aainstitutetext: Universidad Nacional Autónoma de México, Distrito Federal,
Méxicobbinstitutetext: Facultad de Ingeniería, Universidad Nacional de
Asunción, Paraguayccinstitutetext: Centro Atómico Bariloche and Instituto
Balseiro, Comisión Nacional de Energía Atómica (CNEA), Consejo Nacional de
Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional de Cuyo
(UNCUYO), San Carlos de Bariloche, Argentinaddinstitutetext: Instituto de
Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ,
Brazileeinstitutetext: Fermi National Accelerator Laboratory, Batavia, IL,
United Statesffinstitutetext: Eletronuclear, Angra dos Reis, RJ,
Brazilgginstitutetext: Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro,
RJ, Brasilhhinstitutetext: Centro Federal de Educação Tecnológica Celso Suckow
da Fonseca, Angra dos Reis, RJ, Braziliiinstitutetext: Instituto de Inv. en
Ing. Eléctrica “Alfredo Desages” (IIIE), Dpto. de Ing. Eléctrica y de
Computadoras, CONICET and Universidad Nacional del Sur (UNS), Bahía Blanca,
Argentinajjinstitutetext: Departamento de Física, FCEN, Universidad de Buenos
Aires, Buenos Aires, Argentinakkinstitutetext: Instituto Dan Beninson,
Universidad Nacional de San Martín (UNSAM), CNEA and CONICET,
Argentinallinstitutetext: Universität Zürich Physik Institut, Zurich,
Switzerlandmminstitutetext: Departamento de Física, FCEN, Universidad de
Buenos Aires and IFIBA, CONICET, Buenos Aires, Argentinanninstitutetext:
International Center for Advanced Studies & Instituto de Ciencias Físicas,
ECyT-UNSAM and CONICET, Buenos Aires, Argentina

# Search for coherent elastic neutrino-nucleus scattering at a nuclear reactor
with CONNIE 2019 data

Alexis Aguilar-Arevalo b Javier Bernal c Xavier Bertou d,n Carla Bonifazi e
Gustavo Cancelo d Victor G. P. B. de Carvalho a Brenda A. Cervantes-Vergara b
Claudio Chavez f Gustavo Coelho Corrêa a Juan C. D’Olivo g João C. dos Anjos e
Juan Estrada h Aldo R. Fernandes Neto e,i Guillermo Fernandez Moroni d Ana
Foguel e Richard Ford j Julián Gasanego Barbuscio b Juan Gonzalez Cuevas e
Susana Hernandez k Federico Izraelevitch l Ben Kilminster e Kevin Kuk g Herman
P. Lima Jr g,n Martin Makler a Mauricio Martinez Montero d Larissa Helena
Mendes b Jorge Molina g Philipe Mota d,1 Irina Nasteva,111Corresponding
author. i Eduardo Paolini m Dario Rodrigues a Y. Sarkis c,e Miguel Sofo Haro b
Diego Stalder e Javier Tiffenberg<EMAIL_ADDRESS>
###### Abstract

The Coherent Neutrino-Nucleus Interaction Experiment (CONNIE) is taking data
at the Angra 2 nuclear reactor with the aim of detecting the coherent elastic
scattering of reactor antineutrinos with silicon nuclei using charge-coupled
devices (CCDs). In 2019 the experiment operated with a hardware binning
applied to the readout stage, leading to lower levels of readout noise and
improving the detection threshold down to 50 eV. The results of the analysis
of 2019 data are reported here, corresponding to the detector array of 8 CCDs
with a fiducial mass of 36.2 g and a total exposure of 2.2 kg-days. The
difference between the reactor-on and reactor-off spectra shows no excess at
low energies and yields upper limits at 95% confidence level for the neutrino
interaction rates. In the lowest-energy range, $50-180$ eV, the expected limit
stands at 34 (39) times the standard model prediction, while the observed
limit is 66 (75) times the standard model prediction with Sarkis (Chavarria)
quenching factors.

##  1 Introduction

Coherent elastic neutrino-nucleus scattering (CE$\nu$NS) is a standard model
process in which a neutrino scatters elastically off a nucleus in a coherent
way Freedman:1973yd . The enhanced cross-section due to the neutrino
interaction with the entire nucleus makes this process detectable with smaller
detectors, as long as they have a low energy threshold for nuclear recoils.
CE$\nu$NS provides a new window into the low-energy neutrino sector and the
interest in its detection has been growing as a potential probe for new
physics Papoulias:2019 .

The CE$\nu$NS differential cross-section for the coherent elastic scattering
of antineutrinos off a nucleus at rest is

$\frac{d\sigma_{SM}}{dE_{R}}\left(E_{\bar{\nu}_{e}}\right)=\frac{G_{F}^{2}}{8\pi}Q_{W}^{2}\left[2-\frac{2E_{R}}{E_{\bar{\nu}_{e}}}+\left(\frac{E_{R}}{E_{\bar{\nu}_{e}}}\right)^{2}-\frac{ME_{R}}{E_{\bar{\nu}_{e}}^{2}}\right]M|F(q)|^{2}\,,$
(1)

with the weak charge

$Q_{W}=N-(1-4\sin^{2}\theta_{W})Z\,,$ (2)

where $Z$($N$) is the number of protons (neutrons), $M$ the mass of the
nucleus, $G_{F}$ the Fermi coupling constant, $E_{\bar{\nu}_{e}}$ the
antineutrino energy, $E_{R}$ the nuclear recoil energy, and $F(q)$ is the
nuclear form factor.

There are currently two approaches for the observation of CE$\nu$NS. The
first, which uses a stopped pion beam generating neutrinos with energies of
$\sim$20 MeV, presents compelling advantages for the detection of coherent
scattering. The neutrinos are produced at the highest energies where the
coherence of the process is maintained, giving the largest possible nuclear
recoil energies for CE$\nu$NS. In addition, the timing structure of the beam
allows for strong background suppression. The COHERENT Collaboration has
successfully observed CE$\nu$NS for the first time from a stopped pion beam at
SNS using a CsI[Na] detector Coherent , and more recently with a LAr detector
COHERENT:2020iec .

