Eur. Phys. J. C (2017) 77:299DOI 10.1140/epjc/s10052-017-4878-6

Regular Article - Experimental Physics

Dark-photon search using data from CRESST-II Phase 2

G. Angloher1, P. Bauer1, A. Bento1,8, C. Bucci2, L. Canonica2,9, X. Defay3, A. Erb3,10, F. v. Feilitzsch3,N. Ferreiro Iachellini1, P. Gorla2, A. Gütlein4,5,a, D. Hauff1, J. Jochum6, M. Kiefer1, H. Kluck4,5, H. Kraus7,J.-C. Lanfranchi3, J. Loebell6, M. Mancuso1, A. Münster3, C. Pagliarone2, F. Petricca1, W. Potzel3, F. Pröbst1,R. Puig4,5, F. Reindl1,12, K. Schäffner2,11, J. Schieck4,5, S. Schönert3, W. Seidel1, L. Stodolsky1, C. Strandhagen6,R. Strauss1, A. Tanzke1, H. H. Trinh Thi3, C. Türkoglu4,5, M. Uffinger6, A. Ulrich3, I. Usherov6, S. Wawoczny3,M. Willers3, M. Wüstrich1, A. Zöller3

1 Max-Planck-Institut für Physik, 80805 Munich, Germany2 INFN, Laboratori Nazionali del Gran Sasso, 67010 Assergi, Italy3 Physik-Department and Excellence Cluster Universe, Technische Universität München, 85747 Garching, Germany4 Institut für Hochenergiephysik der Österreichischen Akademie der Wissenschaften, 1050 Vienna, Austria5 Atominstitut, Vienna University of Technology, 1020 Vienna, Austria6 Eberhard-Karls-Universität Tübingen, 72076 Tübingen, Germany7 Department of Physics, University of Oxford, Oxford OX1 3RH, UK8 Also at: Departamento de Fisica, Universidade de Coimbra, 3004 516 Coimbra, Portugal9 Also at: Massachusetts Institute of Technology, Cambridge, MA 02139, USA

10 Also at: Walther-Meißner-Institut für Tieftemperaturforschung, 85748 Garching, Germany11 Also at: GSSI-Gran Sasso Science Institute, 67100 L’Aquila, Italy12 Present address: INFN-Sezione di Roma, 00185 Rome, Italy

Received: 22 December 2016 / Accepted: 29 April 2017 / Published online: 10 May 2017© The Author(s) 2017. This article is an open access publication

Abstract Identifying the nature and origin of dark matteris one of the major challenges for modern astro and particlephysics. Direct dark-matter searches aim at an observation ofdark-matter particles interacting within detectors. The focusof several such searches is on interactions with nuclei as pro-vided e.g. by weakly interacting massive particles. However,there is a variety of dark-matter candidates favoring inter-actions with electrons rather than with nuclei. One exam-ple are dark photons, i.e., long-lived vector particles with akinetic mixing to standard-model photons. In this work wepresent constraints on this kinetic mixing based on data fromCRESST-II Phase 2 corresponding to an exposure before cutsof 52 kg-days. These constraints improve the existing onesfor dark-photon masses between 0.3 and 0.7 keV/c2.

1 Introduction

The dynamics of galaxies and galaxy clusters give stronghints for the existence of dark matter [1–3]. Recent mea-surements of the temperature fluctuations of the cosmicmicrowave background are well described with a dark-mattercontribution of 26.6% [4] to the overall energy density of the

a e-mail: achim.guetlein@oeaw.ac.at

universe. However, the nature and origin of dark matter isstill unkown. Solving this dark-matter puzzle is one of themajor challenges of modern astro and particle physics.

Direct dark-matter searches [5–17] aim at the observationof dark-matter particles interacting within detectors. Manyof these experiments focus on interactions between dark-matter particles and nuclei as provided for example by weaklyinteracting massive particles (WIMPs) [1,2]. However, thereis a variety of dark-matter models predicting particles whichwould favor interactions with electrons. One of these dark-matter candidates are dark photons [18–21], i.e., long-livedvector particles. The mass of these vector particles has tobe smaller than two times the electron mass, otherwise theycould decay into electron–positron pairs and their life timewould be too small to be a dark-matter candidate.

