Exploring low-energy neutrino physics with theCoherent Neutrino Nucleus Interaction Experiment (CONNIE)

Exploring low-energy neutrino physics with the
Coherent Neutrino Nucleus Interaction Experiment (CONNIE)

Alexis Aguilar-Arevalo Universidad Nacional Autónoma de México, Distrito Federal, México    Xavier Bertou 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, Argentina.    Carla Bonifazi Universidade Federal do Rio de Janeiro, Instituto de Física, Rio de Janeiro, RJ, Brazil    Gustavo Cancelo Fermi National Accelerator Laboratory, Batavia, IL, United States    Alejandro Castañeda Universidad Nacional Autónoma de México, Distrito Federal, México    Brenda Cervantes Vergara Universidad Nacional Autónoma de México, Distrito Federal, México    Claudio Chavez Facultad de Ingeniería - Universidad Nacional de Asunción, Asunción, Paraguay    Juan C. D’Olivo Universidad Nacional Autónoma de México, Distrito Federal, México    João C. dos Anjos Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ, Brazil    Juan Estrada Fermi National Accelerator Laboratory, Batavia, IL, United States    Aldo R. Fernandes Neto Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Angra dos Reis, RJ, Brazil    Guillermo Fernandez Moroni Fermi National Accelerator Laboratory, Batavia, IL, United States Instituto de Investigaciones en Ingeniería Eléctrica, Departamento de Ingeniería Eléctrica y Computadoras, Universidad Nacional del Sur (UNS) - CONICET, Bahía Blanca, Argentina    Ana Foguel Universidade Federal do Rio de Janeiro, Instituto de Física, Rio de Janeiro, RJ, Brazil    Richard Ford Fermi National Accelerator Laboratory, Batavia, IL, United States    Juan Gonzalez Cuevas Facultad de Ingeniería - Universidad Nacional de Asunción, Asunción, Paraguay    Pamela Hernández Universidad Nacional Autónoma de México, Distrito Federal, México    Susana Hernandez Fermi National Accelerator Laboratory, Batavia, IL, United States    Federico Izraelevitch Universidad Nacional de San Martín (UNSAM), Comisión Nacional de Energía Atómica (CNEA), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina    Alexander R. Kavner University of Michigan, Department of Physics, Ann Arbor, MI, United States    Ben Kilminster Universität Zürich Physik Institut, Zurich, Switzerland    Kevin Kuk Fermi National Accelerator Laboratory, Batavia, IL, United States    H. P. Lima Jr Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ, Brazil    Martin Makler Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ, Brazil    Jorge Molina Facultad de Ingeniería - Universidad Nacional de Asunción, Asunción, Paraguay    Philipe Mota Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ, Brazil    Irina Nasteva Universidade Federal do Rio de Janeiro, Instituto de Física, Rio de Janeiro, RJ, Brazil    Carlos Romero Facultad de Ingeniería - Universidad Nacional de Asunción, Asunción, Paraguay    Y. Sarkis Universidad Nacional Autónoma de México, Distrito Federal, México    Miguel Sofo Haro 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, Argentina. Fermi National Accelerator Laboratory, Batavia, IL, United States    Iruatã M. S. Souza Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ, Brazil    Javier Tiffenberg Fermi National Accelerator Laboratory, Batavia, IL, United States    Stefan Wagner Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ, Brazil Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil
July 1, 2019
Abstract

The Coherent Neutrino-Nucleus Interaction Experiment (CONNIE) uses low-noise fully depleted charge-coupled devices (CCDs) with the goal of measuring low-energy recoils from coherent elastic scattering (CENS) of reactor antineutrinos with silicon nuclei. This standard model process has not yet been observed at recoil energies below 20 keV. We report here the first results of the detector array deployed in 2016, with an active mass of 73.2 g (12 CCDs), which is operating at a distance of 30 m from the core of the Angra 2 nuclear reactor, with a thermal power of 3.8 GW. A search for neutrino events is performed by comparing data collected with reactor on (2.1 kg-day) and reactor off (1.6 kg-day). The results show no excess in the reactor-on data, reaching the world record sensitivity down to recoil energies of about 1 keV (0.1 keV electron-equivalent). A 95% confidence level limit for new physics is established at an event rate of 40 times the one expected from the standard model at this energy scale. The results presented here provide a new window to the low-energy neutrino physics, which allows one to explore for the first time the lowest energies accessible through the CENS with antineutrinos from nuclear reactors.

preprint: APS/123-QED

CONNIE Collaboration

I Introduction

The Coherent Elastic Neutrino Nucleus Scattering (CENS) is a standard model (SM) process predicted over 40 years ago Freedman (1974), shortly after the discovery of neutral-current neutrino interactions Hasert et al. (1973). The coherent enhancement of the elastic scattering cross-section occurs when the energy of the scattering process is low enough ( MeV) and the interaction amplitude of every nucleon adds coherently to the total cross-section Freedman (1974). The CENS has a total cross-section of cm Freedman et al. (1977). Its detection was not possible until recently because of the very low energy deposition in nuclear recoils, below 15 keV for most detector targets.

CENS provides a new window into the low-energy neutrino sector and the interest in this sector has been growing as a potential probe for new physics Scholberg (2006). The process is also relevant to fields beyond particle physics. For example, in astrophysics, the understanding of neutrino interactions at MeV scales is key for the energy transport in supernovae and is a limiting factor in ongoing efforts for developing new supernova models Horowitz et al. (2003). Additionally, in recent years there has been a growing interest in nuclear reactor monitoring using neutrinos Barbeau et al. (2003); Hagmann and Bernstein (2004); Alfonzo et al. (2018).

