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13

Muon-induced background in the EDELWEISS dark matter search

The EDELWEISS collaboration,B. Schmidt∗, a), E. Armengaud b), C. Augier c), A. Benoit d), L. Berge e), T. Bergmann f), J. Blumer a), g),G. Bres d), A. Broniatowski e), V. Brudanin h), B. Censier c), M. Chapellier e), F. Charlieux c), S. Collin e),P. Coulter i), G.A. Cox a), O. Crauste e), J. Domange b), e), L. Dumoulin e), K. Eitel g), D. Filosofov h),N. Fourches b), G. Garde d), J. Gascon c), G. Gerbier b), M. Gros b), L. Hehn g), S. Henry l), S. Herve b),

G. Heuermann a), A. Juillard c), H. Kluck a), V.Y. Kozlov g), M. Kleifges f), H. Kraus i), V.A. Kudryavtsev j),P. Loaiza k), S. Marnieros e), A. Menshikov f), X.-F. Navick b), H. Nieder† a), C. Nones b), E. Olivieri e), P. Pari l),B. Paul b), M. Robinson j), H. Rodenas d), S. Rozov h), V. Sanglard c), B. Siebenborn g), D. Tcherniakhovski f),

A.S. Torrento-Coello b), L. Vagneron c), R.J. Walker a), M. Weber f), E. Yakushev g), X. Zhang i)

a)Karlsruhe Institute of Technology, Institut fur Experimentelle Kernphysik, Gaedestr. 1, 76128 Karlsruhe, Germanyb)CEA, Centre d’Etudes Nucleaires de Saclay, IRFU, 91191 Gif-sur-Yvette Cedex, France

c)Institut de Physique Nucleaire de Lyon, Universite de Lyon (Universite Claude Bernard Lyon 1) et IN2P3-CNRS, 4 rueEnrico Fermi, 69622 Villeurbanne, France

d)Institut Neel, CNRS, 25 Avenue des Martyrs, 38042 Grenoble Cedex 9, Francee)Centre de Spectroscopie Nucleaire et de Spectroscopie de Masse, UMR8609 IN2P3-CNRS, Univ. Paris Sud, bat 108, 91405

Orsay Campus, Francef)Karlsruhe Institute of Technology, Institut fur Prozessdatenverarbeitung und Elektronik, Postfach 3640, 76021 Karlsruhe,

Germanyg)Karlsruhe Institute of Technology, Institut fur Kernphysik, Postfach 3640, 76021 Karlsruhe, Germany

h)Laboratory of Nuclear Problems, JINR, Joliot-Curie 6, 141980 Dubna, Moscow Region, Russian Federationi)University of Oxford, Department of Physics, Keble Road, Oxford Ox1 3RH, UK

k)University of Sheffield, Department of Physics and Astronomy, Sheffield S3 7RH, UKk)Laboratoire Souterrain de Modane, CEA-CNRS, 1125 route de Bardonneche, 73500 Modane, France

l)CEA, Centre d’Etudes Nucleaires de Saclay, IRAMIS, 91191 Gif-sur-Yvette Cedex, France

Abstract

A dedicated analysis of the muon-induced background in the EDELWEISS dark matter search has beenperformed on a data set acquired in 2009 and 2010. The total muon flux underground in the LaboratoireSouterrain de Modane (LSM) was measured to be Φµ = (5.4 ± 0.2+0.5

−0.9)muons/m2/d. The modular designof the µ-veto system allows the reconstruction of the muon trajectory and hence the determination of theangular dependent muon flux in LSM. The results are in good agreement with both MC simulations andearlier measurements. Synchronization of the µ-veto system with the phonon and ionization signals of theGe detector array allowed identification of muon-induced events. Rates for all muon-induced events Γµ =(0.172±0.012) evts/(kg · d) and of WIMP-like events Γµ−n = 0.008+0.005

−0.004 evts/(kg · d) were extracted. Aftervetoing, the remaining rate of accepted muon-induced neutrons in the EDELWEISS-II dark matter searchwas determined to be Γµ−n

irred < 6 · 10−4 evts/(kg · d) at 90%C.L. Based on these results, the muon-induced

background expectation for an anticipated exposure of 3000 kg · d for EDELWEISS-III is Nµ−n3000kg·d < 0.6

events.

Keywords: Dark matter, WIMP search, Muon-induced neutrons, Muon flux underground, Cryogenic Ge detectors

∗Corresponding author, b.schmidt@kit.edu†current address: Karlsruhe Institute of Technology, Institut fur Meteorologie und Klimaforschung, 76021 Karlsruhe, Ger-

many

1

1 Introduction

Astrophysical and cosmological observations [38, 29]have led to the current cosmological concordancemodel that incorporates both dark energy and darkmatter as driving forces in the evolution of the Uni-verse. Dark matter herein constitutes a matter-likefluid ruling the dynamics of structure formation aswell as significantly affecting the dynamics of our owngalaxy today [27]. Assuming extensions of the Stan-dard Model with a new particle originally in ther-modynamic equilibrium, but decoupling shortly af-ter the Big Bang, a promising class of dark mattercandidates called WIMPs (Weakly Interacting Mas-sive Particles) arises. An annihilation cross section ofthe order of the weak scale is needed to produce theobserved cosmic abundance [18], rather independentof the WIMP mass which is typically assumed to beof O(100GeV). With these properties, this candidateis non-relativistic at freeze-out and hence consistentwith our understanding of structure formation.

The challenge of direct dark matter search experi-ments is the detection of the extremely rare WIMP-nucleus scattering events. Furthermore the expectedenergy spectrum from WIMP-nucleus scattering ex-hibits an exponential distribution, tailing off towardshigher energy and can be easily mimicked by back-ground sources. Thus, in order to ensure that a signalis caused by WIMPs one has to understand all back-ground sources and to suppress as many as possible.The overwhelming majority of observed events aregamma and beta particles from ambient radioactiv-ity. These are rejected with the powerful discrimi-nation capabilities offered by the simultaneous read-out of two channels such as phonons and scintillation[7, 8, 20], or phonons and ionization [4, 3], or scintilla-tion and ionization [39, 9, 5], and fiducialization (bulk- surface) in some detectors. In contrast, a neutronbackground causes a WIMP-like signal (a nuclear re-coil) in the detectors and can only be discriminatedvia multiple scattering of neutrons or coincident µ-veto signals if induced by cosmic muons.

At levels of sensitivity to spin-independent elas-tic WIMP-nucleon cross sections of a few 10−44 cm2

(CDMS and EDELWEISS with 614 kg · d of exposure[3]) or lower (XENON100 [9] with 2323.7 kg · d equiv-alent exposure), further reducing the background isa demanding task. It requires a careful analysis of allknown backgrounds and the extrapolation to the nextstages of experiments [14]. For EDELWEISS, promi-nent sources of backgrounds are a potential failureto separate electron recoils from nuclear recoils viathe charge and phonon measurement, and neutronsproduced via (α, n) reactions, spallation as well asneutrons induced by muons. Old results have con-siderable systematic uncertainties due to the lack ofdetailed Monte Carlo modeling of muon transport,secondary particle production and detection within aspecific detector configuration. More recent experi-ments (see for instance [1, 10, 16, 35]) provide morereliable data for different targets but some of themare still not consistent with the existing models basedon the GEANT4 toolkit [2] or FLUKA code [15] (seealso simulations and discussions in Refs. [11, 34]).

In this article we present the results of an investiga-tion of the muon-induced background in the EDEL-WEISS experiment. We start with an introductioninto the experimental setup, describing briefly theGe bolometers and focussing on the µ-veto systemand its data acquisition (Section 2). In Section 3,we derive the muon detection efficiency and recon-struct muon information such as angular distribu-tions and track coordinates. Based on these data,a search for coincidences of muon veto and bolome-ter events has been performed with results presentedin Section 4. We conclude with an outlook for themuon-induced background expectation for the up-coming EDELWEISS-III dark matter search.

