A next-generation liquid xenon observatory for dark matter and neutrino physics

Identifying the true nature of dark matter is one of the most important questions in physics today. As we show in this review, liquid xenon time projection chambers (TPCs) are the leading technology in searches for a large variety of dark matter particle candidates. Following two decades of evolution of this technology, now is the time to design the next-generation dark matter experiment in order to probe the widest possible range of dark matter candidates. A possible realization of such a detector has been proposed by the DARWIN collaboration [1] and is pursued by the XLZD consortium. This experiment will also have competitive sensitivity to search for neutrinoless double-beta decay and other rare events. Furthermore, we show in this review that such an experiment serves as a versatile astroparticle physics observatory that is sensitive to neutrinos from our Sun, the atmosphere, and Galactic supernovae. Figures 1 and 2 illustrate these topics.

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Strong evidence on astronomical and cosmological scales suggests gravitational interaction between baryonic matter and an unknown type of non-luminous matter, called dark matter [2]. First evidence that much matter in the Universe remained unseen in telescopes started to accumulate already in the early 1900s [3, 4]. This motivated the original use of the term 'dark matter' to mean invisible matter whose existence is inferred only from its gravitational effects, possibly in the form of dark stars [5]. In 1922, James Jeans realized that 'there must be about three dark stars in the Universe to every bright star' [6]. The next decade, Jan Oort used the vertical kinematics of Milky Way stars to constrain the local dark matter content [7], while Fritz Zwicky became the first to use the virial theorem to infer the presence of dark matter within the Coma Cluster [8].

Crucial evidence for dark matter in galaxies came in the late 1970s when Vera Rubin and collaborators established that optical rotation velocities of stars in spiral galaxies consistently differ from those expected from the distribution of their baryonic matter [9, 10]. Albert Bosma soon after confirmed this finding by means of 21 cm rotation curves, well outside the edge of stellar disks [11]. Galactic rotation curves [12, 13] and dynamics [14, 15] provide evidence for the existence of a uniformly-distributed halo of dark matter around all spiral galaxies and very likely around every Galaxy [16]. The critical role of dark matter in the formation of galaxies [17] such as our own Milky Way [18] underlines its significance to our very existence.

Evidence for dark matter has now been found across all time and length scales [19], spanning from the Big Bang to today, and from the cosmos as a whole down to individual galaxies [20]. Gravitational effects of dark matter can be observed in the cosmic microwave background (CMB), e.g. with the Planck satellite [21]. Detailed measurements of the power spectrum from the CMB put the dark matter mass–energy density at five times that of baryonic matter [22] and significantly constrain any electromagnetic coupling of dark matter [23]. Our understanding of large-scale structure formation points to the existence of non-relativistic (cold) dark matter [24–26]. Gravitational lensing suggests the presence of a significant amount of non-baryonic matter with no observable electromagnetic interaction [27], both when observing strong (e.g. reference [28]) and weak lensing (e.g. reference [29]). Merging Galaxy clusters, made famous by the initial reports from the Bullet Cluster [30], have now become a laboratory for dark matter physics [31]. Taken together, cosmological and astrophysical observations are not only used to identify some of the characteristics of dark matter [32], but in particular also to constrain its coupling to ordinary matter [33].

A precise determination of the local dark matter halo density is required for interpreting results from direct detection experiments. Observational density estimates come from a variety of studies [18, 34, 35]. Methods used to determine the local dark matter density can be broadly classified into local methods and global methods. Local methods focus on dynamics of stars in a small volume around the Solar System, while global methods determine the dark matter halo in the whole Galaxy and obtain the local dark matter density from our position within it. Global methods based on the galactic rotation curve yield a local density ϱ = (0.4–0.5) GeV cm⁻³ [36]. Using the Gaia data release 2 [37], the local density has recently been determined to be in the range ϱ = (0.3–0.4) GeV cm⁻³ [38], in good agreement with the former values when one adopts the same local speed v_⊙. Local methods in contrast yield a wider range of ϱ = (0.4–1.5) GeV cm⁻³ [39–41] with some tendency toward higher values [42]. Note though that the two methods, global and local, measure, in principle, different quantities: the properties of a sphere of 1 kpc radius around the Sun could be different with respect to the average (D/kpc)² spheres located at the same galactocentric distance D which are considered by global methods. When presenting results from direct dark matter searches, it is common to assume ϱ = 0.3 GeV cm⁻³ [43], which ensures both historical compatibility of the derived direct detection results, as well as a conservative interpretation of such results.

While the existence of dark matter is thus well established, its physical characteristics remain elusive. The absence of electromagnetic coupling observed in the CMB, the lack of any observed thermal emission from dark matter, and the dynamics of merging Galaxy clusters, indicate that dark matter takes the form of new quanta outside the current Standard Model (SM) of particle physics [44]. The nature of this non-baryonic dark matter is still unknown: its existence is one of the strongest pieces of evidence that the current theory of fundamental particles and forces, summarized in the SM, is incomplete. A number of proposed candidates have been put forward over time, with some of the most popular candidates being probed by the experiment discussed here, as elaborated in sections 2 and 3.

The fact the cosmological dark and luminous matter densities are of the same order [21], as well as observed scaling relations in galaxies [45], suggest that the dark sector and the SM are coupled through additional interactions stronger than gravity. Since the 1980s, there have been large efforts to develop experiments on Earth that are able to directly search for dark matter, particularly for weakly interacting massive particles (WIMPs) [46–49], one popular dark matter candidate. Given the low expected interaction strength, the probability of multiple collisions of dark matter particles within a detector is negligible, resulting in a recoil spectrum of single scattering events.

In the effort to directly detect dark matter, many technologies have been developed to measure dark matter interactions with target nuclei. Complementary searches with different targets, discussed further in section 8, are essential to unveil the nature of dark matter. In the most common approach, experiments attempt to measure the nuclear recoil (NR) energy produced by collisions between dark matter candidates and target nuclei in the detector. The recoiling nucleus can deposit energy in the form of ionization, heat, and/or light that is subsequently detected. Different technologies have been explored so far to achieve this goal [50]. Successful targets include solid state crystals [51–59], metastable fluids [60, 61], and noble liquids [62–67].

A possible dark matter signature would be an annual modulation of the interaction count rate due to the motion of the Earth around the Sun [48, 49, 68]. The relative velocity of dark matter particles in the Milky Way halo with respect to the detector on Earth depends on the time of year; therefore, the measured count rate is expected to exhibit a sinusoidal dependence with time, where the amplitude and phase of modulation will depend on the dark matter distribution within the halo [69]. While there is general consensus on standard values to be used to calculate expectations for direct experiments [43], this scenario can be modified in a number of possible astrophysical scenarios such as the presence of dark matter streams [70, 71], halo substructure [72–74], a dark disk [75] or local captured populations of WIMPs resulting from interactions in the Sun [76] and Earth [77], which all have the common feature of increasing the local dark matter density.

Liquid xenon TPCs in particular have demonstrated their exceptional capabilities for rare event detection as a result of an intense, decade-long development. The interested reader is referred to [78–80] for detailed discussions of this technique. The two-phase (or dual-phase) emission detector that underlies liquid xenon TPCs was proposed a half-century ago [81]. Its use for the detection of dark matter particles and neutrinos was proposed in 1995 [82], with more mature conceptional designs developed around the turn of the millennium [83, 84]. Evolving out of ZEPLIN-I [85], the ZEPLIN-II [86] detector was the first two-phase xenon dark matter experiment, with both experiments setting competitive limits on WIMP interactions at that time. This technology was further advanced in ZEPLIN-III [87, 88] and with XENON10 [89] saw the first leading limits on WIMP interactions. XMASS built the first two-phase xenon dark matter detector underground [90], and with a single-phase detector provided an impressive demonstration of fiducialization in liquid xenon (section 7.2) [91]. Further evolution progressed through successively larger, cleaner, and thus more sensitive detectors: from XENON100 [92, 93], LUX [63], PandaX-I [94] and PandaX-II [95] to XENON1T [96] and the current generation PandaX-4T [97], XENONnT [98], and LZ [99] (figure 3).

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In 2021, scientists from the DARWIN/XENON and LZ collaborations signed a Memorandum of Understanding, forming the XLZD consortium, to jointly work on the design, construction and eventual operation of a next-generation detector. This experiment is labeled DARWIN/G3 in figure 3 [100] and represents a natural continuation of this evolution toward larger xenon exposures, as presented in the sensitivity studies shown below. Scaling up the same mature technology (to a compact size of only $\sim 3\enspace \,\mathrm{m}$ in height and diameter), and exploiting the collective experience of the participating scientists, drastically reduces risks otherwise inherent in such projects. Continued research and development is ongoing using dozens of dedicated setups at the participating institutions. At the same time, experience from the operation and analysis of the current generation of detectors provides important lessons. It is thus timely to review the science case of such a rare event observatory.

Conventionally, a next generation liquid xenon TPC will consist of a central liquid xenon volume surrounded by light reflectors for vacuum ultra-violet (VUV) light, allowing maximum light detection [101]. Two arrays of light sensors, such as photomultiplier tubes (PMTs) [102, 103] or silicon photomultipliers (SiPMs) [104, 105], are arranged on the top and bottom part of the TPC to detect light signals, see figure 4.

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A particle incident on the liquid xenon target deposits energy and produces both prompt scintillation light and ionization electrons. The scintillation signal is immediately detected by the photosensors as the S1 signal. The active liquid xenon volume is defined by a cathode and a gate electrode, separated by ∼3 m to provide a drift field for the electrons. These drifting ionization electrons are then extracted into the gas phase above the liquid xenon, where they produce electroluminescent light [106]. Typical dual phase detectors operate at $\sim 1.5\enspace \,\mathrm{b}\mathrm{a}\mathrm{r}$, where 5 kV cm⁻¹ for the extraction field is sufficient to create proportional scintillation. This electroluminescence is then detected by the same photosensors and is known as the S2 signal [101, 107, 108].

The time delay between S1 and S2 in addition to the localization of the S2 light pattern on the top photosensor array [109–111] allows precise reconstruction of the three-dimensional interaction vertex [112]. Fiducialization in event selection (section 7.2) enables an effective way to suppress external gamma and neutron background for all rare event searches and to minimize effects from imperfections of the TPC near its surface. The ratio of S2 and S1 signals further allows for discrimination between different types of interaction in the liquid xenon TPC: NRs and electronic recoils (ER). NRs are most notably induced by WIMPs, through coherent elastic neutrino-nucleus scattering (CEνNS), and by neutrons; whereas ERs are produced by gamma rays and internal beta decays [113, 114]. NRs exhibit a lower S2/S1 ratio and can therefore be distinguished from ERs [114, 115]. Excellent energy resolution further helps to differentiate various signals from relevant background [116]. As we explain in section 3.2, the scientific reach of these TPCs can be extended toward lower energies by dropping the requirement of the presence of an S1; this results in sensitivity to single electrons.

Xenon as a detection medium exhibits several desirable features [117, 118], giving it a significant advantage as a target material. Xenon has a very low work function, requiring only 11.5 eV averaged over scintillation and ionization to produce an excitation [119]. This leads to signal yields as high as ∼65 photons per keV for gamma rays that are of order ∼100 keV [120, 121], similar to other excellent scintillators such as NaI and CsI. For NRs, the yields are still ∼10% of that, even below ∼10 keV [122, 123]. Energy resolutions better than 1% (σ/E) have been achieved at MeV scales [116] and mm-level position resolution can routinely be achieved [105, 124, 125].

Liquid xenon is a well-understood and well-characterized detector medium. Based on world data, its response can be accurately modeled using the Noble Element Simulation Technique (NEST), a code package to simulate interactions in liquid xenon (and argon) and their detection in a TPC [121, 126–128]. This includes various interactions of interest, such as ERs induced by gamma and beta rays, NRs, energy deposits by alphas, and more complex decays such as that from ^83mKr. These models have been demonstrated to correctly reproduce the mean yields and their widths across a wide range of detector parameters and energies even down to 300 eV, making this simulation package a mature, comprehensive tool for liquid xenon experiments. As a result of this and other efforts [129–135], the light and charge yields can now be accurately described and predicted, with good comparisons to existing calibration data sets, as a function of energy, stopping power, drift electric field, extraction electric field, particle and interaction type, and in some cases even concerning density, phase, and angle of the recoil relative to the drift field.

Liquid xenon may be naturally contaminated with radioactive isotopes that could produce a dark matter background, such as ³⁷Ar, ⁸⁵Kr or ²²²Rn. However, purification to very high levels has already been demonstrated in dark matter [63, 96, 136, 137] and neutrinoless double-beta decay experiments [138]. Cosmogenically-produced ³⁷Ar decays away quickly [139], and purity levels achieved for ⁸⁵Kr are already sufficient for the next-generation detector discussed here. Further advantages of xenon are obtained through its high charge number Z, mass number A, and density; these allow for self-shielding of gamma-ray and neutron backgrounds, which will multiply-scatter, especially in the outer limits of the fiducial volume (FV). Xenon also contains odd-neutron isotopes for spin-dependent neutron coupling (section 2.4), and enough residual spin-dependent proton sensitivity to produce competitive results for that science channel. In addition, natural xenon possesses promising isotopes for the search for neutrinoless double-beta decay (section 4.1) and double electron capture (section 4.2). Finally, the mass of the xenon nucleus makes it kinematically ideal for WIMPs in the mass range above ∼10 GeV/c².

In the following sections, we highlight the science case for a large, next-generation liquid xenon TPC detector for astroparticle physics. In section 2, we overview various WIMP dark matter models, and the expected sensitivity when probing such models. In section 3, we discuss other dark matter models that a next-generation liquid xenon TPC is sensitive to. In section 4, we review double-beta processes to probe physics beyond the SM. In section 5, we discuss the science channels using neutrinos for astroparticle physics and particle physics. In section 6, we collect physics channels that are not part of the above categories. Mitigation and rejection of detector backgrounds is sketched out in section 7. The relation of a next-generation liquid xenon TPC to other future experimental efforts is discussed in section 8. Finally, we review some of the already-documented support for such a detector in the particle physics community in section 9 before concluding in section 10.

