Search for Dark Matter with EDELWEISS-III Using a Multidimensional Maximum Likelihood Method
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Search for dark matter with EDELWEISS-III using a multidimensional maximum likelihood method Zur Erlangung des akademischen Grades eines DOKTORS DER NATURWISSENSCHAFTEN der Fakultät für Physik des Karlsruher Instituts für Technologie genehmigte DISSERTATION von Dipl.-Phys. Lukas Hehn aus Herrenberg Tag der mündlichen Prüfung: 24.06.2016 Referent: Prof. Dr. Dr. h.c. J. Blümer Korreferent: Prof. Dr. W. de Boer KIT - Die Forschungsuniversität in der Helmholtz-Gemeinschaft www.kit.edu Abstract The nature of dark matter is one of the most fundamental questions in modern physics. From measurements of the Cosmic Microwave Background, a dark matter fraction of 27% of the total energy in the Universe can be derived. The known baryonic matter makes up only 5%, while the rest is attributed to an unknown dark energy. Evidence from the gravitational effects of this dark matter can be found on all cosmological scales, including our Milky Way. The different observations can be explained in a unified picture with a non-relativistic particle, so-called Cold Dark Matter (CDM). Such a particle is not part of the Standard Model (SM) and would require new physics. A generic class of hypothesised candidates are Weakly Interacting Massive Particles (WIMPs) with masses mχ in the GeV{TeV range and interaction cross sections of the order of the weak scale. Such particles can be found e.g. in the proposed SuperSymmetric extension of the SM. This thesis was performed in the context of the EDELWEISS-III experiment, which is designed to detect the elastic scattering of a WIMP from the galactic dark matter halo in an array of detectors. To shield against the flux of cosmic-ray induced muons, the experiment is located in an underground laboratory with 4800 m w.e.. Multiple layers of active and passive shielding suppress ambient radioactivity. The detectors are 800 g Ge-bolometers, which are cooled down to cryogenic temperatures of 18 mK. A particle interaction in the crystal produces thermal phonons and free charge carriers. They are measured as heat and ionization signals with 2 Ge-NTD sensors and 4 sets of ring electrodes on the detector surfaces. The ratio of ionization over heat energy can be used to discriminate, on an event-by-event basis, between nuclear recoils from a potential signal and electron recoils from backgrounds. Particle interactions on the surface, for which this discrimination can fail due to incomplete charge collection, can be rejected by selecting events from the so-called fiducial volume. In the last years, special interest has risen to explore the physics case of so-called low mass 2 WIMPs with masses mχ = O(1) GeV=c . The major challenge in the detection of such WIMPs is the discrimination of a small O(1) keV nuclear recoil from background events and noise fluctuations near the trigger threshold of a detector. This thesis in particular addresses the search for low mass WIMPs by analysing EDELWEISS data with a multidimensional maximum likelihood method. Therefore, a likelihood model based on two observables, the combined heat energy Ec and the fiducial ionization energy Efid, was constructed in the framework of this thesis. Data from 8 selected detectors, taken during a 10 months long WIMP search run, was analysed in terms of low mass WIMPs. The region of interest (RoI) min min was defined as Ec < Ec < 15 keVee and 0 < Efid < 15 keVee, where Ec is the energy, for which a detector has a trigger efficiency of at least 80%. This resulted in analysis thresholds min between Ec = 0:91 keVee and 1:46 keVee, much lower than in standard EDELWEISS 2 WIMP searches before, allowing to search for low mass WIMPs with mχ 2 [4; 30] GeV=c with a signal efficiency up to 60%. A dedicated fiducial cut was developed, to efficiently reject surface events down to these low energies. After all quality cuts, a total of ≈5 · 104 events were investigated in the analysis region for a combined exposure of 496 kg·days. iii iv For each detector, a likelihood model was constructed, considering all relevant backgrounds in the RoI: electron recoils from Compton scattered γ's, X-rays and tritium decay in the detector, nuclear recoils from neutrons, ionizationless heat-only events and unrejected surface events from the decay chain of 210Pb. The energy spectra of each background were derived from sideband data and a detector response model was used to construct probability density functions (PDFs) in the two observables. The event rate µ of each background was constrained during the fit to the expected rate, including its systematic uncertainties. The maximum likelihood fit of data from individual detectors resulted in no statistically significant signal component for all probed WIMP masses mχ. Depending on the mass mχ of the probed WIMP signal, degeneracies were observed between the signal and different backgrounds from heat-only events and neutrons. Shown for the first time within this thesis, these degeneracies can be efficiently suppressed by