2 Experimental setup

To shield against cosmic backgrounds, the EDEL-WEISS experiment is housed in the LaboratoireSouterrain de Modane (LSM), an underground lab-oratory under the French Alps with an average rockoverburden of 4800m w. e. (meters water equiv-alent). This attenuates the muon flux by six or-

2

ders of magnitude compared to sea level down to∼ 5µ/m2/d. The experimental setup depicted inFig. 1 consists of several layers of active and passiveshielding surrounding the innermost part, a dilutioncryostat. This cryostat with a working temperatureof 18mK contains the ultrapure Ge crystals used asdetectors for the WIMP search.

The outermost shielding is an active µ-veto sys-tem of plastic scintillator modules, described in Sec-tion 2.2. It is mounted on a 50 cm thick polyethylene(PE) layer, inside which the actual cryostat hous-ing is shielded with 20 cm thick lead, of which theinner 2 cm are ancient lead (Pb). The PE moder-ates the neutron energies to sufficiently low levels fora significant fraction of them to be absorbed. Theinnermost 2 cm of the lead were salvaged from thewreck of an ancient Roman galley [32] in order toreduce the 46.5 keV γ-line of the 210Pb as well asX-rays and bremsstrahlung photons from the β− de-cay of 210Bi. The Ge bolometers are described inSection 2.1. Their signals are sampled using a com-mon clock with a 100 kHz frequency. That same clockis transferred to the µ-veto system data acquisition(DAQ) via optical fibers. Apart from this synchro-nization, both systems run individually and muon-induced bolometer events are identified offline withinthe main analysis [13]. An additional 1 ton liquidscintillator detector designed to study muon-inducedneutrons with better statistics was installed at theend of 2008 (Fig. 1a, detector outside the shieldingat the lower right). The detailed setup and first re-sults obtained with this additional detector are de-scribed in [30]. Further measurements of the ambientneutron flux are performed inside and outside of theshielding with bare 3He neutron counters [42, 23].

2.1 Bolometer array and DAQ

The Ge crystals for EDELWEISS-II are grown fromultrapure Ge with less than 1010 impurities per cm3

and cut as cylinders of 70mm diameter and 20mmheight. The simultaneous readout of a heat signalwith a neutron transmutation doped (NTD) Ge sen-sor [37, 36], and the ionization with charge collection

electrodes enables the distinction between electronand nuclear recoils. During the data taking period2009-2010, the dilution cryostat provided a stable de-tector temperature of 18mK for more than one year.Five ID detectors with beveled edges and a mass of360 g each were used together with five plain cylin-drical detectors of 410 g mass. These ID detectorswere equipped with interdigitized collecting and vetoelectrodes [19]. The Al electrodes are evaporated onthe top and bottom of the Ge crystal. Each ringhas a width of 200 µm and 1.8mm pitch, and is typ-ically biased at voltages of ±4V for the collectingand ∓1.5V for the veto electrode. Solid guard elec-trodes covering the outer rim and the beveled facesallow suppression of events in the outer regions ofthe crystals. The electrical field lines run orthogonalto the surface for bulk events, but parallel for surfaceevents. This design therefore allows to exclude eventsin the surface layers of the detector, which are proneto charge collection deficiencies.

In the analysis the discrimination between electronand nuclear recoils is based on the ionization yield Q,which is the ionization energy (calibrated for electronrecoils with the 356 keV line of 133Ba) relative to therecoil energy. For electron recoils the value of Q isset to unity by calibration. Nuclear recoils trans-mit most of their energy directly to vibrations of thecrystal lattice (phonons), without going through ion-ization processes. Thus, they generally have a muchsmaller ionization yield than electron recoils. For theEDELWEISS detectors, the ionization yield of nu-clear recoils as a function of energy follows closelythe prediction of the Lindhard theory [33] and can beparameterized through the expression, determined inan extensive neutron calibration [37, 43]:

QLin = 0.16 · (ERec[keV])0.18. (1)

Assuming a Gaussian uncertainty of the Q value dis-tribution with energy-, detector- and time-dependentresolutions σion(Eion, t,det) and σheat(Eheat, t,det), arecoil band can be defined based on the standard de-viation

σQ = σQ(ERec, σion(t,det), σheat(t,det)). (2)

3

Figure 1: (a) Cross-section of the EDELWEISS experimental setup as implemented in the MC simulations. (b) Schematic viewof the modular µ-veto system.

For the ID detectors, rejection powers of better than1 in 105 for γ rays in the bulk and 1 in 6·104 forsurface events were determined using a 133Ba γ anda 210Pb β source, respectively [19]. Whilst these re-jection powers are very good, the surface event re-jection together with the rejection of events on theradial surface, so-called guard events, significantlyreduces the volume of accepted events. The bulkor fiducial volume, where reliable charge collectionis expected, was defined in the following way. Eachof the signals on veto and guard electrodes, as wellas the charge imbalance between the two collectingelectrodes had to be consistent with zero at 99%C.L.,according to the resolution of these parameters. Theefficiency of those cuts was measured using the low-energy 8.98 keV and 10.34 keV peaks associated withthe cosmogenic activation of germanium, producinga uniform contamination with the isotopes 65Zn and68Ge. Averaged over time and all detectors, a typicalfiducial mass of (166 ± 6) g per detector was found

[13].

With a live data taking period of 307 days dur-ing the cryogenic run from March 2009 to May 2010,an effective fiducial exposure of (481± 17) kg · d hasbeen collected for the analysis of the muon-inducedbackground in the bolometers including a factor of0.9 to account for the region of interest (RoI) beingthe 90%C.L. nuclear recoil band. This exposure islarger than the 384 kg · d used in the WIMP searchin [13], as the present study of coincidences of muonveto and germanium detector events does not requirethe same strict quality cuts on the noise levels in thegermanium detectors. While the fiducial volume cutis paramount for the DM search [13] it can be bene-ficial to include less well reconstructed events closerto the surface of the detectors to increase statisticsfor coincidence studies. Therefore, we also presentthe results of a coincidence study using looser cutsfor events in the whole volume of the detectors, forwhich the exposure amounts to 1504 kg·d.

4

2.2 Muon veto system

The outermost layer of the EDELWEISS setup is theµ-veto system, a layer of plastic scintillator actingas an active shield to tag any muon-induced activ-ity in the bolometer system. It consists of 46 indi-vidual plastic scintillator modules (Bicron BC-412)of 65 cm width, 5 cm thickness and lengths of 2m,3.15m, 3.75m and 4m adding up to a total surfaceof 100m2. The modules are assembled in a stainlesssteel mounting frame and attached to the PE shield-ing to ensure an almost hermetic coverage of the ex-periment setup. Due to the need for access to thecryostat during maintenance intervals, parts of the µ-veto system are positioned on rails on top of the twomovable PE blocks to allow a roll-back during cryo-stat access (Fig. 1). Whereas the upper level (N1)of the µ-veto system almost completely covers thePE shielding, except for small openings for rails, thepart below the cryostat level (N0) has more promi-nent gaps due to the cryogenic supply lines, and thepillars on which the entire experiment is mounted.The overall geometrical muon flux coverage of theµ-veto system amounts to 98%. To ensure properclosure during data taking, the exact positions of thetwo mobile veto parts are monitored via regular po-sition measurements using laser interferometry.

Each module is viewed by two groups of four 2-inchPMTs (Philips Valvo XP2262/PA). Each group hasan individual high voltage (HV) supply and readout,leading to a total of 92 HV and signal channels. Sim-ilar modules have been used as a muon veto counterin the KARMEN experiment [12]. A complete de-scription of the modules including measurements ofthe effective attenuation length and spectral quan-tum efficiency of the scintillator can be found in [40].The data acquisition is based on VME electronicswith special cards developed in-house [25]. An eventrecording in the veto system is triggered once thetwo signals of a module each pass a trigger thresholdwithin a coincidence window of 100 ns. With leadingedge discriminators set at the same level of 150mV,individual modular thresholds are achieved by adjust-ing the HV values. Within an event, all hits above

threshold in the modules are then registered withinan interval of ±125 ns around the trigger time. Foreach signal channel, the individual time of a hit isrecorded in a 128-channel TDC (CAEN V767) andthe analog signals are converted in three 32-channelQDCs (CAEN V792). After the coincidence window,any further input is blocked for about 50µs [25] untilthe event data are read out via the VME bus and allactive elements are reset by the acquisition software.The time information with respect to the bolome-ters is received via an optical fiber which transmitsthe 10µs time stamp in 48 bits of 64 ns width each.This sequence of bits is converted via an FPGA-basedboard and then read out via the VME bus. To moni-tor the overall status of the veto modules, the hit rateof all PMT groups (not requiring any coincidence) isrecorded in scalers. These data are processed contin-uously to check the performance of the µ-veto systemvia a graphical web interface.

