SENSEI: First Direct-Detection Constraints on sub-GeV Dark Matter from a Surface Run

The Sub-Electron-Noise Skipper CCD Experimental Instrument (SENSEI) uses the recently developed Skipper-CCD technology to search for electron recoils from the interaction of sub-GeV dark matter particles with electrons in silicon. We report first results from a prototype SENSEI detector, which collected 0.019 gram-days of commissioning data above ground at Fermi National Accelerator Laboratory. These commissioning data are sufficient to set new direct-detection constraints for dark matter particles with masses between ~500 keV and 4 MeV. Moreover, since these data were taken on the surface, they disfavor previously allowed strongly interacting dark matter particles with masses between ~500 keV and a few hundred MeV. We discuss the implications of these data for several dark matter candidates, including one model proposed to explain the anomalously large 21-cm signal observed by the EDGES Collaboration. SENSEI is the first experiment dedicated to the search for electron recoils from dark matter, and these results demonstrate the power of the Skipper-CCD technology for dark matter searches.


INTRODUCTION
Identifying the nature of dark matter (DM) is one of the most urgent tasks of particle physics today, and direct-detection experiments play an essential role in this endeavor. The search for DM particles with masses 1 GeV represents a new experimental frontier [1]. Traditional direct-detection searches, which are sensitive to recoil energy generated from DM scattering off of nuclei, typically have very little sensitivity to sub-GeV mass DM. Indeed, the best current bounds are limited to very large cross sections below 1 GeV and are absent below ∼ 120 MeV [2][3][4]. As suggested in [5], improved sensitivity to DM masses well below the GeV scale is possible by searching for signals induced by inelastic processes, for which a DM particle is able to deposit much more energy compared to the elastic scattering off of nuclei. In particular, one of the most promising avenues is to search for one or a few ionized electrons that are released due to DM particles interacting with electrons in the detector.
Background-free searches for single or few-electron events are experimentally challenging. Sensitivity to such events has been demonstrated using two-phase time projection chambers with noble liquid targets, using data from XENON10 [6][7][8], XENON100 [7,9], and DarkSide-50 [10]. Significant progress can be made by utilizing solid-state detectors, which exhibit much lower thresh-olds due to their typical low band gap. Recently, silicon Charge-Coupled Devices (CCDs) with a special "Skipper" readout stage [11] and high-voltage cryogenic silicon detectors with transition edge sensor readout [12] have demonstrated single-electron sensitivity. The 1.1 eV band gap of silicon allows for a DM mass threshold that is an order of magnitude lower than that achieved in noble liquid detectors, and permits significantly larger DMelectron scattering rates [5,7,[13][14][15].
The Sub-Electron-Noise Skipper CCD Experimental Instrument (SENSEI) is designed to utilize the Skipper-CCD technology demonstrated in [11] to search for electron recoils from sub-GeV DM [16]. While the ultimate goal of the SENSEI Collaboration is to build a 100-gram detector consisting of multiple Skipper-CCDs, a prototype detector is currently operating ∼100 m underground near the MINOS experiment at Fermi National Accelerator Laboratory (FNAL). This prototype was first tested on the surface, collecting 0.019-gram-days of data (before analysis cuts).
In this letter, we present the first constraints on sub-GeV DM derived from SENSEI commissioning data. We exclude novel parameter space for DM masses below ∼4 MeV, above which the XENON10 constraint from [6,7]  as the noble-liquid detectors mentioned above, have no sensitivity. Despite large cosmic-ray backgrounds, this region can be easily probed by a detector on the surface with a small amount of data. The SENSEI data thus also place novel constraints on DM particles with masses of several hundred MeV.

