Investigation of the 2ν2β-spectrum of 116Cd with the COBRA experiment

Master-Arbeit zur Erlangung des Hochschulgrades Master of Science im Master-Studiengang Physik

vorgelegt von

Julia K¨uttler geboren am 31.05.1995 in Rodewisch

Institut f¨urKern- und Teilchenphysik Fakult¨atPhysik Technische Universit¨atDresden 2019 Eingereicht am 13. M¨arz2019

1. Gutachter: Prof. Dr. Kai Zuber 2. Gutachter: Prof. Dr. Arno Straessner Betreuer: Stefan Zatschler 3

Abstract

The COBRA experiment, which is located at the LNGS underground facility in Italy, searches for extremely rare decay modes of several nuclides that are intrinsically abundant in the semi- conductor detectors made of CdZnTe. In this thesis, the 2ν2β-decay of 116Cd, which has a half-life of 2.62·1019 yr [1], will be investigated. To measure such a rare decay, large efforts regarding the background reduction and offline data analysis have to be spent. To improve the discrimination between signal-like and background-like events, a new pulse shape analysis method is implemented and optimized for the data analysis routine. A better signal acceptance compared to the previous used data cuts can be achieved. To further reduce the background level, a data partitioning was accomplished. Run periods and detectors with a higher rate could be identified and excluded from the final data set. This decreases the count rate in the ROI by a factor of 2.8. The exclusion of a certain depth region of the detectors leads to a further rate reduction by a factor of three. The identified background enriched run periods, detectors and detector regions can prospectively be used as a starting point towards a background model for the COBRA demonstrator.

Kurzdarstellung

Das im Untergrundlabor LNGS in Italien befindiche COBRA Experiment sucht nach extrem seltenen Zerfallsmoden von Nukliden, die im Detektormaterial CdZnTe intrinsich vorhande- nen sind. In dieser Masterarbeit soll der 2ν2β-Zerfall von 116Cd, der eine Halbwertszeit von 2,62·1019 yr [1] hat, untersucht werden. Um solch einen seltenen Zerfall zu messen, m¨ussen besondere Maßnahmen zur Untergrundunterdr¨uckung und bei der Datenauswertung vorgenom- men werden. Um Untergrundereignisse besser von Signalereignissen zu unterscheiden, wurde eine neue Pulsformanalysenmethode in die Datenauswertung implementiert und optimiert. Damit kann eine bessere Signalakzeptanz erreicht werden als mit den bisherigen Auswahlkri- terien. Um den Messuntergrund noch weiter zu reduzieren, wurde eine Datenpartitionierung durchgef¨uhrt.Messperioden und Detektoren mit einer h¨oherenRate wurden identifiziert und von der weiteren Analyse bez¨uglich des 2ν2β-Spektrums ausgeschlossen. In dem f¨urdiese Analyse verwendeten Energiebereich konnte so die Z¨ahlrateum einen Faktor von 2,8 reduziert werden. Der Ausschluss eines bestimmten Tiefenbereiches der Detektoren f¨uhrtezu einer weit- eren Reduktion der Rate um einen Faktor drei. Die ausgeschlossenen Messperioden, Detektoren und Detektorbereiche k¨onnenals Ausgangspunkt f¨urein zuk¨unftigesUntergrundmodell f¨urdas COBRA Experiment dienen.

Contents

1 Introduction 7

2 Double beta decay and neutrino physics 9 2.1 Open questions in neutrino physics ...... 9 2.2 Beta decay ...... 12 2.3 Double beta decay ...... 16 2.4 Neutrinoless double beta decay ...... 20 2.5 Experimental aspects of double beta decays ...... 23

3 The COBRA experiment 27 3.1 Detector setup ...... 28 3.1.1 Shielding ...... 29 3.1.2 Electronic readout system ...... 31 3.1.3 Experimental infrastructure ...... 31 3.2 CdZnTe detectors ...... 32 3.2.1 CdZnTe as a semiconductor ...... 32 3.2.2 Principle of CPG detectors ...... 33

4 Pulse shape analysis method A/E 39 4.1 Background identification with PSA ...... 39 4.2 Currently used data cleaning and PSA methods ...... 40 4.2.1 LSE-cut ...... 40 4.2.2 MSE cut ...... 42 4.2.3 Motivation for a new PSA cut ...... 43 4.3 A/E parameter ...... 44 4.3.1 Definition ...... 44 4.3.2 Experimental data set ...... 44 4.3.3 A/E implementation in MAnTiCORE ...... 46 4.4 Optimization procedure ...... 47 4.4.1 A/E calculation method and smoothing window size ...... 51 4.5 A/E calibration ...... 52 4.5.1 Motivation ...... 52 4.5.2 Calibration procedure ...... 54 4.5.3 Calibration results ...... 57 6 Contents

5 Data partitioning 61 5.1 Potential background sources ...... 61 5.2 Identification of background enriched data periods ...... 63 5.2.1 Hot pixel ...... 64 5.2.2 Bad run period ...... 65 5.2.3 Bad detector ...... 68 5.2.4 Fiducial volume ...... 68 5.3 Results of the data partitioning and the A/E-cut ...... 71

6 Summary and outlook 77

7 Bibliography 79

Appendices 86

List of Figures 87

List of Tables 89

List of Acronyms 91 1 Introduction

The neutrino is the particle of the Standard Model of particle physics which properties are least known. The mass of the neutrino as well as its nature, Dirac or Majorana particle, are still unknown after Pauli proposed it more than 85 years ago [2]. Experiments that search for the neutrinoless double beta (0ν2β) decay can help answering some open questions of neutrino physics. The COBRA experiment is one of these experiments. It is located at the underground labora- tory LNGS in Italy and searches for 0ν2β-decay modes of several nuclides intrinsically abundant in the detector material CdZnTe. Besides the ultra-rare 0ν2β-decay, COBRA allows to study several other extremely rare decays such as the neutrino accompanied double beta (2ν2β) de- cay. One nuclide that can undergo this decay is 116Cd. Due to the half-life and the natural abundance of about 7.5% in Cadmium, the decay rate is in a region that can be accessed with the COBRA experiment. An observation of the spectrum with COBRA would be the first mea- surement with a semiconductor detector and thus could verify the measurements from other experiments that used different detection approaches. A consistent half-life can then be used to improve nuclear models to calculate the involved nuclear matrix elements M 2ν as well as to deepen the understanding of the nuclear structure. The first observation of the 2ν2β-decay for 116Cd by a direct counting method was achieved by the ELEGANT-V experiment in 1995 [3]. It used natural and enriched Cd foils between drift chambers for trajectory reconstruction, plastic scintillators for energy measurement and sodium iodide scintillators as background veto. With an exposure of 0.02 kg·yr in terms of 116  +0.9 19 Cd mass, a half-life of 2.6−0.5 · 10 yr was measured [3]. In the same year an exper- iment located in the Solotvina underground laboratory measured the decay with CdWO4 116  +0.5 +0.9  19 crystal scintillators enriched in Cd. A half-life of 2.7−0.4(stat.)−0.6(syst.) · 10 yr was derived [4]. One year later, the NEMO-2 tracking detector measured the decay with a half-life of (3.75 ± 0.35(stat) ± 0.21(syst)) · 1019 yr [5] (later corrected to (2.9 ± 0.3(stat) ± 0.2(syst)) · 1019 yr [6]). It used source foils surrounded by tracking detectors and a calorimeter made of scintillators. Up to now some of these experiments improved their results (Solotvina experiment

[7] and NEMO-3 [8]). The Aurora experiment at the LNGS also used CdWO4 and measured a half-life of (2.62 ± 0.14) · 1019 yr [1]. In figure 1.1 the results of the different experiments are compared to each other. With the calculation of the number of 2ν2β-decays that can be measured with COBRA, one gets a rough approximation of the sensitivity and the required background level:

ln2 N116 N = c · · Cd = 3.65 · 103 cts/ (kg · yr) , (1.1) T1/2 mCZT 8 1 Introduction

Figure 1.1: 2ν2β half-lives of 116Cd measured with ELEGANT-V [3], NEMO-2 [5], Solotv- ina [4][9][7], NEMO-3 [8] and Aurora [1]. A re-evaluated NEMO-2 result [6] is labelled as (NEMO-2)∗. Picture taken from [1].

19 116 with T1/2 = 2.62 · 10 yr from the Aurora experiment [1] and the number of Cd atoms per CdZnTe mass according to:

N116 N Cd = a · s · A = 235.3 g/mol, (1.2) mCZT hMCd0.9Zn0.1Tei where the natural abundance a = 0.0749 of 116Cd and the stoichiometric factor s = 0.9 are used. NA denotes the Avogadro constant and hMCd0.9Zn0.1Tei the molar mass of CdZnTe in the given stoichiometric composition. The factor c takes the detection efficiency as well as the signal acceptance of the analysis cuts into account. 3650 counts per year and kg of CdZnTe require a background level below 1 cts/(kg·keV·yr).

In this thesis, two possibilities to reach the goal of observing the 2ν2β-spectrum will be in- vestigated. After an introduction into the physics of double beta decay (chapter 2) and the COBRA experiment (chapter 3), the first approach - a new pulse shape analysis method, called A/E - will be investigated (chapter 4). With this, better efficiencies regarding the background rejection and signal acceptance should be achieved. This would enlarge the number of events that can be detected. In chapter 5 a so called data partitioning will be done. This includes a scan for run periods and detectors that have a higher background index, and the subsequent removal of these periods from the data set. The remaining data are than background reduced and can be used for the analysis. 2 Double beta decay and neutrino physics

2.1 Open questions in neutrino physics

1 Within the Standard Model of particle physics, neutrinos are massless spin- 2 particles (fermions). Since they have no electrical or color charge, neutrinos are only observable via weak interac- tions. There exist three neutrino flavors: νe, νµ and ντ [2]. The observation of neutrino oscillation, however, showed that they must have a non-vanishing rest mass. Therefore, studying neutrinos provides a good opportunity to find more physics beyond the Standard Model. There are a number of fundamental questions that still need to be answered, for example [10]:

• What is the neutrino mass ordering:

normal (m3  m2 > m1) or inverted (m2 > m1  m3)?

• What is the absolute neutrino mass scale?

• Is the CP symmetry violated in the lepton sector?

• What is the nature of neutrinos: Dirac or Majorana particles?

• What is the origin and the mechanism of the neutrino mass and mixing?

• Do sterile neutrinos exist?

Since the neutrinoless double beta decay, which is the main focus of the COBRA experiment, can give an access to the nature of the neutrino and the absolute mass scale, these neutrino properties should be discussed in more detail now.

Dirac or Majorana particle

The neutrino is called a Majorana neutrino if particle (ν) and antiparticle (¯ν) are indistin- guishable, otherwise it is called a Dirac neutrino. For massless neutrinos only the left-handed chirality field νL is needed to explain the weak interaction in the Standard Model. Within this framework there are only left-handed neutrino states and right-handed antineutrino states. Neutrino mass terms can be added to the Standard Model Lagrangian L in two ways. The first way can be done analogously to the Dirac masses of quarks and charged leptons, by adding the right-handed chirality component νR of the Dirac neutrino field [11]:

LD = −mD (νLνR + νRνL) . (2.1) 10 2 Double beta decay and neutrino physics

There mD contains a dimensionless Yukawa coupling coefficient and the vacuum expectation value of the Higgs field after electroweak symmetry breaking. ν = ν†γ0 denotes the Dirac adjoint to ν. The chiral spinors νL and νR have only two independent components each, leading to the four independent components in the spinor ν. Majorana first showed, that for neutral particles two of the four degrees of freedom in a massive Dirac spinor can be removed if [12]:

νc = ν, (2.2)

c c where ν is the charge and parity (CP) conjugate of the field ν. By substituting νR = νL into eq. (2.1) one obtains [11]:

1 L = − m (ν νc + νc ν ) . (2.3) L 2 L L L L L mL is a free parameter with the dimension of a mass. If right-handed chirality fields also exist, than a second right-handed Majorana mass term with the mass parameter mR can be constructed [11]:

1 L = − m (ν νc + νc ν ) . (2.4) R 2 R R R R R

Which of the mass terms of LD, LL and LR are realized in nature and which are the numerical values of the corresponding masses mD, mL, mR have to be answered by experiments. The answer to the question whether the neutrino is a Dirac or a Majorana particle can also help to solve cosmological problems. If the neutrino is a Majorana particle, the decay of the heavy Majorana neutrinos into leptons and Higgs particles in the early universe provides an ideal scenario for leptogenesis, which is the theory to describe the matter-antimatter asymmetry in the early universe [11].

Neutrino masses and mixing

From the observation of the neutrino flavor oscillation it is clear that at least one eigenstate has a non-vanishing rest mass. This also means that the mass eigenstates (|νii) and the flavor eigenstates (|ναi) taking part in weak interactions are not identical. The flavor mixing is already known in the quark sector where both types of states are connected by the so called CKM matrix. For neutrinos the flavor eigenstates can be written as:

|ναi = UPMNS|νii. (2.5)

There UPMNS is the Pontecorvo-Maki-Nakagawa-Sakata matrix. Besides the so called mixing angles θ12, θ13, θ23 it also contains the CP-violating Dirac phase δ. If neutrinos are Majorana particles, UPMNS is multiplied by a diagonal phase matrix that contains two additional CP- violating Majorana phases α and β [13]. 2.1 Open questions in neutrino physics 11

With the observation of neutrino oscillation, it could be demonstrated that neutrinos are mas- sive particles. Such experiments could only measure squared mass differences and not the absolute neutrino masses mi. With solar and reactor experiments, the solar mass splitting 2 2 2 ∆msol = m2 − m1 can be measured, whereas atmospheric and accelerator-based experiments 2 2 2 2 are sensitive to the atmospheric mass splitting ∆matm = m3 − m2. The unknown sign of matm leads to two different possibilities in the ordering of the mass eigenstates that are called the normal and inverted mass ordering. In figure 2.1 a scheme of both possible orderings is shown [11].

Figure 2.1: Scheme of the two possible neutrino mass orderings. Left: normal ordering, right: inverted ordering. The colors indicate the fraction of each neutrino flavor present in each mass eigenstate. Picture based on [14].

There are three possibilities to probe the absolute value of the neutrino mass scale [11]:

0ν • Neutrinoless double beta decay: The half-life T1/2 of the hypothetical 0ν2β-decay is pro- 3 P 2 portional to the effective neutrino Majorana mass mββ = miUei if a light Majorana i=1 neutrino exchange is the dominant contribution to the decay. There U denotes the PMNS- matrix. In section 2.4 0ν2β-decay will be discussed in more detail.

• Energy spectrum in β-decay experiments: With the endpoint of a measured β-spectrum 3 2 P 2 2 the neutrino mass mβ = |Uei| mi can be determined. The most sensitive experiments i=1 are based on the decay of tritium like e.g. the KATRIN [15] experiment.

• Cosmological observations: Neutrinos play an important role in the evolution of the Uni- verse. With cosmological observations such as the anisotropies of the cosmic microwave 12 2 Double beta decay and neutrino physics

background or the distribution of large-scale structures, an upper bound on the sum of 3 P neutrino masses can be provided: mcosmo = mi [16]. i=1

The most constrained bound on mββ can be set by the KamLAND-Zen experiment and is in the order of O(0.1) eV. Upper bounds on mcosmo can also reach the level of O(0.1) eV using the data of the Planck satellite mission. The bounds on mβ are a little weaker at present [17]. In figure 2.2 the predicted effective neutrino Majorana mass versus the lightest neutrino mass is shown. Excluded regions from cosmology and 0ν2β-decay searches are also shown.

Figure 2.2: Predicted two-sigma values of the effective neutrino Majorana mass mββ ver- sus the lightest neutrino mass in the case of normal ordering (green region) and inverted ordering (blue region). The excluded regions from cosmology (Planck), the desired goal of the β-endpoint search with KATRIN and 0ν2β-decay experiments like GERDA, EXO-200, CUORE-0 and KamLAND-Zen are also shown. The goal of next generation experiments is to reach a sensitivity that is high enough to cover the region of inverted ordering. Picture from [18].

2.2 Beta decay

The β-decay is a type of radioactive decay, where the nucleons (protons and neutrons) inside a nucleus transform into each other. A neutron rich nucleus can undergo a β−-decay through the transition of a neutron into a proton. There an electron and an electron antineutrino are created (see eq. (2.6)). According to this, a proton rich nucleus can undergo β+-decay by the transition of a proton into a neutron and the emission of a positron and an electron antineutrino (see eq. (2.7)). In all cases where the β+-decay is energetically allowed, the electron capture (EC) is also 2.2 Beta decay 13 possible. Because of a non-vanishing probability of an atomic shell electron to be located inside the nucleus, the electron and a proton can convert into a neutron and an electron neutrino (see eq. (2.8)). The vacancy in the atomic shell (mostly an inner shell like the K-shell or the L-shell) is filled with an electron from an outer shell. There either characteristic X-ray is emitted or an Auger electron leaves the atom. The EC competes with the β+-decay and is energetically preferred since the Q-value of the β+-decay must be higher than 1022 keV, which is two times the electron rest mass me [2].

− − − β : (A, Z) −→ (A, Z+1) + e + νe n −→ p + e + νe (2.6)

+ + + β : (A, Z) −→ (A, Z-1) + e + νe p −→ n + e + νe (2.7)

− − EC : (A,Z) + e −→ (A, Z-1) + νe p + e −→ n + νe. (2.8)

Figure 2.3: The leading-order Feynman diagrams for the β−-decay (left) and the β+-decay (right). On the quark level of the decay this is caused by the conversion of a down quark into an up quark (β−) or vice versa (β+). The emitted W boson decays into a lepton pair.