A muon traversing a scintillator module as a mini-mum ionizing particle deposits on average more than10MeV (see Fig. 2 for a typical Landau spectrum).The average energy deposition is 11.8MeV for hor-izontal modules on the top and bottom, and up to24MeV for modules on the sides [26]. As seen inFig. 2, these values are above typical energy deposi-tion from the ambient radioactivity. For each chan-nel, the energy deposition is stored as the integratedcharge Q in units of ADC values. With the compar-ison of the Landau most probable values (MPV) ofthe integrated charge Q of specific two module coinci-dence cuts with dedicated MC simulations, a module-individual calibration is obtained with a mean cali-bration coefficient of 5.44 keV/ADC-value. The ef-fective threshold of the muon veto modules has beenchosen to be much lower than the MPVs (about5MeV at the center of a module, rising towards themodule ends due to the position-dependent light out-put) to be also able to detect grazing muons and thusto keep the muon detection efficiency as high as pos-sible. As a result, the rate of recorded events in theentire system is of the order of one per second, to becompared to an expected rate of throughgoing muonshitting at least one module per system section N1 and

5

Energy (MeV)0 10 20 30

Ent

ries

0

50

100

150

0.01 x all events

candidatesµ

Landau fit

Figure 2: Distribution of energy depositions in a top module.The histogram (solid black) shows events recorded for a stan-dard trigger condition (internal coincidence of the module),scaled by 0.01. Data points (in red) describe energy deposi-tions of muon candidates selected by requiring full non-zeroADC and TDC information in another module (two modulesin coincidence) and follow a Landau distribution.

N0 of ∼ 3.5× 10−4 Hz. Whereas the rate of recordedevents is dominated by ambient background, candi-dates of throughgoing muons can be easily extractedfrom the data by requiring two modules in coinci-dence.

Vetoing a bolometer event due to activity in theµ-veto system is performed in the offline analysis.A veto is applied in a conservative time window of±1ms around each event recorded in the µ-veto sys-tem, regardless of the fact that these events are dom-inated by ambient background. This offline reduc-tion of effective exposure due to the entire µ-vetosystem results in a deadtime of the order of 0.2%.As the veto system is completely independent of thebolometer system and its data acquisition, data ofthese scintillator modules are acquired continuously,only interrupted by maintenance intervals.

For each event in the µ-veto system, the position ofan energy deposition can be reconstructed using themodule number and the time difference between thesignal arrival at each module end. The time is storedin TDC units, where one TDC unit corresponds to0.8 ns. A typical distribution of the time differencewithin a µ-veto module is shown in Fig. 3. Theblack distribution recorded with the standard trig-

t (ns)∆ -50 0 50

Ent

ries

per

1.6

ns

0

20

40

60

0.01 x all events

candidatesµ

Figure 3: Time difference of PMT signals within a top mod-ule for events with standard trigger condition (internal coinci-dence) in solid black, scaled by 0.01, and for muon candidates(red data points), selected with a two module coincidence cut.

ger condition shows the threshold dependence alongthe module length with the minimum threshold andlargest count rate at the center of the module. Ad-ditional contributions are visible at ∆t ≈ ±30 ns dueto a thicker scintillator and thus higher detection ef-ficiency at the module ends. The tails to much largertime differences are due to the limited time resolutionfor low energy deposition as well as to light emissionin the PMTs. In contrast, muon candidates show amuch more confined distribution of time differencesas can be seen in Fig. 3. The rather flat distribu-tion with sharp edges reflects the physical length of amodule with homogenously distributed hits along themodule axis. Thus, with the event data on energy de-position and time, sufficient information is providedto perform cuts selecting muon candidates and to re-construct muon trajectories (see Section 3.5).

3 Detecting muons

In this section, we derive the detection efficiency ofthe µ-veto system in two different ways. Based on adetailed simulation of muons and their interactionsin the EDELWEISS setup (Section 3.1) using indi-vidual modular efficiency curves determined in situfrom data (Section 3.2), the first method is a combi-nation of MC results and data (Section 3.3). The sec-ond method uses bolometer data identified as muon-

6

30 m10 m μ

reference point

muon generator hemisphere

rock

NEMO

LSM

p

Figure 4: LSM geometry and muon generation as implementedin Geant4. The hemisphere for muon generation is placed inthe rock surrounding the laboratory hall with the EDELWEISSand NEMO setups. The NEMO-III experiment is implementedas simplified PE shields whereas the EDELWEISS-II setup isimplemented with all details (see also Fig. 1).

induced events searching for a coincident signal inthe µ-veto system (Section 3.4) and thus is entirelybased on data extracted during the WIMP searchitself. The measured angular distribution of muons(Section 3.5) as well as the total muon flux are de-termined (Section 3.6).

3.1 Simulation of muons in LSM

Modeling of muons and their interactions is per-formed with the Geant4 package version 4.9.2 [2, 6].For these simulations, the detailed geometry of theEDELWEISS setup as given in Fig. 1 has been ex-tended to incorporate nearby structures in the LSMlaboratory, namely the rock surrounding the labora-tory and the adjacent NEMO-III experiment. Fig-ure 4 shows the implemented geometry as well as thehemisphere at a distance of 30m from the center ofthe experiment on which muons are generated. Thefull MC simulation consists of 2·106 generated muonsin the energy range from 2 GeV-200 TeV. 40.9% ofthe started muons have a momentum vector that ge-ometrically would hit the µ-veto system, the rest illu-minates the close surroundings. However, only 33.9%of the muon tracks actually enter the veto volume.The difference of 7% is due to muons stopped within

the rock overburden.The energy and angular dependent muon flux

above the laboratory is generated according to theenergy dependent muon spectrum at sea level [24]:

dN0

dE0

=0.14(Eµ/GeV)−γ

cm2 s sr GeV·

(

1

1 +1.1EµcosΘ115 GeV

+0.054

1 +1.1EµcosΘ850 GeV

)

, (3)

with the cosmic ray exponent γ = 2.7, which is thenmodified due to energy loss of muons and the shield-ing in the rock overburden of LSM. This rock over-burden h(Θ,Φ) is taken from a detailed elevation mapwith 1◦ × 1◦ resolution [44].

The muons are generated according to the result-ing angular dependent muon flux on a half sphereof 30 m radius centered around the cryostat of theEDELWEISS-II experiment. In order to ensure ahomogeneous illumination of the µ-veto system, thestarting point of a muon with momentum vector ~pis randomized within a distance δ ≤ 5 m of a ref-erence point on the hemisphere. After generation,particles are propagated through the entire setupbased on the QGSP BIC HP reference physics listof Geant4 version 4.9.2 with an adaptation suggestedby [26]. This includes the use of the “low energy ex-tension” packages instead of the standard ones forelectron, positron and gamma interactions. Further,G4MuNuclear was added to model muon-hadronicinteractions, and a CHiral Invariant Phase Space(CHIPS) based model was used for gamma-nuclearphysics.

To model hadronic interactions, especially inelas-tic neutron scattering, two further changes were ap-plied. At energies between 20MeV and 70MeV, thepackage G4PreCompoundModel (PC) mediates thetransition from G4NeutronHPInelastic (HP, up to20MeV) to G4BinaryCascade (BIC, from 70MeV to6GeV). To bridge a model gap at energies 6GeV ≤En,p ≤ 12GeV between BIC and the high energyQuark Gluon String Precompound (QGSP) modelimplemented in G4QGSModel, the Low Energy Pa-rameterized (LEP) model G4LENeutronInelastic was

7

inserted. This description of the physical processeshas been proven to be effective in terms of CPU con-sumption and to be accurate when comparing withexperimental results [26, 28]. Using these interactionmodels, the distance of 30 m of rock between startingpoint and experimental setup allows the developmentof hadronic and electromagnetic showers into equilib-rium and ensures the proper abundance of secondaryparticles in the simulation. Energy depositions bythe primary muon and by all secondary particles arethen stored for each individual veto module as well asfor each bolometer in the cryostat. To avoid bound-ary effects, two additional meters of rock below theentire setup are included in the geometry.

