Search for Dark Matter with CRESST
SSearch for Dark Matter with CRESST
Rafael F. Lang, Wolfgang Seidel
Max-Planck-Institut f¨ur Physik, F¨ohringer Ring 6, D-80805 M¨unchen, GermanyE-mail: [email protected]
Abstract.
The search for direct interactions of dark matter particles remainsone of the most pressing challenges of contemporary experimental physics. Avariety of different approaches is required to probe the available parameter spaceand to meet the technological challenges. Here, we review the experimental effortstowards the detection of direct dark matter interactions using scintillating crystalsat cryogenic temperatures. We outline the ideas behind these detectors anddescribe the principles of their operation. Recent developments are summarizedand various results from the search for rare processes are presented. In thesearch for direct dark matter interactions, the CRESST-II experiment deliverscompetitive limits, with a sensitivity below 5 × − pb on the coherent WIMP-nucleon cross section.PACS numbers: 29.40.Mc, 29.40.Vj, 95.35.+d Submitted to:
New J. Phys. a r X i v : . [ a s t r o - ph . I M ] J un earch for Dark Matter with CRESST
1. Introduction
The overwhelming evidence for dark matter is discussed in great detail in othercontributions to this
Focus Issue [1, 2, 3]. Particularly well motivated candidatesfor dark matter are Weakly Interacting Massive Particles, WIMPs for short [4, 5, 6].On the one hand, the experimental particle physicist tries to produce such particles atcolliders [7, 8, 9]. The observational astrophysicist on the other hand tries to detecttheir signature from Space, by recording their annihilation products [10, 11, 12, 13].Yet a third discovery channel exists through the identification of direct interactions ofWIMPs with a target.Today, this third detection channel is limited by the technological possibilities,which are pushed to their limits. A variety of experiments, each a distinctdevelopment, is set up to discover WIMPs through their direct interaction [14, 15, 16,17, 18, 19]. In this
Focus Issue contribution, we review the search using scintillatingcryogenic calorimeters and present recent advances. This technology is pursued bythe CRESST [20] and ROSEBUD [21] collaborations and will be used for the futureEURECA detector [22].To start, let us define the requirements imposed on any experiment that takes upthe challenge to directly detect interactions induced by WIMPs. For direct WIMP-nucleus scattering, the detection rateΓ = n target Φ σ (cid:48) (1)(where n target is the number of target atoms, Φ the flux of WIMPs, and σ (cid:48) the crosssection of the process) is obviously very low. From this one can already deduce twomajor requirements for any experiment that aims to detect such interactions: ( A ) itneeds to provide a large target mass and ( B ) it needs to be operational for a long time ,so that collected exposures account for many kilogram × weeks.Spin-independent WIMP interactions can take place coherently over the full targetnucleus. Then all the individual WIMP-nucleon scattering amplitudes σ add up inphase, increasing the above detection rate (1) toΓ = n target Φ σA (2)where A is the mass number of the target material. Therefore, it is advantageous fordirect searches to use ( C ) heavy target nuclei to search for spin-independent WIMPinteractions [23].The maximum recoil energy E r , max can readily be estimated to be E r , max = (2 p χ ) m N ∼ (cid:0) ×
100 GeV / c × − c (cid:1) ×
100 GeV / c = 200 keV (3)where m N is the target nucleus’ mass and p χ the WIMP momentum in the laboratoryframe. Here, we assumed a typical WIMP with mass m χ ≈
100 GeV / c expected fromextensions of the Standard Model of particle physics [24, 25], and an average velocity (cid:104) v (cid:105) ≈ − c typical for Galactic velocities in our neighborhood [26, 27]. However, E r , max is an upper limit, and typical recoil energies are much lower, as we will seeshortly. Hence, a major challenge for such experiments are ( D ) an energy thresholdlow enough given the small energies expected from an WIMP interaction , and ( E ) away to calibrate the nuclear recoil energy scale in this range .Properties of the phase space distribution of dark matter in our Milky Way andat the position of the Earth are inferred from N-body simulations [28, 2]. As anapproximation to the true distribution, the isothermal halo [29] is commonly used due earch for Dark Matter with CRESST f MB . In this first approximation, the expected spectrum of WIMP induced nuclearrecoils is a simple exponential:dΓd E r ∝ Φ ∝ (cid:104) v (cid:105) ∝ (cid:90) ∞ v χ f MB ( v ) v d v ∝ e − c v χ ∝ e − c E r (4)where v χ = (cid:112) E r /m N is the minimum WIMP velocity causing a recoil of energy E r , and c , are positive constants to make the exponential dimensionless. Therefore,no line signature is expected in direct WIMP scattering searches, and this leads toadditional requirements for these experiments. Most importantly, very efficient waysto discriminate the signal from various backgrounds are mandatory: Experiments( F ) need to be shielded against ambient radioactivity , need to be placed deepunderground to reduce the background induced by cosmic rays, and care must betaken in the selection of materials used in the vicinity of the detector. Beyond thispassive shielding, experience shows that ( G ) active discrimination between signal andbackground is required. In particular, one needs to have some means to ( H ) distinguishneutron induced nuclear recoils from WIMP induced ones . Information on theinteraction coordinates can help to reduce the background, and of course, a directionalsensitivity would be a good way to distinguish signal from background.Efforts to understand background processes at the energies of interest are showinglarge improvements in recent years. In case of a signal in the experiment, systematiceffects and many radioactive backgrounds can be excluded as alternative explanationsusing different target materials. Given current technology, this ( I ) multi-targetapproach seems a necessary requirement for the community to accept a claim of thedetection of a WIMP induced signal.As long as no discovery is claimed, an upper limit on the WIMP-nucleon crosssection is calculated. Due to the quasi exponential form of the spectrum, one wouldlike to consider energies as close to threshold as possible. To do this, it is necessaryto ( J ) demonstrate the trigger efficiency over the full energy range used.