All β-decays are mediated by the weak force. On the quark level of the hadrons, the β-decay is caused by a conversion of up quarks and down quarks under participation of the W boson, one of the force carrier particle of the weak interaction. In figure 2.3 the Feynman diagrams for the β−- and the β+-decay are shown. A decay is only allowed by energy conservation if the masses of the involved particles and nucleus before the reaction are higher than the sum of the masses of the daughter nucleus and emitted particles. The nucleus mass M (A, Z) can be calculated as follows:

M (A, Z) = N · Mn + Z · Mp − B (A, Z) . (2.9)

There A is the number of nucleons and Z is the number of protons inside the nucleus. The neutron number can be calculated with N = A − Z. Mn and Mp describe the neutron and proton mass. The parametrization of the nuclear masses as a function of A and Z that also considers the binding energy B (A, Z) was first introduced by Weizs¨acker in 1935 [19]. This so 14 2 Double beta decay and neutrino physics called semi-empirical mass formula (or Bethe-Weizs¨acker formula) can be written as [2]:

2 2 2 Z (N − Z) δ 3 B (A, Z) = avA − asA − ac 1 − aa − 1 . (2.10) A 3 4A A 2

The exact values for the parameters av, as, ac, aa and δ0 depend on the range of masses for which they are optimized. For the pairing term δ holds [2]:

  +δ0 for even Z and N (even-even nuclei),  δ = 0 for odd A (odd-even nuclei), (2.11)   −δ0 for odd Z and N (odd-odd nuclei).

The theory behind the semi-empirical mass formula is the liquid drop model that treats the nucleus as a drop of incompressible nuclear liquid. The first term in eq. (2.10) is proportional to the volume of the nucleus since each nucleon is in contact with a certain number of other nucleons. All other terms reduce the binding energy due to less neighboring nucleons for surface nucleons (aS), electric repulsion of protons (aC) and nuclear structure effects (aa and δ). To describe β-decays it is useful to write eq. (2.9) as follows:

2 δ M (A, Z) = α · A − β · Z + γ·Z + 1 . (2.12) A 2 where α, β and γ are functions of the parameters used in (2.10). For constant mass number A, the nuclear mass is now a quadratic function of the atomic number Z. For odd A, the nuclear masses lie on one parabola. For even A, the masses of the even-even and the odd-odd nuclei lie on two vertically shifted parabolas due to the pairing √ energy (∆M = 2δ0/ A). In figure 2.4 these two cases are depicted [2].

Figure 2.4: Nuclear masses for nuclei with A = 101 (left) and A = 106 (right) as a function of Z (zero point of the mass scale is chosen arbitrarily). β+-decays are marked by an arrow to the left, β−-decays are marked with an arrow to the right. Pictures from [2]. 2.2 Beta decay 15

Depending on the angular momentum of the emitted leptons the β−-decays can be classified into (super-) allowed and nth-forbidden transitions. Forbidden means the decay is suppressed in relation to a smaller transition probability compared to decays without angular momentum transfer [2]. Furthermore a division into Fermi and Gamow-Teller transitions can be done. For a Fermi transition the angular momentum of the leptons couples to zero (singlet state), for Gamow- Teller transitions the angular momentum couples to one (triplet state) [2].

Theoretical description of the transition probability

A theoretical description of the decay probability can be done by quantum mechanical con- siderations. The following discussion is based on [20] and [13] and is related to allowed and super-allowed transitions. With first order perturbation theory Fermi’s golden rule can be derived:

2 d N 2π 2 = |hf|Hβ|ii| ρ(E). (2.13) dtdE ~ The formula describes the transition rate of β-decay to produce an electron in the energy interval between E and E + ∆E. hf|Hβ|ii is the matrix element of the Hamiltonian Hβ that describes the transition between the initial state |ii and the final state |fi. ρ(E) denotes the density of the final states and corresponds to the so called phase space factor dn , that describes dEi the density of the possible final states n per energy interval dEi. The matrix element is defined as Z ∗ hf|Hβ|ii = dV ψf Hβψi. (2.14)

The wave function ψi of the initial state is determined by the wave function φi of the nucleons of the initial nucleus. ψf is determined by the wave function φf of the nucleons from the daughter nucleus and the wave functions of the electron and neutrino field φe and φν. The lepton wave functions can be described as plane waves since the interaction of the leptons and the nucleus is weak due to the weak interaction. These plane waves can be expanded in a Taylor series around the origin:

1 1   i~kj ·~r φj (~r) = √ e ≈ √ 1 + i~kj · ~r + ... , (2.15) V V with j = e, ν and the factor √1 to normalize the wave function to the volume V . ~k ·~r  1 since V j −2 the nuclear radius is of the order of fm while ~kj is of the order of 10 fm assuming a 2 MeV electron. Therefore, the usage of the first Taylor expansion term √1 is a good approximation. V Due to the Coulomb field of the daughter nucleus, the electron wave function has to be modified. The correction factor is the so called Fermi function F (Z + 1,E). 16 2 Double beta decay and neutrino physics

With the introduction of a coupling strength g of the interaction one obtains:

2 2 2 2 2 |hf|Hβ|ii| = g F (Z + 1,E) |φν (0)| |φe (0)| |Mfi| g2 ' F (Z + 1,E) |M |2. (2.16) V 2 fi

With the transition operator O the so called nuclear matrix element can be written as follows: Z ∗ Mfi = dV φf Oφi. (2.17)

It describes the transition probability from the initial state of the nucleus to the final state of the nucleus. Mfi does not depend on the energy (under the assumptions made) and is mainly determined by the nuclear structure. For allowed transitions the nuclear matrix elements have contributions from the Fermi nuclear 2 2 matrix element |Mfi| and the Gamow-Teller nuclear matrix element |MGT | since the leptons can form a spin-singlet or a spin-triplet state:

2 2 2 2 2 2 g |Mfi| = gV |MF | + gA|MGT | . (2.18)

The different coupling strength can be taken into account by introducing the vector and axial vector coupling constants gV and gA. For β-transitions where the leptons carry away an orbital angular momentum L 6= 0, higher order terms of the Taylor expansion of the lepton wave function have to be taken into account. The corresponding matrix elements are orders of magnitudes smaller. Depending on the carried away angular momentum L those decays are declared as forbidden, where ∆L is a measure of the order of forbiddenness.

2.3 Double beta decay

The double beta decay (2β-decay) is an extremely rare decay process where the atomic number Z of a nucleus is changed by two units while the mass number A remains unchanged. As for the single β-decay there exist several decay modes:

− − − 2νβ β : (A, Z) −→ (A, Z + 2) + 2e + 2¯νe, (2.19) + + + 2νβ β : (A, Z) −→ (A, Z − 2) + 2e + 2νe, (2.20) + − + 2νECβ : e + (A, Z) −→ (A, Z − 2) + e + 2νe, (2.21) − 2νECEC : 2e + (A, Z) −→ (A, Z − 2) + 2νe. (2.22)

The 2β-decay was first discussed by Goeppert-Mayer in 1935 [21]. In figure 2.5 the Feynman diagram of the 2ν2β−-decay is depicted. The 0ν2β−-decay that is also shown in the figure will be explained in section 2.4. 2.3 Double beta decay 17

Figure 2.5: Feynman diagrams of the 2ν2β−-decay (left) and the 0ν2β−-decay (right). The 0ν2β−-decay (see section 2.4) is only possible if the neutrino is its own antiparticle (Majorana neutrino). The depicted Feynman diagram shows the decay with a light Majorana neutrino exchange.

Furthermore, only the 2ν2β−-decay (see eq. (2.29)) will be discussed exemplary for the addi- tional 2β-decay modes. A necessary requirement for the 2ν2β−-decay to occur is:

M(Z, A) > M(Z+2, A) + 2me, (2.23) where M(Z, A) denotes the nuclear mass defined in eq. (2.9). The 2β-decay can only be observed if the single β-decay is energetically not allowed (M(Z, A) < M(Z+1, A) + me) or at least highly suppressed due to a large difference ∆L in angular momentum of the involved nuclei [13]. Due to the pairing term in the Bethe-Weizs¨acker formula (see eq. (2.10)) 2β-decay is possible, but only for even-even nuclei. For such nuclides both isobaric neighbors can have a higher mass although the nuclide is not the one with the lowest mass on the mass parabola. Especially for nuclides with A > 70 it is more common to have more than one β-stable nuclide on the mass parabola. In figure 2.4 such a case is depicted. 106Cd can not decay into 106Ag because this nucleus has a higher mass. However, the 2ν2β+-decay into 106Pd is possible [2]:

106 106 + 48Cd → 46Pd + 2e + 2νe. (2.24)

The first indirect detection of the 2β-decay was achieved by Inghram and Reynolds in 1950 with a geochemical experiment on 130Te [22]. In 1987 the first direct measurement was successful with a counting experiment on 82Se by Elliott, Hahn and Moe [23].

In total 35 nuclides can decay via 2ν2β−-decay. For only 9 of them (48Ca, 76Ge, 82Se, 96Zr,100Mo, 116Cd, 130Te, 136Xe and 150Nd) the decay has been directly experimentally observed. With radiochemical and geochemical experiments the decay was also indirectly observed for 238U and 128Te [24]. In table 2.1 all possible 2β−-nuclides are summarized. In table 2.2 all 11 2β−-nuclides are summarized for that the decay is experimentally confirmed. 18 2 Double beta decay and neutrino physics

Additionally, the average half-lives and a selection of experiments that have investigated the decay are given.

For another 34 nuclides the decay via 2ν2EC, 2νECβ+ or 2ν2β+ is possible [24]. These modes − + are stronger suppressed compared to 2β -decays, since the Q-value is reduced by 4me for 2ν2β + and 2me for 2νECβ . For 2ν2EC-decays the Q-value is higher due to the absent positrons in the final state. However, the decay is hard to observe since there is only characteristic X-ray radiation for the detection. Because of these difficulties there were only two observations until now. A geochemical measurement on 130Ba [25] and a direct measurement on 78Kr [26].

Table 2.1: Possible 2β−-nuclides and their Q-values (taken from [27]).

Nuclid Q [keV] Nuclid Q [keV] Nuclid Q [keV] 46Ca 988.4 110Pd 2017.1 150Nd 3371.38 48Ca 4268.08 114Cd 544.79 154Sm 1250.8 70Zn 997.1 116Cd 2813.49 160Gd 1731 76Ge 2039.06 122Sn 373.1 170Er 655.2 80Se 133.9 124Sn 2291.1 176Yb 1085 82Se 2997.9 128Te 866.6 186W 491.4 86Kr 1257.42 130Te 2527.51 192Os 406 94Zr 1144.74 134Xe 824 198Pt 1050.3 96Zr 3356.03 136Xe 2457.8 204Hg 419.7 98Mo 109 142Ce 1416.8 232Th 837.3 100Mo 3034.36 146Nd 70.4 238U 1144.6 104Ru 1299.4 148Nd 1928.3

Table 2.2: 2β−-nuclides with their Q-values (taken from [27]), average half-lives (taken from [28]) and a selection of experiments that have investigated the decay. In the last two rows 0ν best present limits on T1/2 (taken from [29]) and the investigating experiments are shown.

2ν 0ν Nuclid Q [keV] T1/2 [yr] Experiment T1/2 [yr] Experiment 48Ca 4268.08 4.4·1019 TPC-experiment, NEMO-3 > 5.8 · 1022 CANDLES 76Ge 2039.06 1.65·1021 Heidelberg-Moscow, GERDA > 3.5 · 1025 GERDA 82Se 2997.9 9.2·1019 NEMO-3 > 3.6 · 1023 NEMO-3 96Zr 3356.03 2.3·1019 NEMO-2, NEMO-3 > 9.2 · 1021 NEMO-3 100 18 24 Mo 3034.36 7.1·10 NEMO-3, ZnMoO4-crystals > 1.1 · 10 NEMO-3 116Cd 2813.49 2.87·1019 Aurora, NEMO > 1.9 · 1023 Aurora 128Te 866.6 2.0·1024 geochem. Exp. > 1.5 · 1024 geochem. Exp. 130 20 24 Te 2527.51 6.9·10 NEMO-3, TeO4-crystals > 4.0 · 10 CUORICINO+CUORE-0 136Xe 2457.8 2.19·1021 EXO-200, KamLAND-Zen > 5 · 1025 KamLAND-Zen 150Nd 3371.38 8.2·1018 NEMO-3, TPC-experiment > 5.8 · 1022 NEMO-3 238U 1144.6 2.0·1021 radiochem. exp.

Decay rate for the 2β-decay

The following discussion is partially taken from [13]. The decay rate of 2β-decay can be calculated the same way as for the single β-decay, with the difference that this is a second 2.3 Double beta decay 19 order process. Hence, the expected decay rates are much smaller. This is also obvious if the much smaller phase space is taken into account, since the kinetic energy is distributed to four instead of two leptons. In the following, only ground-state transitions are discussed. The 2β-decay can be seen as two subsequent Gamow-Teller transitions via an intermediate state. With time-dependent perturbation theory one can derive the transition probability W per unit of time, referred to as Fermi’s golden rule:

dW 2π 2 = |hf|Hif |ii| δ (Ef − Ei) . (2.25) dt ~ In comparison with eq. (2.13) the final state density function is replaced by the δ-function due to the discrete energy levels of the final and initial state. The corresponding nuclear matrix element (NME) is now one order higher in the perturbation series:

Xhf|Hif |mihm|Hif |ii Mfi = (2.26) m Ei − Em − Eν − Ee where m characterize the set of virtual intermediate states. After some more calculations, that should not be discussed here in detail, the decay rate can be written as:

2 h i−1 g2 2ν 2ν 2ν V 2ν T1/2 = G (Q,Z) MGT + 2 MF . (2.27) gA

Since Gamow-Teller transitions are favored by selection rules, which result from the matrix elements [30], one can neglect the Fermi contribution:

h i−1 2 2ν 2ν 2ν T1/2 = G (Q,Z) M (2.28)

2ν 2ν with the Gamow-Teller transition matrix element MGT = M and the accurately known phase-space factor G2ν (Q,Z) that scales with Q11 [20].

Due to this dependency of T1/2 on the Q-value it is quite obvious that from the list of 35 possible 2β−-nuclides (see table 2.1) the decay was only directly observed for the ones with the highest Q-values. Besides the indirectly measured 238U and 128Te there is no observation for nuclides with a Q-value below 2 MeV due to the expected higher T1/2 and the resulting difficulties in observation.

For a theoretical prediction of 2β-decay half-lives, the nuclear matrix elements of the involved nuclides have to be known. In contrast to the well known phase-space factors the calculation of NMEs is quite complicated because a nucleus is a complex many-particle system where the nucleons interact via the strong force. There are many models with different approximations of the nuclear structure and the inter- actions between the nucleons. The main approaches for calculating NMEs for 2β-decay are the Quasiparticle Random Phase Approximation (QRPA), the Interacting Shell Model (ISM) 20 2 Double beta decay and neutrino physics and the Interacting Boson Model (IBM-2). The ISM considers only a limited number of orbits around the Fermi level, but includes interactions between those orbits and pairing correlations of the fermions. The QRPA typically considers single particle states in a Woods-Saxon poten- tial. Pairings between two neutrons and two protons are taken into account and are treated in the Bardeen-Cooper-Schrieffer (BCS) theory, where no particle conservation is assumed. In the IBM-2 model two nucleons are combined to a quasi bosonic particle. The low-lying states are modeled with those bosons and their interaction through one- and two-body forces [31]. Measuring 2β-decay half-lives allows for an experimental determination of NMEs. The compar- ison with theoretical calculated NMEs results in a good possibility for testing nuclear structure models. The half-life values can be used to adjust important parameter of the nuclear models and therefore help to improve NME calculations for the 0ν2β-decay. In figure 2.6 experimentally derived NMEs are shown.

Figure 2.6: The 2ν2β-decay nuclear matrix elements extracted from the average and recom- mended half-life values. gA = 1.25 is assumed. Picture taken from [32].

2.4 Neutrinoless double beta decay

Besides the neutrino accompanied 2β-decay discussed in the previous section, also neutrinoless versions of the decay modes introduced in eq. (2.29) - (2.32) are hypothesized:

0νβ−β− : (A, Z) −→ (A, Z + 2) + 2e−, (2.29) 0νβ+β+ : (A, Z) −→ (A, Z − 2) + 2e+, (2.30) 0νECβ+ : e− + (A, Z) −→ (A, Z − 2) + e+, (2.31) 0νECEC : 2e− + (A, Z) −→ (A, Z − 2). (2.32)

The concept of 0ν2β−-decay was first considered by Furry in 1939 [30] after some pioneering work from Majorana and Racah. Majorana showed in 1937, that β-decay remains unchanged 2.4 Neutrinoless double beta decay 21 under the assumption that the neutrino is its own antiparticle (ν =ν ¯) [12]. In the same year Racah analyzed the possibility of distinguishing Majorana and Dirac neutrinos in the process of inverse β-decay [33]. All neutrinoless 2β-decay modes violate the lepton number conservation by two units (∆L = 2) and are not allowed within the Standard Model of particle physics. In figure 2.5 the Feynman diagram of the 0ν2β−-decay is depicted on the right-hand side. The process can be described with an exchange of a virtual neutrino between two neutrons of the same nucleus. The first neutron decays under the emission of a right-handedν ¯e. This has to be absorbed from the second neutron as a left-handed νe. Therefore, the process is only possible if the neutrino is a Majorana neutrino (ν =ν ¯). As a second requirement the neutrino has to be massive to allow for helicity matching. The wave function describing the neutrino mass eigenstate for mν > 0 has then besides the dominant left-handed contribution also a right-handed admixture. A contribution of a right-handed component in charged weak currents could be another possibility for helicity matching in 0ν2β-decay [13]. Besides the standard interpretation where a light Majorana neutrino is being exchanged, in principle any operator that converts two d-quarks into two u-quarks and two electrons, and at the same time violates lepton number conservation, will trigger the decay. There is a vast number of different theories in which the 0ν2β-decay can be explained such as R-parity violating SUSY, short range decay modes with heavy neutrinos, existence of leptoquarks or extra dimensions [34]. Regardless of the underlying mechanism, Schechter and Valle have shown that a lepton number violation implies that neutrinos have to be Majorana particles [35]. The so called black box theorem states that the 0ν2β diagram can always be inserted in a Standard Model loop diagram giving rise to radiatively generated neutrino masses. However, the contribution to the neutrino mass might be rather small and therefore not the dominant contribution to neutrinoless double beta decay or to neutrino masses itself [34].