A well-motivated candidate for particle dark matter is the WIMP [140, 141]. This is a special case of a thermal relic particle, i.e., one that in the early Universe was in thermal equilibrium with the primordial plasma, permanently annihilating and being produced. Once the annihilation rate becomes slower than the Hubble expansion rate, the particle is said to freeze out, its relic density becoming fixed at that point [20]. While the list of possible dark matter candidates is now quite long, the WIMP model remains a leading scenario, with large regions of well-motivated yet unprobed parameter space [142]. The hierarchy problem [143], specifically the surprisingly and unnaturally low mass of the Higgs particle, continues to strongly motivate searches for new physics and new particles at the ∼100 GeV scale of the electroweak force [44]. In addition, if a new stable particle existed in this mass range, and if it interacted with SM particles via some force also at the electroweak scale, then a simple thermal freeze-out process in the early Universe would result in the observed dark matter density [144]. While this link most tightly constrains the WIMP annihilation cross-section [145], crossing symmetry provides a connection to the direct scattering cross-section as well. It is this surprising connection of particle physics at the weak scale and the evolution of the macroscopic density in the early Universe that continues to motivate searches for WIMP dark matter. Few other models can point to as clear a convergence.

The assumption of a massive (electroweak scale) mediator implies a lower bound on the WIMP mass, the so-called Lee-Weinberg limit [146]. A heavy mediator will suppress the dark matter annihilation cross section. Thus, for dark matter with a mass of less than $\sim 2$ GeV/c², the thermal freeze-out process of the early Universe ends too early and results in a dark matter density that is too high and inconsistent with observation.

Because WIMPs are so well-motivated, searches for particles satisfying these criteria are underway in parallel following three general and complementary strategies [147, 148] (see also section 8): (1) WIMP production at high energy colliders such as the Large Hadron Collider (LHC) [149]; (2) indirectly via WIMP annihilation in dense astrophysical environments that produce astrophysical signals in various SM particle channels [150]; and (3) directly via observation of NRs produced by dark matter scattering as proposed here [48, 151]. This latter approach is particularly powerful. In fact, the original WIMP in the sense of a weak interaction via Z-boson exchange at tree level was ruled out using direct detection already in 1987 [152]. Today, experiments such as the one discussed here probe scattering cross-sections typical of e.g. coupling via a Z boson at loop level, or some of the well-motivated models discussed in this section. The next-generation liquid xenon-based experiment discussed here is thus complementary to the next generation of astrophysical searches [153] and the high-luminosity LHC [154] and at a similar time scale.

Direct detection experiments are particularly interesting for a variety of reasons. As scattering interactions happen at energies far below the electroweak scale itself, the interaction mechanism can be simplified and described as a contact interaction. A diverse set of high-energy models will therefore appear nearly identical at these low energies, distinguished almost exclusively by the characteristic scattering cross section. This generality of direct detection via low-energy scattering is a significant advantage to this detection approach. Also, for a large set of WIMP models and a wide range of WIMP masses, direct dark matter experiments depend only linearly on the local dark matter density, which makes results robust against astrophysical uncertainties. Further, for relics produced by the freeze-out process, such as WIMPs, the relic density is inversely related to the thermal annihilation cross section, such that a dimensional argument can be made that the expected scattering rate in a detector (which goes like density times cross section) should be roughly independent of details of the theory. Another expression of the generality of the direct detection approach is its sensitivity to a large mass range [155]. The kinematics for non-relativistic scattering remain unchanged once the WIMP mass is much larger than the target mass, rendering these experiments sensitive to dark matter masses well beyond 100 TeV (and in principle even up to the Planck mass [156], see section 3.15). Thus, a single experiment can probe many orders of magnitude of the allowed dark matter mass parameter space.

Xenon in particular is expected to couple well to WIMP dark matter for several reasons [157]. First, in the low momentum-transfer regime of direct detection, a generic spin-independent scattering (section 2.3) will interact with the nucleus as a whole as a many-nucleon object, and this coherence provides a significant boost to the corresponding scattering cross section [47, 48], scaling roughly as the square of the number of nucleons. Therefore, a heavy nucleus like xenon is significantly favored over lighter options. A second advantage is the large number of common natural xenon isotopes, resulting in a diversity of nuclear properties. This variety of isotopes gives xenon significant sensitivity to other interaction models as well, such as spin-dependent (section 2.4) or various effective couplings (section 2.5).

Figures 5 and 7 show sensitivity estimates for a liquid xenon TPC with only neutrino-induced backgrounds and the double beta decay of ¹³⁶Xe considered. We use a binned likelihood in position-corrected cS1 and cS2 (see e.g. references [158, 159]), and assume the log-likelihood ratio test statistic is asymptotically distributed [160].

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Particle yields and the detector response to ER and NRs is simulated using NEST v2.1.0 [128] with the LUXrun03 detector model, roughly corresponding to the model presented in reference [161] for the first science run of LUX. The modeled detector response is similar to the models assumed for the sensitivity projections for LZ [99] and XENONnT [98]. For S1 scintillation signals, the detector model assumes a g₁ value of 0.12 phd/photon and a two-fold photon hit threshold for S1s. For S2 ionization signals, the g₂ value depends primarily on the photon yield ${g}_{1}^{\text{gas}}$ and field strength in the gas gap, which are 0.1 phd/photon and 6.4 kV cm⁻¹, respectively; more details can be found in [161]. This corresponds roughly to a g₂ = 13.8 phd/e. The S2 threshold is assumed as 165 phd. The spatially varying drift field for this simulation is between $\sim 90\enspace {\mathrm{V}\ \mathrm{c}\mathrm{m}}^{-1}$ and 300 V cm⁻¹, and the electron lifetime assumed is $\sim 16$ times the maximum drift length. We leave a detailed parametric investigation of the sensitivity of such a next-generation detector to a future study.

The background model is made up of the intrinsic ER and NR backgrounds. The expectation value is dominated by ERs from naturally occurring ¹³⁶Xe and solar (mostly pp) neutrinos scattering off electrons. ER events can be distinguished from a WIMP signal using the ionization signal.

NR events from neutrons scattering in the detector volume can be separated to some degree from a WIMP signal based on the recoil energy spectrum and their tendency to scatter multiple times. Further, neutrons can be tagged surrounding the detector with an active neutron veto. We thus only include NR backgrounds from ⁸B, HEP, diffuse supernovae and atmospheric neutrinos. These neutrino signals, while being an interesting signal in their own right (section 5), may significantly affect the sensitivity to dark matter as they are becoming the dominant background (section 2.17).

The neutrino recoil spectra, as well as flux uncertainties on the different components, are taken to be the same as in reference [98], with spectra from references [162–165]. WIMP recoil spectra are computed using the wimprates package [166], with spin-independent computations from reference [167], spin-dependent computations from reference [168], and WIMP–pion recoil spectra from references [169, 170]. We use the background and signal distributions to construct signal regions for each WIMP interaction and mass as the 50% most signal-like region in S1 and S2, ordered by signal-to-background ratio. We indicate the region at which neutrinos become an appreciable background as the cross section where the WIMP and neutrino expectation in the signal region are equal. Levels where the neutrino signal is equal, 10 times, 100 times etc of the WIMP signal are indicated by the shared gray regions labeled 'neutrino fog' in figures 5 and 7. Estimates of where experimental sensitivity will improve only very slowly with exposure depend crucially on the uncertainty on the neutrino signal and detector response. Attempts to quantify the 'neutrino floor', such as [171, 172] (the former is included as a dashed line in figure 5) often assume e.g. very low experimental energy thresholds in order to reflect the ultimate limit. Further discussion of the neutrino background may be found in section 2.17.

Traditionally, WIMP detection has been limited primarily by the experiment's exposure (expressed in mass × time), and sensitivity has progressed proportionally to that exposure. This linear scaling will hold as long as contamination by any non-WIMP recoils remains small. This next-generation WIMP detector will be the last to benefit from this proportional scaling over much of its operating time. Any larger experiment would face a rate of CEνNS from astrophysical sources [164, 174]. While that is an interesting signal in its own right (section 5), neutrinos present an unavoidable background to WIMP sensitivity.

The energy threshold of this search is also important. A recoil threshold of ∼keV is required in order to efficiently test WIMP hypotheses down to the Lee-Weinberg limit of few GeV/c² mass. The goal for any WIMP dark matter detector, then, can be described as testing the entire WIMP mass range (∼2 GeV/c² to ∼100 TeV/c²) at least down to cross sections limited by neutrino scattering. Such a detector also has sensitivity to many theoretically interesting and yet unexplored dark matter candidates (section 3) and probes the coupling of dark matter to the Higgs boson [175].

To indicate the WIMP mass and cross section resolution expected for a signal from WIMPs roughly one order of magnitude below current constraints (one event per tonne-year), figure 6 shows confidence intervals for spin-independent WIMP signals at 20 and 100 GeV/c². At high masses, spin-independent WIMP spectra are degenerate in WIMP mass (as the kinematics only depend on the reduced mass). This leads to poor mass resolution, which can be significantly improved using additional, different target materials [176]. An excess for intermediate and low masses will be well-constrained both in mass and cross section using a xenon target alone.

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A simple variation of the vanilla spin-independent WIMP scenario is to allow the interaction strength to depend on the nucleon type (proton or neutron) with non-trivial coupling strengths f_p , f_n [177]. The deviation of the ratio f_p /f_n from 1 will then depend on the specific dark matter model. If for a given nuclear isotope, f_p /f_n = (Z − A)/Z, then this isotope would give no constraint. Fortunately, the mixture of multiple isotopes in xenon detectors provides sensitivity to even the most difficult case of f_p /f_n ≃ −1.4 [178–180], providing yet another benefit of xenon as a target material.

The simplest deviation from the spin-independent scattering to a more complicated coupling can be modeled by allowing the WIMP to interact solely with the nuclear spin but with different couplings a_p , a_n to protons and neutrons. This scenario is typically referred to as spin-dependent scattering [182–184]. If one simplifies this picture by assuming that one coupling vanishes, then the derivation of a differential rate of scattering events by WIMPs depends on the spins and nuclear structure (mostly of the unpaired nucleon) of the nuclei in the target. Contributions from two-nucleon currents improve the sensitivity to the spin-dependent WIMP–proton coupling in xenon, see section 2.5.2.

For xenon detectors, the two naturally occurring isotopes ¹²⁹Xe (spin-1/2) and ¹³¹Xe (spin-3/2), with natural abundances of 26.4% and 21.2%, respectively, are most relevant for this spin-dependent coupling. Both have an unpaired neutron, making xenon also an ideal target for detecting the spin-dependent WIMP–neutron cross section. The projected sensitivity for a next-generation liquid xenon TPC is shown in figure 7, calculated using the same assumptions and method as in figure 5.

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The spin-independent and spin-dependent scattering discussed in the previous sections 2.3 and 2.4 are the more frequently studied interactions of the WIMP with SM fields. Their motivation dates back to dark matter candidates in supersymmetric theories [183] defining the leading responses related to the nuclear density (therefore scaling coherently with the number of nucleons A, spin-independent interactions) or to the nuclear spin (spin-dependent interactions). A more systematic picture covering more general WIMP–nucleus interactions beyond standard spin-independent and spin-dependent scattering has been worked out recently using effective field theories (EFTs). This includes both a nonrelativistic framework, see section 2.5.1, as well as chiral EFT, see section 2.5.2, which incorporates the constraints from QCD at low energies.

2.5.1. Nonrelativistic effective field theory

2.5.2. Chiral effective field theory

2.5.3. WIMP–pion coupling

A novel contribution to WIMP–nucleus scattering that emerged from the chiral EFT analysis (section 2.5.2) concerns meson-exchange currents. In the simplest case, the WIMP couples to a virtual pion exchanged between two nucleons within the nucleus. Interestingly, meson-exchange contributions, which enter at subleading order in chiral EFT, can scale coherently with the number A of nucleons. The combination of the nuclear and chiral hierarchies defines a scaling that lies between the spin-independent and spin-dependent responses, coherent but suppressed in the chiral counting. Chiral EFT also predicts the leading meson-exchange currents to dominate over all other NREFT operators except the standard spin-independent one.

As observed in reference [169], once an underlying quark-level operator is specified, the resulting limits can be expressed in terms of a WIMP–pion cross section, in close analogy to the spin-independent and spin-dependent WIMP–nucleon cross sections. The proposed next-generation liquid xenon experiment will improve this result by a similar factor as the standard spin-independent limit, shown in figure 8.

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2.5.4. Three-flavor EFT and the ultraviolet

The WIMP–nucleus cross section is proportional to the nuclear structure factors, which encode the relevant information of the structure of the target nuclei. The EFT operators at the WIMP–nucleon level generate, at the nuclear level, six different nuclear one-body responses analogous to semileptonic weak interactions [225–227]. In addition, chiral EFT predicts two-nucleon nuclear responses associated with meson-exchange currents. The corresponding nuclear structure factors are obtained from the one-body nuclear responses ${\mathcal{F}}^{M}$, ${\mathcal{F}}^{{{\Phi }}^{{\prime\prime}}}$, ${\mathcal{F}}^{{{\Sigma }}^{\prime }}$, ${\mathcal{F}}^{{{\Sigma }}^{{\prime\prime}}}$, ${\mathcal{F}}^{{\tilde{{\Phi }}}^{\prime }}$, and ${\mathcal{F}}^{{\Delta }}$ [183, 187], and the two-body nuclear responses ${\mathcal{F}}_{\pi }$, ${\mathcal{F}}_{\text{b}}$ [170, 206]. The one-body structure factors decompose into isoscalar and isovector (or, equivalently, proton and neutron) contributions, e.g. ${\mathcal{F}}_{\pm }^{M}$. ${\mathcal{F}}^{M}$ and the two-body ${\mathcal{F}}_{\pi }$, ${\mathcal{F}}_{\text{b}}$ can receive coherent contributions from all A nucleons in the nucleus while about one in five nucleons contributes coherently to ${\mathcal{F}}^{{{\Phi }}^{{\prime\prime}}}$. These responses dominate spin-independent $({\mathcal{F}}^{M})$ and scalar WIMP–pion $({\mathcal{F}}_{\pi })$ scattering. ${\mathcal{F}}^{{{\Sigma }}^{\prime }}$ and ${\mathcal{F}}^{{{\Sigma }}^{{\prime\prime}}}$ are usually rewritten in terms of the more common S₀₀, S₀₁, S₁₁ or S_p , S_n in spin-dependent analyses. They are related to the spin distribution in the nucleus and are not coherent because the nuclear pairing interaction couples nucleons in spin-zero pairs.

