Results on light dark matter particles with a low-threshold CRESST-II detector

Today, there is overwhelming evidence for the existence of dark matter. Precision measurements, e.g. of the cosmic microwave background, ascribe roughly one fourth of the energy density of the universe to dark matter, five times more than ordinary matter [1].

However, physicists did not yet succeed to reveal its underlying nature. One of the most favored solutions is the existence of weakly interacting massive particles (WIMPs) thermally produced in the early universe. Those particles are beyond the Standard Model of particle physics and would have a mass in the range of \(\sim \)10 GeV/\(c^2\) to 1 TeV/\(c^2\) and an interaction cross section of the weak scale. The Lee–Weinberg bound excludes WIMPs lighter than \(\sim \)2 GeV/\(c^2\), since they would lead to an overclosure of the universe [2]. However, in the last years light dark matter particles below the WIMP scale gained more and more interest. In particular, asymmetric dark matter models are considered a viable option as they do not only provide an explanation for dark matter, but also connect its generation to the baryon asymmetry [3].

The Cryogenic Rare Event Search with Superconducting Thermometers – CRESST – is one of numerous direct searches around the globe aiming to detect dark matter particles elastically and coherently scattering off target nuclei. To shield against cosmic radiation the experiment is located in the Laboratori Nazionali del Gran Sasso (LNGS) underground laboratory in central Italy. In CRESST-II scintillating CaWO\(_4\) single crystals are cooled to mK temperatures [4, 5]. While most of the energy deposited in a particle interaction induces a phonon (heat) signal, a small fraction (\(\lesssim \)5 %) is emitted as scintillation light. The phonon signal yields a precise energy measurement, whereas the simultaneously recorded light signal allows for particle identification, a powerful tool to discriminate electron recoils (dominant background) from the sought-for nuclear recoils. The signals of phonon and light detector are measured with independent transition edge sensors (TES) read out by SQUIDs [4, 5]. We call the ensemble of phonon and corresponding light detector a detector module. Each detector is equipped with a heater to stabilize the temperature in its operating point in the transition between normal and superconducting state. Via the heater we also inject pulses which are used for the energy calibration and for the determination of the energy threshold.

This technology yields accurately measurable sub-keV energy thresholds and a high-precision energy reconstruction. Combining these features with the light target nuclei, CRESST-II detectors have a unique potential to explore the low-mass regime with dark matter particle masses of below 1 GeV/\(c^2\).

In August 2015 CRESST-II finished its second extensive data taking campaign, referred to as phase 2, featuring 18 detector modules with a total mass of 5 kg. Most of the data acquired in two years of measurement time is dark matter data accompanied by calibrations with 122 keV \(\gamma \)-rays (\(^{57}\)Co-source), high-energy \(\gamma \)-rays (\(^{232}\)Th-source) and neutrons (AmBe-source). In 2014 we reported on first results from phase 2, analyzing the detector module with the best overall performance in terms of background level, trigger threshold and background rejection [6]. This non-blind analysis proved for the first time that CRESST-II detectors provide reliable data for recoil energies down to the threshold of 0.6 keV [6]. Afterwards, we lowered the trigger thresholds of several detectors, achieving 0.4 keV for the module used in [6] and 0.3 keV for the module Lise, which is the lowest value obtained in phase 2.

In contrast to the module used for the 2014 result [6], Lise is not equipped with the upgraded crystal holding design which uses CaWO\(_4\)-sticks instead of metal clamps. The upgraded holding scheme avoids any non-scintillating surface in line-of-sight to the crystal, thus efficiently vetoing backgrounds induced by \(\alpha \)-decays on or slightly below surfaces [7]. We want to emphasize that the lower threshold of Lise is not connected to the holding concept, but solely arising from a superior performance of the phonon detector.

Based on the method already discussed in [6] we analyze 52.2 kg days of data taken with the module Lise (300 g) and its threshold set at 0.3 keV. A blind analysis is carried out by first defining a statistically insignificant part of the data set as a training set. In the previous phase 1 [8] we proved that CRESST-II detectors can be operated stably over long time periods, in particular concerning the energy reconstruction. This is also confirmed for Lise as will be discussed in Sect. 5. Thus, the training set is well suited to develop all methods of data preparation and selection. We then apply them blindly – without any change – to the final data set. Data from the training set is not part of the final analysis.

For cross checks and validation four independent analyses covering the complete process from raw data to final result are performed. Based on the training set results one analysis is chosen a-priori. However, the results on training set and final data of all different analyses are consistent.

The energy calibration uses heater pulses of several defined energies which are injected periodically throughout the entire data taking period [4, 5]. These pulses are of similar shape compared to those induced by particle interactions. The heater pulses are used to define a linear response over the entire dynamic range of the detector. The absolute energy scale is finally set by evaluating 122 keV \(\gamma \)-rays during dedicated calibrations with a \(\mathrm {^{57}}\)Co-source.

