contents=  Submitted to the Proceedings of the US Community Study on the
Future of Particle Physics (Snowmass 2021) ,
scale=1,placement=top,opacity=1,color=black,position=3.25in,1.2in

# Scintillating Bubble Chambers:
Liquid-noble Bubble Chambers for Dark Matter and CE$\nu$NS Detection

E. Alfonso-Pita  Instituto de Física, Universidad Nacional Autónoma de México,
A.P. 20-364, Ciudad de México 01000, México.  M. Baker  Department of Physics,
University of Alberta, Edmonton, T6G 2E1, Canada  E. Behnke  Department of
Physics and Astronomy, Indiana University South Bend, South Bend, Indiana
46634, USA  A. Brandon now at Northrop Grumman Department of Physics and
Astronomy, Northwestern University, Evanston, Illinois 60208, USA  M. Bressler
now at UMass Amherst Department of Physics, Drexel University, Philadelphia,
Pennsylvania 19104, USA  B. Broerman  Department of Physics, Engineering
Physics, and Astronomy, Queen’s University, Kingston, K7L 3N6, Canada  K.
Clark<EMAIL_ADDRESS>Department of Physics, Engineering Physics, and
Astronomy, Queen’s University, Kingston, K7L 3N6, Canada  R. Coppejans now at
Univeristy of Oxford Department of Physics and Astronomy, Northwestern
University, Evanston, Illinois 60208, USA  J. Corbett  Department of Physics,
Engineering Physics, and Astronomy, Queen’s University, Kingston, K7L 3N6,
Canada  C. Cripe  Department of Physics and Astronomy, Indiana University
South Bend, South Bend, Indiana 46634, USA  M. Crisler  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  C.E. Dahl
<EMAIL_ADDRESS>Department of Physics and Astronomy, Northwestern
University, Evanston, Illinois 60208, USA  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  K. Dering  Department of Physics,
Engineering Physics, and Astronomy, Queen’s University, Kingston, K7L 3N6,
Canada  A. de St. Croix  Department of Physics, Engineering Physics, and
Astronomy, Queen’s University, Kingston, K7L 3N6, Canada  D. Durnford
Department of Physics, University of Alberta, Edmonton, T6G 2E1, Canada  K.
Foy  Department of Physics, Engineering Physics, and Astronomy, Queen’s
University, Kingston, K7L 3N6, Canada  P. Giampa  SNOLAB, Lively, Ontario, P3Y
1N2, Canada  J. Gresl* Department of Physics and Astronomy, Northwestern
University, Evanston, Illinois 60208, USA  J. Hall  SNOLAB, Lively, Ontario,
P3Y 1N2, Canada  O. Harris  Northeastern Illinois University, Chicago,
Illinois 60625, USA  H. Hawley-Herrera  Department of Physics, Engineering
Physics, and Astronomy, Queen’s University, Kingston, K7L 3N6, Canada  C.M.
Jackson  Pacific Northwest National Laboratory, Richland, Washington 99354,
USA  M. Khatri  Department of Physics and Astronomy, Northwestern University,
Evanston, Illinois 60208, USA  Y. Ko  Department of Physics, University of
Alberta, Edmonton, T6G 2E1, Canada  N. Lamb  Department of Physics, Drexel
University, Philadelphia, Pennsylvania 19104, USA  M. Laurin  Département de
Physique, Université de Montréal, Montréal, H3T 1J4, Canada  I. Levine
Department of Physics and Astronomy, Indiana University South Bend, South
Bend, Indiana 46634, USA  W.H. Lippincott  Department of Physics, University
of California Santa Barbara, Santa Barbara, California 93106, USA  X. Liu
Department of Physics and Astronomy, Northwestern University, Evanston,
Illinois 60208, USA  R. Neilson  Department of Physics, Drexel University,
Philadelphia, Pennsylvania 19104, USA  S. Pal  Department of Physics,
University of Alberta, Edmonton, T6G 2E1, Canada  J. Phelan now at MIT
Department of Physics and Astronomy, Northwestern University, Evanston,
Illinois 60208, USA  M.-C. Piro  Department of Physics, University of Alberta,
Edmonton, T6G 2E1, Canada  S. Priya  Materials Research Institute,
Pennsylvania State University, University Park, Pennsylvania 16802, USA  S.
Ray  Department of Physics and Astronomy, Northwestern University, Evanston,
Illinois 60208, USA  E. Rich  Department of Physics and Astronomy,
Northwestern University, Evanston, Illinois 60208, USA  Z. Sheng  Department
of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208,
USA  A. Sloss  Department of Physics and Astronomy, Northwestern University,
Evanston, Illinois 60208, USA  X. Struyk  Department of Physics and Astronomy,
Northwestern University, Evanston, Illinois 60208, USA  E. Vázquez-Jáuregui
Instituto de Física, Universidad Nacional Autónoma de México, A.P. 20-364,
Ciudad de México 01000, México.  D. Velasco  Department of Physics and
Astronomy, Northwestern University, Evanston, Illinois 60208, USA  S.
Westerdale  Department of Physics and Astronomy, University of California
Irvine, Irvine, California 92697, USA  T.J. Whitis  Department of Physics,
University of California Santa Barbara, Santa Barbara, California 93106, USA
W. Zha  Department of Physics and Astronomy, Northwestern University,
Evanston, Illinois 60208, USA  R. Zhang  Department of Physics, University of
California Santa Barbara, Santa Barbara, California 93106, USA

###### Abstract

The Scintillating Bubble Chamber (SBC) collaboration is developing liquid-
noble bubble chambers for the quasi-background-free detection of low-mass
(GeV-scale) dark matter and coherent scattering of low-energy (MeV-scale)
neutrinos (CE$\nu$NS). The first physics-scale demonstrator of this technique,
a 10-kg liquid argon bubble chamber dubbed SBC-LAr10, is now being
commissioned at Fermilab. This device will calibrate the background
discrimination power and sensitivity of superheated argon to nuclear recoils
at energies down to 100 eV. A second functionally-identical detector with a
focus on radiopure construction is being built for SBC’s first dark matter
search at SNOLAB. The projected spin-independent sensitivity of this search is
approximately $10^{-43}$ cm2 at 1 GeV$/c^{2}$ dark matter particle mass. The
scalability and background discrimination power of the liquid-noble bubble
chamber make this technique a compelling candidate for future dark matter
searches to the solar neutrino fog at 1 GeV$/c^{2}$ particle mass (requiring a
$\sim$ton-year exposure with non-neutrino backgrounds sub-dominant to the
solar CE$\nu$NS signal) and for high-statistics CE$\nu$NS studies at nuclear
reactors.

## Executive Summary

The Scintillating Bubble Chamber (SBC) collaboration is developing liquid-
noble bubble chambers for large (ton-yr) exposure, quasi-background-free
detection of low-energy (sub-keV) nuclear recoils. This effort addresses the
current lack of a scalable, background-discriminating, low-threshold nuclear
recoil detection technology, enabling searches for low-mass ($\sim$1
GeV$/c^{2}$) dark matter to the neutrino fog and high-statistics measurements
of low-energy ($\mathcal{O}(1)$ MeV) neutrino coherent scattering.

The liquid-noble bubble chamber combines the field-leading electron-recoil
background discrimination of a bubble chamber with the event-by-event energy
resolution of a liquid scintillator detector. Early demonstrations of this
technique revealed that competition between these two detection channels, and
more generally the lack of bubble-nucleating energy-loss mechanisms available
to recoiling electrons in liquid nobles, leads to much _stronger_ electron-
recoil discrimination than in existing Freon-based bubble chamber dark matter
detectors. This in turn allows background-free sensitivity to nuclear recoils
at lower energies than can be achieved in any currently working detection
technique, potentially reaching nuclear recoil detection thresholds as low as
100 eV _while remaining blind to electron-recoil backgrounds._ This feature,
together with the inherent scalability of liquid-based detectors, removes the
critical obstacle to both GeV-scale dark matter detection and coherent
neutrino scattering (CE$\nu$NS) measurements at nuclear reactors.

The low-threshold performance of the liquid-noble bubble chamber technique
will be validated in the SBC collaboration’s first physics-scale device, the
10-kg liquid argon bubble chamber “SBC-LAr10.” This device, now being
commissioned, will undergo a series of source calibrations in the MINOS
underground facility at Fermilab to measure both the discrimination power and
low-energy nuclear recoil sensitivity of the device, calibrating the nuclear
recoil detection threshold with a resolution of 10 eV. At the same time, a
radiopure, functionally-identical clone of SBC-LAr10 is being constructed for
the SBC collaboration’s first dark matter search at SNOLAB, with a projected
sensitivity to spin-independent dark matter-nucleon scattering of $2\cdot
10^{-43}$—$10^{-44}$ cm2 in the 1—10 GeV$/c^{2}$ mass range.