3.2 Trigger efficiency of individual veto

modules

To determine the detection efficiency for a given sim-ulated energy deposition in a module, the individualtrigger threshold of all modules must be known. Al-though this is a position dependent function alongthe axis for a given module i, it can be measured insitu as an efficiency ǫi(E) averaging over all hit posi-tions. Such a measurement provides an accurate effi-ciency curve accounting for the local environment ofthe underground laboratory, ageing of detector com-ponents over the long term measurement as well asadjustments of the high voltage applied to the PMTs.

The measurement of ǫi(E) makes use of the factthat, having an internal coincidence in an individualmodule (TDC data from both ends within a 100 nswindow), all non-zero ADC and TDC data of othermodules are also read out and stored. This additionalinformation allows to deduce the trigger efficiency inthe following way: We select all events where there isan energy deposition in a certain module recorded asnon-zero ADC value(s), but where the trigger condi-tion was fulfilled by another module. Whenever bothTDC channels of the module under consideration arenon-zero, this module would have triggered as well.Otherwise, despite some energy deposition recordedin the ADC, the signals would not have triggered theevent recording. The fraction of potential triggers

Energy (MeV)0 10 20 30

Tri

gg

er

effi

cie

nc

y

0

0.2

0.4

0.6

0.8

1

1.2

Figure 5: Example of the trigger efficiency ǫi(E) as a functionof the energy deposition E in MeV in a module i (shown for atop module, with binomial error estimates). The green bandis the 1σ region of the efficiency fit, fixing the efficiency levelfor large energies to ǫi(E) = 1. The functional form is givenby the convolution of a threshold step-function with a gaussianenergy resolution.

over all events as a function of the calibrated energyis shown in Fig. 5 as an example of the trigger effi-ciency ǫi(E) of a specific module i.

For muons, one can deduce a detection efficiency ǫµiby weighting the energy dependent trigger efficiencywith the measured Landau spectrum of each module:

ǫµi =

∫

∞

6MeVǫi(E)Nµ,i(E)dE

∫

∞

6MeVNµ,i(E)dE

. (4)

At energies below 6MeV, the selection criterion fora muon candidate, i.e. two non-adjacent modules incoincidence, may also select low-energy secondaries inone of the modules instead of throughgoing muons.The energy cut of 6MeV was chosen since the Landauspectra have a negligible fraction of events below thatvalue in contrast to the data with a significant partdue to secondaries. Fig. 6 shows the Landau spectrabefore and after correction of the efficiency, Nµ,i(E)and N c

µ,i(E) = Nµ,i(E)/ǫi(E), respectively.The accuracy of the individual muon detection effi-

ciency is dominated by the uncertainty of the energycalibration based on fitting Landau spectra. Theexpected Landau MPV varies for different modulesdue to the mountain profile, the orientation of themodules and the muon selection cut and amounts to〈EMPV〉 = 16MeV. The Landau distribution itself

8

Energy (MeV)0 10 20 30

ev

en

tsµ

0

20

40

60h tem p e ff1 0 C a l

Entries 41

Mean 0.2386

RMS –

Constant 21.3– 273.7

MPV 0.15– 10.27

Sigma 0.088– 1.379

Figure 6: Measured energy deposition Nµ,i(E) of muon candi-dates for a top module requiring a second module with TDCcoincidence (black); Energy spectrum Nc

µ,i(E) after correctingfor inefficiencies (red). Both distributions have been fit with aLandau distribution excluding events at low energy which aredue to energy depositions of secondary particles.

is significantly broadened in comparison to that ofvertically throughgoing muons. The energy calibra-tion per module is based on a modular comparison ofMPV’s from data fits (in ADC units) with MC sim-ulations in MeV and is estimated to be accurate atthe 20% level. The resulting distribution of energieswhere the individual module trigger efficiency reaches50% is Gaussian with 〈E(ǫi = 0.5)〉 = 7MeV as meanand a standard deviation of σ(E) = 1.9MeV. Aver-aging the modular detection efficiency ǫµi in Eq. 4results in 〈ǫµi 〉 = 95% with σ(ǫµi ) = 4%.

3.3 Muon detection efficiency derived

from MC simulations

In order to evaluate the muon detection efficiencyfor the entire µ-veto system we defined two referencevolumes for entering muons. At first, we take thevolume defined by the µ-veto system itself. A simu-lated energy deposition E in a module i leads, with aprobability p = ǫi(E) as derived in Section 3.2, to apositive trigger flag. Taking all geometrical effects aswell as the modular trigger efficiency into account, adetection efficiency of

ǫtot,MCveto−volume = (93.6 ± 1.5)% (5)

is obtained. Out of the 6.4% of muons entering theveto volume undetected, more than a third of them(2.4% of all) pass through geometrical gaps of thesystem. This reflects the geometrical coverage of theµ-veto system of 98%. In addition, there are 0.9%of all muons missed which pass through a module forwhich the data were not recorded during a small partof the total measurement time. This missing data isaccounted for in the simulation by setting the triggerefficiency of this module to zero for the appropriateamount of simulated time. The statistical and sys-tematic uncertainty of the detection efficiency wasevaluated assuming a set of different threshold val-ues for the modular trigger efficiency. Simulating thecomplete muon flux as described in Section 3.1, it isnoticeable that the number of triggered events is fur-ther increased by ≈ 25% due to muons passing out-side the veto volume but having secondaries hittingat least one module.

Similarly to the detection efficiencyǫtot,MCveto−volume, we also derived a detectionefficiency for a much smaller volume to be pen-etrated by muons, i.e. a sphere with a radius of1m around the center of the cryostat was chosen.This second case is intended as a more adaptedefficiency value in consideration of the WIMP search.Whereas the first volume includes muons passingthrough some corners of the experimental setup withgaps due to mounting structures, the central sphererequires muon tracks that may produce secondaryparticles close to or within the cryostat. For thesemuons we obtain a detection efficiency of

ǫtot,MCcentralsphere = (97.7 ± 1.5)% (6)

Since we rely on the same calibration and mea-sured trigger efficiencies of the indiviual modules,the estimated error is of the same size as forǫtot,MCveto−volume. The remaining inefficiency for thissample is almost entirely caused by the trigger inef-ficiencies of the individual modules and could thusbe reduced by lowering the effective thresholds. Asmost of the muon-induced background in the bolome-ters is due to muons passing near the cryostat (seeSection 4.2 and Fig. 10), ǫtot,MCcentralsphere reflects

9

better the veto efficiency for potential muon-inducedbackground than ǫtot,MCveto−volume.

3.4 Muon detection efficiency derived

from bolometer data

The following approach avoids the uncertainties ofthe energy calibration and MC simulation and in-stead purely relies on data acquired with EDEL-WEISS itself. It is fully independent of the meth-ods described in Section 3.3 and leads to the mostreliable results for the muon detection efficiency . Inthis method, muon candidates are selected in the Gebolometers and the efficiency is probed by a simplecoincidence requirement. Above 6− 7MeV of energydeposition in the bolometers, the fraction of eventsfrom the ambient radioactivity quickly drops andshould be completely zero above 10MeV for anythingbesides throughgoing muons. To ensure suppres-sion of all potential background in a single bolome-ter, an additional multiplicity requirement of at leasttwo detectors was introduced. With a selection ofEheat > 7MeV and a multiplicity of mbolo ≥ 2, a to-tal of 34 µ candidate events was found in the bolome-ters. All of these events were detected in the µ-vetosystem with time differences ∆t = tbolo− tveto as canbe seen in Fig. 7. As will be discussed in detail inSection 4.1, positive values of ∆t of the order of tensof µs are expected for perfect synchronization of thebolometer and µ-veto system. Such differences aredue to the sampling rate of 100kS/s of the bolometersignals and the rise time of the ionization signal ofthe order of a few µs. Larger differences can occurfor high energy events which saturate the ionizationchannel and make the time reconstruction more dif-ficult. In contrast, there are 7 of the coincidenceswith an unphysical timing ∆t < 0 where the fastscintillation signal of the µ-veto was observed up to12.1 ms after the signal in the bolometers (see Fig. 7and Section 4.1 for the discussion of the synchroniza-tion accuracy). Most of the events including the 7events with unphysical timing, have reconstructedmuon tracks (Section 3.5) through the cryostat. Afew of them show multiple hits indicating a shower

s)µ (Veto-tBolot = t∆ -500 0 500 1000

s µE

ntrie

s pe

r 10

0

2

4

6

Figure 7: Time difference between bolometer muon candidatesand their closest µ-veto event. Note that two events with ∆t =−4.1ms and −12.1ms are not shown.

in the whole system. Thus, with an expectation of0.14 events due to accidental coincidences in the timeinterval [−15,+1]ms, all 34 events are considered asmuon-induced coincidences.