The absorption of dark photons is similar to the photoelec-tric effect and the cross section σV is approximately givenby [18–21]:

σV (EV = mV c2)v = κ2σγ (hω = mV c

2)c, (1)

where mV is the mass of the dark photon, v is their velocity,κ is the kinetic mixing of dark photons and standard-modelphotons, and σγ is the photoelectric cross-section for CaWO4

depicted in Fig. 1.

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Fig. 1 Photo-electric cross section σγ for CaWO4. The cross sectionfor energies below 1 keV was taken from [22], for energies above 1 keVfrom [23]

When dark photons are absorbed inside the detectors ofdirect dark-matter searches the dark-photon energy is trans-ferred to an electron similarly as for the photoelectric effect.Due to the short range of electrons in matter all energy isdeposited within the detectors. Thus, the expected signal forthe absorption of dark photons is a peak at the energy corre-sponding to the rest energy mV c2 of dark photons.1 Assum-ing that dark matter consists only of dark photons, the absorp-tion rate RS is given by [18–21]:

RS = NA

A

ρDM

mV c2 · κ2σγ (hω = mV c2)c, (2)

where NA is Avogadro’s number, A is the mass number of thetarget atoms, ρDM = 0.3 GeV/cm3 [24] is the local energy-density of dark matter.

Several direct dark-matter searches provide efficient meth-ods for the discrimination between interactions with elec-trons and nuclei on an event-by-event basis. Since most back-grounds from natural radioactivity and cosmogenics interactwith electrons, those methods allow a suppression of back-grounds for the search for dark-matter particles interactingwith nuclei (e.g. WIMPs). However, since dark-photons alsointeract with electrons such background-suppression meth-ods cannot be applied.

Some dark-matter searches aim at an observation of anannual modulation of their event rate as it is for exampleexpected for WIMPs [6,8,25]. Since the absorption rate (Eq.(2)) is independent of the dark-photon velocity, also thismethod cannot be applied to dark-photon searches.

Nevertheless, direct dark-matter searches set the moststringent constraints for the kinetic mixing for dark-photonmasses below ∼10 keV/c2 [18–21].

1 The kinetic energy is negligible due to the small velocities of colddark-matter.

2 Data from CRESST-II Phase 2

CRESST-II is a direct dark-matter search using scintillat-ing calcium tungstate (CaWO4) crystals as detector material[7]. In Phase 2 of CRESST-II (July 2013–August 2015) 18detector modules with a total detector mass of ∼5 kg wereoperated. For this work we only take into account data fromthe module with the lowest energy threshold of 0.307 keV.The same data set was also used to obtain the strongest limiton the cross section for spin-independent elastic scatteringfor masses of dark-matter particles �2 GeV/c2 [7].

The detector module which obtained the data used forthis work consists of two cryogenic detectors operated atO(10 mK). The so-called phonon detector based on a scin-tillating CaWO4 crystal with a mass of 306 g measures thephonons generated by particle interactions within the crystal.The additional light detector is based on a silicon-on-sapphire(SOS) disc and measures the scintillation light emitted by theCaWO4 crystal. Both detectors are surrounded by a scintil-lating and reflective housing to increase the light-collectionefficiency. In addition, the scintillation light generated withinthe housing can be used for background suppression.

Figure 2 depicts the data analyzed for this work after allcuts. The exposure before cuts is 52 kg-days. The eventsabove the clearly visible electron-recoil band are calledexcess-light events. The origin of these events is not fullyunderstood. However, a likely explanation are β particlespenetrating the detector housing before hitting the CaWO4

crystal. Since the detector housing is also scintillating, suchevents would generate additional scintillation light resultingin a higher detected light-energy than expected for β particles

Fig. 2 The light energy El , i.e., the scintillation light detected by thelight detector, plotted against the phonon energy Ep . The electron-recoilband, where dark-photon events and most of the background events areexpected, is clearly visible. The most prominent features within thisband originate from an accidental irradiation with a 55Fe source (5.9 and6.5 keV) and in intrinsic contamination with 210Pb (46.5 keV). Abovethe electron-recoil band so-called excess-light events are visible (seemain text for further details)

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[26]. Only a fraction of 0.9% of the total number of eventsare excess-light events. However, in the region of interestbelow 5 keV this fraction increases to 9.2%. Thus, excess-light events have to be taken into account as backgroundcomponent for this work.