2. Cryogenic Calorimeters
Most of the energy in an elastic scattering interaction is deposited in a target asphonons. Therefore, it is natural to meet the threshold challenge ( D ) with calorimetricdevices, where the principal part of the deposited energy is converted into a signal.In addition, such devices have the advantage that they can give a precisemeasurement of the deposited energy, as we will see shortly. Also, the excitationenergy of phonons is low compared to that of charge carriers. Statistical fluctuationsin the signal due to Poisson statistics are therefore minimized, which further reducesuncertainties in the energy inferred from an interaction. As a first approximation, we can model the calorimeter as a heat capacity C , andassume the phonons generated in an interaction are in thermal equilibrium. Then,the increase of temperature ∆ T in the calorimeter following a particle interaction issimply ∆ T = ∆ EC , (5) earch for Dark Matter with CRESST E is the deposited energy. Since heat capacities decrease with decreasingtemperature, cooling the calorimeter leads to a larger temperature signal for a givenenergy deposition. Commercially available He / He dilution refrigerators can readilyachieve temperatures in the millikelvin range and are used in many direct dark matterexperiments. More generally, cryogenic calorimeters are a mature technology withapplications in many different fields of science [31, 32].Thermometers with a measurable change of resistance at millikelvin temperaturesare superconducting phase transition thermometers (SPTs), in use for a variety ofdifferent applications [33, 34]. These thin metal films are stabilized in their transitionto the superconducting state, where the change of resistance ∆ R given a change oftemperature ∆ T is large, see figure 1. Figure 1.
Operating principle of superconducting phase transition thermometers(SPTs). The thermometer is stabilized in its transition to the superconductingstate, where its resistance R is strongly varying with temperature T . This allowsto measure the increase of resistance ∆ R following a particle interaction, hencededucing its energy. Materials that become superconducting in the millikelvin range are rare.Tungsten in its alpha phase becomes superconducting below ∼
15 mK [35] and canbe used directly as thermometer film [36]. Monocrystalline iridium has a transitiontemperature of 112 mK [37, 38], too high for the purposes here, but it can be loweredand adjusted using the proximity effect [39] in an iridium-gold bilayer [40, 41].A typical thermometer used in the CRESST-II experiment as a phonon detectoron a target crystal is a 200 nm thick 6 × tungsten film [42]. For metal films,the electronic contribution to the specific heat is γ T with γ ≈ − K − fortungsten [43]. Hence, a particle depositing 10 keV at an operating temperature of20 mK gives a temperature rise of 80 µ K, assuming a heat capacity as for a normalconducting metal film.To read out the corresponding small change of resistance of the low-ohmicthermometer, a SQUID based readout is used [44]. Superconducting QuantumInterference Devices are extremely sensitive in measuring the magnetic flux of aninput coil. A bias current is split in two branches, one through the thermometer,the other through reference resistors and the input coil of the SQUID. This schemeallows to read out the temperature of the thermometer with a precision of a few µK .As a consequence, energy thresholds well below 1 keV are readily obtained with suchdevices [45, 46]. Details of the SQUID system and data acquisition electronics usedin CRESST-II can be found in [47]. earch for Dark Matter with CRESST The thermodynamical picture of equation (5), ∆ T = ∆ E/C , needs to be refinedin order to understand the process of pulse formation in superconducting phasetransition thermometers. A more detailed model has been developed in [48]: An energydeposition in the absorber leads to a spectrum of high frequency optical phonons withinless than a nanosecond. Electron recoils from ionizing radiation eventually result inan almost monoenergetic population of acoustic phonons with about half the Debyefrequency ν Debye . On the other hand, nuclear recoils from elastic scatterings on nucleiresult in a continuous spectrum of acoustic phonons up to ν Debye .For CaWO as a target material, the Debye temperature is Θ Debye = 250 K [49],corresponding to ν Debye / k B Θ Debye / h ≈ E = k B T =8 . × − eV / K ×
15 mK = 1 µ eV. Hence, such THz phonons are called non-thermalphonons. They decay due to crystal lattice anharmonicities with a decay rate that isproportional to ν [50], or scatter with a rate proportional only to ν [51]. At a few100 GHz, still above thermal energies, and on a time scale of a few milliseconds, thephonons spread ballistically throughout the absorber and fill it uniformly after a fewreflections on the surface. ballisticnon-thermalphonons absorber thermalizationonelectron systemheat bath thermometerweakthermalcoupling Figure 2.
