##  1 Introduction

The Short-Baseline Near Detector (SBND) is one of the detectors making up the
Short-Baseline Neutrino (SBN) Program at Fermilab [Machado_2019,
acciarri2015proposal]. The main goals of this program are to address the
existence of eV-scale sterile neutrinos, to study neutrino-nucleus
interactions with high statistics in the GeV energy range, and to contribute
to the advancement of liquid argon detector technology. SBND will measure
neutrino interactions from the Booster Neutrino Beam (BNB), with an energy
spectrum peaking at $\sim$700 MeV. Located at a distance of 110 m from the
start of the beamline, SBND will characterise the BNB flux before significant
flavour oscillations occur, recording millions of neutrino interactions per
year. This event rate enables SBND to perform neutrino-argon cross-section
measurements with the highest statistics to date for many processes, as well
as search for rare events both in the Standard Model and beyond. The role of
SBND will therefore be key not only for the SBN physics program, but also for
future long-baseline neutrino experiments, such as the Deep Underground
Neutrino Experiment (DUNE) [DUNE:2020lwj]. SBND is a liquid argon time
projection chamber (LArTPC) [Rubbia:1977zz] with an active mass of 112 tons
and size 400 cm (X-drift) $\times$ 400 cm (Y-height) $\times$ 500 cm
(Z-length). It is divided into two drift regions of 200 cm each, defined by a
central cathode and two anodes surrounded by the field cage structure, as
shown in Figure 1. Each anode integrates three wire planes at different
orientations (0∘, +60∘, -60∘ to the vertical) with 3 mm spacing between wires
within a plane and between the three planes [SBND:2020scp]. These wires record
the signals due to the drifting electrons from the ionisation produced by
charged particles passing through the detector. The drift coordinate is
perpendicular to the beam in the horizontal direction, and the maximum drift
time corresponds to about 1.3 ms for the nominal electric field of 500 V/cm.
Since SBND is located near the surface, the detector is surrounded on all
sides by scintillator strip planes that serve as a cosmic ray tagger (CRT) and
provide the trajectory and timing of particles (mainly muons) that pass
through the detector walls. Together with ionisation, charged particle
interactions produce excited argon molecules which emit scintillation light as
they dissociate to their ground atomic state. These photons, which traverse
the detector on a time scale of nanoseconds compared to $\mathcal{O}(\rm ms)$
electron drift times, are collected by photon detector (PD) devices. The
detection of these photons is typically used to determine the start time of
the interactions. Although in these detectors the deposited energy is divided
between the generation of electrons and photons, past LArTPC neutrino
experiments have primarily focused on exploiting the information provided by
the charge using the light information in a more limited way. However, the
trend is changing in newer LArTPC designs. The complementarity between the
charge and light signals generated in a LArTPC makes it clear that an advanced
photon detection system (PDS) offers the potential to significantly improve
the performance of the experiment. The LArIAT experiment has demonstrated
light-augmented calorimetry for low-energy electrons in a small LArTPC
[PhysRevD.101.012010], but it remains to be demonstrated in large detectors.
Other benefits will include light-enhanced particle identification, on-the-fly
position reconstruction and improved timing resolution. This will not only
maximise SBND’s performance, but also presents an R&D opportunity for light
detection in liquid argon, with implications for future experiments such as
DUNE. While the scope of this article is restricted to scintillation light
signals, in future work we will study the performance when correlating the
light signals with the ionisation objects from the TPC and CRT systems.

[width=1.angle=0]./Figures/DetectorDesign/SBND_det.pdf

Figure : Drawing showing the SBND detector. The cryostat, part of the vertical
field cage and some CRT panels (facing the north, east and bottom TPC walls)
have been removed to reveal the active volume. The neutrino beam enters the
detector from the south side.

This article is organised as follows: in section 2 we describe the novel
design of the PDS in SBND. Section 3 illustrates the approach followed for the
simulation of the light signals, from generation to detection of the photons.
In section 4 we explain all the detector effects related to the processing of
the light signals. The reconstruction strategy followed in this work is
described in section 5. Section 6 shows the reconstruction efficiency of the
light signals while in section 7 we evaluate the performance of our approach
for the calorimetric, spatial, and timing resolution. Finally, as a case
study, in section 8 we apply the full simulation and reconstruction chain
described above to assess the ability of SBND to resolve the time structure of
the BNB, using only the light detection system.

##  2 Photon detection system design

Scintillation photons in argon are emitted in the vacuum ultraviolet (VUV)
region of the electromagnetic spectrum with the maximum intensity peak at 128
nm and a FWHM of about 6 nm [Doke:1981eac, PhysRevB.27.5279]. These VUV
photons are absorbed by most materials, making them undetectable by standard
devices. To make the detection of scintillation light of liquid argon
possible, parts of the detector (e.g. the windows of the optical sensors) are
typically coated with wavelength-shifter (WLS) compounds which re-emit light
in the wavelength range where it can be detected more efficiently. The PDS in
SBND integrates two different technologies: (i) a system of 120 cryogenic
8-inch diameter optical photomultipliers (PMTs), Hamamatsu R5912-MOD model
[R5912datasheet], and (ii) a system of 192 X-ARAPUCA devices111Similar devices
are planned for the phase I DUNE Far Detectors [DUNE:2020txw]., based on a
photon trap concept [arapucas]. The X-ARAPUCA confines the wavelength-shifted
photons inside a highly reflective box where silicon photomultipliers (SiPMs)
capture them, effectively increasing their collection area. Both systems are
located behind the wire planes of each TPC. The PMT system is read out using
500 MHz sampling CAEN VX1730SB digitiser modules. The X-ARAPUCAs are read out
using an amplifier similar to the DUNE model [Brizzolari:2022fzb] but located
outside the cryostat, and digitised using 62.5 MHz sampling CAEN V1740B
modules. One of the main goals for the X-ARAPUCA system in SBND is to serve as
R&D for this new technology and to demonstrate its operation in a neutrino
beam. In order to maximise the number of detected photons in SBND, the TPC
cathode surface has been covered with reflective foils coated with
tetraphenyl-butadiene (TPB)222The coating was carried out by an evaporation
process reaching an average mass density of $\sim$300 µg/cm2
[phdthesisVincent]. [refTPB]. The foils are held in place using a mesh, with a
79% transmittance, that covers the full foils surface. The use of such foils
is common in dark matter experiments [Acciarri:2010zz, Regenfus:2009fu]. The
LArIAT detector [LArIAT:2019kzd] was the first to successfully implement them
in a single-phase LArTPC using test-beam data, but SBND is the first to do so
to study neutrinos, and at an unprecedented scale. This design allows us to
recover part of the light emitted in the opposite direction to the plane where
the PDs are located that would otherwise be lost. Therefore, the PDS of SBND
is sensitive to two different light components: (i) a direct component, the
photons arriving with VUV wavelengths to the detector windows where they are
wavelength-shifted to the visible and then detected, and (ii) a re-
emitted/reflected component, the photons arriving with visible wavelengths to
the detector windows and then detected. Note that the component called here
direct is the one detected by other single-phase large LArTPC detectors (e.g.
MicroBooNE [MBooNEProposal], ProtoDUNE-SP [DUNE:2020cqd] or ICARUS
[IcarusFirstOp]). In SBND only the PMT system is used to build trigger
signals, and is therefore considered as the primary light detection system.
The 120 PMTs are organised into two arrays of 60 PMTs each, installed in the
two optically-isolated TPC volumes. In each TPC, the windows of 48 PMTs are
TPB-coated and thus sensitive to both direct and reflected light components;
the remaining 12 PMTs per TPC are left uncoated and thus only sensitive to
reflected light. This coated/uncoated configuration is chosen to ensure high
light collection while maintaining the ability to distinguish between the
different light components, enabling the extension of the use of scintillation
light in event reconstruction, as will be discussed in detail in section 7.
Similarly, the X-ARAPUCA system is made up of 96 devices per TPC. Half of them
are coated with para-terphenyl (pTP) [refpTP] to allow the detection of direct
photons, while reflected photons are detected by both uncoated and coated
X-ARAPUCAs. In order to trap the photons, dichroic filter windows (147 cm2 in
size, with nominal cutoffs at 400 nm and 450 nm for coated and uncoated units,
respectively) paired with WLS bars are used inside the X-ARAPUCAs. The actual
cutoff wavelength of the dichroic filters shows a dependence on the angle of
incidence of light, the smaller the angle the larger the cutoff. As a result,
the coated units whose transmittance range is selected for the pTP emission
let some visible light through.