The nuclear structure factors allow one to factorize the nuclear response from the hadronic matrix elements and the couplings of the WIMP. Schematically, the WIMP–nucleus cross section decomposes as

$$\begin{equation}\frac{\mathrm{d}{\sigma }_{\chi \mathcal{N}}}{\mathrm{d}{q}^{2}}\propto \sum\limits _{i}{\left\vert {c}_{i}{\mathcal{F}}_{i}({q}^{2})\right\vert }^{2}+\text{interference}\;\text{terms},\end{equation} \tag{ 1 }$$

where the ${\mathcal{F}}_{i}({q}^{2})$ denote the nuclear structure factors and the c_i involve a convolution of hadronic matrix elements and WIMP couplings. Thus, in the case of scalar operators, the role of the pion–nucleon σ term is well known in the literature [228–233]. In special cases, the WIMP–nucleus cross section can be expressed in terms of single-particle cross sections: (i) if only ${c}_{+}^{M}$ is non-vanishing it can be expressed by the spin-independent isoscalar WIMP–nucleon cross section (section 2.3); (ii) if only the coefficients of S_p or S_n are non-vanishing, by the spin-dependent WIMP–proton or WIMP–neutron cross section (section 2.4); and (iii) if only c_π is non-vanishing, by the scalar WIMP–pion cross section (section 2.5.3).

In general, reliable nuclear structure factors for any nuclear response require a good description of the nuclear target. The only exception is the leading ${\mathcal{F}}_{+}^{M}$ structure factor in spin-independent scattering, for which the purely phenomenological Helm form factor [167, 234] is a common and good description [235]. For heavy targets such as xenon, structure factors need to be calculated from nuclear theory. The nuclear shell model is presently the method of choice with significant progress in recent years. The shell model solves the many-body problem in a relatively small configuration space (one or two harmonic oscillator shells near the Fermi surface) with a phenomenological nuclear interaction adapted to the configuration space [236]. The description of excitation energies, charge radii, and electromagnetic properties of medium- and heavy-mass nuclei, including all stable xenon isotopes, is already very good [168, 170, 235]. State-of-the-art nuclear structure factors are easily available in dedicated notebooks documented in references [170, 187]. Figure 9 shows nuclear structure factors for a general coherent WIMP scattering off ¹³²Xe (26.9% natural abundance) with the hierarchy given by chiral EFT.

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More advanced nuclear structure ab initio calculations treat explicitly all nucleons in the nucleus (see e.g. references [237–242]). They can use nuclear interactions based on chiral EFT, thus consistently providing the nuclear states and WIMP–nucleon operators that enter the calculation of the structure factors. This will allow one to estimate theoretical uncertainties. While nuclear structure factors obtained with ab initio many-body techniques have historically been limited to light nuclei with A ⩽ 6 [207, 209, 243], recent progress has been significant and ab initio spin-dependent structure factors have been calculated very recently [210] with the valence-space in-medium similarity renormalization group method.

The recoil energy spectrum resulting from spin-dependent interactions is similar to the one expected from spin-independent interactions. Using different target materials with other experiments can help to break that degeneracy, as would be a different mixture of isotopes of xenon in a target. In addition, liquid xenon TPCs can even differentiate between these two interaction channels with one and the same exposure, as WIMPs might alternatively scatter inelastically off nuclei that possess low-lying excited states up to ∼100 keV [244], including ¹²⁹Xe and ¹³¹Xe [245–247]. This inelastic scattering in the nuclear sector is not to be confused with dark matter models in which the WIMP can be excited, as is discussed in the context of the inelastic dark matter (iDM) model in section 2.13.

Inelastic scattering is always non-coherent, because of the different initial and final nuclear states. This would allow one to narrow the nature of the underlying WIMP–nucleon interaction, testing the spin-dependent case upon detection in the simplest scenario. In addition to the NR, a prompt ER is caused by the de-excitation of the up-scattered xenon nucleus. Such interactions thus suffer from the larger background of ERs. However, since they would only be expected for non-coherent spin-dependent interactions, given sufficient statistics, a single xenon detector would be able to extract information about dark matter that is inaccessible to the elastic channel alone.

Observation of such inelastic scattering would provide a range of further insights to the nature of dark matter: each unique nuclear excitation is sensitive to a distinct portion of the WIMP halo, so that multiple contributions from the inelastic channel could be combined with that of the elastic channel to constrain the WIMP velocity distribution [245]. In addition, the range of observed recoil energies as well as the energy at which the inelastic channel begins to overtake the elastic one would indicate the mass of the incident WIMP. Finally, in contrast to the elastic channel, the inelastic event rate may be enhanced or suppressed with the enrichment or depletion of ¹²⁹Xe and ¹³¹Xe. This flexibility would allow one to optimize data acquisition in a xenon detector. The most stringent limit on inelastic WIMP–nucleon scattering currently comes from the XMASS detector [248]. Prospects for a future detection of dark matter detection with inelastic xenon transitions are further discussed in reference [249].

Given the number of different nuclear responses (section 2.6), a key question is how they could, in the event of a detection, be distinguished in order to extract information on the nature of the WIMP [195]. One possible strategy concerns the study of inelastic scattering into low-lying excited states of the xenon target, discussed in the previous section 2.7. The detection of the inelastic channel, in addition to the elastic scattering would primarily point to the non-coherent character of the WIMP–nucleus interaction, suggesting a spin-dependent interaction as the prime choice.

A second handle to discriminate the nuclear responses exploits their different dependence on the momentum transfer, see figure 9. The feasibility of this approach has been explored for several WIMP–nucleon interactions [250, 251]. In particular, reference [250] considered realistic detector settings, including projections for a next-generation experiment like the one proposed here, see figure 10. As with inelastic scattering, for most responses a discrimination becomes possible with sufficient statistics. However, due to the similarities in the q-dependence, a separation of isoscalar and isovector responses will be difficult.

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Finally, the nature of the WIMP–nuclear response and in particular its spin-dependent character can be tested by varying the enrichment or depletion on the isotopes with odd A¹²⁹Xe and ¹³¹Xe that is possible with a liquid xenon target. In this case it will be most powerful to combine the results of the proposed experiment with searches using spinless nuclear targets, such as argon, to further test the spin-dependent hypothesis. Likewise, to discriminate between isoscalar and isovector responses the most promising strategy takes advantage of the different proton to neutron ratios in different target nuclei. In this sense, xenon isotopes exhibit the smallest proton to neutron ratios, in contrast to the largest ones which are found e.g. in fluorine or argon.

Traditional momentum- and velocity-independent dark matter models used to drive experimental developments already starting in the 1990s. Those lead to the well-known low-energy recoil spectra, resembling simple distributions exponentially falling with energy [167]. Consequently, significant experimental effort went into lowering the energy threshold, the calibration for NRs in this energy regime, and improved understanding of relevant background sources.

However, many models, such as momentum-dependent effective models or non-trivial mixtures of interactions, result in a more complex NR signature with characteristic peaks in the higher nuclear energy regime. This includes many of the models discussed in the following, such as inelastic, composite, exothermic, and magnetic dark matter [188, 252–256] but also the well-known EFT operators for elastic scattering [189, 257, 258]. These effects manifest themselves often outside the traditionally analyzed energy ranges. The fact that most particles in the SM adhere to such more complex interactions provides strong motivation to explore this important higher-energy parameter space. Figure 11 show possible recoil spectra for selected interactions, taken from reference [259]. Further motivation to also probe higher recoil energies stems from the presence of Galactic streams that may result in higher recoil energies than from the customarily assumed isothermal halo [71, 72, 260–264].

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In case of discovery, features in the higher NR tails of recoil energy spectra might be used to determine the property of the dark matter–matter interaction. Further, the high-energy NR tails of the recoil spectrum are especially sensitive to astrophysical parameters that describe the dark matter velocity distribution, such as the maximum velocity, Galactic escape speed [42, 265], or the presence of tidal streams [74, 266, 267]. By employing multiple experiments with different target materials, it is possible to significantly reduce astrophysical uncertainties. For example, the complementarity between argon and xenon-based targets aids to determine the properties of the dark matter particle [157, 176, 268–271].

Despite the fact that dark matter–nucleus scattering is characterized by low-energy processes (for which EFTs could provide swift analyses and some general conclusions), further exploration of the internal structures in the interactions between dark matter and SM particles would involve high-energy processes such as those probed at colliders and in the early Universe. At sufficiently high energies, the EFT treatment will break down, as the internal mediators generating the effective dark matter–SM couplings become on-shell.

Simplified models of dark matter can provide a predictable framework to remedy the aforementioned problem, while keeping the number of free parameters manageable, see e.g. references [272–276] and references therein for review and [277–282] for some specific studies. In the simplest scenario, only the dark matter mass, mediator mass and a few couplings (depending on the specific models) connecting the dark sector to ours are assumed. This can readily build the interplay among dark matter signals in direct detection, high-energy colliders and astrophysical/cosmological evolution. In light of these complementary approaches, it should be noted that a next-generation xenon experiment is particularly well-suited to probe most of the remaining parameter space in some broad classes of simplified models, e.g. Z' mediated WIMP models [283]. In some realizations of simplified models, the tree-level dark matter–nucleon scattering cross section could exhibit either velocity-suppressed or spin-dependent features to pass the current strong constraints from the existing liquid xenon limits. Examples are a pseudo-scalar or axial-vector current in the interactions of the mediator with the SM quarks and/or the dark sector [284]. It is also worth mentioning that the tree-level interactions between the dark matter and the SM in simplified models can generate loop processes which may still induce detectable signals. These can play important roles in future of direct detection experiments such as the one proposed here [285–303].

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 [304–306]. 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 SM particles are therefore mediated by the SM gauge bosons and the Higgs boson, without the need to introduce additional mediators. Since the interactions are governed by the SM 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. One of the simplest models is a singlet with an additional neutral scalar stabilised by a Z₂ symmetry [307]. In general, we could consider multiplets (1, n, Y) under the SM gauge group SU(3)_C × SU(2)_L × 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 [304, 305, 308–311]. For a large multiplet n > 7, the Landau pole will be about one order of magnitude above the mass of electroweak multiplet [312], which makes the model contrived; conversely, new physics below the scale of the Landau pole may lead to an asymptotically safe scenario [313]. Ultimately, perturbative unitarity of the annihilation cross section provides a limit of n < 14 [311, 314].

Sommerfeld enhancement [315–320] and bound state effects [321–325] need to be included in accurate calculations of predictions. Target masses of the electroweak multiplet dark matter are in the range of 1–30 TeV [306, 324, 326] for n < 7, but can approach the unitarity bound for larger multiplets, which saturates at n = 13 [311, 314]. These masses are beyond the reach of the LHC [327–330] and would require one of the proposed future high energy colliders [311, 331–333]. In contrast, the direct detection of the electroweak multiplet dark matter is through one-loop processes involving the SM W, Z, and Higgs bosons. The spin-independent cross sections have been computed to be around 10⁻⁴⁷ cm² for the Majorana triplet (wino) [334] and 10⁻⁴⁸ cm² for the Dirac doublet (Higgsino) [335]. The other cases are expected to be within the same order [314]. 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 [311, 336, 337]. To avoid confusion, note that the LZ line in reference [311] corresponds to the sensitivity from the LZ design reports [108, 338] instead of the goals shown reference [99]. For an explicit phenomenological framework which captures most minimal supersymmetric Standard Model (MSSM) parameters [339], the significant boost of the next-generation xenon experiment to probe the possibility that the lightest supersymmetric particle is the dark matter, see e.g. figure 3(a) in reference [340].

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One classic WIMP dark matter model is the lightest supersymmetric partner (LSP). Supersymmetric models, such as the MSSM, with an exact R-parity, predicts that a stable electrically neutral LSP could be a cold dark matter candidate [140]. 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 (SUSY) and its low-energy phenomenology, see [341].

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 [342], 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 μ. This reduction is induced by a decrease of the coupling of the bino to the Higgs boson [343], as well as by a destructive interference between the contributions of the standard Higgs with the ones of non-standard Higgs bosons [344, 345]. 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 μ [346]. Moreover, there are regions of parameter space, called blind spots, in which the scattering amplitude is drastically reduced [343, 344, 346, 347]. The precise parameter space associated with these blind spots is slightly modified by loop corrections [348]. Quite generally, for the appropriate signs of μ, the spin-independent scattering cross section can easily be below 10⁻⁴⁷ cm² [346, 349–351]. 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 [220, 352]. The pure wino scenario has been strongly constrained by indirect detection of gamma rays from the Galactic center [353, 354] and local spheroidal satellite galaxies [355, 356], although the former is subject to large uncertainty from the dark matter profile. The spin-independent pure wino-nucleon cross section is around 2 × 10⁻⁴⁷ cm² [334], 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 cm² with a large theoretical uncertainty [335]. Depending on the mass splitting between neutral higgsinos, the inelastic scattering of higgsino dark matter could be potentially probed with such a future experiment [256].

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 [357]. In this scenario, direct detection experiments probe the dark matter fraction of the WIMP times its scattering cross section, and the next-generation experiment is motivated as its improved sensitivity now corresponds to a sensitivity to smaller fractions of dark matter [358–363]. In a most optimistic scenario, this same detector might then even detect multiple different components of dark matter, see section 3.

iDM was originally proposed [252] to resolve the tension between results published by the DAMA/LIBRA collaboration [364–366] and other direct and indirect observations [367–369]. Multiple particle candidates have since been proposed as iDM [319, 370], mostly motivated by the measured DAMA/LIBRA spectrum and the constraints for other experiments. Although ultimately this model failed given later exclusions from XENON100 [371], iDM 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 SM particles through an excited state of the dark matter particle itself. The mass difference of the excited state δ imposes a threshold on the energy transfer of the interaction, below which interactions are suppressed. This threshold on the energy transfer E_nr limits the population of dark matter that can interact with a given target to those with a minimum velocity β_min expressed by

$$\begin{equation}{\beta }_{\mathrm{min}}=\sqrt{\frac{1}{2{M}_{N}{E}_{\text{nr}}}}\left(\frac{{M}_{N}{E}_{\text{nr}}}{\mu }+\delta \right),\end{equation} \tag{ 2 }$$

where M_N is the nucleus mass and μ 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 [71, 252], strong dependencies on the particular target material [372], or halo distributions with differing high velocity behavior [373]. 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 [374]. Calculating this spectrum for a given detector can be done in a model-independent way; software packages have been developed [375] to perform these calculations in a consistent manner. Dedicated searches for iDM are thus required and have been carried out in XENON100 [189], PandaX-II [376], and LUX [377].