3 Search for dark-photon signals

The expected signal from dark photons is a Gaussian peakwithin the electron-recoil band at the energy correspondingto the rest energy of dark photons. In this work we focus ondark-photon masses below 2 keV/c2. For larger masses otherdirect dark-matter searches have better sensitivities due tolarger exposures and smaller background rates [20].

In order to save computation time and also to keep theempirical background model rather simple, we decided totake only events with phonon energies below 5 keV intoaccount for the Bayesian fits described in the next section.Due to the good energy resolution of the phonon detector of0.062 keV (at 0.3 keV) [7] the influence of events with higherphonon energies on the resulting limits is negligible.

3.1 Bayesian fits

To study potential signals from dark photons we performBayesian fits of the potential signal and an empirical back-ground model to the measured data. We decided on this fitmethod since systematic uncertainties and results of othermeasurements or sideband analyses can naturally be includedinto Bayesian methods. In addition, any problems with cover-age as present for some Frequentist methods are avoided. TheBayes’ theorem states that the posterior probability densityfunction (PDF) is proportional to the product of the likelihoodand the prior probability density functions of all parametersθ of model M (see e.g. [27,28]):

P(M, θ |data) = L(data|M, θ)P0(θ)∫dθL(data|M, θ)P0(θ)

(3)

Bayesian fits maximize the posterior PDF with respect to theparameters θ and provide a decent handling of systematicuncertainties and nuisance parameters. For a Bayesian fit wehave to provide the likelihood functionL(data|M, θ) as wellas prior PDFs for all parameters of our model.

3.1.1 Likelihood

In this work we use the following expression for the extendedunbinned likelihood:

L(data|M, θ) = λN

N ! e−λ

N∏

j=1

p(d j |M, θ) (4)

p(d j |M, θ) =∑

i

Ri

λpi (d j |M, θ) (5)

λ =∑

i

Ri (6)

where N is the number of events in the fit range and λ isthe total expected rate which is given by the sum over therates Ri of the different signal and background components.The probability p(d j |M, θ) that a data point d j is compatiblewith model M and its parameters θ is given by the sum overthe probabilities pi (d j |M, θ) that d j belongs to component i .

For all data points d j we take into account their phononenergy Ep, j and their light energy El, j . The ratio betweenlight and phonon energy is important to distinguish betweenexcess-light events and normal electron-recoil events. This isof special importance for energies �1 keV where the largernumber of excess-light events would otherwise decrease thesensitivity of our dark-photon search.

The deposited energy of an event is split between phononand light energy, where the light energy carries only a fewpercent of the total deposited energy. The energy calibrationis done such that for a total deposited energy of 122 keVcaused by γ s from a 57Co calibration source the phonon andlight energies are set to Ep = 122 keV and El = 122 keVee,respectively. With this calibration the phonon energy is equalto the deposited energy if the ratio between light and phononenergy is close to one. This is the case for events withinthe electron-recoil band. However, for nuclear-recoil eventsless light is generated and the phonon energy carries a largerfraction of the total deposited energy. This leads to a slightoverestimation of the deposited energies. In [29] a correctionfor this effect is introduced. Since we are mainly dealing withelectron-recoil events, we decided to not apply the correctionfrom [29] for this work and assume that the total depositedenergy is equal to the phonon energy. This approach is furthersupported by [7] where no influence of the correction from[29] on the results could be found for the data set we areusing for this work.

With the assumption that the total deposited energy isgiven by the phonon energy, the probabilities pi (d j |M, θ) =pi (Ep, j , El, j |M, θ) can be factorized2:

pi (Ep, El |M, θ) = pp,i (Ep|M, θ)pl,i (El |Ep, M, θ), (7)

where pp,i (Ep|M, θ) are PDFs describing the distribution ofphonon energies and pl,i (El |Ep, M, θ) are PDFs describingthe distribution of light energies for a given phonon energy.