Anomalies in reactor neutrino experiments and short baseline neutrino experiments have motivated an extension of the SM adding a sterile neutrino Abazajian et al. (2012). A number of ongoing experiments are looking to address these anomalies Acciarri et al. (2015); Gariazzo et al. (2017). CENS is the ideal probe to study the hypothetical sterile neutrino, because the cross-section for standard neutrinos is flavor-independent and the low energies accessible from CENS would allow oscillation experiments with extremely short baselines Formaggio et al. (2012); Nelson and Walsh (2008); Blanco et al. (2019).

CENS from solar, atmospheric and diffuse supernova neutrinos has been identified as a limiting background for future dark matter searches Anderson et al. (2011) and the next generation of direct dark matter detection experiments is expected to reach sensitivity to CENS. Measuring CENS directly in controlled neutrino experiments is needed to model and subtract this background in future dark matter experiments.

Some extensions of the SM predict a significant enhancement of the cross-section at low energies, which could result in a several orders of magnitude increase in the rate of events Harnik et al. (2012). These include models in which the neutrino has an anomalous magnetic moment, whereby the neutrino-nucleus scattering is mediated by a light boson.

There are two necessary conditions for the detection of CENS. The first is the availability of a source of low-energy neutrinos (below  50 MeV) with high flux. The second requirement is a detector for nuclear recoils with threshold around a few keV. Recent technological advances in detectors for direct dark matter searches have provided several options for CENS detection. These include cryogenic bolometers Agnese et al. (2017), noble liquid detectors Akerib et al. (2018); The DarkSide Collaboration et al. (2018) and semiconducting detectors Aguilar-Arevalo et al. (2016); Abramoff et al. (2019); Aalseth et al. (2016). These new detector technologies have enabled several efforts looking for CENS Hakenmüller et al. (2019); Billard et al. (2017); Singh and Wong (2004); MINER Collaboration et al. (2016).

Low-energy neutrinos can be produced at particle beams. Protons hitting a target make mesons and, if the target is large enough, the slow down and decay at rest, producing neutrinos with peak energies 20 MeV. Using this technique a flux of  /cm/s/MeV is achieved at the Spallation Neutron Source (SNS) Source (2008). The neutrinos from this source produce recoils of up to 10 keV. SNS produces a pulsed neutrino beam, which is very useful to control the backgrounds. The COHERENT collaboration reported the first detection of CENS in 2018, using a low background CsI[Na] scintillator with an active mass of 14.6 kg Akimov et al. (2017). These results have been used to constrain physics beyond the standard model, demonstrating the potential of CENS as a probe for new physics Aristizabal Sierra et al. (2018).

Nuclear reactors are a powerful source of low-energy neutrinos from fission, with a flux of /cm/s/MeV for a large reactor with thermal power of the order of  W. Large reactors used for commercial power generation provide an approximately constant flux that is modulated by the nuclear fuel cycle, with typically one month shutdown every year. Smaller research reactors have a lower flux, according to their thermal power, but offer the advantage of larger flexibility in the duty cycle, providing greater control over backgrounds in the experiment. Research reactors typically allow the detectors to be located closer to their core MINER Collaboration et al. (2016).

Neutrinos from nuclear reactors have an energy spectrum peaking at 1 MeV, producing recoil energies for Si nuclei with energies below 2 keV, significantly lower then neutrinos from spallation sources, making their detection more challenging. The detection of CENS in reactor experiments will allow the extension of the searches for new physics into the low-energy neutrino sector with sensitivity to some models that are not accessible at the energies probed at SNS Harnik et al. (2012).

No detection of CENS from reactor neutrinos has been reported yet, and the neutrino physics at this energy scale remains unexplored. Probing this region is the focus of the CONNIE experiment described here.

Ii The CONNIE Detector

The CONNIE detector is an array of 14 charge-coupled devices (CCDs) operating at the Angra 2 reactor of the Almirante Alvaro Alberto Nuclear Power Plant, in the state of Rio de Janeiro, Brazil. The engineering prototype of the experiment was installed at the reactor site in late 2014 and the results of this run are discussed in Aguilar-Arevalo et al. (2016). A complete upgrade of the sensors was performed in mid 2016, with the main objective of increasing its active mass by a factor of . The slow control systems for the detectors were also upgraded to increase the efficiency for collecting data of scientific quality.

ii.1 CCD sensors

The CCD sensors used by CONNIE were developed by the experiment in collaboration with the LBNL Micro Systems Labs LBN (). These detectors are a spin-off from the fully depleted thick detectors that were originally designed to give astronomical instruments such as DECam Flaugher et al. (2015) and DESI Martini et al. (2018) extended sensitivity in the near-infrared region. CONNIE increased the CCD thickness to 675 m. These are the thickest CCDs ever fabricated and are only possible to fully deplete thanks to the very high-resistivity (10 k-m) silicon wafers used. In order to reduce the thermally-generated dark current in the silicon, the sensors are cooled to temperatures below 100 K and operate in a vacuum ( torr).

Each sensor consists of a square array with 16 million square pixels of 15  15 m pitch each. Given their thickness, a substrate bias voltage of 70 V is applied to the backside of the detector using the method developed in Holland et al. (2003). In CCDs, the charge of each pixel is moved towards the corners of the detectors for readout. In CONNIE, although the CCDs have 4 output stages, one in each corner of the pixel array, the charge of the full array is moved to one corner and the 16 Mpixels are read in series through a single output amplifier. A second output of each sensor is read to monitor the common mode noise of the system (see section III.1).