Future SBC efforts will include a ton-year dark matter search targeting the
solar-neutrino fog at 1 GeV$/c^{2}$ particle mass and the deployment of an SBC
device at a nuclear reactor to measure the CE$\nu$NS cross section at
$\mathcal{O}(1)$ MeV neutrino energy. The technical challenges in these
efforts are modest, taking advantage of expertise gained by SBC collaborators
from all corners of the low-background field, including large-scale bubble
chamber operation (_e.g._ PICO), cryogenics and liquid-noble handling (_e.g._
LUX-ZEPLIN), low-threshold calibration (_e.g._ NEWS-G), and low-background
construction and photon-detection techniques (_e.g._ nEXO).

Section 1 of this white paper describes the unique dark matter and neutrino
physics opportunities targeted by the SBC collaboration; Section 2 reviews the
fundamental principles of the SBC technique, supported by data in bench-scale
prototypes; Section 3 presents the technical design of the SBC-LAr10 device;
Section 4 describes the ongoing effort to calibrate the sensitivity and
discrimination power of the liquid-noble bubble chamber technique; and Section
5 outlines the SBC collaboration’s longer term plans to fulfill the physics
mission described in Section 1.

##  1 Science Opportunities

Measurements of the cosmic abundances of both baryonic and dark matter are
among the greatest triumphs of modern cosmology and are a cornerstone of our
understanding of the universe, but they also give rise to the two greatest
open questions in high energy physics: What is the dark matter? and What drove
the matter/anti-matter asymmetry in the early universe? The liquid-noble
bubble chamber is an enabling technology on both of these fronts, the former
through dark matter direct detection searches and the latter through precision
measurements of neutrino-nucleus cross-sections, where hints may appear of new
interactions linking the asymmetry of the neutrino sector to that observed
cosmically in baryons.

The desired signal in a liquid-noble bubble chamber, for both dark matter and
neutrino interactions, is the elastic scattering of low-momentum particles off
atomic nuclei. With a target detection threshold of 3 MeV$/c$ in momentum
transfer (_e.g._ , producing a 100-eV recoil on an argon nucleus) this
technique can search for dark matter particles with masses down to $\sim$1
GeV$/c^{2}$ and observe coherent elastic neutrino-nucleus scattering
(CE$\nu$NS) from neutrinos and anti-neutrinos with energies down to 1.5 MeV,
just below the 1.8-MeV hydrogen inverse-beta-decay threshold.

Unlike other sub-keV nuclear recoil detection techniques, the liquid-noble
bubble chamber is both scalable and “quasi-background-free,” meaning that the
technique is able to discriminate against all backgrounds to the dark matter
and CE$\nu$NS signals at the level needed to reach expected backgrounds of
$<$1 event in the signal region of interest over an experiment’s lifetime. We
expect quasi-background-free exposures of $\mathcal{O}(1)$ ton-year to be
achievable in a typical low-background (underground, shielded) environment,
noting that at these exposures the solar neutrino CE$\nu$NS and potential dark
matter signals become backgrounds to each other, forming the so-called
“neutrino fog” [1]. As in high-mass dark matter searches, liquid-noble bubble
chambers achieve background-free exposures through a combination of (1)
applying a narrow energy region of interest, (2) identifying multiply-
scattering backgrounds through a combination of position reconstruction within
the target and active vetoes surrounding the target, and (3) differentiating
between electron-recoil (ER) backgrounds (_e.g._ , from beta-decay) and the
nuclear-recoil (NR) signal. No technology has yet shown ER/NR discrimination
below 1 keV (NR energy), and of the technologies with the _potential_ for such
discrimination, only liquid-noble bubble chambers have the scalability needed
to reach the ton-year exposures motivated by the dark matter and neutrino
physics goals described below.

###  1.1 Dark Matter Detection at 1 GeV/$c^{2}$

Many dark matter candidates, including Weakly Interacting Massive Particles
(WIMPs) and dark-sector models, populate the 1–10 GeV$/c^{2}$ mass range [2].
This region is of particular interest for asymmetric dark matter (ADM) models
[3], where the similar cosmic abundances of dark and baryonic matter are not a
coincidence but rather a consequence of a coupled matter/anti-matter asymmetry
in the light and dark sectors. ADM models can span a wide range of masses, but
naturally favor dark matter particles at a few times the proton mass. These
models are inaccessible to indirect detection as they leave too little anti-
dark-matter in the present-day universe to create an annihilation signal, and
at 1 GeV$/c^{2}$ are also above the mass range probed by beam-dump experiments
[4]. This leaves direct detection as the sole method to explore this key mass
range, and was the primary motivation for one third of the “Generation 2” U.S.
dark matter search program [5].

Figure 1 (left) shows the current state of the dark matter direct detection
field in the 1–10 GeV$/c^{2}$ mass range. This mass range is below the
threshold of the ER/NR-discriminating experiments and analyses employed in
heavy WIMP searches (_e.g._ , the lowest mass considered by the recent LUX-
ZEPLIN result is 9 GeV$/c^{2}$ [6]). Instead, existing direct detection
experiments searching for dark matter at masses below 10 GeV$/c^{2}$ do so
exclusively by measuring very small amounts of ionization (few-$e^{-}$),
either with low-noise electronic readout techniques [7] or through built-in
gain mechanisms such as proportional gain [8], electroluminescence [9, 10, 11,
12], or Luke-Neganov phonon production [13, 14]. This approach has two
problems. First, it measures only a fraction of the available energy: in the
case of electron recoil detection the kinematics of dark matter-electron
scattering limit the allowed energy transfer, and in the case of nuclear
recoil detection only a small fraction (in some cases $<$10$\%$ [15]) of the
transferred energy goes towards ionization due to the Lindhard effect [16].
Second, with only a single sensitive energy deposition channel it is
impossible to distinguish electron- and nuclear-recoil signals, putting quasi-
background-free operation well out of reach for both current and next-
generation experiments. All ionization-based GeV-scale dark matter searches
are fundamentally background-limited, depending critically on an experiment’s
ability to model and subtract sub-keV ER backgrounds. To reach the solar
CE$\nu$NS fog, and particularly to make a discovery of GeV-scale dark matter,
a new low-energy ER/NR discriminating technique is needed.

Including liquid-noble bubble chambers, there are three technologies that show
potential for ER/NR discrimination below 1 keV. The detector physics driving
this capability in liquid-noble bubble chambers is the subject of Section 2 —
the other two techniques are ultra-high-resolution cryogenic ($<$100 mK)
calorimeters measuring both direct quasi-particle generation and electronic
energy loss in either germanium/silicon crystals [17] or superfluid helium
[18]. It is reasonable to suppose that both of these techniques will
eventually demonstrate the low-energy ER/NR discrimination needed to suppress
ER backgrounds below the $\mathcal{O}$(100) (ton-yr-keV)-1 solar neutrino
CE$\nu$NS rate, but it will be exceedingly challenging for either to reach the
ton-year exposures needed to explore the solar neutrino fog. Bubble chamber
dark matter experiments targeting ton-year exposures, on the other hand, are
already going forward for high-mass WIMP searches [19]. Furthermore, the
Excess working group [20] has recently identified a possible explanation for
low-energy backgrounds seen in several dark matter search experiments as being
due to the release of stored mechanical energy from stresses induced by
detector holders or microfractures, or from stress intrinsic to target
materials. Liquid-target detectors do not suffer from these types of
backgrounds, making liquid-noble bubble chambers a critical element to any
future GeV-scale dark matter discovery.

If quasi-background-free operation in a liquid-argon bubble chamber at 100-eV
threshold is achieved, a ton-year exposure will explore the solar CE$\nu$NS
neutrino fog at 1 GeV$/c^{2}$ to the $n=2$ boundary as defined in [1], or
roughly to the point where systematic uncertainties in the solar neutrino
model exceed the statistical uncertainty in the measured scattering rate. In
other words, at a ton-year exposure, SBC shifts from performing a dark matter
search to exploring solar neutrino physics through the CE$\nu$NS channel. This
complementarity has been explored in [21].