combining the likelihood functions of all 8 detectors and performing a combined fit with a common signal signal cross section σχ. For each probed mass mχ and individual detectors as well as their combination, an upper limit on the WIMP-nucleon scattering cross section σχ was derived. For this, a hypothesis test based on the profile likelihood test statistics was performed for different values of σχ to find the value which can be excluded with 90% C.L.. The limit was derived with two different methods: with an approximation on the asymptotic distribution of the test statistics and with Monte Carlo generated toy data. A study performed with an extensive number of toy data sets showed that the limit derived with the asymptotic approximation does not provide the correct coverage for a large fraction of the tested likelihood functions, 2 2 especially for low masses 4 GeV=c < mχ < 7 GeV=c . Based on the proper test statistics, exclusion limits derived with the total exposure of 496 kg·days and all 8 detectors, for the lowest and highest mass evaluated here, are up −39 2 2 σχ < 1:6 × 10 cm (90% C.L.) for mχ = 4 GeV=c and up −44 2 2 σχ < 6:9 × 10 cm (90% C.L.) for mχ = 30 GeV=c The limit clearly rules out the existing claims of potential low mass WIMP signals by various other experiments. Thanks to the large signal acceptance and a subtraction of backgrounds, an improvement in the achieved limit by a factor of ≈7 is obtained for 2 mχ = 4 GeV=c WIMPs, compared to a Boosted Decision Tree (BDT) based analysis of a 2 similar data set [1]. At higher masses, mχ > 15 GeV=c , the limits from both analyses are in good agreement. This work shows, that an analysis of WIMP search data based on a maximum likelihood method is significantly improving the sensitivity on WIMP parameters over more simplified cut-based count experiments or even a BDT-based analysis. However, such a complex statistical analysis requires excellent knowledge and modelling of all relevant background sources as well as a careful statistical treatment to extract proper statements on confidence levels. iv Zusammenfassung Die Natur der dunklen Materie ist eine der bedeutsamsten ungel¨osten Fragen der modernen Physik. Aus Messungen der kosmischen Hintergrundstrahlung ist bekannt, dass dunkle Materie einen Anteil von 27% an der Gesamtenergie im Universum hat. Die uns vertraute baryonische Materie ist nur fur¨ 5% verantwortlich, w¨ahrend der Rest einer noch g¨anzlich unbekannten dunklen Energie zugeordnet wird. Hinweise fur¨ den gravitativen Einfluss der dunklen Materie finden sich auf allen Gr¨oßenskalen im Universum, auch in unserer Milchstraße. Diese verschiedenen Beobachtungen lassen sich in einem vereinheitlichten Ansatz durch ein nicht-relativistisches Teilchen erkl¨aren, so genannte kalte dunkle Materie. Da solch ein Teilchen nicht Teil des bekannten Standardmodels ist, wurde¨ es neue Physik implizieren. Eine generische Klasse von hypothetischen Teilchen sind Weakly Interacting Massive Particles (schwach wechselwirkende massive Teilchen, WIMPs), mit Massen im Bereich von GeV bis TeV und Wirkungsquerschnitten im Bereich der schwachen Wechsel- wirkung. Solche Teilchen sind unter anderem Bestandteil der SuperSymmetrischen (SUSY) Erweiterung des Standardmodels. Diese Arbeit wurde im Rahmen des EDELWEISS Experiments angefertigt, welches dafur¨ konzipiert ist, die elastische Streuung eines WIMP Teilchens aus dem galaktischen Halo in einem Detektor Array nachzuweisen. Zur Abschirmung von Myonen als Sekund¨arprodukt der kosmischen Strahlung ist das Experiment in einem Untergrundlabor aufgebaut, wo es von Gestein einer Dicke von 4800 m w.e. abgeschirmt wird. Mehrere aktive und passive Abschirmungen reduzieren die naturliche¨ Strahlung. Die Detektoren sind 800 g Germanium Bolometer, welche auf kryogene Temperaturen von 18 mK gekuhlt¨ werden. Eine Teilchen- wechselwirkung im Detektorkristall erzeugt thermische Phononen und freie Ladungstr¨ager. Diese werden als W¨arme und Ionisationssignal von 2 Ge-NTD Sensoren und 4 Gruppen von Ringelektroden auf den Detektoroberfl¨achen gemessen. Das Verh¨altnis von Ionisations- zur W¨armeenergie kann genutzt werden, um ereignisbasiert zwischen dem potentiellen Signal von Kernruckst¨ ¨oßen und dem Untergrund durch Elektronruckst¨ ¨oßen zu diskrimi- nieren. Teilchenwechselwirkungen an der Oberfl¨ache, bei welchen diese Diskriminierung wegen unvollst¨andiger Ladungsauslese stark limitiert ist, k¨onnen durch die Definition eines sogenannten Vertrauensvolumens (fiducial volume) mithilfe der verschiedenen Elektroden verworfen werden. 2 In den vergangen Jahren sind WIMPs mit niedrigen Massen von mχ = O(1) GeV=c in den Fokus des wissenschaftlichen Interesses geruckt.¨ Die gr¨oßte Herausforderung fur¨ den Nach- weis dieser sogenannten low mass WIMPs ist die Unterscheidung von niederenergetischen Kernruckst¨ ¨oßen mit Energien O(1) keV von Untergrundereignissen sowie Rauschen nahe der Aufnahmeschwelle der Detektoren. Diese Arbeit behandelt insbesondere die Suche nach low mass WIMPs durch eine Analyse von EDELWEISS-III Daten mittels einer mehrdi- mensionalen Maximum Likelihood Methode.