The energy spectrum after cuts is shown in Fig. 3. The peak at 2.7 keV is due to cosmogenic activation of tungsten, the copper fluorescence line can be seen at 8.1 keV. The dominant double peak around 6 keV originates from an accidental illumination with an \(^{55}\)Fe X-ray source installed to calibrate the light detector of a close-by detector module. Despite the significant count rate in the double peak, it only marginally impacts the sensitivity for low-mass dark matter particles because of its high energy and distinct line shape.

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Depicted in Fig. 3 is the result from a fit of a data-driven background model. The model includes the signal survival probability, as discussed previously, a linearly decreasing background (dashed black line) and the observed low-energy lines. The positions of the peaks are free parameters in the unbinned likelihood fit of the model, whereas the widths of the peaks are described by a linear function allowing for an energy dependence of the resolution.

As mentioned earlier, the artificial nuclear recoil events, as used to determine the signal survival probability, are created by superimposing baseline noise samples with signal templates. For those artificial events the baseline noise – equivalent to the resolution at zero energy – is the only effect causing a finite resolution of the reconstructed energy. This method provides a more precise and – due to the high number of empty baselines – statistically superior estimate compared to a fit of lines in the low-energy spectrum. The determined value of \(\sigma _0=(62\pm 1)\) eV is included as a fixed parameter in the background model, whereas the linear term may be varied by the fit.

A comparison between literature values \(\mathrm {E_{lit}}\) and fitted energies \(\mathrm {E_{fit}}\) of low-energy lines can be found in Table 1. Although we do not use these lines for calibration we find an excellent agreement with the nominal energies, demonstrating the outstanding accuracy of our energy reconstruction. Listed in the last column of Table 1 is the energy resolution evaluated at the respective position of the line.²

For every particle interaction the total energy deposited in the crystal is shared between the phonon and the light detector. This split-up differs for different event classes, in particular for \(\gamma \)-rays (used for calibration) compared to nuclear recoils (potential dark matter signal). Nuclear recoils produce less light and, thus, more energy remains in the phonon detector. In [6] we successfully demonstrated that a precise measurement of the scintillation light allows to take into account this effect accurately. Typical light detectors operated in phase 2 (like the one used in [6]) have an energy resolution which is one order of magnitude better than the one of Lise. For the energies of interest, the light signal in Lise is, therefore, dominated by statistical fluctuations of the baseline noise. Thus, we do not apply the correction as used in [6]. This causes the slight overestimation of the reconstructed energies in the order of a few percent, as can be seen in column four of Table 1. In any case, we find this deviation to have negligible influence on the final result.

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The sensitivity for light dark matter critically depends on the ability to trigger and reconstruct events of very low energies. To prove a stable trigger efficiency over time we periodically inject low-energy heater pulses (corresponding to \(\sim \) 0.4 keV). In Fig. 4 the fraction of these pulses triggering is shown in black together with statistical (binomial) errors. The trigger efficiency at 0.4 keV is slightly higher (\(\sim \)95 %) in the final data set compared to the one determined in Fig. 1 (\(\sim \)90 %). Thus, the value of 307 eV measured for the threshold energy is conservative.

The high statistics in the \(^{55}\)Fe double-peak allows us to monitor the accuracy of our energy reconstruction and the stability of the energy resolution at low energies over time. In each time bin a combined fit of two Gaussians is performed to extract the reconstructed peak positions of the \(\mathrm {K_{\alpha }}\) (blue) and \(\mathrm {K_{\beta }}\) (magenta) lines (see Fig. 4). The small variations of the peak positions show the very stable operation of the detector. In addition, a scatter plot of the relevant events (grey dots) further illustrates that the means and also the line widths of the two peaks remain stable over time.

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In Fig. 5 we present the light yield – defined for every event as the ratio of light to phonon signal – as a function of energy. Recoils on electrons have the highest light output, set to one by calibration (at 122 keV). The solid blue lines mark the 90 % upper and lower boundaries of the e\(^-/\gamma \)-band, with 80 % of electron recoil events expected in-between. The band is determined by an unbinned likelihood fit to the data [7]. Two prominent features can be seen in the e\(^-/\gamma \)-band, the double peak at \(\sim \)6 keV originating from the \(^{55}\)Fe-source and a \(\beta \)-decay spectrum from an intrinsic contamination in the crystal with \(^{210}\)Pb starting at 46.5 keV. As mentioned before, in this analysis we do not correct the energy for events exhibiting a different energy sharing between phonon and light detector compared to the 122 keV \(\gamma \)-rays used for calibration. Thus, small statistical fluctuations in light output cause a slight tilt of the left shoulder of the \(^{210}\)Pb \(\beta \)-spectrum [6, 11].

Nuclear recoils produce less light than electron recoils, as quantified by the quenching factor for the respective target nucleus. The quenching factors, including their energy dependence, are precisely known from dedicated external measurements [12] and allow to analytically calculate the nuclear recoil bands for scatterings off tungsten (solid green), calcium (not shown) and oxygen (solid red), starting from the e\(^-/\gamma \)-band. The validity of this approach is, for example, shown in [8] and was confirmed with a neutron calibration.

