2023

# Design Challenges for a Future Liquid Xenon Observatory

Abigail Kopec1  1 Department of Physics & Astronomy, Bucknell University,
Lewisburg, PA, USA 17837  Email<EMAIL_ADDRESS>
(1 August 2023)

###### Abstract

An ultimate liquid xenon dark matter experiment would be limited in its dark
matter science reach by irreducible neutrino backgrounds. To achieve such
sensitivity, other backgrounds that currently plague these detectors must be
better mitigated, and extreme care must be taken in the design and
construction phases. Historically, liquid xenon time projection chambers have
scaled to larger target masses with great success. This paper gives an
overview of challenges that need to be met for the next generation of detector
to obtain a kilotonne$\times$year exposure. Such tasks include the procurement
and purification of xenon, radiopure and reliable detector components,
sensitive outer detector vetoes, powerful data handling and analyses, and an
ability to operate stably for timescales of over a decade.

###### keywords:

Dark MatterNeutrinosDirect DetectionAstroparticle PhysicsNeutrinoless Double-
Beta DecayXenon

††journal: JAIS-ID

##  1 Introduction

For about two decades, liquid xenon time projection chambers (LXe TPCs) have
dominated searches for spin-independent dark matter in the form of weakly
interacting massive particles (WIMPs). Current experiments, including LUX-
ZEPLIN (LZ) LZ:2022ufs , XENONnT XENON:2023sxq  and PANDAX-4T PandaX:2021bab ,
are expected to continue this legacy of excellence, employing world-leading
detection capabilities to search for rare particle interactions over the next
several years LZ:2018qzl ; XENON:2020kmp . To optimally exploit the dark
matter science potential of this technology, a liquid xenon observatory is
being proposed Aalbers:2022dzr . The DARWIN Collaboration has made significant
progress toward the next upgraded detector DARWIN:2016hyl ; DARWIN:2022ewl
and the new XENON-LUX-ZEPLIN-DARWIN (XLZD) Consortium aims to achieve it with
the support of most of the community’s experts Aalbers:2022dzr . Optimally,
coherent elastic neutrino-nucleus scattering (CEvNS) backgrounds from
irreducible solar and atmospheric neutrinos would be the only limitations to
such a detector’s dark matter sensitivity. A target exposure of a
kilotonne$\times$year also has the discovery potential for rare neutrino
physics, leveraging the natural neutrino backgrounds as signal Akerib:2022ort
. Realistically, discriminating between a dark matter particle or CEvNS signal
and backgrounds–such as radioactivity or mistaken events from random signal
coincidences–makes this goal more challenging.

There are several advantages of LXe TPCs. A particle interacting in the target
volume efficiently transfers energy to create excimers, which decay within
nanoseconds by emitting vacuum ultraviolet scintillation photons. Not a
significant amount of energy is converted to heat, although more heat is
produced when a particle interacts with a xenon nucleus in a nuclear recoil
(NR) compared to interactions with a bound electron via an electronic recoil
(ER) due to quenching Hitachi:1983zz . Some excited xenon atoms ionize and, in
an electric field, the electrons can be drifted to an amplification region to
be measured as a secondary signal. In the common dual-phase LXe TPCs, a drift
electric field is applied to the bulk liquid xenon to draw ionization
electrons upward to gaseous xenon. A stronger field is applied across the
liquid surface to extract electrons and accelerate them to the point of
creating proportional scintillation in the gas. Particle interactions
therefore give two correlated signals: the prompt scintillation (S1) and the
delayed ionization electrons’ proportional scintillation (S2).

There are three electrodes to produce the two electric fields: the cathode at
the bottom, the gate just below the liquid surface and the anode in the gas
just above the surface. A field cage of stacked field-shaping rings around the
liquid xenon target volume are set at incremental voltages between the cathode
and gate to reduce distortions in the field at the edge of the detector. At a
constant drift field, electrons in the S2 move at a constant velocity directly
to the gas. The drift time after the S1 to the detection of the S2 provides a
measurement of the depth $(z)$ at which the interaction occurred.
Geometrically, the field cage leaves the top and bottom faces of the detector
as the best locations for photosensors that detect the scintillation photons.
This placement, the usage of photomultiplier tubes (PMTs) as the photosensors,
and the transparency of the electrodes combine to affect the light collection
efficiency. The ratio of S1 photons measured relative to photons produced (g1)
is historically below 20%. Of the current generation, XENONnT has achieved
about 15% XENON:2023sxq .

With photosensors directly above the gas amplification region, the ionization
electron detection relies on the extraction field between the gate and the
anode. The electroluminescence scintillation photons are highly localized in
the photosensors directly above the extraction location, leading to excellent
$(x,y)$ position reconstruction. The S2 electrons have traveled directly
upwards at a constant speed determined by the drift field. With a dielectric
constant of 1.85 Xu:2019dqb  in the liquid xenon and close to 1 in the gas,
there is a potential difference at the liquid-gas interface, usually modeled
as a Schottky Barrier and dependent on the extraction field Gushchin:1979 .
Although it is difficult to define the point at which all electrons have been
extracted, the extraction efficiency starts to saturate above 7.4 kV/cm in the
liquid Xu:2019dqb . The distance from the liquid surface to the anode, the gas
pressure, and the electric field determine how much proportional scintillation
is produced by the ionization electrons Aprile:2008bga . By additionally
considering geometry and PMT characteristics, single extracted electrons
produce signals of hundreds of photons–dozens of which are measured over
hundreds of nanoseconds–and therefore have a high detection efficiency. The LZ
detector has achieved a single electron gain of 47 photoelectrons (PE) with
80% extraction efficiency LZ:2022ufs . At MeV interaction energy scales, there
are roughly $10^{5}$ electrons in the S2, which can lead to PMT and data
acquisition saturation XENON:2020iwh .

