capbtabboxtable[][]

The Q-Pix Collaboration

††thanks: Corresponding author<EMAIL_ADDRESS>Corresponding author<EMAIL_ADDRESS>
# Enhanced low-energy supernova burst detection in large liquid argon time
projection chambers enabled by Q-Pix

S. Kubota  Department of Physics, Harvard University, Cambridge, MA 02138, USA
J. Ho  Department of Physics, Harvard University, Cambridge, MA 02138, USA
A.D. McDonald  Department of Physics, University of Texas at Arlington,
Arlington, TX 76019, USA  Department of Physics, Harvard University,
Cambridge, MA 02138, USA  N. Tata  Department of Physics, Harvard University,
Cambridge, MA 02138, USA  J. Asaadi  Department of Physics, University of
Texas at Arlington, Arlington, TX 76019, USA  R. Guenette  University of
Manchester, Manchester M13 9PL, UK  Department of Physics, Harvard University,
Cambridge, MA 02138, USA  J.B.R. Battat  Physics Department, Wellesley
College, Wellesley, MA 02481, USA  D. Braga  Fermi National Accelerator
Laboratory, Batavia, IL 60510, USA  M. Demarteau  Oak Ridge National
Laboratory, Oak Ridge, TN 37831, USA  Z. Djurcic  Argonne National Laboratory,
Lemont, IL 60439, USA  M. Febbraro  Oak Ridge National Laboratory, Oak Ridge,
TN 37831, USA  E. Gramellini  Fermi National Accelerator Laboratory, Batavia,
IL 60510, USA  S. Kohani  Department of Physics and Astronomy, University of
Hawaii, Honolulu, HI 96822, USA  C. Mauger  Department of Physics and
Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA  Y. Mei
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  F.M. Newcomer
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia,
PA 19104, USA  K. Nishimura  Department of Physics and Astronomy, University
of Hawaii, Honolulu, HI 96822, USA  D. Nygren  Department of Physics,
University of Texas at Arlington, Arlington, TX 76019, USA  R. Van Berg
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia,
PA 19104, USA  G.S. Varner  Department of Physics and Astronomy, University of
Hawaii, Honolulu, HI 96822, USA  K. Woodworth  Fermi National Accelerator
Laboratory, Batavia, IL 60510, USA

###### Abstract

The detection of neutrinos from core-collapse supernovae may reveal important
process features as well as neutrino properties. The detection of supernova
neutrinos is one of the main science drivers for future kiloton-scale neutrino
detectors based on liquid argon. Here we show that for such detectors the
intrinsically 3D readout in Q-Pix offers numerous advantages relative to a
wire-based readout, such as higher reconstruction efficiency, lower energy
threshold, considerably lower data rates, and potential pointing information.

††preprint: APS/123-QED

##  I Introduction

The central role neutrinos play in the fate of massive stars as they reach the
end of their life in a core-collapse supernova (SN) has long been noted in the
field of astrophysics [1]. Observing neutrinos emitted from a supernova
provides new ways to test our understanding of both nuclear and particle
physics at the most extreme densities and energies [2, 3, 4]. A core-
collapsing star is a unique laboratory within which the dynamics of the death
of a star as well as neutrino–neutrino interactions and oscillations may be
observed in a way that cannot be reproduced with a terrestrial experiment.

In the emergent era of multi-messenger astronomy, technological advancements
in neutrino detection are needed to allow a detailed, high-statistics
description of the neutrino burst from a supernova collapse. Thus far, the
direct detection of neutrinos from SN 1987A by three underground experiments
[5, 6, 2] confirmed some aspects of supernova astrophysics and provided
insight into how the detection of neutrinos from supernovae could lead to a
deeper understanding of fundamental neutrino physics.

The dense surroundings of a supernova is the only environment in the universe
where neutrino flavor oscillations can be enhanced by the entirety of neutrino
interaction phenomenon [7] (e.g., multiple neutrino species and energies
impacted by the Mikheyev–Smirnov–Wolfenstein effect, neutrino–neutrino
interactions, and vacuum oscillations) as the neutrinos propagate through the
multiple layers of stellar materials of wildly varying densities and types of
interactions on their way to interstellar space [3]. Through observations of
the energy and timing profiles of those events, fundamental neutrino and
astrophysical parameters could be extracted, such as neutrino mass ordering
[8], neutrino halo model characteristics [9], and the neutrino magnetic moment
[10]. The $\mathcal{O}(10)$ events that were experimentally observed from SN
1987A have already provided crucial information, but future core-collapse
supernovae, plausibly anticipated within the next few decades, may provide
even greater detail. For these reasons, next-generation neutrino experiments
must be prepared to accurately measure the energy, timing structure, and
flavor of the neutrino spectrum [11, 12, 13, 14, 15].

Large-scale noble element time projection chambers (TPCs) [16] play a central
role in many aspects of high-energy physics, both currently running and
planned in the near future. Charged particles traversing the bulk material
produce ionization electrons and scintillation photons. An imposed electric
field forces the ionization electrons to drift toward the detector anode where
they are collected on charge-sensitive readout. The combined measurement of
the scintillation light, providing the $t_{0}$, with the arrival time of the
ionization charge, allows for the 3D reconstruction of the original charged
particle topology. Thus, the TPC provides a fully active and uniform tracking
detector with calorimetric reconstruction capabilities without instrumenting
the bulk volume of the detector.

The capability to drift electrons over many meters has made the use of large-
scale liquid noble TPCs attractive as neutrino detectors to study neutrino
oscillations over relatively short ($<$1 km) [17] and long baselines ($>$1000
km) [18]. Specifically, liquid argon time projection chambers (LArTPCs) [19,
20] offer fine-grained tracking as well as powerful calorimetry and particle
identification capabilities. This makes LArTPCs ideal detectors for studying
neutrino–nucleus and neutrino–electron interactions as well as neutrino
oscillation phenomena. A review of the recent experimental applications of
LArTPCs is given in Ref. [21].

A conventional method for reading out the ionization charge in a LArTPC relies
on the use of consecutive planes of sensing wires to measure two of the three
spatial coordinates using the 2D projections to reconstruct the 3D image. This
method was used for ICARUS [22] and MicroBooNE [23], as well as many other
recent experiments [24, 25, 26]. This configuration was also adopted as a
baseline configuration for the Deep Underground Neutrino Experiment (DUNE) far
detector [18]. Although the concept is proven and has gained considerable
support in the community, it has an intrinsic limitation in resolving
ambiguities in dense, complex topology reconstruction making the event
reconstruction difficult in some cases. Novel event reconstruction techniques
may be employed to overcome these difficulties [27, 28, 29, 30, 31], however,
reconstruction using 3D-based pixel readouts can offer significant
improvements [32]. Moreover, the long sense wires used in large-scale LArTPCs
introduce significant capacitance to the readout electronics [33] which may
limit the extraction of physics signals at low-energy thresholds [e.g.,
$\mathcal{O}(\leq$MeV)] [34]. These detectors also produce large volumes of
raw data as every wire is read out continuously [$\mathcal{O}($ms)]. Finally,
the construction and mounting of massive anode plane assemblies to host the
wires pose difficult engineering challenges and can be quite expensive. For
these reasons, a native 3D, fully-independent pixel readout could provide
advantages.