A particle interaction leads to non-thermal phonons that spreadballistically through the absorber. The thermometer has a strong thermalcoupling to the absorber. Non-thermal phonons penetrate this coupling andare thermalized on the electron system of the superconducting phase transitionthermometer.
Such non-thermal phonons are readily absorbed by the free electrons of the metalfilm in the thermometer (figure 2). This absorption is mediated by a strong couplingdue to space charge variations of the phonon oscillation. The strong interaction amongthe electrons in the thermometer then quickly disperses and thus thermalizes thephonon energy, which results in a heating of the thermometer. With superconductingphase transition thermometers, this temperature change is then measurable as achange in resistance. Since phonons are mostly absorbed in the thermometer alone,this allows to scale up the targets to the large dimensions used in the CRESST-IIexperiment [52, 53] and anticipated for future 1-ton-scale experiments, hence meetingthe challenge ( A ) of a large target mass. Challenge ( G ), being able to actively discriminate the nuclear recoil signal from thedominant electron recoil backgrounds, requires a second detection channel. In this Focus Issue contribution, we consider as discrimination parameter the light produced earch for Dark Matter with CRESST (Eu) or YAlO (Ce) is strongly degraded at cryogenic temperatures.Hence, self-activated scintillators are employed, since these have a high light yieldeven at low temperatures.Most commonly, CaWO crystals are used as a target [20, 58], since they have ahigh light yield even at cryogenic temperatures [59, 60] and were shown to be suitablefor the task already ten years ago [61]. The dimensions of these target crystalsis limited only by the Czochralski crystal growth process [62], and optically cleanCaWO crystals with masses of ∼ [63, 64].Besides being suitable for the application at millikelvin temperatures [65], it promisesto be cleaner and available in larger specimens [66]. ZnWO has a lower meltingtemperature of ∼ ◦ C [67] in comparison to CaWO , which melts only at ∼ ◦ C [68]. If the thermometer is evaporated directly onto the ZnWO crystal,this changes the stoichiometry of the crystal, and hence its scintillation properties.Only recently it was shown that this problem can be overcome using a gluingtechnique [69]. There, the thermometer is evaporated or sputtered [70] on a smallcarrier crystal, which is subsequently glued to the large target crystal. Measurementsshow that non-thermal phonons penetrate the glue layer, as can be described by simplemodels [71, 72]. Results from these investigations look very promising and enable theeasy mass production of such detectors for future ton-scale dark matter searches.Thus, ZnWO crystals with glued thermometers are already used in the search fordark matter [73, 74].CaMoO is an interesting target material due to the strongly differing WIMPrecoil spectrum ( A Mo = 96), but otherwise similar structure, hence ideally meetingthe multi target requirement ( I ). Although available specimen have shown inferiorlight yield at room temperature [74, 75], the light yield increases towards lowertemperatures, and eventually becomes comparable to that of CaWO [76]. CdWO may be used as an alternative target but shows a high intrinsic radioactivity [77].Investigations using BGO [78, 79] and doped sapphire crystals [80, 81, 82, 83] areunder way with very promising results. All these different available materials underconsideration make the multi-target requirement ( I ) easy to meet. Tungsten ( A W = 184) is the dominant scatter center (for experiments with a thresholdenergy below ∼
30 keV) for WIMPs in CaWO , due to the ∝ A dependence ofthe coherent WIMP interaction rate (equation 2 and benefit ( C )). This significantlyenhances the sensitivity of experiments with tungsten targets. However, form factoreffects become important. As is shown in figure 3, the expected spectral shape ofWIMP induced tungsten recoils is completely dominated by the form factor for WIMP earch for Dark Matter with CRESST m ≈
100 GeV / c , introducing a systematic uncertainty to be dealtwith. As a parametrization for the form factor, customarily the Helm form factor [84]is used since shown adequate by J. Engel [85]. Its parameters are adopted fromdata of electron scattering experiments, so an implicit assumption is that the WIMPscattering centers are distributed as the charge in the nucleus [86], and alternativeparameterizations [87, 88] may be used instead. However, we find that the integratedscattering rate above a given energy threshold typically changes only at the percentlevel for most WIMP masses and form factor models. Energy / keV0 20 40 60 80 100 120 140 160 / d E / / ( k e V kg d pb ) G d
