Searches for CE$\nu$NS and Physics beyond the Standard Model
using Skipper-CCDs at CONNIE

The CONNIE sensors are two identical fully-depleted silicon Skipper-CCDs of 675 $\mu$m thickness, designed at LBNL in collaboration with FNAL during the R&D phase of the SENSEI experiment [49] and fabricated at Teledyne DALSA Semiconductor. They are made from high-resistivity ($\sim$18 k$\Omega$-cm) n-type silicon substrate, with a p-type buried channel implant and without backside processing. Each sensor is segmented into $1022\times 682$ pixels of $15\times 15$ $\mu$m² size, giving an area of 1.57 cm² and a mass of 0.247 g.

The sensor is connected to a dedicated Kapton flex-cable with micro-wire bonds, glued to a $7\times 7$ cm² silicon substrate and packaged in a two-piece copper tray, identical to the ones used for the CONNIE standard CCDs, as shown in the left photo of Fig. 1. The two Skipper-CCD packages were installed in the lowest slots of the copper box that holds the sensors in the detector, while the 14 standard CCDs from the previous CONNIE setup remained in their original positions (Fig. 1 center). The Skipper-CCD flex cables connect through new dedicated second-stage flex circuits with signal preamplification to the vacuum side of a newly designed vacuum-interface board (Fig. 1 right), which transfers the signals from the two Skipper-CCDs and two standard CCDs. From the air-side of the interface, the signals are taken to four Low-Threshold-Acquisition (LTA) readout boards [55] using long flat cables.

The rest of the detector setup is unchanged with respect to the previous operations [44, 47]. The sensors operate in a vacuum of 10^-7 torr and are cooled to below 100 K to minimise thermally-generated dark current. The detector is surrounded by passive shielding, including 15 cm of lead to absorb photons and two 30-cm layers of high-density polyethylene to shield against cosmogenic neutrons. After the installation, the experiment took data for commissioning from mid-July to early November 2021, when the full passive shielding was assembled. Since then, the data acquisition has been continuous until the end of 2023, with short interruptions due to technical issues, on-site interventions or power cuts.

The best operational configuration of the 2 Skipper-CCDs in terms of the quality of the acquired images was achieved by measuring half of each sensor using one of the 4 output amplifiers located in its corners. The data acquisition cycle consists of two phases: cleaning and readout. During cleaning, a procedure to reduce surface dark current is performed, in which the sensor surface voltages are reversed [56]. Then, after setting the voltages to their usual operation values, the charge in the CCD active area is clocked and discarded during several minutes, so that the readout starts with a “clean” CCD. The readout is done sequentially by alternating the phasing of the vertical clocks, so that the charge in the row of pixels adjacent to the serial register is first moved into it. Subsequently, the entire row of pixels is retrieved as the charge is sequentially shifted through the amplifier in the serial register, guided by another set of three voltages known as the horizontal clocks.

Both sensors are read out simultaneously with $N_{skp}=400$ samples per pixel, thus taking approximately 2 hours to acquire a raw image and resulting in a nonuniform exposure in different pixels. The data-taking periods are divided into runs, which are usually sets of $\sim$500 images that share a common detector configuration and operation conditions. The current data set contains 300 days of data, collected between November 2021 and December 2022, from which 243 days were taken with the reactor on. There were two periods when the reactor was off: from June 12 to July 25, 2022 and from November 10 to 29, 2022, during which a total of 57 days of reactor-off data were collected.

In order to establish a precise calibration for all the images in a run, a two-step procedure was implemented. Firstly, a rapid image-by-image calibration is conducted by fitting two Gaussian functions over the first two peaks, corresponding to 0 and 1 electrons. In this manner, a gain (in ADU/${\rm e}^{-}$) is determined from the difference between the Gaussian means. Monitoring gain stability helps identify pathological images, which are excluded from the second part of the calibration, which involves determining a global constant for each run.

