]. They may be sought
in the dark matter galactic halo within which they would cluster [966] as a
cold dark matter axion.

Independently of being dark matter, if an axion or axion-like particle exists
in nature, then it should be produced copiously in the hot solar plasma [967,
968]. Due to the $\sim$keV temperature of the Sun, solar axions are produced
with roughly thermal fluxes in the $1-10\,\mathrm{keV}$ energy range, and are
thus well-suited for detection in xenon experiments. Via their coupling to the
photon, $g_{a\gamma}$, the most widely considered process of axion production
is Primakoff conversion in which photons convert into axions inside the
electromagnetic fields of the electrons and ions of the solar plasma. This
flux is dominant in hadronic QCD axion models like the “KSVZ” axion [969,
970]. Another widely considered QCD axion model labelled the “DFSZ” axion
[971, 972] possesses a tree-level coupling to electrons, $g_{ae}$, which
brings sizable fluxes from the so-called “ABC” processes: atomic recombination
and deexcitation, Bremsstrahlung, and Compton scattering [973].

The primary way for xenon experiments to measure the axion is through the
axioelectric effect [564], which allows constraints to be set on $g_{ae}$.
Xenon experiments may also constrain $g_{a\gamma}$: both by measuring the
Primakoff component [974] of the solar flux (which is dependent only on
$g_{a\gamma}$), as well as by exploiting inverse Primakoff conversion inside
the detector [580, 898]: $aZ\rightarrow\gamma Z$. In the latter case, the
sensitivity to solar axions is boosted, even if the value of $g_{a\gamma}$is
small. A final component of the solar axion flux beyond “ABC” and Primakoff
components is the 57Fe axion-nucleon interaction, which depends on $g_{an}$
[975]. A next-generation xenon experiment with a $\sim$1000 tonne-year
exposure may even be able to out-perform devoted solar axion telescopes [580]
such as the planned International Axion Observatory (IAXO) [976].

The electronic recoil background level of the detector is the main limiting
factor for its sensitivity to solar axions. Liquid xenon TPCs are well known
for their very low electronic recoil background levels and are therefore ideal
for this search. Amongst underground detectors, liquid xenon TPCs place the
strongest constraints to-date on $g_{ae}$ with solar axions [977, 978, 565,
567, 568, 470].

The excess of electronic recoil events seen in XENON1T [470] has a spectrum
that matches the expected solar axion flux. However, the amplitude of the
excess would require large couplings that would place the excess in conflict
with more stringent astrophysical bounds [557, 842, 929, 878]. The proposed
next-generation liquid xenon TPC will enable this excess to be robustly
tested, should it persist, perhaps leading to the discovery of solar axions.

###  VI.2 Neutrino Dipole Moments and Light Mediators

Dark matter searches start to probe various novel neutrino-induced signals,
see e.g. [149, 824]. Therefore, the interpretation of potential discoveries as
coming from new neutrino physics becomes increasingly plausible. As a result,
next-generation dark matter detectors will be capable of placing interesting
limits on models of new physics in the neutrino sector, often complementary
with other experiments [828].

This is apparent in limits from electronic recoils. In Figure 32 we show the
observed electronic recoil spectrum observed by several dark matter as well as
neutrino experiments, adopted from Refs. [979, 980] with the most recent
XENON1T measurements [61] included. They represent about two orders of
magnitude improvement over the XENON100 background rate.

Figure 32:  Neutrinos may show up in dark matter experiments well above the
neutrino fog. Shown in red are the electron recoil spectra in several
experiments taken from Ref. [979, 980], with the background level in XENON1T
indicated [61, 470]. The spectrum expected from Standard Model solar neutrinos
is in solid black. The colored curves are the solar neutrino spectra for
several new physics models discussed in the text, with line-styles
corresponding to various mediator masses. The jagged steps below $\sim
5\,\mathrm{keV}$ are an effect of the electron binding energy as discussed in
[981].

