First results from the CRESST-III low-mass dark matter program
CRESST Collaboration, A. H. Abdelhameed, G. Angloher, P. Bauer, A. Bento, E. Bertoldo, C. Bucci, L. Canonica, A. D'Addabbo, X. Defay, S. Di Lorenzo, A. Erb, F. v. Feilitzsch, S. Fichtinger, N. Ferreiro Iachellini, A. Fuss, P. Gorla, D. Hauff, J. Jochum, A. Kinast, H. Kluck, H. Kraus, A. Langenkämper, M. Mancuso, V. Mokina, E. Mondragon, A. Münster, M. Olmi, T. Ortmann, C. Pagliarone, L. Pattavina, F. Petricca, W. Potzel, F. Pröbst, F. Reindl, J. Rothe, K. Schäffner, J. Schieck, V. Schipperges, D. Schmiedmayer, S. Schönert, C. Schwertner, M. Stahlberg, L. Stodolsky, C. Strandhagen, R. Strauss, C. Türkoglu, I. Usherov, M. Willers, V. Zema
FFirst results from the CRESST-III low-mass dark matter program
A. H. Abdelhameed, G. Angloher, P. Bauer, ∗ A. Bento,
1, 8
E. Bertoldo, C. Bucci, L. Canonica, A. D’Addabbo,
2, 9
X. Defay, S. Di Lorenzo,
2, 9
A. Erb,
3, 10
F. v. Feilitzsch, S. Fichtinger, N. Ferreiro Iachellini, A. Fuss,
4, 5
P. Gorla, D. Hauff, J. Jochum, A. Kinast, H. Kluck,
4, 5
H. Kraus, A. Langenk¨amper, M. Mancuso, V. Mokina, E. Mondragon, A. M¨unster, M. Olmi,
2, 9
T. Ortmann, C. Pagliarone,
2, 11
L. Pattavina,
3, 9
F. Petricca, W. Potzel, F. Pr¨obst, F. Reindl,
4, 5, †
J. Rothe, K. Sch¨affner,
2, 9
J. Schieck,
4, 5
V. Schipperges, D. Schmiedmayer,
4, 5
S. Sch¨onert, C. Schwertner,
4, 5
M. Stahlberg,
4, 5, ‡
L. Stodolsky, C. Strandhagen, R. Strauss, C. T¨urko˘glu,
4, 5
I. Usherov, M. Willers, and V. Zema
2, 9, 12 (CRESST Collaboration) Max-Planck-Institut f¨ur Physik, 80805 M¨unchen, Germany INFN, Laboratori Nazionali del Gran Sasso, 67010 Assergi, Italy Physik-Department and Excellence Cluster Universe, Technische Universit¨at M¨unchen, 85747 Garching, Germany Institut f¨ur Hochenergiephysik der ¨Osterreichischen Akademie der Wissenschaften, 1050 Wien, Austria Atominstitut, Technische Universit¨at Wien, 1020 Wien, Austria Eberhard-Karls-Universit¨at T¨ubingen, 72076 T¨ubingen, Germany Department of Physics, University of Oxford, Oxford OX1 3RH, United Kingdom Also at: LIBPhys, Departamento de Fisica, Universidade de Coimbra, P3004 516 Coimbra, Portugal Also at: Gran Sasso Science Institute, 67100, L’Aquila, Italy Also at: Walther-Meißner-Institut f¨ur Tieftemperaturforschung, 85748 Garching, Germany Also at: Dipartimento di Ingegneria Civile e Meccanica, Universit´a degli Studi di Cassino e del Lazio Meridionale, 03043 Cassino, Italy Also at: Chalmers University of Technology, Department of Physics, 412 96 G¨oteborg, Sweden
The CRESST experiment is a direct dark matter search which aims to measure interactions of potential darkmatter particles in an earth-bound detector. With the current stage, CRESST-III, we focus on a low energythreshold for increased sensitivity towards light dark matter particles. In this manuscript we describe the analysisof one detector operated in the first run of CRESST-III (05/2016-02/2018) achieving a nuclear recoil thresholdof 30.1 eV. This result was obtained with a 23.6 g CaWO crystal operated as a cryogenic scintillating calorime-ter in the CRESST setup at the Laboratori Nazionali del Gran Sasso (LNGS). Both the primary phonon/heatsignal and the simultaneously emitted scintillation light, which is absorbed in a separate silicon-on-sapphirelight absorber, are measured with highly sensitive transition edge sensors operated at ∼
15 mK. The uniquecombination of these sensors with the light element oxygen present in our target yields sensitivity to dark matterparticle masses as low as 160 MeV/c . I. INTRODUCTION