The second approach is based on the MeV-energy neutrinos produced in nuclear
reactors TEXONO:2005fmk . These lower-energy neutrinos generate smaller
recoils in the detector material compared to stopped pion beams, and in this
case there is no timing information that could be used to suppress background
in the case of fast detectors. Also, because the reactor neutrino spectrum
peaks at low energies ($\sim$1 MeV), the neutrino flux that can be accessed
depends on lowering the detection threshold. The detection of coherent
scattering from reactor neutrinos is experimentally more challenging but has
some unique features as a probe for new physics in the low-energy neutrino
sector. The lower momentum exchange in CE$\nu$NS from reactor neutrinos
eliminates the dependence on the nuclear form factor, with $F(q)\sim 1$ in Eq.
1, and enhances the sensitivity to potential effects predicted in new physics
scenarios, such as an anomalous magnetic moment MagneticMoment  or millicharge
Millicharge  of the neutrino, light sterile neutrinos Kosmas:2017zbh , weak
mixing angle WeakAngle ; WeakMixingAngle , and non-standard interactions of
neutrinos such as light mediators Proceedings:2019qno ; Farzan:scalar .

Several experiments are either running or in a preparation stage with the aim
of observing for the first time CE$\nu$NS with reactor neutrinos CONUS:2020skt
; MINER ; TEXONO:2005fmk ; RED:2012hpm . The Coherent Neutrino-Nucleus
Interaction Experiment (CONNIE) has so far been the most sensitive at low
energies. Operating with a detector of charge-coupled devices (CCDs) at the
Angra 2 nuclear reactor in Brazil, CONNIE has demonstrated with the results of
its analysis of 2016–2018 data connie:2019  the sensitivity to new physics by
establishing competitive limits for light mediators at the lowest mediator
masses connie:LM . In this work we present the results of the CONNIE
experiment based on data collected in 2019, obtained with a lower energy
threshold thanks to a different readout strategy, in which a hardware binning
in one direction increases the signal-to-noise ratio. In addition, several new
calibration tools and analysis methods were developed to quantify and improve
the detector performance.

This paper is organised as follows. Section 2 describes the CONNIE experiment,
CCD readout strategy and method. Section 3 presents the calibration and
performance of the experiment. Backgrounds are discussed in Section 4. The
selection of the neutrino candidate events is presented in Section 5. The
search for CE$\nu$NS and the measurement results are presented in Section 6,
while the conclusions and outlook are discussed in Section 7.

##  2 The CONNIE experiment and data set

The CONNIE detector consists of 12 fully depleted high-resistivity silicon
scientific CCDs, mounted horizontally in a tower inside a copper cold box,
surrounded by passive shielding. Each CCD sensor is an array of $4120\times
4120$ square pixels of $15\times 15~{}\mu$m2 area each and 675 $\mu$m
thickness, with a mass of 6.0 g. The CCDs operate at cryogenic temperatures
and are contained inside a vacuum vessel, shielded with 15 cm of lead,
sandwiched between two layers of 30 cm of polyethylene. The CONNIE experiment
is operating since 2016 at a distance of about 30 m from the core of the 3.95
GW thermal power Angra 2 nuclear reactor, in a shipping container placed just
outside its containment dome. A more detailed technical description of the
experiment, image processing and event extraction is presented in Refs.
connie:2019 ; connie:2016 . Here we summarise the main features and focus on
the new readout method for the sensors.

A search for CE$\nu$NS events is performed by comparing the energy spectra of
data between the periods with the reactor operating at full power (reactor on)
and during the scheduled shutdown of about 1 in every 13 months (reactor off).
The current data set covers 31.85 days of operation with the reactor on and
28.25 days with the reactor off, collected in 2019 with 8 CCDs that show
stable operation and good quality data, while the remaining 4 CCDs were
excluded from the analysis due to high noise or charge transfer inefficiency.
The experiment active fiducial mass after acceptance effects from geometrical
and event size cuts (as detailed in Section 6) is 36.24 g, giving a total
exposure of 2.2 kg-days.

###  2.1 CCD operation and readout

The CONNIE CCD sensors were developed by the experiment in collaboration with
the LBNL Micro Systems Labs LBNLMSL , as a spin-off from the fully depleted
thick detectors designed for astronomical instruments such as DECam
DES:2015wtr  and DESI DESI:2018kpn . The CCD thickness was increased to 675
$\mu$m, making them the thickest CCDs ever fabricated. The CCDs are mounted
horizontally in a copper box, which is kept inside a copper vacuum vessel
($10^{-7}$ torr). The sensors orientation is such that the pixel gates are on
their front (or top) side, and the substrate depletion voltage of 70 V is
applied to the back (bottom) side. In order to reduce the thermally-generated
dark current in the silicon, the sensors are cooled to temperatures below 100
K by means of a closed-cycle helium cryocooler.

Each CCDs is read out sequentially, by moving the charge of each pixel towards
one corner of the sensor where it is read out via a single output amplifier.
More pixel values are read beyond the physical extent of the CCD, forming the
so-called overscan region, used to monitor the baseline of the readout
electronics. At the same clock rate as the readout amplifier, a second output
of each sensor is read out via a second amplifier, without any charge from the
array, in order to generate a pure noise image used to monitor the correlated
noise of the system. The image formed by the array of charges is processed by
subtracting the mean value of the overscan image, then subtracting the master
bias image formed from the median of a large number (60) of images, and
subtracting the correlated noise obtained from the second amplifier readout.
More details on the image processing can be found in Ref. connie:2019 .

###  2.2 CCD readout mode with hardware binning

A new hardware binning mode of data taking was implemented in 2019, which is
described as follows. By controlling the voltages applied to the phases of the
three pixel gates called vertical clocks, each pixel develops a potential well
that stores charges. The readout of the CCD is done sequentially, one pixel at
a time, by phasing the vertical clocks in an alternate sequence, the charge in
the two dimensional array is first moved into a special register called the
horizontal register. Since the vertical clocks move the charge towards the
horizontal register, that register receives the charge from the last row in
the array. The entire row of pixels is read out by shifting the charge in the
horizontal register serially through the amplifier by phasing another set of
three voltages, the horizontal clocks. The horizontal register can also be
used as an accumulator, a mode of acquisition that we call hardware binning.
The vertical clocks in the array can be applied cyclically to move charges
from subsequent pixels into the horizontal register. Each pixel in the
horizontal register then accumulates the summed charge for as long as its
capacity does not overflow. At the end of the hardware binning sequence the
horizontal register is read out.

Figure 1: A diagram of hardware binning, in which the charges of 5 vertical
pixels are added up and read together (left), and a part of a standard image
(middle) compared to one taken with the hardware binning (right). The binned
image appears compressed in the vertical direction and the full image has 5
times fewer pixels in this direction.