Decay rate of the 0ν2β-decay

Besides the requirement that the neutrino has to be a Majorana particle, a non-vanishing mass or other lepton number violating processes have to be assumed to account for the helicity mismatch. With second order perturbation theory the decay rate can be calculated in analogy to the 2ν2β-decay [13]. A detailed derivation can be found in [36]. The resulting decay rate can be written as:

h i−1 2 0ν 0ν 0ν 2 T1/2 = G (Q,Z) M |f (mi,Uei)| . (2.33)

M 0ν is the nuclear matrix element. The phase space factor G0ν (Q,Z) scales with Q5 and is about a factor of 106 larger then for the 2ν2β-decay because of the larger number of final states. In the 2ν2β-decay case, the emitted neutrinos are real particles and the number of final states is restricted by the Q-value, whereas the virtual neutrino of the 0ν2β-decay is restricted to the volume of the nucleus corresponding to states up to 100 MeV [13].

The function f (mi,Uei) contains the physics beyond the Standard Model that could explain the 22 2 Double beta decay and neutrino physics

decay through the neutrino masses mi and the mixing matrix Uei. It depends on the underlying process that mediates the decay. In the case of a light Majorana neutrino exchange, f (mi,Uei) is proportional to the effectiv neutrino Majorana mass mββ [31]:

m 1 3 f (m ,U ) = ββ = X U 2 m . (2.34) i ei m m ei i e e i=1

The nuclear matrix element M 0ν in eq. (2.33) can be parametrized as follows:

 2 ! 0ν 2 0ν gV 0ν 0ν M = gA MGT − MF + MT . (2.35) gA

0ν The matrix element MT takes the possibility of right-handed currents into account . As already mentioned in section 2.3, the calculation of NMEs is a difficult task because the ground and many excited states of open-shell nuclei with complicated nuclear structure have to be considered. In figure 2.7 NMEs calculated with different models are shown. There are still differences between the models, but compared to the past the disagreement has become smaller [31].

Figure 2.7: 0ν2β-decay nuclear matrix elements calculated with the IBM-2, QRPA-T¨uand ISM models. The results differ among the models, but are not too far away from each other. Picture from [31].

Recently, there has been a large interest in a specific reason of uncertainty in M 0ν, namely the axial coupling constant gA. If gA is decreased in a nuclear medium (quenching of gA) by a factor of δ with gA → gA · (1 − δ), the expected decay rate and therefore the number of signal 4 events S will also decrease, approximatively as S · (1 − δ) . Already a small variation of gA can have a big impact on the experimental search for the 0ν2β-decay [31].

Since no experiment has measured the 0ν2β-decay until now, only half-life limits for the inves- tigated nuclides can be set. With eq. (2.33) a corresponding effective Majorana neutrino mass 2.5 Experimental aspects of double beta decays 23 limit can be extracted. The model dependent value for the NME and the resulting uncertainty plays a crucial role for calculating mββ. One way to reduce the uncertainties is the comparison of experimentally extracted values for M 2ν from 2ν2β-measurements with theoretical values predicted by the various models. If the- oretical prediction and the experimental value are in good agreement, the model can probably also describe the M 0ν quite well. Another possibility is to conduct complementary experiments, mainly charge exchange reactions and single β-decays [37].

2.5 Experimental aspects of double beta decays

The search for a 2ν2β/0ν2β-decay signal relies on the detection of the two emitted electrons. Since the energy of the recoiling nucleus is negligible, the sum of the kinetic energy of the two electrons is equal to the Q-value of the transition in the case of the 0ν2β-decay. In the sum spectrum, a peak at the Q-value is expected due to a finite energy resolution of the detector. For the 2ν2β-decay, the sum spectrum shows a continuous distribution because of the two emitted neutrinos, which are not detected and carry away a part of the released energy. In figure 2.8 the spectra for the 2ν2β and the 0ν2β-decay are shown.

Figure 2.8: Electron sum energy spectra for the 2ν2β and the 0ν2β-decay. For the 0ν2β- decay a peak at the Q-value of the transition is expected. The relative height of the peak is increased in the picture for a better visibility. In the inset the relative rates for both decays are shown in a more realistic way. Picture from [38].

The half-lives for the already observed nuclides that undergo 2ν2β-decay are mostly in the order of 1018 to 1021 yr (see table 2.2). For the nuclides with a lower Q-value the expected half-lives are higher. For the 0ν2β-decay the expected half-life is some orders of magnitudes higher compared to the 2ν2β-decay half-life of the same nuclide, depending on the assumed light Majorana neutrino mass. In the case of a neutrino mass of 30 meV for the inverted ordering 24 2 Double beta decay and neutrino physics or 3 meV for the normal ordering the expected half-lives are of the order of 1027 to 1029 yr and beyond [37]. To detect such extremely rare decay processes, the investigating experiments have to deal with a lot of special conditions and requirements. In the following, different aspects that have to be taken into account while planing an experiment for the search of 0ν2β-decay should be discussed.

Sensitivity

The following section is based on [31]. The sensitivity indicates the half-life limit that an exper- iment is able to reach under the boundary conditions of limited detection efficiency, detector mass, background index, and so on. Starting with the law of radioactive decay and the as- sumption, that the half-life T1/2 is much larger than the measuring time T , T1/2 can be written as:

Nββ T1/2 = ln2 · T ·  · (2.36) NS where  is the detection efficiency, Nββ is the number of source nuclei and NS is the number of observed events in the region of interest (ROI). Nββ can be calculated with the detector mass

M, the Avogadro number NA, the isotopic abundance a, the stoichiometric multiplicity x of the element containing the 2β-emitter and the molar mass ma:

M Nββ = x · a · NA · . (2.37) ma

By assuming a uniformly distributed background spectrum in the ROI and a linearly scale of the background counts with the mass of the detector and the measuring time, the number of background events NB is given by:

NB = M · T · B · ∆E, (2.38) where B is the background index (BI) per unit mass, energy and time and ∆E is the width of the energy window over the ROI based on the energy resolution dE = 2 · FWHM. For a 0ν2β-decay experiment, the sensitivity S0ν is defined as the half-life corresponding to the √ maximum signal that could be hidden by the background fluctuations nB = NB at a given statistical confidence level nσ: s N 1 x · a · N M · T S0ν = ln2 · T ·  · ββ = ln2 ·  · · A · . (2.39) nσ · nB nσ mA B · ∆E

With this relation the important parameters of the experiment and their impact on the sensi- tivity can be discussed. 2.5 Experimental aspects of double beta decays 25

Background

Because of the extremely low decay rates, background suppression is the most important task of 2β-decay experiments. The natural radioactivity of detector components is often the main background. By-products of the natural Thorium and Uranium decay chain are at some level present in all materials. Therefore, a careful selection of materials and purification is necessary and desirable. Radon gas, which is also a decay product of the natural decay chains, can easily diffuse through many materials. It can then be present near the sensitive detector volume. Daughter nuclides tend to be charged and can settle down on surfaces. A flushing with Nitrogen gas or a Radon trap in the air circulation can eliminate Radon. External background, such as cosmic rays, can be suppressed by placing the detector in an un- derground laboratory and enclosing it into a shielding system. At the depth of the underground laboratories muons are the only remaining part of the cosmic rays. Due to muon induced re- actions in the rock or other materials, secondaries such as neutrons or electromagnetic showers can be produced. With a veto system, a part of the charged background can be reduced. The neutrons have to be treated separately. Lead and Copper can be used as a shield against γ-rays originating from radioactive decays in the rock. Cosmogenic activation of detector materials while they are stored and transported on the earth surface can produce radioactive nuclides. Underground fabrication and storage of detector components would be desirable. Depending on the energy resolution at the ROI, also the 2ν2β-decay can be an important back- ground contribution. For very big detectors such as liquid scintillator calorimeters, the solar neutrino flux can also give a contribution to the background [11].

Choice of the isotope

From the theoretical point of view, the NME and the phase space factor of a 2β-nuclide should be as high as possible, since the decay rate would then be lower and a positive signal will get more realistic. The phase space factor G0ν scales with Q5. Therefore, nuclides with a large Q-value are favored. From an experimental point of view a high Q-value is also beneficial due to a lower background index at higher energies. The 2615 keV line of 208Tl is the highest prominent γ-line from the natural decay chains. With a higher natural abundance of the 2β-nuclide of interest and a larger detector mass a higher sensitivity can be reached. The possibility of an isotopical enrichment and the availability of the nuclide have to be taken into account. Also there has to be a working detector technique for the nuclide of choice.

Experimental techniques

The experimental technique that is used determines important parameters like the energy resolution or the reachable detection efficiency. These techniques can be divided into two main categories. 26 2 Double beta decay and neutrino physics

• Calorimetric techniques: the source is embedded in the detector itself. The advantages are the achievable large source masses and a high energy resolution. Since the nuclide of interest has to be inserted into the detector material, constrains on the possible nuclides exist, except from liquid scintillator or bolometer experiments. The event topology re- construction is usually difficult, exept for time projection chambers (TPCs). Examples of detecors using the calorimetric technique are: semiconductors like Ge-detetors, liquid or gaseous Xe TPC, and liquid scintillators loaded with the nuclide of interest [31].

• External source approach: the source and the detector are two separate systems. A large source mass is therefore hardly to achieve due to self-shielding of the source. The energy resolution and detection efficiency is quite low. The advantage of this detector technique lies in the event topology reconstruction. Detectors that can use this aproach are scintillators, gas chambers, solid state and tracking detectors [31]. 3 The COBRA experiment

COBRA (Cadmium-Zinc-Telluride 0-Neutrino Double-Beta Research Apparatus) is an exper- iment to search for the 0ν2β-decay. It was proposed by K. Zuber in 2001 [39]. The experiment is located at the underground facility Laboratori Nazionali del Gran Sasso (LNGS) in Italy and consists of two different experimental stages. One is the so called COBRA demonstrator, that was completed in 2013. It uses 64 Cadmium-Zinc-Telluride (CdZnTe) semiconductor detectors, each with a volume of about 1 cm3, placed in a 4 × 4 × 4 array. For the readout a so called coplanar grid (CPG) electrode is used. More details on the principle of CPG-detectors can be found in section 3.2.2. The other stage, referred to as eXtended DEMonstrator (XDEM), was implemented into the existing setup in 2018. It consists of a new layer with nine 6 cm3 CdZnTe detectors. Each detector has four CPGs on the anode side to prevent too high leakage currents and an additionally guard-ring electrode to veto α- and probable β-decays on the surface. Be- sides the better volume-to-surface ratio, the use of highly radio-pure materials for the detector contacting and a more careful handling during the testing phase and the shipping leads to a reduction of potential background sources compared to the demonstrator detectors. Since the CdZnTe material that is used for the detectors contains nine nuclides that can undergo 2β-decay, the detector-equals-source approach is used. In table 3.1 all nine nuclides with their Q-value and natural abundance are listed. Besides the five 2β−-nuclides, the study of 2β+-, ECβ+-decay and double electron capture (2EC) modes is possible on another four nuclides.

Table 3.1: List of 2β-decay nuclides that are naturally abundant in CdZnTe. The possible decay modes, the Q-value of the decay (taken from [27]) and the natural abundance (taken from [40]) are shown.

Nuclide Decay Mode Q-value [keV] Natural Abundance [%] 106Cd 2β+, ECβ+, 2EC 2775.4 1.245 108Cd 2EC 271.8 0.888 114Cd 2β− 544.8 28.754 116Cd 2β− 2813.5 7.512 64Zn ECβ+, 2EC 1095.0 49.17 70Zn 2β− 997.1 0.61 120Te ECβ+, 2EC 1730.8 0.09 128Te 2β− 866.6 31.74 130Te 2β− 2527.5 34.08

The most promising 2β−-candidates are 116Cd and 130Te. The Q-value of 2813.5 keV of 116Cd is above the 2615 keV γ-line from 208Tl, which is the highest prominent γ-line from natural decay chains. Therefore, the BI in the ROI is smaller than for other nuclides. Additionally, a high 28 3 The COBRA experiment

Q-value leads to a larger phase-space factor and therefore a shorter half-life. An observation will become more likely. 130Te is also a good candidate because of the high natural abundance (34.08%) and the also quite high Q-value of 2527.5 keV that lies between the full energy peak and the corresponding Compton edge of the 2615 keV γ-line from 208Tl. The BI is therefore also expected to be small. For the 2β+-, ECβ+- and 2EC-modes 106Cd is the most promising candidate, because of the high Q-value (2775.4 keV) and a characteristic signal due to the annihilation photons from the two positrons that can be accessed with a coincidence analysis technique. Unfortunately, the natural abundance is quite low. Besides the search for the 0ν2β-decay the study of the also intrinsically abundant 113Cd is possible. It decays via a β−-decay into 113In with a Q-value of 320 keV. Since the spin of the involved nuclides changes by four units, the decay is fourfold forbidden. Therefore, the decay is strongly suppressed resulting in a half-life of 8 · 1015 yr. Despite this long half-life, 113Cd causes the highest amount of measured events in the COBRA experiment. The spectral shape of such a highly forbidden transition strongly depends on the value of the axial-vector coupling strength gA. The comparison of the measured β-spectrum with theoretical predictions from different nuclear model calculations offers a method to determine the effective value of gA. It is assumed that gA is quenched, which means that gA has a different value in nuclear medium. This would, among other things, affect the sensitivities of 0ν2β-decay experiments and the conversion of the 0ν2β-half-life(-limit) into an effective Majorana neutrino mass(-limit). With 113 the COBRA experiment a quenching of gA for Cd could be determined [41].

3.1 Detector setup

The aim of the COBRA experiment is to search for extremely rare decays. A good shielding against cosmic rays and other radiation plays therefore an important role and affects the design of the detector setup. To reduce the cosmic ray flux, the experiment is operated at the LNGS underground laboratory. It is located below the Gran Sasso d’Italia mountain massif about 120 km away from Rome. The coverage of about 1400 m rock corresponds to a shielding of approximately 3800 m water equivalent. The muon flux from cosmic rays is therefore reduced by six orders of magnitude to (3.41 ± 0.1) · 10−4 m−2s−1 [42]. In figure 3.1 a scheme of the LNGS underground laboratory is shown. COBRA is located in a tunnel between hall A and B. Besides experiments that are searching for the neutrinoless double beta decay like COBRA and GERDA, also solar neutrinos (Borexino), nuclear fusion reactions (LUNA) and dark matter (XENON) is studied at the LNGS. COBRA uses two floors. In the ground floor the experimental setup and the first stage of the readout electronic system is located. On the second floor, the rest of the electronics and the data acquisition (DAQ) system is installed, because through this the generated waste heat does not come in contact with the experimental setup. In figure 3.2 the current setup in the ground floor is shown. 3.1 Detector setup 29

Figure 3.1: Overview of the LNGS underground laboratory. COBRA is located in a con- necting tunnel between hall A and B. In this halls larger experiments like GERDA, Borexino or XENON 1T are located. Picture adapted from [43].

3.1.1 Shielding

Besides the surrounding rock there exists also a multi-layer passive shielding to protect the detectors from radiation created in the underground. The outermost part of the shielding is a box that is made of 7 cm thick borated Polyethylene that acts as a neutron shield. Even though the underground is already shielded from cosmic ray neutrons, a non-vanishing neu- tron flux is still present. Furthermore, spallation reactions of highly energetic muons or muon capture processes can create neutrons and photons. α-particles originating from the Uranium and Thorium decay chains can cause (α,n)-reactions. Also spontaneous fission of 238U creates some neutrons [44]. Inside the neutron shield, a shield against electromagnetic interferences (EMI) is installed. The construction that uses several layers of Iron sheets with a thickness of 2 mm acts as a Faraday cage and prevents the induction of currents in the cables inside the setup due to EMI. All cables from inside the setup are fed trough a Copper-filled chute to the outside [45]. The neutron and EMI-shield build the so called outer shielding. Inside that the pre-amplifiers with their cooling-plates as well as the inner shielding, that enclose the detectors, are placed. The inner shielding consists of an air-tight Polycarbonate box, which is constantly flushed with Nitrogen to prevent dust and Radon-gas to diffuse from outside into the setup. Daughter nu- clides of Radon can cause a significant background contribution, which is why their presence should be prevented. The Nitrogen flushing also leads to a low humidity inside the setup, which is beneficial for the detector performance. Inside the Radon shield the so called Lead castle is placed. It uses standard Lead bricks for the outer part and ultra-low-activity Lead bricks (210Pb activity less than 3 Bq/kg) for the inner part to shield the detectors from radiation. 30 3 The COBRA experiment

The innermost part of the shielding, the so called Copper nest, and the detector holder support structure is made of ultra-pure oxygen-free high-conductivity electroformed Copper [45]. Inside the Copper nest, the detectors are placed. For the demonstrator, 16 detectors are mounted on a Delrin frame, which is a radioactively pure thermoplastic also known as Poly- oxymethylene (POM). In total, the demonstrator consists of four such layers. The XDEM- layer is placed on top of the demonstrator layers and holds nine detectors. In figure 3.3 a demonstrator- and the XDEM-layer is shown.