[width=1.angle =0]./Figures/DetectorDesign/PDS_SBND.pdf

Figure : PMT and X-ARAPUCA arrangement in a PDS-box (left), together with a
view of SBND’s photon detection system (right), including the definition of
the coordinate system we use in our work.

Both PMTs and X-ARAPUCAs are grouped into units that we call PDS boxes, with 5
PMTs and 8 X-ARAPUCAs per box as illustrated in Figure 2. Within each of the
two TPC volumes, 12 PDS boxes are arranged in a 4$\times$3 array directly
behind the wires. In order to shield the wires from PDS pulses, a metallic
mesh with 85% transmittance is installed between the TPC wire planes and the
PDS units. With this design, where different active (PMTs and X-ARAPUCAs) and
passive (WLS reflective foils on the cathode) optical components are combined,
the PDS of SBND is the most sophisticated ever installed in a LArTPC. This
represents a major R&D opportunity that contributes to the further development
of this technology and helps build the expertise of the worldwide neutrino
physics community working on future experiments such as DUNE.

##  3 Scintillation light simulation

The simulation and reconstruction of events in SBND is carried out using the
LArSoft package [larsoft1, Snider:2017wjd]. The particle tracking in LArSoft
is done using Geant4 [bib:geant4]. For each energy deposition within the
active volume of the detector, LArSoft generates a certain correlated number
of electrons and photons depending on the value of the ionisation density and
electric field [PhysRevD.101.012010, LArQL]. The sum of both contributions is
proportional to the total deposited energy. Charge and light separately can
also be used to estimate the deposited energy, but in these cases it is
necessary to apply non-trivial, model-dependent corrections to account for
charge lost through recombination effects [AMORUSO2004275, RAcciarri_2013].
After being generated, simulated scintillation photons and ionisation
electrons need to be transported from their production positions to the
readout sensitive channels. Henceforth we will only focus on the simulation of
the scintillation light (an overview of the charge treatment can be found in
[MicroBooNE:2018swd, MicroBooNE:2018vro]). Scintillation photons can undergo
different physical processes as they propagate: Rayleigh scattering,
reflections and refractions in the detector material boundaries, absorptions
and wavelength shifting. A full Geant4 simulation that tracks every single
optical photon taking into account all these processes is available in
LArSoft. However, liquid argon emits $\mathcal{O}$(20000) photons per MeV of
deposited energy at 500 V/cm (and twice as much in the absence of electric
field) [DOKE1990617, Doke_2002]. This makes the full Geant4 simulation very
CPU-intensive and prohibitively slow, especially for large detector sizes and
$\mathcal{O}$(GeV) energy depositions as is the case for BNB neutrinos in
SBND. This makes our scintillation light simulation computationally
challenging and alternative methods, commonly known as fast optical models,
need to be considered. We will next introduce the models that we use within
LArSoft to predict the number of photons arriving to the PDs and their arrival
time distributions.

###  Number of photons detected

In SBND we use the semi-analytic model described in [PredTransportScintLight]
to simulate the transport effects in scintillation light signals. This
approach makes use of the isotropic emission of the scintillation photons to
calculate the geometrical aperture of each PD relative to each scintillation
point on-the-fly. Corrections are then applied to the photon transport to
account for Rayleigh scattering and border effects due to the finite size of
the detector. The model also includes an extension to accurately simulate the
reflected component of the light signals in SBND. This approach, which does
not scale with the size of the detector, is drastically faster (more than
$\times$10) than the full Geant4 optical simulation. One limitation of the
semi-analytic method is that it can only be defined for the active volume due
to its geometric approach. However, light generated outside of the TPC
(especially behind the wire planes) might have a non negligible contribution
to the signals. For example, though the light produced in the non-active
volume can be considered as a second order contribution, it can play a crucial
role for trigger efficiency studies, where crossing cosmic tracks behind the
PDS can lead to fake triggers. To simulate the light generated outside the
active volume in SBND we use the optical library model. It is available in
LArSoft and has been the default light simulation mode pioneered by the LArIAT
[PhysRevD.101.012010] and MicroBooNE [MicroBooNE:2021zul] experiments. In this
approach, the fraction of incident photons for each PD and detector-location
pair is computed once using the Geant4 optical simulation and stored in a
library file, so that it can be read later in subsequent detector simulations.
SBND therefore uses a hybrid model to simulate scintillation light that takes
advantage of both the semi-analytic and the optical library approaches.

[width=.49]./Figures/LightGeneration/scint1.pdf
[width=.49]./Figures/LightGeneration/scint2.pdf

Figure : Left: Scintillation photon arrival time distribution for a BNB
neutrino sample (1,000 events). Both emission and propagation effects are
simulated. Right: Average photon arrival time distribution accounting for TPB
emission time.