The next generation of experiments will have further sensitivity [915, 844].
In Figure 32 we show several spectra from new physics models which lead to an
enhanced scattering rate at low energies. The green curve shows the recoil
spectrum in the case that the neutrino possesses a magnetic dipole moment
around that which is allowed by current solar neutrino data from Borexino
[982]. In this case the differential cross section is

$\frac{\mathrm{d}\sigma}{\mathrm{d}E_{r}}=\mu_{\nu}^{2}\alpha\left(\frac{1}{E_{r}}-\frac{1}{E_{\nu}}\right)$
(10)

where $\mu_{\nu}$ is the neutrino dipole moment and $E_{r}$ is the recoil
energy of the electron. At high recoil energies, the dipole-induced scattering
is lower than the Standard Model rate and in agreement with the Borexino rate.
However, due to the $E_{r}^{-1}$ falloff, the rate is higher at low recoil
energies. Already an analysis of XENON1T [470] improves the limit in dipole
moments to $<3\times 10^{-11}$ times a Bohr Magneton. The next-generation
experiment will precisely measure the $pp$ solar neutrino spectrum at low
energies and thus further improve this sensitivity. In addition to the
neutrino magnetic moment, a new interaction mediated by a scalar propagator
will also fall as $E_{r}^{-1}$ as described in [980]. An example of such a
scalar-mediated interaction is plotted in orange in Figure 32.

One can also consider models with a faster falling spectrum. For example, blue
curves of Figure 32 are the spectra in a model with a new very light $B-L$
gauge boson which is mediating a new interaction between neutrinos and
electrons. The cross section is

$\frac{\mathrm{d}\sigma}{\mathrm{d}E_{r}}=\frac{g_{B-L}^{4}m_{e}}{4\pi(2m_{e}^{2}E_{r}^{2}+m_{B-L}^{2})^{2}}\,,$
(11)

where $m_{B-L}$ and $g_{B-L}$ are the mass and coupling. Here, we have dropped
subleading terms in $E_{r}/E_{\nu}$ as well as interference with the SM
process which is unimportant at most recoil energies. If the mass of the gauge
boson is small, the cross section falls as $E_{r}^{-2}$. This behavior is due
to the $1/(q^{2}-m_{B-L}^{2})$ propagator in the amplitude, with
$q^{2}=2m_{e}E_{r}$. Again it can be seen that a next-generation experiment
will have significant sensitivity, well beyond that achieved by the Borexino
experiment [983], the GEMMA reactor experiment [984], or the XMASS experiment
[985]. In fact, the discussion around the possible excess observed by XENON1T
[470] can already be used to place a constraint on $g_{B-L}<3.6\times 10^{-7}$
for mediators with mass $m_{B-L}<10\,\mathrm{keV}$. This is already comparable
with the constraint from GEMMA [853]. A next-generation liquid xenon
experiment will be able to strengthen this bound.

It is interesting to consider a scenario in which the next generation of xenon
experiments uncovers an excess above the solar neutrino fog. In this case we
will immediately entertain both the possibility of dark matter and that of new
neutrino physics, as evidenced by the list of papers discussing the excess
observed by XENON1T. Fortunately, this degeneracy can be disentangled with
reactor neutrino experiments. To those that stand within 100 m of the core,
nuclear reactors are a brighter source of neutrinos than the Sun. A low-
threshold detector near a reactor, such as GEMMA [984], can thus place strong
limits or distinguish whether an excess is coming from dark matter or
neutrinos. Figure 33 shows the current limits on the neutrino magnetic moment
from both large underground detectors and reactor experiments, as well as the
projected sensitivity for a next-generation liquid xenon detector with a 750
tonne-year exposure, complementary to dedicated experiments such as CONNIE
[986].

Figure 33:  Projected neutrino magnetic moment sensitivity (red) along with
current limits from reactor-based experiments (left markers) and experiments
exposed to a solar flavor mixture (right markers). All the upper limits are
reported at 90% CL, except the XENON1T result, which shows the 10-90%
confidence interval [985, 982, 470].