The best estimate for the efficiency observing 34out of 34 events is ǫtot,Data = 100%. We deter-mine a lower limit for the efficiency value by ex-tracting the lowest efficiency value for which oneexpects to see 34/34 events in 10% of the cases:P (ǫ = x | 34/34 evts) = 10%. According to bino-mial statistics P (k, n, p) =

(

nk

)

pk(1− p)n−k, where pcorresponds to the efficiency ǫ and n = k = 34, wetransform this into

ǫtot,Data >n√0.1 = 0.935 at 90%C.L. (7)

Thus, this method yields a lower efficiency limitof 93.5% entirely due to the statistical uncertainty.From the point of systematics, the candidate selec-tion is biased to close muon tracks. However, this isalso the case for the dominant fraction of all muon-induced events in the bolometers as will be discussedin Sec.4.2. In conclusion, the method described hereis supposed to be adequate for determining the re-jection capability of the µ-veto system. The sys-tematic uncertainty is estimated to be less than 1%and the lower boundary of 93.5% for the µ-veto sys-tem efficiency is regarded as a reliable albeit veryweak boundary limited by the low statistics of the se-

10

lected bolometer event sample. It is in full agreementwith the detection efficiency derived from MC as de-scribed in Section 3.3. With the further data takingof EDELWEISS, the statistics will increase and thusthis method will also yield a more precise determina-tion of ǫtot,Data.

For all following investigations of muon-inducedbackground rates, we will use the muon detection ef-ficiency derived here, i.e. ǫtot = ǫtot,Data.

3.5 Muon track reconstruction

The information provided by the module number andtime difference of the two PMT signals on each end ofa plastic scintillator module are used to reconstructthe coordinates of the energy deposition in the µ-vetosystem. Since there is no information about the po-sition of the event with respect to the module widthof 65 cm and to the thickness of 5 cm, the positionperpendicular to the module axis is set to a ran-dom value between 0 and 65 cm in order not to cre-ate discrete steps in geometrical distributions of therecorded events. The thickness of the module is ne-glected. For each event generating coordinate-signalsin two modules, a track can be defined by connectingthe two penetration points, including their relativetiming. This track allows to reconstruct azimuth andzenith angles as well as the minimum distance of themuon track to the center of the cryostat.

The selection of events with exactly two energydepositions on different sides of the µ-veto systemis supposed to be due to muons, since only thoseare penetrating enough to go through the whole ex-periment. The resulting angular dependent spectraare a negative imprint of the shielding properties ofthe mountain profile convoluted with the geometri-cal coverage and efficiencies of the experiment. InFig. 8, the measured zenith distribution of muonstraversing the EDELWEISS experiment is comparedto MC simulations [26, 28] and previous measure-ments of the Frejus experiment [41]. The MC simu-lation incorporates both the geometry and the singlemodule efficiencies of the EDELWEISS experiment asdetermined in section 3.2. For better comparison of

Zenith angle (degree)0 20 40 60 80

Ent

ries

per

degr

ee

0

100

200

300

Figure 8: Zenith angle distribution of muon tracks in theEDELWEISS µ-veto system (black data points), in the Frejusproton decay detector (dotted blue) [41] and of the correspond-ing simulated tracks (EDELWEISS solid red; Frejus dashedgreen). All spectra are normalized to the EDELWEISS dataset. The simulation incorporates the full geometrical accep-tance functions.

the angular distributions, all spectra are normalizedto the EDELWEISS data set. The MC simulationreproduces well the EDELWEISS data (black datapoints). In contrast, the Frejus experiment [17] hasa different geometry and hence the acceptance is sig-nificantly different leading to a different zenith angledistribution as confirmed by simulated tracks withthe according acceptance function. From Fig. 8, onecan see that the differences in the measurements ofEDELWEISS and Frejus are due only to the differ-ent acceptance functions. The simulated zenith angledistributions based on the same muon flux generatorreproduce both angular distribution once the accep-tance of the experiments is incorporated.

The actual profile of the EDELWEISS data with amaximum at 35◦ is well understood with a large rockoverburden of 1800m at zero degree and the small-est rock overburden at the flanks of the mountain.The spectral shape of the MC simulation is sensitiveto the implemented energy thresholds of the individ-ual modules. The consistency of the simulation withthe EDELWEISS data underlines that both the cal-ibration and single module efficiency determinationas well as the track reconstruction with an estimatedreconstruction uncertainty of σl = 15 cm along themodule axis are well controlled. The zenith spec-

11

Azimuth angle (degree)0 100 200 300

Ent

ries

per

4 de

gree

0

100

200

300

Figure 9: Azimuth angle distribution of muon tracks in theEDELWEISS µ-veto system (black data points), in the Frejusproton decay detector (dotted blue) [41] and of simulated tracksthrough EDELWEISS (solid red) and Frejus (dashed green).The Frejus detector has vanishing detection efficiency at 0 and180 degrees. Frejus data and simulation results were normal-ized to the EDELWEISS data set.

trum has been cut at 80◦ since both the map of themountain profile as well as the initial muon spectrumof the muon generator used in the MC have large un-certainties at such horizontal zenith angles.

The azimuth angle distribution (Fig. 9) also showsgood agreement between the measured data inEDELWEISS and the MC simulation modeling de-tected muon tracks. The zero degree direction isaligned with the laboratory direction. In the geo-graphical coordinate system this corresponds to anoffset of 16◦ to the north direction. There are twoartificial peaks at 90◦ and 270◦ in the data. Thesepeaks result from the fact that the modular positionof events which have a TDC signal that would placethem outside of a plastic scintillator module is setto be at the end of the module. For the top mod-ules, the module ends are in plane with the Northand South vertical scintillator modules giving recon-structed tracks with 90◦ or 270◦ azimuth angle. Thegood agreement between the data and the simulationsuggests that it describes well the spatial resolutionand the proportion of tracks reconstructed near themodule edges.

The profile measured by Frejus is rather similarto this work with a few exceptions. One immedi-ately notes two dips in the angular spectrum. For

-track to center cryostat (m)µDistance 0 1 2 3 4 5

Ent

ries

per

10cm

0

200

400

600

800

Figure 10: Muon track distance to the center of the cryostat.EDELWEISS µ-candidates are shown as black data points andthe MC simulation in solid red.

azimuthal angles of 0◦ and 180◦ muons passed parallelto the detector planes of the Frejus experiment andcould not be detected [17]. Again, the same muongenerator reproduces the two experimental azimuthalspectra once the according acceptance functions areincorporated into the simulations.

Another application of the µ track reconstructionis the identification of muons passing close to or pen-etrating the bolometers. The distribution of the min-imum track distance to the center of the cryostatis shown in Fig. 10. The characteristic shape ofthe distribution originates from the number of muontracks in a thin spherical shell with a certain fixedradius around the center of the cryostat and the factwhether this shell is contained within the µ-veto sys-tem or not. As the cryostat is 1.9m away from thetop and the four upper sidewalls, this distance corre-sponds to the maximum of the muon track distribu-tion. Afterwards the number of muon tracks withinthe spherical shell still increases, but the number ofdetected traces decreases again. The maximal dis-tance of a muon veto module to the center of the cryo-stat is d ≈ 4m. The simulation reproduces very wellthe data and underlines the reliability of the muontrack reconstruction.