The binning technique is used to minimise the readout noise, which is added by
the readout amplifier. Since the charge of $N$ pixels is added up before
reading, the effective readout noise per pixel is $N$ times smaller. The price
paid for using binning is loss of pixel resolution in the direction of the
binning, as each pixel represents a silicon area $N$ times larger in size.
Different binning schemes and image exposure times were studied, in order to
have low readout noise while also keeping a low pixel occupancy due to
background. The optimal readout strategy was found to be with a binning of
$N=5$ in the vertical direction and exposure times of 1 hour per image. Pixels
therefore have an effective size of 15 $\mu$m by 75 $\mu$m (see Fig. 1).

###  2.3 Strategy to search for CE$\nu$NS

Several new tools and calibration techniques have been employed in the
analysis in this work. They were developed using the reactor-off data that
provide only the radioactive and cosmogenic background and sensor performance
information, without any neutrino events expected. A blind analysis was
performed, without looking at reactor-on data, in order not to bias the
selection with respect to a possible signal.

The calibration techniques and selection tools were developed using a
combination of reactor-off data and simulations. Energy calibration is
performed using fluorescence peaks in the data (Section 3.1), and depth
calibration is derived from the width of muon tracks (Section 3.2). The
background data sample was then studied in the low-energy range (below around
1 keV), where neutrino interactions are expected, and at higher energies. On-
chip noise sources were quantified in the reactor-off data and a study of fake
events that can mimic a neutrino signal at very low energies was conducted.
The evaluation of the uncertainties and contributions of spurious events is
critical for the sensitivity to low-energy events in the region of interest
for reactor neutrinos, and special care is therefore needed. The event size
information was found to be a very efficient way to remove defective tracks
that do not fit into a single hit in the CCD (Section 4.2).

After this, the neutrino selection criteria (Section 5) are defined using
samples of simulated neutrino events, as in the previous analysis connie:2019
. Neutrino scattering events are generated with a uniform probability in the
active volume and a uniform distribution in energy, and are then added to raw
images from the reactor-off data set and reconstructed in the same way as
data. Consistency checks are applied to the events passing the selection
criteria.

Finally, the reactor-on data sample is unblinded. The rates of the high-energy
background events are compared between the reactor-on and off periods to check
detector stability. The selection criteria determined previously are applied
to the low-energy events in the reactor-on period and sanity checks are again
performed on these data. Then, in order to compute the neutrino rate, the
total event rate during the shutdown period of the detector is subtracted from
the total event rate measured with the reactor running (Section 6).

##  3 Detector calibration and performance

The techniques and tools to calibrate the sensor and to measure key
performance parameters were updated with respect to the previous analysis of
2016–2018 data connie:2019 . The following subsections detail these new tools
and their use in the 2019 data analysis.

###  3.1 Gain calibration

Figure 2: (Left) Energy spectrum from 100 images taken from the edge regions
of one CCD, superimposed with the fit to the main fluorescence x-ray peaks.
(Right) Time evolution of the three x-ray peak positions of the same CCD
during the data taking period.

The energy, or gain, calibration of the CCDs is based on the emission of
copper and silicon fluorescence x-rays from excitation of cosmogenic origin or
due to the natural radioactivity of the surrounding materials. Because of the
silicon CCD substrates and copper structures surrounding them, the
$\rm{Cu}_{\alpha}$ (8.047 keV), $\rm{Cu}_{\beta}$ (8.905 keV) and Si (1.740
keV) emissions are readily observed as peaks in the energy spectrum. The
calibration procedure was expanded with respect to the previous analysis to
include information from all three peaks, and was applied to samples of 100
consecutive images, corresponding to around four days of data taking, for each
CCD. The peak positions are determined from a fit to the energy spectrum of
events from the edges of the CCD, where most fluorescence events lie,
described by a function that is the sum of three Gaussians for the peaks and a
constant background term. An example energy spectrum with the fit overlaid is
shown in Fig. 2. The Gaussian means, width of the $\rm{Cu}_{\alpha}$ peak, and
all normalisations are free to vary in the fit, while the widths of the other
two Gaussians are determined from the one of the $\rm{Cu}_{\alpha}$ peak,
assuming a constant Fano factor and Poisson charge carrier distributions.

To obtain the gain, the peak positions are fitted with a second-order
polynomial with a zero constant term, in which the linear term is the
reciprocal of the gain and the small quadratic term reflects possible non-
linearity. The maximum non-linearity for all CCDs was found to be smaller than
1% and non-linearity effects were therefore discarded as negligible within the
low-energy range considered. The validity of using 100 images was cross-
checked by applying the calibration to smaller groups of images and showed
variations compatible with the limited sample sizes. The gain stability is
also shown in Fig. 2 for one CCD and the whole data taking period. All CCD
gains are found to be stable with time.

###  3.2 Size versus depth calibration

Figure 3: Image of a y-axis muon. For details see text.

The depth calibration is essential to determine the detection efficiency and
to identify fake events that may mimic neutrino interactions. The calibration
curve relates the lateral spread (or size) of low-energy events with their
interaction depth in the CCD silicon substrate. Although the holes are
initially produced inside the volume of a single pixel, while they drift to
the collection wells of the pixels they diffuse and by the time they reach the
potential well on the front, they spread over a few pixels haro2020studies .
Holes produced close to the CCD back side have more time to diffuse before
being collected, and therefore, they spread more than the holes produced close
to the pixel collection wells. Given the fact that each pixel is affected by
readout noise, those events with the holes distributed over a few pixels
become less likely to be detected than events with only one pixel once a
threshold is applied to extract them, due to their lower signal-to-noise
ratio.

Figure 4: Data points and curve that relates the spread of the events with
their interaction depth for one of the CCDs. The fitted function
$\sqrt{\alpha\ln(1-\beta z)}$, where $z$ is the depth in microns, is derived
from the charge transport physics in the CCD haro2020studies .

Muon tracks are used to determine the calibration curve. Cosmic muons easily
pass through the whole detector depth, leaving a straight track. The electric
field in the CCD volume causes the holes generated to drift perpendicularly to
its front side, in the direction of the pixel collection wells. Therefore, the
muon event observed in the image is the projection of the muon track in the
plane of the CCD front-side surface. Figure 3 shows an event of a so-called
y-axis muon, whose track is perpendicular to the CCD horizontal register and
is in the direction of the vertical pixel binning. Highlighted in the event
image is a one-pixel slice, which includes one pixel in the y-direction
(corresponding to five CCD pixels after the binning, or 75 $\mu$m) and all the
event pixels in the x-direction.