Figure 3.2: Setup of the COBRA experiment at the LNGS. The outer shielding (neutron- shield and the EMI-shield) is opened. Inside the pre-amplifiers and the Radon-tight Poly- carbonate box are visible. The actual detector layers are not visible due to the surrounding Copper and Lead castle. This picture shows the setup before the installation of the XDEM layer.

Figure 3.3: In the left picture one layer of the demonstrator is shown. 16 CdZnTe detectors are mounted on a Delrin frame. The orange Kapton foil contains conducting paths cables for the grid bias and the read-out signals. The high voltage supply is provided by the silver wires visible in the top right of the picture. The right picture shows the XDEM layer that is placed on top of the demonstrator. Also the surrounding Copper- and Lead-shield is visible. 3.1 Detector setup 31

3.1.2 Electronic readout system

The electronic readout system is distributed over the two floors of the building to protect the detectors from too much waste heat. Therefore, the devices that produce a large amount of waste heat are placed in an air-cooled room on the second floor. In figure 3.4 a scheme of the setup with the readout system is shown. The first component of the readout electronics, the pre-amplifiers, are placed next to the Lead castle inside the outer shielding. They convert the charge signal from the detectors into differ- ential voltage signals to ensure a stable transmission. One pre-amplifier box is used for each layer of the demonstrator and can handle 32 input signals, two signal chanels for each detector. For the XDEM layer three pre-amplifier boxes are needed because of the quad-grid. Moreover, the bias voltage and the grid bias, as well as signals from a pulse generator, are supplied via the pre-amplifiers. The injected pulses are used to monitor the long-term stability of the readout system and to synchronize the flash analog to digital converters (FADCs), which is necessary for a coincidence analysis. To reduce the waste heat that is generated by the pre-amplifiers, metal plates that are flushed with a liquid coolant, are placed above all devices. With this a cooling below room temperature is possible and can be controlled by remote. Eight ethernet network cables per pre-amplifier are needed to transmit the differential detector signals to the linear amplifiers. They are located in the second floor and represent the last com- ponent of the analog readout system. Since the following FADCs have a defined signal input range, the linear amplifiers amplify the detector signals to match this range. Furthermore, the differential signal is converted back into a single-ended signal. The FADCs produce a digital signal with a 100 MHz sampling frequency and a 12-bit resolution. 1024 samples build one event trace resulting in a trace length of 10.24 µs per event [45].

3.1.3 Experimental infrastructure

To ensure a stable operation of the experiment, several uninterruptible power supply (UPS) units are used. Therefore, external voltage breakdowns shorter than 20 min do not affect the experiment. Additionally, the input power is filtered and galvanically decoupled from the main supply. Since different voltages are needed for the experiment, low noise voltage supply devices are placed on the ground floor. The liquid Nitrogen that is used for the Radon shield is stored in a dewar outside the building. With a thermal resistor the liquid Nitrogen can be evaporated more rapidly and the gaseous phase is used for the flushing of the setup. The filling level is measured with a capacitor. To monitor the environmental conditions, sensors to measure the humidity, temperature and pressure for several locations of the setup are installed. Also the pre-amplifier cooling and the supply voltage are monitored. The DAQ server is located on the second floor. The main computer can be accessed from outside via a network. With that, all tasks like starting a data taking run or communicating with sub-systems can be done [45]. 32 3 The COBRA experiment

Figure 3.4: Overview of the main components of the DAQ chain and the experimental infrastructure of the COBRA setup. For detailed information about the components see section 3.1.2 and 3.1.3. Picture taken from [45].

3.2 CdZnTe detectors

3.2.1 CdZnTe as a semiconductor

For the COBRA experiment, CdZnTe semiconductor detectors are used. In table 3.2 some properties of this intrinsic II − IV semiconductor material are compared to other conventional semiconductor materials. The high effective atomic number (Zeff ∼ 50) and density, as well as a high band gap compared to other materials are some of the main advantages.

Since the interaction probability of γ-radiation depends on the atomic number, the high Zeff is beneficial for a high detection efficiency. Compared to CdTe, the band gap is even larger due to the small Zinc component. This high band gap prevents the creation of electron-hole-pairs due to thermal excitation and leads to the possibility to operate the detectors at room temperature. However, it turned out that a slight cooling leads to a better energy resolution. Unfortunately, a wide band gap limits the reachable energy resolution since more energy is needed to create an electron-hole-pair. The manufacturing process of such a three component crystal is quite complicated. Since Zinc and Cadmium are in the same period of the periodic table of elements, their content in the crystal structure is hard to monitor. The stoichiometric composition is therefore often given by Cd1−xZnxTe with the fraction x of Zinc beeing around 0.1 [46]. The transportation properties of the charge carriers (electrons and holes) can be described with the mobility µ and the lifetime τ as well as the product of both µτ. Charge carriers can be trapped in the lattice due to impurities or recombination, resulting in a loss of the total charge. 3.2 CdZnTe detectors 33

The lifetime τ is the average time for a charge carrier to get trapped [47]. Since trapping mechanisms are different for electrons and holes, the so called trapping length µτ for holes is two orders of magnitudes lower than for electrons in CdZnTe material (see table 3.2). Therefore, mostly electrons contribute to the produced signal and make it depth dependent if a normal planar anode and cathode is used. Since the signal depends also on the energy of the incoming particle, a reconstruction of the energy is not possible due to this ambiguous dependency. For a depth independent signal a special anode configuration, the so called coplanar grid, can be used. The working principles will be discussed in the following section.

Table 3.2: Properties of CdZnTe compared to other semiconductor materials like CdTe, Ge and Si. Table taken from [46].

property Cd0.9Zn0.1Te CdTe Ge Si atomic numbers 48, 30, 52 48, 52 32 14 density ρ [g/cm3] 5.78 5.85 5.33 2.33 band gap Eg [eV] 1.57 1.50 0.67 1.12 pair creation energy Epair [eV] 4.64 4.43 2.95 3.63 resistivity R [Ωcm] 3 · 1010 109 50 < 104 2 electron mobility µe [cm /Vs] 1000 1100 3900 1400 −6 −6 −3 −3 electron lifetime τe [s] 3 · 10 3 · 10 > 10 > 10 2 hole mobility µh [cm /Vs] 50-80 100 1900 480 −6 −6 −3 −3 hole lifetime τh [s] 10 2 · 10 10 2 · 10 2 −3 −3 (µτ)e [cm /V] (3 − 10) · 10 3.3 · 10 > 1 > 1 2 −5 −4 (µτ)h [cm /V] 5 · 10 2 · 10 > 1 ≈1

3.2.2 Principle of CPG detectors

The following section is based on [48]. The basic principle of a wide range of radiation detectors is the generation of a freely moving amount of charge q within the sensitive detector volume by the incoming radiation. The movement of q induces a charge Q on an electrode, which is then amplified and converted to the output signal. The deposit energy can then be deduced from the amplitude of the output pulse. In the case of a semiconductor such as CdZnTe, the incoming radiation interacts with the material and produces a number of electron-hole-pairs that is proportional to the deposited energy. An applied electric field between anode and cathode leads to a movement of the electrons to the anode and holes to the cathode. As a first approximation, the movement and the charge collection of the holes can be neglected due to a much smaller mobility-lifetime product compared to electrons. The movement of the electrons cause a variation of the induced charge Q on the anode that is converted into a voltage pulse. For the calculation of a time dependent output signal, the induced charge Q has to be calculated as a function of the actual position of the moving charge q. Therefore, the electric field E~ of each point of the trajectory has to be calculated. By integrating the normal component of E~ over the surface that is surrounding the electrode, one obtains the induced charge Q. Due to the large number of different E~ configuartions that have to be calculated, this process is quite 34 3 The COBRA experiment tedious. A simplified method to calculate the induced charge Q and current i on an electrode was found by Shockley [49] and Ramo [50]:

Q = −q · φ0 (~x) (3.1)

i = q~v · E~0 (~x) . (3.2)

The relations are known as the Shockley-Ramo theorem. ~v is the actual velocity of the charge q. φ0 (~x) and E~0 (~x) are the so called weighting potential and weighting field that refer to the field and potential that would exist at the actual position ~x of q under the assumption that the selected electrode is at unit potential, all other electrodes are at zero potential and all charges are removed. Using this theorem, only the weighting potential, which is independent of the moving charge, has to be calculated. It depends only on the configuration of the device, especially on the electrode configuration.

The charge induced by the movement of the charge q from point ~xi to point ~xf can then be calculated as follows:

Z ~xf ∆Q = qE~0 · d~x (3.3) ~xi

= −q (φ0(~xf ) − φ0(~xi)) . (3.4)

For a planar electrode configuration where the holes travel to the cathode at z = 1 and the electrons to the anode at z = 0, the total change of induced charge on the anode can be calculated as:

∆QAnode = −(ne)(φ0(1) − φ0(z)) + (ne)(φ0(0) − φ0(z))) (3.5) = − (ne) (0 − z) + (ne) (1 − z) = ne, (3.6) since the weighting potential φ0 is a linear function of the interaction depth z from 1 at z = 0 to 0 at z = 1 . There e denotes the electric charge and n the number of created electrons and holes. If the holes can only move a short distance (small mobility-lifetime product), the induced charge on the anode is depth dependent, since only the electrons contribute to ∆QAnode :

∆QAnode ≈ ne (1 − z) . (3.7)

Under such conditions no spectroscopic information can be obtained. To overcome this effect, techniques in which the pulse amplitude is only sensitive to one type of charge carriers, normally the electrons, has been investigated. This so called single polarity charge sensing technique was first implemented in gas detectors and is known there as Frisch grid. In semiconductor detectors the technique was first implemented by Luke in 1994 [51] by use of coplanar grid electrodes. In figure 3.5 a scheme of a detector with the coplanar grid used by COBRA can be seen. Instead of using a planar anode electrode, parallel strips that are connected in an alternate manner, forming an independent set of grid electrodes, are used. Since a different voltage is applied on both of the electrodes, the electrons are always collected by one electrode, the so called 3.2 CdZnTe detectors 35 collecting anode (CA). The other anode is called non-collecting anode (NCA). In the COBRA experiment the bias voltage between CA and NCA is on the order of -50 V and is referred to as grid bias (GB). The bias voltage between anode and cathode is on the order of -1 kV [46].

Figure 3.5: Schematic drawing of the electrode configuration for coplanar grid detectors used by COBRA. The anode consist of parallel strips that are connected in an alternate manner, forming two independent sets of grid electrodes. The blue anode is the so called non-collecting anode (NCA) while the red anode is referreed to as collecting anode (CA). The height of the detector is normalized to unity with z = 0 referring to the anode and z = 1 to the cathode. The grey dashed line indicates the plane for that the weighting potentials in figure 3.6 has been calculated. Picture taken from [46].

The weighting potential for both anodes can be calculated by setting the potential of the investigated electrode to one and the potential of the other electrodes to zero. The so calculated weighting potentials are practically equal if the moved charge is far away from the anode, due to the symmetry between the two anodes. In the region z < 1 − P with P being the period of the coplanar grid, the potential differs, since the electrons move to the CA due to the GB. The difference signal of CA and NCA corresponds to the difference of the two weighting potentials. Since this is zero in the region of 1 − P < z ≤ 1, the amplitude of the difference signal is independent of the interaction depth while neglecting electron trapping. In figure 3.6 calculated weighting potentials for the CA and the NCA as well as the reconstructed difference potential are shown. In analogy to eq. (3.5) the total change of induced charge on the CA and NCA can be calculated:

∆QCA = ne (φCA(0) − φCA(z)) (3.8)

∆QNCA = ne (φNCA(0) − φNCA(z)) . (3.9) 36 3 The COBRA experiment

Figure 3.6: Simulated weighting potentials for the CA (red) and the NCA (blue) for a plane in the middle of the detector (grey dashed line in figure 3.5). The difference weighting potential is shown in green. With that an interaction depth independent signal height can be obtained. Picture taken from [46].

1 With φCA = φNCA = 2 (1 − z) for 0 < z ≤ 1, φCA(0) = 1 and φNCA(0) = 0 one obtains: 1 ∆Q = s = ne (z + 1) (3.10) CA CA 2 1 ∆Q = s = ne (z − 1) . (3.11) NCA NCA 2

∆Q directly correspond to the signal amplitude s. In the following discussion, which is adapted from [52], these signal amplitudes will be used. By calculating the difference signal of CA and NCA, the deposit energy can be deduced:

sdiff = sCA − sNCA = ne ∼ Edep. (3.12)

The interaction depth can also be reconstructed by using the two signals:

s + s z = CA NCA . (3.13) sCA − sNCA

In practice the formulas for the energy and the interaction depth have to be corrected, since the trapping of electrons can not be ignored. About 4-10% of the electrons can be trapped across 1 cm of CdZnTe and a bias voltage of 1 kV [48]. By applying a weighting factor w on the NCA signal in eq. (3.12) one obtains the so called weighted difference signal swdiff. With that a trapping corrected energy can be deduced:

swdiff = sCA − w · sNCA. (3.14)

By applying a weighting factor w < 1 on the NCA signal the pulse amplitude gets effectively reduced in a linear way. The longer the drift path of the electrons, the more of them get trapped. The optimal weighting factor can be found by optimizing the energy resolution. To deduce a trapping corrected interaction depth, one first has to assume a mean trapping 3.2 CdZnTe detectors 37 length λ over the whole drift path. With that the charge q can be written as a function of the drift distance d:

 −d/λ q = −en = −en0 · e . (3.15)

For simplification the weighting potential can be approximated as follows:

  1  2 (1 − z) for 0 < z ≤ 1,  φCA/NCA (z) = 1 for z = 0 and CA, (3.16)   0 for z = 0 and NCA.

With (3.3) the signal amplitude can be calculated. The integral is divided into two parts: For d the region with the uniform weighting potential with E = − dz φ0 = 1/2 follows:

Z 0 1  −(z−z0)/λ 0 1  −z/λ s1 = · (−e) n0 e dz = n0eλ 1 − e . (3.17) z 2 2 The second part of the calculation corresponds to the sharp change of the weighting potential at z = 0. Inserting this into the integral in eq. (3.3) one obtains:

1 s = en e−z0/λ (3.18) 2,CA 2 0 1 s = − en e−z0/λ. (3.19) 2,NCA 2 0

In total, the CA and NCA signal can be written as follows:

1 h   i s = en λ 1 − ez0/λ + e−z0/λ (3.20) CA 2 0 1 h   i s = en λ 1 − ez0/λ − e−z0/λ . (3.21) NCA 2 0

In the limit of large λ the equations simplify to the equations without electron trapping (3.10) and (3.11). By linear combination of the two signals an energy proportional quantity can be deduced:

λ − 1 λ s − s = n e ∼ E . (3.22) CA λ + 1 NCA λ + 1 0 dep

With an energy calibration, the constant factor on the right-hand side of the equation can be eliminated.

An expression for the trapping corrected interaction depth can be found by eliminating n0e from eq. (3.20) and (3.21):

 1 s + s  z = λln 1 − CA NCA . (3.23) λ sCA − sNCA 38 3 The COBRA experiment

The parameter λ can be calculated by using the weighting factor, since:

1 + w λ = . (3.24) 1 − w

Besides the electron trapping, which can be corrected in a quite simple way by optimizing the weighting factor, there are some other problems by reconstructing the energy and the interaction depth [53]:

• Hole contribution: The trapping length for holes is much smaller than for electrons. Their contribution to the signal is therefore small and equal for the CA and NCA signal for the largest part of the detector. By calculating the difference signal this contribution cancels out, except for a small part that is reintroduced by the weighting factor. Since this effect is nearly equal over the whole detector, this can be taken into account by the energy calibration. For events close to the cathode holes are immediately collected leading to a slightly underestimation of the energy. The depth reconstruction based on the sum of both signals leads to an overestimation of the depth.

• Near anode distortions: For the derivation of eq. (3.12) an equal weighting potential for CA and NCA at each point of the detector, except for z = 0, was assumed. In the region close to the anode this assumption is not true. Due to the CPG the weighting potential

is distorted as it an be seen in figure 3.6. This leads to a disturbed reconstruction of Edep and z. For the analysis events with z < 0.2 will be discarded.

• Charge sharing effect: For a low grid bias potential, some field lines could end at a NCA. Then a part of the electron charge will be shared between the CA and NCA leading to an underestimation of the energy and overestimated depth.

More details on this effects can be found in [53]. 4 Pulse shape analysis method A/E

Pulse shape analysis (PSA) is a commonly used background reduction technique that uses the time structure of detector signals to distinguish between signal-like and background-like events. In Germanium based experiments like GERDA or MAJORANA, this PSA is routinely used to discriminate single-site (SSEs) from multi-site events (MSEs) [54][55]. COBRA also uses PSA. Besides the standard data cleaning cuts and the z-cut there are methods to identify MSEs and lateral surface events (LSEs). In section 4.2 these methods will be explained in more detail. With MSE- and LSE-cut the signal acceptance is around 70%. In order to reach a higher signal acceptance, the advantages and the implementation of a new PSA-cut, called A/E-cut, will be discussed in this chapter.