A pixel-based readout scheme has been utilized in small-scale gas TPCs [35]
but had not been previously considered for very large LArTPCs because of the
much larger number of readout channels, and the high data rate and power
consumption. A transformative step forward for future LArTPCs would be the
ability to build a fully pixelated low-power charge readout capable of
efficiently and accurately capturing signal information. The potential for
scientific gain through the realization of a low-power, pixel-based charge
readout for use in LArTPCs has independently inspired two research groups to
pursue complimentary approaches to solving this problem. The LArPix [36] and
Q-Pix [37] consortia have undertaken the needed R&D to realize such a readout.

The Q-Pix solution, discussed in more detail in Section II and in Ref. [37],
targets the daunting requirements established for the DUNE far detectors [38].
These detectors must be capable of high efficiency
${\nu}_{\mu}/\bar{\nu}_{\mu}$ and ${\nu}_{e}/\bar{\nu}_{e}$ discrimination and
precise energy reconstruction to provide a definitive measurement of the
$CP$-phase and to identify the neutrino mass hierarchy. Additionally, these
detectors must be capable of detecting low-energy neutrinos originating from
supernovae bursts and have the ability to detect the signature of baryon
number violation (via proton decay or neutron/anti-neutron oscillations) [39].
These far detector modules will only record $\sim$4 beam events/day/10 kton
module with mean neutrino energies $\mathcal{O}$(GeV) while having to be
simultaneously sensitive to much rarer and significantly lower energy events
(such as those that come from a supernova burst) which will give
$\mathcal{O}(100\textrm{-}1000)$ events (depending on the distance of the
supernova) in a short time window [$<$$\mathcal{O}(10)$ seconds]. A
description and first study of supernova burst signals in the DUNE far
detector are provided in Ref. [13].

In this paper we further elaborate low-energy reconstruction in the Q-Pix
scenario for supernova events. Section II provides an overview of the Q-Pix
architecture. Section III describes the simulation tools used to model the
supernova neutrino interactions, the simulation of the detector and of the
radiogenic backgrounds, and the simulation of the Q-Pix readout. Finally,
Section IV presents the results focusing on Q-Pix’s ability to reconstruct
low-energy ($<$5 MeV) events with high efficiency and purity in the presence
of radiogenic backgrounds, the trigger efficiency from a “charge-only”
readout, the data rates expected from a Q-Pix module, and finally the ability
to do directional pointing using supernova neutrino events reconstructed in
the simulation.

Figure 1: Representation of the charge integrator/reset circuit where a free-
running oscillator increments a Gray-code counter in order to create a local
clock. A $reset$ signal causes the local clock to be stored in a buffer
register. The data is a string of clock snapshots, from which a Reset Time
Difference (RTD) can be calculated.

Figure 2: Charge integration simulation results for two different pixels near
the vertex of a simulated neutrino interaction. The current arriving at the
pixel is shown in blue; the corresponding resets are shown in orange and the
reconstructed current from the Reset Time Differences (RTDs) is shown in
green. Signal waveforms can be reconstructed from RTDs since $I\propto
1/\mathrm{RTD}$ where $I$ is the average current over an interval $\Delta T$
and thus $I\cdot\Delta T=\int I(t)\,\mathrm{d}t=\Delta Q$. The $\Delta Q$ for
the charge-integration/reset is fixed and was chosen to be 1 fC.

##  II Overview of the Q-Pix readout

The fundamental idea of the Q-Pix readout scheme is to use pixel-scale self-
triggering ‘charge integrate/reset’ blocks with free-running clocks and
dynamically established data networks robust against single-point failure
(SPF) [37]. This pixelization concept is targeted as a ‘technology of
opportunity’ for a multi-kiloton DUNE far detector (FD). In the DUNE FD, high-
precision data across all spatial and energy ranges is desired for signal
events, but most of the time, nothing of interest is occurring in the detector
and the data acquisition scheme should be idle until something happens. The
ethos of “do not do anything unless there is something to do” can be thought
of as an electronic principal of least action and is a design philosophy at
the heart of the Q-Pix architecture. This design idea provides a solution to
the needed low-power architecture to operate in a single-phase (SP) LArTPC as
well as simultaneously solving the large data rates which come with a high-
granularity readout.

The basic concepts of the Q-Pix circuit is shown in Fig. 1. The input pixel,
labeled as “In,” is envisioned to be a simple circular trace connected to the
Q-Pix circuit by a via in a printed circuit board. The circuit begins with the
Charge-Integrate/Reset (CIR) circuit. This charge sensitive amplifier
continuously integrates incoming signals on a feedback capacitor until a
threshold on a Schmitt trigger (regenerative comparator) is met. When this
threshold is met, the Schmitt trigger starts a rapid “reset” which drains the
feedback capacitor and returns the circuit to a stable baseline and the cycle
is free to begin again. This “reset” transition pulse is used to capture and
store the present time of a local clock within one ASIC (application-specific
integrated circuit). This changes the basic quantum of information for each
pixel from the traditional “charge per unit of time” data format to the
difference between one clock capture and the next sequential capture, referred
to as the Reset Time Difference (RTD). This new unit of information measures
the time to integrate a pre-defined charge ($\Delta Q$). Physics signals will
produce a sequence of short [$\mathcal{O}(\mu s)$] RTDs. In the absence of a
signal, the quiescent input current from backgrounds (^39Ar, cosmogenic, and
other radioactivity) would be small and the expected RTDs are on the order of
seconds.

Signal waveforms can be reconstructed from RTDs by exploiting the fact that
the average input current and the RTD are inversely correlated ($I\propto
1/\mathrm{RTD}$), where $I$ is the average current over an interval $\Delta T$
and thus $I\cdot\Delta T=\int I(t)\,\mathrm{d}t=\Delta Q$. The signal current
is captured with fixed $\Delta Q$, determined by the charge integrator/reset
circuit, but with varying time intervals. An initial study of the requirements
for the minimum $\Delta Q$ for the Q-Pix circuit ($\sim$6000 electrons) as
well as the range and precision of $\Delta T$ has been carried out using
simulated signals from neutrino interactions fed into a full simulation of the
Q-Pix circuit in the TSMC 180 nm process design kit (PDK), however, the
ultimate limit of how low in threshold this technology can achieve is yet to
be determined and is the focus of an upcoming prototype and subsequent paper.
For the purposes of this paper, we have assumed conservative and realizable
benchmarks for both the minimum $\Delta Q$ and precision of $\Delta T$,
summarized in Section III.3. Fig. 2 shows two examples of the conversion from
RTDs back to arbitrary charge input of a particular $\Delta Q$ of one
femtocoulomb (6250 electrons, or equivalently, 147.5 keV in LAr).

The time-stamping architecture currently envisioned for the Q-Pix readout will
utilize a technique first pioneered by the IceCube Neutrino Observatory [40]
and shown to work with high reliability and precision. A local clock based on
a free-running oscillator within the ASIC is used and its value captured in a
buffer register when a “reset” transition occurs. The string of “reset” times
are transmitted periodically out of the cryostat and a linear transformation
from local clock frequency to central master clock allows one to recover the
universal time RTDs. The interrogation of the local clock by surface systems
need only occur as necessary to monitor and correct for oscillator drift. For
nominal electron drift speeds in liquid argon of 1.6 mm/$\mu$s, a global
timing accuracy of $\pm 1~{}{\mu}s$ corresponding to $\sim$1.6 mm in the drift
direction can be easily obtained.