THE SENSEI PROTOTYPE DETECTOR
We use a single Skipper-CCD with an initial active mass of 0.094 grams of silicon fabricated parasitically in a production run for astronomical CCDs. The CCD has 724 × 1248 pixels of size 15µm × 15µm and a thickness of 200µm. The Skipper-CCD was packaged in a light-tight copper housing that was cooled to an estimated 130 K to reduce the dark current on the sensor and to reduce the emission of infrared photons from black-body radiation. The sensor was read by a modified Monsoon electronics system described in [11].
This detector was used to take a small amount of commissioning data on May 11, 2017, at the Silicon Detector Facility (SiDet) at FNAL. SiDet has an elevation of ∼220 m above sea level and a roof consisting of about 7.6 cm of concrete, 2 mm of aluminum, and 1 cm of wood. The thickness of the light-tight copper housing in which the sensor was placed is 3 mm. The Skipper-CCD was read continuously for 427 minutes producing 18 images with 200 rows each. The single-sample noise of the CCD varied slightly from quadrant to quadrant. One of the quadrants had unusually high noise due to a charge transfer inefficiency problem in the readout stage, and all data from it were immediately discarded, leaving an active mass of 0.071 grams. The other three had a single-sample readout noise of ∼ 4 e − ; 800 samples were taken for each pixel, reducing the noise to ∼0.14 e − .

DATA SELECTION
The prototype Skipper-CCD has a dark current that was measured to be ∼ 1.14 e − /pixel/day (this is orders of magnitude higher than is expected from the Skipper-CCDs that will be used by SENSEI in the future, which are produced in a dedicated production run using highresistivity silicon). This leads to a large number of 1-, 2-, and 3-electron events. In this paper, we do not attempt to analyze the dark current in detail or to remove any background events. Instead, we place conservative limits by assuming that all events are from DM.
After data collection, we implemented several standard quality cuts for CCD-based detectors [18,19] as well as cuts specific to our analysis: • Single pixel. A DM event consists of one or more electrons that are created initially in a single pixel and spread with uniform probability along the height of the pixel. However, the electrons can drift apart as they diffuse to the surface, allowing some electrons to diffuse to a neighboring pixel. To simplify our analysis, we require the DM signal to fall within a single pixel. This cut also rejects neighboring dark-current coincidences. • Nearest Neighbor. A DM event can fall adjacent to another signal or background event. Due to the singlepixel cut above and the poor timing resolution, we must remove the four nearest neighbors from all pixels that contain one or more electrons. • Noise. We veto images in which the readout noise is 30% larger than the expected readout noise as inferred from an over-scan region in which virtual (nonexistent) pixels are read. • Bleeding. At low temperatures the electron mobility may be impeded, implying a small probability that an electron can get stuck in a given pixel for several downward shifts. If an event, such as a cosmic ray, produces a large number of electrons in some pixel(s), then pixels with several electrons may be found upstream in 2. The 95% C.L. constraints on the DM-electron scattering cross-sections, σe, as a function of DM mass, mχ, from a commissioning run above ground at FNAL using the SENSEI prototype detector. We show different DM form factors, FDM(q) = 1, αme/q, and (αme/q) 2 . The purple, blue, green, and red lines correspond to the strongest constraints, from using events with exactly 1, 2, 3, or 4 electrons, respectively. The blue shaded regions are the current constraints from DM-electron scattering from XENON10, XENON100, and DarkSide-50. For large cross sections, the DM is stopped in the Earth's crust (atmosphere) and does not reach the noble-liquid (SENSEI prototype) detectors: the dark-shaded regions (labelled |gp| = |ge|) show preliminary results from [17] and are the excluded parameter regions assuming the interaction between DM and ordinary matter is mediated by a heavy dark photon (left), an electric dipole moment (middle), or an ultralight dark photon (right). The light-shaded regions (labelled gp = 0) are the approximate excluded parameter regions assuming a mediator that couples only to electrons. The terrestrial effects shown here are order-of-magnitude estimates only, and more detailed calculations will appear in [17]. the image. We mask 10 pixels upstream of any pixel containing more than 100 electrons.
In what follows we bin the data, after the above selection cuts, according to the number of electrons per pixel, and derive constraints for each bin separately. Table I lists the selection efficiencies for electron bins 1 − 5, calculated in a data-driven manner. The spectrum after cuts is shown in Fig. 1, together with gaussian fits to the first three bins. We use the bins with 1 − 100 electrons in our analysis.