The S1 and S2 coincidence requirements strongly suppress backgrounds, and an
interaction’s deposited energy can be determined with a resolution of a few
percent, depending on total deposited energy and therefore quanta of photons
and electrons measured XENON:2020iwh . Xenon has self-shielding properties,
and most radiation from the walls does not penetrate more than a few
centimeters into the target. Therefore, excellent position reconstruction
leads to fiducialization of the monolithic target volume to select the
cleanest xenon in the detector’s center with the lowest rates of backgrounds.
Due to the mass difference between recoiling nuclei and electrons, NRs have
shorter recoil paths with higher densities of excimers, giving a higher
probability for some ionization electrons to recombine and produce a
scintillation photon contributing to the S1. For this reason and due to
quenching in NRs, ERs have a higher ratio of S2 ionization electrons to S1
scintillation photons measured compared to NRs. The drift electric field is
also vital in controlling the relative magnitudes of the ratios. A WIMP NR
search region can be defined to reject over 99% of ER backgrounds while
accepting 50% of NRs. The optimal field is taken to be between 200-350 V/cm
with a leakage fraction of $7.3\times 10^{-4}$ ER events in the WIMP search
range of 2-65 keV NRs LUX:2020car ; Szydagis:2022ikv . When scaling up the
current generation of detectors, special care is required to optimize the
electric fields and maximize sensitivity to dark matter or CEvNS signals over
backgrounds.

This work outlines several considerations for, and current limitations to,
realizing a kilotonne$\times$year exposure with liquid xenon. The topics
covered fit broadly into two categories. Section 2 explores material and
equipment considerations to build the next generation detector, while the
limitations in the technology at the current generation constitute Section 3.
Significant progress has already been made in each successive experiment, and
research and development is underway to ensure success.

##  2 Detector Component Considerations

The atmospheric concentration of xenon is roughly 90 parts per billion by
volume and, at the time of writing, about 60 tonnes are produced annually in a
$250 million USD industry business:2022 . In addition to the expense of
obtaining xenon, radioactive contaminants, whose decay products interact with
the xenon and create background signals, must be removed. The purity of the
xenon regarding oxygen and other impurities is critical at larger scales,
since electronegative species of these capture drifting electrons and reduce
the detection efficiency of S2s. It is optimistically feasible for the XLZD
consortium to collect about 100 tonnes of xenon over the coming years. With
such a detector, a kilotonne$\times$year exposure would need to accumulate for
over a decade, which requires the detector to be incredibly durable.

###  2.1 Xenon

Xenon currently costs a few million USD per tonne, and buying tens of tonnes
of xenon has large implications for the market. Other significant uses for
xenon include satellite propulsion, lighting and imaging, and semiconductor
and electronics manufacturing business:2022 . These applications all consume
the xenon, and it eventually returns to the environment mixed with other
byproducts or is lost in space. Liquid xenon particle detectors retain xenon
over the lifetime of the experiments. Therefore, consumer companies could lend
xenon to an experiment and have it returned in better condition with better
purity after the experiment is decommissioned. Great care is needed when
procuring xenon to optimize budgets and timelines. There may be several viable
strategies, but the timescales to obtain a kilotonne$\times$year exposure
require advanced planning over several years, in addition to over a decade of
data-taking.

There are historic precedents for expensive community projects with decades-
long timelines. In the last few decades, the detectors have not only grown in
size, but also in the number of collaborators and overall lifetime. Over 500
individuals contributed to outlining the physics possibilities of a future
xenon observatory Aalbers:2022dzr . Argon-based particle detectors with tens
of tonnes of liquid argon are already being built. In particular, DarkSide-20k
has outlined their procurement plan, starting with the extraction of
underground argon in Colorado, USA, and processing it in Sardinia, Italy to
remove the 39Ar isotope DarkSide-20k:2021nia . Although argon is plentiful and
inexpensive, the facility required to remove the 39Ar requires a significant
initial capital investment. In the context of contemporary experiments, this
next generation liquid xenon detector is reasonable to fund, but care and time
will need to be spent accumulating xenon in the small global market.

###  2.2 Radioactive Backgrounds

The natural isotopic abundances of xenon are particularly stable. Even the
most common radioactive isotope, 136Xe, only undergoes a double-beta decay
with a half-life of $2.165\times 10^{21}$ years and at energies far above dark
matter search energies EXO-200:2013xfn . This double-beta decay process is of
significant scientific interest for probing the nature of neutrinos. A future
liquid xenon observatory is able to search for neutrinoless double-beta decay
and evidence for Majorana neutrinos with a half-life on the order of $10^{27}$
years DARWIN:2020jme , which is competitive with dedicated neutrinoless
double-beta decay experiments. The half-life of the other main radioactive
isotope, 124Xe, is so long that it was only recently measured to be $1.8\times
10^{22}$ years in the XENON1T detector XENON:2019dti . In addition to natural
isotopes, trace amounts of shorter-lived xenon isotopes have been observed,
particularly after neutron NR calibrations due to neutron capture
XENON:2020rca . These decay in a matter of days, and the next-generation xenon
detector should be able to run stably for years without requiring regular
neutron calibrations. Xenon undergoes some activation by cosmic rays to
produce 127Xe, but it has a half-life of 36.4 days and mostly disappears once
the xenon is housed underground Baudis:2015kqa . With roughly 100 tonnes of
xenon, detectable rates of cosmogenic activation will still happen depending
on the underground site DARWIN:2023uje . Neutron and muon backgrounds will
have to be constrained to both limit neutron NR backgrounds and characterize
the production of radioactive nuclei in the xenon through muon spallation
products and neutron capture.