Figure 1: Image of a package including the CCD, which is glued to a silicon frame, the upper and lower copper frames and the Stage-1 flex cable.
Figure 2: The cold box with the 14 CCD packages installed. On top is the inner lead shield.

ii.2 Packaging of the CCDs and electronics

Packaging of the sensors for operating in cryogenic conditions and without introducing additional sources of background is essential for low-energy measurements. The sensors are packaged as shown in Fig. 1. The back of the 6 cm  6 cm sensor is epoxied to a slightly oversized silicon frame (7 cm  7 cm). In order to avoid introducing any new materials close to the detectors, this frame is made from the same single crystal ingot used for the fabrication of the CCDs. The frame leaves most of the back of the detector exposed, only covering a few hundred rows/columns on each side. A flexible circuit (Stage-1) is attached to the silicon frame and micro-wire bonds are used to connect it to the pads providing the control clocks, bias voltages, and signal output of the CCD. The CCD sensor, frame, and Stage-1 flexible circuit are then mounted on a two-piece copper tray covering both sides of the frame, but leaving the CCD exposed. The copper tray provides the mechanical support for the CCD package and is also the thermal connection for cooling the CCDs. Oxygen-free copper is used for its purity and low isotopic contamination.

The Stage-1 circuit has no active components and serves to provide a high-density connector to the Stage-2 flexible circuit. The Stage-2 flexible circuit was designed for DECam Flaugher et al. (2015) and provides a source follower and preamplifiers (with gain 1.5) for the signal output. The Stage-2 circuit is connected to a vacuum interface board which brings the signals of all CCD packages to a Monsoon acquisition system Moore et al. (2008). The signal path after the Stage-1 circuit is exactly the same as that for the DECam imager Shaw et al. (2012).

ii.3 Cryogenic system

The array of CCD packages is mounted inside a copper cold box with capacity to hold 20 packages. Currently 14 packages are installed in the cold box (Fig. 2), of which 12 are operating. The cold box is designed with the goal of shielding the sensors from any infrared radiation from the environment. It is connected to a closed-cycle helium cryocooler and the temperature of the box is controlled with a three-term controller with a precision better than 0.1 K. The cold box, Stage-1 and Stage-2 circuits are kept inside a copper vacuum vessel that is continuously evacuated using a turbo-molecular pump. The vacuum vessel is shown in Fig. 3 inside a partially-assembled radiation shield.

ii.4 Shielding and laboratory

The radiation shield is the same as in the CONNIE engineering run Aguilar-Arevalo et al. (2016). It consists of an inner layer of 30 cm of polyethylene, followed by 15 cm of lead, and an additional outer layer of 30 cm of polyethylene (Fig. 3). Lead is a good shield for gamma radiation, while polyethylene is an efficient shield for neutrons. Since neutrons are produced when cosmic muons interact with lead, a fraction of the polyethylene shield is kept inside the lead layer. There is also a lead cylinder of 15 cm height inside the vacuum vessel, above the cold box containing the detectors (Fig. 2). This cylinder shields the detectors from any radiation generated in the active components of the Stage-2 circuit and the vacuum interface board.

Figure 3: Image of the CONNIE detector showing the shielding partially disassembled. At the center we see the cylindrical dewar holding the copper box with the CCDs, cables, and inner lead shield. On top of it are the readout electronics. The inner and outer polyethylene layers and the lead layer of the shielding surround the detector.

As in the engineering run, the detector is installed inside a shipping container, located 30 meters away from the core of the Angra 2 nuclear reactor. The same container hosts a water-based neutrino detector, the Neutrinos Angra experiment Alfonzo et al. (2018). Angra 2 is a pressurized water reactor with a thermal power of 3.8 GW that started commercial operation during the year 2000. In steady-state operation, the total neutrino flux produced by the reactor is 1.21 s Fernandez Moroni et al. (2015), and the flux density at the detector is 7.8 .

ii.5 Operation

The experiment is operated remotely and its operating parameters and conditions are monitored and logged continuously. The electronic readout noise is among the most important performance parameters for the CONNIE detectors. This noise depends on the CCD sensors and on-chip electronics, the Monsoon readout electronics, and the interference from equipment installed inside the shipping container and outside the container. It is crucial to control all sources of electronic noise when the detectors are being read out. In order to reduce the effect of external sources of noise, all circuits, including the CCD electronics, are disconnected from the AC power network when the detectors are being read out. This is done using an uninterrupted power supply (UPS) system that powers all the electronics connected to the detector, including the Monsoon, sensors, the computer that controls the experiment and the vacuum pump. During the readout stage the cryocooler is switched off, in order to eliminate the noise from its compressor.

In order to minimize the fraction of time spent reading out the CCDs and to increase the signal-to-noise ratio, the longest possible CCD exposures are desirable. However, the background events (mainly cosmic muons) quickly populate the pixels. The exposure time was therefore chosen to keep the occupancy (fraction of pixels associated to events) below 10%, setting that time to 3 hours. The duration of the readout was optimized with respect to individual pixel noise, yielding a total of 16 min to read the full CCD array Aguilar-Arevalo et al. (2016).

Iii Image processing and catalog generation

As mentioned in section II.1, two output amplifiers are used for each CCD. The charge in the CCD is moved to the left (L) amplifier. The readout of empty pixels is performed on the right (R) amplifier to generate a pure noise image, at the same time as the physics data are read on L. A few columns are read out prior to moving the charge, forming the prescan region. More pixel values are extracted after the charge is read, by overclocking the horizontal and vertical registers beyond the physical extent of the CCD, defining the overscan regions of the image Janesick (2001); Aguilar-Arevalo et al. (2016) (see Fig. 4). The pixel values are recorded in Analog-Digital Units (ADU) and the data are stored as a FITS file (a standard format for CCD images Pence et al. (2010)).