Today, the Standard Model of particle physics provides awidely consistent description of the visible matter in the Uni-verse. However, the ever-growing precision of cosmologicalobservations substantiates the finding that the visible mattercontributes comparatively little to the matter density of theUniverse which is, instead, dominated by dark matter. Nu-merous experiments strive to decipher the nature of dark mat-ter, either by a potential production of dark matter particles incollisions of Standard Model particles, by searching for sec-ondary Standard Model particles originating from the annihi-lation of dark matter particles, or by aiming at the direct obser-vation of interactions of dark matter particles in earth-bounddetectors. As of today, none of these three channels deliveredan unambiguous hint for dark matter particles.Since, in particular, the mass of the dark matter particle(s)is a-priori unknown, direct searches for dark matter need tocover the widest possible mass range. This necessarily implies ∗ Corresponding author: [email protected] † Corresponding author: fl[email protected] ‡ Corresponding author: [email protected] the use of different experimental techniques. In the standardscenario, assuming spin-independent and elastic scattering ofdark matter particles off nuclei, liquid noble gas experimentstake the lead in the high mass range. Solid-state or gas detec-tors are best suited for light ( (cid:46) ) dark matter due totheir lower energy thresholds. For spin-dependent interactionssuperheated bubble chambers play an important role.The CRESST-III experiment operates scintillatingCaWO crystals as cryogenic calorimeters, simultaneouslymeasuring a phonon/heat and a scintillation light signal. Adistinctive feature of the phonon signal is a precise determi-nation of the energy deposited in the crystal, independentfrom the type of particle interaction. This property, incombination with a low energy threshold, makes cryogeniccalorimeters particularly suited for low-mass dark matterdetection. Contrary to the phonon signal, the scintillationlight strongly depends on the type of particle interaction,yielding event-by-event discrimination between the dominantbackground ( β / γ -interactions) and the sought-for nuclearrecoils. Phonon and light signals are acquired by transitionedge sensors (TESs) operated at around 15 mK and read outby SQUID amplifiers [1].In this work we analyze data acquired with detector A,which has the lowest threshold among all detectors operated a r X i v : . [ a s t r o - ph . C O ] M a r in the first run of CRESST-III. II. CRESST-III SETUP AND DETECTOR DESIGN1. Experimental Setup
CRESST is located in the Laboratori Nazionali del GranSasso (LNGS) underground laboratory in central Italy whichprovides an overburden against cosmic radiation with a water-equivalent of 3600 m [2]. Remaining muons are tagged byan active muon veto with 98.7% geometrical coverage [3].In addition, the experimental volume is protected by concen-tric layers of shielding material comprising - from outsideto inside - polyethylene, lead and copper. The polyethyleneshields from environmental neutrons, while lead and coppersuppress γ -rays. A second layer of polyethylene inside thecopper shielding guards against neutrons produced in the leador the copper shields.A commercial He/ He-dilution refrigerator provides thebase temperature of about 5 mK. Cryogenic liquids (LN andLHe) are refilled three times a week causing a down-time ofabout 3 h per refill.