While the Q-Pix ASIC chip itself represents the smallest unit for the system,
a more useful architecture which is resilient against single-point failure is
to define a tile as an array of $N\times N$ Q-Pix ASIC chips. As an
illustrative example, if each Q-Pix ASIC chip, shown as black squares in the
lower left of Fig. 3, were to serve 16 pixels (in a matrix of ${4\times 4}$
pixels), then this would constitute an array of a ${64\times 64=4096}$ pixel
block per tile, as the fundamental unit of the system. The number of Q-Pix
ASICs, $N^{2}$, per tile and exact dimensions of the tile will be determined
by the pixel pitch and number of channels per ASIC. These quantities
themselves need to be studied to ensure the maximum physics reach for the
given readout design, but will likely result in a tile size $\mathcal{O}(625$
cm2) with pixel pitch of 4 $\times$ 4 mm2. These are the dimensions used in
the study presented here.

The design of the tile and the network between the “$N^{2}$” ASICs will be
built following the design principle to make it intrinsically fault-tolerant
and robust to as many possible failure modes. Each ASIC on the tile will have
signal sensing, self-triggering, local clock, time-stamping, buffering,
input/output, and state machine capabilities. Local time capture and data
transfer could occur along any of the corner ASICs, offering a robust system
design protective against SPF. The layout of the architecture suggests that 8
bits will be required to specify the ASIC position within the tile. 16 bits
are needed to specify which individual pixel initiated the reset. For a clock
running at 50 MHz, a 32-bit timestamp gives 43 seconds before wrap-around
would occur (deemed more than sufficient for LArTPC operation) and leaves 8
bits yet unspecified to be used for other purposes. Preliminary studies
suggest the power consumption of such a readout is quite low ($\sim$50
$\mu$W/channel). The quiescent data rate for a kiloton scale detector would
also be low as discussed further in Section IV.3.

Figure 3: A conceptual representation of what a 10-kton DUNE far detector
module using the Q-Pix tile readout. The top left figure shows a cutaway of
the cryostat (in red) with a single TPC. The top right shows the dimensions of
a TPC with the cathode in the center and the anode plane assemblies (APAs)
with the Q-Pix tiles held in place. The tile boards can be housed in a frame
similar to that used for the high voltage cathode and deployed in the existing
design for the DUNE cryostat with minimal modifications. The lower left figure
shows a conceptual drawing of the Q-Pix tile with each black square
representing a single ASIC. The lower right shows a zoomed-in view of a single
APA with tiles mounted.

The envisioned 10-kton module, which would serve as home to the Q-Pix readout,
is similar by design to the “conventional” DUNE horizontal drift [38] targeted
as the first module and is illustrated in Fig. 3. The idea is to simply
substitute the existing anode plane assembly (APA) which houses the wire-based
projective readout with a slightly modified cathode plane assembly (CPA)
capable of hosting Q-Pix tiles. The most significant change is the central-
most APAs which in the conventional DUNE design serve two drift regions
simultaneously via a wrapped wire design. Instead, these central APAs will
have a pair of “back-to-back” pixel planes oriented such that each drift
region is independent. Thus the total number of APA drift regions for a
10-kton Q-Pix design will be 200 (instead of the 150 wire-based APAs).

However, it may very well turn out that a doubling of drift length is
feasible, given technical advances in LAr purification. Drift lengths of 6.5
meters are already envisaged for the recently proposed vertical drift approach
[41]. In this case, the central plane would be a single cathode plane, and the
number of Q-Pix tiles and modified CPA assemblies would be reduced by a factor
of two, with concomitant savings in cost and system complexity.

For the analysis presented in this study, no photon detection is used and all
the analysis is done using the collected ionization charge. The exact photon
detection scheme to be used for such a multi-kiloton pixel-based readout is an
area of active ongoing R&D and thus is omitted from further discussion.
Instead, only where noted, we assume that whatever photon system which is
ultimately used will be able to provide $t_{0}$ for the events of interest.

##  III Low-Energy Physics Simulation

One area of particular interest to the multi-kiloton scale liquid argon
experiments is the physics which can be enabled through exploration of low-
energy ($<$100 MeV) phenomena [42, 43]. Measurements of MeV-scale activity
from accelerator neutrino interactions [44], radiogenic backgrounds [45, 46],
and Michel electrons [47, 48, 34] have already been performed by the ArgoNeuT,
LArIAT, MicroBooNE, and ICARUS experiments. Low-energy LArTPC signatures from
a variety of possible sources have been investigated and described in
literature, including those from solar neutrinos [49, 50], accelerator
neutrinos [51, 42], hidden sector [52, 53] particle and WIMP [54]
interactions, neutrinoless double beta decay [55], and supernova neutrinos
[13, 42], which will be the physics focus of this study. In this section we
present the simulation framework used to quantify the increased physics reach
of a DUNE LArTPC with Q-Pix readout relative to an APA readout.

Section III.1 provides an overview of the event generator and the supernova
neutrino model utilized in this analysis. Section III.2 presents the
radiogenic backgrounds in the detector and the techniques utilized to
integrate them into the simulation. Section III.3 provides details on the
architecture of the Q-Pix readout simulation that was implemented.

###  III.1 Supernova Neutrinos

Our simulation of supernova neutrino events is based on supernova luminosity,
energy, and time distributions provided by the “Garching” electron-capture
supernova model [56] as propagated through SNOwGLoBES [57] to provide event
rates per 10-kton LAr module. This approach is similar to that of Ref. [13].
This benchmark model was chosen as a pessimistic case as it predicts the
fewest number of neutrino interactions per 10-kton detector. As has been done
in other works [58, 59, 60, 61], we assume a supernova distance of 10
kiloparsecs (kpc) which predicts 220 charged-current (CC) electron neutrino
($\nu_{e}$) and 19 electron neutrino–electron (${\nu_{e}\text{--}e^{-}}$)
elastic scattering (ES) interactions within a 10-kton module (Table 4). The
energy and timing profiles of the simulated supernova neutrinos are shown in
Fig. 4 and serve as inputs into our simulation.

For the simulation of the supernova neutrino–nucleus interactions, the MARLEY
(Model of Argon Reaction Low Energy Yields) event generator [62, 63] is used.
The latest version of MARLEY (v1.2.0) utilized in this study includes both
$\nu_{e}$ CC and ${\nu_{e}\text{--}e^{-}}$ ES events. Thus the primary
channels analyzed in this analysis are

$\displaystyle\nu_{e}+\ce{{}^{40}Ar}$ $\displaystyle\rightarrow
e^{-}+\ce{{}^{40}K^{*}}$ ($\nu_{e}$ CC) $\displaystyle\nu_{e}+e^{-}$
$\displaystyle\rightarrow\nu_{e}+e^{-}$ (${\nu_{e}\text{--}e^{-}}$ ES)

where MARLEY handles the subsequent nuclear de-excitation and produces a list
of final-state observable particles. The electron anti-neutrinos
($\bar{\nu}_{e}$) and neutral-current interactions of any neutrino flavors
(${\nu_{X}+\ce{Ar}\rightarrow\nu_{X}+\ce{Ar}^{*}}$) are not taken into account
in this analysis.

Figure 4: Top: the supernova $\nu_{e}$ energy spectrum of the “Garching”
electron-capture supernova model used as an input to the MARLEY event
generator. Middle: the supernova $\nu_{e}$ timing profile indicated with
different eras in the supernova evolution. Bottom: the time-dependent
$\nu_{e}$ flux of the supernova separated into different eras in the supernova
evolution. Adapted from Ref. [13].