Self-interacting dark matter (SIDM) [379, 380] 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 [381] for a review. SIDM phenomenology is also expected if the dark matter is composite (section 3.10) or arises from a mirror world scenario (section 3.12). 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 [382–385]. In many particle physics realizations of SIDM, there exists a light force carrier that mediates dark matter self-interactions [386–397]. When the mediator couples to SM particles, it may generate dark matter signals in direct detection experiments [398]. For a typical SIDM model, the mediator mass is comparable to or less than the momentum transfer in NRs. Compared to WIMPs with a contact interaction, the SIDM signal spectrum is then more peaked toward low recoil energies [378, 399], 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 $\sim 1{0}^{-10}$ [400, 401] 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 [402]. 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.

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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 [403] and AMS-02 [404], as well as the bright 511 keV x-ray signal from the Galactic Center [405], and the high-energy cosmic ray electron data from DAMPE [406]. Leptophilic dark matter is easily realized in concrete models. This is the case, for instance, if dark matter interactions with the SM particles are mediated by a new gauge boson that couples predominantly to leptons [407–409]. Another example are dark matter interactions mediated by new scalar particles carrying lepton number, such as the sleptons in supersymmetric models [410–414].

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 [409, 413, 415–421]. The reason for this is the more favorable kinematics: the scattering of a heavy WIMP (≫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 [415, 420, 422], and searches for this process have been carried out by many experiments, including XENON100 [423–425] and LUX [426]. Scattering on electrons is particularly efficient for sub-GeV dark matter [427], 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 [415, 428, 429]. 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 [430]. Future lepton collider would lead to further improvements [431–433]. Progress with these experiments will be complementary to advances from the experiment proposed here.

As the Earth revolves around the Sun, a sinusoidal annual modulation should be observable in the dark matter flux hitting direct detection experiments underground [49, 434], with details depending on the phase space distribution of the halo [435, 436]. The DAMA/LIBRA collaboration upholds a long-standing claimed observation of an annually modulating event rate [366] with a statistical significance in excess of 9σ. 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 [69, 437]. Moreover, experiments such as ANAIS [438, 439], COSINE-100 [440, 441] and SABRE [442] 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 [443–446]. Such shadowing effect also provides additional sensitivity to cosmic-ray boosted dark matter (CRDM) with mass lower than around 1 GeV [447]. Many models within the scope of a future xenon experiment will exhibit such a modulation (section 3).

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 [64, 108], especially when coupled to frequent calibrations using fast-decaying radioisotopes such as ^83mKr [448, 449].

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 CEνNS signal of astrophysical neutrinos [164, 174, 450]. While there is a substantial science case for the detection of astrophysical neutrinos in their own right (section 5), 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 ER [451, 452] and NR channels [164, 453–456]. 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 [457]. Just like any generic limit on dark matter, the shape of a neutrino fog is dependent on nuclear [458], astrophysical [172] and particle model [258, 454, 455] inputs for the dark matter signal. Given non-standard neutrino-nucleus interactions, these could be further modified [459, 460] and even raised by several orders of magnitude [461].

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 [462], or the complementarity between different target nuclei [463]. However, only direction-dependence provides enough of a discriminant to fully subtract the background [464–468], but measuring this in any large-scale experiment is extremely challenging.

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 ∼10 GeV/c², and atmospheric neutrinos above that. The ⁸B flux is measured at the 2% level from Solar neutrino data [469]. 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 ∼20% uncertainty (section 5.3 and [165]). 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+ [470], JUNO [471] and DUNE [472, 473] 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 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 ∼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 [474]. This is where much of the remaining supersymmetric WIMP candidates [352, 475–477], as well as many alternative WIMP models [289, 478, 479] lie.

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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 [498].

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 [499]) 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.

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 [500] (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 [501]. 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 ∼10%–20% given liquid xenon scintillation light [502, 503].

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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 [503] (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 [505].

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Interactions from WIMP candidates below ∼GeV/c² 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 [181, 491, 505–508]. 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 [507–515]. 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 ER signals, as their S1 is much smaller than for a NR 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).

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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 [415, 427]. 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 [181, 492, 507]. To avoid confusion, here the dark photon acts as force carrier, as opposed to the analysis described in section 3.8.1, 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 [415, 427].

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 [517]. 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 section 2.5.1), reference [517] 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 [518] 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.

The progressive loss of the scintillation (S1) response with decreasing NR 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 [521] 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 [522]. Since ERs produce a more detectable signal than NRs, this channel enables liquid xenon detectors to reach dark matter masses of order ∼100 MeV/c² [494, 519, 523, 524], 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 [56, 58, 490]. 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 [525]. This could provide a direct test of the theoretical predictions of the Migdal effect.

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Similar to the Migdal effect, nuclear bremsstrahlung searches leverage the fact that in liquid xenon at low energies, ERs produce a stronger signal than NRs [497]. 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 [526]. The theoretical motivation and event rates for bremsstrahlung have been derived in reference [497] and searches using liquid xenon detectors have been published in reference [66, 494, 527].

Kinematically, the large xenon nucleus (average mass 122 GeV/c²) is not well suited for an efficient transfer of energy from Galactic dark matter with mass ≲1 GeV/c². As a result, nearly all of the resulting xenon NRs 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 [528]. 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 [529]. 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 [530]. 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 [531], although there is a reported loss of about half of the S1 and electron signals for an H₂ mole fraction of 1.1%. 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 [532], but could be considered if SiPMs are used instead of PMTs.

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 [456, 533–538]. This process, often denoted 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. σ_χN ≳10⁻³¹ cm² for m_χ = 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 [447, 533, 535], which have sensitivity in a similar region of parameter space. Additionally, cosmic-ray upscattering extends the sensitivity of liquid xenon detectors to iDM models with mass splittings up to $\sim 100$ MeV [539].

Another upscattering mechanism extending the sensitivity of liquid xenon detectors to dark matter masses down to keV scales is a process called 'solar reflection' [540–545]. 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.

In several models of so-called 'neutrino portal' dark matter, Galactic dark matter self-annihilates into neutrinos [546–550]. These in turn may be detected at direct detection experiments with high rates via CEνNS (see section 5.1.1). 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] GeV/c² [551]. The sensitivity to this neutrino flux would complement neutrino detectors such as Super-Kamiokande.

Similarly, dark matter may annihilate into another component of dark matter, which, if relatively light, may receive a Lorentz boost [552, 553]. Thanks to its higher kinetic energy, such a light annihilation product might in turn be discovered in a direct detection experiment. 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 [551].

Alternatively, dark matter may annihilate or decay within the target volume of future liquid xenon detectors [554]. Considering deposited energies up to a few MeV, the relevant final states include annihilation into γγ and e⁻ e⁺, and decays into γγ, γν and e⁻ e⁺. Although the sensitivity obtained is not as high as the current limits from cosmological considerations [555] and x-ray measurements [556], this is a complementary approach in a well-understood background environment and free of the large uncertainties typically present in indirect detection experiments.

Broad classes of non-WIMP dark matter candidates are feebly interacting massive particles (FIMPs), which are produced by the thermal freeze-in mechanism [557, 558], 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 SM [559]. Both classes share the feature that they couple to SM particles with cross sections far smaller than the weak scale. These include fermions such as sterile neutrinos [560] and gravitinos, both of which only couple to the SM 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 SM particles in such way to be observed with low-background experiments [561–563]. 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 keV/c² ≲ m ≲ 100 MeV/c² with relatively large scattering cross section with nucleons and/or electrons, which blurrs the distinction between FIMPs and WIMPs [564]. In the following, we give two examples of possible keV-scale candidates, namely dark photons and axion-like particles (ALPs), and discuss related signals.

3.8.1. Dark photons

3.8.2. Axions and axion-like particles

3.8.3. Solar axions, dark matter, and baryon asymmetry

As discussed in section 6.1, a liquid xenon TPC can detect the QCD axion and ALPs 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 [577–579, 603] 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 references [604–610], with couplings that are sufficiently large to be detected in the proposed detector.

In one such cosmological scenario for example [609], a non-zero field velocity delays the onset of field oscillations, enhancing the axion abundance relative to the conventional misalignment mechanism. For ALPs, this field velocity can simultaneously explain the baryon asymmetry of the Universe [611]. Fitting the ratio of dark matter to baryon abundances predicts the axion coupling in terms of its mass m_a

$$\begin{equation}{g}_{a\gamma }\simeq 2\times 1{0}^{-11}{c}_{\gamma }\enspace {\mathrm{G}\mathrm{e}\mathrm{V}}^{-1}{\left(\frac{{m}_{a}}{\mathrm{m}\mathrm{e}\mathrm{V}}\right)}^{1/2},\end{equation} \tag{ 3 }$$

where c_γ 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_aγ ∼ 3 × 10⁻¹¹ GeV⁻¹ [612], corresponding to m_a ∼ meV.

Asymmetric dark matter is one of the most motivated non-WIMP dark matter candidate. Similar to the physics that sets the SM 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 [613–624]. Then, similarly to protons and baryon number, the lightest symmetry-carrying state in the dark sector is cosmologically stable. If η_B and η_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

$$\begin{equation}\frac{{{\Omega }}_{\mathrm{d}\mathrm{m}}}{{{\Omega }}_{\mathrm{B}}}=\left\vert \frac{{\eta }_{\mathrm{d}\mathrm{m}}}{{\eta }_{\mathrm{B}}}\right\vert \frac{{m}_{\mathrm{d}\mathrm{m}}}{{m}_{\mathrm{B}}}.\end{equation} \tag{ 4 }$$

Here, m_dm is the mass of the lightest asymmetry-carrying dark matter particle.

In many beyond the SM 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, Ω_dm ≃ 5Ω_B, if m_dm ∼ few GeV/c². This strongly motivates searches for dark matter particles in the ∼1–10 GeV/c² mass range. Independently-motivated theories, such as those based on 'neutral naturalness' Twin Higgs [625] or composite Higgs explanations of the LHC-data driven little hierarchy problem for the weak scale also predict dark-sector states in this mass range [395, 626–628].

In theories such as Twin Higgs, the leading interactions of the individual asymmetric dark matter particles with the SM 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. In other cases the leading higher-dimensional interaction of the individual asymmetric dark matter particles arises from the 'connector' interaction that determines the relation between η_dm and η_B [389, 629–632], or can sometimes be related to a freeze-out process involving heavier states [633]. In effect, since the freeze-out mechanism is no longer setting the dark matter density, the scattering cross section of asymmetric dark matter with the SM can be smaller (or larger) than that for WIMPs.

Similar to the rich set of cosmologically stable composite states that exist in the SM 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 if the dark matter is part of a dark sector (as is in turn often so in explicit constructions of physics beyond the SM), or if the dark matter is self-interacting. These composites may be strongly-bound 'dark (hidden) pions' or 'dark (hidden) baryons' in dark (hidden) QCD [634–638]; 'dark nuclei' or 'dark nuggets' [255, 639–644] of possibly extremely large dark nucleon number; 'dark atoms' [395, 645, 646] made of dissimilar stable dark matter particles; or they could be weakly bound two-body 'dark-onium' states of identical or conjugate particles [321, 647–650]. Further, topological solitons such as 't Hooft–Polyakov monopoles [651, 652] might exist in the dark sector and provide a form of composite dark matter with a rich phenomenology [392]. Q-balls [653] can also be thought of as a form of nontopological composite states, carrying a conserved quantum number, the Q-ball description sometimes applying to bound states of bosonic dark matter particles.

Such composite states typically give rise to a variety of new or modified signatures in direct detection experiments. One of the most studied case is that of large dark nuclei in which case the recoil spectrum is modified by a characteristic quasi-universal dark sector form factor [255, 654–656]. Since there is often an N² (N ≫ 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 significantly weakened [255]. In addition, many of these composite states have low-lying excitations, leading to a rich set of possible inelastic signatures (section 2.13). 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 [657].

If a dark matter particle is absorbed in a direct detection experiment, its mass energy may be transferred to the nucleus, leading to a recently-proposed, distinct dark matter direct detection signal [658, 659]. Such a process can be realized from a UV-complete theory where the dark matter has a mass-mixing with the SM neutrino and the incoming dark matter is converted into a neutrino after scattering through a neutral current (NC), χ + N → ν + N. Since the mass of the dark matter dominates this process, the resulting NR energy has a sharp peak at ${E}_{r}\sim {m}_{\chi }^{2}/(2{m}_{N})$. The first search for such a mono-energetic recoil signature was performed in PandaX-4T [660], with a resulting constraint on the absorption dark matter–nucleon scattering cross section at the level of 10⁻⁵⁰ cm².

Another possible absorption process is the induced beta-decay through a charged current (CC) $\chi +{}_{Z}{}^{A}\mathrm{N}\to {e}^{-}+{}_{Z-1}{}^{A}N$. The corresponding signature has multiple correlated signals: the ejected energetic electron, the recoil of the daughter nucleus, a gamma from the de-excitation of the daughter nucleus, and possibly another beta-decay of the final nucleus if that is unstable. It is also possible that such an absorption happens when dark matter interacts with electrons [661–663]. The signature in a direct detection experiment is a mono-energetic ER. Currently the strongest constraints on this channel are also provided by PandaX-4T [664].