###  Arrival time distributions

The other key component needed to have a complete light simulation is the time
structure of the scintillation signals. In all measurements the overall
scintillation light emission in liquid argon exhibits a double exponential
decay characterised by two very different times, commonly known as fast and
slow components [PhysRevB.27.5279, PhysRevB.20.3486]. The value used in our
simulations for the fast component is $\tau_{\text{fast}}$ = 6 ns. The slow
component $\tau_{\text{slow}}$ is less well known with measurements ranging
from 1000 ns to 1700 ns. Moreover, the existence of an intermediate third
component (with a time constant of about 100 ns), first reported by various
experiments [Heindl_2010, Acciarri_2010_thirdcomp], has been proposed.
However, recent studies [Segreto_2015] have shown that these discrepancies on
the value of $\tau_{\text{slow}}$ could be related to the intrinsic emission
time of the wavelength shifters needed to enable the VUV photons detection.
Dedicated measurements of light signals without WLS333VUV photons are directly
detected by MgF2-window PMTs. reported a slow decay time of
$\tau_{\text{slow}}$ = 1300 ns [Heindl_2010], which is the value used in SBND
simulations. In a detector the size of SBND, photon trajectories will be
affected at first order by Rayleigh scattering, and at second order by
reflections from solid surfaces in the detector volumes. These effects will
act cumulatively to lengthen and broaden the time distribution of photons
arriving at each PD, especially for detectors whose size is comparable to the
Rayleigh scattering length in liquid argon of $\sim$100 cm
[MBabicz2020LightPI]. To account for these transport delays in our
simulations, we use the semi-analytic model’s method to estimate the photon
propagation time [PredTransportScintLight]. Figure 3-Left shows the averaged
photon arrival time distribution of the direct light component generated by a
simulated sample of BNB neutrino events interacting in SBND. An exponential
fit to the fast (blue/dashed-line) and slow (orange/solid-line) components has
been performed. As expected, photon transport effects are more pronounced for
the fast scintillation component, producing a relative deviation of $\sim
400\%$ with respect to the emission lifetime. In comparison, the slow
component is largely unaffected, with the expected distribution smeared by
only $\sim$1%. As mentioned above, the wavelength shifting process is not
instantaneous. According to reference [Segreto_2015], the TPB time response
can be described by a four-exponential function with time constants
(abundances) given by: $\tau_{1}$ $<$ 10 ns (60%), $\tau_{2}$ = 49 ns (30%),
$\tau_{3}$ = 3550 ns (8%), and $\tau_{4}$ = 309 ns (2%). The TPB effectively
changes the time structure of the light signals. In SBND this delay will be
present in all PMT light signals. Figure 3-Right shows the photon arrival time
distribution for the same neutrino sample used in Figure 3-Left after
including the TPB re-emission time. It can be seen how the effective lifetimes
become larger ($\sim$50% and $\sim$10% for the fast and slow components
respectively) with respect to the averaged emission + propagation time
constants. In order to quantify the scintillation signal time density for a
given interaction in the LAr, Figure 3-Right also shows the cumulative
distribution (right vertical-axis). It is interesting to notice that about 99%
of the scintillation photons are expected to reach the PDs within the first
$\sim$8 µs. This result helps inform the length of the integration window set
in the reconstruction.

Light |  |
---|---|---
Component |  PMT |
|  X-ARAPUCA |
PDE [%] [SBND_Internal] |  |
Coated / VUV | 12% [Bonesini_2018] | 2.19%
Coated / Visible | 17% [SBND_Internal] | 0.43%
Uncoated / VUV | 0% | 0%
Uncoated / Visible | 25% [R5912datasheet] | 2%
Table : Photon detection efficiencies for the different optical sensors used
in our simulations.

For the VUV light, the pTP-coated X-ARAPUCA time response is modelled after a
dedicated Geant4 simulation that accounts for the pTP emission
($\tau_{\text{pTP}}$ = 1.14 ns) and the inner WLS bar (EJ-286 plastic,
$\tau_{\text{EJ-286}}$ = 1.2 ns) decay times [Marinho:2018doi,
Paulucci:2019omb, EljenWLSbar]. For the visible light, in addition to the time
response of the TPB described above, the time response of the WLS bar (EJ-280)
used inside the uncoated X-ARAPUCAs is modelled with an exponential decay time
of 8.5 ns [EljenWLSbar], while no bar-response is simulated for the pTP-coated
X-ARAPUCA as the EJ-286 bar is transparent to this wavelength.

##  4 Detector response simulation

[width=.49]./Figures/RecoAlgorithms/SERPMTZoom.pdf
[width=.49]./Figures/RecoAlgorithms/SERX-ARAPUCA.pdf

Figure : Measured single electron response for the PMTs (top) and X-ARAPUCAs
(bottom) in SBND. Note the logarithmic scale used for the PMT SER to optimise
the simultaneous display of the positive and negative parts of the signal,
given the large difference in their duration. The fluctuations included in our
simulations, 22% for the PMTs and 10% for the X-ARAPUCAs, are also shown.

The photon detection efficiencies (PDEs) in our simulations are included as
global factors on the number of detected photons. Table 3 summarises the
values used in this work, for the different light components and optical
detectors. For the PMTs, the deviations from the pure quantum efficiency of
the device (25%) are related to the presence of a WLS in the detection window.
For the case of VUV photons, the WLS isotropic emission reduces the detection
efficiency by 50% since visible photons are equally likely to be re-emitted
back into the liquid argon volume and away from the PMTs. For the visible
photons the transmittance of the TPB has been measured to be 70%
[SBND_Internal], reducing the amount of cathode-reflected photons detected by
the coated PMTs. Regarding the X-ARAPUCAs, the global efficiency accounts for
the WLS coating emission (for the VUV-sensitive modules), dichroic filter
transmittance, WLS bar conversion efficiency and SiPM efficiency. While the
X-ARAPUCAs have PDEs smaller than PMTs, they offer substantial enhancements
over bare SiPMs, making them ideal for instrumenting large areas with tight
space constraints. After amplification and digitisation, each converted photon
results in an output signal at the end of our detection chain, known as the
single electron response (SER). To make the readout faster and to minimise the
number of cables in SBND, the PDs are in AC-coupled configuration, allowing
high voltage application and signal readout using a single cable. In this
scheme SER signals are bipolar and integrate to zero. Depending on the readout
polarity, negative (positive) for our PMTs (X-ARAPUCAs), they show a main
pulse followed by an overshoot (undershoot). The SER signals for PMTs and
X-ARAPUCAs444For all the X-ARAPUCAs we use a measurement of the Onsemi
MICROFC-30050-SMT SiPM [SiPMs:onsemi] boards with an alternative amplifier and
digitiser that produce a similar response to the final one installed in the
detector. This does not impact our results as the electronics response is
effectively removed during the signal deconvolution as explained in section
5.1. have been measured at dedicated test-stands. Results are represented in
Figure 4, where the shaping due to the AC-couplings are clearly visible. For
the PMTs (X-ARAPUCAs) the FWHM of the SER is 10 ns (250 ns) with an overshoot
(undershoot) amplitude of 1.8% (18.4%) of the signal peak and extending for
about 1.5 µs (2.9 µs) before baseline restoring (90-percentile). Simulated
optical waveforms are generated by first scaling the number of photoelectrons
(PEs) arriving at each PD by its efficiency from Table 3, and then convolving
this arrival time distribution with the measured SER described previously.
Random fluctuations in the SER integral are applied to better mimic data
[donati2000photodetectors] (see Figure 4). For the PMTs, this fluctuation
comes from estimations of the gain variation in the first dynode; for the
X-ARAPUCAs, the standard deviation of the first PE peak in the spectrum is
used. To model electronics noise, we use an uncorrelated additive white
Gaussian noise with an RMS of 2.6 ADC counts for the PMT signals and 0.65 ADC
counts for the X-ARAPUCA signals, corresponding to the measured intrinsic
noise of the readout boards.