The data taking periods are divided in runs, which are defined as a collection of exposures that share a common detector configuration and happen during a sufficiently long and stable data-taking period. Some steps in the processing chain and in the energy calibration require the combination of several exposures per CCD for statistical purposes. A set of 60 consecutive images from the same run provides a large enough sample for these purposes and at the same time guarantees stable conditions in the detector. This corresponds to roughly one week of data, which provides a sufficient cadence for the data analysis and to test modifications in the data taking conditions. We refer to this set of images as a sub-run. Some runs contain only one sub-run, while long and stable runs may contain many sub-runs.

Figure 4: Schematic representation of a CONNIE image from the standard data acquisition. For memory handling reasons, the images are divided in 4 parts () as shown here. The charge is moved only to the left (L) amplifier, such that the right one (R) only reads the noise. A few columns with zero exposure time are read prior to moving the charge (prescan) and a larger number is read after the charge has been moved (overscan). After each column is read the readout continues for some more pixels (vertical overscan, thin strip at the bottom of ).

iii.1 Image processing sequence

The raw images are subjected to a sequence of processing steps aimed at removing unwanted offsets and subtracting electronic noise from the pixel values. As mentioned above, the processing is carried out in batches of images that we call sub-runs. The standard processing steps that are applied to the acquired images are: i) Overscan subtraction, ii) Master Bias subtraction, iii) Subtraction of correlated noise.

The overscan region of the CCD image is defined in Fig. 4 and is used to monitor the baseline of the readout electronics. The overscan subtraction is an image-by-image process where the mean of the pixel values read from the overscan region is subtracted from each pixel value across the whole image. This has the effect of removing an image-dependent offset, making the baseline of different images comparable.

The Master Bias subtraction is a statistical procedure applied to the images in one sub-run. First, two new images called the “master bias” (MB) image and the “median absolute deviation” (MAD) image are constructed. Each pixel in the MB image, in the left (L) and right (R) sides, contains the median of the values of that pixel over the exposures. Likewise, each pixel in the MAD image, but only for the physical L side, contains a measure of the width of the distribution of the values of that pixel over the images. A set of “master bias subtracted” images is formed by subtracting the MB image from each of the original images. The MAD image is used at catalog extraction to provide a mask of misbehaving pixels, applicable to all of the images.

The subtraction of correlated noise consists of constructing a corrected image for CCD , in an array with sensors (). The left side of the new image is equal to the uncorrected image L minus a linear combination of the R (), i.e.,

(1)

with . The coefficients are obtained from the solution of a linear system of equations with unknowns that results from requiring that the variance of the image over all the pixels is minimum: .

iii.2 Event extraction

Once the final images are obtained, the next step is the extraction of catalogs of events, i.e., pixel clusters that are associated with energy depositions in the CCDs. A cluster is formed by finding its “seed” or “Level 0” pixels: adjacent pixels whose value is above a given threshold (set to 4 times a representative value for the noise in the CCDs). Layers of adjacent pixels are then added to the seed pixels without any threshold requirement: “Level 1” pixels are all the pixels in immediate contact with the “Level 0” pixels, “Level 2” pixels are all the pixels in contact with the “Level 1” pixels, and so on. For pixel levels greater than 2, the corner pixels are left out. A cluster is the union of all pixels in all the defined layers. Fig. 5 shows two examples of clusters with five pixel layers. In the current CONNIE processing, the number of pixel layers is fixed to three. A catalog file containing the information of every reconstructed event in all the images in one sub-run is stored.

Figure 5: A cluster with one seed pixel (top), and a cluster with 164 seed pixels (bottom). Seed or “Level 0” pixels are in white. Pixels “Level 1” through “Level 5” are shown in colors.

As a cross check to the CONNIE event extraction pipeline, we have used SExtractor 111https://www.astromatic.net/software/sextractorBertin and Arnouts (1996), which is widely employed in astronomical applications. By adapting the SExtractor configurations to the CONNIE images, we obtained very similar detections. In particular, the spectra obtained from the CONNIE extractions and the one from SExtractor, in a same sub-run, are in very good agreement. However, at low energies (0.2 keV) the CONNIE pipeline performs better, with more efficient and less contaminated detections.

Iv Calibration of the sensors

iv.1 Energy calibration

As described in section II.2, the CCDs are attached to a frame made of the same high-purity silicon as the detectors themselves and are embedded in a copper-rich environment. Therefore, the emission of Cu and Si fluorescence x-rays from excitations by cosmogenic particles and gammas from inherent radioactivity is readily observed in all the sensors as peaks in the energy spectrum. The two principal Cu fluorescence x-rays have energies of 8.047 keV (K) and 8.905 keV (K), while the Si fluorescence x-rays have an energy of 1.740 keV. These peaks provide a way to monitor the detector calibration continuously. The linearity and resolution in the energy response of these CCDs have been thoroughly characterized down to energies of in previous work Aguilar-Arevalo et al. (2016); Chavarria et al. (2016).

A calibration constant (in units of keV/ADU) is calculated for each CCD in every sub-run of 60 images using the Cu K peak. Fig. 6 shows the region of the spectrum around the two Cu fluorescence lines for all the events in a sub-run. Fig. 7 shows the calibrated spectrum for the same sub-run in the energy range (0–10.5) keV where the Si fluorescence line is visible.