10 GeV/c
30 GeV/c
100 GeV/c
300 GeV/c Figure 3.
The expected WIMP recoil spectrum in a pure tungsten target forvarious WIMP masses, calculated for the standard WIMP scenario [27]. Unitsare per 1 kg d of exposure, for a WIMP-nucleon cross section of 1 pb, and per1 keV energy bin. For light WIMPs, the recoil spectrum is almost the simpleexponential expected from equation 4. For heavy WIMPs, the spectral shape iscompletely dominated by the form factor, here assumed to be of Helm type.
To detect the scintillation light, the operation of photomultiplier tubes is not feasible,because at these low temperatures, the photocathode becomes non-conductive. Inaddition, photomultipliers are generally not radiopure, and the required high voltagecauses problems in millikelvin applications. Hence, a dedicated cryogenic light detectoris used in addition to the phonon detector.This light detector consists of a thin light absorbing substrate, equipped withanother phase transition thermometer [89]. Following a particle interaction in thecrystal, the scintillation light is absorbed in the wafer, creates phonons there, andcan hence be detected with a similar phase transition thermometer. This allows todiscriminate electron or gamma events from nuclear recoils [90], as is illustrated infigure 4 showing data from the original proof-of-principle experiment.This discrimination scheme has distinct advantages over other techniques:Degradation of the light signal for events that happen close to the crystal surfaceis not present [91], in contrast to ionizing detectors where surface effects may leadto a misidentification of an electron recoil as a nuclear recoil. This can also be seenin figure 4, since the gamma lines which originate throughout the crystal are in thesame band as the continuous background from electrons scattering on the surfaceof the crystal. In addition, since only a few percent of the signal are emitted aslight [92, 93, 94], the quenching of the phonon channel can be neglected, giving adirect measurement of the energy from that channel. earch for Dark Matter with CRESST Figure 4.
Operating a scintillating crystal as cryogenic target together with anappropriate light detector allows the discrimination of electron and nuclear recoilsat the low energies relevant for a dark matter search. Shown is a scatter plot ofthe energy in the light detector versus the energy in the phonon detector, on theleft with a Co gamma source and a Sr beta source, and on the right withan additional Am / Be neutron source. Electron and gamma events are clearlyseparated from neutron induced events. In addition, one can see that electronand gamma events form one common band. This demonstrates the absence ofany measurable light yield degradation near the surface of the crystal. Figurefrom [61].
In CRESST-II, silicon-on-sapphire wafers are commonly used as light absorbingstructure [89], but superconducting materials are an interesting alternative [95]. TheNeganov-Luke effect describes the enhancement of the light signal by the use of anelectric field [96, 97]. This can be used to obtain an improved performance of the lightdetectors [98], but stability issues have not yet been resolved to the precision requiredfor the long exposures needed in a WIMP search.
The target crystal with its phonon detector and the light absorber with its phonondetector are paired together in a housing and then referred to as a detector module.Figure 5 illustrates the concept, and figure 6 is a picture of an opened CRESST-IIdetector module. This modular structure makes these experiments almost triviallyscalable to larger target masses, as dictated by the large mass requirement ( A ).To increase the amount of light collected by the light absorber, the module isencapsulated in a reflector. Due to the cylindrical geometry of the holder, light mayundergo many reflections before it hits the light absorber, so a highly effective reflectoris mandatory. Hence, the CRESST-II detectors are encapsulated in a Radiant MirrorFilm VM2000/VM2002 from 3M [99]. These polymeric foils achieve a high reflectivitythrough a multilayer structure which is optimized for light guide applications, butsuitable also for the CaWO emission spectrum [100].A dangerous background for the search for dark matter comes from alpha decaysin the vicinity of the crystal. If the alpha escapes, the recoiling daughter nucleus mayimpinge on the crystal and mimic a heavy nuclear recoil [101, 20]. In order to be ableto distinguish such events from dark matter induced tungsten recoils, the reflectivefoil is also scintillating. Then the escaping alpha will produce additional scintillationlight, allowing to reject this background [102]. earch for Dark Matter with CRESST Reflective andscintillatinghousingTungsten thermometermeasuring scintillation lighttungsten thermometermeasureing total energy inputlight absorberCaWO target (300g) LightdetectorPhonondetector Heat bath (~6mK) Weak thermal coupling
Figure 5.