Figure 3 also shows a plot of the charge of each muon slice and its lateral
spread. The lateral spread is Gaussian with variance that depends on the time
that free carriers have to diffuse laterally before being collected by the
potential wells at the front of the sensor haro2020studies . This time is
proportional to the depth of the ionisation location. The thinner side of the
muon track corresponds to holes that were produced close to the CCD front
side, and the thicker side, to the holes produced close to the back side. Due
to the straight trajectory of the muon, simple trigonometry can be used to
assign a depth to the lateral spread of each muon slice and compose a
calibration curve.

The spread in each muon slice was estimated by an unbiased maximum likelihood
estimator described in haro2020studies . The resulting calibration curves,
obtained separately for each CCD, show smaller spread at a given depth than in
the previous CONNIE study connie:2019 . Figure 4 shows the resulting curve
obtained for one CCD. These size-to-depth calibration curves are used to
estimate the neutrino detection efficiency for each CCD. It should be
mentioned that the event size also depends on the energy deposit per pixel and
that the muon curves give therefore a conservative estimate for low-energy
deposits from neutrino interactions, as the muon energy deposits are more
spread out due to the charge repulsion effect, compared with the small energy
deposits by neutrinos that undergo diffusion only haro2020studies .

###  3.3 Readout noise and single electron event stability

Figure 5:  Readout noise (x-axis, in e-) and single electron event levels
(y-axis, in e-/h/pix) for each CCD in reactor off and on datasets.

The main contribution to the pixel charge uncertainty is given by the readout
noise (RN) added by the output amplifiers and by the spurious charge
accumulated in the pixels (due to spontaneous thermal emission or dark
current, Cherenkov and recombination photons du2020sources ), the so-called
single electron events (SEE) Barak:2021crb . The two effects are independent
but are present in the active region of the CCD. To decouple the two, the RN
is extracted directly from the overscan (unexposed) region by fitting a
Gaussian function to the charge distribution of the pixels. The SEE is modeled
by a Poisson distribution and is estimated using the pixels without events in
the active region. For this, the combined probability distribution
$f(E)=P(q;\lambda)*G(E;\sigma,\mu)$ is computed, given by:

$f(E)=P(q;\lambda)*G(E;\sigma,\mu)=\frac{e^{-\lambda}}{\sqrt{2\pi}\sigma}\sum_{q=0}\frac{\lambda^{q}}{q!}\exp\left(-\frac{(E-(\mu+gq))^{2}}{2\sigma^{2}}\right)\,,$
(3)

where $E$ is the measured pixel charge value in analog-to-digital units (ADU),
$q$ runs over all possible numbers of electrons from the thermal process with
a Poisson parameter $\lambda$, $g$ is the gain in ADU/e- and $\sigma$ is the
RN extracted by the Gaussian fit in the overscan region.

Both quantities are continuously monitored for all the acquired images. Figure
5 shows the measured SEE and RN distributions for each CCD in the different
reactor periods. The stability of the values between reactor on and off data
is an indication that the sensors were running with similar performance in
both periods.

##  4 Background studies

###  4.1 Muon and $\rm{Cu}_{\alpha}$ x-ray rate stability

Fluorescence x-rays are used to measure the stability of the natural
radioactivity background rate and detector gain during reactor on and off
operation. For this purpose we monitor the intensity of the $\rm{Cu}_{\alpha}$
peak, the most prominent background peak. A Gaussian function for the peak
plus a constant background is fitted to the data spectra, split into groups of
twenty consecutive images. The position of the copper peak (gain), amplitude
(rate) and underlying flat background rate are checked for stability for all
CCDs, and the gain and rates are compared between the reactor on and off
periods. The chi-square per degree of freedom is computed from the sum over
the CCDs of the differences between the values divided by their total
uncertainty,
$\chi^{2}/n=\sum(\frac{(\mu_{ON}-\mu_{OFF})}{\sigma\mu_{tot}})^{2}/n$ with
$n=8$, obtaining values close to one, $\chi^{2}_{gain}/n=0.98$,
$\chi^{2}_{peak-rate}/n=1.03$ and $\chi^{2}_{bkg-rate}/n=1.07$.

The muon rate is also checked for stability in the data taking period. Muons
are extracted from the datasets with a Deep Convolutional Neural Network
machine learning algorithm tuned for the specific hardware binned images of
the 2019 data taking method. The algorithm was found to have a very high
purity (above 96%) and the resulting muon rates were found to be stationary
using a Dickey-Fuller test dickey_fuller .

###  4.2 Low-energy region studies

Figure 6: A two-dimensional histogram of the energy and size of low-energy
events in reactor-off data. The horizontal bands are artifacts of the
quantisation effect in the size fitting algorithm.

Two new background sources were identified in the data, that have a large
impact on the event selection process in the region of interest for CE$\nu$NS
interactions. Figure 6 shows a two-dimensional histogram of the size and
energy of the events after selecting an area of good pixels in the output
images (excluding the edges of the sensor and any bright columns, as described
in Section 5). To reconstruct the size and energy of the events, similar
techniques are applied as in the previous study connie:2019 .

Three densely populated regions are highlighted in the plot. Around 1.7 keV
there are two clusters compatible with silicon x-rays produced by fluorescence
in the adjacent materials and entering by the front and back of the sensor.
Since the attenuation depth of the photons at these energies is a few microns,
most interactions occur at the very front and back of the sensor as depicted
in the plot. There are two extra unexpected excesses of events: one called
partial charge collection (PCC) events, small one-pixel events that are
present in the full energy range from 0 to 2 keV; and another source called
large low-energy (LLE) events, with sizes greater than 1.2 pixels and energies
below 0.4 keV. Both sources have a great impact on the sensitivity to neutrino
interactions at low energies. The following sections describe the processes
that produce these events and the selection criteria to reject them.

####  4.2.1 Large low-energy events

LLE events can mimic the expected neutrino interactions, but their size is
greater than that of expected events from the bulk of the sensor. Figure 4
shows that the maximum size for a physics induced event in the CCD is
approximately 1.1 pixels. Two different mechanisms have been identified that
may produce LLE events, based on studies of identifying their characteristic
signatures in the CCD images.