Figure 6: Energy spectrum (in ADU units) around the copper fluorescence peaks for 60 consecutive three-hour exposures. The first peak, corresponding to K at 8.047 keV, is fitted by a Gaussian and its mean is used to obtain the calibration constant. The second peak is fitted by the same function.
Figure 7: The calibrated energy spectrum in the region up to 10.5 keV. The Si fluorescence peak at 1.740 keV is fitted by a Gaussian plus an exponential.

The stability of the calibration within sub-runs was monitored by looking at the position of the Cu-K peak in groups of five consecutive images, fitted with a Gaussian plus constant-background model. The calibration constants extracted from these smaller groups of images were found to be stable within 0.2% over periods of time extending for several months.

iv.2 Energy resolution

The energy resolution for photons is a well-understood quantity for CCD sensors: at high energies (several keV) the energy resolution is dominated by the silicon ionization efficiency which is proportional to the energy of the photon through the Fano factor Janesick (2001). This factor was evaluated in the laboratory, for the same type of CCD as CONNIE, using x-rays (typically of 5.9 keV from a Fe source) giving a value of 0.133 Aguilar-Arevalo et al. (2016). At low energies (below 0.1 keV) the energy resolution is dominated by the readout noise of the sensor and is evaluated by adding low-energy events to the data and measuring the energy dispersion for those events after reconstruction, which is found to be 0.034 keV. The total energy resolution for photons is the sum of both effects and can be modelled by a normal distribution with variance

(2)

where 3.745 eV is the adopted mean ionization energy required to produce an electron-hole pair for photons taken from Ryan (1973), is the Fano factor and is the photon energy in eV.

iv.3 Size-depth calibration

The event shape in the data depends on the transport of charge carriers in the depleted silicon before they are trapped by the potential well of each pixel. Once the free carriers are generated, they drift under the electric field of the depleted silicon. This electric field has only one component transverse to the array plane and free holes have essentially no restriction to move laterally before being trapped by the pixel well. The magnitude of the lateral dispersion is determined by the drift time, which is set by the distance from the primary ionization point (depth in the silicon) to the well positions (approximately 2 m below from the front face of the sensor). In particular, neutrinos deposit such a small amount of energy when scattering off nuclei that the primary ionization volume is much smaller than the subsequent dispersion of the free carriers. Measuring this process is needed for the complete characterization of the shape of the neutrino events and is a key ingredient for the simulations used to characterize the reconstruction strategy.

The lateral dispersion produced by thermal diffusion follows a Brownian motion with a position probability that can be modeled by a two-dimensional Gaussian distribution Holland et al. (2003) with equal standard deviation () in both directions, given by

(3)

where and are parameters that condense several physical constants of the sensor and is the depth of the interaction in the bulk of the silicon.

Figure 8: A typical muon event crossing the entire thickness of the detector where the color scale indicates the charge value of each pixel in arbitrary units. The lines perpendicular to the track define the segments where the transverse standard deviation is measured.
Figure 9: Two-dimensional histogram illustrating the measurement of the size-depth relationship in one of the sensors. The vertical axis shows the width of the muon segments for each depth in the horizontal axis as measured from muons traversing the CCD. The color scale indicates the number of measurements that lie in each diffusion-depth bin. The solid line is the best fit of Eq. (3) to the distributions.

Since the parameters in Eq. (3) depend on fabrication and operation parameters such as the doping content, sensor thickness and substrate voltage, we measure them independently for each detector using a high-purity sample of atmospheric muons. They produce a continuous ionization trace in the output data with a very high probability of crossing the entire detector thickness. An example of a muon track is shown in Fig. 8. These events are reconstructed as continuous straight lines with a thicker end corresponding to ionization produced in the back of the sensor and a thinner end from ionization at the front (close to the pixel potential well). The width of the track can be mapped as a function of the distance from the first interaction point, which is proportional to the depth of the hit in the CCD. In practice, the track is divided into segments where the transverse standard deviation is measured. An example of this mapping using many muons is shown in Fig. 9. The average values for the detector array are m and m, with a 10% dispersion between detectors and a maximum diffusion width of  m.

V Detector performance

v.1 Stability of the background radiation

The full energy spectrum for the data collected in the CONNIE experiment is shown in Fig. 10 (red curve). The excess at around 250 keV corresponds to minimum ionizing cosmic muons traversing the silicon sensors. The steep increase in the rate at low energies is dominated by secondary products of these muons, showering in the detector and in the nearby shielding components. This is demonstrated with a full Geant4 Agostinelli et al. (2003) simulation of atmospheric muons hitting the detector, following the energy and angular distribution of Smith and Duller (1959), which reproduces reasonably well the moun distribution at sea level Chatzidakis et al. (2015). The resulting spectrum matches the shape of the overall CONNIE spectrum above 5 keV, as shown in Fig. 10 (black curve). The simulated spectrum gives an overall background rate consistent with the total rate observed in CONNIE. The search for low-energy events in these data is thus limited by the stability of the muon background and its secondary products. A more sophisticated background model including all the low-energy processes below 5 keV is left for future work.

Figure 10: Comparison of the simulated spectra from muons and data in one of the sensors. The red curve represents data from one of our runs (0.048 kg-day), while the black curve represents the muon contribution obtained with the Geant4 package. The simulated spectrum is based on the expected rate of muons at sea level and has not been fitted to the data.

We monitor the stability of the background both looking at the rate at the fluorescence peaks as well as in regions away from the peaks. As our CENS analysis is based on a comparison of reactor on and off data, we study the stability grouping the data collected during these two states of the reactor (the selection of the specific periods used in this analysis is presented in Sec. VI.1).