There are four events (blue circles) in the data well below the 5\(\sigma \) lower boundary of the e\(^-/\gamma \)-band (dashed blue). These events are statistically incompatible with leakage and, thus, indicate the presence of an additional source of events in this module, apart from e\(^-/\gamma \)-background. As discussed in the introduction, Lise is of a conventional module design using non-scintillating clamps to hold the crystal and, therefore, is not capable of vetoing all events originating from \(\alpha \)-decays on or slightly below surfaces [7, 8]. Additional data from Lise (before lowering the threshold) and the ten other conventional modules further underpins this explanation.

To calculate the expected recoil spectrum of dark matter particles we make use of the following standard assumptions on the dark matter halo: Maxwellian velocity distribution, asymptotic velocity of 220 km/s, galactic escape velocity of 544 km/s and local dark matter density of 0.3 GeV/cm\(^3\). We use the Helm parametrization of the form factors [15] quantifying effects of the nuclear substructure on the scattering cross-section. Finally, the choice of the acceptance region in the light yield - energy plane and the energy resolution at zero energy (baseline noise) are taken into account. For the latter we use the value of \(\sigma _0=(62\pm 1)\)  eV as determined by the evaluation of the artificial signal events (see Sect. 4).

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Figure 7 shows the number of expected events to be observed by the detector Lise in the final data set as a function of the mass of the dark matter particle. The lines are normalized to a dark matter particle-nucleon cross section of 1 pb (\(\equiv \) \(10^{-36}\) cm\(^2\)). The colored curves (see legend) correspond to the three target nuclei oxygen, calcium and tungsten. The total sum of the three constituents is drawn in solid black.

Due to the anticipated A\(^2\)-dependence of the cross section, dark matter particles are supposed to dominantly scatter off the heavy tungsten. The energy transferred in the scattering process is a function of the reduced mass of target nucleus and dark matter particle. Thus, for a given mass of the dark matter particle the fraction of the expected energy spectrum above threshold depends on the mass of the target nucleus.

As a result, for dark matter particles with masses above 5  GeV/\(c^2\) recoils off tungsten are expected to be far more numerous compared to oxygen and calcium. For lighter masses a substantial part of the tungsten recoils have energies below threshold leading to a strong decrease of the number of counts. This results in a mass range completely dominated by scatterings off oxygen, because the drop for oxygen and calcium is shifted towards lower masses (see Fig. 7).

In the limit of very low masses, the reduced mass converges to the mass of the dark matter particles, causing less pronounced differences in the shape of the recoil spectra on the different target nuclei. This effect is further augmented by the influence of the baseline noise. Since the A\(^2\)-scaling of the cross sections still persists, scatterings off tungsten account for a slightly larger proportion of the total expected signal again.

For each dark matter particle mass we use the Yellin optimum interval method [16, 17] to calculate an upper limit with 90 % confidence level on the elastic spin-independent interaction cross-section of dark matter particles with nucleons. While this one-dimensional method does not rely on any assumption on the background, it exploits differences between the measured (see Fig. 6) and the expected energy spectrum (see Sect. 8).

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The resulting exclusion limit of this blind analysis is drawn in solid red in Fig. 8. For higher masses this module does not have a competitive sensitivity, due to the large number of background events. In particular, the leakage from the \(^{55}\)Fe-source (see Fig. 6) results in an almost flat limit for masses of 5–30 GeV/\(c^2\). However, for dark matter particles lighter than 1.7 GeV/\(c^2\) we explore new regions of parameter space.

The improvement compared to the 2014 result [6] (red dashed line) is a consequence of the almost constant background level down to the threshold which was reduced from 603 to 307 eV. The lower the mass of the dark matter particle the more relevant these improvements become. With this analysis we explore masses down to 0.5 GeV/\(c^2\), a novelty in the field of direct dark matter searches.

The transition point of the dominant scattering target nucleus manifests itself as kink in the corresponding exclusion curve. Due to the lower threshold Lise starts to be dominated by scatterings off tungsten already at \(\sim \)3 GeV/\(c^2\) (see Fig. 7) compared to \(\sim \)4.5 GeV/\(c^2\) for the 2014 result [6].

Due to the rather large number of leakage events into the acceptance region the result is already not limited by exposure any more. Consequently, only small statistical fluctuations are expected. This is confirmed by calculating limits for 10,000 Monte Carlo sets sampled from the data-driven background model discussed in Sect. 4. The resulting 1\(\sigma \) contour is shaded in light red in Fig. 8.

In CRESST-III we will substantially size down the absorber crystals in order to achieve lower energy thresholds. Furthermore, we expect two beneficial effects on the light signals: Firstly more light reaches the light detector and secondly the light detector can also be scaled down which leads to an enhanced energy resolution. Both improvements will increase the background discrimination power. All modules will feature an upgraded holding scheme and will mainly be equipped with absorber crystals produced in-house due to their significantly lower level of intrinsic radioactive contaminations. Combining these measures with the enhanced discrimination power, a drastically reduced background leakage is expected.

In this letter we prove that a low energy threshold is the key requirement to achieve sensitivity to dark matter particles of \(\mathcal {O}(\)1 GeV/\(c^2\)) and below. We expect significant progress exploring the low mass regime with the upcoming CRESST-III experiment, featuring next-generation detectors optimized towards the detection of recoil energies as small as 100 eV.