[width=.49]./Figures/RecoAlgorithms/WaveformDisplay-crop.pdf -150162PMT8.5
[width=.49]./Figures/RecoAlgorithms/XA_evd-crop.pdf-150162X-ARAPUCA8.5

Figure : Examples of simulated photon arrival time distributions for a
neutrino interaction (top), corresponding digitised waveforms (center) and
reconstructed unipolar signals after deconvolution (bottom) for a coated PMT
(left) and a coated X-ARAPUCA (right).

Figure 4 shows examples of simulated PMT and X-ARAPUCA waveforms in SBND,
before (top) and after (centre) digitisation, where the bipolar shapes in the
digitised signals are clearly visible. For the PMTs, we have set the baseline
value to minimise possible saturations due to the dynamic range of their
14-bit digitisers, allocating 90% of the range to the negative peak and 10% to
the overshoot. For the X-ARAPUCAs, we set the baseline of their 12-bit
digitisers so that 83% of the dynamic range is reserved for the positive peak
and 17% for the undershoot. For the PMTs, the observed delay between the
photon arrival times (at the photocathode) and the digitised signal (at the
anode) accounts for the PMT transit time (55$\pm$2.4 ns [R5912datasheet]). In
the case of the X-ARAPUCAs the photon propagation time within the module is
negligible and the SiPM transit time is at sub-nanosecond level and therefore
not simulated. We also account for the non-linearity of the PMT response at
high light intensities. This behaviour has been characterised for the PMT
model used in SBND [Babicz:2019pll, Jetter:2012xp]. To incorporate this effect
into our PMT simulation, we employ a data-driven model that effectively
accounts for the reduction in the number of PEs reaching each digitisation
bin. Finally, we simulate a Dark Count Rate (DCR) of 2000 Hz [Belver_2018] in
all our PMTs, and 10 Hz in the X-ARAPUCAs with a 42% crosstalk
[SBND_Internal].

##  5 Light signal reconstruction

Depending on the detection technology and readout electronics, SER signals can
vary significantly. For example, the response to a single photon typically
spans around 50 ns and 500 ns for the PMTs and X-ARAPUCAs, respectively, as
can be seen from the peak time of the waveforms in Figure 4. Therefore,
requiring different reconstruction algorithms and parameter settings. For this
reason, in this work we have studied both systems independently with the goal
of showing their performance separately. In future work, we will explore the
combination of both systems. The standard strategy for extracting the number
of PEs from a PDS waveform involves a linear area-to-PE conversion. However,
as mentioned before, the SBND light signals are bipolar (with a main pulse
followed by an overshoot or undershoot) due to the AC-coupled readout. In this
situation, multiple photons arriving close in time can shift the waveform
baseline, resulting in a large cumulative deviation (see Figure 4-centre
panels). The baseline estimation becomes challenging for these bipolar
signals, as its value is different from that of the nominal baseline for
certain regions of the signal, and the area-to-PE approach fails in estimating
the number of photons. Hence a different reconstruction approach is required
for an accurate PDS signal processing in SBND. Next we describe a
deconvolution-based method which aims to remove the signal bipolarity,
providing an estimator for the number of PEs and their arrival times.

###  Waveform deconvolution

If a completely linear response is assumed for the PDs, the raw signals $f(t)$
are the convolution of the photon arrival time distribution $s(t)$ and the
detector response $r(t)$:

$f(t)=s(t)\ast r(t)\equiv\int_{-\infty}^{\infty}s(t)r(t-\tau)d\tau.$ (1)

This makes possible the recovery of our true signals by using the convolution
theorem:

$s(t)=\mathcal{F}^{-1}\left\\{\frac{F(\omega)}{R(\omega)}\right\\},$ (2)

where $F(\omega)$ and $R(\omega)$ represent the Fourier transforms
$\mathcal{F}$ of $f(t)$ and $r(t)$, respectively. However, this simple
approach starts to degrade when we take into account the presence of noise.
Therefore, for the correct processing of our signals we implement different
strategies to mitigate noise. For the finely-sampled PMT signals, we apply a
two-step waveform smoothing before the Fourier transform
[aguilararevalo2021dark]:

  1. 1.

Exponential average smoothing:
$\tilde{f}_{i}=(1-\alpha)\tilde{f}_{i-1}+\alpha f_{i}$

  2. 2.

Unweighted average smoothing:
$\tilde{\tilde{f}}_{i}=(\tilde{f}_{i-1}+\tilde{f}_{i}+\tilde{f}_{i+1})/3$,

where $f_{i}$ stands for the waveform value at a given time-tick $i$, and
$\tilde{f}_{i}$ and $\tilde{\tilde{f}}_{i}$ stand for the smoothed value after
steps 1 and 2 respectively; with $\alpha$ a free parameter set to 0.3 after an
empirical optimisation. For the X-ARAPUCA system the smoothing is not needed
as the slower sampling already works as a low-pass filter. Next, for both
systems we apply a filter in the frequency domain ($G(\omega)$) to maximise
our signal-to-noise ratio, leaving Equation 2 in the following form:

$s(t)=\mathcal{F}^{-1}\left\\{G(\omega)\frac{F(\omega)}{R(\omega)}\right\\}.$
(3)

Among the different options available we have chosen a Gaussian filter due to
its simplicity and good performance (see section 6)

$G(\omega)=e^{-\frac{1}{2}(\frac{\omega}{\omega_{c}})^{2}}\ (\omega>0),$ (4)

with $\omega_{c}$ a free parameter that is set by fitting Equation 4 to the
Wiener filter [wienerbook] estimated for the SER signals. The best fit result
obtained is $\omega_{c}=49.0\pm 0.2$ MHz for the PMTs and $\omega_{c}=3.2\pm
0.3$ MHz for the X-ARAPUCAs. Figure 4-bottom shows one example for a
deconvolved signal, following the procedure described above, for both a PMT
and an X-ARAPUCA, where it can be seen how the deconvolution has eliminated
the bipolarity of the signals while maintaining the relative size and temporal
position of the peaks.

###  Optical hit and flash objects

[width=1.angle=0]./Figures/RecoAlgorithms/OpHitExample.pdf

Figure : Example of the OpHit finder algorithm performance for a PMT
deconvolved waveform. The start/end point of the OpHits are indicated by the
vertical lines along the baseline. The different estimates available for the
OpHit-times are also shown.

The next step in the optical reconstruction is to recover each scintillation
photon arriving to the optical channels by looking for pulses along the
deconvolved waveforms. These optical hits (OpHits) are the basic objects in
the optical reconstruction. Following the subtraction of the baseline, that we
estimate using the start and end portion of the deconvolved signals (400 ns on
each side), pulses are found by identifying samples with a value higher than
1/4 the amplitude of the deconvolved SER signal and 3 times the standard
deviation of the baseline RMS. Figure 5 illustrates the performance of the
OpHit finder algorithm for a PMT waveform. It can be seen how multiple peaks
are merged into a single OpHit when multiple photons arrive simultaneously (or
very close) to the PD. This is particularly relevant for the fast light.

[width=1.]./Figures/RecoAlgorithms/OpFlashExampleFull.pdf

Figure :  Illustration of the OpFlash finder reconstruction algorithm. The
dotted orange (solid green) horizontal line represents the OpFlash length
(fast emission) window parameter. The gap observed after the fast emission is
caused by the large width of the OpHits reconstructed for this light
component. The solid histogram (OpFlash X-axis projection) represents the time
intervals satisfying the multiplicity condition along the OpFlash length. The
dashed pink line shows the minimum number of PEs per optical channel required
to identify an OpFlash.