Closely related to both asymmetric and composite dark matter is the idea of mirror dark matter [665–668]. This is the intriguing idea that an exact copy of the SM 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 NRs similar to those expected from $\sim 7\enspace \,\mathrm{G}\mathrm{e}\mathrm{V}/{c}^{2}$ WIMPs with a cross section around 10⁻⁴⁴ cm², as well as in ERs [669–671]. The strongest direct detection constraint on the kinetic mixing currently comes from LUX [672], with a factor of ∼2 better projected sensitivity for the current-generation detectors [572]. Mirror dark matter as a hypothesis is potentially entirely falsifiable by the next-generation liquid xenon experiment discussed here [673].

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 [674, 675]. The excited state could be populated through upscattering in or near the detector (and have short lifetimes $\sim 1\enspace \mu \mathrm{s}$) or in the Earth (lifetimes ∼ (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 keV-order mass splitting. Such 'luminous dark matter' was first proposed as a potential explanation of the DAMA/LIBRA modulation [674] and has since been used to explain the recent XENON1T excess [676]. While the former scenario is now strongly constrained, the latter scenario will be confirmed or ruled out by a next-generation liquid xenon experiment.

A natural scenario where dark matter dominantly scatters off nuclei through an inelastic transition in the dark sector (section 2.13) is the case of a magnetic dipole interaction [677]. 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 [678–681].

For magnetic iDM, 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 [677]. 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 NR from the initial scatter and an ER from the decay shortly thereafter. Searching for the photons produced by this decay can be an additional handle on uncovering such a scenario [675, 682]. A dedicated search has been performed by XENON100 [683], 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.

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 ≃10¹⁹ GeV/c², as opposed to numerous lighter particles. Super-massive species are motivated by supersymmetric and grand unified theories (GUTs) [684], or production by Hawking evaporation of early Universe primordial black holes [685, 686]. 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 [687], and provide excellent targets. The detection of any such particles could help determine parameters of the early Universe such as inflation [688], or an epoch of early matter domination [687, 689] leading to efficient primordial black hole production. Their existence could also imply new light mediators beyond the SM [690].

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 ≃ 10¹⁹ GeV [156], in a complementary way to the range that could be probed using dedicated neutrino experiments [691–693]. A dedicated search using the DEAP-3600 liquid argon detector has already been published [694]. Clusters of dark matter formed through self-attraction [640, 654, 695], such as 'dark blobs' or 'dark nuggets' [255, 640, 655, 656] could exist at these high masses and create tracks if they have sufficiently large cross-sections.

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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 (0νββ) [696–699]. The observation of this rare nuclear decay process, forbidden in the SM, 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 [700] and ¹³⁶Xe, with the latter offering a larger sensitivity to the 0νββ half-life $({T}_{1/2}^{0\nu })$. The best experimental constraint on the ¹³⁶Xe 0νββ half-life, ${T}_{1/2}^{0\nu } > 1.07\times 1{0}^{26}\enspace \,\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s}$ (90% CL), is set by the KamLAND-Zen collaboration using ¹³⁶Xe dissolved in a liquid scintillator [701]. Among double-beta experiments, only ⁷⁶Ge, ⁸²Se, ¹⁰⁰Mo and ¹³⁰Te offer 0νββ half-life limits comparable to ¹³⁶Xe [702–707]. The EXO-200 collaboration demonstrated that better energy resolution and background rejection can be achieved with a liquid xenon TPC [708], and the PandaX-II collaboration conducted a first search using a dual-phase natural xenon detector [709]. XENON1T recently demonstrated that energy resolutions below σ/μ = 1% at Q_ββ can be achieved in liquid xenon TPCs used for dark matter searches [116].

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 $\sim 40\,000\enspace \,\mathrm{k}\mathrm{g}$ of non-enriched xenon can already improve the sensitivity to 0νββ 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 (section 7.2). Figure 22 shows the relevant sources of background with a hypothetical 0νββ signal for the innermost 5000 kg of natural xenon in the TPC of a proposed next-generation detector [710]. The background from material-induced gamma rays will be further reduced in more massive detectors than the one simulated in figure 22.

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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) [715, 716], 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 0νββ 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 (2νββ) of ¹³⁶Xe and β-decay of ¹³⁷Xe.

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In addition, there exist mechanisms of 0νββ 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 EFT approach [717–726] which in the case of chiral EFT also provides a hierarchy for the relevant nuclear matrix elements [727–736], along similar lines as described in section 2.5 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 0νββ decay, precision measurements of the 2νββ decay can reduce the experimental uncertainty on the 2νββ nuclear matrix element [737] and constrain the underlying nuclear theories [699, 738, 739]. In situ measurement of this decay can be performed directly in the detector, even with a natural xenon target [740]. This is especially relevant regarding 0νββ 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 [699, 739]. The nuclear many-body methods used to calculate 0νββ nuclear matrix elements are generally the same that are also used to obtain the nuclear structure factors in section 2.6. The nuclear shell model among other more phenomenological approaches yields most predictions [725, 741–749], complemented by recent ab initio studies [736, 750–752]. A precise 2νββ spectrum shape measurement can provide insights toward reliable 0νββ nuclear matrix element calculations [753]. In addition, precision measurements of 2νββ decay can also be used to probe new physics. For example, right-handed lepton currents affect the angular and energy distributions of the decay [754], MeV-scale sterile neutrinos can be searched for through kinks in the 2νββ spectrum [755, 756], and neutrino self-interactions can leave an imprint on the spectrum as well [757]. Because lepton number is not necessarily violated in 2νββ decay, this is independent of the neutrino nature and can be used to constrain or pinpoint properties of both Majorana and Dirac neutrinos.

Similar to double beta decay, double electron capture is a second order weak interaction process [758, 759] with extremely long half-lives. Two electrons are captured from the atomic shell and two protons are converted into neutrons. In the SM decay, two neutrinos carrying virtually the total Q-value are emitted and leave the active volume undetected (2νECEC). 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 keV for the double K-capture [760] as the most likely case [761]. 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 [762–764]. A precise measurement would help to narrow down uncertainties, which in turn have implications on the neutrino mass scale derived from 0νββ as discussed in section 4.1.

Following hints in XMASS [765], the half-life of the ¹²⁴Xe double K-capture has recently been measured by XENON1T [766]. At ${T}_{1/2}^{2\nu \text{KK}}=(1.8\pm 0.{5}_{\text{stat}}\pm 0.{1}_{\text{sys}})\times 1{0}^{22}\enspace \,\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s}$, it agrees with recent theoretical predictions [762–764]. For comparison, this is about one order of magnitude slower than the 2νββ 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 [761]. Their measurement would help to decouple the nuclear matrix element from phase-space factors.

Beyond the SM, the double electron capture on ¹²⁴Xe without neutrino emission (0νECEC) can complement 0νββ in addressing fundamental questions about the mass and nature of the neutrino [767, 768]. To conserve energy and momentum, 0νECEC 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 [769]. 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 [760]. If this decay is realized, the experimental signature contains multiple γ-rays emitted in a cascade, so coincidence techniques could increase experimental sensitivity [770].

The ¹²⁴Xe Q-value of 2857 keV also allows second-order decays involving positrons [771]. Examples are the as-yet unobserved SM 2νECβ⁺ and 2νβ⁺ β⁺ decays, as well as the hypothetical 0νECβ⁺ and 0νβ⁺ β⁺ decays. The decay 2νECβ⁺ is predicted to have a half-live one order of magnitude above that of 2νECEC [772]. 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 [770, 773] and be a sure signal in the next-generation detector. The 2νβ⁺ β⁺ decay is expected to be several orders of magnitude slower [772]. It exhibits a unique signature with five point-like ionization clusters, located in the same plane with the central vertex [774].

On the neutrinoless side, 0νECβ⁺ would be favoured in the absence of resonance enhancement for 0νECEC, even though the decay rate is expected to be suppressed by about three orders of magnitude with respect to the 0νββ decay of ¹³⁶Xe [772, 775–777]. Here, the current lower limits on the half-lives are on the order of 10²¹ years [778–780]. 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 γ-rays. Moreover, limits on half-lives of neutrinoless second-order weak decays in ¹²⁴Xe could complement 0νββ searches in ¹³⁶Xe and other nuclei and help to identify the decay mechanism [770, 781–783]. These channels provide an exciting avenue for the next-generation detector discussed here to complement ongoing searches for double-weak processes.

Neutrinos can interact with liquid xenon through CC and/or NC interactions to produce detectable ER and NRs. The neutrino-induced rate is

$$\begin{equation}\frac{\mathrm{d}R}{\mathrm{d}{T}_{\mathrm{R}}}=\mathcal{N}\times {\int }_{{E}_{\nu }^{\mathrm{min}}}\phi \left({E}_{\nu }\right)\times \frac{\mathrm{d}\sigma ({E}_{\nu },{T}_{\mathrm{R}})}{\mathrm{d}{T}_{\mathrm{R}}}\,\mathrm{d}{E}_{\nu }\end{equation} \tag{ 5 }$$

where $\mathcal{N}$ is the number of target nuclei or electrons per unit of mass of detector material (for nuclear and ERs, respectively), $\phi \left({E}_{\nu }\right)$ is the neutrino flux as a function of the neutrino energy as shown in figure 25 [786], and ${E}_{\nu }^{\mathrm{min}}\enspace$ is the minimum neutrino energy required to generate a recoil at an energy T_R. For a NR, in the limit where m_N ≫ E_ν , the minimum energy is given by

$$\begin{equation}{E}_{\nu }^{\mathrm{min}}=\sqrt{\frac{{m}_{N}{T}_{\mathrm{R}}}{2}},\end{equation} \tag{ 6 }$$

whereas in the case of an ER, it is given by

$$\begin{equation}{E}_{\nu }^{\mathrm{min}}=\frac{1}{2}\left({T}_{\mathrm{R}}+\sqrt{{T}_{\mathrm{R}}\left({T}_{\mathrm{R}}+2{m}_{e}\right)}\,\right).\end{equation} \tag{ 7 }$$

The differential cross section depends on the nature of the interaction. In the next two sections, we discuss CEνNS and the electroweak interaction, which constitute the major contributions to the potential detectable signal for liquid xenon detectors.

5.1.1. Coherent elastic neutrino-nucleus scattering

In the SM, elastic neutrino-nucleon scattering proceeds only through NC interaction with the exchange of a Z-boson. The resulting differential neutrino-nucleus cross section as a function of the NR energy T_R and the incoming neutrino energy E_ν is

$$\begin{equation}\frac{\mathrm{d}\sigma ({E}_{\nu },{T}_{\mathrm{R}})}{\mathrm{d}{T}_{\mathrm{R}}}=\frac{{G}_{\mathrm{f}}^{2}}{\pi }{m}_{N}{\left(Z{g}_{v}^{p}+N{g}_{v}^{n}\right)}^{2}\left(1-\frac{{m}_{N}{T}_{\mathrm{R}}}{2{E}_{\nu }^{2}}\right){F}^{2}({T}_{\mathrm{R}}),\end{equation} \tag{ 8 }$$

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 ${g}_{v}^{p}=1/2-2\,{\mathrm{sin}}^{2}\,{\theta \,}_{w}$, where θ_w the weak mixing angle. Because sin²  θ_w ≃ 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) → 1. In lieu of experimental data on the neutron distribution in the nucleus, a typical parameterization is the Helm form factor [234] that is also commonly used for WIMP direct detection [167, 789]. Note that equation (8) gives the leading form of the cross section, keeping only the coherently enhanced part of the vector interaction; reference [790] has the complete expressions.

In effect, this CEνNS [791] 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 [792, 793].

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5.1.2. Electroweak interaction

The neutrino-electron electroweak interaction proceeds through both CC (W-boson exchange) and NC (Z-boson exchange) interactions. In the free electron approximation, the resulting differential neutrino-electron cross section as a function of the ER energy T_R and the incoming neutrino energy E_ν is

$$\begin{align}\hfill \frac{\mathrm{d}\sigma ({E}_{\nu },{T}_{\mathrm{R}})}{\mathrm{d}{T}_{\mathrm{R}}}& =\frac{{G}_{\mathrm{f}}^{2}{m}_{e}}{2\pi }\left[{\left({g}_{v}+{g}_{a}\right)}^{2}+\left({g}_{a}^{2}-{g}_{\nu }^{2}\right)\frac{{m}_{e}{T}_{\mathrm{R}}}{{E}_{\nu }^{2}}+{\left({g}_{v}-{g}_{a}\right)}^{2}{\left(1-\frac{{T}_{\mathrm{R}}}{{E}_{\nu }}\right)}^{2}\right],\hfill \end{align} \tag{ 9 }$$

where m_e is the electron mass, G_f is the Fermi coupling constant, g_v = 2 sin²  θ_w − 1/2 and g_a = 1/2 are respectively the vectorial and axial coupling, and θ_w is the weak mixing angle. In the context of ν_e + e → ν_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 → g_v + 1 and g_a → g_a + 1. This is then contributing to enhance the ν_e + e → ν_e + e scattering cross section with respect to the ν_τ,μ + e → ν_τ,μ + 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 ER 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 reference [163]. The inclusion of these atomic effects result in a reduction of the neutrino-induced ER event rate below $\sim 5$ keV. Importantly, this reduces the neutrino background in the [2–10] keV energy range by ∼22%. Figure 27 shows the ER 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.

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Experimental studies of solar neutrinos date back to over half of a century ago [794]. 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 [795]. 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 [796]. With this solution, at low energies ≲5 MeV, vacuum oscillations describe the neutrino flavor transformation, and the electron neutrino survival probability is ≳50%. At energies ≳5 MeV, matter-induced transformations describe the flavor transformation, with a corresponding survival probability of ≳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 [797], SNO [798], and Borexino [799]) that are sensitive to ERs from neutrino-electron elastic scattering find that, at ER 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 [797], is discrepant at the $\sim 2\sigma$ level relative to that measured by KamLAND [800]. Non-standard interactions (NSIs) provide a possible solution to this discrepancy [801].

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 [803] relied on many simplifying assumptions, but nevertheless fit solar observables well, in particular helioseismology data. More recent calculations however [804], while more sophisticated in construction, were ultimately worse fits to the data [804–807]. 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 [808], and has not yet been resolved. A global analysis of all solar neutrino fluxes remains inconclusive [469]. A step toward resolving this problem will be to accurately measure the flux of solar neutrinos from the carbon, nitrogen, oxygen (CNO) nuclear fusion cycle, first achieved by Borexino [809], which is possible with the experiment discussed here (section 5.2.4).