The main radioactive backgrounds limiting xenon dark matter and neutrino
physics sensitivity are from other noble elements mixed into the xenon: 214Pb
from the 222Rn decay chain, 212Pb from the 220Rn decay chain, and 85Kr. The
current experiments have effectively eliminated 85Kr by processing the xenon
before it enters the system. Cosmogenic activation of xenon stored above
ground also produces 37Ar, which has a half-life of 35 days. The first results
of LZ notably contain elevated levels of 127Xe and 37Ar LZ:2022kml ;
LZ:2022ufs , but they are expected to decay away over the lifetime of the
experiment. If the rates of cosmogenic activation even underground are
noticeable in a future liquid xenon observatory, it is important to actively
reduce this background. XENON operates a distillation column that is also able
to remove 37Ar when run in reverse XENON:2021fkt . Again, for about a hundred
tonnes of xenon, characterizing the underground environment becomes more
important to constrain the production of these radioactive isotopes.

The principle material coating the inside of these detectors is
polytetrafluoroethylene (PTFE). It enables the near perfect reflection of
vacuum ultraviolet xenon scintillation photons, but it is porous and can
easily introduce electronegative impurities, which are discussed in the next
section, such as oxygen into the xenon via outgassing. More problematically,
it can trap radioactive impurities, which can alpha decay in the PTFE and
subsequently create neutrons Cichon:2020ytl . Since neutron NRs are a
problematic background for WIMP dark matter searches and neutron capture can
produce radioactive isotopes, it is worthwhile to consider investigating other
reflective materials, or reducing the amount of PTFE to the minimum
requirements for reflection. For a future liquid xenon observatory, limiting
the amount of PTFE and maintaining the highest standards of cleanliness
reduces the levels of contaminants in the detector.

Ultimately, 222Rn is the primary contaminant since it is present in all
materials as a decay product of ubiquitous 238U. Although usually present in
lower concentrations and despite decaying away faster, 220Rn poses the same
challenges. The beta decay spectra of 214Pb and 212Pb span the entire low-
energy recoil range. The decay has characteristics of an ER event, so the S2
vs S1 ratio discrimination is vital to reducing the background in the WIMP NR
region of interest. Figure 1, shows radon rates as detectors increase in size.
Rigorous cleaning protocols and strict material radio-purity selections lead
to a slight improvement over trends for LZ LZ:2020fty , which significantly
improved over LUX Bradley:2015ina . In addition to their own radio-assay
program and cleanliness XENON:2021mrg , XENONnT employs a Rn-distillation
column Murra:2022mlr . Online distillation of the gaseous xenon has enabled
XENONnT to achieve a record background of 1.7 $\mu\mathrm{Bq/kg}$ in the
initial science data, which was subsequently dropped below 1
$\mu\mathrm{Bq/kg}$ by also distilling from the liquid xenon. Strikingly, the
XENONnT ER spectrum has reduced radon so much that the lower part of the 136Xe
double-beta decay spectrum is starting to dominate the ER event rate
XENON:2022ltv .

Figure 1: Achieved radon rates in LXe dark matter detectors (blue dots) and
baseline proposed rate for an example 40 tonne volume of DARWIN (blue-outlined
diamond) DARWIN:2016hyl . As the mass increases, a detector with an equal
aspect ratio has a surface area that scales with the height squared, while the
volume scales as the height cubed. For a given target xenon mass, the detector
height scales with $m^{1/3}$. Since Rn emanates from the wall materials, the
concentration should follow the ratio of surface area to volume which evolves
according to $m^{-1/3}$. The red dashed line extrapolates from XENON10 and
XENON100 radon emanation levels according to the $m^{-1/3}$ model. Adapted
from rn_rate .

This incredibly low radon rate is not sufficient for the proposed liquid xenon
observatory accumulating a kilotonne$\times$year exposure. On the one hand,
since the radon emanates from detector materials surrounding the xenon target
volume, the radon concentration may naturally decrease as the detector size
increases. The ratio of the detector’s surface area to its volume decreases
proportionally to mass contained in the volume $m^{-1/3}$. However, scaling
the efforts of XENONnT would still result in millions of radon ER events, of
which potentially thousands would leak into the WIMP NR region of interest. A
conservative goal for DARWIN of 0.1 $\mu\mathrm{Bq/kg}$ for an early 14 tonne
fiducial volume results in over 100 radon ER events per year Baudis:2013qla .
For statistical significance, to only see 100 radon ER events in a
kilotonne$\times$year exposure would require on the order of $\sim$nBq/kg.
With fewer than one radon event per day and a good understanding of xenon
fluid motion, it may be possible to remove 214Pb candidates by tracking the
decay chain of individual 222Rn atoms and daughters. From successive 222Rn and
218Po alpha decays and later merged 214Bi and 214Po decays, it is certain that
a 214Pb lead decay happened in the meanwhile Qin:2023 . If the rates can be
better quantified and statistically subtracted based on spectra, it would
allow for a higher radon budget.

Also according to the DARWIN estimate, 136Xe double-beta decay events begin to
dominate the ER spectrum. These are well-constrained and can be subtracted in
rare-event searches. Regardless, the uncertainties in the relative abundances,
shape of the energy spectrum, and the half-life will need to be known with
high precision (one part in a thousand) to statistically retain sensitivity
when subtracting the background. Due to several factors, 214Pb and 212Pb
concentrations are much harder to constrain. Their beta decay rate spectra are
relatively flat over a large energy range, the emanation from materials and
fluid mixing are complicated and metallic lead can plate on metal surfaces
such as the cryostat walls or electrodes. Therefore levels must either be
reduced as much as possible XENON:2022ltv ; LZ:2022psu  or a better way of
constraining the rates must be developed.