12

3.6 Determination of the muon flux

To conclude, we determine the integral muon fluxthrough a horizontal surface. Requiring a module be-ing hit in at least two surfaces of the µ-veto system,we accumulated 18503 muon candidates which cor-responds to a measured rate of Γµ−cand. = (108.7 ±0.8)/d. Due to the rather cubic geometry and theindividual detection efficiencies of each module, theoverall detection acceptance for a given muon selec-tion must be determined through simulations. Forthe applied muon selection cuts, a combined detec-tion acceptance aMC = 20.0± 0.4 candidates/(µ/m2)was derived from simulations accounting for the ge-ometry of the setup and modular efficiencies ǫµi . Thisleads to an acceptance-corrected total flux of muon-induced events of

Φµ = Γµ−cand./aMC

= 5.4 ± 0.2(stat.)+0.5−0.9(syst.)µ/m

2/d. (8)

The systematic uncertainty is made up of three con-tributions. The first one arises from backgroundevents not induced by muons but being in coincidencein modules of two geometrical surfaces. This mayhappen in corners of the µ-veto system. To checktheir influence, we analyzed subsamples where adja-cent surfaces are not allowed. This reduces Γµ−cand.

as well as aMC leading to an overall reduction of Φµ

by 10%. As described in Section 3.2, the modu-lar efficiencies ǫµi depend on the calibration param-eters. Allowing a variation of ±20% leads to an-other 10% uncertainty. Third, there is a remain-ing uncertainty of the derived flux due to modelingthe muon flux based on single muons produced onthe hemisphere and neglecting muon bundles whichwere measured in the Frejus experiment contribut-ing 5% to the overall muon flux [17]. In our sim-ulations, the average number of muons per event isonly slightly larger than one due to secondary muonsproduced in the rock between the start hemisphereand the lab. Deriving alternatively from the 18503measured muon candidates the muon flux through asphere leads to asphMC = 16.4 ± 0.4 candidates/(µ/m2)

and subsequently Φsphµ = 6.6µ/m2/d.

The measured flux as given in equ. 8 is slightlyhigher but yet compatible with the measurementsof the Frejus experiment. To compare the values,the different definitions and cuts have to be takeninto account. The event rate determined here cor-responds to the sum of events with muon multiplic-ity m ≥ 1, including muon bundles. In addition,no zenith angle cut of Θ < 60◦ as in [17] was ap-plied in our measurement. Since it is not statedin [17] whether the muon flux was measured for ahorizontal area or a sphere, we give the appropri-ate values for both assumptions here. Interpretingthe quoted flux in [17] as a flux through a horizon-tal plane and correcting it for the inefficiency of the60◦ cut, evaluated from our measurements, a value ofΦhorizontalFrejus = (5.2±0.1stat.)µ/m

2/d is calculated. Thealternative interpretation of the values in [17] as theflux through a sphere would lead to a smaller flux ofΦhorizontalFrejus = (4.2 ± 0.1stat.)µ/m

2/d to be comparedwith the value given in equ. 8.

4 Coincidences in the µ-veto sys-

tem and bolometers

For WIMP searches, every background componenthas to be well understood and maximally suppressed.In this section, the muon-induced event population inthe bolometers is studied in situ, for the specific geo-metrical arrangement of bolometers during the dataacquisition period from March 2009 to May 2010.In addition to quantifying the muon-induced neutroncomponent for the WIMP analysis [13], the topologyof muon-induced events is investigated. With thisderived information, an estimate of muon-inducedneutrons can be deduced for the next phase of theexperiment, EDELWEISS-III. The investigation isperformed using a newly developed data framework,KData [22] that allows the event-based storage andanalysis of both bolometer and µ-veto data in thesame structure.

13

-1000 -500 0 500 1000

sµ

En

trie

s p

er

10

1

10

210

(µs)Veto-t

Bolo∆t = t

-1000 -500 0 500 1000

sµ

En

trie

s p

er

10

-110

1

10

Figure 11: Time difference between bolometer events and hits in the µ-veto system. (a) data taken after September 2009, (b)data taken from March to September 2009. Black indicates coincidences while the blue dotted line corresponds to the expectedrate of accidental background. The vertical lines represent timing cuts applied for further investigation of coincidences. Solidlines indicate the applied cut for the appropriate data period while the dotted lines describe the cut used for the other dataperiod.

4.1 Determination of the coincidence in-

terval

Searching for delayed coincidences between a promptmuon veto hit and a secondary bolometer event, atypical time delay ∆t = tbolo − tveto of a few tensof microseconds is expected. This time difference ismainly due to the rise time of the bolometer pulsesand their sampling rate of 100 kS/s. The accuracy ofthe synchronization of the separate acquisition sys-tems leads to a broadening of a few tens of microsec-onds. The overall recorded time difference as shownin Fig. 11 is thus not caused by physics processessuch as thermalization of neutrons. The exact exper-imental coincidence window to select muon-inducedsignals is determined by the ∆t distribution itself.In the following, we select events where at least twomodules were hit (mveto ≥ 2 with at least one ADCor TDC entry per module being non-zero) leading toan event rate of 0.12Hz. This is a much stricter re-quirement than in vetoing potential backgrounds inthe dark matter search where bolometer events arerejected whenever there is any event recorded in the

µ-veto system within a ±1ms time interval. Withan event rate of 0.41Hz in the µ-veto system, theapplied dead time amounts to less than 0.1% of thetotal measuring time. Having a muon candidate withmveto ≥ 2, we then extract the time difference ∆t tothe nearest event in the bolometer data set.

This time difference is shown in Fig. 11 for twodistinct periods of data taking. Fig. 11a shows thedistribution for the data after September 2009 withfully functioning synchronization between µ-veto sys-tem and bolometers. A clear peak of muon-inducedcoincidences can be identified and a time intervalof 20µs ≤ ∆t ≤ 80µs was chosen maximizing thesignal-to-background ratio containing at least 97.5%of the peak population. For the early data set fromMarch 2009 to mid-September 2009 corresponding toabout 1/3 of the total exposure, some data losses inthe optical transfer of the 48-bit clock from bolome-ters to the µ-veto system degraded the synchroniza-tion performance. An offline correction to the syn-chronization could reproduce a peak in ∆t, but atslightly unphysical time differences (Fig. 11b). The

14

corresponding interval for coincidences was derived tobe -300µs ≤ ∆t ≤ 0µs. However, not all of the syn-chronization errors could be corrected in the offlineanalysis. A detailed investigation of coincidenceswith synchronization problems resulted in the quan-tification of (12 ± 8)% of all cases with ∆t < −1ms(including the two outliers at ∆t = −12.1ms and∆t = −4.1ms in Section 3.4). An attributed un-certainty of a few ms in synchronizing the systemsis much larger than the vetoing interval of ±1msaround each veto hit. When deriving the muon-induced background in the WIMP search in Sec-tion 4.3, we therefore conservatively treat these peri-ods with an exposure of (17± 11) kg · d as bolometerdata without functioning µ-veto system.

With the two coincidence intervals as shown inFig. 11, a total of 76+158 = 234 events summing overthe 1st and 2nd period were selected for further in-vestigation. An accidental background of 6.75± 0.03events was determined in a two second wide windowwith an offset of 5 seconds before the veto event.This corresponds to an achieved signal to noise ratioof better than 33/1. After subtraction of accidentalbackground, the remaining excess of coincidences inEDELWEISS-II is entirely due to events induced bymuons.

4.2 Topology of muon-induced bolometer

events

A WIMP scattering off a Ge nucleus would lead to asingle scatter event in a bolometer, i.e. a bolometermultiplicity mbolo = 1. Any event with mbolo > 1 cantherefore be rejected. The multiplicity of bolometerhits in a bolometric array is thus a potentially pow-erful tool to reject background, depending on the na-ture of the background as well as on the total detec-tor mass and the granularity of the crystal array. Themultiplicity of the 234 extracted µ-induced bolometerevents is shown in Fig. 12. For the specific setup ofEDELWEISS-II, (46.6 ± 0.6)% of all muon-inducedevents in the complete energy range would be rejectedin a WIMP search due to mbolo,µ > 1, with an aver-age bolometer multiplicity of 〈mbolo,µ〉 = 2.27± 0.18.