In the second step, the pixel charge distributions are summed to increase the data sample size in the electron peak distributions. By summing all the good images of a run, it becomes possible to observe more than 100 electron peaks with good resolution (see Fig. 2), and the information from all available peaks is taken into account by fitting them with independent Gaussian distributions. Finally, a linear fit is applied to the obtained Gaussian means to derive the global gain from the slope and the baseline residual correction from the intercept. The nonlinearity obtained with this method in the energy range of interest is less than 1%, in good agreement with previous works [53].

When a pointlike energy deposition within the CCD volume produces a number of charge carriers (holes), the electric field present in the bulk causes them to drift towards the potential wells at the pixel top surface of the CCD where they are collected. As they drift, the holes diffuse laterally in the plane perpendicular to the drift direction ($z$). As shown in Ref. [58], the lateral spread is Gaussian with a variance that depends on the time the holes are allowed to diffuse before being collected, which is proportional to the depth of the ionisation event. 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 collection wells.

The size-to-depth calibration curve is determined from muon tracks using the same procedure as in standard CCDs [47]. Cosmogenic muons pass through the CCD leaving a straight track which is narrow at the entry point at the top of the CCD and widens as it progresses towards the back surface, where it exits. A sample of muon tracks perpendicular to the horizontal register is used to determine the lateral spread as a function of depth. Since the muon trajectory is a straight line, and the thickness of the CCD is known, a depth can be assigned to each muon slice and therefore to each value of the lateral spread, hence composing the calibration curve. The behavior of the size-to-depth relation from a sample of 45 muons in one sensor and one typical run is plotted in Fig. 3. Each point is a measurement of the size and depth of one slice of a muon track. The fitted curve $\sqrt{\alpha\ln(1-\beta z)}$ with parameters $\alpha=-212~{}\mu{\rm m}^{2}$, $\beta=1.02\times 10^{-3}\mu{\rm m}^{-1}$, shown by the red dashed curve, gives the spread in $\mu$m, with variations of up to 4% between sensors and runs. It is known that the event size also depends on the energy deposit per pixel and that the muon curves slightly overestimate the event size at a given depth 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 [58].

Due to the sub-electron noise, an order of magnitude lower than standard CCDs, the Skipper-CCD sensors have a high image resolution, making it possible to spot artifacts of charge smearing and defective pixels that can mimic low-energy events from diffusion-limited hits and become a background soure. To eliminate these features, a masking procedure to correctly flag these background events in the images was developed using reactor-off data and empty images formed by reading out serial registers without movement of pixel charges, and was applied prior to the event extraction.

The features, known as serial-register events (SRE), manifest in the images as charge deposits along a single row, originating from charge diffusion in the inactive silicon region that extends to the serial register. They frequently occur in clusters of adjacent pixels and occasionally in more dispersed arrangements along a single row. The latter may include isolated pixels reconstructed independently from the group of pixels associated with a single SRE, leading to potential misidentification as a diffusion-limited hit mimicking a neutrino event.

Consequently, for each image, an individual mask is generated in which entire rows with SRE candidates are marked for exclusion. The approach used to search for SRE candidates is based on the geometry of the charge distribution along a single row and requires the presence of at least two pixels in the same row, each with a minimum of $1.5\,{\rm e^{-}}$, not separated by more than two pixels, and with no adjacent pixels above and below with a charge greater than $1.5\,{\rm e^{-}}$. The threshold value of $1.5\,{\rm e^{-}}$ was chosen to exclude single-electron events, such as spurious charges or dark current [59]. The SRE identification algorithm was tested using images without events, by applying the event extraction (Section III.4) to these images with and without masks. The extraction efficiency was greater than 99%.

In addition to the SRE, another common background source in CCDs consists of hot pixels that produce bright columns and rows, or in some cases appear as individual hot pixels. These are identified by searching the image regions without particle tracks for rows or columns with more than 12 unmasked pixels with a charge greater than $0.6\,{\rm e^{-}}$. Also, to exclude hot features that appear frequently in a run, a single mask per run is built containing the flagged columns and rows that were found hot in more than 5$\%$ of the images. Furthermore, individual pixels that appear occupied with at least $2.56\,{\rm e^{-}}$, 16 times the readout noise, in more than 10% of the images in a run are also flagged as bad pixels. Merging the two hot pixel masks and the SRE individual masks results in an individual global mask for each image in a run.