2 For better readability we omitted the indices j .

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We will first discuss the PDFs pp,i (Ep|M, θ) we usedto describe the phonon energies of signal and backgroundcomponents. Afterwards we will describe in detail the corre-sponding PDFs pl,i (El |Ep, M, θ) for the light energies.

For the expected dark-photon signal we use a Gaussianpeak to model the distribution of the phonon energies. Theposition and the width of the Gaussian are fixed for eachfit. However, we performed several fits where we varied thepositions in 0.05 keV steps from 0.3 to 2 keV. For the widthwe use the energy dependent energy resolution of the phonondetector given by a linear interpolation between a resolutionof 0.062 keV at the threshold of 0.307 keV and a resolutionof 0.100 keV at the 5.9 keV line.

The empirical background model has three components.One component which describes the electron-recoil back-ground from natural radioactivity and cosmogenics is mod-eled as a constant. The distribution of excess-light eventsis modeled by two components: one exponentially decayingfunction for events with small phonon energies �2 keV and aconstant for excess-light events with larger phonon energies.

We studied several different empirical parametrizationsfor the background model. The model presented here deliv-ers the best description of the measured data in terms ofBayes factors, i.e., the ratios of the denominators of Eq. (3).However, the limits for the kinetic mixing of dark photonsare similar for all studied models.

All the PDFs pp,i (Ep|M, θ) are multiplied with theenergy dependent signal-survival probability [7], i.e., theprobability that an event survives all cuts.

Figure 3 shows the PDFs of all model components. Fora meaningful comparison of the components we scaled allPDFs with the respective rates obtained by the fit (compareSect. 3.2). The influence of the energy dependent signal-survival probability is best visible for the constant back-ground components.

Fig. 3 The PDFs pp,i (Ep|M, θ) of all model components scaled bythe respective rates obtained by the fit of the model to the data (compareSect. 3.2)

To describe the PDFs for the light energy we use twodifferent models, one for the electron-recoil band and onefor excess-light events.

For events inside the electron-recoil band, i.e., the dark-photon signal and the constant background, the scintillationlight is only generated within the CaWO4 crystal. For a givenphonon energy the statistical fluctuations of the light ener-gies are caused by the baseline noise of the light detector andthe counting statistics of the absorbed scintillation light. Inprinciple, the light energies should follow a Poisson distribu-tion. However, for large deposited energies a large numberof photons is generated. Thus, the Poisson distribution canbe approximated by a Gaussian. For small energies wherethis approximation would fail, the energy resolution of thelight detector is dominated by the baseline noise. This noise isalso very well approximated by a Gaussian (see also [30,31]).Thus, we use a Gaussian PDF for the description of the lightenergies of the electron-recoil band:

pe-recoil(El |Ep, M, θ) = 1

σ(Ep)√

2πe− El−μ(Ep )

2σ(Ep ) (8)

σ(Ep) =√S0 + μ(Ep)S1 (9)

μ(Ep) = P0

(

1 − P1e− Ep

P2

)

· Ep (10)

where the mean μ(Ep) and the width σ(Ep) depend on thephonon energy Ep. The parameters S0 and S1 are relatedto the baseline noise of the phonon and light detectors andthe counting statistics of absorbed scintillation light, respec-tively. The parameter P0 describes the proportionality of thescintillation light with respect to the phonon energy. Dueto the calibration of the light energies, P0 is close to 1. Theparameters P1 and P2 describe the deviation from proportion-ality for low energies Ep. This so-called non-proportionalityeffect [32–34] is related to the energy-dependent stoppingpower of electrons, i.e., dE/dx is larger for electrons withlow energies leading to a decreased light output [32–34].

Excess-light events are not described by the already men-tioned Gaussian PDF for the electron-recoil band. As alreadystated in Sect. 2, we assume that excess light events originatefrom external βs traversing the scintillating detector hous-ing before hitting the CaWO4 crystal. Within this model, theadditional scintillation light generated within the housing isadded to the normal scintillation light generated by βs hittingthe CaWO4 crystal. The statistical fluctuations of the latterfollow the distribution given by Eq. (8). We use an exponen-tially decaying function to model the additional scintillationlight which is generated when particles penetrate the hous-ing.3 The distribution of the sum of two random variables