Bolometer hits per event0 5 10

Ent

ries

-210

-110

1

10

210

Figure 12: Bolometer multiplicity for muon-induced events(solid red). For comparison, a scaled histogram of the multi-plicity of all bolometer events is superimposed (dotted black).

This is in clear contrast to 〈mbolo,all〉 = 1.05 for allbolometer events, with the mbolo,all distribution alsoshown in Fig. 12.

The fraction of events with mbolo,µ > 1 stronglydepends on the geometrical setup. This can be seenin a comparison of the present results with the sim-ulations based on a fully equipped cryostat with 120Ge crystals, each with a mass of 320 g [26], adding upto 38.4 kg. As described in Section 2.1, the currentstudy incorporates only 10 ID detectors with a totalmass of 3.6 kg. In the ideally packed array used in thesimulations, a fraction of 84% of all muon-inducedevents have a multiplicity of mbolo,µ > 1. Thus, withincreasing numbers of bolometers in a densely packedarray, a muon-induced background can be efficientlysuppressed due to its high multiplicity.

Furthermore, muon-induced background events ex-hibit an energy spectrum which is very different toan exponentially decreasing recoil spectrum expectedfrom WIMP scattering. Fig. 13 shows the sum en-ergy of all energy depositions in the detectors asso-ciated with a muon-induced event. The spectrum iscomposed of two main regions. Up to 1MeV the en-ergy deposition in the bolometers is caused by singleor multiple energy depositions of secondaries, mainlyelectrons and gammas. From 50 keV to several 100keV the dominant interaction is Compton scattering.The second feature is a broad peak between 5 and100MeV with a maximum around 20MeV caused by

15

(E in keV)10

Log0 1 2 3 4 5

En

trie

s

0

10

20

30

40

0

2000

4000

6000

8000

10000

Figure 13: Sum of energy deposition in the bolometers forthe 234 coincidence events (dashed black - 4 bins per decade)as well as for muon-induced single bolometer hits (long-dashedgreen) and background events in individual bolometers (dottedblue - 64 bins per decade). For comparison, a subsample of 109events is shown for which a muon track could be reconstructed(solid red, see text for more details).

muons passing through the Ge crystals (energy lossof muons in Ge ≈ 10MeV/cm). For those events,the energy deposition is mainly dependent on thepath length of the muon in the crystals. For sin-gle scatter events (Fig. 13 long-dashed green) thisfeature is strongly suppressed, indicating that theseare mainly caused by secondaries. Last, there isa small fraction of events below 50 keV, where thedominant component is elastic scattering of muon-induced neutrons as will be discussed later. Fig. 13also shows the energy deposition in the bolometersfor background events (dotted blue histogram) whichclearly contrasts the muon-induced distribution. Thepeaks in this spectrum can be associated to α decaysof 210Po (5.4MeV), which can be further suppressedby a fiducial volume cut, a Compton backscatteringbump above 100 keV as well as the 10 keV gammaline from cosmogenic activation.

Apart from the bolometer multiplicity and energydeposition of muon-induced events, the distance ofthe muon track from the center of the cryostat couldbe deduced from the information in the muon vetomodules. Fig. 14 shows the distance of 109 out ofthe 234 sequential events. For these 109 events, themuon track could be reconstructed unambiguouslydue to full spatial information in exactly two of the

Distance (m)0 1 2 3

Ent

ries

per

10 c

m

0

5

10

15

20

25

Figure 14: Distance to the center of the cryostat for 109 co-incidence events with track reconstruction (solid black), withenergy depositions in the bolometers below (dotted blue) andabove 1MeV (dashed red). Also shown is the scaled distribu-tion of muon events identified in the µ-veto system withoutrequiring a coincidence (dash-dotted green) with its maximumat ≈ 2m as described in Section 3.5 and Fig. 10.

veto modules. More than 90% of these muon-inducedbolometer events are produced by muons passingwithin a distance of less than 1m to the cryostat’scenter whereas the overall distribution of all identi-fied muons is much broader with a maximum aroundd = 2m. Although muon-induced bolometer eventshave short track distances to the cryostat, it is impor-tant to note that this does not translate directly intomuons hitting the Ge crystals with large energy de-positions. As can be seen in Fig. 14 the distances forevents with energy depositions in the bolometers be-low (dotted blue) and above 1 MeV ( dashed red)have almost identical distributions. Thus, muonseven passing through the cryostat lead to energy de-positions below 1MeV, reaching the typical WIMPrange of tens of keV, indicating energy deposition bysecondary particles. On the other hand, distances ofd > 0.7m correspond to muons passing outside thecryostat, where secondary electrons and gammas areunlikely to reach the Ge bolometers due to the var-ious shields. In this case, coincident events can beinterpreted as muon-induced neutrons scattering offthe Ge nuclei.

The requirement for reconstructing muon tracksmay introduce a slight bias in selecting muon-induced

16

1-10 -8 -6 -4 -2 0 2 4 6

-4

-2

0

2

4

6

8

10

12

100

1000

10

north-south distance [m]

top

-bo

tto

m d

ista

nce

[m

]

Figure 15: Simulation of production vertices of neutrons inmuon-induced showers leading to an energy deposition by nu-clear recoils in the bolometers [26]. Shown is a side projectionof the underground laboratory LSM. Most of the neutrons areproduced in the Pb shield and the steel of the support struc-ture.

events with high energy deposition in the bolometersas can be seen in Fig. 13. Low energy depositionsoriginating from muon-induced neutrons might alsobe connected to muons passing outside the µ-vetosystem. However, the production vertices for theseneutrons are dominantly positioned in the Pb shield-ing as can be seen in Fig. 15. From these simulations,one expects only 0.05% of all neutrons produced out-side of the µ-veto system, while more than 90% areproduced within the lead shield or the cryostat it-self. In conclusion, muon-induced bolometer events(including potential neutron scattering events) aremainly caused by muons with a track of less than1m distance from the center of the cryostat and thuspotentially can be vetoed with the µ-veto system.

4.3 Muon-induced background for dark

matter search

The muon-induced background for the WIMP analy-sis is determined as the product of the rate of muon-

induced single hit events in the nuclear recoil band,the accumulated exposure of 384 kg · d and the µ-veto system inefficiency (1 − ǫtot) as determined ineq. (7). For a DM search, it is crucial to have thehighest muon detection efficiency possible. Hence, inthis analysis we abandon the requirement for muoncandidates as used in Sections 4.1 and 4.2, i.e. havinghits in more than one veto module. The total num-ber of coincidences then moderately increased fromNm>1

C = 234 to NC = 283 events, while the rate ofaccidental background increased by a factor of 3.5from Nm>1

A = 6.75 ± 0.03 to NA = 23.61 ± 0.06. Asfor the 234 coincidences studied before, there was norejection of periods with high baseline noise nor anyselection of fiducial bolometer events. Thus, the totalexposure is much larger than in the WIMP analysisand amounts to 1504 kg · d. With a net number ofN = NC − NA = 259 ± 17 coincidences, the rate ofmuon-induced events in the complete energy range,not discriminating between electron and nuclear re-coils, amounts to

Γµ−ind. evts = (0.172 ± 0.001) evts/(kg · d). (9)

The rate of muon-induced background events withinEDELWEISS-II is in good agreement with earlier in-vestigations [21] based on a much smaller event sam-ple and slightly different selection cuts. Fig. 16 showsthe events as individual bolometer hits with an en-ergy deposition below 250 keV. Applying a fiducialvolume cut inferring reliable charge collection andthus ionization yield and a χ2-cut comparing heatand ionization pulse fits with their template pulses,bolometer hits shown as dots are rejected. After atime-averaged 90% C.L. nuclear recoil band selectionapplied for each single detector, seven bolometer hitsremain (see Fig. 16 within the red bands). Out ofthese seven, six are above the 20 keV analysis thresh-old, and only four (shown as red crosses) are singlebolometer hits without a coincident hit in anotherbolometer as required for a WIMP candidate. (Thebolometer hit at 60 keV is in coincidence with anotherone, the hit at 70 keV is outside the predefined nu-clear recoil band.) Three of these events have recon-structed muon tracks going through the lead shield