Figure 1: Left: Current limits and projections in the search for GeV-scale
dark matter. All curves are 90% C.L. limits (solid lines [6, 10, 11, 22, 23,
24, 25, 26, 27, 28, 29, 30]) or projected limits in the absence of a dark
matter signal (dotted lines [5, 18, 31, 32, 33]) on the spin-independent DM-
nucleon scattering cross section. Additional projections circulated during the
Snowmass process are collected at [2]. The dashed brown curves are benchmarks
indicating the exposure and threshold necessary to reach the solar CE$\nu$NS
floor, assuming no background except for the CE$\nu$NS signal, which is
subtracted assuming zero uncertainty on the CE$\nu$NS rate. The neutrino
(CE$\nu$NS) floor is taken from [1], where “$n=2$” indicates the point at
which sensitivity grows with the square-root of exposure, or roughly where
systematic uncertainties in the CE$\nu$NS signal overtake statistical
uncertainty in the measured CE$\nu$NS rate. Right: Sensitivity to a new B$-$L
coupling for an argon nuclear-recoil detector with 100-eV threshold measuring
coherent scattering rates of reactor neutrinos, showing exclusion limits at
95% C.L. in the $g^{\prime}-M_{Z^{\prime}}$ plane. Setup A refers to a 10-kg
chamber 3 m from the 1-MWth research reactor at ININ near Mexico City. Setup B
refers to a 100-kg chamber 30 m from a 2-GWth power reactor. Both curves
include background models (excluding electron-recoil backgrounds) and neutrino
flux uncertainty. Current limits from the CONNIE reactor CE$\nu$NS search
[34], stopped-pion-decay CE$\nu$NS measurements [35, 36, 37], collider
experiments [38, 39, 40], and beam dump experiments [41, 42, 43, 44, 45, 46,
47, 48, 49, 50] are also shown. Plot published in [51].

###  1.2 Coherent Neutrino Scattering at $\mathcal{O}$(1 MeV)

The CE$\nu$NS interaction was first observed by the COHERENT collaboration,
measuring neutrinos produced by stopped-pion and -muon decay at the Oak Ridge
National Laboratory’s Spallation Neutron Source (SNS) scattering off cesium
and iodine nuclei, producing recoils with momenta of $\sim$50 MeV$/c$
($\sim$10 keV recoil energy) [35]. COHERENT has since measured this process on
argon nuclei as well [36], but the CE$\nu$NS process from either solar
neutrinos or nuclear reactor anti-neutrinos has yet to be measured.

The neutrino physics motivation for a reactor CE$\nu$NS measurement is driven
by three qualitative features. First, reactor neutrinos are an order of
magnitude lower in energy than the neutrinos produced by a stopped-pion
source, producing fully-coherent scattering and probing BSM neutrino physics
in a new regime — _i.e._ , the neutrino-nucleus effective field theory at
$\sim$2 MeV contains different information than the effective field theory at
$\sim$50 MeV. Second, the neutrino flux at a typical reactor site is up to
$10^{5}$ times higher than that at the SNS. Finally, reactors are a pure
$\bar{\nu}_{e}$ source, complementing the mixed
$\bar{\nu}_{e},\nu_{e},\bar{\nu}_{\mu},\nu_{\mu}$ produced at spallation
sources. Figure 1 (right) shows a case study of the physics reach of a reactor
CE$\nu$NS measurement using an SBC chamber [51], examining sensitivity to a
new B–L coupling; other specific physics targets include other non-standard
interactions [52, 53], sterile neutrino oscillations at short-baselines [54,
55] and neutrino magnetic moments [56]. Additional studies on the reach of SBC
to non-standard neutrino interactions and sterile neutrinos have been
performed [57]. A precision measurement can also be made of the weak mixing
angle at low momentum transfer [58, 56].

There are currently operating or planned efforts to observe reactor CE$\nu$NS
with a number of techniques including p-type point contact Ge (CONUS, TEXONO),
Si CCD (CONNIE), NaI (NEOS), dual-phase Xe TPC (RED-100, NUXE), cryogenic Si,
Ge and Zn bolometer (MINER, RICOCHET) and cryogenic CaWO4 and Al2O3
calorimeter (NUCLEUS) detectors [59, 60, 34, 61, 62, 63, 64, 65, 66]. Recent
results reported by CONUS [59] elucidate the challenge faced by these efforts;
due to high background and limited reactor-off time available for background
subtraction, the reported upper limit remains a factor of seven above the
Standard Model CE$\nu$NS prediction. As in GeV-scale dark matter searches,
sub-keV electron-recoil discrimination is the most effective means of
background reduction, granting SBC the potential to achieve a signal-to-
background ratio much better than one.

In addition to searches for new neutrino physics, neutrino detectors have been
considered for several applications related to nuclear non-proliferation [67,
68]. In particular, LAr detectors sensitive to CE$\nu$NS may have applications
in near-field, non-intrusive, real-time reactor power monitoring [69]. A
10-kg-scale SBC detector has the potential to make a significant CE$\nu$NS
detection of neutrinos from a nuclear reactor in much less than a day.

##  2 Scintillating Bubble Chambers

Bubble chambers for dark matter searches, liquid-noble or otherwise, take
advantage the field’s most straightforward and powerful ER/NR discrimination
technique: nuclear recoils make bubbles in the superheated liquid target and
electron recoils do not. Underlying this statement is a trade-off between the
nuclear recoil detection threshold and the electron recoil discrimination
power, both of which are determined by the thermodynamic state (temperature
and pressure) of the target fluid. The key phenomenon driving the SBC program
is a fundamental, additional suppression of ER-induced bubble nucleation in
superheated noble liquids, enabling quasi-background-free operation at NR
detection thresholds an order of magnitude or more below those achievable in
existing Freon-based chambers.

This section gives a brief review of bubble chamber operation and the unique
low-threshold capability of liquid-noble bubble chambers. For an in-depth
modern review of the thermodynamic theory governing bubble chamber operation,
see the appendices of [70]. For comparisons between the thermodynamic model
and experimental data in superheated molecular fluids, see [70, 71] (electron-
recoil calibrations) and [72] (nuclear-recoil calibrations). For experimental
data from the SBC liquid-xenon prototypes, see [73] (first data) and [74]
(low-threshold data).

###  2.1 Bubble Chamber Operation

The scintillating bubble chamber is an extension of the moderately-superheated
bubble chamber technique pioneered by COUPP [75] and now used by PICO [29] to
search for dark matter. The target material in any of these devices is a
homogeneous fluid that is superheated by dropping the pressure of the fluid
below its vapor pressure at a given temperature. This state is maintained, for
$\mathcal{O}$(10) minutes or more in a low-background environment, until a
particle interaction creates a nucleation site or “proto-bubble” in the fluid.
Within milliseconds the bubble grows to visible size and continues to grow
until the chamber is compressed by the experimenter, driving the fluid back to
a stable liquid state. After a roughly half-minute delay to re-equilibrate,
the pressure is reduced again to place the liquid back in the superheated
state. We refer to this cycle, from stable liquid, to superheated liquid, to
bubble, and back to stable liquid, as an “event.”

The great advantage of the bubble chamber for dark matter searches is its
intrinsic insensitivity to electron-recoil backgrounds. This insensitivity is
a direct consequence of the thermodynamics of bubble nucleation, which require
the formation of a critically sized proto-bubble to overcome the free energy
barrier arising from the surface tension of the bubble [76]. A particle
interaction can create this critically-sized proto-bubble by locally heating
the fluid, as described in the Seitz “Hot-Spike” model [77]. In typical PICO
chambers an energy deposition of a few keV is required to create the necessary
$\sim$50-nm-diameter proto-bubble [29]. Low-energy nuclear recoils meet this
local heating criterion, and the Seitz calculation is a good approximation of
the measured nuclear recoil energy threshold for bubble nucleation [29, 72,
78, 79, 80]. Recoiling electrons, on the other hand, cannot achieve the
required $\sim$100-eV/nm stopping power, allowing PICO chambers to set the
operating conditions such that only 1 in $10^{10}$ electron recoil events will
nucleate a bubble. A comprehensive picture of ER/NR discrimination in bubble
chambers and a complete derivation of the critical radius and Seitz
thermodynamic threshold are given in [70].

###  2.2 Liquid-Noble Bubble Chambers

The liquid-noble bubble chambers built by the SBC collaboration differ from
the Freon bubble chambers operated by COUPP and PICO in two fundamental,
related ways. The obvious difference is that the target fluids used by SBC are
liquid scintillators, so that nuclear recoils simultaneously create
scintillation light and nucleate a bubble, as shown in Fig. 2, while electron
recoils create light only. The scintillation signal gives a measure of the
total energy deposited in the detector with up to $\sim$keV resolution; by
contrast, the acoustic signal accompanying bubble nucleation measured by PICO
gives $\sim$MeV energy resolution [81, 82].