Concept of a CRESST-II detector module. Each module contains twoseparate tungsten thermometers. One is directly attached to the target crystal,measuring the total deposited energy. To measure the scintillation light, a thinlight absorber together with the second thermometer is placed in the vicinity ofthe crystal. The structure is encapsulated in a reflective and scintillating housing.
Figure 6.
Picture of an opened detector module as used in CRESST-II. On theleft, the (orange) wafer is the silicon-on-sapphire light absorber, the transitionedge sensor is the tiny structure on it. On the right, the crystal can be seen withthe phonon detector evaporated on it. The crystal is enclosed by the scintillatingreflective foil and held by custom made springs. Bonding wires for thermal andelectrical contact are just about visible. earch for Dark Matter with CRESST In a compound material like CaWO , neutrons will be seen above threshold mainlyif they scatter from light elements (like oxygen) due to simple two-body kinematics.On the other hand, we saw already in the introduction that we can expect WIMPs toscatter mainly from heavy elements (like tungsten) due to the ∝ A enhancement of thecoherent scattering cross section. With scintillators, different recoiling nuclei can bediscriminated by their different light yield. This opens the possibility to discriminatethe neutron background from WIMP induced events (as required by challenge ( H ))even when the neutrons do not double scatter, a feature unique to this method. Tothis end, precise knowledge of the light yield from tungsten recoils is required.We define the light yield of an event as detected light over detected energy,normalized to unity for electrons of 122 keV. One approach to measure this valueuses neutron scattering on a CaWO target at room temperature [103]. The crystalis irradiated with neutrons of known energy from an accelerator, and the scintillationlight is measured with a photomultiplier. The angle and the time of flight of thescattered neutrons are recorded. Hence, the kinematics are fixed, and the energytransfer can be calculated. This allows to identify on which nucleus the neutronscattered, and hence to derive the light yield for nuclei present in the crystal. However,for tungsten recoils, only a limit on their light yield could be given [104].The measurement with the usual cryogenic setup with superconductingthermometers for both energy and light determination proves to be difficult, since theobserved nuclear recoils induced by common neutron sources are dominantly oxygenrecoils, whereas tungsten recoils become dominant only well below 10 keV. Only veryrecently this approach was successful in giving a value of the light yield of tungstenrecoils using a dedicated cryogenic setup with accelerator produced neutrons [105].Experiments combining both above variants are under way [106]. Measuring therecoil energy via the cryogenic phonon detector as well as the angle of the scatteredneutron and its time-of-flight gives redundant information which helps to reducesystematic errors.A third way to measure the light yield of various recoiling nuclei uses a massspectrometer technique. The starting point for this approach is the understandingthat the scintillation light is not caused by the incident gamma, neutron, or WIMP,but by the recoiling nucleus. Hence, different ions can be accelerated onto the CaWO target. The only difference between such external nuclei and nuclear recoils is due tothe binding energy of an atom within the crystal, but since this is of the order of eV,it can safely be neglected when dealing with nuclei which have energies in the keVrange. Therefore, in the absence of surface effects, the light output following such anexternal irradiation will just be the same as if the nucleus recoiled following a particleinteraction within the crystal. This method has the major advantage that a largevariety of different nuclei can be studied. In addition, the energy of the impingingnucleus can be freely adjusted in the range of interest. Making use of the known time-of-flight of the nuclei through the mass spectrometer allows for clean trigger conditionsand hence a low energy threshold. Measurements were done using a 5 × × cubic CaWO crystal at room temperature, and the scintillation light was read outwith a photomultiplier [107, 108].Figure 7 shows the light yield for various recoiling nuclei, measured at differenttemperatures and using the above independent methods. Two additional points fromin situ measurements with the CRESST-II setup are shown in the graph: One comes earch for Dark Matter with CRESST Pbat room temperature [109] and using the CRESST-II setup [102], which is not yetexplained. A general trend is observable which can be understood theoretically [108].To summarize, we can expect the light yield of alpha particles as 0 . ± . . ± .
006 and of tungsten recoils as 0 . ± .
002 (values relativeto the light yield of electrons).
Atomic Mass of Recoiling Nucleus / amu0 20 40 60 80 100 120 140 160 180 200 L i gh t Y i e l d Figure 7.
Various measurements of the light yield of different recoiling nuclei: (cid:72) : From the mass spectrometer technique at room temperature [107]. (cid:78) : Refinedmeasurements with the mass spectrometer technique at room temperature, alsousing a refined error estimation [109]. • : From neutron scattering at roomtemperature [110]. (cid:3) : Preliminary results from neutron scattering at cryogenictemperatures [105]. (cid:70) : In situ measurements at cryogenic temperatures using theCRESST-II setup [91, 102].