3 In principle, the distribution of this contribution should follow a Lan-dau distribution. However, after the convolution with a Gaussian theLandau distribution and an exponential decay have similar shapes. Since

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follows the convolution of the distributions of the two ran-dom variables (see e.g. [35]). Thus, the distribution of thelight energies for excess-light events is given by:

pexcess(El |E, M, θ) = padditional ∗ pe-recoil

=∫ ∞

0

1

El,0e− E ′

lEl,0

1

σ(E)√

2πe− (El−E ′

l−μ(E))2

2σ(E) dE ′l

where El,0 is the slope of the exponential decay for the addi-tional scintillation light, μ(E) and σ(E) are the mean andwidth of the PDF describing the electron-recoil band.

3.1.2 Prior distributions

In Bayesian statistics the prior distributions of the modelparameters are an important input. These prior distributionsmodel the knowledge on each parameter before the experi-ment. Typically, the prior distributions are based on previousexperiments, side-band analysis, or theoretical predictions.

For this work we have chosen uniform priors for mostparameters4 to model our ignorance of these parameters.Uniform PDFs can only be defined for a finite range. Thus,we chose ranges which include the majority of the posteriorPDFs for all parameters. Of course, we excluded unphysicalregions of the parameter space (e.g. negative rates).

Only for the parameters Pi of Eq. (10) we use Gaussiansinstead of uniform PDFs. Parameter P2 describes the energyscale of the non-proportionality effect. For our data set thisparameter is ∼20 keV. Thus, the exponential decay of themean of the electron-recoil band is not pronounced in ourfit region below 5 keV. In order to obtain meaningful priordistributions, we performed a dedicated fit of the events withenergies above 5 keV. As a result of this fit we use GaussianPDFs centered around the best-fit values and widths of ∼10%for the prior distributions of the parameters Pi .

3.2 Fit results

Figures 4 and 5 show the results of a Bayesian fit for a fixedposition of 0.4 keV for the signal peak. Figure 4 shows thephonon energies of all events in the region used for fitting.Figure 5 shows the light energies of the events within thephonon-energy slice between 0.3 keV and 1 keV. In both pan-els a good agreement between the data and the fit modelbecomes evident. The origin of the peak between 2.5 and

Footnote 3 continuedan exponential leads to a simpler solution of the convolution integral,we decided to use an exponential distribution.4 i.e., Rates of signal and background components, decay constantsfor the exponentials in phonon and light energy for escess-light events,and S0 and S1 describing the width of the light-yield distribution ofelectron-recoil events.

Fig. 4 Top panel Fit results for the phonon energies. In addition to themeasured data, the stacked contributions of all components are shown.The fixed mean of the signal peak was set to 0.4 keV. The drop in themodels below 2 keV is related to the decreasing signal-survival prob-ability. Bottom panel The differences between the data and the fittedmodel in each bin are depicted as solid black line. In addition, the sta-tistical uncertainties (central 90% region) of the fitted model are shownas green-shaded region

Fig. 5 Top panel Fit results for the light energies. Only events withinthe phonon-energy slice between 0.3 and 1 keV are shown in this plot.In addition to the measured data, the stacked contributions from theelectron-recoil band and excess-light events are shown. Bottom panelThe differences between the data and the fitted model are depicted assolid black line. In addition, the statistical uncertainties (central 90%region) of the fitted model are shown as green-shaded region

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Fig. 6 Top panel Distribution of phonon energies of excess-lightevents. For this plot only events with light energies larger than the 99%quantile of the electron-recoil band (Eq. (8)) were taken into account. Inaddition, the stacked distributions of all components of the fit model areshown. The contribution by the signal is too small to be visible in thisplot. The drop in the models below 2 keV is related to the decreasingsignal-survival probability. Bottom panel The differences between thedata and the fitted model are depicted as solid black line. In addition,the statistical uncertainties (central 90% region) of the fitted model areshown as green-shaded region

3 keV is not fully understood and, thus, we conservativelydid not include this peak into the background model. Thisleads to the discrepancies between data and model visible inFig. 4. However, it should be mentioned that this peak hasno influence on the result of the peak search performed onlyfor energies below 2 keV.