Figure 2:  Sample nuclear recoil event from the prototype xenon bubble chamber
[73]. Top: Stereo image of a single xenon vapor bubble. Middle: Acoustic
record (blue) of bubble formation, giving the time of nucleation to $\pm$25
$\upmu$s. In this case nucleation is coincident with a scintillation trigger
(red). The lag between the scintillation pulse and acoustic onset matches the
sound speed in liquid xenon. Bottom: PMT waveforms showing xenon
scintillation. The bubble-coincident pulse is shown in red. Electron recoils
generate scintillation pulses without coincident bubble nucleation (gray
traces).

Liquid-noble bubble chambers are also able to run at much lower thresholds
(higher superheat) than Freon bubble chambers while remaining blind to
electron recoils. In Freon chambers, sensitivity to electron recoils turns on
sharply at a Seitz threshold of a few keV, setting a lower limit on useful
thresholds for dark matter searches. Liquid-noble bubble chambers have
fundamentally suppressed sensitivity to electron recoils, with ER bubble
nucleation rates several orders of magnitude below that predicted by the
models applied to Freon chambers (see Fig. 3). To our knowledge, bubble
nucleation by electron recoils has never been observed in pure xenon [83], and
has been observed only at extreme superheat (thresholds of $\mathcal{O}(10)$
eV) in pure liquid argon (LAr) [84, 85].

The absence of bubble nucleation by electron recoils in superheated noble
liquids is a consequence of the lack of molecular degrees of freedom for
recoiling electrons to excite. Without energy loss to molecular vibrational
modes, the only way particle interactions can locally heat the fluid is
through the center-of-mass motion of individual atoms. While this is achieved
directly by the atom-atom collisions that are the dominant mode of energy loss
for nuclear recoils (_i.e._ , the Lindhard effect [86, 16]), the kinematics of
elastic electron-atom collisions make this an extremely inefficient means of
energy loss for electrons. Instead, electron recoil energy is almost entirely
carried away by scintillation light, IR radiation (including bremsstrahlung
from electron-atom scattering), and slowly or incompletely recombining
ionization. This was well known in the bubble chamber heyday, and liquid-xenon
tracking bubble chambers explicitly mixed in molecular components (ethylene
and propane) to allow bubble nucleation by delta ray electrons [87].

The thermodynamic threshold at which electron recoils may become a background
in pure noble liquids is not yet known (see existing limits in Fig. 3), but
the threshold at which thermal fluctuations can spontaneously nucleate bulk
bubbles is well studied [88], and in liquid argon corresponds to $\sim$1
bubble per ton-year at a 40-eV Seitz threshold. This target threshold sets the
required pressure (1.4–25 bara) and temperature (90–130 K) ranges for the
SBC-10LAr device described in Section 3.

###  2.3 Results from the Prototype Xenon Bubble Chamber

The first detection of simultaneous scintillation and bubble nucleation by
nuclear recoils was made in a 30-gram xenon bubble chamber at Northwestern
University in 2016 [73] (see Fig. 2). This chamber has since operated with
xenon at thermodynamic thresholds down to 500 eV, limited only by the pressure
rating of the device. There is to-date no evidence for bubble nucleation by
electron recoils in this device, giving the electron-recoil sensitivity limits
shown in Fig. 3. The same device showed sensitivity to 152-keV neutrons from a
88Y-Be photo-neutron source [89] (maximum xenon recoil energy of 4.8 keV),
confirming that the Seitz model remains an $\mathcal{O}(1)$ guidepost for
nuclear recoil detection thresholds in noble liquids at thresholds down to at
least 1 keV (see Fig. 4).

Figure 3:  Electron recoil sensitivity of the prototype xenon bubble chamber
as a function of superheat (Seitz threshold), taken from [74]. No evidence for
bubble nucleation by gamma sources is seen. Dashed lines show the
sensitivities of the measurements based on source strengths, background rates
and exposures. Square points show 90% confidence intervals with background
subtraction per [90] (giving upper limits in all cases but one), and fall at
the expected sensitivity for each source. Round points are 90% C.L. upper
limits without background subtraction — background data was not available at
all operating conditions, particularly at the lowest thresholds. The blue
curves shows the gamma sensitivity expected for a molecular fluid with the
same thermophysical properties as xenon, following the electron recoil bubble
nucleation models for delta rays (dotted line, [70]) and Auger cascades
following xenon K-shell capture (dot-dashed line, [71]).  Figure 4:  Nuclear
recoil sensitivity of the prototype xenon bubble chamber — both plots taken
from [74]. Left: Chamber response to 152-keV neutrons from a 88Y-Be photo-
neutron source. The 88Y-Al points (gammas only) correspond to the 88Y points
in Fig. 3. The extrapolated onset of sensitivity is at $Q\approx 2.5$ keV for
the 4.8-keV maximum recoil energy. Right: The probability of bubble nucleation
as a function of nuclear recoil energy at a fixed Seitz threshold of 1.48 keV.
The efficiency curve is constrained by observed bubble rates when exposed to
252Cf, 88YBe, and 207BiBe sources, following the analysis strategy described
in [72]. The solid blue line and shaded blue region indicate the best fit
efficiency curve and 1-$\sigma$ allowed region, respectively, with the red
line indicating the calculated Seitz threshold. Both plots show a factor of
$\sim$2 between the calculated Seitz threshold and nuclear recoil detection
threshold, matching the threshold behavior seen in Freon bubble chambers [29,
80, 72].

###  2.4 Strategies for Quasi-background-free Operation

For a dark matter search, the thermodynamic state of the bubble chamber will
always be chosen such that the bubble nucleation rate from electron recoils
(_e.g._ the Bq/kg of 39Ar beta-decays present in natural argon) is much less
than one bubble per live-year. There are, however, other backgrounds that do
nucleate bubbles. These are explained below, each with the corresponding
mitigation employed to reach the goal of quasi-background-free operation.

Bulk alpha decays in the target fluid (_e.g._ 222Rn, 220Rn, and the subsequent
decay chains) nucleate a single bubble that is visually indistinguishable from
those created by low-energy nuclear recoils, despite depositing $\sim$104
times more energy in the target. Such bubbles are trivially identified by the
accompanying scintillation signal, as was shown even with the rudimentary
scintillation detection employed in the xenon prototype (see Fig. 5).

Figure 5:  Scintillation response for a mock “signal” (in this case fast
neutrons from a 252Cf source) and background in the prototype xenon bubble
chamber, taken from [74]. Left: The absolute rate, broken down by bubble
multiplicity. Right: The same data with unit normalization for both signal and
background. The background rate in this chamber consists primarily of high-
energy events, including alpha-decays and through-going muons that nucleate a
bubble by Coulomb scattering off a xenon nucleus, both of which saturate the
scintillation detection system. The SBC-LAr10 chamber will detect 1
scintillation photon per $\sim$5 keV nuclear recoil energy, or roughly
$\times$10 the photon detection efficiency of the data shown here.

Surface alpha decays may deposit much less energy in the target fluid, _e.g._
giving only the tail end of a 206Pb recoil following 210Po decay, while still
nucleating a bubble. When this occurs at the chamber walls, these events are
easily tagged by mm-resolution stereoscopic bubble imaging. Standard low-
background cleanliness protocols are necessary and sufficient to control the
rate of such events from suspended particulate in the bulk target fluid.

Fast neutrons, produced by fission and $(\alpha,n)$ reactions in detector
materials and by cosmic rays in the surrounding rock, are reduced primarily
through shielding and careful screening of detector materials. Any residual
fast neutron flux can be measured and rejected by (1) tagging the multi-bubble
events typical of a neutron’s $\sim$10-cm mean free path, (2) using the
scintillation channel to reject nuclear recoils greater than $\sim$5 keV
(target scintillation detection threshold in SBC-LAr10), and (3) rejecting
events with coincident scintillation in surrounding materials. The last of
these methods will become increasingly important as detectors grow in size,
and may include scintillating thermal/hydraulic bath fluid (already in place
in SBC-LAr10, see Section 3) and gadolinium-doped materials generating large
neutron-capture gamma cascades to increase neutron-tagging efficiency.