The average fraction of pixels that were flagged in the global masks corresponds to 8% of the Skipper-CCDs (6% for one sensor and 10% for the other). The impact of the masking, concentrated on a few hot columns and rows, is a reduction by almost two orders of magnitude in the total charge.

Once the images are calibrated and masked, an event extraction procedure is applied to identify the pixel clusters associated to energy depositions and to create an event catalog for each image. The event extraction algorithm is the same as the one described in Ref. [44], but uses a charge threshold of 1.6$\;{\rm e^{-}}$ ($10\sigma$ above the noise level) for the seed pixel and of $0.64\;\rm e^{-}$ ($4\sigma$ above the noise) for its adjacent pixels. These values were chosen in order to reconstruct the total event charge.

Additional event variables computed in the extraction algorithm are the widths $\sigma_{x}$ and $\sigma_{y}$, obtained from a 2D Gaussian fit to the cluster charge distribution and giving information on the event shape and size. The coordinates of the barycenter position of the event in the image are also calculated as

where $(x_{i},y_{i})$ is the position of the $i-$th pixel in the event and $E_{i}$ its energy. The subsequent data selection is performed on the image catalogs containing the event variables.

To establish a set of selection criteria for defining good-quality data, the performance of three parameters was analysed: the readout noise, the single-electron event rate and the number of flagged pixels in the global masks. The analysis was performed using only reactor-off data in order to establish a maximum limit for the parameters and exclude potentially compromised images.

The readout noise is the fluctuation added by the output amplifiers, while the single-electron events [59] are caused by spurious charge accumulated in the pixels due to spontaneous thermal emission or dark current, Cherenkov and recombination photons [60] or clock-induced charge [59]. Both the noise and the rate of single-electron events of each image are calculated during the data processing, and continuously monitored during data taking, together with the local gain. The procedure to compute the noise and single-electron rate is analogous to the one in the analysis of standard CCDs [47], by calculating the two parameters independently from the overscan and active regions, respectively. In order to exclude from the calculation pixels with large charges that do not represent sources of single-electron events, in addition to applying the SRE mask, all pixels with more than 5 e^- and a halo of 10 pixels around each are excluded from the active region in the calculation, leaving contributions from mostly pixels with 0 and 1 electrons.

Figure 4 shows the readout noise and single-electron-event rate distributions of one Skipper-CCD. The mean readout noise of the reactor-off data set is measured to be ($0.150\pm 0.007$) e^-. In order to exclude the outlier noisy images, only the ones with noise below 0.17 e^- are kept in the subsequent analysis. The single-electron rate is obtained as ($0.045\pm 0.021$) e^-/pix/day. Since single-electron events can interfere significantly in the background rates, a cut is chosen to reduce these background sources, by keeping images with single-electron rate of less than 0.14 e^-/pix/day. Lastly, to ensure a good spatial coverage, images with more than 25% of masked pixels in the active region were excluded from the analysis. The effect of the data quality cuts is a reduction of 2.9% (5.6%) in the reactor-off (on) data sample.

After the data quality criteria, two event selection criteria are applied, based on the event positions within the active region and their shapes, in order to search for neutrino interactions in the sensor volume. The first is a geometrical cut, adopted from the previous analysis [47], that excludes the sensor borders of 10 pixels in the active region to avoid edge effects in the morphology of reconstructed events [61]. The result is a small reduction in the effective area of the sensor and is reflected in the total exposure.

The second is a selection cut based on the size of the events. Following the same approach as the analysis of standard CCDs [47], events are required to have widths $\sigma_{x}$ and $\sigma_{y}$ smaller than 0.95 pixels to exclude events that are large or come from the back CCD layer which has only partial charge collection and can produce fake low-energy events [62]. In addition, a lower limit of 0.2 pixels is set on the widths, considering the sensitivity of the reconstruction algorithm.