The first and main type of LLE events come from the tails of very energetic
events. Very large ionisation packets can generate tails when the charge of
the pixels is transferred in the column direction. These tails are observed to
span up to a few hundred pixels. This pattern does not follow the charge
transfer inefficiency process observed in CCDs janesick2001scientific . At the
very end of the tail, where the charge is comparable to the readout noise, the
event extraction routine might identify isolated regions of low-energy pixels.
This kind of event can be rejected by either looking at its proximity to very
energetic events or by making a selection cut based on its size.

A secondary source of LLE events are charge depositions in the inactive volume
of the sensor, in which some of the carriers can diffuse to the active region.
If these depositions are produced close to the auxiliary horizontal register
during the readout of the sensor, they can be erroneously seen as true
depositions in the active region. Since these carriers are collected by a
single line in the sensor, the final event shows a distinctive one-dimensional
shape, generally with a broad distribution due to the diffusion in the
inactive volume. These events can also be rejected by setting a maximum
allowable size for neutrino-induced events.

In this analysis, both types of LLE events are rejected by requiring a maximum
event size, defined in Section 5.

####  4.2.2 Events from the partial charge collection layer

Figure 7: Size distribution of background events with energies 0.1 and 0.2 keV
from reactor-off data (blue data points), compared with simulated
distributions for events from the front (black), bulk (cyan) and back (pink)
regions. The red line is the sum of the simulated distributions. For events
with size smaller than 0.2 pixels, most of the event charge is collected by a
single pixel, so the reconstruction algorithm has little information for the
size estimation and gives larger errors. This effect causes the varying
structured pattern of the distributions in that region.

Recent studies fernandezmoroni2020charge  have shown that extra fake events at
low energy can be produced by a partial charge collection (PCC) layer in the
bulk of the CCD. The PCC layer is approximately 4 $\mu$m thick at the back
side of the sensor and has a high dopant concentration that prevents its
depletion with the external substrate voltage. Free carriers are more likely
to recombine in this volume before they can diffuse to the depleted silicon in
the bulk of the sensor and finally be collected by the pixels. By this
process, large charge depositions in this region by high-energy interactions
can be seen as low-energy interactions if most of the free carriers recombine
and only a small fraction reach the bulk of the sensor. Since the PCC layer is
in the back of the sensor, events from it have large width, as observed in
Fig. 6, which shows a clear excess of events with size close to 1 pixel.

This effect was investigated with simulations. Figure 7 shows the size
distribution of events with energy between 0.1 and 0.2 keV collected during
reactor-off operation in 2019, together with the theoretical distributions
from events interacting in the very front of the sensor, uniformly distributed
in the bulk, and in the back. These distributions are obtained by simulating
low-energy interactions and transporting the free electrons until they are
trapped by the pixel storage well. There is a good agreement between the
summed contributions and the measured points. Although there is no preference
in the incoming flux from the front and back at low energy, the fit reports
that 10% of events come from the front, 54% from the bulk, and 36% from the
back, showing a clear excess from the back side. As in the LLE case, most of
these events can be rejected in the data analysis by setting a maximum
allowable size for neutrino events.

##  5 Selection of neutrino candidate events

The criteria applied to data to select neutrino candidates fall into three
categories: temporal, geometrical and morphological selection. As a temporal
selection, the images that show outlier values for the on-chip noise sources
are removed. Any image with RN or SEE value 5 standard deviations above the
measured mean values was excluded from further analysis. To be conservative,
we exclude all the images obtained at the same time interval as an outlier.
This process removes less than 0.1% of the data sample under analysis.

The geometrical criteria are based on the selection of good pixel regions in
the sensors, and exclude all events from the edges. The electric field in the
volume of pixels in the edge of the sensor is different from that of pixels in
the center of the array due to the different border condition
janesick2001scientific . This may change the effective volume size of those
cells and therefore the charge collection efficiency and the morphology of the
measured events. Events within 140 columns and 10 rows of the edge of the
sensor were excluded from further analysis in all images. Moreover, CCDs can
show defects in the silicon that appear as bright columns
janesick2001scientific , in a pattern that can be different in each sensor.
The positions of these columns are identified and no events closer than 10
pixels from them are considered.

Figure 8: Cumulative distribution functions of reactor-on data and simulations
for the four statistics defined in the test. The p-values are also shown.

The expected shape in the output images from a neutrino interaction is studied
using the size calibration in Section 3.2. Since the primary ionisation volume
from the neutrino scattering is expected to be much smaller than the pixel
size, the final shape of the event is defined by posterior diffusion of the
free carriers in the silicon. The calibration of this process allows to
simulate events and optimise the selection criteria based on the morphology of
the cluster. To reject the fake events produced by the on-chip noise sources,
a cut on the energy of the core of the event ($E_{0}$) was applied,
corresponding to about 4–5 times the RN, depending on the CCD. Only events
with $E_{0}>45$ eV are considered in the current analysis. This threshold was
optimised from simulation of the on-chip noise sources to keep the rate of
fake events below 10% of the level of events measured during reactor-off
operation, at low energies where the neutrino signal is expected. The second
cut is based on the size of the event, which is required to be less than 0.95
pixels wide. This selection completely rejects the LLE background sources and
maximises the signal-to-noise ratio for the events in the PCC layer.

Figure 9: Time evolution of p-values for groups of ten images.

The spatial uniformity expected for neutrino events is then used to test the
consistency of the data. Four distributions of event variables are studied:
the distance to the first CCD row, the distance to the first column, the
distance to the first pixel, and the distance between pairs of events. Figure
8 shows the distributions from data compared to the simulated samples used in
the efficiency calculation, which were generated under the scenario in which
the spatial distribution of neutrino events is uniform. A two-sample
Kolmogorov-Smirnov test was applied to each pair of simulated and data
distributions to determine the p-value associated with the null hypothesis
that both samples are drawn from the same distribution. The four p-values are
much larger than 0.05, the usual significance chosen to accept the null
hypothesis, confirming the spatial distribution of data is uniform.

The same test was also applied to study the data distributions as a function
of time, grouping them into sets of ten images, as shown in Fig. 9. The
resulting p-values from the four considered distributions do not exhibit any
trend with time. The fraction of the values that are smaller than 0.05 is
around 5%, corresponding to a uniformly distributed random variable.

##  6 Reactor on and off spectra and CEvNS sensitivity

The result of the analysis is a measurement of the neutrino interaction rate
in bins of energy, which is then compared to the expected neutrino rate. In
order to obtain the expected neutrino rates at the detector, the neutrino
interaction rates predicted by the standard model are corrected for the
effects of detector acceptance, selection efficiency and resolution, obtained
from simulation, as well as for the quenching factor that relates the amount
of ionisation measured to the nuclear recoil energy in silicon. The events are
simulated following a uniform random distribution in the active volume, as
expected from neutrino interactions and following the same procedure as in
Ref. connie:2019 .