###  2.3 Other Impurities

Other impurities in the xenon also hurt detector performance and sensitivity.
Particularly, electronegative impurities, such as diatomic oxygen, capture
electrons in the drift column, detracting from S2s. Air becomes trapped in
materials during detector construction and then emanates out of the materials
during detector operation. As mentioned, PTFE is a major contributor. The
number of impurities that the cloud of electrons encounters as it drifts to
the gas depends on how deep in the detector the interaction occurred. Events
deeper in the detector, and therefore with longer drift times, have lower
survival probabilities for electrons. Typically, the purity is described by
the electron lifetime, which is the exponential rate constant by which
electrons are lost depending on how deep in the detector the interaction
occurred. For $N$ electrons initially in a cloud, if they have a drift time of
$t_{d}$ and the electron lifetime is $\tau_{e}$, then the electrons that are
measured $N_{S2}$ are given by Equation 1.

$N_{S2}=Ne^{-\frac{t_{d}}{\tau_{e}}}$ (1)

Roughly a hundred tonnes of xenon are difficult to purify efficiently compared
to material out-gassing rates. The strict protocols undertaken by LZ achieved
an excellent electron lifetime of over 5 ms, despite only purifying through
the gas phase at a rate of 3.3 tonnes/day LZ:2022ufs . XENONnT has developed a
liquid xenon purification system Plante:2022khm  that is able to handle 8.3
tonnes/day, operating with an electron lifetime above 10 ms XENON:2022ltv .
Figure 2 shows the electron lifetimes recorded for previous LXe TPCs. For an
example drift field of 250 V/cm in the ideal range LUX:2020car ;
Szydagis:2022ikv , the current XENONnT electron lifetime is sufficient for
over 80% of electrons at the bottom of a future 100 tonne liquid xenon
observatory to reach the liquid surface.

Figure 2: The electron lifetimes of current and previous detectors (blue dots)
with detector mass. As mass increases, the detector gets larger and the drift
times become longer. The grey shaded bands outline deciles for the survival
probability of electrons at the bottom of the detector, assuming a drift
velocity of 1.7 mm/$\mu$s and a 250 V/cm drift field EXO-200:2016qyl . The red
dashed line denotes the 9th decile, above which over 90% of electrons from the
bottom of the detector survive. At lower drift fields, the slower drift
velocities necessitate longer electron lifetimes for the same survival
probability, and the shaded regions shift upward. Data points gathered from
XENON:2010xwm ; XENON:2016sjq ; LUX:2020vbj ; PandaX:2020oim ; XENON:2021qze ;
PandaX:2021bab ; XENON:2022ltv ; LZ:2022ufs .

In terms of sensitivity, scaling the current technology can ensure excellent
electron lifetime and S2 detection capabilities. However, there are more
subtle and dangerous consequences of non-radioactive impurities. XENON100
showed that small isolated S2 rates, particularly single-electrons, increase
with more impurities XENON:2013wdu . Other studies into small S2s support this
conclusion, although the dependence of rates on the electron lifetime is
complicated XENON:2021qze ; LUX:2020vbj . There are also impurities that do
not capture electrons, thus not contributing to the electron lifetime
calculation, which are harder to quantify. These might absorb photons, and
even emit electrons. The stability of the S1 light yield is important for
monitoring impurities that absorb photons, but their relationship to isolated
S2s is not established. After bright S2 scintillation, single electrons
continue to be measured at high rates for a maximum drift time. XENON100 used
copper field-shaping rings on the inside wall of the detector and observed
electrons from the photoelectric effect of S2 photons on the rings
XENON:2013wdu . The elevated rates also appeared to originate in the bulk
xenon, based on timing and $(x,y)$-position. Such photoionization has largely
been ignored because it can be cut with a time veto after an event that
reduces exposure negligibly, depending on event rates. However, the junk data
can burden the data acquisition (DAQ) and extra electrons soon after an S2
might be considered part of the S2 and negatively affect S2 energy resolution.

Beyond a maximum drift time, there are still small S2s at elevated rates
correlated with previous interactions XENON:2021qze ; LUX:2020vbj ;
Kopec:2021ccm . Understanding these is vital to reducing incorrectly paired
S1s and S2s that form accidental coincidence events. Discussion of such
accidental backgrounds is continued in Section 3.4.1. For a
kilotonne$\times$year exposure, purity is very important so that electrons
deep in a larger detector are able to be measured. It is also critical for
background suppression, but the electron lifetime parameter is proving
insufficient for judging xenon purity. Further work is required to
characterize and mitigate impurities beyond electronegative impurities, which
are expected to have significant effects on backgrounds in the form of AC
events and put an unnecessary burden on the DAQ.

###  2.4 Durability

A difficult challenge to a future liquid xenon observatory is to run stably
for over a decade. The failure rates of pumps, electronics, and stressed
components must be evaluated in shorter time windows and usefully extrapolated
to the lifetime of the experiment. Many components in the purification loops
must be accessible and have redundancies, enabling regular maintenance. The
ability to perform maintenance on the xenon TPC components with minimized
down-time will need to be considered. All surfaces in contact with xenon must
be scrutinized for impurities, but also the cryostat and pipes must contain
the system without leaks. Outer detectors that tag neutrons and muon-induced
events are typically based in liquid: concentric muon and neutron vetoes in
water in XENONnT XENON:2023sxq  and a liquid scintillator neutron and water
muon outer detector in LZ LZ:2022ufs . The stability of the purification,
containment, and instrumentation of these detectors requires careful
consideration, particularly if the xenon cryostat needs to be accessible.

With an increase in detector size and number of photosensors, the DAQ will
need to handle large quantities of data with a timing resolution on the order
of nanoseconds for years. Many other experiments, particularly at the Large
Hadron Collider have managed, and a future LXe observatory data system is
still within the scope of current technology. The failure rate of the
photosensor readouts would need to be estimated, but is expected to be sub-
percent annually for current technology.