As discussed in Sec. IV.1 the cooper peaks are fitted by a Gaussian plus a constant, providing the energy calibration (position of the peak) and also the event rate integrated on the peak. In Fig. 11 we show the distribution of these two quantities for the Cu K peak for exposures during the periods of reactor on and off. As mentioned before, we see that the calibration is extremely stable during the operations and is independent of the reactor state. The rate is also very stable, with fluctuations consistent with Poisson statistics and no significant difference between the reactor on and off periods.

Figure 11: Top: distributions of the fitted calibration constant (Cu K) from spectra of groups of 5-6 images, for reactor on (blue) and reactor off (red). Bottom: distributions of the event rate under the Cu K peak per image calculated as the area of the fitted Gaussian. The distributions are normalized by the reactor on/off exposure, respectively. The mean () and width () of the distributions are also shown.

The position and rate of the Si fluorescence peak in the low-energy region of the calibrated energy spectrum were also monitored and found to be consistently stable. The Si peak is also stable comparing the on and off periods, with a mean of 1.738 (1.736) keV (using the Cu K calibration) and width of 0.001 (0.003) keV during the on (off) period.

We have also monitored the stability of the background radiation in two energy ranges. The first, from 3 to 7 keV, was chosen to be between the Cu and Si fluorescence peaks and is dominated by low-energy photons. The second range, from 250 to 350 keV, was chosen to include the muon peak and, thus, is dominated by muon events. Fig. 12 shows the distribution of the event rate in one of the sensors in these two energy ranges for the periods of reactor on and off. For the low energy range, the distributions show that the radiation background is constant on the two periods, within statistical uncertainties. In the high-energy region, we notice a 2.5% variation in the rate, but it does not affect the low energy spectrum, at least at the level of precision achieved in this paper. The differences appear not only in the on versus off periods, but have a long term variation along the months.

Figure 12: Histograms of events per image in the energy ranges 3–7 keV (top) and 250–350 keV (bottom), for the reactor on (blue) and off (red) periods. The mean () and width () of the distributions are also shown.

v.2 On-chip noise sources

Figure 13: On-chip noise components in one of the sensors for all exposures considered for this paper. Each point corresponds to a three-hour exposure. The red points are taken during reactor off periods, while the blue ones are during on periods.

On-chip noise sources are the main contribution to the measurement error in the pixels Janesick (2001). The dominant effects are produced by two independent processes: the readout noise (RN) added by the output amplifier of the sensor to the output signal and the dark current (DC) which is a spurious generation of charge by thermal excitations in the crystal. The RN follows a Gaussian distribution while the DC follows a Poisson distribution Janesick (2001). Both quantities are constantly monitored in the experiment by measuring the parameters of their distributions with fits to the combined probability function of the pixels without events for each image. Since both noise sources are independent, the joint probability function for the energy in a given pixel due to the combined DC plus RN processes () can be calculated as the convolution of the marginal contributions:

(4)

where is the energy in ADU units, is the gain of the system in units of ADU/e calibrated with x-ray lines, runs over all the possible numbers of generated charges from the DC process, is the mean number of generated charges per pixel by the DC, is the standard deviation of the RN process in units of e, and is an external parameter added to account for a small remnant in the baseline subtraction processing step. Note that the central value of each term in the sum is adjusted by , which is not part of the original Poisson marginal probability function. It is included in order to correct for the effect of subtracting the median image in the processing chain.

The method was used to evaluate the noise sources on each output image. The distribution of DC () and RN () for a single CCD is shown in Fig. 13 for all exposures considered in this paper (see Sec. VI.1). For all sensors the typical ranges are:  e/pix/hr and  e.

The effect of these noise sources in the event selection is different: the RN fluctuations dominate the root mean square (RMS) error of the pixel and have an impact on the energy resolution of low-energy events, while the DC, with a larger-probability tail for positive values, has more impact on the number of spurious (false positive) events. These two mechanisms are taken into account for the event selection cuts, as described in section VI.2.

Vi Event selection and efficiency

vi.1 Data quality selection criteria

The detector has been taking data continuously since August 2016, with short interruptions due to planned on-site interventions (repairs and upgrades in the control system and container infrastructure) or power cuts. The data collection can be divided in 3 seasons. The first, from August 2016 to March 2017, includes one of the reactor shutdowns and ended with the planned period of maintenance of the detector. The second one, from March to December 2017, does not include any reactor off period and was defined by the infrastructure upgrade of the lab. The third season, from January to August 2018, includes the second reactor shutdown used in this measurement. For the analysis presented in this paper we consider data that were acquired in the first and third seasons of the experiment, when the CCDs used in the analysis have similar performance. More specifically, we required RN better than 2.2 e and DC less than 0.3 e/pix/h.

From the total of 14 CCDs installed in the experiment 2 were disconnected due to issues that appeared at the beginning of the operation of the experiment. Of the 12 remaining detectors, we selected 8 that have shown good performance in terms of noise, charge transfer efficiency, and long-term stability.

After removing edge effects, the effective size of each CCD is 4093 4111 pixels, giving a total mass of 47.6 g for the array of 8 CCDs. We remove from the analysis the columns that have an excess of hot pixels in comparison with the rest of the sensor. Hot columns detected on any image are eliminated from the analysis of the complete data set. This is done to ensure that we use the same parts of the detector in both reactor-on and reactor-off data sets.