17

(keV)rec E0 50 100 150 200 250

Ion

iza

tio

n y

ield

Q

0

0.2

0.4

0.6

0.8

1

1.2

1.4 1504 kg d

Figure 16: Scatter plot of bolometer hits in the coincidenceanalysis for energies below 250 keV. Fiducial events that are ex-pected to have a full charge collection and thus a reliable valuefor Q are drawn as crosses (blue and red). The events marked inred satisfy all WIMP criteria. Other events are shown as blackdots. The lines correspond to the 90% C.L. gamma region(blue), the 90% C.L. nuclear recoil band (red), the analysisthreshold of 20 keV used in the WIMP analysis (black) and anionization threshold for fiducial events of 3 keV (green). Exceptfor the analysis threshold, all resolutions and bands are timeand bolometer dependent. For illustration, the time-averagedbands of an exemplary detector, ID401, are drawn here.

and even through the cryostat itself. The fourthevent is in coincidence with an event in the µ-vetosystem, where 11 plastic scintillator modules havebeen hit, indicating a muon-induced shower. Fig. 16shows individual bolometer hits. Rates in Table 1refer to bolometer events with potentially more thanone bolometer hit.

Applying all cuts required for WIMP candidatesresults in an effective fiducial exposure of 481 kg·d.Thus, the rate of muon-induced WIMP-like eventsamounts to

Γµ−n = (0.008+0.005−0.004) evts/(kg · d). (10)

Assuming a conservative veto efficiency as in Eq. 7,the rate of muon-induced WIMP-like events amountsto an irreducible background rate of Γµ−n

irred < 5.8 ·10−4 evts/(kg · d) at 90%C.L.

From Equations 7 and 10 for the µ-veto detection effi-ciency and the rate of muon-induced WIMP-like events,the number of expected unvetoed muon-induced singlescatter neutron events Nµ−n within the WIMP analysis is

Table 1: Rates of coincidences. All results are given after back-ground subtraction. The cuts on recoil energy Ehit

rec and Q-valueQhit

rec are fulfilled, when at least one bolometer hit within anevent fulfills the condition. For fiducial nuclear recoil (NR)events, the 90% signal region is defined following the Lindhardparametrization [33].

Selection cut Γµ−ind (evts/kg/d) Exposure (kg d)

None 0.172 ± 0.012 1504

Ehitrec < 250 keV 0.095 ± 0.009 1504

Ehitrec < 250 keV; Qhit

rec < 0.6 0.035 ± 0.005 1504

Ehitrec < 250 keV; fid. NR 0.017 ± 0.006 481

Ehitrec < 250 keV; fid. NR; single 0.008+0.005

−0.004481

calculated according to

Nµ−n = MB+VExp Γµ−n(1 − ǫtot) +MB

ExpΓµ−n = 0.40 (11)

Here MBExp = 38 ± 11 kg · d denotes the sum of exposure

of a short period where only bolometer data was acquired(21 kg·d) and the earlier period where a hardware mal-function led to a faulty synchronization in 12% of themeasuring time (17±11kg·d). MB+V

Exp = 384 kg · d−MBExp

is the exposure of the WIMP search data set, when bothacquisition systems (bolometer and µ-veto system) wererunning with full synchronization. The above expectationvalue Nµ−n is dominated by the contribution from MB

Exp.

Taking into account all uncertainties on Γµ−n, ǫtot andMB

Exp we derive an upper limit of Nµ−n < 0.72 events(90%C.L.). Comparing this result with other back-ground estimates for the EDELWEISS-II WIMP searchfrom misidentified gamma events Nγ < 0.9, from surfaceevents Nβ < 0.3 [13] and from ambient neutrons Nn < 3.1[14], muon-induced background contributes less than 20%to the total background. Note that this is dominantly dueto including periods in the WIMP search where the µ-vetosystem was not synchronized properly to the bolometersystem. For future searches as in EDELWEISS-III, suchperiods will not be included and thus an even better re-jection of muon-induced background can be achieved.

5 Expected background for

EDELWEISS-III and EURECA

For the forthcoming phase of EDELWEISS-III as well asfuture experiments, an accurate number for the muon-induced neutron background can be predicted only withfull modeling of the specific geometry due to the suppres-sion of multiple scattering signatures in a densely packed

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detector array and the benefits from additional shielding.A larger number of detectors, such as the forty 800 g detec-tors planned for EDELWEISS-III, will increase the gran-ularity and hence the number of multiple bolometer hits.Also, the effective area of Ge bolometers exposed to themuon flux remains approximately constant while the de-tector mass increases proportionally with the number ofdetector planes. Furthermore, the introduction of an ad-ditional PE shield inside the cryostat is going to moderatethe neutron flux induced in the lead. All effects will reducethe rate of muon-induced WIMP-like background events.

Taking the measured rate of muon-induced nuclear re-coil events (Eq. 10) and the derived efficiency of the µ-vetosystem of 97.7% as in Eq. 6, a total of Nµ−n

3000kg·d = 0.6+0.7−0.6

(90%C.L.) irreducible background events due to muon-induced neutrons are projected for EDELWEISS-III fora 6-month exposure of 3000 kg · d. Both the backgroundrate and the muon detection efficiency will be measured inthe ongoing analysis of the EDELWEISS-III experimentand in parallel modeled with its specific new setup andbetter shielding.

Going further to ton-scale experiments such as the en-visaged EURECA experiment, the muon-induced neutronbackground could be of sizable contribution. The strategyof reducing it with respect to the EDELWEISS design isto reduce the high-Z material close to the bolometers aswell as including a highly efficient water Cerenkov activeshield around the cryostat [31].

6 Conclusion and outlook

The angular dependence of the muon flux through theEDELWEISS experiment has been analyzed and is wellmodeled by MC simulations. Two independent methodsto determine the µ-veto system efficiency have been pre-sented, giving results limited so far by small statistics.A conservative value of ǫtot > 93.5% has been used forthe calculation of muon-induced background in the WIMPsearch data set. The data of the bolometer array togetherwith the modular structure of the µ-veto system alloweda detailed study of the topology of muon-induced eventswithin EDELWEISS. The analysis of muon-induced back-ground has been performed in the specific setup of the dataacquisition of 2009/2010 with 10 Ge bolometers. For thisconfiguration, the rate of muon-induced events that mimicWIMPs has been determined to Γµ−n = (0.008+0.005

−0.004)events/(kg ·d). In conclusion, the muon-induced back-ground with an expectation of Nµ−n < 0.72 events withinthis WIMP search was small compared to other back-

grounds. Thus, only a minor fraction of the five eventsobserved in the dark matter search [13] is assumed to bedue to muon-induced interactions.

The feasibility of a background free data taking of atleast 3000 kg · d (EDELWEISS-III 6 months) has beenshown with a conservative extrapolation from currentdata. Expected benefits from larger bolometer granularityand hence larger multiplicity of events as well as from theadded shielding have been briefly discussed and shouldenable background free operation beyond a sixth monthexposure. However, future ton-scale experiments, like theEURECA experiment, need different shielding conceptswith less high-Z material close to the bolometers.

7 Acknowledgements

The help of the technical staff of the Laboratoire Souter-rain de Modane and the participant laboratories is grate-fully acknowledged. This project is funded in part bythe German ministry of science and education (BMBF)within the ”Verbundforschung Astroteilchenphysik” grant05A11VK2, by the Helmholtz Alliance for AstroparticlePhysics (HAP) funded by the Initiative and NetworkingFund of the Helmholtz Assocication, by the French AgenceNationale de la Recherche under the contracts ANR-06-BLAN-0376-01 and ANR-10-BLAN-0422-03 and by theScience and Technology Facilities Council (UK). The dedi-cated neutron measurements (ambient and muon-induced)were partly supported by the EU contract RII3-CT-2004-506222 and the Russian Foundation for Basic Research.

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