Figure 6 depicts the distribution of the phonon energiesfor excess-light events. For this plot only events with lightenergies above the 99% quantile of the electron-recoil band(Eq. (8)) were taken into account. It is clearly visible that theexcess-light events are well described by the fitted model.

4 New limit for kinetic mixing

Before we can set a limit on the kinetic mixing of dark pho-tons we first have to estimate a limit on the signal rate RS ,i.e., the rate of the signal component of the fit model. There-fore, we first have to create the marginalized posterior PDFof the signal rate by integrating the posterior PDF over allother parameters:

P(RS|data) =∫

P(M, θ |data)dθ

∣∣∣∣θ �=RS

(11)

Fig. 7 Marginalized posterior PDF for the signal rate RS . For thisexample with a fixed peak position of 0.4 keV the upper 90% limit is1.77 counts kg−1 day−1

Fig. 8 Upper limits on the kinetic mixing of dark photons. Limitsfrom anomalous energy loss in the sun, horizontal-branch stars, andred giants are shown as shaded regions [20]. Limits from XENON10and XENON100 [20] are shown as (blue) solid and dashed lines, respec-tively. The limit from DAMIC [21] is shown as solid black line. Ourlimit obtained from data from CRESST-II Phase 2 is depicted as a (red)solid line

Figure 7 shows the marginalized posterior PDF for thesignal rate RS for a peak position of 0.4 keV as an example.This marginalized PDF was obtained by a Markov ChainMonte Carlo algorithm [28] which was used to perform allfits for this work.

An upper limit for the signal rate can be obtained asthe corresponding quantile of P(RS|data), e.g., the upper90% limit for RS corresponds to the 90% quantile ofP(RS|data). For the example of Fig. 7 this upper 90% limitis 1.77 counts kg−1 day−1.

This limit on the signal rate RS can be converted into alimit on the kinetic mixing using Eq. (2). We repeated thedescribed Bayesian fit-procedure with different fixed posi-tions for the dark-photon signal in 0.05 keV steps from 0.3to 2 keV. The resulting limit for the kinetic mixing is shown

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in Figure 8 as a function of dark-photon mass. In addition,existing limits (90% confidence level) from astronomy, theXENON and DAMIC experiments are shown. Our resultimproves the existing constraints for dark-photon massesbetween 0.3 and 0.7 keV/c2.

The recently started (July 2016) Phase 1 of CRESST-IIIhas the potential to further improve this limit. The detec-tors operated in this phase of CRESST-III will have energythresholds of �0.1 keV [36]. Thus, with these detectors wecan extend our limits towards smaller dark-photon masses of�0.1 keV/c2.

5 Conclusions

The dynamics of galaxies and galaxy clusters give evidencefor the existence of dark matter. However, its origin andnature remain unknown up to now. There is a variety oftheories for dark matter. In recent years, theories predict-ing interactions of dark-matter particles with electrons ratherthan nuclei became more popular. One example are dark pho-tons, i.e., long-lived vector particles with a kinetic mixing tostandard-model photons.

Like several other direct dark-matter searches, CRESST-IIis optimized for an observation of dark-matter particles inter-acting with nuclei. However, the obtained data can also beused to search for dark-matter candidates with different inter-actions. In this work we present the limits for the kinetic mix-ing of dark photons based on data from Phase 2 of CRESST-IIcorresponding to an exposure of 52 kg-days. To obtain thislimit we performed Bayesian fits of an empirical backgroundmodel and a potential dark-photon signal to the measureddata. Our new limit improves the existing constraints fordark-photon masses between 0.3 and 0.7 keV/c2. Due to itslow energy thresholds, the recently started CRESST-III Phase1 has the potential to further improve this limits.

Acknowledgements We are grateful to LNGS for their generous sup-port of CRESST, in particular to Marco Guetti for his constant assis-tance. This work was supported by the DFG cluster of excellence: Originand Structure of the Universe, by the Helmholtz Alliance for Astropar-ticle Physics, and by the BMBF: Project 05A11WOC EURECA-XENON. In addition, we would like to thank J. Pradler for helpfuldiscussions about the physics of dark photons. Also we would like tothank M. Tüchler and L. Lechner for their help with the software usedto perform the Bayesian fits.