The total accumulated exposure of data considered in this work, corresponding to 8 CCDs operating during the two seasons, is 3.7 kg-days: 2.1 kg-days taken with the reactor on and 1.6 kg-days with the reactor off.

vi.2 Low-energy event selection

As discussed in section III.2, events are selected to contain energy above a threshold () for the seed, which is set at 10 e, corresponding to roughly four times the standard deviation of the RN: e keV. Some pixel fluctuations from on-chip noise sources (section V.2) could be large enough to produce fake events that resemble low-energy neutrino events given this threshold. A statistical test is used to separate neutrino-like events from spurious ones from on-chip noise sources at low energies. The test is based on the likelihood of the pixel values of an event to follow the probability density function of the Gaussian readout noise. The log-likelihood is calculated from the pixels of the -th event as:

(5)

where are the pixel values of level 0 and 1 pixels of the event and (0) if (). It should be noted that corresponds to a Gaussian probability distribution and is included to maximize the power of the statistical discriminator for negative fluctuations in the pixel value. The log-likelihood selection criterion is chosen to maintain contributions from on-chip noise much below background radiation contribution (dominated by Compton scattering). Images consisting purely of on-chip noise (DC and RN) were simulated to evaluate their distribution in and the on-chip noise contribution to the low-energy spectrum in the experiment.

Figure 14: distribution from simulated noise events for different DC and RN conditions.

Fig. 14 shows the distribution of simulated events for three different conditions of DC and RN in our sensors, which are representative of the values obtained during the selected periods (see sec. V.2). Each condition was evaluated over a group of 1500 images with similar size as the data of the experiment, equivalent to an exposure of 1.125 kg-days. All the events with pixel seeds above are extracted and those with energy above 0.075 keV are evaluated by the likelihood and incorporated in the plot. The red histogram represents the most extreme DC and RN condition for our sensors ( e/pix/hr and  e). A likelihood cut of gives a number of fake events 5000 eV/kg/day, similar to the expected flat Compton spectrum in the energy range from 0.075 to 0.275 keV. To prevent this systematic error form impacting the analysis, a cut of was chosen, which gives a contribution three orders of magnitude smaller than the Compton process in the (0.075–0.275) keV energy range.

vi.3 Efficiency for CENS events

The conservative selection cut is used to separate neutrino-like events from the noise-like ones for all the sensors. Although this cut is applied to all events, it is only relevant at low energies ( keV). Since the behaviour of the sensors is stable, the same cut is used for all runs.

To evaluate the detection efficiency at low energies, while ensuring that the small variations in the noise and other statistical fluctuations do not impact the reconstructed number of neutrino events in all data sets, simulated neutrino-like events are added in the vertical overscan of the output images of the experiment. Since this region has a very short exposure of about 10 minutes, they have almost no background events and the contribution of small RN fluctuations can be easily evaluated. The simulated neutrino events are then reconstructed using the same processing tools and their reconstruction efficiency is evaluated for each data set of every run. Neutrino-like simulated events with energies up to 2.5 keV were added and their reconstruction efficiency is shown in Fig. 15 for all the sub-runs used in this analysis for one representative CCD. The fluctuations of the sub-run efficiencies at low energies (below 0.5 keV), where the calculation is more sensitive to small RN variations, are the same as for higher energies and all lie within the statistical uncertainty of the measurement. This shows that the different noise conditions do not impact the efficiency.

Figure 15: Reconstructed efficiency of neutrino-like events simulated in the vertical overscan region of one sensor. Each color corresponds to a different sub-run in the detector covering all data used for the analysis in the paper.
Figure 16: Overall efficiency of neutrino event reconstruction.

To obtain an overall reconstruction efficiency for neutrinos for all CCDs and periods, we add neutrino-like events on the active region of the sensor, which accounts for the reduction in the total exposure by overlapping with higher-energy events. Only data sets without expected neutrino events (reactor off periods) were used, to avoid any efficiency reduction due to the neutrino signal. Neutrinos are simulated with uniform probability in the active volume of the sensor, with shape determined by the calibration in section IV.3 and with a uniform distribution in energy up to 2.5 keV. A set of 1000 events are simulated per CCD image. This number was chosen to provide a large enough sample to evaluate the efficiency with a low uncertainty, without having a significant impact on the total occupancy. The images with simulated neutrino events are processed using the standard chain and the selection rules described above are applied. The measured efficiency for each sensor is then weighted by the exposure, yielding the overall efficiency curve presented in Fig. 16.

Figure 17: Observable neutrino recoil spectrum in the CONNIE detector array using two versions of the quenching factor measured from Chavarria Chavarria et al. (2016) and Lindhard James F. Ziegler (1985).

Vii Search for the standard model CENS signal

Figure 18: Energy spectrum for reactor-on and reactor-off data.
Figure 19: Energy spectrum difference of reactor-on minus reactor-off data.

Using the overall efficiency discussed in the previous section, the expected rate of CENS events in the detector array is calculated following the prescription in Fernandez Moroni et al. (2015) and the results are shown in Fig. 17. For the CENS process, the relevant energy is the silicon recoil energy. However, as mentioned before, our data is calibrated using electron recoils and therefore the energy is in electron-equivalent. To convert from electron-equivalent to recoil energy we use the quenching factor. Here we employ a recent measurement of this factor for nuclear recoils in CCDs from Chavarria et al. (2016) to compute the expected event rate. For comparison with previous work Aguilar-Arevalo et al. (2016), the expected event rate is also calculated using the quenching model from Lindhard James F. Ziegler (1985). The energy resolution for the detectors discussed in section IV.2 has been included in the calculation, smearing the measured energy of the simulated nuclear recoils. The recoil spectrum is convolved with a Gaussian resolution, where the width of the Gaussian varies according to the model of Eq. (2). As a result of this smearing and the steep fall of the recoil energy spectrum, a fraction of low-energy events gets promoted to higher observable energies.