The number of PEs in the signals is recovered by the integral of the OpHits.
The possible broadening of the OpHits due to the simultaneous arrival of
photons, together with the smearing resulting from the deconvolution process,
can introduce biases in the estimation of the arrival time of photons from
these objects. To minimise these issues, in the PMT system we define the
OpHit-time as the time sample in which the deconvolved signal goes above a
certain fraction of the maximum peak value. Using a rise-time threshold of 15%
we obtain a resolution of about 1.6 ns in the estimation of the arrival time
of the first photon contributing to each OpHit. For the X-ARAPUCA system, due
to the coarser sampling, a Gaussian function is fit to the deconvolved
waveform to estimate its peak time, achieving a resolution of 5.9 ns. We use
the sum of the OpHits to reconstruct the amount of light generated by a given
interaction within each TPC. We will refer to clusters of OpHits as optical
flashes (OpFlashes). An OpFlash is built if a multiplicity condition is
satisfied: a minimum number of 6 PE is detected by more than 3 optical
channels within a time interval of 10 ns for the PMTs or 60 ns for the
X-ARAPUCAs. The length of an OpFlash is set to 8 µs to account for the total
amount of light generated in the interaction (see Figure 3-Right).

Parameter | Value
---|---
Minimum number of PEs | 6 PE
Minimum number of optical channels | 3 ch
Time interval (PMT / X-ARAPUCA) | 10 ns / 60 ns
PEs threshold | 20 PE
OpFlash length | 8 µs
Time window for t0 | 30 ns
Veto-window | 8 µs
Table : List of OpFlash parameters used in the SBND optical reconstruction.
All the parameters are shared by PMTs and X-ARAPUCAs, except the time interval
due to the different behaviour of the two systems.

The start time of an OpFlash represents the time of the interaction (t0), so
it must be reconstructed with great care. To obtain the value of t0 we average
the OpHit times for the channels that collectively contribute 50% of the total
light within a 30 ns window around the time interval with the largest number
of PEs. Once an OpFlash candidate has been defined, it will only be saved if
the integrated number of reconstructed PEs is above 20 PE. This cut is set to
avoid selecting candidates originating from dark counts or low energy
backgrounds like 39Ar. Finally, a 8 µs veto-window is also applied to prevent
other flashes being created during the OpFlash duration, although multiple
flashes can be found within an event. Figure 5 illustrates the OpFlash
reconstruction procedure. Table 5 summarises the parameters used to build
OpFlash objects in SBND. The value of the parameters used in the
reconstruction of both OpHits and OpFlashes are the result of an optimisation
process which seeks to maximise the amount of useful information from the
light signals and the number of reconstructed neutrino events, but their final
values may be revisited once data becomes available.

##  6 Reconstruction efficiency

[width=.49]./Figures/FlashEfficiency/EffEVis_combined.pdf
[width=.49]./Figures/FlashEfficiency/EffDrift_combined.pdf

Figure : OpFlash reconstruction efficiency for a sample of BNB neutrino +
cosmic events as a function of the deposited energy (left) and drift distance
(right) for PMTs (red) and X-ARAPUCAs (blue). The dashed (solid) lines
represent the number of events with a reconstructed OpFlash (all the events).
The shape of the distributions on the left is the combination of the BNB
spectrum, cosmic spectrum and detector acceptance, with the bump around 1000
MeV caused by muons crossing the detector volume.

In this section we show the overall efficiency of reconstructing the light
signals in SBND. To carry out these studies we have used a sample of 30,000
BNB neutrino events simulated in LArSoft and using GENIE [Andreopoulos:2009rq,
Andreopoulos:2015wxa] for the generation of neutrino interactions. We have
excluded waveforms where saturation occurs. On average, for the PDEs
considered in this work, this translates into not using 2 PMT and 1 X-ARAPUCA
waveforms per BNB event, and therefore we expect the impact to be negligible.

###  OpFlash reconstruction efficiency

An efficient reconstruction of the OpFlash objects is of great importance as
they represent the light associated with an interaction. To study their
reconstruction efficiency, we have used our neutrino sample together with the
corresponding cosmic ray overlay, since we are interested in studying the
reconstruction efficiency of neutrino events in the presence of the cosmic
background, as will be the case for real data. We have simulated the cosmic
ray interactions in LArSoft using Corsika [Heck:1998vt] as the event
generator. In this study we have also considered an interaction as visible if
its energy deposition is larger than 5 MeV, excluding the events at lower
energies. The OpFlash reconstruction efficiency, defined as the ratio between
the number of interactions with a reconstructed OpFlash and the total number
of interactions, is shown in Figure 6 as a function of the deposited energy
and average drift distance ($\rm d_{\text}{drift}$)555Hereafter, with the
label MC we will refer to variables that have been obtained using true level
information.. As expected, the efficiency drops at low energy depositions.
However, some flashes are also lost at high energy values. They correspond to
in-time interactions (neutrino-cosmic or cosmic-cosmic) occurring within the
OpFlash time length. As explained in section 5, a veto window is applied after
identifying an OpFlash, meaning that no other OpFlash can be claimed during
the veto time. In these cases only one OpFlash is recovered, typically
initiated by the interaction producing the larger amount of photons, but with
photons coming from the two interactions (OpFlash pile-up). The reduction of
efficiency due to coincident events has been estimated to be around 2% for
both PMTs and X-ARAPUCAs. The dependence of the reconstruction efficiency with
the drift distance is very small (within 1% for the PMTs and 5% for the
X-ARAPUCAs). Overall, we obtain a global OpFlash reconstruction efficiency of
95.8% with the PMT system and 92.2% with the X-ARAPUCA system.

###  OpFlash reconstruction completeness

[width=.49]./Figures/Calorimetry/Completeness1.pdf-160142PMT8.5
[width=.49]./Figures/Calorimetry/Completeness2.pdf-160142X-ARAPUCA8.5

Figure : Number of reconstructed PEs from OpHits within an OpFlash, and
accuracy ($\equiv$ Bias) and resolution ($\equiv$ StdDev), as a function of
the total number of simulated PEs within one channel in the PMT (left) and
X-ARAPUCA (right) systems. The non-linear behaviour of PMTs is clearly visible
from 3000 PEs onwards.

To study the resolution in the reconstruction of the number of PEs, we use the
OpHit objects within an OpFlash. We compare the integral of the OpHits at each
PD ($\rm PE^{reco}$) with the total number of simulated photons arriving to
the same channel ($\rm PE^{MC}$). Results are shown in Figure 6. In the PMT
system we obtain an almost flat resolution better than 3% for channels with
more than 1000 PEs. The trend of the bias shows the non-linearity of the PMTs
starting at about 3000 PEs, where we go from underestimations smaller than 2%
to values between 8-10% for channels with more than 6000 PEs. For the
X-ARAPUCAs, the number of photons is reduced as their area and efficiency are
smaller than those of PMTs, achieving a resolution and bias better than 6% and
1% respectively, for channels with more than 250 PEs.