Open Access This article is distributed under the terms of the CreativeCommons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,and reproduction in any medium, provided you give appropriate creditto the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made.Funded by SCOAP3.

References

1. G. Bertone et al., Phys. Rep. 405, 279 (2005)2. G. Jungman et al., Phys. Rep. 267, 195 (1996)3. D. Clowe et al., Astrophys. J. Lett. 648, L109 (2006)4. Planck Collaboration: P.A.R. Ade et al., A&A 594, A13.

arXiv:1502.01589 (2016)5. C.D.E.X. Collaboration, Q. Yue et al. Phys. Rev. D 90, 091701

(2014). arXiv:1404.49466. CoGeNT Collaboration: C.E. Aslseth et al., Phys. Rev. D 88,

012002 (2013). arXiv:1208.57377. CRESST Collaboration: G. Angloher et al., Eur. Phys. J. C 76, 25

(2016). arXiv:1509.015158. DAMA Collaboration, R. Bernabei et al., Eur. Phys. J. C 73, 2648

(2013). arXiv:1308.51099. DAMIC Collaboration: A. Aguilar-Arevalo et al., Phys. Rev. D 94,

082006 (2016). arXiv:1607.0741010. DarkSide Collaboration: P. Agnes et al., Phys. Rev. D 93, 081101

(2016). arXiv:1510.0070211. EDELWEISS Collaboration: E. Armengaud et al., JCAP 05, 019

(2016). arXiv:1603.0512012. KIMS Collaboration, H.S. Lee et al., Phys. Rev. D 90, 052006

(2014). arXiv:1404.344313. LUX Collaboration: D.S. Akerib et al., Phys. Rev. Lett. 118, 021303

(2017). arXiv:1608.0764814. PandaX Collaboration: A. Tan et al., Phys. Rev. Lett. 117, 121303

(2016). arXiv:1607.0740015. PICO Collaboration: C. Amole et al., Phys. Rev. D 93, 052014

(2016). arXiv:1510.0775416. SuperCDMS Collaboration: R. Agnese et al., Phys. Rev. Lett. 116,

071301 (2016). arXiv:1509.0244817. XENON100 Collaboration: E. Aprile et al., Phys. Rev. D 94,

122001 (2016). arXiv:1609.0615418. M. Pospelov et al., Phys. Rev. D 78, 115012 (2008)19. H. An et al., Phys. Rev. Lett. 111, 041302 (2013)20. H. An et al., Phys. Lett. B 747, 331 (2015). arXiv:1412.837821. DAMIC Collaboration: A. Aguilar-Arevalo et al.

arXiv:1611.03066 (2016)22. Elettra-Sincrotrone Trieste S.C.p.A. https://vuo.elettra.eu/

services/elements/WebElements.html23. NIST, Photon Cross Section Database. http://physics.nist.gov/

PhysRefData/Xcom/html/xcom1.html24. J. Bovy et al., Astorphys. J. 779, 115 (2013)25. XENON100 Collaboration: E. Aprile et al., Phys. Rev. Lett. 115,

091302 (2015). arXiv:1507.0774826. R. Strauss et al., JCAP 06, 030 (2015). arXiv:1410.418827. A. Caldwell et al., Phys. Rev. D 74, 092003 (2006).

arXiv:physics/060824928. A. Caldwell et al., Comput. Phys. Commun. 180, 2197 (2009).

arXiv:0808.255229. CRESST Collaboration: G. Angloher et al., Eur. Phys. J. C 74,

3184 (2014). arXiv:1407.314630. A. Gütlein et al., Astropart. Phys. 69, 44 (2015). arXiv:1408.235731. R. Strauss et al., Eur. Phys. J. C 75, 352 (2015). arXiv:1410.175332. W.W. Moses et al., IEEE Trans. Nucl. Sci. 55, 1049 (2008). doi:10.

1109/TNS.2008.92280233. R. Lang et al. arXiv:0910.4414 (2009)34. S. Roth, Ph.D. thesis, TU München (2013). https://mediatum.ub.

tum.de/node?id117201935. G. Cowan, Statistical Data Analysis (Oxford University Press,

Oxford, 1998)36. CRESST Collaboration: G. Angloher et al. arXiv:1503.08065

(2015)

123