Thermal neutrons can also nucleate bubbles in the target fluid through
$(n,\gamma)$ (neutron capture) reactions in the target itself, where the
capturing nucleus recoils against the high-energy (several-MeV) photons
emitted. As in the case of fast neutrons, this background is reduced primarily
through shielding, with any residual rate identified by the scintillation
produced by the correlated gammas interacting in the scintillating target and
surrounding sensitive media.

In a similar fashion, external high-energy photons (1.5 MeV and above) can
nucleate bubbles by generating nuclear recoils through Thomson scattering [91]
— the photon equivalent of the CE$\nu$NS signal. These photons must be
considered in shield design, and their flux can be monitored in-situ through
the scintillation produced by their much more common electronic interactions.

Finally, if a positive signal inconsistent with the above backgrounds is
observed — _i.e._ without an associated multi-bubble or scintillation-tagged
event rate — several generic checks can be performed to rule out possible
detector pathologies. The NR bubble nucleation threshold can be varied to
build a recoil energy spectrum, and moreover can be varied both by scanning in
pressure or temperature to check for a consistent NR-like nucleation
threshold. A more powerful check, however, is to swap target fluid entirely —
all current SBC chambers are designed to run with either LAr or LXe targets
(with the additional possibility of N2 and CF4) granting a unique capability
for self-verification of any future dark matter signal.

##  3 Design and Construction of SBC-LAr10

The SBC collaboration’s first physics-scale detector, SBC-LAr10, is currently
being commissioned at the Fermi National Accelerator Laboratory. The primary
purpose of this device is to characterize the low-threshold performance of the
liquid-noble bubble chamber, validating the physics reach of the technique
through the calibration campaign described in Section 4. A functionally-
identical device with a focus on radiopure construction will be deployed at
SNOLAB for SBC’s first dark matter search. These chambers have been designed
to meet the following specifications:

SBC-LAr10 Design Goals
---
Target Volume | 10 L (10 kg LAr @ 130 K)
Target Fluid | Xe-doped Ar,
| with options for pure Ar, Xe, N2, and CF4
Achievable Superheat | 40 eV (LAr @ 1.4 bara, 130 K)
Thermodynamic Regulation |  $\pm$0.5 K, $\pm$0.1 bar ($\pm$5 eV Seitz Threshold)
Scintillation Detection | 1 photon per 5 keV NR in Xe-doped Argon
| ($g_{1}\approx 0.02$)
Bubble Imaging | 100 fps, mm-resolution stereoscopic imaging
Acoustic Reconstruction | time-of-nucleation reconstructed to
|  $\pm$25 $\upmu$s resolution
Zero-scintillation single-bubble rate | 1 background event per live year
(SNOLAB chamber) |

Figure 6 shows the schematic and mechanical layout of the SBC-LAr10 detector.
The remainder of this section details the technical design of this detector,
driven by the design goals listed above.

Figure 6: Schematic (left) and annotated solid model (right) of the SBC-LAr10
detector.

###  3.1 Sites and Shielding

As with all low-background detectors, SBC-LAr10 will require shielding in
order to operate, however the requirements are very different for the two
iterations of the detector. Calibration of the detector will be a relatively
low-rate process ($\sim$1,000 events per day, already much lower than the
cosmic-induced background rate on surface), however the full dark matter
search necessitates a dramatically reduced rate achievable only through
multiple levels of shielding.

The calibration-focused chamber will be deployed at Fermilab in the MINOS
tunnel, approximately 100 m underground. This will reduce the cosmic-ray muon
rate by an amount sufficient to allow the low-energy calibration without
additional shielding. The dark matter search chamber will be deployed at
SNOLAB in the ladder labs (the space allocated following SBC’s successful
Gateway 1 review at SNOLAB) to achieve a significant reduction in the muon-
induced background rate. The detector will be deployed in a shield consisting
of 50 cm of water to reduce the rock-based neutron rate and 10 cm of copper to
attenuate high-energy gamma rays that would lead to a Thomson scattering
background.

###  3.2 Thermo-mechanical design

As in other bubble chamber dark matter detectors, the SBC-LAr10 chamber must
hold the target volume in the desired superheated state with at at least
$\pm$0.5 K and $\pm$0.1 bar precision (corresponding to a $\pm$5 eV Seitz
threshold at the target operating condition), waiting for a bubble nucleation
event. When bubble nucleation does occur, the chamber is recompressed within a
fraction of a second to drive the fluid volume back to an entirely liquid
state. Both the precision regulation and fast compression must be achieved
without exposing the superheated liquid to rough surfaces that can lead to
spurious bubble nucleation. SBC-LAr10 adopts a buffer-free, dual-temperature-
zone strategy to achieve this, as is also used by PICO-40L and PICO-500 [19]
and has been implemented successfully in SBC and PICO test chambers [71, 73,
74, 92, 93].

####  3.2.1 Pressure Control

To avoid surface nucleation, the superheated fluid target is contained in a
radiopure, UV-transparent, fused silica vessel (Hereaus Suprasil 310), with a
second concentric, smaller-radius vessel acting as a piston to control the
pressure of the target fluid. Both vessels are sealed to a stainless steel
bellows with spring-energized polytetrafluoroethylene (PTFE) seals. The
bellows, seals, and connected stainless steel piping are held at a lower
temperature than the target fluid, such that the fluid contacting them is a
stable liquid even in the depressurized state, with a temperature gradient
(130 K to 90 K for LAr) in the annular space between the fused silica vessels.
A test assembly of the complete vessel-and-bellows system is shown in Fig. 7
(left).

Figure 7: Left: Test of the SBC-LAr10 “inner assembly” comprising the inner
and outer fused silica vessels, stainless steel bellows, bellows guides and
support structure, and spring-energized PTFE silica-to-metal seals. Right: The
partially-assembled HDPE “castle” isolating the warm (superheated) target
region from the cold (stable) region, enclosing the copper SiPM support
structure that surrounds the target volume. At the bottom of the castle, three
of the eight piezoelectric acoustic sensors are visible.

Typical operating pressures in SBC-LAr10 are 1.4 bara and 25 bara in the
superheated and compressed states, respectively, well above the $\sim$1.3 bar
differential pressure rating of the silica vessels. The space outside the
vessels is therefore filled with a cryogenic hydraulic fluid that drives the
inner vessel “piston” to equalize the pressure inside and outside the silica
vessels. This hydraulic fluid must be a stable liquid (not superheated) over
the full operating pressure range — for operation with a LAr target the
cryogenic hydraulic fluid is CF4, a condensed inert gas with similar freezing
point but much higher boiling point than LAr [94].

The cryogenic hydraulic fluid is contained in a stainless steel pressure
vessel, and during bubble chamber operation both the hydraulic fluid and
target fluid are isolated from the outside world by cryogenic valves
immediately below the pressure vessel, creating a sealed space with fixed
fluid mass. The pressure of the cryogenic hydraulic fluid, and thus of the
target fluid, is controlled by a bellows piston that is in turn driven by an
external, room-temperature, double-acting hydraulic cylinder with 15-cm stroke
and 55-ton capacity. That cylinder is connected to a custom 2,000 psi
hydraulic system with a 1.5-gpm hydraulic power unit, pneumatic bladder
accumulator to drive fast compression, and servo valve for fine pressure
control. Figure 8 shows the completed hydraulic system and results from the
first performance tests.

Figure 8: Left: SBC-LAr10 pressure vessel beside the hydraulic test stand. The
hydraulic system was commissioned with the hydraulic cylinder (yellow) driving
a pair of heavy springs. In normal operation, the cylinder will connect to the
bottom of the piston shaft seen at the base of the pressure vessel. Right:
Sample “fast compression” in the hydraulic test stand, transitioning from a
position-regulating mode to a high-pressure mode. In normal operation, the
cylinder will regulate chamber pressure rather than shaft position — in the
test stand the position regulation is limited by the resolution of the
position transducer readout ($\sim$0.5 mm). The initial sharp pressure rise
driven by the accumulator is sufficient to halt bubble growth, while the
subsequent slow rise driven by the hydraulic power unit drives the vapor back
to the liquid state. Figure taken from [74].