Since the Skipper-CCDs do not have an exposure time prior to the readout stage, a single pixel in the sensor is only exposed during the sequential readout of other pixels before it in the readout line. This is taken into account to calculate the effective exposure of each image. A time map is built assigning to the $n$-th pixel an exposure time $t_{exp}=t_{ro}(n-1)/(N_{pix}-1)$, where $t_{ro}$ is the total image readout time and $N_{pix}$ is the total number of pixels in the image. By removing all the regions excluded in the geometrical cut and the individual global mask, the image exposure time is designated as the average exposure time of the remaining pixels in the time map.

The detection efficiency determination uses the same methodology as in previous analyses [44, 47] by simulating 40 neutrino-like events per image from the reactor-off period, with a uniform probability in the active volume and a uniform energy distribution between 5 and 2005 eV, using the depth-size calibration based on muon tracks. Comparing the energy and 3D position of the simulated events before and after the image processing and event extraction, it was found out that almost all events were extracted with $\sim$100% acceptance. A small fraction, less than 1.3%, of simulated events generated traces similar to serial-register events and were flagged by the masking routine, Section III.3.

The overall detection efficiency, shown in Fig. 5, accounts for the event extraction acceptance and the selection cuts. Compared to the previous runs with standard CCDs, the new sensors extend their efficient operation to lower energies and reach full efficiency around 100 eV, gaining a significant improvement. Based on this, the energy threshold for rare event searches was reduced to 15 eV, thus achieving the lowest energy threshold among all the current CE$\nu$NS experiments.

All the processing, data quality and event selection criteria were fixed before unblinding the reactor-on data. The events that pass all selection cuts correspond to an effective exposure of 3.5 g-days with the reactor-off and 14.9 g-days with the reactor-on.

The resulting event rate distributions of the energy spectra for the selected events over the two periods, accounting for their effective exposure, are shown in Fig. 6 (details in Appendix A). The mean event rates are comparable at approximately 4 kdru, and are consistent with the previous analyses [44, 45, 47]. The difference between the reactor-on and off energy spectra is also shown, demonstrating no significant excess. Nevertheless, due to the record low energy threshold and the low single-electron-event rates, the current data set can be employed to search for rare processes in and beyond the SM.

In order to obtain the expected neutrino rates at the detector, the SM neutrino coherent interaction rates are corrected for the effects of selection efficiency and resolution, obtained from simulation, as well as for the quenching factor that represents the fraction of nuclear recoil energy that creates ionisation. Here a similar procedure is used as the one in Ref. [63].

The predicted antineutrino flux at the detector is calculated following the summation method described in [64, 65, 66, 67], updated with improved antineutrino spectra for the fissile isotopes ${}^{235}\rm{U}$, ${}^{238}\rm{U}$, ${}^{239}\rm{Pu}$ and ${}^{241}\rm{Pu}$. The contribution from activation (neutron capture) of structural and fuel elements relevant for energies below 1.27 MeV was also updated following [68]. The detection threshold of 15 $\rm{eV_{ee}}$ corresponds to a minimum observable neutrino energy of $\sim$0.44 MeV, according to the Sarkis quenching factor model [69]. Above this energy, the updated flux model and the one used previously [63] agree to within 3% and are thus considered equivalent in this analysis (details can be found in Appendix A).