In addition to the physics discussed in subsection VI.5, a mono-energetic
neutrino source in combination with a large xenon detector could set very
competitive sensitivities to neutrino magnetic dipole moments and sterile
neutrino oscillation [987]. A 50-day run with a 3 MCi ${}^{51}Cr$ source
produces 82 $\nu-e$ elastic scattering events in the XENON1T detector, which
corresponds to 9.8 times better signal-to-noise ratio compared to using solar
neutrinos [877]. The next-generation experiment discussed here could set much
more stringent bounds on the neutrino magnetic moment, if combined with an
electron capture source.

###  VI.3 Fractionally Charged Particles

The quantization of the electric charge has been one of the long-standing
mysteries stemming from empirical observation. In principle, the Standard
Model $U(1)$ allows arbitrarily small real-number charge, but so far,
experiments indicate that there is a fundamental unit of electric charge of
1/3 e. This has sparked theoretical explanations including Dirac quantization
[988] and provides one of the major motivations for a Grand Unification Theory
(GUT) [989, 990]. The search for such fractionally charged or millicharged
particles is a test of the paradigm of charge quantization [991, 992, 993,
994, 995, 996, 997, 998, 999, 1000, 1001, 1002, 1003, 1004, 1005]. If such a
particle was found, its small charge may or may not be the new electric charge
unit, but in either case it will inevitably change our understanding of the
current charge quantization built on quark charges, and contradict the
predictions of certain GUTs.

One can consider the kinetic mixing between the SM $U(1)_{Y}$ and an
additional gauge group $U(1)_{D}$, with additional matter particles $\xi$
charged under a dark $U(1)_{D}$. In the limit when the dark $U(1)_{D}$ vector
boson (often called a dark photon, see subsubsection III.8.1) is massless, the
would-be dark sector particles which are charged under $U(1)_{D}$ become
electromagnetically “fractionally charged” or “millicharged”. The level of
kinetic mixing is often $\sim 10^{-3}$ or smaller, from loop effects in either
QFT or String Theory [537, 1006, 1007], which naturally gives small electric
charges. For masses of such new particles below $\sim{\rm MeV}/c^{2}$, the
limits on the kinetic mixing parameter (and thus the fractional charges) are
stringent $<10^{-15}$ [993]. For heavier states, the limits are weaker [1008].
Direct detection experiments can possibly observe bound state formation
between $q<0$ millicharged particles and nuclei [1009]. One can also look for
millicharged particles without massless gauge bosons in regimes where the dark
photon is constrained [1004]. A search for such a particle can be a test of
GUTs and certain string compactification scenarios [1010]. Further, liquid
xenon detectors are sensitive to the possible millicharge of solar neutrinos
[985].

###  VI.4 Nucleon Decay

In the Standard Model, the conservation of baryon number $B$ is an empirically
observed symmetry. If $B$ were an exactly conserved quantum number, then
protons, being the lightest baryons, would be stable. However, baryon number
could be an approximate symmetry of Nature, and violated by small amounts, as
predicted for example by many Grand Unified Theories. This could explain the
observed matter-antimatter asymmetry of the universe [1011].

Several liquid xenon detectors, such as DAMA-LXe [1012, 1013] and EXO-200
[1014], explored the possibility to investigate nucleon decay through so-
called invisible decay modes, where the final states (neutrinos, or more
exotic particles such as dark fermions) are not detected. One example for an
invisible mode is $n\rightarrow\nu\nu\nu$, as proposed in [1015]. Following
such a decay, the daughter nuclei would be left in an excited state, and would
emit a detectable signal, such as a $\gamma$-ray, once they de-excite. Table 1
illustrates the various signatures for two xenon isotopes, 129Xe and 136Xe.
These decays can be searched-for with a next-generation liquid xenon detector
with unprecedented sensitivity.