####  3.2.2 Thermal Control

To achieve the dual temperature zones necessary to avoid bubble nucleation on
the stainless steel components and seals in the inner assembly, the SBC-LAr10
pressure vessel is cooled to the “stable” temperature (90 K for LAr) and an
isolated region around the target fluid is heated to the superheated
temperature (130 K for LAr at target threshold). To achieve this gradient with
an acceptable heat load, a high-density polyethylene (HDPE) “castle” is
constructed around the target volume and annular target region, as shown
partially assembled in Fig. 7 (right). Vertical tubes with custom check valves
inside the castle connect the warm and cold regions at multiple locations to
allow bi-directional fluid flow, preventing pressure build-up between the
regions while restricting convection. Flexible plastic “wipers” extend outward
from the castle to the inner wall of the pressure vessel, further restricting
convection. A nichrome wire heater at the inside base of the castle provides
the heat necessary to establish the warm temperature zone.

In the warm region the CF4 liquid has low viscosity providing a highly-
convecting, uniform thermal bath for the superheated target. In the cold
region the CF4 is much more viscous and insulating, and inner-assembly metal
components are thermally tied to the cold pressure vessel wall with spring-
loaded copper fins. Thin layers of liquid CF4 serve as a thermal grease to
complete the heat conduction path from the inner-assembly through the copper
fins to the pressure vessel wall.

Heat is transferred from the pressure vessel wall to a copper band wrapping
the exterior of the pressure vessel immediately below the bottom of the
castle, seen in the left of Fig. 8. That band is in turn cooled by three
closed-loop nitrogen thermosyphons [95], each capable of carrying 100 W to a
Cryomech AL300 cold-head immediately above the pressure vessel (see Fig. 6).
This 300-W Gifford-McMahon cryocooler finally rejects the heat to the outside
world.

The pressure vessel, thermosyphons, and cold head are wrapped in multi-layer
insulation and enclosed in a common vacuum jacket with penetrations for the
compression system as well as fluid and electrical feedthroughs. The total
estimated heat load on the pressure vessel is 220 W, roughly half of which
goes towards maintaining the thermal gradient between the warm and cold
regions.

####  3.2.3 Process Controls

The complete SBC-LAr10 system includes approximately 125 channels of “slow”
instrumentation — pressure, temperature and position sensors, and the valves,
heaters and pumps that control the chamber state. These instruments, including
the hydraulic pressure control system, the thermosyphon system, the target
fluid (argon) and cryogenic hydraulic fluid (CF4) fill and recovery systems,
and the heaters and thermometry for temperature regulation are controlled by a
Programmable Logic Controller, or PLC. This PLC shares instrument readings in
real time with a custom python-based SCADA (supervisory control and data
acquisition, or “slow-control”) system that provides a graphical user
interface, records a continuous history of all instrument readings, and
broadcasts alarms if detector parameters exceed allowed ranges.

The PLC also contains logic to regulate and manipulate the chamber state. This
logic is organized in three categories: control loops, interlocks, and
automated procedures. Control loops include PID-controlled heaters for
temperature control and PID-control of the servo valve for pressure control.
Interlocks are rudimentary if-then objects that can, for example, cut power to
a heater or open a valve if a given temperature or pressure reading goes out
of range. Most interlocks are intended to protect detector hardware against
unexpected conditions and operator error. Automated procedures are sequences
of steps that are either repeated too often to be human controlled (_e.g._ the
pressure cycling of the chamber for every event) or require a precision
exceeding that achievable with manual controls (_e.g._ the metered flow of N2
gas into a thermosyphon circuit).

Finally, the PLC can also store 10-ms resolution traces of select instruments
for asynchronous downloading, providing a more fine-grained view of chamber
operation than can be achieved with the $\sim$1-second resolution provided by
the real-time communication with the slow-control system. This functionality
produced the data shown in Fig. 8 (right), and is a key element of the data
acquisition system described in the next section.

###  3.3 Instrumentation and Data Acquisition

Scintillating bubble chambers are somewhat unique in the variety of data, and
the range of time scales over which data are taken, that are critical to event
reconstruction. From fast to slow, these include scintillation signals
($\mathcal{O}$(100) ns), acoustic signals ($\mathcal{O}$(100) $\upmu$s),
bubble images ($\mathcal{O}$(10) ms), and pressure and temperature histories
($\mathcal{O}$(0.01–1000) s). This section describes each of these signal
pathways and the Run Control system that coordinates data acquisition between
them.

####  3.3.1 Event Structure

All SBC-LAr10 data are organized by bubble chamber “event” as defined in
Section 2 — that is, one cycle from the pressurized state, to the superheated
state, and back. The transition from the superheated state back to the
compressed state can be triggered in a number of ways, including detection of
a bubble in the imaging system, detection of a pressure rise by the PLC, a
random trigger generated by Run Control, or even an operator-generated manual
trigger. In all cases this “bubble chamber trigger” is broadcast
simultaneously to all data acquisition subsystems, allowing for offline
synchronization of the different data streams.

The Run Control software initiates data acquisition in each data stream at the
start of every event, and confirms the complete writing of data from each data
stream after the bubble chamber trigger, closing the event. For example, at
the start of an event, Run Control instructs the PLC described in the previous
section to begin recording 10-ms resolution data for later download. Once all
data subsystems are similarly primed, Run Control instructs the PLC to begin
the pressure cycle. On the bubble chamber trigger the PLC compresses the
chamber. Finally Run Control tells the PLC to halt acquisition and copies the
PLC data to the event record. The other data streams described below follow
similar patterns.

####  3.3.2 Bubble Imaging

Three cameras continuously image the chamber, providing both a trigger on
bubble nucleation and video record of the growing bubble(s) in the target
volume. SBC-LAr10 uses Arducam OV9281 1-Megapixel global shutter cameras,
mounted in the vacuum space and viewing the chamber through three separate
sapphire pressure windows at the top of the pressure vessel. Three RaspberryPi
– 4B’s (RPi’s) mounted immediately outside the vacuum jacket capture images
from each camera at 100 frames-per-second, storing images in a ring buffer.
The RPi also runs a simple motion detect algorithm, generating a bubble
chamber trigger if a minimum number of pixels fluctuate by more than a set
threshold between successive images. When the bubble chamber trigger (which
may or may not originate from the RPi) is received, the RPi takes a set number
of post-trigger images and writes the images in the ring buffer to disk,
typically capturing the $\sim$100 ms before and after bubble nucleation.

Tests with the Arducam OV9281 have shown it to be vacuum compatible but not
compatible with cryogenic temperatures, making it necessary to separate the
OV9281 sensor from the camera optics. This is accomplished with a fused silica
relay lens system, shown in the left of Fig. 9. This system also serves to
distance the camera sensor from the target volume, relaxing radiopurity
constraints on the sensor in the SNOLAB chamber. Tests are underway to verify
that the relay lens systems maintains focus through thermal cycling of the
chamber.

Figure 9: Left: Relay lens test stand, transferring an image 17 cm from the
objective fisheye lens (1.65-mm focal length) at the left end of the relay to
the OV9281 sensor at the right. Right: Sample zoomed-in images taken using the
OV9281 Arducam with the objective lens mounted directly to the sensor (above)
and transferred by the relay lens (below).

Illumination for bubble images is provided by three rings of 850-nm LEDs
immediately inside the pressure vessel, providing a front-lit view of the
PTFE-lined inner assembly. The LEDs are pulsed in sync with the camera
exposures (which are also synced between cameras), with a typical 10% duty
cycle to allow scintillation detection during the 90% of the time with the
chamber is dark. A custom LED driver ensures stable illumination with sharp
rise- and fall-times in the LED current.

Both the camera illumination and scintillation detection system (see next
section) have been tested in a cryogenic CF4 pressure test cell. Both
components function at the required temperatures and pressures, but the tests
revealed a significant level of fluorescence in the cell, with an elevated
single-photon detection rate lasting many seconds after each illumination
flash. If the same fluorescent behavior is seen in SBC-LAr10, it is possible
to operate the imaging system with illumination active only _after_ the bubble
chamber trigger is received, sacrificing the video trigger in favor of a
darker chamber for scintillation detection while preserving the post-trigger
images necessary for event reconstruction.

####  3.3.3 Scintillation Detection

Vacuum ultra-violet scintillation photons are detected by silicon photo-
multipliers (SiPMs) immediately outside the target volume (_i.e._ immersed in
the cryogenic hydraulic fluid). The copper mounts for the SiPMs are shown in
the right of Fig. 7. Because the 128-nm argon scintillation light is absorbed
by the fused silica walls of the inner assembly, the argon target is doped
with $\mathcal{O}$(10) ppm xenon, shifting the scintillation wavelength to
175-nm [96, 97, 98, 99, 100, 101] where both the fused silica and CF4
hydraulic fluid have long absorption lengths. All surfaces visible to the
target volume except for the SiPMs, camera viewports, and annular region
between vessels are covered with reflective PTFE, giving an estimated light
collection efficiency of $\sim$10% (dependent on the reflectivity of PTFE in
liquid CF4 and on the CF4 absorption length, neither of which is yet well
measured), which combined with the 20–25% quantum efficiency of the VUV SiPMs
achieves the target 2% photon detection efficiency.