Isotope | Rate [Bq/kg] | Region | Region mass [kg] | Rate [Bq] |  Number of decays (per 10 s window)
---|---|---|---|---|---
^210Po | 0.2 | PD [Bq/m2] | 2.46856 | 0.493712 | 5
^60Co | 0.0455 | CPA | 90 | 4.095 | 41
^40K | 0.49 | APA | 258 | 1,264.2 | 12,642
^39Ar | 1.010 | bulk LAr |  $\sim$70,000 | 70,700 | 707,000
^42Ar | 0.000092 | bulk LAr |  $\sim$70,000 | 6.44 | 64
^42K | 0.000092 | bulk LAr |  $\sim$70,000 | 6.44 | 64
^222Rn | 0.04 | bulk LAr |  $\sim$70,000 | 2,800 | 28,000
^214Pb | 0.01 | bulk LAr |  $\sim$70,000 | 700 | 7,000
^214Bi | 0.01 | bulk LAr |  $\sim$70,000 | 700 | 7,000
^85Kr | 0.115 | bulk LAr |  $\sim$70,000 | 8,050 | 80,500

Table 1: Summary of the radiogenic backgrounds, adapted from Ref. [64],
outlining the particular radioactive isotope, the region the isotope
originates from, the estimated decay rate for the isotope, and the expected
number of decays in a 10-second simulation window.

###  III.2 Backgrounds

An important part of the analysis of supernova burst detection capabilities is
the inclusion of background events from radiogenic sources within the detector
and the bulk argon. A previous analysis did not include these backgrounds [13]
since their selected signals required a minimum of 5 MeV of deposited energy
within the argon [65, 13] and thus would exclude the majority of the
radiogenic backgrounds. To explore the capabilities of detection at lower
energies, it is critical to include an estimate of these backgrounds. An
initial estimate of the expected radiogenic isotopes and their expected
activity levels was taken from Ref. [64] with exact dimensions of the
structures described in the detector taken from Ref. [38]. This information is
summarized in Table 1.

The typical timing profile of the neutrinos from a supernova burst spans
$\sim$10 seconds and thus the radiogenic backgrounds are calculated over a
full 10-second window. To appropriately handle the backgrounds and their
associated rates, the decays associated with the radiogenic backgrounds are
simulated as a single “event” over a 10-second window. Thus the single “event”
contains $\sim$842,000 primary radioactive decays and are randomly distributed
uniformly in time over that 10-second window. The radioactive isotopes are in
equilibrium at time $t=0$ seconds to account for previous decays that could
have occurred prior to the start of the readout.

To realistically model the background events, the radioactive decays are
simulated from the location of the material which produces them (see Table 1
for the detailed locations). For example, the isotopes that decay in the LAr
are placed uniformly and randomly in the liquid at the appropriate rate. When
the source of the background is listed as coming from the anode-plane assembly
or cathode-plane assembly, the background is generated originating from those
planes with the geometry in accordance with the DUNE far detector technical
design report (TDR) [38]. In the case where an isotope decayed to a progeny
that is unstable, the progeny is then allowed to decay with its characteristic
lifetime. This is particularly important in the case of isotopes such as
^214Bi which decay to ^210Po, which itself has a short half-life. As noted in
Section II, the envisioned geometry of a 10-kton Q-Pix module is slightly
modified from the one presented in the DUNE FD TDR, specifically the APA is
reduced in size and mass. However, the results presented here do not include
this modification for simplicity of presentation and comparisons to other
DUNE-related works. While the pixel-based readout does add more mass and
potentially more sources of radiogenic backgrounds via the inclusion of
printed circuit boards (PCBs), the discrimination power afforded by the Q-Pix
readout (shown in Section IV.2) in conjunction with the ability to produce
low-background PCBs [66, 67, 68] provides confidence that this can be
effectively mitigated. Fig. 5 shows the energy and timing spectra of the
signal and backgrounds used in this analysis.

(a)  (b)

Figure 5: Left: stacked histogram of the Geant4 truth-level deposited energy
from $\nu_{e}$ CC signal events (magnified by $\times 10^{3}$) in a typical
supernova (SN) simulation over 10 seconds and from the radiogenic background
events. Note that ionization charge quenching of $\alpha$ particles in LAr is
not taken into account here, so the BiPo and RnPo signatures are higher than
they should be. Right: stacked histogram of the timing profile of Geant4 hits
from simulated SN signal and radiogenic background events.

###  III.3 Q-Pix Simulation

The simulation framework developed for Q-Pix primarily consists of two
C++-based packages: (1) a Geant4-based [69, 70, 71] package for simulating the
interactions and ionization of particles within a liquid argon volume, and (2)
a Q-Pix-specific package for converting Geant4 hits (a Geant4 hit is defined
here to be a segment of a simulated particle’s trajectory and carries
information about its position, timing, and energy deposited) into ionization
electrons that are then propagated to a pixel plane where the pixel response
is simulated. The framework simulates single DUNE-SP APA drift volumes (one
volume consists of a $2.3$ $\times$ $6$ m2 charge collection/readout plane
with a $3.6$ m drift length) which are then analyzed individually. A 10-kton
module’s sensitivity can then be extracted by joining 200 APA drift volumes;
performing the simulation in this manner was required to keep the files
produced to a manageable size.

The Q-Pix-specific “Reset-Time Difference” (RTD) package simulates the
response of the Q-Pix electronics. This is done by first converting the Geant4
hits into ionization electrons with the assumed LAr W-value of 23.6
eV/electron. Next, the simulation accounts for recombination using the
“modified box” model [72], and removes those electrons from consideration. The
electrons that remain are then uniformly distributed between the start and end
of the Geant4 hit. At this point the drift time for each electron is
calculated. This drift time is used to account for a reduction in the arriving
signal due to electron lifetime as well as to smear the position of the
electrons according to the longitudinal and transverse diffusion coefficients.
This process is done for every ionization electron coming from a Geant4 hit in
an event. All the electrons in a hit are sorted by drift time. The electrons
are then subdivided into groups based on their $(x,y)$ position corresponding
to which 4 $\times$ 4 mm2 pixel they will land on. This results in an array of
hit pixels, each containing an array of time-sorted electrons.

Producing the associated Q-Pix resets is then done by integrating the charge
on each pixel with a time step of 10 ns. The time step size is assumed to be
exact for simplicity. This assumption is justified since any 10 ns deviation
would be sub-leading to a measurement of which is microseconds in length. At
each time step, the equivalent noise charge is added to mimic the current ASIC
simulation of the Q-Pix front-end. The leakage current present on the front-
end is a sub-leading noise component. Without a prototype chip produced, the
actual value of the leakage current is unknown. For the purposes of this
study, we assume it to be 100 aA. This number is comparable to the leakage
current measured by the LArPix ASIC [36], which shares similar technology and
geometric considerations to Q-Pix. Finally, in the absence of a prototype to
benchmark, we further assume no charge is lost or perturbed during a reset.
Such an assumption can be realized in the ASIC using a various techniques
under exploration (e.g., charge-pump front-end). Ultimately, the impact of any
charge loss can be calibrated and is thus taken as a safe assumption. When a
pixel collects enough electrons to undergo a reset (e.g., 6250 electrons, or 1
fC), the time and pixel number is logged and the electrons are drained from
the pixel. Performing the simulation in this manner closely resembles the
actual electronics response as well as the data format that is produced. The
pixel ID and reset times are then stored in the same ROOT [73] file as the
Geant4 information. The different parameter values used in the simulations
described above are listed in Table 2. The RTD code can be configured to
produce current profiles, which can be exported and use as inputs to other
simulation software. An example current profile with corresponding reset
stamps can be seen in Fig. 6, which illustrates the same event placed at two
drift distances (e.g., 10 cm and 150 cm). The change in the current profile,
and thus the subsequent number and frequency of the resets, can be seen due to
this change in drift distance.