The photosensors and electrodes inside the detector have the largest impact if
they fail, and would require significant downtime and effort to fix. Further
discussion on the limitations of the current generation of this technology is
pursued in the next section.

##  3 Technological Challenges

Vital research and development is ongoing for a future detector. For a target
of about a hundred tonnes of liquid xenon, current solutions will not be as
effective. Calibrations must be carefully considered to acquire necessary
statistics and avoid unmanageable event rates. PMTs and electrodes are fragile
and prone to failures. Accidentally coincident S1s and S2s are a major problem
that necessitates a deeper understanding of isolated S1 and S2 rates, and
creative analyses. Improvements in these categories ensure the success of a
future liquid xenon observatory.

###  3.1 Calibrations

The detector response to NRs and ERs is typically calibrated with externally-
applied point sources or dissolved sources, respectively. The ER response of
LZ is calibrated with dissolved tritium LZ:2022ufs , while XENONnT and
PANDAX-4T use injected 220Rn. The NR response of LZ is calibrated with both an
external deuterium-deuterium (DD) neutron generator aimed at the cryostat and
an external 241AmLi point source to additionally measure the outer neutron
detector efficiency LZ:2022ufs . PANDAX-4T is also calibrated with an external
DD neutron generator for NR PandaX:2021bab . Meanwhile, XENONnT uses a 241AmBe
neutron source near the cryostat, which also calibrates the outer neutron veto
detector XENON:2022ltv . All three current experiments calibrate the position
reconstruction and resolution with dissolved 83mKr Kastens:2009pa . XENONnT
additionally calibrates low-energy position dependencies by injecting 37Ar,
since it can be removed with the distillation column XENON:2022ivg .

The dissolved sources are still viable in a future liquid xenon observatory,
but they calibrate the ER response. A disadvantage of external neutron sources
is that events will be localized outside the fiducial volume near the source
along the edge of the detector where the electric field is less uniform.
Neutrons are more likely to multiple-scatter in a large detector, so it may be
necessary to split multiple-scatters into individual single-site scatters via
analysis techniques to increase statistics. For a target with roughly a
hundred tonnes of xenon, novel solutions for point sources would optimize
calibration statistics. For example, if neutrons could be emitted from the
center of the xenon target, they would calibrate the fiducial volume directly.
The practicality of such a neutron insertion device would need to be
rigorously investigated.

Maintaining the same concentrations of dissolved sources when scaling up can
lead to an unmanageable event rate in a larger detector. There would be event
pile-up, making it difficult to distinguish which S1s go with which S2s in a
given amount of time. The type of source also matters. 220Rn calibrations
produce high-energy alphas that can limit the usable concentrations of the
source without blinding photosensors. The calibration signal, 212Pb, beta
decays with a half-life of about half an hour after its parent 216Po decays.
Due to xenon flow and metallic 212Pb plating onto surfaces, there will always
be more measured 216Po and 220Rn alphas than the desired 212Pb beta decays. On
the other hand, tritium is the more efficient calibration source, since it
purely produces tritium beta decays. The trade-off is that 212Pb calibrates a
larger energy range. Also, tritium can easily contaminate the system, and the
first results of PANDAX-4T contain significant levels of tritium
PandaX:2021bab . Calibrating the ER response of a future detector warrants
consideration for other beta radiation sources. With a radon distillation
column, 222Rn may be itself used as a calibration source to characterize the
detector against its natural background levels. It has a longer decay chain,
allowing the detector to be off when alpha rates are high, and then take data
while 214Pb betas dominate at later times.

Both 83mKr and 37Ar may still be well-suited to a future detector. However,
the usable rates of any source in a detector will decrease as the volume
increases to avoid pile-up. This means that accumulating statistics for
precision will require these calibrations to last longer at lower rates, which
can be accommodated. As discussed, current external NR calibrations may be
impractical for such a large volume, and improvements in ER calibrations is
also necessary. The calibration of this liquid xenon observatory warrants an
upgrade in the technology to calibrate the xenon target, particularly in
calibrating the NR response.

###  3.2 Photosensors

The current generation of PMTs have a high failure rate for an experiment that
needs to run for over a decade. Recent protocols have improved tests of PMT
quality to choose ones less likely to fail. For example, elevated levels of
argon in a PMT predict a higher failure rate due to vacuum leaks
Antochi:2021wik . In XENONnT, 17 of 494 PMTs were not working before the end
of the first year XENON:2022ltv . This 3% failure rate includes commissioning,
which is the most stressful time for the PMTs. The passive failure rate of the
good surviving PMTs is expected to be lower. However, depending on the true
typical rates of vacuum leaks, failure rates are still higher than acceptable
for the lifetime of a future xenon observatory.

Advantages of PMTs include high quantum efficiency, low dark count noise rates
and the 20% probability to measure a double-photoelectron signal for xenon
scintillation light Akerib:2021pfd ; XENON:2020gfr . However, recent
developments in silicon photomultipliers (SiPMs) indicate that they may be a
more reliable choice Baudis:2018pdv . While PMTs do not work well in electric
fields, SiPMs would be able to completely tile the inside of a detector
DARWIN:2022ewl . Hybrid detectors, such as ABALONE DAndrea:2021fro , leverage
some advantages of both. There may also be promise for other Single-Photon
Avalanche Diodes (SPADs). It is clear that photosensors for an future-
generation xenon observatory are a high community priority to maximize quantum
efficiency and durability while minimizing intrinsic radioactivity and dark
count backgrounds.