##  7 Reconstruction performance

After assessing the reconstruction efficiency of our primary reconstructed
objects (OpFlashes) and the resolution in the reconstruction of the number of
PEs, in this section we proceed to evaluate the detector performance based on
several key metrics derived from the OpFlash objects.

###  Light yield

[width=.49]./Figures/Calorimetry/LightYield1.pdf
[width=.49]./Figures/Calorimetry/LightYield1XAs2.pdf

Figure : Expected LY in SBND as a function of the mean drift distance for the
different PMT (left) and X-ARAPUCA (right) flavours, according to the
detection efficiencies in Table 3. Note that the large size of the error bars
as we approach the detection plane is primarily due to border effects (large
difference in the registered light between events occurring near or far from
the edges of the detector) and not to uncertainties in the simulation.

The expected LY for each optical detector type is shown in Figure 7 as a
function of the drift distance. The number of reconstructed PEs is obtained
from the OpFlash objects, while the amount of deposited energy and its average
drift position are taken from truth-level information. The total LY from
uncoated PMTs is much lower than that of coated PMTs, not only because they
are only sensitive to the reflected light component, but also because they are
in a ratio 1:4. For the X-ARAPUCAs, since there are equal number of coated and
uncoated units, this asymmetry is not present and the difference is simply due
to the larger total amount of light detected by the coated ones. When
comparing the two systems, the PMTs collect more light as their PDEs are
higher and have a larger photo-coverage than the X-ARAPUCAs (9.6% and 7% of
the anode plane, respectively). As no PMT is VUV-only sensitive, the LY for
the direct light in Figure 7-Left (points with dashed error bars) has been
simply estimated by subtracting to each coated signal its closest uncoated one
(after correcting for the different efficiencies)666At each PDS box (see
Figure 2) the distance between the central (uncoated) PMT and the corner
(coated) PMTs is 50 cm.. This gives an estimate of the PMT system without the
TPB-coated reflector foils on the cathode. As expected, the LY for the
uncoated PDs increases as the interactions approach the cathode
(d${}_{\text}{drift}$= 200 cm), where visible light is re-emitted from the WLS
reflectors. On the other hand, the closer to the anode, the more direct light
is collected. The anti-correlation between the two components makes the LY
significantly larger and more uniform than using the direct component alone,
which is a highly desirable behaviour that SBND is able to achieve thanks to
the innovative design of its PDS. In particular, the fraction of light gained
by the coated PMTs ranges from 50% in the centre of the TPC to 400% in the
region close to the cathode. For the coated X-ARAPUCAs the gain is much more
modest as the choice of the dichroic filter and WLS bar is not well suited for
trapping visible photons, but it is compensated by the fact that the other
half of the system is dedicated to these wavelengths. In the X-ARAPUCAs, the
improved uniformity comes from the sum of both coated and uncoated units
(blue-circle points in Figure 7-Right). The large error bars777All error bars
in this work represent the standard deviation of the distribution of points in
each case. in Figure 7 are driven by border effects, as the total light
collected can vary significantly for energy depositions near or far from the
edges of the active volume, even if they are at the same drift distance.

###  Position resolution

[width=.5]./Figures/RecoAlgorithms/BarycenterDisplay
[width=.47]./Figures/GeoReco/GeoZ_PMTs_and_XAs.pdf

Figure : Left: Illustration of the (Y, Z) reconstruction procedure. Right:
Accuracy and resolution in the estimation of the interaction point in the beam
direction (Z-coordinate) using only scintillation light for PMT (solid
markers) and X-ARAPUCA (empty markers) flashes. The difference in resolution
is mainly caused by the higher LY of the PMT system.

An important application of the scintillation signals in a liquid argon
neutrino detector is the determination of the position of the events that
generate the light flashes. The location of events using only the PDS will
never be as good as that obtained using the TPC information (which needs an
external time reference to resolve the degeneracy along the drift coordinate).
Even so, an estimation of the position with light is extremely important in
detectors located near the surface as it allows us to match ionisation
patterns to the precisely timed light signals, which will help identify which
interactions happened inside of the beam gate (signal candidate) and which
happened outside of it (background). In standard LArTPCs, the light-based
position reconstruction is generally performed in the coordinates defining the
PDS plane (Y-Z plane in our coordinate system). The achieved resolution will
then be largely determined by the spacing between adjacent optical channels.
Taking advantage of the high PD-density in SBND we have developed a simple
threshold algorithm to reconstruct the (Y, Z) of the interaction using only
light signals. We perform the PE summation at constant Y and Z positions for
each PD type. For the position estimation, we only consider the PDs whose PE
summation at each Y/Z position deviates less than a certain fraction from the
one with the most light. By an optimisation process, using a sample of BNB-
like neutrinos, we set a value of 20% for this difference. Figure 7-Left
illustrates the (Y, Z) reconstruction procedure for a simulated neutrino event
using the PMT system. Each circle represents a PMT in the PDS-plane with a
colour gradient showing the signal integral relative to the maximum. The fixed
threshold at 80% of the maximum is also shown by dashed lines. In Figure
7-Right we show the resolution we obtained for the reconstruction of the
interaction point along the beam direction d${}_{\text{beam}}$ (Z) with both
systems. We observe minimal bias and a resolution of 25 cm within 1 m inside
the detector volume. Outside that region, some border effects appear that bias
our estimate up to a value of 50 cm for interactions occurring just at the
boundary of the active volume. Similar results are obtained for the Y position
reconstruction.

[width=0.49]./Figures/GeoReco/PMTRatioCalReco2.pdf
[width=0.49]./Figures/GeoReco/Reco_drift_coord.pdf
[width=0.49]./Figures/GeoReco/GeoX_PMTs_and_XAs.pdf

Figure : Top and middle: Calibration curves for the $\eta_{\rm{}_{PMT}}$ and
$\eta_{\rm{}_{\text}{X-ARAPUCA}}$ parameters. Bottom: Accuracy and resolution
in the estimation of the drift distance using the $\eta_{\rm{}_{PMT}}$ (solid
markers) and $\eta_{\rm{}_{\text}{X-ARAPUCA}}$ (empty markers) parameters.