2. CRESST-III Detector Design block-shaped target crystal(with TES) reflective and scintillating housingCaWO iSticks(with holding clamps & TES)light detector (with TES)CaWO light detector holding sticks (with clamps) FIG. 1. Schematic of a CRESST-III detector module (not to scale).Parts in blue are made from CaWO , the TESs are sketched in red.The block-shaped target (absorber) crystal has a mass of ∼
24 g, itsdimensions are (20x20x10) mm . It is held by three instrumentedCaWO holding sticks (iSticks), two at the bottom and one on top.Three non-instrumented CaWO holding sticks keep the square-shaped silicon-on-sapphire light detector in place. Its dimensionsare (20x20x0.4) mm . The CaWO crystal of a CRESST-III detector module hasa size of (20x20x10) mm and a mass of ∼
24 g (23.6 g for de-tector A). A schematic drawing is shown in figure 1. The tar-get crystal is held by three CaWO -sticks, each with a lengthof 12 mm, a diameter of 2.5 mm and a rounded tip of approx-imately 2-3 mm in radius. The sticks are themselves instru- mented with a TES, thus denoted iSticks. This novel, instru-mented detector holder allows an identification and veto ofinteractions taking place in the sticks which might potentiallycause a signal in the target crystal due to phonons propagat-ing from the stick to the main absorber through their contactarea. Since we veto interactions in any of the sticks, the threeiSticks are connected in parallel to one SQUID, thus substan-tially reducing the number of necessary readout channels [4].Each target crystal is paired with a cryogenic light detec-tor, matched to the size of the target crystal, consisting of a0.4 mm thick square silicon-on-sapphire wafer of 20 mm edgelength, also held by CaWO sticks and equipped with a TES.However, an instrumentation of these sticks is not needed asevents within them would cause quasi light-only events whichare outside the acceptance region for the dark matter search(see subsection IV 4). The remaining ingredient to achieve a fully-active sur-rounding of the target crystal is the reflective and scintillat-ing Vikuiti TM foil encapsulating the ensemble of target crys-tal and light detector. Such a fully-active design ensures thatsurface-related backgrounds, in particular surface α -decays,are identified and subsequently excluded from the dark matteranalysis. A detailed study of the event classes arising fromthe iSticks and the light detector holding sticks is beyond thescope of this work; performance studies on the parallel TESreadout may be found in [5]. III. DEAD-TIME FREE RECORDING AND OFFLINETRIGGERING
In CRESST-III, the existing hardware-triggered data acqui-sition (DAQ) is extended by transient digitizers allowing fora dead-time free, continuous recording of the signals with asampling rate of 25 kS/s. Recording the full signal stream al-lows the use of an offline software trigger adapted to eachdetector. Our software trigger is based on the optimum filteror Gatti-Manfredi filter successfully used e.g. by the CUOREexperiment [6, 7]. The optimum filter maximizes the signal-to-noise ratio by comparing the frequency power spectrum ofnoise samples to that of an averaged pulse (a standard event).More weight is then given to pulse-like frequencies comparedto those dominantly appearing in the noise samples. A fulldescription of the method can be found in [8].The complete stream is filtered with the optimum filter anda trigger is fired whenever the filter output for phonon or lightchannel exceeds a certain threshold value. For each chan-nel we select a record window 655.36 ms for further analysis.More details may be found in [9]. The output of the optimumfilter is not only used for the software triggering, but is also the A small fraction of the light emitted by the stick might be absorbed by thetarget crystal creating a small phonon signal therein, thus these events aredenoted quasi light-only. basis of the energy reconstruction (see section IV), yielding aprecise value of the threshold in energy units.
1. Optimal Trigger Threshold
Thanks to the continuously recorded data stream, the trig-ger threshold can be optimized based on a pre-defined crite-rion as described in [10], namely the number of noise triggersin a given time period (see figure 2). For this analysis onenoise trigger surviving event selection (see section IV 4) perkg day was allowed, corresponding to a trigger threshold of30.1 eV.
FIG. 2. Number of expected noise triggers surviving event selectionper kg day as function of a chosen trigger threshold for detector A.The threshold chosen for this work is indicated by the dashed line at30.1 eV.
IV. ENERGY CALIBRATION AND EVENT SELECTION1. Energy Calibration
For CRESST-III, challenges arise from the greatly en-hanced sensitivity. This leads to strong saturation effects atthe 122 keV γ -line from an external Co source used in for-mer CRESST phases to calibrate the detectors. To directlyprobe the linear, non-saturated range of the detectors lower γ -ray energies would be required. Those, however, cannotefficiently penetrate the cryostat. Therefore, we perform aninitial, approximate calibration using the K α and K α escapepeaks of tungsten with a (weighted) mean energy of 63.2 keVand later on fine-adjust by scaling to the 11.27 keV peak (HfL shell, [11]). The latter originates from cosmogenic activa-tion of tungsten and is visible in all CRESST-III detectors (seefigure 6).The optimum filter offers a better resolution for the energyreconstruction than the standard event fit [9], as used in pre-vious analyses. With the optimum filter we achieve a baseline resolution, i.e. resolution at zero energy, of 4.6 eV. However,saturation effects, that cannot be compensated by the optimumfilter algorithm, set in at 2.5 keV with complete signal satura-tion around 75 keV. To partially overcome this limitation, wecompare the amplitude determined by the optimum filter to theamplitude determined by a truncated standard event fit. Therelation between these two quantities is obtained from the highstatistics neutron calibration data and allows to extend the us-able range for the optimum filter up to 16 keV. Above 16 keV,the saturation is too large to be reasonably corrected by thisprocedure and we therefore restrict our dark matter analysisto energies below 16 keV.