Finally, we note here that the ionization charge produced from $\alpha$
particles in a liquid noble element medium tends to be relatively small and
more scintillation light is produced [74]. This ionization charge quenching is
not taken into account in the Q-Pix simulation, so the BiPo and RnPo
signatures in the energy spectrum on the left in Fig. 5 are higher than they
should be. The Noble Element Simulation Technique (NEST) [75, 76, 77] software
package, which is capable of modeling the ionization charge quenching in LAr,
will be integrated into the Q-Pix simulation for future work.

Parameter | Value
---|---
W-value for ionization in LAr |  23.6 eV/e-
Drift electric field | 500 V/cm
Drift velocity | 164,800 cm/s
Longitudinal diffusion |  6.8223 cm2/s
Transverse diffusion |  13.1586 cm2/s
Electron lifetime | 0.1 s
Reset threshold |  1 fC (6250 e-, or
147.5 keV in LAr)
Sampling time | 10 ns

Table 2: Summary of the physical parameters used in the Q-Pix simulations.
Figure 6: Examples of the current profiles (black lines) produced with the
Q-Pix simulation package. The corresponding resets can be seen as the vertical
lines and represent a 1 fC reset threshold. Left: current profile of the most
active pixel of a 30 MeV electron event that is located 10 cm away from the
pixel plane and launched perpendicular to the pixel plane. Right: current
profile for the same event with the location of the electron 150 cm away from
the pixel plane. One can see the expected broadening of the input signal due
to the simulated diffusion as well as the reduction in the integrated current.

##  IV Results

In this section, we present the results of the supernova simulation done with
the Q-Pix readout and show how this readout architecture can enhance supernova
burst reconstruction for large-scale LArTPCs. In Section IV.1, we give an
overview of the energy reconstruction and, in particular, the improvement seen
in low-energy events. Section IV.2 provides the algorithm developed to
identify supernova events and distinguish them from background. This
identification is not the same as a trigger efficiency since, as highlighted
in Section IV.3, the amount of data to readout an entire 10-kton module is
remarkably low. Section IV.4 provides details for taking the identified events
and understand what additional criteria needs to be applied to allow for a
large-scale LArTPC using Q-Pix to serve as a trigger to the SuperNova Early
Warning System (SNEWS) [78] and the associated supernova burst trigger
efficiency. Finally, Section IV.5 discusses the use of the intrinsic 3D
information provided by Q-Pix to reconstruct the direction of the supernova
source from an analysis of the neutrinos detected.

###  IV.1 Energy Reconstruction

In order to compare this work to others, an energy reconstruction conversion
factor is derived. The energy is reconstructed from collected charge and
compared to true neutrino energy. In this conversion factor, the reconstructed
energy fraction depends on 3D information of the event, drift, diffusion, and
topology. From this conversion factor, a correction matrix based on the 3D
reconstruction of the charge is generated, similarly to the method used in
Ref. [13]. The correction matrix takes into account the generation, transport,
and detection of ionization signals in energy steps of 0.1 MeV and drift steps
of 50 cm. This was done to get a fine energy sampling at low energy ($<$5 MeV)
and to account for the drift and diffusion of such events throughout the
detection volume. Single electrons were generated isotropically at the various
energies relevant to supernova and drift distances. From this dataset,
parameterizations are computed to produce the correction matrix of the true
energy for a given number of resets observed as a function of drift distance.
In this work, the unspecified Q-Pix photon detection system is assumed to
provide the drift distance with an uncertainty of $\pm 25$ cm. This correction
only applies to this section for comparing to other works by correcting for
drift-dependent attenuation of the deposited energy relative to the true
energy.

Fig. 7 shows the reconstructed energy as a function of the true neutrino
energy simulated with MARLEY with and without the energy corrections. While
the uncorrected energy distribution is linear as a function of true neutrino
energy, there is a clear offset and difference in slope. By the application of
the correction matrix the slope is increased, while an overall offset remains.

Figure 7: Left: the reconstructed energy for supernova events as a function of
true neutrino energy with no energy correction applied. Right: the
reconstructed energy for supernova events as a function of true neutrino
energy after application of the energy correction matrix which takes into
account electron lifetime, diffusion, event topology, and the mapping between
deposited energy and true energy as a function of drift distance.

Fig. 8 shows the event reconstruction efficiency for two different energy
thresholds. The Q-Pix architecture increases the reconstruction efficiency at
lower neutrino energy compared to the results presented for DUNE in Ref. [13].
The efficiency rises to nearly 100% very rapidly and maintains this high
efficiency down to lower neutrino energy. Given the current level of
simulation, it appears that a Q-Pix-based readout can successfully identify
and reconstruct very low energy supernova neutrino interactions, and has a
performance in this task comparable to that exhibited in existing DUNE wire
readout simulation and reconstruction.

Figure 8: Supernova event reconstruction efficiency as a function of true
neutrino energy for different minimum total deposited energy requirements, or
energy thresholds. For comparison, the efficiencies for DUNE from Ref. [13]
are shown in blue triangles for a minimum of 5 MeV deposited and in orange
triangles for a minimum of 1 MeV deposited.

###  IV.2 Event Identification

Figure 9: Top row: event ID efficiency (left) and purity (right) for the full
supernova energy spectrum. The colors represent different reset thresholds.
Bottom row: same as above, but only considering events with less than 5 MeV of
energy in order to optimize the background reduction. Both are plotted as a
function of the cluster time window. Figure 10: Event ID efficiency (black)
and purity (red) as a function of minimum number of resets per cluster for the
3$\mu$s time window. Results are shown for the full energy spectrum (solid
line) and for the low-energy events ($\leq$5 MeV) (dashed line).

Due to the addition of radiogenic backgrounds in this work, it is necessary to
define an identification scheme to separate the radiogenic backgrounds from
the supernova signal events. This is done by taking advantage of the inherent
3D information of the pixelization, as well as the unique timing information
that Q-Pix produces. This allows for a rather simple algorithm that clusters
the resets together to build 3D trajectories (referred to as tracks). By
selecting on the number of resets required to form a 3D track, the radiogenic
backgrounds can be distinguished from the supernova neutrino interactions due
to the track extent and energy.

However, there is an optimization on where to place this selection in time
between resets, number of resets in a track, and how localized these resets
are in space. For spatial localization, a simple assumption is made that only
neighboring 4 $\times$ 4 mm2 pixels are considered when grouping together
pixels. This means that if a given set of energy depositions has a sufficient
distance in space and time it will be clustered into two distinct tracks. An
example of this in a supernova interaction is energy deposition due to de-
excitation photons that can be further away than the primary electron track
and are likely to produce separate tracks. This ultimately leads to a limit in
this analysis achievable efficiency as the focus of the reconstruction is to
distinguish between radiogenics and deposits due to supernova neutrinos.