A unique feature of SBND’s PDS design is its ability to reconstruct the mean
drift distance at which the energy is deposited. This can be done by
exploiting the correlation between $\langle$d${}_{\text}{drift}\rangle$ and
the relative amount of photons of the direct and reflected light components
measured for a given interaction. For our PMT system, we define the $\eta$
parameter as the ratio between the number of photons seen by the uncoated and
the coated PMTs,

$\eta_{\rm{}_{PMT}}\equiv\frac{\sum\rm PE_{uncoated}}{\sum\rm PE_{coated}}.$
(5)

For the X-ARAPUCA system, given the low efficiency for visible photons of
their coated devices, to reduce statistical fluctuations in the denominator
for events near the cathode, we add $\rm\sum PE_{uncoated}$ so the $\eta$
parameter is defined as

$\eta_{\rm{}_{\text}{X-ARAPUCA}}\equiv\frac{\sum\rm PE_{uncoated}}{\sum\rm
PE_{coated}+\sum\rm PE_{uncoated}}.$ (6)

Both quantities can be directly obtained from the OpFlash reconstructed number
of PEs. Figures 7-Top and Middle show the correlation between
$\langle$d${}_{\text}{drift}\rangle$ and the $\eta$ parameters. These
calibration curves were obtained from a simulated sample of cosmic muons with
a well defined drift coordinate, i.e. muon tracks contained in narrow (10 cm)
slices along the drift. In practice, these tracks can be selected in SBND data
using the external CRT system that can directly trigger on these muon
topologies with a resolution better than 2 cm. Figure 7-Bottom shows the
resolution obtained in the estimation of the drift distance for our sample of
BNB-like neutrinos using the $\eta$ parameters. For the PMT system we see a
small bias ($<$ 5 cm) and a resolution better than 15 cm for distances larger
than 50 cm. The loss of sensitivity at the shorter distances is mainly driven
by two effects: the PMT non-linearity for large signals, and energy
depositions happening inside and outside the active volume where the
probability of detecting photons generated on those regions is quite
different. Again, the slightly worse result of the X-ARAPUCAs is mainly due to
the lower LY of this system.

###  Timing resolution

In a LArTPC, light travels about a million times faster than charge, so it is
the signal of choice to indicate the time of the interaction. To quantify the
timing resolution of our system, we define $\rm\Delta t_{0}$ as the difference
between the OpFlash time and the true interaction time. A constant and
homogeneous timing resolution throughout the detector requires accounting for
the light propagation time from the energy depositions to the PDs. For this
purpose, and bearing in mind that visible light travels almost twice as fast
as VUV light in LAr, we will distinguish among three different regions in our
detector:

[width=1.angle=0]./Figures/TimeReco/TimeDrift1.pdf

Figure : OpFlash time difference to the interaction time, as a function of the
drift distance using the PMT system. The error bars correspond to the standard
deviation in each drift bin. A cartoon of the two light component paths is
also shown: VUV photons can either propagate from the energy deposition point
(yellow star) directly to the PDS or propagate to the cathode where they are
re-emitted with visible wavelengths. The tipping point at about 45 cm from the
cathode is clearly visible.

(a) Direct-component dominated region, where the first photons arrive from the
direct component (VUV wavelengths). The time of the photons increases linearly
with the distance to the anode.

(b) Tipping point, or drift distance where the photons from the two light
components arrive at the same time to the PDs. At this point the propagation
time reaches its maximum value.

(c) Reflected-component dominated region, where the first photons arriving to
the PDs come from the re-emitted component (visible wavelengths). In this
region, the time of the photons increases with the distance to the cathode
(light has to travel as VUV photons from the interaction point to the cathode,
where they are wavelength shifted, and then propagate back along the 200 cm of
maximum drift distance with visible wavelengths).

An illustration of the arrival path of the two light components to the PDS can
be seen in Figure 7. The points represent the values of $\rm\Delta t_{0}$ from
our PMT system and for our neutrino sample as a function of the drift
distance. It can clearly be seen that $\rm\Delta t_{0}$ follows the trends
described above, ranging from a few to about 15 ns.

[width=.49]./Figures/TimeReco/TimeDrift0A.pdf
[width=.49]./Figures/TimeReco/TimeEVisA.pdf

Figure : Time accuracy and resolution of the PMT system as a function of the
drift distance (left) and deposited energy (right), after corrections for
propagation effects.

The average drift coordinate of the interaction
$\langle\text{X$_{\text}{reco}$}\rangle$ can be estimated from the calibration
curves in Figure 7 taking as input the measured $\eta$ value. Once
$\langle\text{X$_{\text}{reco}$}\rangle$ has been estimated, and defining the
tipping point as

$\text{X}_{\text}{T}\equiv\frac{\text{X}_{\text}{PDS}}{2}\left(1-\frac{\text{V}^{\text}{VUV}_{\text}{group}}{\text{V}^{\text}{Vis}_{\text}{group}}\right),$
(7)

we can correct for the light propagation delay as follows:

$\text{T}_{\text}{OpFlash}\rightarrow\dcases&\text{T}_{\text}{OpFlash}-\frac{\text{X}_{\text}{PDS}-\langle\text{X_{\text}{reco}}\rangle}{\text{V}^{\text}{VUV}_{\text}{group}}\\\
\text{\quad if}\langle\text{X_{\text}{reco}}\rangle>\text{X}_{\text}{T},\\\
\text{T}_{\text}{OpFlash}-\left(\frac{\langle\text{X}_{\text}{reco}\rangle}{\text{V}^{\text}{VUV}_{\text}{group}}+\frac{\text{X}_{\text}{PDS}}{\text{V}^{\text}{Vis}_{\text}{group}}\right)\\\
\text{\quad if}\langle\text{X}_{\text}{reco}\rangle<\text{X}_{\text}{T},$ (8)

where $\text{V}^{\text}{VUV}_{\text}{group}$ and
$\text{V}^{\text}{Vis}_{\text}{group}$ are the group velocity for the VUV and
visible photons888We have used $\text{V}^{\text}{VUV}_{\text}{group}$=13.5
cm/ns and $\text{V}^{\text}{Vis}_{\text}{group}$=23.9 cm/ns. , respectively,
and $\text{X}_{\text}{PDS}$ is the location of the PDS in the drift direction.
After correcting for the photons time-of-flight (ToF) delay, the final
$\rm\Delta t_{0}$ resolution (both bias and standard deviation) obtained in
SBND for the PMT system using only scintillation light can be seen in Figure 7
as a function of the drift distance and visible energy. A visible energy cut
($<$50 MeV) has been applied to avoid events with poor photon
statistics999This represents $\sim 5\%$ of the neutrino events with a
reconstructed OpFlash.. We obtain an almost flat bias of 2 ns (within $\sim$1
ns) for most drift distances and energy depositions. Note that the maximum
bias in $\langle\text{X$_{\text}{reco}$}\rangle$ (about 15 cm very close to
the anode) represents a bias in time of $\mathcal{O}$(1 ns). The standard
deviation is also at the level of 2 ns, except for energy depositions below
$\sim$200 MeV where the resolution is expected to be worse due to the small
number of photons detected in the events, affecting the resolution in the
OpFlash-time reconstruction. The lower number of photons detected, the slower
time response and the longer sampling interval (16 ns) prevent the X-ARAPUCA
system from reaching a resolution below $\mathcal{O}$(10 ns), as the OpFlash
time determination is affected by these system parameters. Future
reconstruction techniques beyond those used for this work may overcome this
hardware limitation in the X-ARAPUCAs.

##  8 Application example: resolving the BNB bucket structure

[width=.49]./Figures/BNBTruth/BNBTruth.pdf
[width=.49]./Figures/BNBTruth/BNBTruth2.pdf

Figure : Left: Time delay of neutrinos arriving to the most upstream SBND wall
relative to the proton bunch delivery time, as a function of their energies.
The minimum delay around 367 ns represents the case when the parent hadron
decays just after the beryllium target, at 110 m from the beginning of the
active volume. Right: BNB-neutrinos ToF along the 5 m length active volume of
SBND TPC, for the first five bunches, including the simulated parent hadron
decay time (left panel).