ANALYSIS AND RESULTS
We calculate the DM recoil spectrum for several models, deriving constraints both on DM-electron scattering and on bosonic DM being absorbed by an electron [20][21][22][23]. For the scattering case, we use the calculations and conventions from [5,13]. We present our results in the σ e versus m χ parameter space for various DM form-factors, F DM (q), where m χ is the DM mass and σ e is the cross section for DM to scatter off a free electron with the momentum transfer fixed to its typical value, q = αm e , where α is the fine-structure constant and m e is the electron mass. F DM (q) parameterizes the model-dependent momentum dependence of the DM interaction: a "heavy" mediator with mass αm e has F DM (q) = 1; an "ultralight" mediator with mass αm e has F DM (q) = (αm e /q) 2 ; and an electric-dipole-moment interaction with the Standard-Model photon produces F DM (q) αm e /q. For bosonic DM, we will consider that the DM is a dark photon, denoted A , with mass m A , that is stable on the lifetime of the Universe. We follow the calculations and conventions in [21], and present results in the versus m A parameter space, where is the parameter that characterizes the strength of the kinetic mixing between the A and the photon.
For each model, we calculate conservative 95% confidence level upper limits using Poisson statistics and assuming that all observed electrons in a given bin are DM events. We compare the resulting limit from each bin with the predicted number of DM events (for a given value of σ e or ), after correcting for the efficiencies.
Our main results, for σ e versus m χ are shown in Fig. 2 for the three form factors discussed above. The black line denotes the overall SENSEI limit, while the colored lines show the limits from each bin separately. The 1-, 2-, and 4-electron bins essentially set the strongest constraints in different parts of the mass range.
Despite a small exposure time on the surface, the SEN-SEI commissioning run already probes novel parameter space for light DM (mass 4 MeV) and for DM with large cross sections. This is the first time that a directdetection constraint is derived for DM masses as low as ∼500 keV. In contrast, noble-liquid experiments (especially XENON10) probe lower cross sections for masses 4 MeV.
The 95% C.L. constraint on σe versus mχ for FDM(q 2 ) = (αme/q) 2 from a surface run at FNAL using the SENSEI prototype detector (red region, bounded below by a solid line and above by a dashed line that is the same as the |gp| = |ge| line in the right plot of Fig. 2 [17]). We assume that χ couples to an ultralight dark-photon mediator, and Ωχ = 0.01ΩDM, which may explain the 21-cm signal observed by EDGES. Other constraints are described in the text. The SENSEI surface run disfavors a small region of previously open parameter space for σe 10 −25 cm 2 and mχ greater than a few hundred MeV.
Second, the noble-liquid detectors that have previously constrained sub-GeV DM are operated underneath the Gran Sasso mountain. DM that interacts strongly with ordinary matter cannot reach these detectors due to scattering in the Earth. In contrast, much larger interaction strengths can be probed with the SENSEI surface run, since only the atmosphere (and a thin roof) can stop the DM.
The terrestrial effects on MeV-to-GeV DM scattering off nuclei or electrons are model-dependent and have so far only been explored partially in the literature [24,25]; a full exploration is beyond the scope of this paper (see [26][27][28][29][30][31] for larger DM masses). However, to illustrate that SENSEI constrains novel parameter space at large cross sections, we include very preliminary results from [17]. If the interaction between DM and ordinary matter is mediated by a dark photon or an electric-dipolemoment, the DM will dominantly scatter off nuclei in the atmosphere or Earth before reaching the detector, where it scatters off an electron to leave an observable signal. The darker shaded regions in Fig. 2 (labelled "|g p | = |g e |") illustrate the cross sections above which the respective detectors have no sensitivity, assuming the DM interaction with ordinary matter is mediated by a heavy dark photon, an electric dipole moment, or an ul- tralight dark photon in the left, middle, and right plots, respectively. If the mediator only couples to electrons (and not to nuclei), a very naive rescaling of the preliminary results in [17] leads to the excluded regions labelled "g p = 0" (lighter shaded regions). We see that the SEN-SEI prototype constraints are largely complementary to existing noble-liquid detector constraints.