2. Light Yield Description using Neutron Calibration Data
To discriminate different types of particle interactions, wedefine the light yield of an event as the ratio of the energiesdeposited in light and phonon channel: LY = E l / E p .For this analysis, the phonon energy E p is considered tobe the total deposited energy of an event; this approximationneglects any small possible dependence of E p on the eventtype and is motivated in appendix VIII 1.Figure 3 shows the events surviving the selection criteria(see section IV 4) in the AmBe neutron calibration data. Thesolid blue lines mark the 90 % upper and lower boundariesof the β / γ -band. The red and green lines mark the bands ex-pected for recoils off oxygen and tungsten, respectively. Thecalcium band lies in between the oxygen and the tungstenband and is not drawn for clarity.The description of the bands is done according to [12]. Themean of the Gaussian β / γ -band is given by a linear functionplus a term accounting for the non-proportionality effect caus-ing the bending down of the β / γ -band towards low energies[13]. Quenching factors quantify the reduction in light outputof a certain event type compared to a β / γ -event of the samedeposited energy. They were precisely measured in [12] andallow to calculate the nuclear recoil bands.For the present work we fit the neutron calibration data( β / γ -band plus nuclear recoil bands) utilizing an unbinnedmaximum likelihood approach. Using the neutron calibra-tion data, instead of the dark matter data directly, has sev-eral advantages. Firstly, it was found in [12] that differentcrystals exhibit a slightly different quenching for nuclear re-coils which, however, commonly affects all three nuclear re-coil bands. In previous analyses we determined this commonshift outside the likelihood fit by looking at oxygen scattersin neutron calibration data with energies above 150 keV. Thenew likelihood fit, instead, directly obtains the common shiftfrom the position of the nuclear recoil bands. The second ad-vantage of performing the fit on neutron calibration data is amore populated β / γ -band compared to dark matter data (com-pare figures 3 and 5).We would like to note that the term β / γ -band should morecorrectly be denoted β -band, as γ -rays are known to produceslightly less scintillation light than β -particles [13]. This is FIG. 3. Neutron calibration data for detector A in the light yieldversus energy plane. We fit these data to determine the bands for β / γ -events (blue), nuclear recoils off oxygen (red) and tungsten (green),where the respective lines correspond to the upper and lower 90 %boundaries of the respective band. The band description follows [12]. particularly apparent for the discrete γ -populations at 2.6 keVand 11.27 keV in figure 5 that are clearly centered below the β / γ -band. We model this effect in the new maximum likeli-hood fit. However, for means of clarity and convention, westick to the term β / γ -band.The neutron calibration data also confirm that nuclear re-coils and β / γ -events have only a negligible pulse-shape dif-ference. This justifies to use a single standard event as thebasis for triggering and energy calibration.
3. Data Pre-Selection
With stops in data taking for refills of cryogenic liquids,there are three data segments per week in standard data takingmode. In the rare cases of synchronization issues between thetwo data acquisitions (hardware-triggered and continuous) theaffected segments are discarded. To establish the analysis pro-cedure we define a non-blind training set by random selectionof twenty percent of the collected data segments. This proce-dure is then blindly applied to the remaining 80 %. All resultspresented in this work, apart from the calibration steps, referto the latter, ”blind” dark matter dataset.A binned rate cut is applied to remove periods of abnor-mally high rate, mainly due to small electronic disturbances,which were found to cluster in time. In total, this rate cutexcludes 14 % of measuring time.Through the injection of large heater pulses (control pulses)which heat the TES completely out of its transition, the cur-rent operating point in the transition curve is evaluated foreach detector. The measured height of the control pulses isfed to an online feedback loop which maintains a constant op-erating point by adjusting the heating power accordingly. Thecontrol pulses are saved for offline analysis to remove time intervals where the measured control pulse height deviates bymore than 3 σ from the mean of its Gaussian-shaped distribu-tion. The additional amount of measuring time removed bythis stability cut is 3 %.