The BNB is created by extracting protons from the Booster accelerator at
Fermilab and impacting them on a beryllium target. The time structure of the
delivered proton beam consists of a series of 81 bunches, each about 1.3 ns
wide and 19 ns apart, defining a spill length of 1.6 µs [osti_1128043,
RWMBeamMeasurement]. An OpFlash in time coincidence with the expected arrival
of the proton delivery spill is a strong indication for a neutrino
interaction. However, cosmic rays can also interact during the proton beam
delivery, resulting in background triggers. One out of $\sim$300 beam spills
are expected to have an in-time cosmic muon [acciarri2015proposal]. SBND is
potentially able to reduce the random cosmogenic background happening during
the beam spill. As we have seen in section 7, the OpFlash t0 gives an
estimation of the neutrino interaction time with a resolution of the order of
2 ns for our PMT system. This timing resolution allows us to correlate the
reconstructed OpFlash with the BNB bunches, allowing SBND to develop
sophisticated selection criteria and reject cosmic interactions happening
between the beam bunches.

[width=.99]./Figures/BNBReco/BNBReco1.pdf

Figure : True neutrino arrival time distributions at the SBND upstream wall
(dashed-grey) and inside the active volume (solid-blue), and reconstructed
neutrino interaction time after ToF correction (black). All the times are
referred to the proton on target interaction time.

However, there are two sources of delays that cause the interaction times of
neutrinos to differ from that of the proton extraction time structure. One is
due to the decay time of their parent hadrons. To quantify this effect, Figure
8-Left shows the delay of the neutrinos arriving to the frontmost wall of the
detector relative to the proton bunch delivery time [PhysRevD.79.072002]. We
see how the cumulative delays caused by this effect are below 2 ns. The second
source of delay is due to neutrinos interacting along the 5 m length of SBND’s
active volume in the beam direction. Therefore, there will be an additional
delay that depends on where the neutrino interacts in the TPC. This additional
time ranges from 0 to about 17 ns, for neutrinos interacting in the upstream
or the downstream wall of the detector respectively. As can be seen in Figure
8-Right, proper reconstruction of the interaction point along the detector
length allows to resolve the individual neutrino bunches. Figure 8 illustrates
how the beam time structure degrades for the neutrino interaction times. This
undesired effect could be minimised by correcting for the position of the
neutrino interaction in the beam direction (Z). The millimetre-level particle
tracking capability of the LArTPC technology will enable this correction in a
very precise manner [MicroBooNE:2023ldj]. However, in this work we will use
the method described in section 7 to demonstrate the PDS-only performance
reconstructing the Z coordinate. The result after this correction is also
shown in Figure 8. This demonstrates how using only the scintillation light
signals recorded by the PMTs in SBND, we are able to precisely correct the
different sources of delay to the neutrino interaction time and recover the
BNB time structure.

[width=1.]./Figures/BNBReco/BNBStats4.pdf

Figure : Neutrino interaction times of the BNB bunches merged into a single
peak after applying all the corrections described in the text.

Finally, to quantify the overall timing resolution we have fit with a Gaussian
function all the 81 bunches merged in one single peak. As can be seen in
Figure 8, we get an average bias of 1.45 ns with a standard deviation of 2.34
ns. If we subtract from this width the intrinsic BNB bunch width
$\langle\sigma_{\text}{BNB}\rangle$=1.3 ns, we end up with a global timing
resolution of 2 ns, as expected.

##  9 Conclusions

SBND has the most advanced PDS to date installed in a neutrino LArTPC. It
integrates passive elements with a high density of detectors using two
different technologies: 8-inch cryogenic PMTs and a variety of new X-ARAPUCA
devices. Both systems mix WLS-coated and uncoated units to be sensitive to the
direct and reflected light components available in SBND. This PDS design
increases the LY and makes it more uniform across the whole detector (by more
than doubling the amount of light detected in the region furthest away from
the plane of detection, thanks to the addition of the reflected light
component), with the aim of improving its performance and extending its use in
physics analysis. The experiment employs an efficient and accurate optical
simulation, overcoming the challenges that this entails mainly due to the
prolific nature of liquid argon as a scintillator. The simulation model is
hybrid, combining two photon propagation approaches to simulate scintillation
light in the entire argon volume and for our two different light components,
with high accuracy in both the number of detected photons and their arrival
times. SBND has employed a deconvolution procedure to undo the effects of AC-
coupling of our detectors. We have demonstrated that with this procedure we
are able to reconstruct the number of PEs for BNB events with a resolution
better than 4% for both systems of PMTs and X-ARAPUCAs. This, together with
the high LY opens the door to improving the accuracy of calorimetric energy
reconstruction by incorporating the information provided by our PDS signals.
Future work will explore the combination of PDS and TPC systems for this
purpose. In addition, the novel ability to distinguish between direct and
reflected light components allows SBND to reconstruct the average drift
coordinate where the energy depositions occur, with a resolution between
$10-15$ cm ($10-20$ cm) for the PMT (X-ARAPUCA) system, and allows a 3D
reconstruction of the average position of the interactions using only
scintillation light. This possibility has, for instance, the potential to
improve our signal vs background tagging, which can be challenging in near-
surface detectors like SBND. It could also enable 3D-based readout of parts of
the detector. Finally, we have shown that with the reconstruction algorithms
developed in this work, the SBND PMT system, which is the system used to
construct trigger signals, can reconstruct the time of the events with a
resolution of the order of 2 ns. This result, together with the fact that the
SBND PDS can accurately reconstruct the positions where particles interact,
makes it possible to correct for the neutrinos’ ToF inside the detector (from
the Z-coordinate reconstruction) and the photons ToF until they are recorded
(from the drift-coordinate reconstruction). This allows us to correlate the
neutrino interaction times with the times of the proton delivery that generate
the neutrino beam, and therefore to identify events occurring within or
outside the BNB time structure. This event-by-event capability has, for
example, applications in searches for long-lived massive particles as
predicted in some beyond Standard Model physics models, or in rejecting
cosmogenic events in coincidence with the beam. The SBND Collaboration
acknowledges the generous support of the following organisations: the U.S.
Department of Energy, Office of Science, Office of High Energy Physics; the
U.S. National Science Foundation; the Science and Technology Facilities
Council (STFC), part of United Kingdom Research and Innovation, The Royal
Society of the United Kingdom, and the UK Research and Innovation (UKRI)
Future Leaders Fellowship; the Swiss National Science Foundation; the Spanish
Ministerio de Ciencia e Innovación (MICIN/ AEI/ 10.13039/ 501100011033) under
grants No PRE2019-090468, PID2019-104676GB-C31 & C32, RYC2022-036471-I, and
Comunidad de Madrid (2019-T2/TIC-13649); the European Union’s Horizon 2020
research and innovation programme under GA no 101004761 and the Marie
Sklodowska - Curie grant agreements No 822185 and 892933; the São Paulo
Research Foundation 1098 (FAPESP), the National Council of Scientific and
Technological Development (CNPq) and Ministry of Science, Technology &
Innovations-MCTI of Brazil. We acknowledge Los Alamos National Laboratory for
LDRD funding. SBND is an experiment at 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.