###  3.3 Electrodes

In order to measure S2s, the electric fields are critical. Figure 3 shows that
the typical operating fields of experiments are decreasing. This is
particularly problematic for the extraction field, since the electron
extraction efficiency has an abrupt roll-off Xu:2019dqb . The drift field also
has significant importance for discriminating between ER backgrounds and NR
signal. With larger detectors and larger electrode spacing, higher absolute
voltages are required to create the same field strengths. For an 100 tonne
detector and equal aspect ratio, the drift region would be about 3 m, which
would require a potential difference of roughly 75 kV for a drift field of 250
V/cm. To achieve an extraction field of 7.5 kV/cm in the liquid would require
optimization of the gate-anode spacing and the liquid level above the gate.
Lower potential differences are required for smaller spacing, and when the
liquid xenon level is a higher fraction of the space between the gate and
anode. However, that negatively affects the proportional scintillation yield
with a smaller gas gap.

Figure 3: In scaling up in mass, LXe TPCs have seen a reduction in relative
performance of electrodes. Data points gathered from XENON:2010xwm ;
XENON:2016sjq ; LUX:2020vbj ; PandaX:2020oim ; XENON:2021qze ; PandaX:2021bab
; XENON:2022ltv ; LZ:2022ufs . Left: The drift fields of current and previous
experiments (blue dots) with a typical optimal field for NR/ER discrimination
as determined in LUX:2020car ; Szydagis:2022ikv  (grey band). Right: The
extraction fields of current and previous experiments (blue dots) with grey
shaded bands of the deciles of electron extraction from Xu:2019dqb . The 100%
and 50% decile lower limits are marked with red horizontal dashed and dotted
lines respectively.

The target electric fields are well motivated for a LXe TPC. However, there is
significant room for improvement to curtail current trends toward lower
fields. For electrodes 3 m in diameter, the transparency and mechanical
strength have to be optimized so that S1 light reaches photosensors, and S2
electrons proportionally scintillate. The woven mesh electrodes of LZ appear
to be performing the best among the current generation of detectors LZ:2022ufs
. Electrodes with large diameters would also be under electrostatic strain to
distort in the middle, creating field variations across the detector. The
anode in the gas sags down due to gravity and electrostatic strain. The gate
and cathode in the liquid experience less gravitational strain due to
buoyancy, and actually bow upward with electrostatic strain.

There is another option to consider: proportional scintillation in the liquid
phase. A single-phase TPC has more thermodynamic stability and liquid xenon is
a better insulator than gaseous xenon. One tested design consists of a radial
detector with photosensors around the barrel and a single anode wire down the
middle Qi:2023bof . Fiducialization is easy, based on drift time to the center
and vertical position as determined by the photosensors. So far, a reasonable
single electron gain has not yet been achieved to be distinguishable from
single photon signals. Also, the detector observed high rates of such photon
signals. It is unclear that such a detector can easily scale over four orders
of magnitude in mass for a liquid xenon observatory, but the technical
challenge of enormous planar electrodes warrants the exploration of creative
solutions.

###  3.4 Background Rejection

As xenon detectors scale toward 100 tonnes, the characterization and
suppression of backgrounds becomes more important to cover the most parameter
space. The outer detectors must have a high detection efficiency for muons and
their effects, namely also a high detection efficiency for neutrons. As
previously mentioned, high rates of radiogenic ER events result in significant
leakage into NR signal regions, otherwise obscuring potential rare processes
that indicate new physics. While these listed backgrounds can be modeled and
anticipated, little is known about AC backgrounds; events created from the
random pairings of unrelated S1s and S2s.

Neutrons are more likely to multiply scatter in a larger detector, but it is
important to characterize their background contributions, since neutrons are
the only expected NR backgrounds beyond neutrino CEvNS to WIMP searches. The
LZ outer detector has achieved an 89% tagging efficiency in the Gadolinium-
loaded liquid scintillator LZ:2022ufs . The type of rock overburden above the
experiment has an impact on ambient neutron and muon rates. Deeper is better
to avoid muons, which are also a main contributor to free neutrons. PANDAX-4T
in China’s Jinping Underground Laboratory experiences a muon flux of
$3.5\times 10^{-10}$ cm-2s-1 PandaX:2021lbm , while XENONnT in Italy’s Gran
Sasso National Laboratory experiences a muon flux about two orders of
magnitude higher. Even so, XENONnT estimated their neutron background to be
about 1 event/tonne/year with only a 53% tagging efficiency XENON:2023sxq .
With better neutron tagging and a larger target, the currently achieved
neutron rates are acceptable, with good characterization for a
kilotonne$\times$year exposure.

One advantage of xenon TPCs is the ER/NR discrimination based on S1 and S2
ratios. As previously stated, the experimentally achieved best leakage
fraction of ER events in the NR S1 vs S2 space was determined to be $7.3\times
10^{-4}$ between 200-350 V/cm LUX:2020car ; Szydagis:2022ikv . This paper
assumes around 250 V/cm. As with argon, S1 pulse-shape discrimination is an
option in xenon. However the singlet state, which dominates ERs, and the
triplet state, which is higher for NRs, have time constants that are about 3
ns and 25 ns, respectively. These time constants are fast compared to the
typical readout electronics of 10 ns samples and lead to a leakage fraction of
only $4\times 10^{-3}$ LUX:2018zdm . Unless better operating conditions and
analysis techniques can further improve the ER/NR discrimination, reducing ER
backgrounds must be a major focus for a future experiment.

####  3.4.1 Accidental Coincidences

Lastly, let us consider a challenging background to low-energy searches that
is becoming more relevant for larger detectors: accidental coincidences (ACs).
LXe TPCs have observed ambient rates of unpaired S1-like signals and S2-like
signals, skewed to lower energies XENON:2019izt . Statistically, the
probability of unrelated S1s and S2s being matched into events depends on the
rates of these lone S1s ($R_{lS1}$) and lone S2s ($R_{lS2s}$) and the drift
time ($t_{d}$) of the detector. Equation 2 gives the form for the accidental
coincidence rate PandaX-II:2022waa . Interaction quality selections ensure
that most ACs are not considered signal, but the fraction of AC events that
pass these data cuts, $\eta$, becomes more significant for larger exposures.