5.2.1. Boron-8 solar neutrinos (NR)

5.2.2. Hep solar neutrinos (NR)

5.2.3. pp solar neutrinos (ER)

5.2.4. CNO neutrinos (ER)

5.2.5. Neutrino capture on xenon-131 and xenon-136

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.

While the atmospheric neutrino flux for energies ≳ 1 GeV has been well studied by the aforementioned experiments, the low-energy flux of atmospheric neutrinos, ≲100 MeV, is difficult to both model and measure [818]. 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 [819] will be challenging to discern, given the low interaction rates. In fact, measuring atmospheric neutrinos will require an exposure of order 700 tonne-years [165], thus providing a benchmark target exposure for a next-generation liquid xenon observatory.

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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 [820, 821]. 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 [822–824]. 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 [825, 826].

5.4.1. Galactic supernova neutrinos

5.4.2. Pre-supernova neutrinos

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 [839, 840]. 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 [841]. Figure 29 indicates that a next-generation liquid xenon experiment operating at 0.1 keV energy threshold would detect, in a 12 h window prior to collapse, $\mathcal{O}$(100) pre-supernova neutrinos from a massive star 200 pc away, e.g. Betelgeuse [838]. 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 [842–844].

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5.4.3. Supernova early warning system

5.4.4. Diffuse supernova neutrinos

The Earth is a rich source of antineutrinos with energies in the MeV range, due to radioactive decays in Earth's crust and interior [849]. A signal from these geoneutrinos has been measured at Kamland [856] and Borexino [857]. 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.

5.6.1. 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 $\sim 0.4$% [469]. The dependence of the neutrino-electron cross section on the Weinberg (weak) angle sin²  θ_w thus allows for an independent measurement of this quantity, at energies far below the reach of colliders. Precision determinations of sin²  θ_w must be made by running LEP measurements (at ∼100 GeV) down to lower energies. At present, the lowest-energy determination of sin²  θ_w remains above the MeV scale [858]. ERs from pp neutrinos yield an exchanged momentum on the order of ∼keV, so a detection of the pp flux via ERs in next-generation xenon experiments will cover new and uncharted territory. The next-generation xenon detector discussed here would be able to constrain sin²  θ_w with (4–5)% precision [815] 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 sin²  θ_w with a precision of 1.5% at the keV scale [859]. This is complementary to measurements using CEνNS of pion-decay neutrinos as achieved by the COHERENT collaboration [860]. Applying the RRPA correction (see section 5.1.2 and [163]), the expected ER 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 sin²  θ_w down to 1.4% for the energy transfer in the range of (0–15) keV.

A deviation of sin²  θ_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 Q². Figure 30 shows an example of the variation that could be produced by a 50 MeV Z'-mediator, with a coupling in the range required to simultaneously explain the muon (g − 2)_μ anomaly [861–863].

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5.6.2. 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% [815]. Such a measurement would serve as a test of the Mikheyev–Smirnov–Wolfenstein large mixing angle (MSW-LMA) solution of neutrino oscillation and a probe of exotic neutrino properties and NSIs. 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 [864].

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5.6.3. Searching for new physics of neutrinos

Originally postulated to resolve the strong CP problem in QCD [574–576], axions have emerged as a suitable non-baryonic dark matter candidate [577–579, 1005, 1006]. 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 [594, 1007–1012]. They may be sought in the dark matter galactic halo within which they would cluster [1013] as a cold dark matter axion.

Independently of being dark matter, if an axion or ALP exists in nature, then it should be produced copiously in the hot solar plasma [1014, 1015]. Due to the ∼keV temperature of the Sun, solar axions are produced with roughly thermal fluxes in the 1–10 keV energy range, and are thus well-suited for detection in xenon experiments. Via their coupling to the photon, g_aγ , 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 [1016, 1017]. Another widely considered QCD axion model labeled the 'DFSZ' axion [1018, 1019] 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 [1020].

The primary way for xenon experiments to measure the axion is through the axioelectric effect [596], which allows constraints to be set on g_ae . Xenon experiments may also constrain g_aγ : both by measuring the Primakoff component [1021] of the solar flux (which is dependent only on g_aγ ), as well as by exploiting inverse Primakoff conversion inside the detector [612, 945]: aZ → γZ. In the latter case, the sensitivity to solar axions is boosted, even if the value of g_aγ 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 [1022]. A next-generation xenon experiment with a ∼1000 tonne-year exposure may even be able to out-perform devoted solar axion telescopes [612] such as the planned International Axion Observatory (IAXO) [1023].

The ER 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 ER background levels and are therefore ideal for this search. Among underground detectors, liquid xenon TPCs place the strongest constraints to-date on g_ae with solar axions [495, 597, 599, 600, 1024, 1025].

The excess of ER events seen in XENON1T [495] 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 [589, 890, 926, 976]. 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.

Dark matter searches start to probe various novel neutrino-induced signals, see e.g. references [164, 872]. 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 [876].

This is apparent in limits from ERs. In figure 32 we show the observed ER spectrum observed by several dark matter as well as neutrino experiments, adopted from references [1026, 1027] with the most recent XENON1T measurements [64] included. They represent about two orders of magnitude improvement over the XENON100 background rate.

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The next generation of experiments will have further sensitivity [892, 962]. 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 [1029]. In this case the differential cross section is

$$\begin{equation}\frac{\mathrm{d}\sigma }{\mathrm{d}{E}_{r}}={\mu }_{\nu }^{2}\alpha \left(\frac{1}{{E}_{r}}-\frac{1}{{E}_{\nu }}\right),\end{equation} \tag{ 10 }$$

where μ_ν 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 SM 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 [495] improves the limit in dipole moments to $< 3\times 1{0}^{-11}$ 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 reference [1027]. 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

$$\begin{equation}\frac{\mathrm{d}\sigma }{\mathrm{d}{E}_{r}}=\frac{{g}_{\mathrm{B}\text{\mbox{--}}\mathrm{L}}^{4}{m}_{e}}{4\pi {(2{m}_{e}^{2}{E}_{r}^{2}+{m}_{\mathrm{B}\text{\mbox{--}}\mathrm{L}}^{2})}^{2}},\end{equation} \tag{ 11 }$$

where m_B–L and g_B–L are the mass and coupling. Here, we have dropped subleading terms in E_r /E_ν 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 $1/({q}^{2}-{m}_{\mathrm{B}\text{\mbox{--}}\mathrm{L}}^{2})$ propagator in the amplitude, with q² = 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 [1030], the GEMMA reactor experiment [1031], or the XMASS experiment [1032]. In fact, the discussion around the possible excess observed by XENON1T [495] can already be used to place a constraint on g_B–L < 3.6 × 10⁻⁷ for mediators with mass m_B–L < 10 keV. This is already comparable with the constraint from GEMMA [901]. 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 [1031], 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 [1033].

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In addition to the physics discussed in section 6.5, 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 [1034]. A 50 days run with a 3 MCi ⁵¹Cr source produces 82 ν–e elastic scattering events in the XENON1T detector, which corresponds to 9.8 times better signal-to-noise ratio compared to using solar neutrinos [925]. The next-generation experiment discussed here could set much more stringent bounds on the neutrino magnetic moment, if combined with an electron capture source.

The quantization of the electric charge has been one of the long-standing mysteries stemming from empirical observation. In principle, the SM U(1) allows arbitrarily small real-number charge, but so far, experiments indicate that there is a fundamental unit of electric charge of 1/3e. This has sparked theoretical explanations including Dirac quantization [1035] and provides one of the major motivations for a GUT [1036, 1037]. The search for such fractionally charged or millicharged particles is a test of the paradigm of charge quantization [1038–1052]. 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 ξ charged under a dark U(1)_D . In the limit when the dark U(1)_D vector boson (often called a dark photon, see section 3.8.1) 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 $\sim 1{0}^{-3}$ or smaller, from loop effects in either QFT or string theory [569, 1053, 1054], which naturally gives small electric charges. For masses of such new particles below ∼MeV/c², the limits on the kinetic mixing parameter (and thus the fractional charges) are stringent $< 1{0}^{-15}$ [1040]. For heavier states, the limits are weaker [1055]. Direct detection experiments can possibly observe bound state formation between q < 0 millicharged particles and nuclei [1056]. One can also look for millicharged particles without massless gauge bosons in regimes where the dark photon is constrained [1051]. A search for such a particle can be a test of GUTs and certain string compactification scenarios [1057]. Further, liquid xenon detectors are sensitive to the possible millicharge of solar neutrinos [1032].

In the SM, 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 GUTs. This could explain the observed matter–antimatter asymmetry of the Universe [1058].

Several liquid xenon detectors, such as DAMA-LXe [1059, 1060] and EXO-200 [1061], 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 → ννν, as proposed in reference [1062]. Following such a decay, the daughter nuclei would be left in an excited state, and would emit a detectable signal, such as a γ-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.

Persistent anomalies in short baseline experiments, including LSND and MiniBooNE, are suggestive of an additional undiscovered neutrino mass eigenstate at the $\sim 1\enspace \,\mathrm{e}\mathrm{V}$ mass scale [1063]. However, there is significant tension between different experiments that has yet to be explained [1064]. 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 [1034]. 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 [1034].

Muons traversing detectors or surrounding materials will induce primary backgrounds as well as secondary neutrons and cosmogenic backgrounds from activation of materials [1065, 1066]. Dark matter detectors are thus deployed in deep underground laboratories, where cosmic-ray muon backgrounds are greatly reduced by the rock overburden [1067]. Nevertheless, for high-sensitivity experiments, active muon shielding is still required in order to tag remaining muon-related background events and reduce the muon-induced background to a negligible level compared to other sources. Muon fluxes at the typical underground laboratories range from 1 muon m^{− 2} h⁻¹ at the Laboratori Nationali del Gran Sasso (LNGS, 3100 m water equivalent deep) [1065, 1068] to about 5 muons m^{− 2} month⁻¹ at China's Jinping underground laboratory (CJPL, 6720 m water equivalent deep) [1069, 1070] (figure 34).

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There are a host of underground laboratories that can be considered as location for the next-generation observatory discussed here. This includes the laboratories hosting the current generation of liquid xenon detectors: LNGS [1084] (location of XENONnT), CJPL [1085] (location of PandaX-4T) and SURF [1086] (location of LZ). The Boulby Underground Laboratory has a similar muon flux to LNGS with notably low radon levels [1087]. The Modane Underground Laboratory [1088] includes a facility for radon-free air, and the entire scientific campus of SNOLAB [1089] is equipped as a cleanroom with some of the lowest available muon flux. Several of these laboratories entertain feasibility studies for creating additional underground space for scientific use. All in all, there is a favorable outlook that suitable underground space can be made available for the next-generation liquid xenon observatory. While radioactive and muon-induced backgrounds are dominated by the rock composition and overburden, respectively, the varying geomagnetic field at different latitudes has a (modest) impact on the science that can be done with atmospheric neutrinos [819]. To select an adequate underground location for the next-generation detector, in addition to such background considerations, relevant questions are related to e.g. the availability of underground space, constraints in accessing it, operational considerations, the local support infrastructure, and funding.

The dominant background component in liquid xenon detectors at a given energy range has evolved with increasing detector size. In earlier detectors (e.g. XENON100 [1090], LUX and PandaX-I/II), the gamma radiation from radioactive contaminants of detector construction materials contributed significantly to the ER background for dark matter searches in the keV energy range. A FV selection is typically applied to reduce these backgrounds, which predominantly appear toward the boundaries of the bulk xenon: with larger detector masses and hence smaller surface-to-volume ratios, fiducialization can preserve a higher proportion of the active volume for a physics search. Gamma-induced ERs will remain a significant background for rare event searches at the MeV scale such as the 0νββ-decay of ¹³⁶Xe (section 4.1, figure 22).

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

Design studies for a next-generation detector will need to optimize the use of veto systems to achieve the largest possible FV. From the inside to the outside, this required research concerns the xenon skin region as used in XENON100 [92] and LZ [1091]; a neutron veto for which LZ uses boxed gadolinium-loaded liquid scintillator [1091] whereas XENONnT implements a gadolinium-loaded water Cherenkov design [98]; and the size of a muon veto, which may be constrained by or put constrains on the respective underground laboratory. Further studies to optimize the FV concern the electric field configuration inside the TPC, in order to reduce the loss of signal from regions near the surface where charge collection is reduced or signal yields are non-optimal [1092].

The selection of materials featuring the lowest contamination with radioactive impurities is the most important strategy for background mitigation in current and future liquid xenon experiments [1093, 1094]. Trace amounts of uranium and thorium can be detected by means of highly sensitive gamma-spectrometers, inductively-coupled plasma mass spectrometry measurements or neutron activation analysis. Radon emanation rates are determined in dedicated setups where the radon which is emanating from the sample accumulates in an ambient carrier gas, before the radon activity in this sample gas is measured, typically using proportional counters or electrostatic radon monitors [1094, 1095].

Various material samples are measured in intensive screening campaigns in order to pre-select and built radiopure detector components which fit the requirements for a next-generation liquid xenon experiment [103]. Once the materials are selected, the screening measurements are used for background modeling by means of simulation. Precise knowledge of emanation sources can further be used to optimize the online purification systems. Following multiple iterations of low-background xenon experiments, much of this process is now well-established. However, its application to a next-generation detector can be challenging, as substantial dedicated screening infrastructure is needed with sufficient measurement time to achieve the required sensitivity. This in turn necessitates an early start, years ahead of the construction of the next-generation detector.

Sources of so-called intrinsic backgrounds are typically radioactive noble gases which are homogeneously mixed within the liquid xenon target. Thus, any type of shielding remains ineffective. Trace amounts of ⁸⁵Kr that stay in the xenon during its distillation from air will cause, if not removed, a low-energy ER background from its beta decay. Due to the absence of krypton sources within the detector, the ⁸⁵Kr contamination is constant over time and scales with the liquid xenon mass. ⁸⁵Kr thus needs to be removed through cryogenic separation of the xenon target, as pioneered by the XMASS collaboration [136]. The purification of xenon from trace amounts of ⁸⁵Kr has been successfully demonstrated using both cryogenic distillation [136, 1096, 1097] and adsorption [1098, 1099] as separation techniques. Cryogenic distillation in particular is appropriate to process large amount of xenon gas before being filled into the experiment, but also an online krypton purification at a running detector has been demonstrated. Starting with a Kr-nat contamination of several ppm in commercial xenon, a purification to (360 ± 60) ppq was achieved in XENON1T using the online krypton purification [1100]. The lowest concentration to-date was measured in the outlet of the XENON1T distillation system to be below 26 ppq (90% CL) [1097], using an enhanced rare gas mass spectrometer with a sensitivity of 8 ppq [1101]. This level is well below even the requirements of a next-generation liquid xenon experiment.