The detection efficiency discussed in Section IV.3 is used as a multiplicative correction to the expected event rate as a function of the measured ionisation energy, $E_{M}$. For the quenching factor, $f_{n}(E_{\rm nr})=E_{I}/E_{\rm nr}$, with $E_{I}$ the ionisation energy, we use the updated model of Sarkis et al. [69], which allows to calculate the ionisation efficiency for nuclear recoil energies in silicon down to 0.05 $\rm{keV_{nr}}$. This model, based on the original ideas by Lindhard [70], incorporates improved descriptions of the electronic stopping, interatomic potential and electronic binding at sub-keV energies, covering the Skipper-CCD low-energy range ($E_{\rm{nr}}>0.240\;\rm{keV_{nr}}$) corresponding to events above the 0.015 keV_ee threshold. The energy resolution $R(E_{I},E_{M})$ is modeled as a Gaussian with variance $\sigma^{2}=\sigma^{2}_{0}+F_{e}E_{eh}E_{I}$, where $\sigma_{0}=3.04$ $\rm{eV_{ee}}$ is the readout noise, $F_{e}=0.119$ is the electronic Fano factor, and $E_{eh}=3.752$ $\rm{eV_{ee}}$ is he mean energy to create an electron-hole pair in silicon [71].

The resulting predicted rates for the CE$\nu$Ns spectrum for Skipper-CCDs are shown in Table 1, using the same binning as the data. A comparison with the Chavarria quenching factor [72], valid for $E_{\rm{nr}}>0.30\;\rm{keV_{nr}}$, and out of range for Skipper-CCD data near the threshold, is also given for reference. The uncertainties in the expected rates take into account systematic variations due to the quenching factor [69, 72], efficiency (see Appendix B for details) and reactor budget [73, 66].

Based on the difference between the measured reactor-on and off event rates in Fig. 6, a 95% confidence-level (C.L.) upper limit on the observed event rate is established [74, 75], shown in the third column of Table 1. The observed limit in the lowest-energy bin, where the expected rates are highest, lies at 76 times the SM prediction using the Sarkis quenching factor [69]. The expected limits are also calculated and shown in the last column of the table. Comparing the results for the observed limit obtained with Skipper-CCDs and the previous result using standard CCDs [47], they are of similar size. This can be explained by the fact that, on one hand, the sensitivity on the current limit is restricted by the large rate uncertainties due to the low exposures, while on the other hand it benefits from the significant improvement in detection efficiency at low energies. This enhanced sensitivity motivates the need to increase sensor mass in order to harness the full potential of Skippers-CCDs in the search for CE$\nu$NS with reactor neutrinos.

Theories beyond the SM that include light mediators are highly motivated by the experimental results in various fields of particle physics [79, 80, 81, 82], including dark matter and neutrino physics. New mediators can be probed under the framework of the so-called “simplified models” which, accounting only for representative new particles and interactions, allow to characterise new physics with a small number of parameters [83]. Reactor neutrino experiments, sensitive to low-energy interactions, have demonstrated their competitiveness in constraining new light mediators in the mass region below $\sim$10 MeV [46, 78].

Here, the CONNIE results from the Skipper-CCD run are employed to constrain the parameter space of a light vector mediator $Z^{\prime}$ in the framework of the simplified universal model [76], using the CE$\nu$NS detection channel. Considering the lowest energy bin, between 15 eV and 215 eV, the expected event rate in CONNIE, $R_{SM+Z^{\prime}}$, is computed when accounting for the presence of the new mediator in addition to the SM interactions. The exclusion region in the phase space of the $Z^{\prime}$ mass ($M_{Z^{\prime}}$) and coupling ($g_{Z^{\prime}}$) is then calculated as the one in which this rate is greater than the observed upper limit on the event rate at the 95% C.L. for the same energy bin.

Figure 7 (left) shows the resulting CONNIE limits from the Skipper-CCD run with the updated Sarkis (2023) quenching factor [69]. For illustration purposes, the limit corresponding to the Chavarria quenching factor is also given [72], although recent measurements and calculations suggest it may be less valid at such low energies. The exclusion regions derived from the CONNIE Skipper-CCDs improve slightly the bounds imposed with the CONNIE standard-CCDs using the Chavarria quenching factor [46], mostly as an effect of the updated quenching factor at low energies, and to a lesser extent because the significantly higher Skipper-CCD rate uncertainty is compensated by the lower threshold, which enhances their sensitivity. A comparison with other experimental results in Fig. 7 (right) shows that the new CONNIE limit is less stringent but approaches that based on the COHERENT experiment CE$\nu$NS detection with CsI+Ar and its own quenching factor measurement [77]. The limit is more stringent at low mediator masses compared to the CONUS experiment, which uses germanium detectors and the Lindhard model with a quenching parameter of $k=0.16$ [78], thanks to the Skipper-CCD reach to lower energies.