SBC-LAr10 at Fermilab uses Hamamatsu VUV4 SiPMs. Gamma screening of these
sensors reveals them to be far too high in U/Th content for a dark matter
search, given their location immediately outside the target volume, so SBC has
joined nEXO in procuring low-background SiPMs from FBK for the SNOLAB SBC-
LAr10 clone. In both cases, the SiPMs are powered by custom bias boards
designed and produced at TRIUMF. This package also provides amplification of
the SiPM signals, which are then passed to a CAEN 62.5-MS/s multichannel
digitizer. The CAEN is configured to self-trigger when any input channel
exceeds a set threshold (with $>$95% efficiency for triggering on single
photons, see Fig. 10), recording thousands of $\sim$1-$\upmu$s waveforms over
the course of an event. Both the individual waveform triggers and the bubble
chamber trigger are timestamped by the CAEN, allowing for later
synchronization with other data streams.

Figure 10 shows the signal-to-noise observed from a Hamamatsu VUV4 SiPM
immersed in a pressurized, cryogenic CF4 test cell, using the full SiPM
electronics chain. These tests also indicated that liquid CF4 generates
$\mathcal{O}$(100) optical-wavelength scintillation photons per MeV deposited
by external gamma sources, and 16 of the 48 SiPM mounting locations shown in
Fig. 7 are positioned to collect this light, providing an additional
scintillation veto for external backgrounds. CF4 scintillation has been
previously studied in gaseous CF4 [102, 103], but this is to our knowledge the
first use of scintillation from liquid CF4. A publication on liquid CF4
scintillation is in progress.

Figure 10: Left: Three simultaneous traces from separate SiPMs in a Hamamatsu
VUV4 Quad package, operating inside a pressurized, cryogenic liquid CF4 test
cell. One SiPM trace shows a single photon (or single pixel avalanche). Right:
Histogram of LED calibration data showing both the clear separation between
the noise and single-photon peaks as well as the CAEN’s ability to efficiently
self-trigger on single photons. Separation between discrete photon peaks is
clear in larger signals as well, persisting up to at least 10 photons.

####  3.3.4 Acoustic Detection

In previous low-background bubble chambers, analyzing the acoustic information
from each event has been vital to the discrimination of events generated by
nuclear recoils from those generated by alphas [29]. This role has largely
been supplanted with the addition of information from the scintillation, with
acoustic data now used primarily to determine the precise time of bubble
nucleation, with 25-$\upmu$s accuracy demonstrated in the xenon prototype
[73]. The shockwave produced by the growing bubble and subsequent
$\mathcal{O}$(10)-kHz ringing of the detector is sensed by a set of textured
lead zirconate titanate (PZT) piezoelectric elements mounted in the HDPE
castle and spring-loaded against the outer fused silica vessel (see right of
Fig. 7). These signals are then passed through a pre-amplifier (both cold and
warm preamp options are being prepared, mounted inside and outside the vacuum
jacket, respectively) and digitized at 1.25 MS/s over a window extending
$\sim$100 ms before and after the bubble chamber trigger. A thorough
discussion of these sensors, both in terms of constituents and use, can be
found in [81].

###  3.4 Offline Analysis

Interpretation of the raw data occurs in multiple modules, with the
information from each module stitched together to form the full event. These
modules define basic data quality cuts to catch excursions in pressure and
temperature control, identify bubbles in camera images, reconstruct the 3-D
position of each bubble, determine the time of nucleation from acoustic
information, and identify any scintillation signal coincident with bubble
nucleation. All scintillation signals, whether coincident with a bubble or
not, are analyzed to build the background LAr scintillation and CF4 veto
spectra.

The 2-D bubble positions in each image can be determined by identifying
clusters pixels with significant frame-to-frame variation [81]. Each 2-D
bubble position corresponds to a ray through the bubble chamber, and from
multiple images the point of closest approach of multiple rays can be
identified, giving both the 3-D bubble position and a goodness-of-fit
(distance of closest approach).

A template fit to a spectrogram of the acoustic signal from each acoustic
sensor gives the time the bubble shockwave reaches each sensor. A spread of
$\sim$100-$\upmu$s is expected due to the speed of sound in the target fluid
and silica vessel walls, varying with bubble position. The position dependence
of the acoustic lag will be calibrated using bubbles with unambiguous
coincident scintillation pulses (giving the true time of nucleation),
generating a position-corrected, acoustically-reconstructed time of nucleation
with a target precision of $\pm$25 $\upmu$s.

Once the bubble position and time of nucleation are determined, coincident
scintillation in the target or hydraulic fluid can be identified. For a dark
matter search with an energy region-of-interest of 0.1 keV to 10 keV, signal
events are not expected to create scintillation light, and an event can be
rejected as a dark matter candidate when coincident with any scintillation
signal. Conversely, events with expected associated scintillation, either from
a high energy recoil or coincident gamma ray emission, can be tagged by the
scintillation signal — this can be useful for the calibration studies
described in the following section.

##  4 Calibration Strategy for SBC-LAr10

The immediate objective of the SBC-LAr10 chamber is the determination of
background rejection as a function of the nuclear recoil bubble nucleation
threshold in superheated LAr. This calibration will be entirely data-driven,
with no input from the thermodynamic model described in Section 2.

###  4.1 Electron Recoil Discrimination Calibrations

The SBC calibration strategy begins by identifying the target operating
condition (pressure and temperature) of the chamber by observing the onset of
bubble nucleation by electron recoils, determined by exposing the chamber to a
strong (mCi) gamma source. External gamma sources will also be used to
calibrate the scintillation light yield in both the target LAr volume and in
the outer LCF4. These light yields do not play a major role in the nuclear
recoil calibrations below, as most sub-keV nuclear recoils will have no
detected scintillation light — but they are of key interest to the background
characterization and mitigation strategy for later rare event searches.

###  4.2 Nuclear Recoil Sensitivity Calibrations

The approach to nuclear recoil calibration in SBC differs significantly from
other sub-keV nuclear recoil experiments. Because the nuclear recoil region of
interest for low mass dark matter ($\sim$100 eV–1 keV) is below SBC’s
scintillation detection threshold ($\sim$5 keV per photon detected), the
chamber is effectively a threshold detector and calibrations must rely on
integrated recoil energy spectra. Furthermore, because the total nuclear
recoil detection rate in the chamber is limited to $\mathcal{O}(10^{3})$
events per day, high-energy neutron scattering experiments where much of the
rate is far above threshold (including most tagged scattering experiments),
are effectively unfeasible. These difficulties are offset by the extreme
insensitivity of the device to electron recoils, making sources with high
rates of ER background, including photo-neutron sources [89, 104], high-energy
gamma sources for Thomson scattering [91], and thermal neutron capture viable
options to generate low-energy nuclear recoils [105, 106]. Each of these
calibration techniques will be utilized as described below.

####  4.2.1 Photoneutron sources

Once the gamma calibration program has identified the target operating
temperature and pressure, the chamber will be exposed to a sequence of three
photoneutron sources, each producing a different mono-energetic neutron,
leading to different recoil energy spectra in the detector, as simulated in
Fig. 11. The different sources also lead to different bubble multiplicity in
the detector, easily resolved with stereoscopic imaging. The ability to
measure bubble multiplicity in the chamber is crucial, as (1) ratios of rates
at different multiplicities are insensitive to uncertainties on source
strength, and (2) events with different bubble multiplicities sample different
portions of the nuclear recoil spectrum, with lower recoil energies probed in
high-multiplicity events. This calibration strategy was used successfully at
few-keV thresholds by the PICO collaboration [29, 72], and can be extended to
$\sim$1-keV threshold with the photon-neutron source choices shown in Fig. 11.

Figure 11: Simulated nuclear recoil spectra in the SBC-LAr10 chamber for
photoneutron scattering (left), high energy photon-nucleus Thomson scattering
(center), and thermal neutron capture (right). The capture nuclear recoil
spectrum for natural argon is taken from [106].