To optimize the remaining two parameters (i.e., the time between resets and
number of resets in a track) a sample of 10,000 unique background sets of
events along with a sample 10,000 unique supernova interactions were generated
in a single APA volume. It is important to note here that these two samples
are not mixed (i.e., the events analyzed are either purely background or
purely signal), and the optimization is performed on an isolated background or
signal event for simplicity. As clearly seen on the left in Fig. 5, radiogenic
background events are problematic mostly for events with $<$5 MeV of deposited
energy. We therefore focus on the optimization of the parameters with low-
energy events (e.g., total deposited energy $\leq$5 MeV).

The event identification efficiency is calculated as the number of
reconstructed signal resets in a given time window divided by the total number
of true signal resets in an event, where the number of signal resets in a time
window is the summed number of resets of all tracks which contain more resets
than the chosen threshold. In a similar manner, the event identification
purity is defined as the number of reconstructed signal resets in a time
window divided by the total number of reconstructed signal and background
resets. An example of such efficiency and purity can be seen in Fig. 9, where
each line represents a different reset thresholds for a given track. From Fig.
9, the optimal time window between any two resets is chosen to be 3 $\mu$s.
While a slightly shorter or significantly longer time could be chosen without
impacting the efficiency or purity, 3 $\mu$s is the $3\sigma$ longitudinal
diffusion threshold for a point source diffusing in LAr from 3.6 m away in a
drift electric field of 500 V/cm. The plateau in efficiency shown in Fig. 9 at
$\sim 90\%$ results from the clustering algorithm “missing” charge from de-
excitation photons which radiate further away than the 4 mm pixel pitch. More
advanced spatial clustering algorithms could improve this, but this choice was
found sufficient to accept the supernova neutrino signals while continuing to
reject radiogenic backgrounds.

After choosing the optimal 3 $\mu$s time window between resets, we next define
the threshold on the number of resets per cluster. Using the time window of 3
$\mu$s, the event identification efficiency and purity as a function of the
threshold is shown in Fig. 10. For the events with $\leq$5 MeV of total
deposited energy a purity of $>$95% can be achieved at an efficiency of
$\sim$80% with a threshold of 13 resets (equivalent to $\sim$1.85 MeV
deposited energy). The purity across the full supernova neutrino energy
spectrum is $>$99% for an efficiency of $\sim$88% when using the 13 reset
threshold. This last point of optimization can be tuned based on the analysis
for different purity and efficiency choices.

###  IV.3 Data Rates

A challenge for supernovae detection with a kiloton-scale LArTPC is managing
data rates for low-energy thresholds of $<$10 MeV. One of the remarkable
outcomes of the Q-Pix principle of electronic least action is the ability of
the detector to achieve low-energy thresholds while maintaining very low data
rates.

Fig. 11 shows the data rate per APA based on the radiogenic backgrounds
outlined in Table 1. The rate is calculated from the average number of resets
observed in an APA over a 10-second readout window using 10,000 unique sets of
radiogenic backgrounds. On the left axis of Fig. 11, the average data rate is
calculated per second per APA assuming each reset is encoded by 64 bits of
information. Even at the lowest threshold of 1 reset (which corresponds to 147
keV of deposited energy) the data rate per full 10-kton module (assuming 200
APAs for the Q-Pix readout) is only 5.7 MB/s. This number drops by two orders
of magnitude if 7 resets ($\sim$1 MeV of deposited energy) is required.
Moreover, since the rate of radiogenics dominates, the inclusion of the
supernova burst events from the previous sections leaves this estimated data
rate largely unchanged.

Figure 11: The data rates shown here are the average of 10,000 unique
10-second-long APA drift volumes as a function of the threshold on the number
of resets. Data rates for one APA from radiogenic background events will be a
function of the threshold on the number of resets. The rates are shown in
number of resets per APA per 10 seconds (left axis) and the corresponding data
rate (right axis).

In order to compare these data rates to the ones from the current DUNE FD
design, some context is needed. First, the envisioned Q-Pix 10-kton module
consisting of 200 APAs with 4 mm pixel pitch means there are $\sim$172 million
channels to be compared to the 384,000 channels for the projective wire
readout for the DUNE 10-kton module. This has to be taken into account when
comparing data rate per channel. Second, the TPC data rates in the DUNE FD TDR
[38] assume 100 seconds of readout, a threshold of 10 MeV neutrino energy
($\sim$5 MeV of deposited energy), and are quoted as an annual data volume. As
a comparison, the numbers calculated above for Q-Pix in this paper assume much
lower energy thresholds and are calculated per second. With this context,
Table 3 presents data rates for the Q-Pix architecture that can be directly
compared to the ones predicted for the DUNE projective readout.

System |  Data rate per 10 kton per year (petabytes) |  Data rate per channel per second (kilobytes)
---|---|---
Q-Pix 10 kton pixel readout | $1.03\times 10^{-6}$ | $1.9\times 10^{-10}$
DUNE 10 kton projective readout |  $<$2 | 1.6

Table 3: Comparison of data rates between a 10-kton DUNE projective readout as
described in Ref. [38] and a Q-Pix 10-kton module described in this work. In
both cases, a 10 MeV energy threshold is assumed.

For the Q-Pix readout, assuming a threshold of 10 MeV neutrino energy ($\sim$5
MeV of total deposited energy, or 34 resets), the data rate from the dominant
source of radiogenic background events is estimated to be ${16.5\times
10^{-5}}$ kB/s/APA or equivalently 0.032 kB/s/10 kton which is 1.03 GB/year/10
kton. This last number is to be compared to the estimated DUNE FD data rates
of less than 2 PB/year/10 kton, which is about six orders of magnitude larger.

Figure 12: Reset times in a 10-kton Q-Pix detector module before (top) and
after (bottom) clustering for a supernova burst (SNB) simulated at 10 kpc. In
this example, the SNB reset clustering efficiency is
${\frac{7002}{8196}\approx 85\%}$ and purity is ${\frac{7002}{7002+38}\approx
99\%}$.

The anticipated full data rate from a DUNE projective readout 10-kton module
with a 10 MeV neutrino energy threshold including beam events, astrophysical
sources of neutrinos, and calibrations has been presented in various Refs.
[39, 79, 38], and is estimated to be between 25-30 petabytes (PB) per year.
While beyond the immediate scope of this paper, it is very clear that the
Q-Pix architecture can vastly reduce these data rates across all the different
neutrino sources and can allow for much lower energy thresholds for comparable
data rates (e.g., for Q-Pix, the data rate would be 0.18 PB/10 kton/year for a
147 keV threshold based on radiogenic backgrounds).

Furthermore, these anticipated low data rates coupled with the ability to
store the resets locally and to have all the ASIC chips periodically read out
could remove the need for a dedicated “trigger” whereby an external system
forces the readout of all detector channels. However, in the case of punctual
events, such as a supernova burst, it is of the utmost importance that the
data can alert or trigger the scientific community. In the next section, we
explore what such a “trigger” would look like within the Q-Pix architecture.

###  IV.4 Supernova Neutrino Burst Triggering

In the event of a supernova burst (SNB), the Q-Pix-enabled detector module
must be sensitive to the increase in MeV-scale neutrino activity in the LAr
detector volume and be capable of identifying that it is indeed a SNB event
with high confidence. This, paired with the ability to determine the direction
of the supernova burst (discussed in Section IV.5), will allow a detector
module with Q-Pix readout to be a contributor to the SuperNova Early Warning
System (SNEWS). In this section, we define a “trigger” to be an alert given by
a near real-time analysis of a possible supernova burst.