Figure 7 (left) also shows the 95% C.L. upper limit projections assuming a zero difference between the reactor-on and off rates and a statistical error five times smaller in the lowest-energy bin. These limits may be achieved if CONNIE can collect 25 times more data by, for example, increasing its mass.

Dark matter (DM) direct detection experiments using Skipper-CCDs have the best current constraints for light dark matter candidates interacting with electrons in most of the energy range of interest ($0.5-1000$ MeV) [84, 86]. These constraints are limited in the lowest energy bin by the single-electron background rates. However, they can be improved by searching for a diurnal modulation, as explained in Ref. [87] and summarised below.

Due to the Solar System movement around the galaxy, there is a preferred direction of arrival of dark matter particles, which is known as the DM wind. This wind comes, on average, from the latitude 40^∘ N. In the region of parameter space to which Skipper-CCDs are sensitive, DM particles interact with nuclei and electrons inside the Earth, and therefore can suffer elastic or inelastic collisions, producing a sidereal day modulation of their flux at the location of the detector. The “isodetection angle” is defined as the angle formed between the direction of the DM wind and the normal to the surface of the Earth at the detector location. Experiments located at the northern hemisphere scan low isodetection angles, meaning that the expected modulation is smaller (the DM particles only traverse the atmosphere and a small portion of the Earth crust in their trajectory). However, in the southern hemisphere, the isodetection angle spans over larger angles and the expected modulation becomes bigger. CONNIE is located at 23^∘ S, allowing to scan a range of isodetection angles roughly between [65–161]^∘.

Stable single-electron-event rates are needed in order to look for the modulation. To that end, we limited this analysis to the most stable data taking run. Each image has an exposure of around one hour, and an average isodetection angle is assigned to it using the date and time information. The rates computed for each image are then binned in the isodetection angle. Simulations are carried out using DaMaSCUS [88, 89] to calculate the expected rate for each isodetection angle bin. The simulations are then compared to the measured rates and a 90% C.L. constraint for the DM parameters is calculated using a binned likelihood method.

The results are given in Fig. 8, considering models with MeV-scale DM, which couple to SM particles via a kinetically-mixed dark photon ($A^{\prime}$) [90, 91]. The plots show the DM phase space limits in terms of the DM particle mass ($M_{X}$) and its interaction cross-section with electrons ($\sigma_{e}$). The DM-electron scattering cross-section depends on the DM form-factor, $F_{\rm DM}=(\alpha m_{e}/q)^{n}$, with $\alpha$ the fine structure constant, $m_{e}$ the electron mass and $q$ the momentum transfer, which varies with the mediator mass, $M_{A^{\prime}}$ [92]. For heavy dark photon mediators ($M_{A^{\prime}}\gg\alpha m_{e}$) $n=0$ and thus $F_{\rm DM}=1$, while for ultralight mediators ($M_{A^{\prime}}\ll\alpha m_{e}$), $n=2$. The limits for the heavy and ultralight dark photon mediators are given in the left and right plots, respectively.

The figure also presents a comparison with other experiments. The plots in solid lines correspond to surface-level experiments, while dashed lines indicate underground experiments. In the [$0.6-10$] MeV region, our analysis establishes the best limits for a surface-level experiment by 1–3 orders of magnitude in the DM-electron cross-section. Our limits are not competitive with underground experiments due to the cosmic background, which introduces extra single-electron events produced by effects such as Cherenkov radiation in silicon [60]. However, these are promising results for future searches in which a better stability of the detector is accomplished and the backgrounds are better understood.