4.1 Background identification with PSA

The pulse shapes created by the radiation that interacts with the detector have the same origin independent of the kind of radiation (e.g. α, β, γ or µ). The energy of the incident particles is transferred to electrons, which then travel to the anode and induce a current. However, different types of radiation interact with matter in different ways. Highly energetic γ-particles have a range of several centimetres in CdZnTe. A 2.6 MeV photon, for example, has a mean free path length of 4.6 cm [56]. For such energies, Compton scattering is more probable than photoelectric absorption. The photon can therefore deposit energy several times inside one detector crystal. Such events are called multi-site events (MSEs). Above 1.022 MeV, pair creation is possible, which causes an additional signature. In contrast to photons, electrons only have a short range in CdZnTe. For a 1.5 MeV electron the CSDA range (continuous slowing down approximation range) is around 2 mm [57]. The energy loss is almost continuous and mainly due to Coulomb interactions. Such a highly localized energy deposition is called a single-site event (SSE). 2β-decay, regardless of whether neutrino accompanied or not, emits two electrons. The signal that is searched for is therefore a SSE. The main background contributions for COBRA will be explained in section 5.1, but background events in the bulk region of the detector are mostly photon interactions. Since they likely scatter multiple times they can be identified by searching for MSEs. The identification of MSEs presents a powerful tool to distinguish between signal and background. Unfortunately, not all photons can be identified with a MSE search. Due to the small crystal size of the CdZnTe detectors it is not unlikely, that a photon scatters only once inside the detector and then leaves it without further interactions. Such an event presents as a SSE. Furthermore, a 2β-event can look like a MSE. For higher electron energies 40 4 Pulse shape analysis method A/E

the emission of bremsstrahlung gets more likely. Depending on the electron energy Ee and the average atomic number Z of the material, the ratio between energy loss due to ionisation and due to bremsstrahlung is approximately (Ee · Z) /700 MeV [58]. For a 1.5 MeV electron the fraction of energy loss in CdZnTe due to bremsstrahlung is around 10%. Most photons will have a short range because of their small energy, but also high-energetic photons with larger range can be emitted. However, MSE identification is important and necessary for background rejection.

4.2 Currently used data cleaning and PSA methods

For each event with a signal amplitude higher than a certain trigger threshold, the CA and NCA signal heights are recorded over a time of 10.24 µs. This allows for a complex offline analysis. The first stage of this analysis is the so called data cleaning. Unphysical events such as EMI distortions are identified and removed from the data set. Parameters like the expected pulse rise time, pulse heights, non-negative reconstructed energy and pre- and post- pulse baseline variations are used for that. Due to the distorted weighting potential near the anode, events close to the anode (z < 0.2) are removed as a part of the data cleaning. Due to a depth depending trigger threshold, a cut removing events below threshold to ensure a depth independent exposure is additionally applied [46]. After all data cleaning cuts, the data set should only contain physical events, apart from some cut survivors. To discriminate between signal- and background-like events, physics cuts can be applied. Before introducing them, the pulse shape of a signal-like event must be known. In figure 4.1 a typical SSE-pulse is shown. Before the triggering signal rise happens, the CA and NCA amplitudes are on the baseline (1). Due to the interaction of a particle with the detector material, a charge cloud is produced. The applied bias voltage between cathode and anode leads to the drift of the charge cloud through the detector to the anode. The CA and NCA signal show a common rise (2). When the charge cloud is close to the anode it feels the grid bias voltage and drifts to the CA. This leads to the splitting point at (3) and the sharp rise of the CA and the fall of the NCA pulse since the charge cloud drifts away from the NCA. When all charge is collected at the CA (4), the final pulse height is reached and the exponential decrease begins (5). With the signal heights of CA and NCA, the energy E and interaction depth z of the event can be calculated (see section 3.2.2). Background events from α- and β- contaminations are expected to originate from the detector surfaces. Events close to the anode and cathode can be rejected with the reconstructed interaction depth (z-cut). To discard events from the other four surfaces the lateral surface event cut (LSE-cut) was developed [59].

4.2.1 LSE-cut

In figure 4.2 pulse shapes of LSEs are compared to a pulse shape originating from an event in the bulk region (central event). They can be also illustrated with the difference weighting potential in figure 3.6. For a charge cloud drifting straight to a CA strip, the difference pulse 4.2 Currently used data cleaning and PSA methods 41

Figure 4.1: Typical pulse shape of a SSE. The amplitude of CA (red) and NCA (blue) signal as well as the difference signal (green) is shown. The main features are: pre-baseline before trigger (1), common rise due to the bias voltage potential (2), splitting point due to grid bias potential (3), charge collection at CA (4) and final pulse height with exponential decrease (5). shows a relatively smooth rise since the cloud follows the peak structure in the difference weighting potential. A charge cloud that drifts on a path pointing to a NCA strip will move to the CA strip near the anode and during this, passes the valley structure in the difference weighting potential. The difference pulse will fall below the baseline before the sharp rise to the maximum pulse height. All pulses originating from events in the bulk region of the detector can show such a behavior. But for pulse shapes from events close to the lateral surfaces, these features are expected to be much stronger. The reason is the more strongly disturbed weighting potential near the lateral surfaces. Depending on the outlying electrode strip, the difference pulse shows an early rise (CA-side event) or a dip below the baseline (NCA-side event).

Figure 4.2: Pulse shapes for an event close to the lateral surface with an outlying CA strip (left), a central event (middle) and an event close to the lateral surface with an outlying NCA strip. In contrast to a central event the difference pulse of the CA-side event shows an early rise and those from the NCA-side shows a dip below the baseline.

The strength of these pulse shape distortions depends on the specific grid design and the operation parameters. If the guard ring, which is an additional electrode surrounding the anode grid, is held on a fixed potential, weighting potential distortions will be reduced and the pulse shape distortions are expected to be much smaller [59]. 42 4 Pulse shape analysis method A/E

To distinguish LSEs from central events, two quantities are used since the distortion for a CA- side and a NCA-side event differs. The so called early rise time (ERT) is defined as the time in FADC samples between the points where the difference pulse rises from 3% to 50% of its maximum height. For a sampling frequency of 100 MHz, one sample corresponds to 10 ns. The ERT value is characteristically larger for CA-side LSEs than for central events. For a NCA-side event the difference pulse falls significantly below the baseline. This behavior is quantified by the so called DIP-value, which is the maximum amount by which the value of the difference pulse falls below the baseline. It is measured in FADC channels. Since also central events have DIP and ERT values, an optimal cut threshold has to be found. Both thresholds are therefore tuned to 90% signal acceptance, which means that 90% of the central events are kept by DIP and ERT. This results in 81% signal acceptance for the LSE cut that combines DIP and ERT.

4.2.2 MSE cut

A MSE is defined as at least two spatially separated energy depositions within one detector crystal. The induced current signal on the anode can then be seen as the superposition of two or more individual current pulses. The drift time of the produced charge clouds differs and causes two splitting points in the difference pulse, except for all charge clouds created in the same z-plane. In figure 4.3 the typical pulse shape of a MSE is shown. The characteristic changes in the slope of the difference pulse can be studied with the first derivative of this pulse, which is also shown in the same figure. The number of peaks can be associated with the number of collected charge clouds and hence with the number of interactions inside the crystal.

Figure 4.3: Typical pulse shape of a MSE (left) and the corresponding derivative of the difference pulse (right). The CA and NCA pulse show two splitting points leading to a plateau region in the difference pulse. The corresponding derivative shows two peaks indicating two collected charge clouds. To distinguish between peak and noise a certain threshold (RMS-cut) is used. The noise level is indicated with the horizontal blue line that is calculated with the root mean square (RMS) of the first hundred samples.

The currently used algorithm to search for MSEs uses the number of peaks in the derivative pulse (deriv) to discriminate between SSE and MSE [46]. To reduce the influence of noise, a smoothing algorithm is used to receive the derivative. Instead of a simple pointwise deviation by subtracting neighboring samples of the difference pulse (diff) and division by the corresponding 4.2 Currently used data cleaning and PSA methods 43 time distance, the following formula is used:

deriv [i] = diff [i + 2] − diff [i − 2] . (4.1)

This smoothing window size of five samples has turned out to be the optimal size for noise reduction. To distinguish between MSEs and SSEs, the algorithm counts the number of peaks above a certain threshold, which is calculated with the root mean square (RMS) of the first hundred samples multiplied by a constant factor xthresh. If there is more than one peak, the event is flagged as MSE. Due to the missing division with the window size in (4.1), deriv[i] can not be equated to the mathematical derivative. But since only the number of peaks has to be identified, this is not important for the peak search algorithm. In order to gain a high signal acceptance and at the same time a high background rejection, xthresh can be optimized. As a result the signal acceptance is 90% whith an background rejection of 60% [46].

4.2.3 Motivation for a new PSA cut

The currently used cuts are working quite well for the pyhsics data, but they also have some disadvantages. Since two cut parameters (DIP and ERT) are used for the LSE-cut and both are tuned to an efficiency of 90%, the total LSE-cut efficiency is limited to 81%. The DIP value is an integer value since it is counted in FADC channels. The efficiency could be better if one is not limited by such an integer value and can choose the most suitable floating value. Another important aspect is the misidentification of MSEs as LSEs. MSEs can also have large ERT values due to the plateau in the difference pulse (see left picture of figure 4.3). Therefore, the LSE-cut is also sensitive to MSEs. This leads to problems in the calculation of the combined cut efficiency, since MSE- and LSE-cut efficiency are not independent from each other. However, an accurate cut efficiency is essential to analyze the physics data in order to gain a half-life or half-life limit. The MSE-cut also has some disadvantages. The peaks in the derivative pulse have to be well separated to be found by the algorithm. If the two charge clouds are produced with only a small difference in the z-direction, then both will arrive nearly at the same time on the anode. The peaks in the derivative will then be close together. Furthermore, the optimization procedure for the MSE-cut requires quite some effort, since there has to be a complete processing of the data per investigated cut. For all these reasons, it could be beneficial to search for a PSA method that is able to identify LSEs and MSEs with only one parameter. Besides that, the method should be robust and should calculate the results in an appropriate time. The so called A/E parameter fulfills these conditions and could be used as a new cut for the COBRA physics analysis. 44 4 Pulse shape analysis method A/E

4.3 A/E parameter

4.3.1 Definition

For a MSE, the total energy that is deposited during the event is distributed over two or more charge clouds, whereas a SSE creates only one charge cloud containing the total energy of the event. The amplitude A of the current pulse (derivative of the difference pulse) corresponds to the maximum current dQ/dt during the collection of a charge cloud with charge Q. Since each peak of the current pulse corresponds to one collected charge cloud, the amplitude A of the highest peak created by a MSE is still smaller than the amplitude of a SSE of the same total energy. A good parameter to distinguish between SSE and MSE is the ratio of the amplitude A of the current pulse to the amplitude of the charge pulse E of the event, called A/E parameter. For E the calibrated energy, the uncalibrated energy or even the pure pulse height of the diff pulse can be used. In section 4.3.3 these different definitions are investigated. In figure 4.4 the two quantities needed for the A/E calculation are shown in the pulses of a SSE and a MSE.

Figure 4.4: CA, NCA and difference pulse (left) as well as current pulse (right) of a SSE (top) and a MSE (bottom) with nearly equal energy. The two quantities needed for the A/E-cut are marked: E is the amplitude of the charge pulse, A is defined as the highest amplitude of the current pulse (derivative pulse). Although both events have nearly the same total energy, the amplitude A is smaller for the MSE than for the SSE.

4.3.2 Experimental data set

To study parameters of influence as well as the efficiency of the A/E-cut, a defined data set of SSEs and MSEs would be beneficial. Since such a data set is not available, the most useful alternative is to use 228Th calibration measurements. 228Th is one of the nuclides that are routinely used for energy calibrations. Therefore, a large amount of data is available for 4.3 A/E parameter 45 analysis. 208Tl, which is a daughter nuclide of 228Th, emits a highly energetic γ-line of 2614 keV with almost 100% emission probability. For this energy region, Compton scattering is the dominant interaction process. However, pair creation in the Coulomb field of the nuclei of the detector material is also possible (15% probability). The produced leptons are likely stopped within 1 mm. The positron annihilates with an electron of the detector material resulting in two annihilation photons of 511 keV energy each. Due to the small size of the CdZnTe crystals, it is possible that one or both photons escape and do not interact inside the detector volume. In this case not the full energy is deposited. In figure 4.5 a 228Th calibration spectrum is shown.

Figure 4.5: 228Th calibration spectrum of detector 22 of the COBRA demonstrator. Promi- nent lines coming from 208Tl decay are highlighted: full energy peak (FEP) at 2.614 MeV, single escape peak (SEP) at ESEP = EFEP − me = 2.103 MeV and double escape peak (DEP) at EDEP = EFEP − 2 · me = 1.592 MeV. For each peak the ROI and the side-band regions, which are needed for the efficiency analysis in section 4.4, are shown.

Besides some prominent lines below 1.2 MeV, there are three peaks visible. The full energy peak (FEP) at 2.614 MeV originates from full energy deposition of the 208Tl photon inside one detector crystals due to various interaction processes. The single escape peak (SEP) at 2.103 MeV originates from the pair creation process described above. One of the annihilation photons leaves the detector without further interaction while the other one deposits its full energy inside the detector. The double escape peak (DEP) results if both annihilation photons leave the detector without further interaction. In figure 4.6 a schematic drawing of the process leading to a SEP and a DEP event is shown. SEP events are expected to be almost always multi-site due to the underlying event topology, whereas DEP events are expected to be almost always single-site. Therefore, SEP and DEP events are suitable to study and optimize the A/E-cut. 46 4 Pulse shape analysis method A/E

Figure 4.6: Schematic drawing of a SEP event (left) and a DEP event (right). A highly energetic photon (here from 208Tl) can create an e+e−-pair. They cause a localized energy deposition indicated with the yellow spot. The positron annihilates with an electron of the detector material leading to the creation of two photons with 511 keV each. If one photon is detected within the detector (indicated with the yellow spot) while the other escapes, a SEP event is detected. Such an event is a proxy for a MSE since there are two energy depositions inside the detector. If both photons escape, a DEP event is detected having the signature of a SSE.

4.3.3 A/E implementation in MAnTiCORE

To calculate properties like deposited energy or interaction depth, the recorded raw data has to be processed. COBRA developed the processing tool MAnTiCORE (Multiple-Analysis Toolkit for the COBRA Experiment) for this task. It uses the analysis framework ROOT [60] version 6-14-08 developed by CERN and is written in the programming language C++. MAnTiCORE will also be used to calculate A/E. There are multiple possibilities to construct A/E since both involved quantities (A and E) can be used in their raw or corrected form: The amplitude A is the maximum height of the derivative of the difference pulse. The raw difference pulse (diff) can be calculated as:

diff = CA − NCA. (4.2)

As explained in section 3.2.2, the application of a weighting factor w improves the energy resolution. Following, an alternative possibility to calculate the difference pulse is referred to as adiff and can be calculated as:

adiff = CA − w · NCA. (4.3)

Consequently, there are two possibilities in calculating the amplitude A:

Adiff = max (deriv (diff)) , (4.4)

Aadiff = max (deriv (adiff)) . (4.5)

The energy E is calculated from the pulse height of the difference pulse using an moving window average (MWA). In order to gain a correct translation between reconstructed energy and real energy, an energy calibration with radioactive sources of known gamma spectrum is used. The 4.4 Optimization procedure 47

resulting calibrated energy is named Ecal. Therefore, there are three possible methods to calculate the E for A/E:

Ediff = max (MWA(diff)) , (4.6)

Eadiff = max (MWA(adiff)) , (4.7)

Ecal = a + b · max (MWA(adiff)) , (4.8) where a and b are the calibration parameters. For A/E there are 2 · 3 = 6 possibilities in total. In section 4.4.1 three of them will be investigated with regard to the cut efficiency in order to achieve the best cut result:

Adiff (A/E)diff = , (4.9) Ediff Aadiff (A/E)adiff = , (4.10) Eadiff Aadiff (A/E)ecal = . (4.11) Ecal

All other combinations are not well-motivated since they would use one quantity with weighting factor and one without. The derivative of the difference pulse at the point i, which is needed for A, can be calculated as follows:

i+nsmth−1 diff [j − n ] − diff [j + n ] deriv [i] = X smth smth . (4.12) 2 · nsmth j=i−nsmth

Instead of subtracting neighboring samples of the difference pulse a smoothing over a window of 2 · nsmth (with nsmth ∈ N) is applied. For the derivative of the weighting factor corrected difference pulse, diff has to be replaced by adiff. In section 4.4.1 the influence of the smoothing window size on the cut efficiency is investigated.

4.4 Optimization procedure

To decide which A/E implementation method or parameter of influence achieves the best cut result, a method to compare between these different A/E definitions is necessary. Good indicators that quantify the cut result are the cut efficiency as well as the peak sensitivity. The efficiency can either refer to the number of signal events that are kept by the cut, called signal acceptance SSE, or to the number of background events identified by the cut, called background rejection MSE.