We give one example of a concrete model that can give rise to large cross sections in Fig. 3. We assume that a subdominant DM component, χ, interacts with an ultralight dark photon (m A keV), with Ω χ = 0.01Ω DM . This model is motivated by the EDGES measurement of the 21-cm spectrum at z 17, which revealed an anomalously large absorption signal [32] [33] (see also [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]). The SENSEI constraint (red) is bounded by the solid (dashed) line for small (large [17]) σ e . It disfavors novel parameter space for DM masses above a few hundred MeV for σ e 10 −25 cm 2 , which is the preliminary value of the upper boundary of the XENON10 constraint [17]. Other constraints arise from the SLAC millicharge experiment [50], red-giant (RG) and horizontalbranch (HB) stars [51], the BBN and CMB measurements of the number of relativistic degrees of freedom (N eff ) [51], and Supernova 1987A (SN) [52]. A more careful analysis of other possible constraints in this re-gion is, however, warranted, including a re-analysis of low-threshold DM-nuclear recoil data [2,3], and an analysis of whether such a DM candidate would be evacuated from the Galactic disk by Galactic magnetic fields and supernova shock waves (as may be the case if the DM has a millicharge [53]).
We next present the SENSEI prototype constraints on versus m A for dark-photon DM (A ), which can be absorbed by an electron, in Fig. 4. At small , the SENSEI prototype constraint is weaker than other constraints due to its small exposure, however, for large new grounds are explored. We estimate the maximal coupling, max = 1/ √ ρLσ abs above which the A is absorbed by molecules in the atmosphere or by atomic electrons in the Earth's crust and sensitivity is lost. Here σ abs is the measured photoabsorption cross-sections per molecule, N is the average density, and L is the depth. For simplicity, we take the Earth's crust to consist of silicon with ρ = 2.7 g/cm 3 , with L = 0.7 km (CDMSlite), 1.4 km (XENON10/100), or 2 km (DAMIC). We take the atmosphere to consist of O 2 and N 2 [54] (with ρ = 1.2 × 10 −4 g/cm 3 and L = 86 km). These dominate the absorption for m A 5 eV, the bond-dissociation energy of O 2 (no data on σ abs is available below m A 10 eV, so we extrapolate the available data down to 5 eV). For m A 5 eV, ozone dominates the absorption, but its abundance is very small and does not affect the region shown in Fig. 4. We see that SENSEI closes a gap in laboratory probes of the large-region: the gap was bounded above by a measurement of the Rydberg constant (we show a 2σ constraint adapted from [55][56][57]) and below by our analysis of terrestrial absorption effects for XENON10, XENON100, CDMSlite, and DAMIC [4,[20][21][22]58] Note that stellar constraints [59,60] may already disfavor this region; however, a more careful analysis of these bounds at high-is warranted.

SUMMARY AND OUTLOOK
We present results from a low-exposure commissioning run of a SENSEI prototype detector. We demonstrate the first use of Skipper-CCD technology for a DM search, the first direct-detection constraints for DM masses 0.5 − 4 MeV, and the first direct-detection constraints on strongly interacting DM for masses between 0.5 MeV and a few hundred MeV. Over the next few years, the SENSEI Collaboration aims to construct a detector consisting of ∼100 grams of Skipper CCDs that are fabricated in a dedicated production run using highresistivity silicon. These detectors are expected to have a dark current several orders of magnitude lower than the prototype detector and an improved single-sample noise. We expect to collect an exposure that is almost 2 million times larger than the exposure of the surface run and with far fewer background events, allowing us to explore vast new regions of DM parameter space.

ACKNOWLEDGMENTS
We are grateful to Timon Emken, Chris Kouvaris, and Mukul Sholapurkar for extensive discussions and for letting us include very preliminary results from the upcoming paper [17]. We also thank Alex Drlica-Wagner for carefully reading a draft of the paper and for numerous useful comments. We are grateful for the support of