To search for a CENS signal, the selection criteria discussed in section VI.2 are applied to the data with the reactor on and off periods. Fig. 18 shows the observed spectrum for both periods at energies below 15 keV. The data for each CCD in the detector array are weighted by their exposure mass and included in this spectrum. The x-ray fluorescence lines for silicon in the sensor active volume and copper surrounding the sensors are clearly observed.

The reactor-off spectrum is subtracted from the reactor-on one for each sensor in the detector array and the results binned in energy are weighted by the sensor exposure mass and combined in Fig. 19. The error bars in this figure reflect the statistical uncertainty in the binned spectrum subtraction.

There is no significant excess of events in the reactor-on minus reactor-off subtraction. The maximum excess consistent with the data at 95% confidence level (CL) is shown in Fig. 20 and Table 1. This limit is compared to the expected CENS event rate using the quenching factor measured from Chavarria Chavarria et al. (2016) and the Lindhard James F. Ziegler (1985) models. The results show that the 95% CL limit established by this work is a factor of 40 above the prediction from the standard model for deposited energies about 0.1 keV, or recoil energies of 1 keV.

Energy CENS-rate CENS-rate 95% C. L.
range (keV) Lindhard Chavarria from data
0.075–0.275 11.4 4.8 197
0.275–0.475 3.6 1.3 109
0.475–0.675 0.8 0.3 47
Table 1: Expected rate from CENS, in events/day/kg/keV, assuming quenching factors from Lindhard James F. Ziegler (1985) and Chavarria Chavarria et al. (2016) together with the 95% CL limit from the data presented in this paper.
Figure 20: CENS event rate: 95% confidence level limit from the reactor on - off measurement (solid line) and neutrino signal expected from the Lindhard James F. Ziegler (1985) (dotted line) and Chavarria Chavarria et al. (2016) (dashed line) quenching factors.

Viii Discussion and concluding remarks

The CONNIE experiment is operated remotely at the Angra 2 nuclear power plant. During 2017 and 2018 an operating efficiency of more than 95% was achieved, thanks to a monitoring, alarms and interlock system developed to record and report the status of all the critical values of the experiment. The CONNIE results demonstrate the operation of low-threshold detectors next to a commercial power plant to search for CENS, while maintaining good control of the reactor related background. The capability to monitor the stability of the environmental radiation background is also demonstrated thanks to the excellent energy resolution and particle identification performance of the sensors.

The results presented here constitute the first search for CENS at a nuclear reactor reaching recoil energies down to 1 keV (0.1 keV electron-equivalent). This measurement was made possible thanks to the development of a detector based on thick fully-depleted low-threshold CCDs, specifically designed for this purpose. Low-threshold CCDs open a new window into the low-energy neutrino physics sector, probing for physics beyond the standard model Okun et al. (1986); Nelson and Walsh (2008); Pospelov (2011); Essig et al. (2013); Ilten et al. (2018). The threshold explored by CONNIE is one order of magnitude lower than the threshold of 20 keV used for the first detection of CENS Akimov et al. (2017). These results can be used to impose constraints on models predicting higher rates of low-energy events from neutrinos, compared to the standard model. Studies of the constraints to the models predicted in Harnik et al. (2012) will be presented elsewhere.

The sensitivity to the standard model CENS obtained in this measurement is somewhat lower than the expectation from the forecast presented in reference Fernandez Moroni et al. (2015). There are three reasons for the reduced sensitivity. First, the updated measurements for the quenching factor in Chavarria et al. (2016) reduce significantly the expected signal compared to the Lindhard model James F. Ziegler (1985). The CONNIE collaboration is working to reduce the uncertainty in the quenching factor, in collaboration with other teams using silicon targets for the detection of nuclear recoils Aguilar-Arevalo et al. (2016); Crisler et al. (2018); Abramoff et al. (2019); Agnese et al. (2017). The second is the lower detection efficiency than the estimations used for the forecast in Fernandez Moroni et al. (2015). We expect to recover most of the efficiency by upgrading the experiment with the recently demonstrated skipper-CCD sensors Tiffenberg et al. (2017). Finally, the low-energy background measured in the CONNIE experiment is about a factor of 10 higher than the estimations in the forecast. Repeating the experiment at a facility with some overburden shielding would reduce this environmental background.

The CONNIE detector array was designed to have a geometry appropriate for track and shower reconstruction as an additional tool to identify background events, however these capabilities were not exploited for the analysis presented here. We expect to make use of the shower reconstruction capabilities of the detector in future work, extending the sensitivity of the experiment.

The analysis discussed here for the CONNIE data is based on a reactor-on minus reactor-off subtraction. This model-independent analysis is strongly limited by the statistics of the reactor-off data, equivalent to less than 10% of the total data that is possible to collect. A model-dependent analysis using the spectral details of signal and background based on a full simulation of the detector at low energies will increase the sensitivity to the standard model CENS signal and is planned for future work.

Acknowledgements.
We thank Eletrobras Eletronuclear for access to the Angra 2 reactor site and for the support of their personnel to the CONNIE activities. 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. We acknowledge the support from the former Brazilian Ministry for Science, Technology, and Innovation (currently MCTIC), the PCI program at CBPF and the Brazilian funding agencies FAPERJ (grants E-26/110.145/2013, E-26/210.151/2016), CNPq, and FINEP (RENAFAE grant 01.10.0462.00); and México’s CONACYT (grant No. 240666) and DGAPA-UNAM (PAPIIT grant IN108917). The Mexican group acknowledges Ing. Mauricio Martínez for his technical assistance. We acknowledge Marcelo Giovani for his IT support. CB and MM acknowledge the hospitality of Fermilab, where part of this work was done. 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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