For a potential A/E-cut value (A/E)cut, all events of a calibration measurement can be assigned to two spectra: If A/E ≥ (A/E)cut, the event belongs to the so called signal spectrum (sig spec); If A/E < (A/E)cut, the event belongs to the so called background spectrum (bg spec). For comparison, a reference spectrum (ref spec) containing all the events is defined. In figure 4.7 the signal and background spectrum for three different cut values are shown. 48 4 Pulse shape analysis method A/E

Figure 4.7: 228Th calibration spectra for different A/E-cut values. The signal spectrum contains all events with an A/E value higher than the cut value. The background spectrum contains all events with A/E values smaller than the cut value. The higher the A/E-cut value the less events are in the SEP of the signal spectrum and therefore the less MSEs remain. However, the peak entries in the DEP of the signal spectrum also decreases. An optimal cut value has to be found where the DEP entries in the signal spectrum are as high as possible and simultaneously the SEP entries in the background spectrum are as high as possible. Such

an optimal value ((A/E)cut = 0.75) is shown in the middle picture. 4.4 Optimization procedure 49

With those different spectra, SSE and MSE can be calculated:

NDEP, sig spec SSE = , (4.13) NDEP, ref spec NSEP, bg spec MSE = . (4.14) NSEP, ref spec

For the signal acceptance the DEP is used since almost all events are expected to be single-site. For the background rejection the SEP is used since most of the events are multi-site.

The higher the (A/E)cut, the less events are stored in the signal spectrum and the more events are stored in the background spectrum. Additionally, with increasing (A/E)cut, the peak entries in the SEP of the signal spectrum decreases. This shows that the A/E-cut is able to discriminate MSEs from the signal data set.

To calculate the peak entries (Npeak) in the DEP (NDEP) and SEP (NSEP) for eq. (4.13) and (4.14), a certain region of interest (ROI) in the 228Th calibration measurements is defined. To take the underlying Compton continuum into account, an area to the left (sbl) and right (sbr) of the peak, referred to as side-bands, is defined and the number of entries in the side-bands

Nsb are subtracted from NROI. The number of peak events is therefore:

Npeak = NROI − Nsb. (4.15)

The ROI is defined as the following energy interval:

ROI = [Epeak − FWHM (Epeak) ,Epeak + FWHM (Epeak)] . (4.16)

FWHM is the energy resolution according to the full width at half maximum at a certain energy. This value is routinely calculated within the energy calibration for each individual detector. The combined side-band area has the same width as the ROI. To prevent double counting, a small gap between ROI and side-band, referred to as Eshift, is used:

sbl = [Epeak − 2 · FWHM (Epeak) − Eshift,Epeak − 1 · FWHM (Epeak) − Eshift] , (4.17)

sbr = [Epeak + 1 · FWHM (Epeak) + Eshift,Epeak + 2 · FWHM (Epeak) + Eshift] , (4.18)

sb = sbl + sbr. (4.19)

In figure 4.5 the ROI and the side-band regions are highlighted for the DEP, SEP and FEP in the 228Th calibration spectrum. Another quantity to characterize the quality of a cut is the peak sensitivity s, which is defined as:

N − N s = ROI√ sb . (4.20) Nsb

It assumes a Poisson distributed background and describes the strength of a peak in units of the background fluctuation. 50 4 Pulse shape analysis method A/E

To find the optimal A/E-cut value where signal acceptance and background rejection are as high as possible, SSE and MSE are calculated for a range of (A/E)cut-values for one calibration measurement. In figure 4.8 these calculated efficiencies and sensitivities are shown.

Figure 4.8: Normalized sensitivity (top row) and efficiency (bottom row) for signal and back-

ground events in the DEP (left), SEP (middle) and FEP (right). With increasing (A/E)cut the signal acceptance decreases but simultaneously the background rejection increases. The red vertical line indicates the A/E value where the product of these two quantities is maximal. The green vertical line indicates the A/E value for which a 90% signal acceptance is reached. The sensitivity and efficiency values for the highlighted cut values can be found in table 4.1.

The green vertical line indicates the (A/E)cut where a 90% signal acceptance is achieved, referred to as (A/E)90%. It could be beneficial to lose some signal events in order to gain a higher background rejection. The corresponding A/E value is indicated with the red vertical line and referred to as (A/E)opt. This value is obtained by maximizing the product of signal acceptance and background rejection. In table 4.1 the efficiencies and sensitivities for the cut values (A/E)90% = 0.75 and (A/E)opt = 0.78 are summarized.

Table 4.1: Normalized sensitivity and efficiency for the A/E cut-values (A/E)90% = 0.75 and (A/E)opt = 0.78 in different energy regions (DEP, SEP and FEP) and for signal and background events. The corresponding plots are shown in figure 4.8.

DEP SEP FEP signal background signal background signal background (A/E) 98.49±1.72 21.97±1.32 42.33±6.00 1.00±6.00 83.14±3.21 59.55±2.29 sensitivity [%] 90% (A/E)opt 95.14±1.79 37.80±1.40 29.86±5.93 90.02±5.47 66.73±3.68 78.08±2.45 (A/E) 90.70±1.64 9.29±0.48 37.00±5.54 63.05±5.02 56.10±1.12 43.92±0.97 efficiency [%] 90% (A/E)opt 77.27±1.44 22.72±0.74 22.02±4.45 77.97±6.36 30.73±0.76 69.28±1.32 4.4 Optimization procedure 51

4.4.1 A/E calculation method and smoothing window size

As pointed out in section 4.3.3, there are three possible methods for calculating A/E:(A/E)diff,

(A/E)adiff and (A/E)ecal. Additionally, the smoothing window size that is needed to calculate the derivative of the difference pulse can have an influence on the cut efficiency. In figure 4.9 the influence of the calculation method and the smoothing window on the A/E distribution of DEP events is shown.

Figure 4.9: Influence of the calculation method (left) and the smoothing window size (right) on the A/E distribution of DEP events of detector 23. For the left plot a constant smoothing

window of nsmth = 8 was chosen. The (A/E)ecal distribution is shifted to lower values since the calibrated energy is used. For the right plot (A/E)diff was used. With increasing nsmth, the width of the distributions decreases while the mean is shifted to higher A/E values.

The (A/E)diff and the (A/E)adiff distributions show only a minor difference of the shape and the mean. The (A/E)ecal distribution is shifted to lower A/E values and the width is smaller compared to the other distributions. With increasing nsmth, the width of the distributions de- creases. Additionally, the mean is shifted to higher A/E values. Since the distribution of DEP events dominantly contains SSEs, they form a Gaussian distribution. Due to the underlying Compton continuum also a small fraction of MSEs is present, which build a low side tail. With the nsmth parameter, a better or worse discrimination between these two contributions can be achieved. To decide which A/E calculation method with which smoothing window reaches the highest efficiencies, the optimization procedure described above is used. The calibration measurement from the 24th of April 2014 was chosen because the measurement is one with the highest statistic. For each pulse shape, 3 · 14 = 42 A/E values were calculated with MAnTi- CORE; three different calculation methods combined with 14 different smoothing window sizes between 2 and 32. For each of these 42 data sets the optimization procedure was executed to

find the (A/E)opt value, where the optimum of signal acceptance and background rejection is reached. Additionally, this was done for (A/E)90%. In figure 4.10 the results are shown.

The (A/E)diff definition reaches the highest efficiencies while (A/E)adiff and (A/E)ecal are some percentage points lower and nearly equal. The only difference between (A/E)ecal and (A/E)adiff is that the calibrated energy is used for the first definition. Since a linear energy calibration is done, the two values only differ by nearly a constant factor. The behavior regarding the cut efficiency stays unaffected. Up to nsmth = 7 the efficiency strongly increases for all methods. For higher smoothing window sizes the efficiency decreases slightly. An optimal value is around 52 4 Pulse shape analysis method A/E

Figure 4.10: Average cut efficiencies for different A/E calculation methods ((A/E)adiff, (A/E)diff and (A/E)ecal) and smoothing window sizes nsmth. In the upper row (A/E)90% is used. The resulting background rejection increases strongly up to nsmth = 7. Then there is a slightly drop of MSE with increasing nsmth. The diff method achieves a better background rejection. In the bottom row the (A/E)opt cut is used. Compared to (A/E)90% the signal acceptance is around 4 percentage points lower while the background rejection is around 7

percentage points higher. Also for this cut the (A/E)diff method achieves higher efficiencies.

nsmth = 8. For the A/E calibration, which will be explained in section 4.5, it turned out that a smoothing window size of 32 is more beneficial. Since the efficiency decrease is only small, this causes only a minor loss. For the following analysis the (A/E)diff method with nsmth = 32 will be used.

4.5 A/E calibration

4.5.1 Motivation

The 64 detectors of the COBRA demonstrator can not be treated all equally. Starting from the challenging manufacturing process, defects during the crystal growth can affect the detector performance. Additionally, the Zn content is hard to monitor leading to a slight content variation. Since each individual crystal is cut from different boules, they may differ slightly due to these effects. Therefore, the optimal working point for each detector has to be found by applying different BV and GB voltages. Moreover, electronic effects arising from small variations due to the hardware specifications, e.g. different amplifications of the CA and NCA signals (gain-balancing) are used. To do a combined data analysis for all detectors, a calibration that corrects for such individual effects has to be done. Routinely an energy calibration is done for each detector including the determination of the weighting and the gain-balancing factor. According to these experiences, a different behavior regarding the A/E values is expected for 4.5 A/E calibration 53 each detector. In figure 4.11 the A/E distributions for five different detectors are shown. The position and the shape of the distributions vary quite substantially. Therefore, each detector has its individual optimal A/E-cut value. The distribution of these cut values is shown in figure 4.12.

Figure 4.11: A/E distributions of DEP events for five different detectors of the COBRA demonstrator. The position as well as the shape of the distributions vary between the single detectors. Therefore, the A/E values have to be calibrated.

Figure 4.12: Distribution of the (A/E)90% (left) and (A/E)opt cut values (right) of all running detectors. For comparison, the A/E distribution of DEP events of detector 23 is shown in the background.

There are two possibilities when using A/E as a new PSA method: Each detector gets its own optimal cut value or the A/E values is calibrated leading to one global cut value valid for all detectors. In the process of data analysis the method with A/E calibration is more convenient. To obtain a cleaner signal data set, the A/E-cut value can easily be increased whereas with the other method each individual detector specific cut value has to be changed. And since all A/E 54 4 Pulse shape analysis method A/E distributions show a different width, a constant increase in these cut values leads to different changes in the efficiencies of background rejection and signal acceptance.

4.5.2 Calibration procedure

DEP events from the 228Th calibration measurement show an A/E distribution with a Gaussian part from the SSEs and a low side tail from the MSEs. In figure 4.13 the A/E distribution of detector 23 in the DEP region is shown.

Figure 4.13: A/E distribution of detector 23 in the DEP region. The red line shows the fit function (4.22) that consists of a Gaussian part and a low side tail.

In order to obtain a global cut value all Gaussian parts of the individual detectors should have the same mean and width, which can be chosen arbitrarily. The calibrated A/E values should form a distribution with the mean of the Gaussian part at µ0 = 1 and a width described with the standard deviation of σ0 = 0.1. Therefore, the A/E distribution is fitted to obtain the actual mean µ and width σ for all detectors. These two parameters will be the A/E calibration parameters. During the data processing with MAnTiCORE, the A/E values will then be corrected to (A/E)calib according to:

σ0 (A/E) = · ((A/E) − µ) + µ0. (4.21) calib σ

Since these A/E calibration parameters should later on be calculated automatically after the energy calibration, a robust fit method has to be used. GERDA already uses A/E and in order to calibrate their A/E values they fit their distribution with [54]:

2 f(x−l) n − (x−µ) e + d f (x = A/E) = √ · e 2σ2 + m · . (4.22) σ · 2π e(x−l)/t + l

The first term describes the Gaussian part with the integral n. The MSE term is parametrized empirically by the parameters m, d, f, l and t. In figure 4.13 this fit function is shown. 4.5 A/E calibration 55

Unfortunately, this fit function turned out to be not really suitable when applying it on the COBRA data. If the shape of the distribution is only slightly different from expectations, the Gaussian part and the tail part can be mixed up. This is inconvenient when the process should be automatized. Additionally, the number of fit parameters is eight, which is also quite high. To improve this situation, alternative approaches were investigated. A tailed Gaussian can also be described with an exponentially modified Gaussian distribution (EMG), which is defined as follows:

2 ! λ λ 2µ+λσ2−2x µ + λσ − x f (x = A/E) = · e 2 ( ) · erfc √ . (4.23) 2 2σ

The parameter λ describes the strength of the tail. erfc is the complementary error function defined as erfc(x) = 1 − erf(x). In a logarithmic plot, a Gaussian forms a parabola. The tail, however, shows as a linear behavior. In figure 4.14 the A/E distribution of detector 27 is shown on a logarithmic scale. One EMG distribution alone can not describe the data due to the kink. The sum of a EMG distribution and a Gaussian is recommended. To get a better fit result, a second EMG distribution with a different λ factor is used instead of the Gaussian. Nevertheless, the second λ factor is expected to be rather small. Following definition will be used as a fit function:

2 ! λ λ1 2 x − µ + λ σ 1 (2(x−µ)+λ1σ ) 1 f (x = A/E) = n1 · · e 2 · erfc √ 2 2σ 2 ! λ λ2 2 x − µ + λ σ 2 (2(x−µ)+λ2σ ) 2 +n2 · · e 2 · erfc √ . (4.24) 2 2σ

In comparison with eq. (4.23), (µ − x) is substituted with (x − µ) in order to get a left side tail. The fit function is shown in figure 4.14.

Figure 4.14: A/E distribution of detector 27 on logarithmic scale. The fit function consists of two EMG distributions, in which the second EMG distribution has nearly no tail and is almost a Gaussian. 56 4 Pulse shape analysis method A/E

This fit function enables an easy automatization of the fitting process since the important fit parameters µ and σ are less sensitive to varying shapes of the A/E distribution. Compared to the first fit attempt, two fit parameters less are needed. Unfortunately, the fit parameters µ and σ are not suitable for the intended calibration. µ is not directly the mean of the Gaussian component and does not describe the position of the distribution maximum. Depending on the tailing, µ and σ do not match with the optical impression. Even though the real mean and width can be determined via the fit function by calculating the maximum and full width at half maximum (FWHM), the uncertainties on these parameters can not be derived from the fit. This is why the fit function is not found to be suitable for the calibration. Finally, a fit approach using a two-sigma-Gaussian function reaches satisfying results:

 2 − (x−µ)  2σ2 c · e 1 + m · (x − µ) + n for x ≤ µ, f (x = A/E) = 2 (4.25) − (x−µ)  2σ2 c · e 2 + m · (x − µ) + n for x > µ.

For A/E ≤ µ, a larger σ1 takes the left side tail into account. The σ2 for A/E > µ corresponds to the width of the SSE-distribution and can therefore be used as parameter σ in eq. (4.21). The linear component in the fit function helps to approximate the left side tail. In figure 4.15 the A/E distribution of DEP events of detector 27 together with the two-sigma-Gaussian fit function is shown. Within the fit procedure, the fit range is varied if χ2/n.d.f. > 1.3 in order to optimize the fit result.

Figure 4.15: A/E distribution of detector 27 with a two-sigma-Gaussian fit function (see eq. (4.25)).

Some detectors, nearly all of layer three, show a different A/E distribution as expected. In the right picture of figure 4.16 this behavior is shown for detector 43 compared to a normal distribution presented by detector 23 on the left. Disproportionately many events have a higher A/E value leading to a non-Gaussian shape. This behavior still causes difficulties when the 4.5 A/E calibration 57 distribution is automatically fitted with function (4.25). In figure 4.16 the distributions are also shown for a larger smoothing window. Compared to the expected shape there are nevertheless differences, but the shape is much more like a Gaussian, if nsmth = 32 is used. This leads to the conclusion that such disturbances get reinforced by the smoothing process when the smoothing window size is too small. The physical explanation for these disturbances might be characteristic noise affecting especially the DAQ chain of layer three or the general worse performance of detectors of this layer that will also be seen during the data partitioning (see chapter 5). Instead of using a smoothing window size around eight, which reaches the highest efficiencies, nsmth = 32 will be used instead. The small loss in signal acceptance, which is around 4%, is manageable.

Figure 4.16: A/E distribution of DEP events of detector 23 (left) and 43 (right) for two different smoothing window sizes. Detector 23 represent the expected A/E distribution. In contrast detector 43, as well as nearly all other detectors of layer three, shows a non Gaussian distribution. With a greater smoothing window size this effect reduces slightly and the distribution is more Gaussian like.

4.5.3 Calibration results

To verify the accuracy of the A/E calibration, the calibration data is reprocessed with the deduced A/E calibration parameters in order to gain the calibrated A/E values. In figure 4.17 the A/E distribution of DEP events for five detectors is shown after the calibration. The maximum of the distribution is now centered around A/E = 1 and the width is equal for all detectors. The results of the optimization procedure that finds the optimal A/E-cut value are shown in

figure 4.18. Compared to the values before the calibration, the spread of (A/E)90% is much smaller. Also there are no outliers any more. Hence, the calibration was successful. The spread of (A/E)opt is only slightly smaller. The reason may arise from the calibration data itself. The calibration source is usually placed between the innermost layers. Each detector has a different distance to the source and additionally more or less other detectors in between that act as a shielding. For detector 23 there are 37700 events in the DEP region, while detector 48 only has 2600 events in this region for the same calibration period. The fraction between DEP events and the underlying Compton continuum can vary strongly. This can also be seen in figure 4.17. Detector 18 has a much higher fraction of MSEs than detector 50 because it has more events 58 4 Pulse shape analysis method A/E

Figure 4.17: A/E distributions, which are scaled to a maximum height of one, for five different detectors of the COBRA demonstrator after the A/E calibration. The maximum of the distribution is now centered around A/E = 1 and the width on the right side is equal for all detectors. Detector 28 and 37 are shown because their distribution vary the most from the other distributions, also before the A/E calibration.

in the tail region and less events in the Gaussian region. Thus the spread of (A/E)opt is not a good quantity to evaluate the success of the A/E calibration.