| Invisible |  |
---|---|---|---
| decay |  |
Isotope | mode | Daughter | Subsequent decays
129Xe | n |  128Xe | stable
| p |  128I |  128I $\rightarrow[Q=2.217]{\text{$\beta^{-}$}}$ 128Xe
|  |  |  or 128I $\rightarrow[Q=1.258]{\text{EC+$\beta^{+}$}}$ 128Te
| nn |  127Xe |  127Xe $\rightarrow[Q=0.664]{\text{EC}}$ 127I
| pn |  127I | stable
| pp |  127Te |  127Te $\rightarrow[Q=0.694]{\text{$\beta^{-}$}}$ 127I
136Xe | n |  135Xe |  135Xe $\rightarrow[Q=1.151]{\text{$\beta^{-}$}}$ 135Cs
| p |  135I |  135I $\rightarrow[Q=2.648]{\text{$\beta^{-}$}}$ 135Xe
|  |  |  135I $\rightarrow[Q=1.151]{\text{$\beta^{-}$}}$ 135Cs
| nn |  134Xe | stable
| np |  134I |  134I $\rightarrow[Q=4.175]{\text{$\beta^{-}$}}$ 134Xe
| pp |  134Te |  134Te $\rightarrow[Q=1.550]{\text{$\beta^{-}$}}$ 134I
|  |  |  134Te $\rightarrow[Q=4.175]{\text{$\beta^{-}$}}$ 134Xe
| nnn |  133Xe |  133Xe $\rightarrow[Q=0.4274]{\text{$\beta^{-}$}}$ 133Cs
| nnp |  133I |  133I $\rightarrow[Q=1.770]{\text{$\beta^{-}$}}$ 133Xe
|  |  |  133I $\rightarrow[Q=0.4274]{\text{$\beta^{-}$}}$ 133Cs
| npp |  133Te |  133Te $\rightarrow[Q=2.920]{\text{$\beta^{-}$}}$ 133I
|  |  |  133Te $\rightarrow[Q=1.770]{\text{$\beta^{-}$}}$ 133Xe
|  |  |  133Te $\rightarrow[Q=0.4274]{\text{$\beta^{-}$}}$ 133Cs
| ppp |  133Sb |  133Sb $\rightarrow[Q=4.003]{\text{$\beta^{-}$}}$ 133Te
|  |  |  133Sb $\rightarrow[Q=2.920]{\text{$\beta^{-}$}}$ 133I
|  |  |  133Sb $\rightarrow[Q=1.770]{\text{$\beta^{-}$}}$ 133Xe
|  |  |  133Sb $\rightarrow[Q=0.4274]{\text{$\beta^{-}$}}$ 133Cs
Table 1: The daughter isotopes and their decay modes that follow the invisible
mono- and di-nucleon decays of 129Xe and 136Xe as well as the tri-nucleon
decays of 136Xe. This table is adapted after [1012, 1013]. The Q-values are
reported in MeV.

###  VI.5 Short-Baseline Oscillations

Persistent anomalies in short baseline experiments, including LSND and
MiniBooNE, are suggestive of an additional undiscovered neutrino mass
eigenstate at the $\sim 1\,\mathrm{eV}$ mass scale [1016]. However, there is
significant tension between different experiments that has yet to be explained
[1017]. Given the energy of 51Cr neutrinos, the oscillation pattern is
expected to be within a meter-scale detector. This would make a next-
generation liquid xenon TPCs well-suited to conclusively test the existence of
sterile neutrinos [987]. In addition, such an experiment would be able to rule
out portions of currently allowed parameter space, potentially resolving the
existing tension if sterile neutrinos do not exist [987].

##  VII Background Considerations

As discussed in this present paper, the proposed next-generation liquid xenon
experiment is a versatile observatory for a number of relevant science
channels, spanning low-energy nuclear recoils in particular for dark matter,
electronic recoils for a number of measurements, and reaching up to high
energy events expected from neutrinoless double-beta decay. In order to
support this broad physics reach, multiple background sources must be
considered. In addition to improved xenon purification, further scrutiny of
materials in assays and exploration of discrimination techniques will be
necessary to minimize backgrounds for rare event searches. The choice of host