###  6.1 Detector acceptance and selection efficiency

The expected neutrino detection rate is determined as a function of the
measured ionisation energy $E$ by applying detection effects to the neutrino
rate as a function of the ionisation energy. It is computed by convolving this
rate, corrected by the detector acceptance due to event extraction, with the
Gaussian detector response and applying the efficiency of the selection cuts:

$\frac{{\rm d}R}{{\rm d}E}=\varepsilon(E)\int_{-\infty}^{+\infty}{\rm d}E_{\rm
I}G\left(E_{\rm I}-E-\mu(E_{\rm I});\sigma(E_{\rm
I})\right){\mathcal{A}}(E_{\rm I})\frac{{\rm d}R}{{\rm d}E_{\rm I}}\,.$ (4)

The acceptance, ${\mathcal{A}}(E_{\rm I})$, takes into account the ionisation
energies, $E_{\rm I}$, that can be reconstructed by the extraction procedure,
and is computed by simulating neutrino events on top of the reactor-off images
and putting them through the full processing chain. It represents the fraction
of neutrino events that can be extracted from the image for a given ionisation
energy. The acceptance is parameterised by the function:

${\mathcal{A}}(E_{\rm I})={\mathcal{A}}_{\rm
sat}\left(\frac{1}{2}\tanh\frac{E_{\rm
I}-{\mathcal{A}}_{0}}{{\mathcal{A}}_{\sigma}}+\frac{1}{2}\right)^{10}\,,$ (5)

and the parameters are extracted from fits to the simulated events. Table 1
shows the parameter values obtained for each CCD, while the acceptance
distributions for the CCDs with highest and lowest acceptances with the
overlaid fits are given in Fig. 10. The parameter ${\mathcal{A}}_{\rm sat}$
represents the maximum reconstruction acceptance of 87%, which is reached at
ionisation energies around 140 eV and 200 eV for the most and the least
efficient CCDs, respectively. This is a significant improvement at low
energies compared to the previous analysis connie:2019 , in which the maximum
was reached around 500 eV. The improvement in reconstruction acceptance at low
energies is a result of the higher signal-to-noise ratio due to the hardware
binning applied at the readout stage, combined with the reduced SEE due to the
shorter image exposure time of 1 hour.

CCD | ${\mathcal{A}}_{\rm sat}$ |  $\mathcal{A}_{0}$[eV] |  $\mathcal{A}_{\sigma}$[eV] |  $\mu_{0}$[eV] |  $\mu_{1}$[eV] |  $\mu_{2}$[eV] |  $\sigma_{0}$[eV] |  $\sigma_{1}$[eV]
---|---|---|---|---|---|---|---|---
2 | 0.878 | 9.50 | 53.2 | $-4.14$ | 3.04 | 3.83 | 33.3 | 3.31
3 | 0.876 | 0.00 | 46.4 | $-2.87$ | 2.64 | 3.07 | 28.8 | 2.32
4 | 0.876 | 4.34 | 52.8 | $-3.71$ | 0.88 | 3.73 | 30.9 | 2.80
5 | 0.874 | 5.02 | 48.2 | $-3.10$ | 2.78 | 3.37 | 30.5 | 2.74
8 | 0.874 | 3.44 | 43.8 | $-2.83$ | 3.96 | 3.44 | 29.4 | 2.51
9 | 0.870 | 4.38 | 41.2 | $-3.54$ | 2.88 | 3.79 | 29.7 | 2.47
13 | 0.870 | 0.41 | 40.1 | $-2.60$ | 1.39 | 2.94 | 28.0 | 2.31
14 | 0.869 | 3.24 | 43.3 | $-3.07$ | 0.91 | 2.95 | 29.3 | 2.74
Table 1:  Parameter values obtained for each CCD from the fits of: the
acceptance in Eq. (5) (${\mathcal{A}}_{max}$, $E_{0}$,
$\sigma_{\mathcal{A}}$); the mean ionisation energy as a function of measured
energy, $\mu(E_{\rm I})$ in Eq. (6) ($d$, $e$, $f$, $g$); and the standard
deviation of the ionisation energy as a function of the measured energy,
$\sigma(E_{\rm I})$ in Eq. (7) ($h$, $j$, $k$).  Figure 10:  Extraction
acceptance as a function of the ionisation energy, ${\mathcal{A}}(E_{\rm I})$,
for the CCD with highest and lowest acceptance. The overlaid fits are
performed with the function in Eq. (5).

The Gaussian convolution takes into account the shift, $\mu(E_{\rm I})$, and
dispersion $\sigma(E_{\rm I})$, in the energy determination comparing the
measured energy, $E$, and the ionisation energy, $E_{\rm I}$. For this
purpose, the measured energy is computed after the processing chain and
compared with the simulated ionisation energy. The mean and standard deviation
for the ionisation energies are then computed as a function of the measured
energy. The convolution takes into account all ionisation energies that
contribute to a given measured energy. This step is important to properly take
into account the experimental limitations in determining the ionisation energy
from the measured energy. The mean is determined from a fit to the simulated
data as:

$\mu(E_{\rm I})=\frac{\mu_{2}}{E_{\rm I}^{2}}+\frac{\mu_{1}}{E_{\rm
I}}+\mu_{0}\,,$ (6)

and the standard deviation as:

$\sigma(E_{\rm I})=\sigma_{1}\log{E_{\rm I}}+\sigma_{0}\,.$ (7)

Finally, the selection efficiency, $\varepsilon(E)$, is applied to the
expected neutrino rate as a function of the measured energy to take into
account the effect of the selection cuts. The efficiency is calculated using
simulations by comparing the neutrino events that pass the selection criteria
to those that survive the extraction phase, and is parameterised as:

$\varepsilon(E)=(\varepsilon_{\rm sat}+\varepsilon_{\delta}{\rm
e}^{-E/\varepsilon_{\gamma}})\left(\frac{1}{2}\tanh\frac{E-\varepsilon_{0}}{\varepsilon_{\sigma}}+\frac{1}{2}\right)^{10}\quad{\rm
if}\,\,E>50\,{\rm eV,\ else\ }\varepsilon(E)=0\,,$ (8)

with the parameters from the fit listed in Table 2. Figure 11 shows the
selection efficiency as a function of energy for the most and least efficient
CCDs. The maximum efficiency of about 70% is reached at energies of around 120
eV, an improvement with respect to connie:2019 .