3. The CRESST-II Experiment
The Cryogenic Rare Event Search with Superconducting Thermometers CRESST-II [111] is located in the Laboratori Nazionali del Gran Sasso [112] under a minimumrock overburden of 1400m of dolomite rock, where the surface muon flux is reducedby six orders of magnitude to about 2 m − h − [113, 114]. The He / He dilutionrefrigerator needed for operation at millikelvin temperatures is commercially availablebut contains various materials that are not suited for low background applications.This gives the CRESST-II setup its peculiar arrangement, shown in figure 8. In thissetup, the cryostat is kept away from the shielded detectors, and the cooling poweris transferred into the shielded volume via a 1 . crystals. All parts within the experimental volume are custom made,mostly from ultra pure copper [45, 20]. The experimental volume is surrounded, fromthe inside to the outside, by the thermal shields of the cryostat, 14 cm of copper and earch for Dark Matter with CRESST F ). Figure 8.
The CRESST-II setup. The cryostat, in the upper half of the picture,is kept away from the detectors since it is made from standard, i.e. non-radiopure,materials. The shielding consists of copper (orange), lead (grey), the radon box(thin line), the muon veto (blue), the neutron moderator (polyethylene in yellow,water in blue and the helium and nitrogen in the cans of the cryostat). The wholeshielding is mounted on wagons movable on rails to allow access to the detectors. earch for Dark Matter with CRESST
4. Detector Operation
To facilitate the operation of superconducting transition thermometers for thesearch for dark matter, an additional heater structure is used. This heater consistsof a gold film with a thickness of a few 10s of nanometers that is evaporated directlyonto the thermometer film. Pulses of given energies are injected to this gold film inregular time intervals. The response pulse of the thermometer to this injected energycan then be used to infer a variety of very useful informations, as we describe in thefollowing.
A superconducting phase transition thermometer is characterized by its transitioncurve. The lower the transition temperature, the smaller the heat capacity of thethermometer film, hence the larger the signal for a given interaction. The steeper thetransition, the better the sensitivity of the film. Conversely, the wider the transition,the larger the linear dynamic range of the thermometer. The latter is however nota crucial point since even pulses that drive the thermometer normal conducting canreadily be analyzed with still excellent energy resolution, as we will see in section 5.2.For a fixed bias current, heater pulses of varying amplitude are injected to theheater structure, thus directly probing the response of the detector to various injectedenergies. One is then free in choosing the operating point to give the detector thedesired properties. The thermometers are usually set up at the top half of thetransition since the noise is generally smaller there [117, 31].
The low energy interactions of interest here result in temperature changes of thethermometer film of a few µ K. Hence, the film temperature needs to be stabilizedto similar precision. This requires a weak thermal coupling of the detector modulesto the cryostat as well as an active temperature control. To this end, heater pulsesare injected to the heater structure every few seconds, which is frequent enough tosample temperature variations of the cryostat, but does not introduce too much deadtime. These injected heater pulses are large enough to drive the thermometer out ofits transition. The response pulse from the thermometer is evaluated online and servesas an input variable for a PI control of the operating point through an adjustment ofa steady current through the heater structure.Figure 9 shows the amplitude response of the light detector to injected heaterpulses, demonstrating the highly stable conditions achievable. The small width ofobserved spectral lines in the phonon detector (see section 5.3) is only obtainable undersuch stable running conditions. In addition, the readiness of the detector to identifydark matter interactions is monitored by this procedure, hence meeting challenge ( B )concerning long measuring times. A Co calibration gives calibration lines at 122 keV and 136 keV as well as a set ofescape lines between (50 −
80) keV. Figure 10 shows a typical calibration spectrum ofa phonon detector and its light channel [118]. earch for Dark Matter with CRESST Figure 9.
The amplitude response of the light detector to injected heater pulsesis constant within resolution and demonstrates the high stability of the detectorsover many weeks of running time [58]. The energy is in units of keV ee (keVelectron equivalent), defined such that an electron of 122 keV deposits 122 keV ee in the light detector. Energy / keV0 20 40 60 80 100 120 140 160 180 E n t r i e s p e r e V E n t r i e s p e r e V ee Figure 10.