4. Event Selection
Events where only the light channel triggered are removedfrom the dark matter analysis. The veto information fromthe instrumented CaWO sticks is exploited by removing allevents with a pulse height in the iStick channel above noise.Additionally, we apply dedicated cuts to remove artifactsmimicking a pulse and events with distorted baselines whichwould potentially impair the energy reconstruction.We quantify deviations of a real pulse from its nominalpulse shape during the application of the optimum filter al-gorithm. This is done by calculating the RMS difference be-tween the filtered real pulse and the filtered standard event,where the latter is scaled to the amplitude of the real pulse. Toincrease the sensitivity to such deviations, we restrict this cal-culation to a window of ±
30 ms around the peak of the pulse.We call this quantity RMS OF .The RMS of the truncated standard event fit (RMS SEF ) de-scribes the agreement between a measured event and the stan-dard event in the linear part of the detector response. This fitis performed simultaneously for phonon and light channel.RMS OF was found to be less affected by changing noiseconditions compared to RMS SEF , which indicates that RMS OF is more sensitive to the real pulse shape than RMS SEF . How-ever, for energies above 2.5 keV (see section IV 1) saturationeffects start to corrupt RMS OF while RMS SEF remains unaf-fected. For this reason we apply cuts on both RMS quan-tities, aiming to remove events deviating from the nominalpulse shape.A conservative muon veto cut is applied by rejecting detec-tor events in a time interval of [-5 ms, +10 ms] around a muonveto trigger. Most of the events triggering the muon veto arenot muons, but are due to radioactivity in the muon veto panelsor the PMTs which does not penetrate the shielding. Thus, thiscut almost exclusively removes randomly coincident events.The total loss is 7.6 % of measurement time, which is consis-tent with the muon veto trigger rate of 5.2 Hz. The cut valuesare conservatively based on considerations of detector timeresolutions; no apparent correlation between muon panel hitsand detector events was found. An additional cut on coinci-dences between detector A and other detectors, using a co-incidence window of ±
10 ms, is applied which causes negli-gible overall dead time and removes no further events in theacceptance region (see section V). The main purpose of thiscut is to remove potential neutron events which have a certainprobability to cause energy deposits in multiple detectors, incontrast to dark matter particles.The total exposure of the dark matter dataset after cutsamounts to 3.64 kg days; the average survival probability forsignal events, neglecting energy dependence, lies at approxi-mately 65 % (see next section).
5. Efficiency / Signal Survival Probability
FIG. 4. Efficiency obtained from simulated events and defined asprobability for a valid signal event to be triggered (light gray) andpass the selection criteria (dark gray) as a function of injected (sim-ulated) energy. The red line is a fit of the threshold with an errorfunction, confirming the claimed value of 30.1 eV.
To determine the probability for a valid signal to be trig-gered and survive the selection criteria we pass simulated sig-nal events through the complete analysis chain. The simu-lated events are created by superimposing the standard eventonto the continuous data stream at randomly selected points intime. The events are simulated with high statistics ( ∼ . · events for the full dark matter data set) and scaled in heightcorresponding to a flat energy spectrum from 0 to 20 keV.As the timing of the simulated pulses is random and theyare processed in the analysis chain exactly the same way asreal pulses, the resulting loss in the simulated spectrum ac-counts for all artifacts on the stream, as well as cut effects,pile-up between events and dead-time due to injected heaterpulses, providing an elegant and straightforward way of deter-mining the signal survival probability. In addition, this proce-dure implicitly accounts for potential time-dependencies suchas changing noise conditions. It should be noted, however,that pulse saturation effects are not taken into account in thesimulation. This implies that the optimum filter amplitude forsimulated pulses behaves strictly linearly, and a linearizationusing truncated fit results as discussed in section IV 1 is notperformed.Figure 4 shows the efficiency in bins of 1 eV where theefficiency is defined as the ratio of surviving events to sim-ulated events in the respective bin. The spectrum in lightgray corresponds to all triggered events, the one in dark grayto events remaining after applying all selection criteria. Asa cross-check we model the threshold with an error func-tion depicted in red. Its fit yields a value for the threshold of (30 . ± .