CCD |  $\varepsilon_{\sigma}$[eV] |  $\varepsilon_{0}$[eV] | $\varepsilon_{\rm sat}$ |  $\varepsilon_{\gamma}$[eV] | $\varepsilon_{\delta}$
---|---|---|---|---|---
2 | 54.3 | $-32.9$ | 0.662 | 303 | 0.083
3 | 57.1 | $-15.4$ | 0.680 | 124 | 0.225
4 | 51.9 | $-20.8$ | 0.671 | 225 | 0.092
5 | 59.8 | $-24.1$ | 0.682 | 185 | 0.127
8 | 50.8 | $-7.82$ | 0.684 | 171 | 0.132
9 | 44.1 | 0.283 | 0.685 | 236 | 0.081
13 | 40.5 | 6.35 | 0.682 | 263 | 0.069
14 | 47.9 | $-5.71$ | 0.593 | 158 | 0.102
Table 2:  Parameter values for the efficiency as a function of the measured
energy, $\varepsilon(E)$, obtained from a fit with Eq. (8).  Figure 11:
Selection efficiency as a function of the measured energy, $\varepsilon(E_{\rm
M})$, for the CCD with highest and lowest efficiency. The overlaid fits are
performed with the function in Eq. (8).

###  6.2 Expected neutrino rate

$E$ range | Chavarria rate | Sarkis rate | Expected 95% CL | Observed 95% CL
---|---|---|---|---
[eVee] | [kg-1d-1keV-1] | [kg-1d-1keV-1] | [kg-1d-1keV-1] | [kg-1d-1keV-1]
50 – 180 | 13.4 | 15.3 | 520 | 1006
180 – 310 | 4.6 | 4.8 | 519 | 610
310 – 440 | 1.2 | 1.3 | 504 | 422
440 – 570 | 0.41 | 0.43 | 496 | 275
570 – 700 | 0.15 | 0.16 | 475 | 43
700 – 830 | 0.063 | 0.069 | 477 | 120
830 – 960 | 0.028 | 0.031 | 485 | 719
Table 3:  Expected neutrino rate at CONNIE in bins of measured energy in
events/kg/day/keV, after applying the detector acceptance, analysis selection,
and quenching factors from Chavarria chicago_qf  and Sarkis QF , and expected
and observed upper limits on the rates at 95% confidence level.

The reactor antineutrino flux at the detector is obtained as described in
connie:LM , from the antineutrino spectra of fissile isotopes taken from
Vogel:1989iv  and TEXONO:2006xds . It is then convolved with the interaction
cross-section to give the neutrino rate as a function of nuclear recoil
energy, $\frac{{\rm d}R}{{\rm d}E_{\rm R}}$. The recoil energy neutrino rate
is in turn transformed into the rate as a function of ionisation energy,
$\frac{{\rm d}R}{{\rm d}E_{\rm I}}$ in Eq. 4, by applying the ionisation
efficiency or quenching factor, which gives the fraction of recoil energy that
causes ionisation in silicon. The quenching factor reflects the fact that the
amount of electronic excitation produced by a recoiling ion is typically
smaller than that produced by a recoiling electron of the same energy
QFSarkis2021 . Finally, the resulting expected neutrino rate is obtained from
Eq. 4 after applying the selection efficiency, acceptance, and energy
resolution.

The expected neutrino rates as a function of measured energy are obtained
separately for each CCD, and are then combined into a total rate by using the
same weights as the differential (on$-$off) measured rate, given in Section
6.3.

The integrated expected neutrino rate values in bins of 130 eV are shown in
Table 3 for energies up to 1 keV. Two scenarios are considered, reflecting two
different models for the quenching factor. The Chavarria quenching factor
chicago_qf , which comes from a measurement of the ionisation efficiency in
the same type of CCD used by CONNIE and reaches energies down to 60 eVee, is
included for comparison with our previous results connie:2019 . The newer
Sarkis model QF ; QFSarkis2021  uses a composite solution with a model based
on the extended Lindhard equation solved by a numerical method for nuclear
recoil energies above 300 $\rm{eV}$, which includes the effect of the binding
energy in silicon mainly relevant at low energies. This quenching factor shows
good agreement with all of the available data for silicon and reaches energies
down to 28 eVee, covering the CONNIE acceptance range at low energies. The
Sarkis model predicts slightly higher expected detection rates, especially at
the lowest energies. The expected neutrino rates in Table 3 have an
uncertainty of around 5% due to the reactor antineutrino flux which differs by
that amount in different models Giunti:2021kab . This uncertainty is currently
subleading to that due to the quenching factor model choice and will become
relevant once the quenching factor precision is improved in future studies.

###  6.3 Measured neutrino rate

The experimental reactor-on and off event rates in bins of energy for each CCD
are obtained from the events that survive the selection during the
corresponding period, in order to compare with the previously computed
theoretical expected rates. The active mass of each CCD is 5.56 g excluding
the detector edges which are not considered in the analysis. The mean fiducial
mass of a CCD is 4.53 g, accounting for the effect of the event size cut,
which excludes interactions produced at a depth larger than about 550 $\mu$m,
thus effectively reducing the active volume. Therefore the total experiment
fiducial mass of the 8 CCDs is 36.24 g. The total exposure time is 31.85 days
with the reactor on and 28.25 days with the reactor off. The event rate is
calculated for each CCD and period in bins of measured energy by dividing the
event count by the CCD active mass, event size cut (fiducial) efficiency,
exposure time and energy bin size. The total event rate measured by the CONNIE
experiment is then obtained in bins of energy and by period, by taking the
average of the 8 CCD rates, weighted by the inverse of their squared
uncertainties.

Figure 12: Total event rates in bins of measured energy for reactor-on and
reactor-off data. Both spectra are averaged over all CCDs.  Figure 13:
Difference of the event rates between reactor-on and reactor-off data in bins
of measured energy, averaged over CCDs.

Figure 12 shows the total event rates for reactor-on and off periods with all
the selection cuts applied. The two spectra show a good agreement. There is a
substantial improvement in the background level at low energies below 1 keV,
compared to the previous analysis connie:2019 , especially in the increase of
the measured spectrum towards the lowest energies. The small increase of the
rates at very low energies that still remains can be explained by the low-
energy event contribution from the PCC layers. Although the events are
produced in the back of the sensor, the size reconstruction algorithm has
worse resolution due to their low energy. The reconstructed sizes have a
larger dispersion and some of the events pass the cut as events produced in
the bulk of the sensor, as shown in Fig. 6. The net effect is that the
selection has less rejection power at energies below 0.5 keV and some of the
contribution is observed in the final spectrum. Further measurements in the
laboratory are needed to confirm this assumption quantitatively.