As A/E-cut value A/E = 0.872 will be used. It is the mean over all detector specific (A/E)90% values shown in the left bottom figure in 4.18. A 90% signal acceptance with an average background rejection of 65% can so be achieved.

In figure 4.19 the A/E calibration parameter are shown exemplary for two detectors for all calibration measurements done between 2014 and 2016. They are deduced by fitting the A/E distribution with a fine and a coarser binning. The fit method is stable and does not depend on the choice of bins, since only marginal differences are seen. µ is nearly equal for all calibrations. However, the fluctuation of this parameter can be of the order of 30% of the distribution width for some detectors. The σ value varies more over the different calibrations. In order to gain an accurate result, the parameters have to be deduced for each calibration run. In total, 38 calibrations were done between 2011-09-29 and 2016-09-29. For each physics run an interpolation between the calibration parameter of the pre and the post-calibration is used. After the A/E calibration of all physics runs, the new cut can be applied on the physics data. The results on the combined energy spectra will be shown in the next chapter after introducing the data partitioning in section 5.3. 4.5 A/E calibration 59

Figure 4.18: Distribution of the (A/E)90% (left) and (A/E)opt cut values (right) of all running detectors after the A/E calibration (bottom row). In the top row this distribution is shown again (see fig. 4.12) for cut values before the calibration. The A/E distribution of DEP events of detector 23 is shown in the background to compare the spread of the cut values with the width of the A/E distribution. 60 4 Pulse shape analysis method A/E

Figure 4.19: A/E calibration parameter for all calibration runs between 2014 and 2016 for detector 19 (top row) and detector 42 (bottom row). The number of bins of the A/E distribution was changed to check if the fit depends on that. The green bands in the left plots indicate the mean width of the A/E distribution for comparison to evaluate the impact of µ variations. 5 Data partitioning

To measure the 2ν2β spectrum of 116Cd, the background should be as low as possible. As already described in the introduction, two different approaches towards this goal will be investigated in this thesis. This chapter will focus on the so called data partitioning.

The installation of the first layer of the COBRA demonstrator was finished in the end of September 2011. The setup was subsequently extended with additional detector layers before the demonstrator was completed by the end of 2013. Since the installation of the first layer, the COBRA demonstrator is continuously taking data, except for some breaks for calibration, maintenance or due to technical failures. In total an exposure of 400 kg·d was accumulated until 2016-09-27. The term data partitioning means to divide this complete data set into a background reduced and a remaining background enriched data set. The background reduced data set can then be used for the 2ν2β-spectrum analysis. The background enriched data set can be used to get a better understanding of the background composition and potential origin in the COBRA experiment. This can help to investigate new background reduction techniques and to develop a background model. After the application of data cleaning cuts to remove non-physical events, the data can be parted into different time periods, detectors and detector areas (fiducial volume).

5.1 Potential background sources

To identify background enriched data, a detailed overview over potential background sources is needed. Prominent background features can be identified in the energy spectrum of the physics data. A two-dimensional plot in which the count rate is shown in dependency of the reconstructed interaction depth and the deposited energy can help to get more information about the origin of the background. In figure 5.1 this illustration is shown for 216 kg·d exposure. The low energy region is dominated by the β-decay of 113Cd, which is intrinsically abundant in CdZnTe and uniformly distributed over the whole interaction depth. The high half-life of 8 · 1015 yr results in a constant decay rate and enables to check the time stability of each detector [61]. Straight vertical lines can be identified as γ-lines from 40K at 1460.8 keV and 22Na at 1274.5 keV, which is not highlighted in the plot. The 511 keV annihilation line is also visible. 22Na, which is clearer visible in the spectrum 5.12, may originates from contaminations of 22Na in the Copper nest, since only some nearby detectors detect this line. Horizontal structures with higher count rate point to localized contaminations. On the cathode 62 5 Data partitioning surface at z = 1 must be alpha contaminations due to the peaks around 3.2 MeV and 5.3 MeV and the low penetration depths. The first peak can be identified as 190Pt, which decays by emission of 3.175 MeV α-particles with a half-life of 6.5 · 1011 yr. Platinum is part of the electrode metallization between the CdZnTe crystal and a Gold layer. Despite the small natural abundance of 0.01% of 190Pt, it represents a dominant background source. The second peak at 5.304 MeV is caused by the α-decay of 210Po, which is part of the Uranium-Radon decay chain. The most likely explanation for this contamination are the ionized Radon daughters, which can get trapped on the cathode due to the applied negative bulk voltage. To prevent the presence of Radon inside the setup, it is constantly flushed with Nitrogen. But since the detectors were tested and stored in environments where Radon was part of the ambient air, and additionally the Nitrogen flushing fails some times, Radon daughters can be present on the detectors surfaces.

Figure 5.1: Count rate of physics data in dependency of reconstructed interaction depth and deposited energy. Prominent background contributions such as alpha contaminations on anode and cathode, γ-lines from 40K, and the intrinsically abundant 113Cd β-decay are highlighted.

Distortions in the weighting potential near the anode (z = 0) effect the energy reconstruction of events near the anode. One particular example for this is the observed double energy peak of 190Pt. It is caused by the collection of both holes and electrons by the anode electrodes NCA and CA. Since the energy reconstruction is solely based on the electron signal, the resulting signal amplitude is enhanced by the hole contribution. The result is an energy entry twice as high as the original energy released by the decay. Besides the contaminations with α-emitters on the anode and cathode, contaminations on the lateral surfaces are also very likely. The detector crystals are covered with an encapsulation lacquer that could also contains α-emitter. Since the coating is 20 µm thick, the α-particles already loose energy before they reach the 5.2 Identification of background enriched data periods 63 crystal. Hence, lots of events below 5 MeV can be caused by these lateral surface events. In a depth around 0.95 > z > 0.7 the rate is much higher compared to smaller depths. The origin of this background feature is not quite clear. One explanation could be contaminations on the Delrin detector holder. The holder covers the bottom of the detector until z = 0.96. If there are contaminations on it, they cause events only above (z < 0.96), but not where the holder sits, because it acts as a shielding. Actually, there is a lower rate at the position of the detector holder in the spectrum.

5.2 Identification of background enriched data periods

The half-lives of the investigated 2β-decays, and also of the β-decay of 113Cd, are so high that their decay rate is constant over the lifetime of the experiment. To identify run periods and detectors with a higher background index, a higher count rate compared to other runs or detectors can help to find them. In figure 5.2 the count rates for all 64 detectors of the COBRA demonstrator in dependency of the measuring date are shown in form of a heat map.

Figure 5.2: Count rate for all 64 detectors of the COBRA demonstrator between end of 2011 and fall 2016 for events in the energy region 350 keV ≤ E ≤ 2800 keV. Only data cleaning cuts are applied. White horizontal areas indicate turned off detectors. Blank vertical areas indicate the complete shut down of the setup for maintenance or certain disabled layers. The big white area on the left shows the layer-wise extension of the setup.

Only events with an energy between 350 keV ≤ E ≤ 2800 keV are used since the Q-value for 116Cd is 2813.5 keV. Below 350 keV the count rate is dominated by the β-decay of 113Cd. Such a comparatively high rate would hide rate fluctuations on a lower level and hence, this region is excluded from the further investigation. Blanc areas indicate that no data were recorded during that time with the related detector channels. This can happen for the whole setup in 64 5 Data partitioning case of an installation shift or maintenance or only for a single detector that had to be turned off for a certain time because of too high noise rates. The steps on the left show the layer-wise extension of the setup. The heat map illustration also shows areas with higher rate, which have to be identified, cate- gorized and removed from the data set in order to achieve a significant background reduction. For clarity these areas can be assigned to three different categories and will be discussed in more detail in the next sections:

• Hot pixel: only one detector has a high rate during a short time period,

• Bad run period: all detectors show a higher rate during a certain time period,

• Bad detector: one detector has a higher rate compared to others during the whole mea- suring time.

Additionally, following aspects will be used for the data partitioning:

• Fiducial Volume: with z-cut and LSE-cut only a certain detector volume can be chosen for the analysis.

• Multiple detector hits: time coincident events in two or more different detectors can be removed from the data set since they are not caused by 2ν2β-events. Within this work only coincident events of detectors that are read out by the same FADC can be removed, since each FADC uses its own clock. At most 1% of the events are rejected by this. With a recently developed synchronization tool [62] also simultaneous events of detectors that are not on the same FADC can be identified. This is not incorporated into the analysis for this thesis but can help to increase the efficiency of the removal of multiple detector hits in the future.

5.2.1 Hot pixel

If the count rate of a single detector is much higher than for other detectors during a short time period, then it is called a hot pixel. In table A1 in the appendix all identified hot pixels are summarized. In figure 5.2 such a hot pixel is visible for detector 60 between 2016-05-15 and 2016-06-13. The count rate is by a factor of 102 higher than for other detectors during that time. When a z < 0.97 cut is used, the rate is comparable with others. A closer look into the data of this detector indicates the origin of this behavior. In the left part of figure 5.3 a histogram of the reconstructed interaction depth for events of this period is shown. Most of the events have a non-physical depth of z > 1, which would be outside the crystal region. On the right side an example for a corresponding pulse is shown. In figure 4.1 the shape of a normal pulse is shown, where the NCA signal falls below the baseline after the common rise of CA and NCA signal. Due to those missing prominent features for pulses during this period, they are not caused by the interaction of radiation with the detector. Probably they are caused by disturbances of the electronics at some point of the DAQ chain. Although these non-physical events can be removed by using the z < 0.97 cut, which is already used to 5.2 Identification of background enriched data periods 65

Figure 5.3: Left: interaction depth of events during a hot pixel time period of detector 60. Most of the events have a non-physical interaction depth of z > 1. Right: example of a corresponding pulse for such an event. Since it does not show the typical features of physical interactions with the detector, such an event is likely caused by electronic disturbances. remove events from the α-contaminations on the cathode surface, these hot pixel period will be removed from the data set, since the origin of these disturbances is not totally clear and may cause other problems.

5.2.2 Bad run period

If all detectors show a higher rate in a certain time period, the whole period is classified as a bad run period. In figure 5.2 such periods can be found as vertical lines like for example the three prominent periods in the first half of 2016. But also in 2015 there are several short bad periods, which can be seen more clearly in figure 5.4. In contrast to figure 5.2 it shows the overall count rate of all detectors. Due to the increased statistics a better time resolution is possible which makes the identification easier. All identified bad run periods are summarized in table A1 in the appendix.

Figure 5.4: Count rate for all detectors of the COBRA demonstrator within six weeks in 2015. The increase in rate is caused by the failure of the Nitrogen flushing. 66 5 Data partitioning

During a bad run period, the rate increases before it falls back on the baseline level. This happened several times in 2015. In figure 5.5 the humidity, which is measured on top of the Lead castle, is shown for comparison. Every time the humidity rises, the count rate rises also. The humidity is kept at a low level with the help of the Nitrogen flushing. Periods with higher rate can therefore be caused by a failure of the Nitrogen flushing.

Figure 5.5: Count rate for all detectors of the COBRA demonstrator within six months. The red curve shows the humidity on top of the Lead castle. The increase in the rate and the humidity are correlated and caused by the failure of the Nitrogen flushing.

A higher humidity leads to a worse detector performance. Additionally, the Nitrogen flushing should prevent the presence of normal air inside the setup, since it contains Radon gas. Radon is part of the natural decay chains of Thorium and Uranium, which are shown in figure 5.6. All daughters of Radon can cause potential background. The energy spectrum of all those bad run periods in figure 5.7 proves the assumption that the higher rate during these periods is caused by the decay of Radon. Besides some additional peaks in the spectrum of the bad run periods, the overall rate is increased by a factor of 5-10 above 350 keV. In the high energy region, peaks from α-decays of Polonium from the Uranium decay chain (214Po at 5.3 MeV, 218Po at 6.0 MeV and 214Po at 7.7 MeV) are clearly visible. Below 2 MeV, prominent γ-lines of the Radon decay chain are visible. For a better visibility the spectrum is shown in an energy region between 0.2 − 2 MeV in figure 5.8. Additionally, the MSE-spectrum is shown, where only events flagged as MSE are contained. This is helpful to identify γ-lines, since γ-particles in this energy region mainly interact via multiple Compton scattering to deposit their full energy, which results in MSEs. The arrows indicate the expected γ-lines from nuclides of the Radon decay chain. 5.2 Identification of background enriched data periods 67

Figure 5.6: Illustration of natural decay chains starting at 232Th (left) and 238U (right). Daughters of Radon can cause γ-lines within the physics spectrum when normal air is inside the setup. Pictures from [63].

Figure 5.7: Energy spectrum of the data set with bad run periods and for the data set without bad run periods. The rate of the bad run periods is by a factor of 5-10 higher than for good periods. Also some additional peaks, that can be identified as decay products of Radon, are visible. This leads to the assumption that these bad run periods are caused by a failure of the Nitrogen flushing and the resulting high humidity and Radon concentration inside the setup. 68 5 Data partitioning

Figure 5.8: Energy spectrum of bad run periods for all events and only for MSEs, where γ-lines are more clearly visible. The arrows indicate expected γ-lines from nuclides of the Radon decay.

5.2.3 Bad detector

In figure 5.9 a heat map illustration of the rate for all detectors and measuring dates is shown after the removal of bad run periods and hot pixels. Detectors with a higher rate for the whole data taking phase can now easily be identified. In table A1 in the appendix these detectors labeled as bad detectors are listed. Besides some isolated detectors of layer one, two and four, mainly layer three detectors have a higher rate compared to others. During the installation of this layer some construction works were ongoing, like the extension of the hole through the wall that acts as a cable feed-through. This probably caused a contamination of the detectors and holder structure with dust, that could not be removed entirely during the installation. The energy spectrum of the layer three detectors can help to find the precise contamination. In 5.10 this spectrum is compared to the spectrum without bad run periods and bad detectors. The rate for layer three detectors is anywhere higher than for the good data set. There are no γ-lines that can give a clear hint on the origin of this higher rate.

5.2.4 Fiducial volume

With eq. (3.23) the interaction depth of an event can be calculated, which enables for a depth dependent fiducial volume. The weighting potential near the anode is strongly distorted due to the grid bias, which affects the depth and energy reconstruction of near anode events. Events with z < 0.2 are already removed as a part of the data cleaning. Due to α-contaminations on the cathode surface from 190Pt and 210Po, the so called high z-cut of 0.2 < z < 0.97 is necessary. A further reduction of the remaining volume could be beneficial, since there is a 5.2 Identification of background enriched data periods 69

Figure 5.9: Count rate for all 64 detectors of the COBRA demonstrator between end of 2011 and fall 2016 for events in the energy region 350 keV≤ E ≤2800 keV after the removal of hot pixels and bad run periods. Only data cleaning cuts are applied. Detectors that have a higher rate during the whole data taking can now easily be identified. Mainly layer three detectors (detector 33-48) have a higher rate. region with higher rate for z > 0.7 (see figure 5.1). In figure 5.11 the spectrum of the depth region 0.2 < z < 0.7 and 0.7 < z < 0.97 are compared to each other. In an energy range between 350 − 4000 keV the rate of the high-z events is continuously higher than for low-z events. There are no γ-lines visible, which can be caused by contaminations with certain nuclides. The most likely explanation assumes contaminations on the detector holder. α and β-particle can already lose energy before they interact with the detector and cause events below 4 MeV. The optimal z-cut is therefore defined as 0.2 < z < 0.7, referred to as low z-cut. Events from the lateral surfaces can be identified with the LSE- or A/E-cut. Their identification is based on the slightly different weighting potential near the surfaces. These cuts are therefore not able to reject events in a specified x- or y-region as it can be defined for the z-dimension. 70 5 Data partitioning

Figure 5.10: Energy spectrum for layer three detectors compared to the data set without bad run periods and bad detectors. Since the rate for layer three detectors is higher than for other detectors, they have to be removed from the good data set. The spectrum gives no hint about the origin of this higher rate since no γ-lines pointing to certain nuclides are visible.

Figure 5.11: Energy spectrum for events in the depth region 0.7 < z < 0.97 and 0.2 < z < 0.7 scaled to the same mass. In the energy range of 350 − 4000 keV the rate of the high-z events is continuously higher than for low-z events. A likely reason for that are contaminations on the detector holder. 5.3 Results of the data partitioning and the A/E-cut 71

5.3 Results of the data partitioning and the A/E-cut

After the removal of all bad run periods and detectors, the energy spectrum of the good data set can be compared with the expected spectrum of the 2ν2β-decay of 116Cd. Additionally, the effect of the efficiency for the previous cut combination (z-cut, LSE, MSE) and the new approach (z-cut, A/E-cut) will be shown in the following. For the expected 2ν2β-spectrum, 6·106 decays were simulated with the COBRA simulation tool VENOM. It is based on GEANT4 (version 10.04.p02) [64] and uses the shielding physics list, which is recommended for low-background experiments. The initial kinematics of the decay are generated with Decay0. Decay0 contains the theoretical momentum distributions including the angular correlation of the involved leptons for most of the known double beta decay modes. It is based on [24]. Since the efficiency for a full energy detection is only depdending on the detector geometry, it is already included in the VENOM simulation. In contrast to this, detector effects such as the finite energy resolution have to be applied separately. The simulated 2ν2β-spectrum is folded with the average detector resolution function that is known from calibration measurements. For the 2ν2β-spectrum this is only a minor effect since it is a continuous distribution without characteristic peaks. Only the endpoint is slightly affected by the resolution smearing. With a half-life of 2.62 · 1019 from the Aurora experiment [1] and the number of 116Cd atoms per CdZnTe-mass (see eq. (1.2)), the simulated spectrum was scaled to cts/(kg·keV·yr). An additional scaling factor is necessary to take the cut efficiencies into account. Due to the hole contribution near the anode and the related overestimation of the depth in this region, the (z > 0.2)-cut is not as strong as 20%. Only 13% of the events are rejected. In the higher z-regions the excluded depth interval corresponds to the rejected event fraction due to the holes getting trapped and not contributing to the induced signals. With the high z-cut of 0.2 < z < 0.97, 16% of the events are rejected. With the low z-cut of 0.2 < z < 0.7, 43% of the events are rejected. The MSE- and A/E- cut have an efficiency of 90% while the LSE-cut only has 81%. The combined efficiencies are summarized in table 5.1.