####  4.2.2 Photon-nucleus scattering

A second nuclear recoil calibration technique, also taking advantage of the
bubble chamber’s insensitivity to electron recoils, is to look for photon-
nucleus Thomson scattering by high-energy gamma rays. For example, the 2.6-MeV
gamma from 208Tl (228Th decay product) will produce argon recoils up to 370
eV. These sources do not generate multi-bubble events, but they do produce
much sharper low-energy spectral features than the photoneutron sources (see
Fig. 11).

####  4.2.3 Thermal neutron capture

Thermal neutron capture on 40Ar results in a 6.1-MeV gamma cascade with most
of the energy typically released in a 4.7-MeV gamma ray [105, 107], producing
a 41Ar recoil spectrum peaked at $\sim$320 eV. Thermal neutron capture on 36Ar
is also significant despite its low abundance, giving a nearly mono-energetic
1.1-keV 37Ar recoil (see Fig. 11). Neutron capture events may be tagged via
the scintillation signal from the gamma cascade, which for 41Ar typically
includes a characteristic 167-keV gamma from the end of the cascade.

####  4.2.4 Analysis techniques to constrain bubble nucleation efficiency

Each of the measurements described above can be used to constrain the nuclear
recoil nucleation efficiency curve, or the probability of bubble nucleation as
a function of recoil energy at a fixed thermodynamic condition (see _e.g._ the
right-side of Fig. 4). SBC and PICO collaborators have together developed a
Markov-Chain Monte-Carlo-based method to combine constraints from diverse
calibration sources with appropriate handling of systematic uncertainties
[72], mitigating the different systematic uncertainties associated with each
measurement. SBC will use this method to achieve 20% energy resolution on the
nuclear recoil bubble nucleation threshold in SBC-LAr10, sufficient to
determine the dark matter reach for the LAr bubble chamber technology.

###  4.3 Extended calibration program

As the first attempt at an ER-blind, sub-keV-threshold bubble chamber, it is
entirely possible that SBC-LAr10 will not initially achieve the desired ER
discrimination at low threshold. In this eventuality, there are at least four
pathways to follow, using the same SBC-LAr10 hardware, to improve low-
threshold discrimination: (1) Operation without (or with reduced) xenon
doping, eliminating potential Auger-cascade backgrounds described in [70, 108,
71]; (2) Operation with pure LXe, potentially reducing prompt local heating
associated with dimer formation along the electron track; (3) Operation with
an applied $\mathcal{O}$(100)-V/cm electric field, reducing heating associated
with electron-ion recombination; (4) Operation at reduced pressure and
temperature, shown in [70] to reduce ER sensitivity at constant Seitz
threshold.

On the other hand, if low-thresholds are immediately realized, extended
calibrations will aim to achieve the 5% threshold uncertainty needed for
precision CE$\nu$NS physics, as described in [51]. Precision calibration will
be enabled by a set of photon-nucleus Thomson scattering sources with recoil
endpoints near the operating threshold [109]. Long term calibration plans with
SBC-LAr10 will also include operation and threshold characterization in pure
xenon as well as with N2 and CF4 targets, which can also be deployed in SBC-
LAr10 and which, while molecular, are simple molecules with high-energy bonds
and do produce scintillation light, indicating that low-threshold
discrimination may be achievable in those fluids as well.

##  5 Next Steps and Long Term Opportunities

The future of SBC’s liquid-noble bubble chamber program depends critically on
the results of the work described in Sections 3 and 4, and specifically on the
achievable ER-blind NR detection threshold. This section describes the steps
to be taken after SBC-LAr10, assuming the 100-eV threshold motivated in
Section 2 is achieved, in order to fulfill the science goals described in
Section 1, as well as longer term opportunities that may become available as
the liquid-noble bubble chamber technology matures.

###  5.1 Dark Matter Next Step: Solar CE$\nu$NS Floor at 1 GeV

As shown in Fig. 1, a 100-eV argon nuclear recoil detection threshold in a
chamber that can discriminate electron recoils puts the solar CE$\nu$NS floor
squarely in reach for an SBC device of similar scale to the PICO-500 detector,
which will operate at SNOLAB concurrently with the radiopure SBC-LAr10 [19].
As in every dark matter experiment, however, increases in exposure bring
increased demands on background mitigation techniques, in this case for the
bubble-nucleating backgrounds discussed in Section 2.4. The primary strategy
to suppress these backgrounds will be increased SiPM coverage coupled with
additional scintillating material outside the superheated target, decreasing
veto thresholds and giving additional opportunities to tag external
backgrounds.

###  5.2 Dark Matter Long Term Opportunities

The neutrino fog is largely seen as the end of the road for searches for spin-
independent (SI) dark matter-nucleus interactions. However, by using low-A
targets with large spin-dependent (SD) sensitivity and low SI sensitivity such
as fluorine, nitrogen, and hydrogen, it is possible in principle to explore
orders of magnitude more SD parameter space than is accessible to argon- and
xenon-based experiments [2] with useful exposures up to a kton-year and
beyond. R&D into the technology advances necessary for such a large scale
detector, including new vessel materials [93] and bubble imaging methods,
would be performed in collaboration with PICO, as would any subsequent dark
matter search. The background-rejection power of a scintillating superheated
target such as CF4 or N2 may be a key element to a future deep exploration of
the SD parameter space.

###  5.3 Reactor CE$\nu$NS Next Step: First Detection

The SBC-LAr10 chamber at 100-eV threshold is capable of detecting dozens
(hundreds) of CE$\nu$NS events per day at a typical research (power) reactor
site. The challenge, once the threshold is achieved, is to locate a site with
sufficient overburden and shielding (or space to build shielding) to suppress
the rate of cosmic- and reactor-induced neutron events to below the CE$\nu$NS
signal rate. SBC collaborators are currently characterizing the neutron
environment at the Instituto Nacional de Investigaciones Nucleares (ININ)
TRIGA Mark III reactor near Mexico City [110], a 1 MWth reactor with a movable
core allowing as little as a 3 m baseline to an exposure room, with 3 m
overburden to shield cosmic rays (see Fig. 12).

Figure 12: Cross section of the ININ TRIGA Mark III 1 MWth reactor. SBC
collaborators are investigating the feasibility of operating an SBC device in
the exposure hall, allowing baselines as short as 3 m from the movable reactor
core. Figure copied from [110].

###  5.4 Reactor CE$\nu$NS Long Term Opportunities

The many possible reactor CE$\nu$NS programs described in Section 1, including
measurements of neutrino interactions, sterile neutrino oscillation searches,
and reactor monitoring, all benefit from the increased CE$\nu$NS rate that
comes with a larger target mass. This is at odds with the inherent rate
limitations in bubble chambers — even a 10-kg chamber requires significant
shielding or overburden to reduce the ambient cosmic-induced bubble rate to
levels below the $\sim$1,000 event/day maximum acquisition rate. These events
are mostly far above the CE$\nu$NS signal energy region of interest, but none-
the-less inhibit the live time of the bubble chamber. This live-time hit can
be avoided by modularizing the detector so that only a portion of the target
mass must be re-pressurized after each event. Many strategies for this
modularization are possible, but all would benefit from a more rugged design
than the fused-silica vessels and sapphire viewports used in monolithic
chambers, leading to similar underlying R&D challenges to those in kton-scale
dark matter detection: namely, identifying viable alternatives to silica
vessels and optical bubble reconstruction.

##  6 Acknowledgements

This document was prepared by the Scintillating Bubble Chamber (SBC)
collaboration using the resources of the Fermi National Accelerator Laboratory
(Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility.
Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under
Contract No. DE-AC02-07CH11359. The SBC collaboration also wishes to thank
SNOLAB and its staff for support through underground space, logistical and
technical services. SNOLAB operations are supported by the Canada Foundation
for Innovation and the Province of Ontario Ministry of Research and
Innovation, with underground access provided by Vale at the Creighton mine
site. The SBC-LAr10 chamber at Fermilab and its twin at SNOLAB have been
supported primarily by the Fermilab Lab-Directed R&D program and the Canada
Foundation for Innovation (CFI), respectively, with additional support from
the Natural Sciences and Engineering Research Council of Canada (NSERC), the
DOE Office of Science Graduate Instrumentation Research Award fellowship, the
Arthur B. McDonald Canadian Astroparticle Physics Research Institute, the
projects CONACyT CB2017-2018/A1-S-8960, DGAPA UNAM grant PAPIIT IN108020,
Fundación Marcos Moshinsky, the Indiana University South Bend Office of
Research, the URA Visiting Scholar program, the Fermilab Cosmic Physics
Center, and DOE Office of Science grants DE-SC0015910, DE-SC0017815, and DE-
SC0011702.

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