1) eV with a width of σ = ( . ± . ) eV; bothvalues agree with expectations for the optimum trigger (seesection III 1) within uncertainties. Two features become ap-parent for the light gray trigger efficiency. Firstly, there is apedestal of 12 % originating from pile-up of simulated eventswith previous large energy deposits or injected heater calibra-tion pulses. Such events are efficiently rejected by our selec-tion cuts, thus the pedestal vanishes for the efficiency aftercuts. Secondly, pulses corresponding to energy deposits ofless than ∼ . In order to obtain a dark matter exclusion limit, we needto know what the expected dark matter signal looks like af-ter triggering, energy reconstruction and event selection. Wesimulate this by injecting artificial pulses into the continuousstream that follow the pulse height distribution of the expectedrecoil spectrum for each dark matter particle mass (the darkmatter model will be discussed in section VI). This methodautomatically includes all relevant aspects, in particular trig-gering efficiency and energy resolution, thus resulting in adark matter recoil spectrum as it would be seen by our detec-tor . It should be explicitly noted that this newly implementedmethod overcomes the necessity of an analytic modeling ofthe detector response, in particular of the finite energy resolu-tion. This represents a simplification in the extraction of darkmatter results from the data, but above all avoids uncertaintiesintroduced by the model of the detector response and/or thedetermination of the efficiencies of the analysis pipeline.To save computation time we perform only the aforemen-tioned simulation, with a uniform energy distribution from0 keV - 20 keV, and re-weigh each simulated event accord-ing to the expected recoil spectrum for a specific dark matterparticle mass.We ensure the robustness of our dark matter results by twoconservative choices: Firstly, we do not make use of sub-threshold energies, i.e. energies below 30.1 eV, where the trig-ger efficiency is 50 %. Secondly, we reject simulated eventswhose reconstructed energies differ by more than two stan-dard deviations from the injected/simulated energies. Thelatter criterion defends against the impact of single outlierscaused by pile-up of a simulated event with a real particleevent. Such pile-up may result in an overestimate of the sur-vival probability of very small energy deposits.
V. DARK MATTER DATASET
The data used for dark matter analysis were taken betweenOctober 2016 and January 2018. The gross exposure beforecuts is 5.689 kg days. Typically, the optimum filter shows one global maximum at the position ofthe pulse and several local maxima before and after the main pulse [6, 9].The size of these local maxima for a control pulse (maximal possible pulseheight) approximately equals the size of a 0.4 keV energy deposition.
FIG. 5. Light yield versus energy of events in the dark matter dataset,after selection criteria are applied (see section IV 4). The blue bandindicates the 90 % upper and lower boundaries of the β / γ -band, redand green the same for oxygen and tungsten, respectively. The yel-low area denotes the acceptance region reaching from the mean of theoxygen band (red dashed line) down to the 99.5 % lower boundary ofthe tungsten band. Events in the acceptance region are highlighted inred. The position of the bands is extracted from the neutron calibra-tion data as shown in figure 3.
1. Light Yield
Figure 5 shows the dark matter data after all the cuts de-scribed before in the light yield versus energy plane. In accor-dance with figure 3, the blue, red and green bands correspondto β / γ -events and nuclear recoils off oxygen and tungsten, re-spectively. The red dashed line depicts the mean of the oxygenband, which also marks the upper boundary of the acceptanceregion, shaded in yellow. The lower bound of the acceptanceregion is the 99.5 % lower boundary of the tungsten band,its energy span is from the threshold of 30.1 eV to 16.0 keV.Events in the acceptance region (highlighted in red) are treatedas potential dark matter candidate events. We restrict the en-ergy range to 16 keV for this analysis since for higher energiesthe energy reconstruction cannot be based on the optimum fil-ter method due to saturation effects. This choice, however,hardly affects the sensitivity for the low dark matter particlemasses of interest. The choice for the acceptance region wasfixed a-priori before unblinding the data. We do not includethe full oxygen recoil band in the acceptance region becausethe gain in expected signal is too small to compensate for theincreased background leakage from the β / γ -band.