²²²Rn is not immanent in the xenon gas, but continuously emanates from surfaces of detector materials. Due to its subsequent beta decays, radon is the dominant background source in current liquid xenon detectors. A smaller surface-to-volume ratio will naturally decrease the radon concentration in next-generation liquid xenon detectors. However, further mitigation strategies are needed to achieve a level of about 0.1 μBq kg⁻¹ that is required in order to render radon-induced backgrounds sub-dominant versus the irreducible contributions from neutrino signals. Once a new detector has been built, its emanation rate of ²²²Rn is set and expected to be constant over the lifetime of the experiment. A further suppression of the radon induced background can be achieved through continuous purification of the xenon target. The key for an efficient radon removal is a good separation technique and a high purification flow which revolves the entire xenon target fast with respect to the 3.8 days half-life of radon. Radon removal based on cryogenic distillation has been successfully tested in large scale liquid xenon experiments [1102] and is used also in XENONnT [1103]. Radon purification systems designed for small purification flows can also significantly reduce the radon concentration in xenon. Since the dominating radon emanation sources in an experiment are known from screening, dedicated purge flows toward the radon removal system can prevent radon to enter the liquid xenon target [1094]. For the next-generation detector discussed here, a strict radon mitigation protocol will need to be developed and implemented, including extensive screening for radon emanation; strategies to limit radon emanation (e.g. reference [1104]); radon removal from xenon both within the TPC and outside the shielding; optimized xenon flow; etc.

Another intrinsic background source is the decay of ¹³⁷Xe, with particular relevance for the search for neutrinoless double-beta decay [710, 716]. It is naturally created inside the xenon target through activation by muon-induced neutrons. Thus, the ¹³⁷Xe induced background strongly depends on the muon rate at the experimental site. Short-lived cosmogenic isotopes such as ³⁷Ar are of little concern for the anticipated experiment [139].

Due to the large electroluminescence gain that is exploited in dual-phase liquid xenon TPCs, even a single extracted electron can produce a detectable S2 of tens of photoelectrons in size [509, 1105–1110]. A standalone search with S2s (i.e. without requiring an accompanying S1 signal, see section 3.2) can thus lower the energy threshold, improving the reach to low-mass WIMPs, solar axions and solar neutrinos, and other physics that have associated low-energy recoil signatures [181]. However, this sensitivity to any process that can release even single electrons from their shell brings in additional instrumental backgrounds. Several sources of S2-only, single and few-electron backgrounds are known [507, 509–515, 1111]; significant research is needed to further understand and eventually mitigate those backgrounds. Photoionization backgrounds caused by large S2s die away within a maximum drift time after the S2 [509]. Emission from metal surfaces would be evident in specific locations that could be avoided with positional cuts. The most impactful background appears to be S2s up to five electrons in size that continue for times up to seconds after a large S2. The rates of these correlated small S2s, which appear in the same location as a previous large S2, decrease according to a power law with time after the large S2 [507, 513, 514]. This background can be mitigated with positional and temporal cuts after large S2s.

S1-only backgrounds also exist due to interactions in areas insensitive to the charge channel. One such origin of lone S1 events is from outside of the main drift field region of the TPC, notably below the cathode. Another origin is from volumes where charges are depleted, or where electrons cannot reach the extraction region. Most notably this can be as a result of the field configuration toward the edges of the detector [63]. Unrelated, isolated S1-only and S2-only signals can be close enough in time to be mis-identified as a single event. Such accidental coincidences of instrumental backgrounds can thus mimic a physics interaction for a conventional search in S1–S2 phase space. As both lone S1s and S2s are more likely to manifest at smaller signal values, these accidental coincidence backgrounds are particularly problematic for the WIMP search ROI. The absolute incidence of such accidental events could increase in a next-generation detector, as the corresponding surfaces and volumes from which lone S1s and S2s can arise become larger. However, their impact on the WIMP search will decrease with increasing detector size, due to the favorable surface-to-volume ratio. In the XENON1T experiment, this background was tackled in a data-driven approach (reference [1112] and figure 35): lone S1 and lone S2 events where characterized with high statistics in the available parameter spaces. The expected distribution of accidental coincidences was then simulated by randomly drawing an S1 and an S2 event from these distributions. This allowed for a detailed characterization of this background and thus modest impact on sensitivity. Combined with detailed detector simulations, and the lower rate per exposure unit, such an approach is expected to be sufficient to control this background for a next-generation experiment.

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7.6.1. Background model

7.6.2. Generation of S1 and S2 signals

Generally, energy depositions are converted to observable S1s and S2s to construct PDFs for background components and signal for likelihood-based analysis [1126]. The microphysics behind the interactions of particles with the active xenon is captured by the NEST [121, 126–128, 1127]. NEST offers a comprehensive and mature framework to simulate the atomic and nuclear physics of energy deposition and the resulting detector response. Using world data from previous experiments including LUX, XENON, PIXeY [515, 1128], neriX [1129, 1130], ZEPLIN-III [502], and Xurich [105, 1131], the NEST collaboration has developed models for the light and charge yields of various interactions. These models are semi-empirical and reproduce calibration data from alphas, betas, gammas, NRs, and exotic interactions like the two-step internal conversion of ^83mKr. The excellent agreement between the NEST models and data can be seen in figure 36. Further research will be needed to further improve this understanding in particular at even lower recoil energies. Physicists on a next-generation liquid xenon experiment are thus able to take advantage of NEST to accurately simulate the signals induced by both signals and backgrounds, including their S1, S2, position, and pulse timing.

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The results of simulating events from a type of source, be it ER or NRs, are a list of S1 and S2 values for each event. Binning these events into a 2D histogram will show how a given type of interaction looks like in terms of the signals received. An example shown in figure 37 is the histogram of a 50 GeV spin-independent WIMP, which is lower in S2 than that of ER events. This difference allows for distinction between these two types of interactions and can be measured quantitatively in a few ways. Leakage is the proportion of ER events per bin that lie below the NR median line; rejection is the percentage of background events that are not in the ROI given by (1 − leakage). Various instrumental parameters affect the discrimination capability. For example, the drift field affects the gap between the nuclear and ER spectra, as does the g₁ parameter which measures the S1 light yield in the detector. As can be seen from figure 37, even moderate drift fields provide satisfactory ER/NR discrimination. Discrimination is also affected by the atomic structure of xenon, leading to increased leakage from neutrino and Compton scatters on L-shell electrons due to the accompanying atomic de-excitation via Auger electron cascades. This effect is still under study, but available measurements indicate a reduction in rejection by a factor of 6× near the L-shell binding energy (5.2 keV) compared to predictions from valence ERs and β-decays [1132, 1133]. Including this effect for the solar neutrino-induced ER background results in an 8% relative increase in leakage from 5.2–8 keV, for 50% NR acceptance.

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Importantly, already with the performance of running detectors, discrimination between ER and NRs in liquid xenon is sufficient to achieve the various science goals presented in this review, whether they pertain to WIMPs, neutrino-induced signals in both the ER and NR band, or the search for neutrinoless double-beta decay. The accuracy of these simulation results is confirmed in situ using dedicated calibration sources, such as dissolved gamma line sources ^83mKr [448], dissolved beta-spectrum sources ²²⁰Rn [1134, 1135], TH₃C [1121], as well as various neutron sources [1119, 1136, 1137].

Production, decay and scattering of dark matter particles are often governed by the same or similar interaction. Relic particles such as WIMPs are a textbook example of this situation, where the production through freeze-out from the thermal equilibrium in the early Universe creates the observed relic density [32, 1138, 1139]. The three principal approaches to discover thermal freeze-out relic particles correspond to the s- or t-channel processes of dark matter production or scattering, and the time-reversed process to production, which might lead to annihilation of dark matter. This results in the following detection channels, related through crossing symmetry [1140] (see also figure 38):

• (a)  
  Direct detection: direct detection of particle dark matter in the Galactic halo in underground experiments as described here;
• (b)  
  Collider production: production of dark matter in the laboratory, usually using high energy particle collisions;
• (c)  
  Indirect detection: detection of products of dark matter annihilating or decaying in our local Universe.

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The electroweak energy scale is powerfully probed by the LHC at CERN [1141]. The freeze-out mechanism requires significant couplings between the dark matter and the SM, which further motivates searches at a particle collider. Moreover, many 'beyond the SM' theories in high energy physics require new particles at the electroweak scale, which are either viable dark matter candidates or might couple to particle dark matter. The most prominent example of such a theory that connects naturally astrophysical and theoretical motivation is SUSY, which not only remedies many known problems of the SM, such as the hierarchy problem, but also provides an excellent dark matter candidate [140, 341, 1142, 1143].

Another motivation for collider searches is the potential to study dark matter in the laboratory. Collider production implies production of the mediator, i.e., the force carrier that connects the dark sector with the visible sector of the SM. Hence, collider dark matter searches are in essence searches for the mediator rather than dark matter. Most collider dark matter searches assume maximal decay of the mediator into dark matter [212, 213]. This is in particular true for 'mono-X' searches, where the main signature is missing momentum in the transverse plane due to the dark matter particle escaping the detector undetected. Constraints placed on the mediator masses are typically about twice as strong as the constraints on the dark matter mass itself. Other analyses attempt to place constraints on the nature of dark matter by looking for deviations in the properties of known particles, for example the Higgs boson, or to search for the mediator directly, such as in dijet searches [1144]. Further complementarity stems from searches at colliders for ALPs and dark photons, see e.g. references [1145, 1146].

Dark matter annihilation and decay into SM particles lead to potential signatures in the CMB [555, 1147, 1148] and astrophysical observables such as x-rays [1149–1151], gamma rays [367, 1152–1178], antiprotons [1179–1184], positrons [358, 1185–1189], neutrinos [1190–1201], or other particles [1202–1212]. Thermal relic dark matter candidates are generically expected to have a thermally averaged annihilation cross section ⟨σv⟩ ≃ 2.2 × 10⁻²⁶ cm³ s⁻¹ [20, 145], though other production mechanisms or annihilation channels are known to predict much smaller or larger annihilation cross sections, e.g. Sommerfeld enhancement [319, 1213], non-thermal/out-of-equilibrium production [1214–1217], asymmetric dark matter [624, 1218–1220], co-annihilation [1221–1223], velocity-dependent annihilation, or non-standard cosmologies [1214, 1215, 1224–1230]. The thermal relic cross section, however, provides an important benchmark for indirect detection efforts. While this leads to a characteristic signature of dark matter in the corresponding cosmic ray spectrum [150, 1152, 1155], the topology, spectral shape and strength of such a signal is rather model dependent and affected by astrophysical foregrounds.

Since the annihilation rate of dark matter is proportional to the square of the dark matter density at the location of annihilation, the brightest signals are expected to come from dense structures. Present searches for annihilation signatures aim at a variety of targets, with the Galactic center and local spheroidal satellite galaxies (dSphs) of the Milky Way being among the most prominent ones. The former is expected to be the brightest source in the sky because of the large dark matter overdensity, but it also has the brightest foregrounds and complex dynamics. The latter are the most extreme dark matter-dominated galaxies known to us, but have a much lower J-factor [1231, 1232] compared to the Galactic center (around 10¹⁷ to 10¹⁹ GeV² cm⁻⁵ for dSphs and about 10²² GeV² cm⁻⁵ for the Galactic center, leading to a fainter potential signal.

In contrast, the flux of particles from decaying dark matter is only proportional to a single power of density, so it is predicted to give rise to less clumpy signals compared to those from annihilating dark matter. Constraints on decaying dark matter come for example from isotropic gamma-ray and neutrino observations [1175, 1197].

There is more than just phenomenological support for the hypothesis that dark matter self-annihilates. N-body simulations suggest that dark matter halos, in the absence of baryonic effects, follow a density profile which behaves like ϱ ∝ r⁻¹ irrespective of initial conditions. This is referred to as a Navarro–Frenk–White profile [1233, 1234]. Measured profiles of disk and spheroidal galaxies appear to follow a shallower density profile: ϱ ∝ r⁰ [1235–1239]. This disagreement is referred to as the 'core-cusp-problem' and could possibly be resolved by co-annihilating or SIDM [379] (section 2.14).

In some models of dark matter, the dark matter mass and nucleon–dark matter scattering cross section are predicted or bounded as functions of SM parameters such as the top quark mass and the strong coupling constant. In such scenarios, dark matter searches constrain the SM parameters, which can be precisely measured by future colliders [1240–1244] and lattice QCD computations [1245].

For example, in a model that solves the strong CP problem by a space–time parity symmetry [1246], the dark matter mass is proportional to the energy scale at which the SM Higgs quartic coupling vanishes (10⁹ to 10¹² GeV), which is sensitive to the SM parameters. Dark matter couples to a massless dark photon and the dark matter–nucleon scattering arises from unavoidable quantum corrections leading to photon-dark photon mixing.

The resultant correlation between the dark matter signal rate and the SM parameters that determine the scale where the Higgs quartic coupling vanishes is shown in figure 39. Here, to estimate the projections for next-generation experiments, we scale the limit from XENON1T according to the projections in the high mass region shown in figure 5. Another example is sneutrino or higgsino dark matter in supersymmetric theories, where the dark matter mass is predicted to be smaller than the scale at which the SM Higgs quartic coupling vanishes [1247]. Dark matter scatters with nuclei via tree-level Z-boson exchange, generating signals detectable in a 1000 tonne-year exposure even for a dark matter mass as large as 10¹² GeV. Detection of or constraints on nucleon–dark matter scattering signals will give an upper bound on the top quark mass and a lower bound on the strong coupling constant.