Figure 14: Upper limits on the coherent neutrino interaction rate at 95%
confidence level. Observed limit (blue) and expected limit (orange) in bins of
measured energy, compared with the standard model rate predictions, calculated
with quenching factors from Sarkis QF  (green) and Chavarria chicago_qf
(red).

Figure 13 shows the difference of the event rates between reactor-on and off
data, resulting from the subtraction of the two spectra in Fig. 12. To reduce
the possible systematic effects, the subtraction is performed separately for
each CCD first and then the individual results are combined optimally by the
statistical uncertainty. The resulting difference in event rates is
statistically compatible with zero.

We do not expect significant reactor-induced background, given the location of
the CONNIE detector with respect to the core of the nuclear reactor. Such
expectations are corroborated by a detailed study of reactor-correlated
neutron backgrounds by the CONUS experiment, which is housed at 17 m from the
core inside the dome of an identical nuclear reactor in Brokdorf, Germany. The
performed measurements and simulations of the reactor-induced neutron fluence
at the CONUS site found it to be at least an order of magnitude lower than the
expected neutrino signal Hakenmuller:2019ecb . Considering the same reactor
thermal power at the two experiments, the larger distance of CONNIE from the
core and the extra material of the concrete reactor dome wall, and the
comparable overall effect of the polyethylene shielding of the two
experiments, any contribution from reactor-induced neutrons would be
negligible compared to the expected signal and muon-induced backgrounds, and
would fall below the current experimental sensitivity. The continuous
measurement of the fluorescence peaks in the energy spectrum discussed in
Section 4.1 is used currently to monitor the reactor-correlated background.
Additionally, neutron detectors are being considered in the future to measure
potential neutron background from the reactor.

The event rate differences between reactor-on and off data for the lowest-
energy bins up to 1 keV, where the expected neutrino rates are highest, are
used to set upper limits on the measured neutrino rates at CONNIE. The 95%
one-sided confidence level limit is computed from the averaged differential
rate and the same averaging weights are used to combine the expected neutrino
rates for each CCD. Figure 14 shows the comparison between the expected and
observed limits of the differential measured rate, and the expected rates from
the standard model using the Chavarria and Sarkis quenching factors. The
values of the limits and expected rates in each bin are given in Table 3. The
observed upper limit in the lowest-energy range of $50-180$ eV is larger than
the standard model rate by a factor of 66 (75) times for the Sarkis
(Chavarria) quenching factor. While this result is not as strong as our
previous one connie:2019 , it should be noted that the sensitivity of these
new data is a factor of 2 better. The expected limit from the new data would
be larger than the standard model rate by a factor of 34 (39) times for the
Sarkis (Chavarria) quenching factor in the same range. However, due to a
positive fluctuation of the on-off rates the actual observed limit is worse.
The opposite happened in connie:2019  where a lucky negative fluctuation of
the difference between reactor-on and off spectra allowed to set a limit of
about 40 times the standard model rate, while the expected limit for the
previous data was around 65.

##  7 Conclusion

In summary, the CONNIE experiment operated in 2019 with a readout mode of
hardware binning of 5 in the vertical direction, which permits to decrease the
readout noise and achieve a detection threshold energy of 50 eV. The analysis
of 2.2 kg-days of 2019 data makes use of a number of new calibration tools and
studies that improve the detector performance and the understanding of
backgrounds. As a result, the background rate at low energies is reduced with
respect to the previous analysis.

The measured energy spectra show no excess of reactor-on data in comparison to
reactor-off, yielding an upper limit at 95% confidence level for the neutrino
interaction rate in the $50-180$ eV energy range of 551 counts/keV/kg/day
(expected limit) and 1055 counts/keV/kg/day (observed limit). The expected
(observed) limit corresponds to 39 (75) times the standard model expectation
when using the Chavarria quenching factor, and 34 (66) times the expected rate
with the more recent Sarkis quenching factor. The possible combination of
these results with the previous limit, obtained from 2016-2018 CONNIE data
connie:2019 , would require combining strongly-correlated measurements and
predictions for detectors with different efficiencies, and is left for future
work.

The perspective to further lower the detection threshold can be achieved by
employing the recently developed skipper CCD Tiffenberg:2017aac  sensors, in
which the readout stage is modified to allow multiple non-destructive sampling
of the same pixel. This decreases the noise down to sub-electron levels and
makes them capable of counting the number of electrons in each pixel. The
CONNIE detector was updated with two skipper-CCD sensors and their dedicated
readout electronics Cancelo:2021qmc  in mid 2021 and is currently
commissioning the new setup, performing background measurements and detector
characterisation since July 2021. This is the first step in the direction of a
future skipper-CCD experiment of larger mass that will be able to achieve the
increased sensitivity necessary to detect the coherent scattering of reactor
antineutrinos.

###### Acknowledgements.

We thank the Silicon Detector Facility team at Fermi National Accelerator
Laboratory for being the host lab for the assembly and testing of the
detectors components used in the CONNIE experiment. The CCD development work
was supported in part by the Director, Office of Science, of the U.S.
Department of Energy under Contract No. DE-AC02-05CH11231. We express
gratitude to Eletrobras Eletronuclear, and especially Ilson Soares and Livia
Werneck Oliveira, for access to the Angra 2 reactor site, infrastructure and
the support of their personnel to the CONNIE activities. We thank Ronald
Shellard for supporting the experiment and Marcelo Giovani for his IT support.
We acknowledge the support from the Brazilian Ministry for Science,
Technology, and Innovation and the Brazilian funding agencies FAPERJ (grants
E-26/110.145/2013, E-26/210.151/2016, E-26/010.002216/2019,
E-26/210.079/2020), CNPq (grant 437353/2018-4), and FINEP (RENAFAE grant
01.10.0462.00); and Mexico’s CONACYT (grant No. 240666) and DGAPA-UNAM (PAPIIT
grant IT100420). This work made use of the CHE cluster, managed and funded by
COSMO/CBPF/MCTI, with financial support from FINEP and FAPERJ, and operating
at the Javier Magnin Computing Center/CBPF.

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