$R_{AC}=\eta R_{lS1}R_{lS2}t_{d}$ (2)

Figure 4: Estimations of the AC rates of current and previous detectors
XENON:2011cza ; LUX:2016ggv ; PandaX:2020oim ; XENON:2018voc ; PandaX:2021bab
; XENON:2023sxq ; LZ:2022ufs . The red lines follow an AC model outlined by
Equation 2 that is roughly scaled to XENON1T. Three lone S1 rate scenarios
were explored by setting the lowest-energy S1 threshold to include 2-fold
(dashed), 3-fold (dash-dotted) and 4-fold (dotted) coincident contributing
PMTs. Considerations for the model are described in detail in the text.

There are a few identified contributions to the lone S1 rates. One source is
from interactions where the ionization electrons are not measured. Along the
edges of the detector, electric field lines can drift electrons to the wall.
Between the bottom PMT array and the cathode is a region where any electrons
in an interaction drift downward and do not create an S2 signal. Measured lone
S1s could result from any type of interaction in these charge-insensitive
volumes. There are also events where the S2 electrons are captured on
electronegative impurities in the drift column, resulting in a few-photon
isolated S1. With higher electron lifetime and xenon purity, the rates of
these S1s are reduced. An optimization is required between distancing the
bottom PMTs from the increasingly high voltage of the cathode to protect them
from discharge, and reducing charge-insensitive volumes.

Depending on the single electron gain and the height of the gas amplification
region, electrons could create narrow signals that may be misclassified as
S1s. S2 light is usually more distributed in time, but the width of s2s
containing more than one electron is dominated by electron diffusion along the
drift column, leading to a continuum of extraction times. A single electron
extracted into the gas produces light along its path through the gas. As
discussed previously, there are high rates of single electrons for long times
after interactions XENON:2021qze ; LUX:2020vbj ; Kopec:2021ccm . In optimizing
the anode and gate spacing for the extraction electric field, the ability to
distinguish single electrons from S1s should be a consideration to avoid high
rates of false lone S1s with energies around the single electron gain value.
Improved signal characterization algorithms between S1s and S2s, and better
signal quality selection criteria can also reduce this lone S1 contribution,
complementing hardware efforts.

High rates of the smallest S1s are attributed to the random pile-up of photons
or photon-like signals in the PMTs. Recently, a background of single-photons
has also been observed Qi:2023bof ; XENON:2021qze ; LUX:2020vbj . It is not
known how these rates might scale with detector size, but they appear
connected to the overall interaction rate in the detector. Photosensor dark
counts are where sensors measure a photon-like signal despite no physically
incident photons. The current detectors use Hamamatsu R11410 PMTs
Antochi:2021wik ; LopezParedes:2018kzu ; Yang:2021hnn , and the typical PMT
dark rate is conservatively on the order of 40 Hz LopezParedes:2018kzu . For
larger detectors, the higher number of photosensors leads to a higher
probability that two photons or photon-like dark counts are observed within
the photon time-of-flight distribution for the detector, which would be on the
order of 100 ns for meter-scale detectors.

Figure 4 shows the AC background rates of previous and current experiments and
includes three red lines from a model based on Equation 2. The red lines
correspond to three lone S1 rates $R_{lS1}$ depending on how many PMTs must
measure photons to identify the smallest S1. They are scaled to XENON1T, which
had a three-fold PMT coincidence requirement. The parameter $R_{lS1}$ includes
pile-up based on an n-fold PMT coincidence requirement within 100 ns for PMTs
with a 40 Hz dark count rate and an ambient photon rate depending on the event
rate ($R_{\mathrm{event}}$). The event rate for XENON1T was about 5 Hz
XENON:2021qze . Therefore, the typical spacing between events was on the order
of 0.1 s, corresponding to a photon rate in 248 PMTs XENON:2018voc  of about
$10^{4}$ Hz XENON:2021qze . The ambient photon rate was therefore chosen to
scale with $10R_{\mathrm{event}}$. It also has a weak
($10^{-3}R_{\mathrm{event}}$) component depending linearly on the event rate
for real events that are missing S2s, or are single electrons misclassified as
S1s. The weak dependence was chosen to give the XENON1T $R_{ls1}$ value of
around 1 Hz, and the parameter $R_{lS2}$ was taken from XENON1T as 2.6 mHz
XENON:2018voc , which was about $10^{-3}R_{\mathrm{event}}$. The lone S1 and
S2 rates are assumed to depend on event rate, which is dominated by
radioactivity of the materials surrounding the walls and should scale with
mass as $m^{2/3}$. The total number of photosensors also scales with
$m^{2/3}$. The drift time scales with $m^{1/3}$, using the drift velocity 1.7
m/ms. This leaves an $\eta$ of around 1% to scale the model to XENON1T.

There are several differences between experiments. The typical photosensor
dark rate has decreased with better technolgy, the event rates per kilogram
have decreased faster than $m^{-1/3}$. Also, analyses have become more
complicated to select against ACs, reducing $\eta$. Most critically, the
dependence of the lone S1 and S2 rates on event rate and other parameters is
not understood, and only roughly estimated here. As can be seen, the number of
photosensors and their dark rates do eventually dominate the lone S1 rate.

To suppress the high AC rates, it makes sense to require an additional PMT to
contribute to a measured S1 and reduce the probability that an S1 is from
pile-up dark counts. Current and previous experiments have used 3-fold
coincidence, except LUX, which used 2-fold and even single-photons LUX:2019npm
. However, that worsens the sensitivity to low-energy interactions by
increasing the energy threshold. Particularly, there is a significant drop in
sensitivity to CEvNS from solar 8B neutrinos XENON:2020gfr  when requiring
more measured photons in the S1.