Data from a Co calibration of a phonon detector (lower spectrumin red and scales on the left and bottom) and its light detector (upper spectrumand scales on the top and right). The resolution of the phonon channel is an orderof magnitude better than that of the light channel. The 122 keV and 136 keV linesfrom Co and escape lines between (50 −
80) keV are visible. earch for Dark Matter with CRESST O (100 keV) gammas, but the energy range of interestis O (10 keV). To meet the energy calibration challenge ( E ), a method is thereforerequired to take the energy calibration down to lower energies. This is also achievedwith the help of the heater structure on the thermometer. Heat pulses with energies inthe range of interest are injected to the heater at regular time intervals, typically every30 seconds. Since one has the injected energy under control, the amplitude responseof the thermometer can then be used to take the energy calibration from O (100 keV)down to below 10 keV [118].This energy calibration procedure is validated by the location of spectral lines atthe expected energies. A variety of such features can be identified. Of particularinterest are spectral features recorded during the search for dark matter, whichconstitute an in situ calibration during the long exposure [118]. The lowest energyexample of such a feature is the decay of Ca at 3 . E ). The trigger efficiency to low energy nuclear recoils is a crucial parameter especiallywhen a limit on the WIMP-nuclear scattering cross section is to be placed. Anyexperiment aiming to do so needs to demonstrate its trigger efficiency over the fullenergy range used for the WIMP analysis, as pronounced in requirement ( J ). Inaddition to the usual usage of a neutron calibration and its comparison to expectedscatter rates, the heater structures on CRESST-II detectors provide the possibility todirectly measure this value. Heat pulses are injected to the phonon detector over thefull energy range of interest. The number of pulses that trigger are a direct measure ofthe trigger efficiency, and can be seen in figure 11 to be constant over the full energyrange probed. Energy / keV0 5 10 15 20 25 30 35 40 45 E n t r i e s p e r B i n Figure 11.
Heater pulses from a set of fixed energies are injected every fewseconds throughout the WIMP search. The number of triggered responses isshown here and can be seen to be constant, proving the constant trigger efficiencyin the probed energy range. For the search for dark matter, an analysis thresholdof 10 keV is imposed [20], well in the range of constant trigger efficiency. earch for Dark Matter with CRESST The position of the gamma and electron recoil band and the resolution of the lightdetector is determined from calibration data or directly from the WIMP search data.The position of the expected WIMP induced signal region is then calculated basedon the light yield of tungsten recoils. To demonstrate the validity of this approach,data is taken with a neutron source present. The position of the neutron inducednuclear recoil band is expected to follow the calculated band of oxygen recoils. Thiscan indeed be seen in figure 12, where the calculated line below which 90% of oxygenrecoils are expected is also drawn, hence validating this procedure [20].
Energy / keV0 10 20 30 40 50 60 70 80 90 100 L i gh t Y i e l d -0.500.511.52 0510152025303540 Figure 12.
Testing a detector with an external neutron source. Negative lightyield values arise from the fitting procedure which allows for negative amplitudesin order to treat baseline noise in an unbiased way. The upper electron recoilband as well as the lower nuclear recoil band are well separable above ∼
10 keV.Below the dashed line, 90% of oxygen recoil events are expected based on theindependent light yield measurements described in section 2.7. The data can beseen to agree well with this expectation [20].
5. Results
The main objective of the CRESST experiment is of course the search for dark matter.Yet the unique properties of the employed detectors led to a variety of other notableresults. In this section, we briefly review these results before presenting the currentstatus of the experiment regarding the search for dark matter.
First measurements using large (non-scintillating) sapphire crystals led to a triggerrate orders of magnitude above the expected level. A statistical analysis showed thatevents were not Poissonian distributed. Eventually these events were identified asbeing due to cracks developing in the crystals due to a too tight clamping [119, 120].Today, such devices can be used to make the most sensitive measurements of stress earch for Dark Matter with CRESST
All naturally occurring tungsten isotopes are expected to alpha decay into hafnium,but with extremely long lifetimes. Since the decay energies for all these decays arein the same energy range as beta and gamma backgrounds from the natural decaychains, their observation is a difficult task. Yet with cryogenic scintillator experiments,these backgrounds can be discriminated from the alpha signal, leading to a basicallybackground free measurement of such alpha decays, see figure 13. Hence, the naturaldecay of
W was observed unambiguously for the first time. The half-life wasdetermined to be T / = (1 . ± . × years at a precisely determined Q-valueof (2516 . ± . ± . T / > × years could be set. Energy / keV2350 2400 2450 2500 2550 2600 2650 C oun t s / e V B i n Figure 13.
Alpha events observed in one crystal with an exposure of 12 . W alpha decay, togetherwith a Gaussian fit to the peak. The measurement can be seen to be basicallybackground free [91] and constitutes the first unambiguous measurement of thisdecay.
All materials that are exposed to cosmic rays are activated. The activation of tungstenin reactions W( p, α ) Ta or W( p, t ) W leads to X-ray lines at 65 . . Ca,which decays with a half-life of 10 years via electron-capture to K. The resultingsignal in the calorimeter is the K shell binding energy of potassium at 3 .
61 keV.This line has been observed with the CRESST-II detectors with an activity of only(26 ± µ Bq [118], corresponding to only one Ca isotope in (2 . ± . ×
16 40
Caatoms, see figure 14. This constitutes the most precise measurement of this abundanceto date, more than an order of magnitude more sensitive than other measurementswhich are typically done by accelerator mass spectrometry [129, 130]. earch for Dark Matter with CRESST Energy / keV0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 C oun t s / ( k e V kg d ) Figure 14.