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In the search for dark matter directly interacting with a laboratory target, a host of synergistic detectors are required to overcome signal degeneracies, particularly as experiments begin probing the neutrino fog. With different technologies and targets, complimentary experiments can confirm potential dark matter signatures and disentangle them from both neutrino-induced (CEνNS) signals and instrumental backgrounds. Additionally, a large variety of detectors can probe a wider dark matter mass range, as shown in figure 40. Target materials range from solid state crystals to dense liquids [44, 151]. Even within the context of liquid xenon TPCs, larger detectors are required for dark matter nuclear scattering searches, but smaller detectors optimized for single-electron signals might achieve better sensitivity to lower masses and dark matter scattering with electrons [1248].

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8.5.1. Solid state detectors

8.5.2. Liquid target detectors

Experimental searches for 0νββ decay [1249] span a variety of isotopes, including ⁷⁶Ge, ⁸²Se, ¹⁰⁰Mo, ¹³⁰Te, ¹³⁶Xe, and ¹⁵⁰Nd. The choice of isotope is driven by the Q-value of the 2νββ mode, the ability to obtain high isotopic abundance, and compatibility with a suitable detection technique. Detection techniques include semiconductor crystals, cryogenic bolometers, TPCs, and organic and inorganic scintillators. The choice of detection technique is a balance of the detector energy resolution at the Q-value, the scalability of the technology to large masses, and ability to achieve ultra low backgrounds. The leading experimental efforts to date include MAJORANA [705], GERDA [1250], CUORE [1251], EXO-200 [706], and KamLAND-Zen [701, 1252]. The next generation of 0νββ searches includes LEGEND [1253], nEXO [713], NEXT [1254], CUPID [1255], KamLAND2-Zen [1256], and SNO+ [1257]. Compared to the experiments using semiconductors and bolometers, a next-generation liquid xenon detector will have significantly larger isotopic mass, even with a natural abundance of ¹³⁶Xe, but it will have poorer energy resolution compared to other technologies. The ability to fiducialize the detector means that the backgrounds from radiogenic sources are significantly reduced. A next-generation liquid xenon dark matter detector can have a 0νββ sensitivity comparable to those of the next generation of dedicated 0νββ experiments (section 4.1).

The identification of neutrinos in dark matter experiments, in particular through the CEνNS channel, will be complementary to terrestrial neutrino experiments which operate in a similar energy regime. The COHERENT experiment [1258] uses a stopped-pion source of neutrinos, generated by the Spallation Neutron Source (SNS) at the Oak Ridge National Laboratory. Muon neutrinos with energy 30 MeV are produced from charged pion decays, and ${\bar{\nu }}_{\mu }$ and ν_e are produced with a Michel energy spectrum from the subsequent decay of muons at rest. ${\bar{\nu }}_{\mu }$ and ν_e from muon decays are delayed relative to the 30 MeV ν_μ neutrinos produced from the prompt pion decay. With characteristic energies of tens of MeV, a large sample of the neutrino-nucleus interactions are coherent, which together with the timing structure, permits a measurement of the CEνNS process.

Using 14.6 kg CsI[Na] scintillator detectors, the COHERENT collaboration announced the first detection of CEνNS in 2017 [791], with a best-fit count of 134 ± 22 CEνNS events, which is 77 ± 16 percent of the SM prediction. From this initial detection, COHERENT was able to constrain NSIs in a regime of parameter space that had not been possible to probe. In particular, the COHERENT data is sensitive to u- and d-type NSIs for flavor-diagonal muon components, _μμ . The COHERENT detection also set new constraints on exotic solutions to solar neutrino mixing, places novel constraints on new physics that manifests through the neutrino sector (e.g. reference [1259]), constrains the neutron form factor for CsI [1260], sterile neutrinos [1261, 1262], and the g − 2 anomaly [862, 863, 1263]. The collaboration has since also measured CEνNS on argon [1264].

Nuclear reactors have been purposed as a copious source of electron anti-neutrinos. The characteristic neutrino energy is ≲1 MeV; as such, the coherence condition for the recoil is largely preserved over the entire reactor energy regime. The primary difficulty in detecting CEνNS using reactors is that detectors have not been able to achieve the low threshold required to identify the CEνNS NR signal. With further improvements in detector technology, several experiments are poised to identify CEνNS at reactors [1033, 1265–1271]. The two-phase noble gas detection technique is very promising for this purpose [1271, 1272], and currently the RED-100 detector (with $\sim 160\enspace \,\mathrm{k}\mathrm{g}$ of active liquid xenon) is being tested at the Kalinin NPP site. This is the first CEνNS experiment using a two-phase emission technique, and other experiments, such as NUXE with liquid xenon and CHILLAX with xenon-doped liquid argon, are currently being developed.

Direct real-time measurements of solar neutrinos have been observed for the first time by the Borexino experiment [799, 809, 1273]. A next-generation liquid xenon experiments can offer complementary measurements when detecting solar neutrinos through elastic neutrino-electron scattering (section 5.2). Neutrinos that contribute to the signal are generated from the pp-reaction chain, produced from the electron-capture decay of beryllium-7, and emitted in the CNO fusion cycle. The measurement of CNO neutrinos in liquid xenon-based detectors is limited by the presence of the two-electron spectrum arising from the 2νββ-decay of ¹³⁶Xe. Depletion of ¹³⁶Xe by at least a factor of 100 relative to its natural abundance would be necessary to detect the CNO solar neutrino component in the next-generation xenon-based detector [802].

Liquid xenon-based detectors can be utilized to look for neutrinos and gamma-rays released in association with gravitational waves emitted during cataclysmic cosmic events. Such 'simultaneous' observation is related then to supernova detection and multi-messenger astrophysics, as discussed in section 5.4.

The great advantages of using liquid xenon for medical imaging have been noticed already back in the 1970s [1274, 1275]. Its fast primary scintillation and sufficiently large ionization yield make it especially attractive for positron emission tomography (PET). The two-phase emission detector with condensed xenon as working medium has been tested in the 1980s as a high-quality gamma-camera for nuclear medicine [1276]. The 1990s saw compressed xenon gas being proposed for very effective, collimator-less SPECT systems [1277–1279]. The first liquid xenon detector prototypes for PET scans were built and tested around the same time [1280–1282]. Further developments of liquid xenon detectors for PET came recently [1283–1286]. In a PET scan, patients are injected with small amounts of chemicals, such as sugar, where molecules have had common stable carbon atoms replaced with positron-emitting isotopes. Position–electron annihilation in the electron shells of atoms in the body leads to back-to-back 511 keV γ-rays. Cancerous tumors will preferentially absorb more sugar than other parts of the body due to higher rates of metabolic activity [1287]. Liquid xenon is being explored due to its advantageous spatial, temporal, and energy resolutions. Already, PETALO is a full-body PET scanner using the S1 signals in liquid xenon to achieve a high resolution image with reduced patient radioactivity exposure [1288]. Many of the developments in liquid xenon detector technology for particle physics thus directly benefit other scientific disciplines, such as medicine, as evidenced here.

Xenon in its gaseous form has also come into use as an alternate anesthetic with minimal dangerous side-effects [1289]. Xenon anesthesia results in a more stable blood pressure, a lower heart rate, and faster emergence from anesthesia than other conventional methods, despite a higher risk of nausea [1290]. Most oddly and uniquely, there are some studies that suggest it is useful for treating traumatic brain injuries and post-traumatic stress disorder [1291, 1292]. While in the United States these claims have not been evaluated by the Food and Drug Administration (FDA), in Russia, the inhalation of xenon is used for selective 'deletion' of traumatic memories, associated with negative emotions [1292]. All this serves to illustrate the extreme versatility of the element. The study of xenon for particle physics may thus have side-effects spilling over into numerous other fields that seem entirely unrelated.

The neutron is the gold-standard calibration particle of choice for any WIMP detector, since it is supposed to emulate the NR generated by dark matter WIMPs. This implies that a WIMP dark matter detector is also an outstanding neutron detector. Liquid xenon TPCs stationed at seaports and airports can allow for non-intrusive inspection of fissionable materials in cargo, by detecting gamma rays and fast neutrons emitted spontaneously or by stimulation from nuclear materials [1293]. The ability of discriminating between nuclear and ERs allows to better discriminate against activation from other backgrounds. This holds true even through shielding, given the low ∼keV energy thresholds achieved recently for dark matter searches.

Another homeland security application is monitoring of nuclear reactors at power plants for fuel rod theft, which could change the outgoing neutrino (and not just neutron) flux, or rod type replacement, which could change the balance of uranium and plutonium amounts. This concept has been explored by the Nucifer Experiment [1294] with a scintillating liquid. Liquid xenon could be ideal for detecting the resulting change in the rate of CEνNS, already discussed in detail above. Liquid xenon is being considered for detecting CEνNS by the RED [1271] and NUXE [1272] collaborations.

All of the aforementioned scientific deliverables require the development of cyber-infrastructure such as algorithms, methods, and tools, for the wider benefit of data-intensive sciences. Years of substantial improvements in dark matter detectors means that the field launched into the realm of petabyte data science. The computational science pursued in this field includes, but is not limited to: how ultra-low-energy simulations are performed, including relevant microphysics (section 1.6); how event reconstruction can be performed with the aid of e.g. machine learning [1295]; and how high-throughput/high-level triggers can be deployed on such non-collider experiments.

This effort requires computational science developments, which can benefit other scientific efforts at both small and large scales. For small scales, there has been an explosion in the number of experiments in recent years. Examples of advancements in this field that are broadly impactful to those having to harness their data are integrating smaller efforts into existing infrastructure using frameworks such as GAUDI [1296]; data management systems such as OSG [1297]; and demonstrating the effectiveness of columnar compilers in tackling data-intensive applications in high-level descriptive languages. For large scales, overcoming computational science hurdles with novel technologies means serving as a test bed for technologies for big science projects such as the HEP software project [1298]. Therefore, achieving our physical science goals requires novel computational science and cyber-infrastructure development.

In the past two decades, the goal of liquid xenon TPCs has been to detect theorized elastic scatters of WIMP dark matter off xenon nuclei. In addition to WIMPs, these detectors have sensitivity to a large host of well-motivated dark matter candidates, as outlined in this work. About 10 different xenon-based dark matter detectors were built over the years, increasing the xenon target mass by almost three orders of magnitude, reducing the ER background by about four orders of magnitude and improving the sensitivity to WIMP dark matter by more than a factor 1000. After the pioneering work by ZEPLIN-II/III and XENON10, XENON100, LUX and PandaX managed to build a suite of detectors with world-leading sensitivity. XENON1T was the first TPC with a target above the tonne-scale. The current generation of detectors, XENONnT [98], LUX-ZEPLIN (LZ) [99], and PandaX-4T [97], feature multi-tonne liquid xenon targets. Despite a lack of definitive signal so far, these detectors are clear leaders in sensitivity to WIMPs and other physics channels, and scale reliably in mass [96]. It is for these reasons that a next-generation liquid xenon TPC is of such high interest to the international physics community.

The Update of the European Strategy for Particle Physics (ESPP) from 2020 points out that the search for dark matter is a crucial part of the search for new physics and that experiments that offer 'potential high-impact' should be supported [1306]. The APPEC report on the direct detection of dark matter (2021) states that 'the search for dark matter with the aim of detecting a direct signal of dark matter particle interactions with a detector should be given top priority in astroparticle physics, and in all particle physics' [1305]. Already in 2014, the US Particle Physics Project Prioritization Panel (P5) highlighted the identification of the new physics of dark matter as one of the five science drivers for all of particle physics and recommended that US funding agencies 'support one or more third-generation (G3) direct detection experiments...(with) a globally complementary program and increased international partnership in G3 experiments' [1307]. Consolidation of the world-wide xenon community already took place when the members of the ZEPLIN collaboration joined LUX, and XMASS teamed up with XENON. Another important step toward the realization of this next-generation detector happened in 2021, when the scientists from the XENON/DARWIN and LUX-ZEPLIN collaborations agreed to join forces in the XLZD consortium toward the realization of this observatory.

The German [1308], Swiss [1309] and Dutch [1310] particle physics communities likewise identified the multi-tonne liquid xenon observatory DARWIN of particular interest for their national strategy roadmaps and support R&D toward this goal via national funding programs. Other countries are strong members of the XENON experiment and it is expected that its follow-up project (e.g. DARWIN) will also be supported. The UK's Particle Astrophysics roadmap also stresses the importance of a xenon-based next-generation ('G3') observatory, explicitly recommending R&D toward this detector as the highest priority in dark matter. Relevant R&D is also supported through multiple European Research Council (ERC) grants.

Understanding the physics of neutrino mass is another important science driver for particle physics identified by the US P5 and APPEC, which noted the importance of neutrinoless double beta decay searches in that context [1301, 1307]. Such experiments are also a top priority in the 2015 US Long Range Plan for Nuclear Science [1311], with one of the four main recommendations being the construction of a massive detector. The European APPEC double beta report (2019) states that 'the search for neutrinoless double beta decay is a top priority in particle and astroparticle physics' and acknowledges that the 0νββ sensitivity of a next generation dark matter detector opens up an exciting scenario [1312]. Similar statements of support for neutrinoless double beta decay detection, especially in dark matter detectors, can be found in UK [1313], Russian [1314], CERN/European [1315], and Chinese [1316] particle and nuclear physics priority planning documents. The APPEC dark matter report states on this topic that 'the potential of dark matter detectors to search for rare nuclear decays has been demonstrated spectacularly when XENON1T observed for the first time double electron capture on ¹²⁴Xe [766]' [1305].

Recently, the observed phenomenon of CEνNS [791] has made large dark matter detectors, such as the one discussed here, particularly desirable for studying neutrinos. Such a detector would be invaluable to the field of astrophysics for measuring Galactic supernovae neutrinos of all flavors. A next-generation liquid xenon detector would be able to probe multiple solar, atmospheric and supernova neutrino signals, which are invaluable measurements in their own right. The US Nuclear Physics community, in the 2015 Long Range Plan for Nuclear Science (LRP) [1311], notes that measuring the CNO cycle and addressing the 'metallicity problem' in the Sun—both accessible to this detector technology—are the next big challenges in solar neutrino research.

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