2. Energy Spectrum
The corresponding energy spectrum is shown in figure6 with events in the acceptance region highlighted in red.In both figures 5 and 6, event populations at 2.6 keV and ∼
11 keV are visible. These originate from cosmogenic activa-
FIG. 6. Energy spectrum of the dark matter dataset with lines visibleat 2.6 keV and 11.27 keV originating from cosmogenic activation of
W [11]. Gray: all events, red: events in the acceptance region (seefigure 5). tion of the detector material and subsequent electron capturedecays:
W + p → Ta + α , Ta EC −→ Hf + γ . The latter decay has a half-life of 665 days, which impliesa decreasing rate over the course of the measurement after ini-tial exposure of the detector material. The energies of the linescorrespond to the L and M shell binding energies of Hfwith literature values of E M =2.60 keV and E L =11.27 keV,respectively [14]. As already mentioned in section IV 1, theclearly identifiable 11.27 keV line was used to fine-adjust theenergy scale, and therefore to give an accurate energy infor-mation in the relevant low-energy regime. These features werealready observed in CRESST-II [11, 15]. Additionally, a pop-ulation of events at ∼
540 eV is visible, which hints at ECdecays from the N shell of Hf with a literature value ofE N =538 eV [14].Below 200 eV, an excess of events above the flat back-ground is visible, which appears to be exponential in shape.Due to decreasing discrimination at low energies, it cannot bedetermined whether this rise is caused by nuclear recoils or β / γ events (see figure 5). It should be emphasized that noisetriggers are not an explanation for this excess, as it extends toofar above the threshold of 30.1 eV. According to the definitionof the trigger condition in section III 1, the expected number ofnoise triggers for the full dataset would be around 3.6. We ob-serve an excess of events at lowest energies in all CRESST-IIIdetector modules with thresholds below 100 eV; the shape ofthis excess varies for different modules, which argues againsta single common origin of this effect. No clustering in time ofevents from the excess populations is observed. FIG. 7. Experimental results on elastic, spin-independent dark mat-ter nucleus scattering depicted in the cross-section versus dark mat-ter particle mass plane. If not specified explicitly, results are reportedwith 90 % confidence level (C.L.). The result of this work is depictedin solid red with the most stringent limit between masses of (0.16-1.8) GeV/c . The previous CRESST-II result is depicted in dashedred [16], the red dotted line corresponds to a surface measurementperformed with a gram-scale Al O detector [17]. We use a color-coding to group the experimental results: Green for exclusion limits(CDEX [18], CDMSlite [19], DAMIC [20], EDELWEISS[21, 22],SuperCDMS [23]) and positive evidence (CDMS-Si (90 %C.L.) [23],CoGeNT (99 %C.L.)[24]) obtained with solid state detectors basedon silicon or germanium, blue for liquid noble gas experiments basedon argon or xenon (DarkSide [25], LUX [26, 27], Panda-X[28],Xenon100[29], Xenon1t[30]), violet for COSINE-100 (NaI) [31],black for Collar (H) [32], magenta for the gaseous spherical pro-portional counter NEWS-G (Ne + CH ) [33] and cyan for the super-heated bubble chamber experiment PICO (C F ) [34]. The gray re-gion marks the so-called neutrino floor calculated for CaWO in [35]. VI. RESULTS
We use the Yellin optimum interval algorithm [36, 37] toextract an upper limit on the dark matter-nucleus scatteringcross-section. In accordance with this method, we considerall 441 events inside the acceptance region to be potential darkmatter interactions; no background subtraction is performed.The anticipated dark matter spectrum follows the stan-dard halo model [38] with a local dark matter densityof ρ DM = 0.3 (GeV/c )/cm , an asymptotic velocity of v (cid:12) =
220 km / s and an escape velocity of v esc =
544 km / s.Form factors, which are hardly relevant given the low trans-ferred momenta here, follow the model of Helm [39] in theparametrization of Lewin and Smith [40].The result of the present analysis on elastic scattering ofdark matter particles off nuclei is depicted in solid red in figure7 in comparison to the previous CRESST-II exclusion limit indashed red and results from other experiments (see caption and legend of figure 7 for details). The red dotted line cor-responds to a surface measurement with a 0.5 g Al O crys-tal achieving a threshold of 19.7 eV using CRESST technol-ogy [17].The improvement in the achieved nuclear recoil threshold,in the respectively best performing detectors, from 0.3 keVfor CRESST-II to 30.1 eV for CRESST-III, yields a factor ofmore than three in terms of reach for low masses, down to0.16 GeV/c . At 0.5 GeV/c we improve existing limits by afactor of 6(30) compared to NEWS-G (CRESST-II). In therange (0.5-1.8) GeV/c we match or exceed the previouslyleading limit from CRESST-II. VII. CONCLUSION