The lone S2 background is not well-characterized, and only assumed here to
scale with the overall event rate and detector surfaces ($m^{2/3}$). Since
electrons have a much higher detection efficiency than individual photons,
many low-energy events are analyzed in an S2-only channel. The beta decays of
214Pb and 212Pb extend into this energy region, and CEvNS from solar 8B
neutrinos are maximum at the edge of detection thresholds. However, there are
also S2-like signals where the origin of the measured electrons is unlikely to
be a direct particle interaction. The cathode emits groups of electrons at a
non-negligible rate XENON:2019gfn . LUX observed electron bursts after events
that may be attributed to poor extraction efficiency and charge buildup at the
liquid surface LUX:2020vbj . For S2s containing fewer than 5 electrons, there
is a delayed electron background that appears for seconds after the previous
events that cause them XENON:2021qze ; Kopec:2021ccm . Better xenon purity and
low detector event rates begin to mitigate these lone S2 rates, but more
characterization is needed to give a satisfactory estimate of how the AC rates
scale in a larger detector.

The model in Figure 4 based on Equation 2 assumes the event rate is dominated
by the radioactivity of the materials around the detector and scales with
$m^{2/3}$. The leakage into analysis $\eta$ is a constant scaled to XENON1T
XENON:2018voc , despite expected improvements in analysis techniques. The
model also assumes the drift velocity of 1.7 mm/$\mu$s and that the maximum
drift time is increasing with $m^{1/3}$. For an AC to adequately mimic a
signal event, the S2 is likely to be slightly larger than 5 electrons, and
therefore dominated by interactions missing S1s, and hence the conservative
scaling with detector surfaces. Preliminary work in a single-phase detector
does not observe delayed S2s smaller than 5 electrons Qi:2023bof , indicating
that these could be an effect of the liquid-gas surface and might scale with
$m^{2/3}$ anyways. The goals for reducing 222Rn rates are expected to reduce
AC rates by reducing overall detector event rates and the electron and photon
backgrounds that are correlated with each event. Thus, this limited
understanding of the AC rates indicates that they could be reduced to
tolerable levels in a future experiment by reducing the overall event rates,
which is a requirement anyways.

For discovery potential with a liquid observatory, backgrounds must be
mitigated. Radioactive impurities must be minimized in the detector building
stage as well as physically removed, such as via online distillation. Optimal
detector operation must be achieved regarding photosensor dark count rates and
electric fields, maximizing ER/NR discrimination. New analysis techniques must
be pursued to select signal candidates and reject backgrounds, particularly
AC. Machine learning techniques present an attractive opportunity. For
example, a Bayesian network was applied to XENONnT data to discriminate S1s
and S2s as a proof of concept that would reduce misclassification in lone S1
and S2 rates XENON:2023dar . More work is needed to understand and accurately
model AC backgrounds. Although the required amount of background suppression
appears daunting, the previous and current generations of detectors have
established the groundwork for meeting these goals.

##  4 Summary and Outlook

This work has discussed several aspects of current and previous experiments
that cannot directly scale to a future liquid xenon observatory without
improvement. In order to reach the best dark matter sensitivity, the detector
materials must be carefully considered, and technological aspects of the
detector and supporting systems must be improved. Acquiring the xenon requires
a well-considered timeline over several years.

Regarding detector components, event rates become extremely important to
quantify and control. The monoenergetic peaks of 124Xe and the double-beta
decay spectrum of 136Xe are able to be constrained and subtracted, but they
still have larger uncertainties than required for a kilotonne$\times$year
exposure. As with previous generations, 222Rn will continue to be the major
threat that requires a multifaceted approach with minimization, removal and
quantization. Strict radio-assay requirements of materials and active online
radon removal are vital components of a future detector. Signal sensitivity in
a kilotonne$\times$year exposure requires all backgrounds to be either at
levels below what have been achieved to date, or characterized to a higher
degree than currently known in order to be subtracted or otherwise removed
through analysis. Beyond the radiopurity of the materials, the experiment is
required to run for over a decade, necessitating durable components that are
easy to maintain.

There are several limitations in the current technology. Nuclear recoil
calibrations as they are currently conducted from outside the detector are not
sustainable for statistics and detector characterization. Rigorous testing of
photosensors and electrode configurations is necessary to mitigate failure
risks and determine durability. Isolated S1 and S2 rates are alarmingly high
in current experiments, and longer drift times exacerbate AC backgrounds,
which could become the most problematic if left unconsidered in the design
process.

The wealth of science opportunities of a future liquid xenon observatory
Aalbers:2022dzr  invites the participation of the whole LXe community. In the
coming decades, such a project promises rich results spanning many interesting
fields. The technological challenges, and the research and development still
required to overcome them, have wider applications beyond WIMP dark matter
searches. There is the exciting possibility to measure CEvNS from the next
galactic supernova Lang:2016zhv . Additionally, the guaranteed measurement of
CEvNS from solar neutrinos has momentous astrophysical implications, and
neutrinoless double-beta decay searches probe the very nature of neutrinos.
While scaling up in mass comes with growing pains, LXe TPCs are well-
positioned to overcome these challenges and continue their successful lineage.

## Acknowledgments

The author thanks the XENON, LUX-ZEPLIN, and DARWIN Collaborations in the XLZD
consortium for vital discussions and preliminary guidance. Particularly, I
acknowledge Dr. Tina Pollmann for expertise in the contributing factors to
Accidental Coincidence. This work was partially supported by the National
Science Foundation Mathematical and Physical Sciences Ascending (MPS-Ascend)
Postdoctoral Research Fellowship 2137911.

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