The identification of a supernova burst event in a Q-Pix-enabled detector
module can be done by first clustering resets to achieve a high-purity sample
of neutrino interactions, taking the sum of the number of resets within some
time window, and then placing a minimum number of resets required for a
“trigger.” The clustering algorithm used is based on DBSCAN [80] with a
Chebyshev metric [81]; this algorithm can process up to five hundred 10-second
time windows per minute which is more than sufficient to provide a near real-
time identification of a supernova burst with a Q-Pix-enabled detector module.
Here, we run the clustering algorithm over simulated samples with a mix of
both signal and background events so these parameters are optimized
differently from Section IV.2 (where the clustering is performed on individual
neutrino interactions or radioactive decays) and thus more realistic. The
maximum $\Delta t$ between each reset (for a reset to be considered to be in
the neighborhood of another reset) is optimized to 6 $\mu$s, and the minimum
number of resets to form a cluster is optimized to 14 ($\sim$2.065 MeV). An
example of reset times in a single 10-kton Q-Pix-enabled detector module
before and after clustering within a time window is shown in Fig. 12 for a
supernova burst at 10 kpc; the effectiveness of reducing the radiogenic
background (shown in blue) from the supernova interactions (shown in orange)
with very little contamination remaining can be quantified with a SNB reset
clustering efficiency of $\approx$85% and purity of $\approx$99%.

The burst triggering efficiency, defined as the number of detected SNBs
divided by the total number of SNBs, as a function of the number of neutrino
interactions from a supernova burst is shown in Fig. 13. A minimum of 60
resets required within a 10-second time window corresponds to a minimum
visible energy of $\sim$8.85 MeV and yields less than one fake trigger per
month. This triggering scheme allows a Q-Pix-enabled detector module to be a
more efficient supernova burst detection module than the baseline DUNE single-
phase (SP) or dual-phase (DP) detectors and currently envisioned triggering
schemes, which are described in detail in Ref. [13]. This enhancement in
efficiency means that with fewer supernova burst events, a Q-Pix-enabled
detector module can still faithfully trigger on the presence of the excess
activity caused by a supernova burst. This expands the distance at which a
supernova burst could occur for the detector to still be capable of
identifying it. This highly efficient trigger can easily be achieved for a
supernova occurring at distances that would yield tens of neutrino
interactions ($\mathcal{O}(60\textrm{-}70)$ kpc) in a single 10-kton module.

Figure 13: Supernova burst triggering efficiency as a function of the number
of $\nu_{e}$ interactions in a 10-kton Q-Pix-enabled detector module. The blue
points indicate the case where the total number of Q-Pix resets after
clustering within a 10-second window is required to be at least 60 ($\sim$8.85
MeV). The DUNE SP (single-phase) and DP (dual-phase) efficiencies are shown
for comparison and are taken from Ref. [13].

###  IV.5 Directionality Determination

The intrinsically high spatial resolution of LArTPCs, both wire-based and
pixel-based, has the ability to determine the 3D spatial topology of the
events. This enables the possibility of reconstructing the direction from
which neutrinos originate, and in this section, we demonstrate for the first
time how such a pointing analysis can be done with a LArTPC, specifically with
the Q-Pix readout.

The ability to perform “neutrino pointing” that could enable multi-messenger
astronomy is accomplished by providing directional information about where in
the sky astronomers should look [82, 83, 84]. The neutrino signal from a
collapsing star emerges on very prompt timescales [$\mathcal{O}$(seconds)]
while the electromagnetic signal emerges on much slower timescales
[$\mathcal{O}$(hours-days)]. Thus directional information can be used to
provide an “early warning” [78] to astronomers. Moreover, as it has been
pointed out in Refs. [85, 86, 87], some supernovae may not produce any obvious
electromagnetic signature while still producing copious amounts of neutrinos.
These so-called “failed” supernovae could still be identified if the field of
search could be narrowed by neutrino pointing. Finally, even without
identifying the astronomical source of the neutrinos, directionality
determination of the neutrinos can help evaluate the trajectory the neutrinos
took en route to detection and thus allow for estimates of neutrino matter
effects originating from their interaction with the Earth [88].

For the analysis presented here, we focus on reconstructing the primary
electron coming from electron neutrino charged-current ($\nu_{e}$ CC)
interactions and from electron neutrino–electron elastic scattering
(${\nu_{e}\text{--}e^{-}}$ ES). As can be seen in Fig. 14, only the ES events
preserve most of the progenitor neutrino directionality and can be used to
perform neutrino pointing.

Figure 14: Histogram of the true neutrino energy as a function of cosine of
the difference in the true neutrino angle ($\theta_{\nu_{\text{true}}}$) minus
the true electron angle ($\theta_{e_{\text{true}}}$) for $\nu_{e}$ CC events
(left) and for ${\nu_{e}\text{--}e^{-}}$ ES (right). The $z$-axis color scale
units are events per 0.5 MeV per 0.04. Figure 15: Stacked energy spectrum of
interacted supernova neutrinos with 220 $\nu_{e}$ CC (red) and 19
${\nu_{e}\text{--}e^{-}}$ ES events (blue) in 10 kton of liquid argon computed
using SNOwGLoBES.

Interaction channel | Number of events
---|---
$\nu_{e}+\ce{{}^{40}Ar}\rightarrow e^{-}+\ce{{}^{40}K^{*}}$ | 220
$\bar{\nu}_{e}+\ce{{}^{40}Ar}\rightarrow e^{+}+\ce{{}^{40}Cl^{*}}$ | 5
$\nu_{e}+e^{-}\rightarrow\nu_{e}+e^{-}$ | 19
$\bar{\nu}_{e}+e^{-}\rightarrow\bar{\nu}_{e}+e^{-}$ | 4
$\nu_{\mu}+e^{-}\rightarrow\nu_{\mu}+e^{-}$ | 3
$\bar{\nu}_{\mu}+e^{-}\rightarrow\bar{\nu}_{\mu}+e^{-}$ | 2
$\nu_{\tau}+e^{-}\rightarrow\nu_{\tau}+e^{-}$ | 3
$\bar{\nu}_{\tau}+e^{-}\rightarrow\bar{\nu}_{\tau}+e^{-}$ | 2

Table 4: Event counts of $\nu_{e}$ CC, $\bar{\nu}_{e}$ CC, and
${\nu_{X}\text{--}e^{-}}$ ES interactions in 10 kton of liquid argon for a
core-collapse supernova at 10 kpc computed with SNOwGLoBES.

To reconstruct the electron track for a candidate event, we first require that
the event has at least 13 resets. Based on the analysis presented in Section
IV.2, this ensures $<$1% contamination from radiogenic backgrounds while still
maintaining a relatively high signal detection efficiency. The collection of
3D reset positions are then analyzed using a random sample consensus (RANSAC)
algorithm [89] in order to determine the resets that are along the main trunk
of electron’s path (inlier points) from resets coming from radiative processes
from the electron interacting in the argon (outlier points). A graphical
representation of this method can be seen on the left of Fig. 16 where inlier
and outlier reset points are identified. Once so labeled, a RANSAC linear fit
is performed on the inlier reset points and the reset points furthest in
distance from each other are identified from the inlier reset points. The
linear fit provides the axis for the direction determination, but there is an
ambiguity as to which end of the line constitutes the starting reset point
(SRP) and which end constitutes the ending reset point (ERP), as illustrated
on the right of Fig. 16.