In this paper, we report newly implemented data process-ing methods, featuring in particular the optimum filter tech-nique for software-triggering and energy reconstruction. Thisallows one to make full use of the data down to threshold. Thebest detector operated in the first run of CRESST-III (05/2016-02/2018) achieves a threshold as low as 30.1 eV and was,therefore, chosen for the analysis presented.In comparison to previous CRESST measurements, an in-dication of a γ -line at approximately 540 eV compatible withthe N shell electron binding energy of Hf could be ob-served. Together with the reappearance of known lines, thiscorroborates the analysis of background components outlinedin [11], as well as the energy calibration in this work.At energies below 200 eV we observe a rising event ratewhich is incompatible with a flat background assumption andseems to point to a so-far unknown contribution. At the timeof writing, dedicated hardware-tests with upgraded detectormodules are underway to illuminate its origin.We present exclusion limits on elastic dark matter particle-nucleus scattering, probing dark matter particle masses below0.5 GeV/c and down to 0.16 GeV/c . VIII. APPENDIX1. Study of Systematic Uncertainties
As discussed in section IV the energy scale is adjusted us-ing the 11.27 keV γ -peak (Hf L shell). As a consequencethe energy scale is only strictly valid for events with a lightyield of one. In particular, for a nuclear recoil less scintilla-tion light is produced and, thus, more energy remains in thephonon channel leading to an overestimation of the phononenergy. Based on the fact that we measure both energies –phonon ( E p ) and light ( E l ) – one can account for this effect aswas shown in [15] by applying the following correction: E = η E l + ( − η ) E p = [ − η ( − LY )] E p . (1) FIG. 8. Illustration of the systematic uncertainty introduced by anoverestimation of the nuclear recoil energy scale as a consequenceof not correcting for the reduced scintillation light production of nu-clear recoils via equation 1. Drawn are the result of this work in solidred (also see figure 7) and an exclusion limit obtained via scaling ofthe energy scale by 7 % (dashed blue line), which corresponds to themaximal possible overestimation. It can be seen that this systematicuncertainty has only a minor impact on the exclusion limit. Not ap-plying the correction leads to a conservative exclusion limit for alldark matter particle masses.
In the above equation η is the scintillation light efficiencywhich was determined to be ( . ± . ) % in [15] for a crys-tal of the same origin as detector A, also grown within theCRESST collaboration.However, for very low energies, the baseline noise of thelight detector dominates the light signal, preventing a reason-able application of this correction. It should be noted that theresulting overestimation of the nuclear recoil energy scale isconservative as displayed in figure 8 where we show the exclu-sion limit after a reduction of 7 % of all event energies. Thisis the maximal possible systematic uncertainty introduced bynot applying the correction outlined in equation 1.
2. Results on Spin-Dependent Interactions
In this article we present first results of CRESST-III onspin-independent elastic dark matter nucleus scattering. How-ever, it deserves to be noted that the isotope O yields sensi-tivity for spin-dependent neutron-only interactions. The the-oretical framework as well as the calculation of the expectedrate exactly follows [41] and, thus, just the result is given here.Compared to [41], values for the nuclear spin ( J = + / A =
17) and the spin matrix element ( (cid:104) S n (cid:105) =0.5)[42, 43]are adjusted. We assume the O content to follow the min-imal natural abundance of 0.0367 % [44] which results ina gross O-exposure of only 0.46 g days. Following [45]and considering the rock composition of the LNGS overbur-den [46], we ensured that spin-dependent cross-sections of
FIG. 9. Results on spin-dependent neutron-only interactions via theisotope O in solid red (this work) and a result with Li in dashedred [41]. Additionally, we plot results from CDMS-lite on Ge [47],LUX [48], Panda-X [49] and XENON1t [50], all three on
Xe and
Xe. O (10 pb) can be probed over the whole mass range underconsideration. However, a more precise calculation of the up-per boundary of the exclusion is subject to future work.It should be stressed that nothing in the analysis chain butthe signal expectation was changed when switching from thespin-independent to the spin-dependent case. The result is de-picted in figure 9 in solid red, together with a result from anabove ground measurement of a Li MoO crystal in dashedred and exclusion limits from CDMS-lite, LUX and Panda-X(see caption for references).Obviously, the small exposure for this measurement com-bined with the very low abundance of O results in a compa-rably modest limit for dark matter particles above 1.5 GeV/c .However, the low nuclear recoil threshold of the presented de-tector A allows us to explore new parameter space for spin-dependent, neutron-only interactions from dark matter parti-cle masses of 1.5 GeV/c down to 0.16 GeV/c . ACKNOWLEDGEMENTS
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