A low energy background spectrum, recorded with one crystal afteran exposure of 21 . Ca at 3 .
61 keV is clearly visible [118].The line at 8 . The coherent WIMP-nucleon scattering cross section has been constrained with datafrom two detector modules taken during the prototyping phase of the CRESST-IIexperiment [58], and from two detector modules taken during the commissioning phaseof the new setup [20]. Data from the latter are shown in figures 15 and 16 after anexposure of about three months to background radiation alone.
Energy / keV0 10 20 30 40 50 60 70 80 90 100 L i gh t Y i e l d -0.50.00.51.01.52.0 Figure 15.
Scatter plot of events observed in one detector with an exposureof 24 . earch for Dark Matter with CRESST Energy / keV0 10 20 30 40 50 60 70 80 90 100 L i gh t Y i e l d -0.500.511.52 Figure 16.
Scatter plot of events observed in another detector with a similarexposure of 23 . In the absence of a clear signal, a limit on the coherent WIMP-nucleus scatteringcross section is calculated using standard assumptions on the dark matter halo [27, 86].The fact that a nucleus is not point-like is taken into account by assuming the Helmform factor [84], which basically limits the energy transfer to the tungsten nucleito energies below 40 keV for all WIMP masses. In the energy region above 10 keV,where recoil discrimination becomes efficient, to up to 40 keV, three events in thetungsten recoil area were observed in the data of figures 15 and 16. The upper limitfor the WIMP scattering cross-section per nucleon is set using Yellin’s maximum gapmethod [131], and shown as the solid curve in figure 17. The minimum of this curveis below 5 × − pb.Besides the standard WIMP scenario, other models of the nature of dark matterand its interactions have to be considered. One such example is the Inelastic darkmatter model [138, 139]. There, the WIMP undergoes a transition to an excitedstate in the scattering process. Hence, the total energy E CM that is available in thescattering process needs to be larger than the splitting energy of the excited level,which is O (100 keV) above the ground state. Trivially, E CM = 12 µv (6)with the relative velocity of dark matter particle v and the reduced mass µ .Interactions in a heavy target have a large reduced mass µ and hence a largeenergy E CM available to excite internal states of the WIMP. Thus, the CRESST-II experiment, with tungsten as the heaviest target nucleus used in any direct WIMPsearch today, places the most stringent constraints on these models. Figure 18shows as an example one such exclusion for a particular set of splitting energy andhalo parameters. In particular, the figure also shows the exclusion curves from theXENON10 and CDMS experiments for comparison with figure 17. earch for Dark Matter with CRESST WIMP Mass / GeV/c10 20 30 40 50 100 200 300 400 1000 W I M P - N u c l e on C r o ss S ec ti on / pb -8 -7 -6 -5 -4 WIMP Mass / GeV/c10 20 30 40 50 100 200 300 400 1000 W I M P - N u c l e on C r o ss S ec ti on / pb -8 -7 -6 -5 -4 Figure 17.
Current upper limits on the coherent WIMP-nucleon cross sectionas a function of WIMP mass. The solid line comes from the CRESST-II experiment [20]. The grey region is a prediction from theory [132].Limits from other experiments are also shown: CDMS [133] (lower dotted)and EDELWEISS [134] (upper dotted), XENON10 [135] (lower dashed) andWARP [136] (upper dashed), and ZEPLIN-III [137] (dash-dotted). WIMP Mass / GeV/c60 80 100 120 140 160 180 200 220 240 W I M P - N u c l e on C r o ss S ec ti on / pb -4 -3 -2 WIMP Mass / GeV/c60 80 100 120 140 160 180 200 220 240 W I M P - N u c l e on C r o ss S ec ti on / pb -4 -3 -2 Figure 18.
Current upper limits on the WIMP-nucleon scattering cross sectionfrom the CRESST-II experiment (red solid line) as a function of WIMP massin an Inelastic dark matter model with an excited WIMP state 120 keV abovethe ground state, and for a Galactic escape speed of 500 km / s [139]. Theshaded areas are the 90% and 99% confidence contours from the DAMA/NaIand DAMA/LIBRA experiment. The constraints from the two most stringentexperiments in the standard scenario (figure 17) are also shown for this model:XENON10 (dashed) and CDMS (dotted). More details as well as limits fromother experiments can be found in [139]. earch for Dark Matter with CRESST
6. Conclusions
We have formulated a set of requirements for any experiment that aims to directlydetect the interaction of WIMPs with a target, and shown in turn how theserequirements are met by the CRESST-II experiment. We gave examples for thesensitivity of experiments with cryogenic scintillators to rare decays, such as the alphadecay of
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