(a)  (b)

Figure 16: Left: hits produced by the outgoing electron in an example
supernova neutrino event. The black line is the linear RANSAC fit. The darker
blue points and lighter blue points represent the inlier and outlier reset
points identified by the RANSAC algorithm respectively. The two red dots (A)
and (B) are the farthest reset points apart from each other among the inlier
reset points. Right: 2D cartoon representation of inlier reset points. The two
red dots are the left-most and right-most point among the inlier reset points.
The black line represents the linear RANSAC fit performed to find the
trajectory and the cyan points and green lines illustrate inlier reset points
to identify the direction of travel of the electron. Figure 17: 2D histogram
for energy and angles between the neutrino’s true momentum and the electron’s
reconstructed momentum after applying the directional correction for a sample
of ${\nu_{e}\text{--}e^{-}}$ ES events.

This ambiguity can be broken by taking a topological approach. As the primary
electron travels in the argon, it will lose energy and experience larger
scattering angles. Therefore, the spatial spread of the resets is a good
indication of the directionality of the track. The right-hand side of Fig. 16
shows a 2D projection of the method used to determine which of the farthest
inlier points should be considered as the SRP. The process begins by drawing a
line between the two farthest reset points and then for each reset point
within the inlier points, lines are drawn from the assumed SRP and ERP, and
the cosine of the angles between each of those lines and the central line is
calculated. The point with the larger sum of cosine of angles is taken to be
the ERP. Fig. 17 shows the resulting difference between the true neutrino
direction and the reconstructed neutrino direction as a function of neutrino
energy for a sample of ${\nu_{e}\text{--}e^{-}}$ ES events after applying the
correction for the ambiguity of the start point. A clear peak at
${\cos(\theta_{\nu_{\text{true}}}-\theta_{e_{\text{reco}}})\approx 1}$
indicates that this reconstruction preserves the directionality with
relatively high fidelity.

With the directionality method established on an event-by-event basis, we now
focus on how to use this information for an entire simulated supernova burst
event. As mentioned before, we use the Garching benchmark model to simulate a
typical burst topology observed in a DUNE 10-kton module, leading to 220
$\nu_{e}$ CC and 19 ${\nu_{e}\text{--}e^{-}}$ ES events (see Fig. 15 and Table
4). Each neutrino interaction ($\nu_{e}$ CC and ${\nu_{e}\text{--}e^{-}}$ ES)
generates a direction vector which we can project onto a unit sphere as is
shown on the left of Fig. 18 (or projected onto a $\theta$–$\phi$ plane as
seen on the right). Principal component analysis (PCA) [90, 91, 92] is
performed on this collection of points and a primary axis is chosen which
penetrates the most populated area.

Figure 18: Representation of the direction vector generated for each neutrino
interaction in a simulated supernova burst event shown on a unit sphere (left)
and projected onto a $\theta$–$\phi$ plane. Solid blue triangles
($\blacktriangle$) represent events from ${\nu_{e}\text{--}e^{-}}$ ES
interactions and hollow red circles ($\circ$) represent events from $\nu_{e}$
CC interactions. Figure 19: Angular resolution for the supernova pointing in
terms of $\theta$ and $\phi$. The $\sigma$ bands correspond to a 2D Gaussian
fit to the peak to reduce the bias from the tails from poorly reconstructed
events. A clear peak at $\Delta\theta=\Delta\phi=0$ can be observed.

With the axis chosen, we can determine the direction of the supernova
neutrinos using the same topological disambiguation method we used on an
individual neutrino interaction, but now using all the points from the
collection of neutrino interactions reconstructed. Using the most prominent
point in this distribution to specify the direction from which the supernova
burst occurred, we evaluate how well we reconstruct the supernova burst
position by simulating 10,000 supernova burst directions and randomly
distributing their origin. Analysis of this sample shows that for $\approx$80%
we correctly identify the direction of the supernova burst with a
${(\theta_{\text{reco}}-\theta_{\text{true}})>25^{\circ}}$ and the remaining
$\approx$20% have their direction incorrectly reported “backwards” with
respect to the origin of the supernova burst. This restriction in the possible
area of the sky a supernova burst search should be directed toward can provide
a powerful tool for astronomical observations. In this analysis, we did not
distinguish between ES and CC events, the latter of which can be identified by
the presence of de-excitation photons. Identifying and removing these
extraneous, non-pointing CC events would substantially improve the pointing
analysis, and will be taken into account in future work.

Fig. 19 shows the angular resolution achievable with the methods described
above. A clear peak at $\Delta\theta=\Delta\phi=0$ can be seen. The
$\phi$-projection is a Gaussian distribution while the $\theta$-projection has
two additional shoulders around $-\pi$ and $\pi$ due to cases where the
reconstructed direction points to the opposite of the true direction. The
$1\sigma$, $2\sigma$, and $3\sigma$ contours of a 2D Gaussian fit to the
difference between the true neutrino direction and the reconstructed neutrino
direction are also shown. These results show that the 10 kpc supernova would
be reconstructed within $\theta=33^{\circ}$ and $\phi=45^{\circ}$ at
1$\sigma$, and $\theta=99^{\circ}$ and $\phi=135^{\circ}$ at 3$\sigma$.

##  V Conclusions

The opportunity to observe neutrinos emitted from the next core-collapse
supernova offers a unique laboratory to test our understanding of particle
physics under some of the most extreme conditions. These supernova produce a
large number of neutrinos in the MeV energy range and a measurement of the
timing and energy profiles can potentially provide answers to many
astrophysical questions. As these neutrinos emerge promptly from a core-
collapsing star, while the first observable electromagnetic signals may not
manifest for hours to days later, the prompt identification of the neutrinos
can be used to provide an early warning of an imminent visible supernova.

The Q-Pix detector concept presented in this paper provides a path to
pixelated, kiloton-scale LArTPCs providing low-energy threshold detection that
maximizes the physics potential while keeping data rates manageable and
preserving the 3D information.

Using standard simulation tools for supernova neutrino interactions in
LArTPCs, the Q-Pix readout can offer low-energy detection and reconstruction
capabilities that have already been demonstrated with the conventional
projective wire-based readout currently envisioned for DUNE. Even when we take
into account estimated radiogenic backgrounds coming from the bulk liquid
argon and detector material, which has not previously been considered in
published work, the Q-Pix readout offers very high efficiency and purity event
identification for individual supernova neutrino interactions and the ability
to have a near-line, near real-time supernova trigger. Finally, due to the
preservation of the 3D information afforded by a pixel-based readout, an
angular resolution of 33∘ in $\theta$ direction, and 45∘ in $\phi$ direction
for 1$\sigma$ can be achieved within a single 10-kton module. The easily
achievable physics reach provided by the Q-Pix readout, especially in the area
of low-energy physics, makes compelling the further pursuit of this technology
for kiloton-scale LArTPCs. Future work is currently underway to fully
demonstrate the capabilities of this readout by examining beam, solar,
atmospheric neutrinos as well as the capability to explore various beyond the
Standard Model signatures.

###### Acknowledgements.

This material is based upon work supported by the U.S. Department of Energy,
Office of Science, Office of High Energy Physics Award No. DE-0000253485 and
No. DE-SC0020065. R. Guenette is also supported by the Alfred P. Sloan
Foundation. S. Kubota is also supported by the Ezoe Memorial Recruit and
Masason Foundations. J. B. R. Battat is supported by the Brachman Hoffman
Fellowship through Wellesley College.

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