Table 5.1: Combined cut efficiencies (signal acceptance) for the combination of z-, MSE- and LSE-cut and for z- and A/E-cut.

z+MSE+LSE z+A/E z < 0.97 61.2% 75.6% z < 0.7 41.6% 51.3%

The intrinsic detection efficiency is nearly 100% for COBRA. In comparison, the NEMO-3 experiment estimated a 1.8% signal acceptance efficiency for their 2ν2β-analysis of 116Cd [8]. The intrinsic detection efficiency is very small due to the particular setup configuration with thin source foils between sensitive detector elements. The Aurora experiment has also a nearly 100% intrinsic efficiency and an additional 98% signal acceptance after PSA and Bismuth- Polonium selection [1]. In figure 5.12 the energy spectrum before the data partitioning is shown. γ-lines from 214Pb at 352 keV and 214Bi at 609 keV and 1120 keV are clearly visible and originate from the Radon decay 72 5 Data partitioning chain. Additionally, the 511 keV line, 22Na at 1275 keV and 40K at 1461 keV are visible. The α-peak from 190Pt at 3175 keV can be removed from the spectrum with the standard z-cut. Due to the well-known spectral shape of the 2ν2β-spectrum of 116Cd, a small energy region is enough for a spectral fit in order to extract a half-life. The energy range of 1.5 MeV < E < 2.6 MeV is the most suitable region for this since no γ-lines are expected in the data set after the data partitioning. In table 5.2 the number of counts N in this energy region are summarized and compared with the number of events from the 2ν2β-simulation. N is calculated after the application of all cuts. With these two quantities, the signal-to-background ratio S/B can be calculated. In figure 5.13 the energy spectrum is shown after the data partitioning. In comparison to the full data set with 400 kg·d exposure, only 234 kg·d exposure is remaining. Since the bad run periods, where the Nitrogen flushing failed, are excluded, no more γ-lines from the Radon decay chain are visible. The 511 keV line as well as the γ-lines from 22Na and 40K are still there. The count rate is reduced with both cut combinations resulting in a signal-to-background ratio that is increased by nearly a factor of three. In figure 5.14 the high z-cut is replaced by the low z-cut of z < 0.7. The rate is again reduced and S/B ratio is increased by a factor of more than three compared to the high z-cut. Both cut combinations reach a signal-to-background ratio of 25.6%. Unfortunately, this does not allow for an analysis of the 2ν2β-spectrum of 116Cd since there are still more events than predicted by the simulation. The comparison of the new A/E-cut to the LSE- and MSE-cut shows no big improvement. With the high z-cut even a slightly lower signal-to-background ratio is reached. The A/E-cut seems to be not sensitive on LSEs with a large DIP value. With the low z-cut, the S/B ratio is the same for both cut combinations. For A/E the number of kept events is higher due to the better cut efficiency, which is a small improvement. If an A/E-cut value of 0.93 is used, the same efficiency as for the LSE- and MSE-cut is achieved. This allows for a direct comparison of both cut combinations. Only for the low z-cut the A/E-cut reject about 5% more events than the LSE- and MSE-cut. For the high z-cut less events are rejected. This again shows the bad sensitivity on LSEs, were further investigations are necessary to improve the A/E-cut.

Table 5.2: Number of events N in the energy region 1.5 MeV< E < 2.6 MeV of the physics spectrum after the applied cuts z+MSE+LSE or z+A/E in comparison to the simulated 2ν2β-spectrum of 116Cd after the data partitioning.

z+MSE+LSE z+A/E physics data simulation physics data simulation no data part. N [1/(kg·yr)] 11126 393 17142 485 z < 0.97 S/B 0.035 0.028 N [1/(kg·yr)] 4691 393 6091 485 z < 0.97 S/B 0.084 0.080 N [1/(kg·yr)] 1045 267 1283 329 z < 0.7 S/B 0.256 0.256 5.3 Results of the data partitioning and the A/E-cut 73

Figure 5.12: Energy spectra of the complete data set without data partitioning. In the upper plot the cut combination of z-, MSE- and LSE-cut is applied on the data. In the lower plot the z- and A/E-cut are used. For both the high z-cut of z < 0.97 is used. The simulated 2ν2β-spectrum of 116Cd is scaled to the corresponding cut efficiency (see table 5.1). 74 5 Data partitioning

Figure 5.13: Energy spectra of the complete data set after data partitioning. In the upper plot the cut combination of z-, MSE- and LSE-cut is applied on the data. In the lower plot the z- and A/E-cut are used. For both the high z-cut of z < 0.97 is used. The simulated 2ν2β-spectrum of 116Cd is scaled to the corresponding cut efficiency (see table 5.1). 5.3 Results of the data partitioning and the A/E-cut 75

Figure 5.14: Energy spectra of the complete data set after data partitioning. In the upper plot the cut combination of z-, MSE- and LSE-cut is applied on the data. In the lower plot the z- and A/E-cut are used. For both the low z-cut of z < 0.7 is used. The simulated 2ν2β-spectrum of 116Cd is scaled to the corresponding cut efficiency (see table 5.1).

6 Summary and outlook

In the course of this thesis improvements towards the measurement of the 2ν2β-spectrum of 116Cd could be achieved by exploring new background reduction techniques. A new event selection, referred to as A/E-cut, based on pulse shape analysis was implemented into the data processing routine. The A/E value is significantly lower for MSEs than for SSEs of the same energy, which allows for a good discrimination between signal-like and background-like events. 228Th calibration measurements were used to optimize the cut. The DEP of the 2614 keV γ-line contains a high fraction of SSEs due to the underlying event topology. By counting the number of peak entries, the cut efficiency can be obtained. All 64 detectors of the COBRA demonstrator show a slightly different A/E distribution, what would result in different cut values, if all detectors should achieve exactly 90% signal acceptance. In order to use the same cut value for all detectors, the A/E values were calibrated. With

(A/E)cut = 0.872 a signal acceptance of 90% can be achieved. The corresponding average background rejection is 65%. In comparison with the previous cut combination (MSE- and LSE-cut), the A/E-cut reaches the same signal-to-background ratio for the low z-cut in the 2ν2β-ROI (1.5 MeV < E < 2.6 MeV), but with an higher signal acceptance. For the low z-cut or without the removal of background enriched data periods, the A/E-cut reaches a slightly smaller signal-to-background ratio. The A/E-cut does not seem to be sensitive to LSEs with a large DIP value. In such a case the difference pulse falls below the baseline before its sharp rise to the final amplitude. The corresponding amplitude of the derivative is therefore not smaller resulting in an A/E value that is comparable with one from a central event. To also reject these events, the DIP criterion has to be combined with the A/E-cut. Since this would reduce the combined cut efficiency, the utility of this approach has to be investigated. As a second investigated background reduction technique, the complete data set was divided into a background enriched and a background reduced data set. Electronic disturbances can cause short intervals, where a detector measures a strongly increased rate by a factor of 100 or more. Such hot pixel events features likely a non-physical interaction depth or other non-physical properties. Data cleaning cuts should actually identify such events. Such survivors can therefore be used to improve these cuts. Short time periods with higher count rate of all detectors are mainly caused by an increased humidity and Radon concentration inside the setup due to a failed Nitrogen flushing. The energy spectrum of these periods shows γ-lines from the decay of nuclides of the Radon decay chain. Additionally, 21 detectors were excluded from the analysis because of their overall high rate. A possible explanation assumes localized contaminations on the detector surfaces and holders that need to be studied further. With the removal of all bad run periods and detectors the rate in the ROI could be decreased 78 6 Summary and outlook by a factor of 2.8. For this comparison, the high z-cut and the A/E-cut was used on both data sets (background reduced and background enriched). With the low z-cut the rate could be reduced further. Using the low z-cut increases the signal-to-background ratio by more than a factor of three compared to the high z-cut. The higher rate for the z > 0.7 region can also be caused by contaminations on the detector holder. All the information from the excluded data set can be use to develop a background model for the COBRA demonstrator. To make further improvements, the recently developed synchronization tool can be used to remove potentially more time coincident events. This tool could even enable a Bismuth-Polonium tagging due to the characteristic time signature of the decay chain. Background events caused by the Uranium and Thorium decay chains can so be removed more effectively. If all these improvement ideas and approaches would enables a 2ν2β-spectrum measurement with the COBRA demonstrator, can not be predicted. The latest preliminary results obtained with the new XDEM layer of the first 20 kg·d exposure are already promising. Due to the better volume-to-surface ratio of the larger detector crystals as well as through the guard ring that suppresses LSEs, the background level is lower then for the demonstrator making a 2ν2β-spectrum measurement possible. The obtained A/E-cut results can be adapted to the XDEM detectors with some adjustments regarding the quad grid readout anode in order to get an even better background reduction. 7 Bibliography

[1] F. A. Danevich et al., Journal of Physics: Conference Series 718, 062009 (2016).

[2] B. Povh et al., Particles and Nuclei, 7th ed., Springer Berlin Heidelberg (2015).

[3] H. Ejiri et al., Journal of the Physical Society of Japan 64, 339 (1995).

[4] F. A. Danevich et al., Physics Letters B 344, 72 (1995).

[5] R. Arnold et al., Zeitschrift f¨urPhysik C: Particles and Fields 72, 239 (1996).

[6] A. S. Barabash, Physical Review C 81, 10 (2010).

[7] F. A. Danevich et al., Physical Review C 68, 1562 (2003).

[8] R. Arnold et al., Phys. Rev. D 95, 170 (2017).

[9] F. A. Danevich et al., Physical Review C 62, 247 (2000).

[10] Y. Kudenko and V. Paolone, Nuclear and Particle Physics Proceedings 260, 167 (2015).

[11] J. J. Gomez-Cadenas et al., La Rivista Del Nuovo Cimento 2, (2012).

[12] E. Majorana, Il Nuovo Cimento 14, 171 (1937).

[13] K. Zuber, Neutrino physics, 2nd ed., Taylor and Francis (2012).

[14] R. N. Cahn et al., Proceedings, 2013 Community Summer Study on the Future of U.S. Particle Physics (2013).

[15] L. Bornschein et al., Fusion Science and Technology 71, 485 (2017).

[16] J. Lesgourgues and S. Pastor, Advances in High Energy Physics 2012, 1 (2012).

[17] F. Capozzi et al., Phys. Rev. D 95, 096014 (2017).

[18] Silvia Pascoli, Cern Courier 56, (2016).

[19] C. F. v. Weizs¨acker, Zeitschrift fr Physik 96, 431 (1935).

[20] H. V. Klapdor-Kleingrothaus and A. Staudt, Teilchenphysik ohne Beschleuniger, Vieweg+Teubner Verlag (1995).

[21] M. Goeppert-Mayer, Physical Review 48, 512 (1935). 80 7 Bibliography

[22] M. G. Inghram and J. H. Reynolds, Physical Review 78, 822 (1950).

[23] S. R. Elliott, A. A. Hahn, and M. K. Moe, Physical review letters 59, 2020 (1987).

[24] V. I. Tretyak and Y. Zdesenko, Atomic Data and Nuclear Data Tables 80, 83 (2002).

[25] A. P. Meshik, C. M. Hohenberg, O. V. Pravdivtseva, and Y. S. Kapusta, Physical Review C 64, 035205 (2001).

[26] Y. M. Gavrilyuk et al., Physical Review C 87, 035501 (2013).

[27] M. Wang et al., Chinese Physics C 41, 030003 (2017).

[28] A. S. Barabash, Nuclear Physics A 935, 52 (2015).

[29] A. S. Barabash, Talk at The 2nd International Conference on Particle Physics and Astro- physics, 10-14 October 2016, Moscow, Russia (2017).

[30] W. H. Furry, Physical Review 56, 1184 (1939).

[31] S. Dell’Oro, S. Marcocci, M. Viel, and F. Vissani, Advances in High Energy Physics 2016, 1 (2016).

[32]F. Simkovic,ˇ Nuclear Physics B - Proceedings Supplements 221, 260 (2011).

[33] G. Racah, Il Nuovo Cimento 14, 322 (1937).

[34] H. P¨asand W. Rodejohann, New Journal of Physics 17, 115010 (2015).

[35] J. Schechter and J. W. F. Valle, Phys. Rev. D 25, 2951 (1982).

[36] F. Boehm and P. Vogel, Physics of massive neutrinos, Cambridge University Press (1992).

[37] J. D. Vergados, H. Ejiri, and F. Simkovic,ˇ International Journal of Modern Physics E 25, 1630007 (2016).

[38] O. Cremonesi, Nuclear Physics B - Proceedings Supplements 118, 287 (2003).

[39] K. Zuber, Physics Letters B 519, 1 (2001).

[40] J. Meija et al., Pure and Applied Chemistry 88, 252 (2016).

[41] L. Bodenstein-Dresler et al., arXiv: 1806.02254v1 (2018).

[42] G. Bellini et al., Journal of Cosmology and Astroparticle Physics 2012, 015 (2012).

[43] https://www.lngs.infn.ut/en/shuttle, 30.07.2018 .

[44] J. A. Formaggio and C. J. Martoff, Annual Review of Nuclear and Particle Science 54, 361 (2004). 7 Bibliography 81

[45] J. Ebert et al., Nuclear Instruments and Methods in Physics Research Section A: Acceler- ators, Spectrometers, Detectors and Associated Equipment 807, 114 (2016).

[46] S. Zatschler, Diplomarbeit, TU Dresden (2014).

[47] G. Ari˜no-Estrada et al., Journal of Instrumentation 9, C12032 (2014).

[48] Z. He, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 463, 250 (2001).

[49] W. Shockley, Journal of Applied Physics 9, 635 (1938).

[50] S. Ramo, Proceedings of the IRE 27, 584 (1939).

[51] P. N. Luke, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 65, 2884 (1994).

[52] M. Fritts et al., Nuclear Instruments and Methods in Physics Research Section A: Accel- erators, Spectrometers, Detectors and Associated Equipment 708, 1 (2013).

[53] T. Wester, Diploma Thesis, TU Dresden (2012).

[54] M. Agostini et al., The European Physical Journal C 73, 2330 (2013).

[55] R. J. Cooper et al., Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 629, 303 (2011).

[56] XCOM: Photon Cross Sections Database, https://physics.nist.gov/PhysRefData/Xcom /html/xcom1.html, 27.11.2018 .

[57] ESTAR: stopping-power and range tables for electrons, https://physics.nist.gov /PhysRef- Data/Star/Text/ESTAR.html, 27.11.2018 .

[58] M. E. Noz, G. Q. Maguire Jr, and G. Q. Maguire, JR, Radiation Protection In The Health Sciences, World Scientific Publishing Company (2007).

[59] M. Fritts et al., Nuclear Instruments and Methods in Physics Research Section A: Accel- erators, Spectrometers, Detectors and Associated Equipment 749, 27 (2014).

[60] R. Brun and F. Rademakers, Nuclear Instruments and Methods in Physics Research Sec- tion A: Accelerators, Spectrometers, Detectors and Associated Equipment 389, 81 (1997).

[61] J. Ebert et al., Nuclear Instruments and Methods in Physics Research Section A: Acceler- ators, Spectrometers, Detectors and Associated Equipment 821, 109 (2016).

[62] J. Volkmer, Masterarbeit, TU Dresden (2018).

[63] https://en.wikipedia.org/wiki/Decay chain, 28.01.19 .

[64] J. Allison et al., Nuclear Instruments and Methods in Physics Research Section A: Accel- erators, Spectrometers, Detectors and Associated Equipment 835, 186 (2016).

Appendices

85

Table A1: Identified background enriched data periods according to the categories in section 5.2 between 2011-09-27 and 2016-09-27. The start and end time is given in Unix time and real time. Unix time real time detector 1373350000 - 1383831000 2013-07-09 08:06 - 2013-11-07 14:30 Layer 3 1373350000 - 1423422000 2013-07-09 08:06 - 2015-02-08 20:00 39 1385048328 - 1385084328 2013-11-21 16:38 - 2013-11-22 02:38 37 1385787566 - 1385859555 2013-11-30 05:59 - 2013-12-01 10:59 47 hot 1398510000 - 1400070000 2014-04-26 13:00 - 2014-05-14 14:20 59 pixel 1423820000 - 1461440000 2015-02-13 10:33 - 2016-04-23 21:33 3 1451898935 - 1455702588 2016-01-04 10:15 - 2016-02-17 10:49 62 1462910663 - 1465826265 2016-05-10 22:04 - 2016-06-13 15:57 60 1468301506 - 1468733495 2016-07-12 07:31 - 2016-07-17 07:31 5 1361287823 - 1361659831 2013-02-19 16:30 - 2013-02-23 23:50 1386490000 - 1386970000 2013-12-08 09:06 - 2013-12-13 22:26 1387790000 - 1390560000 2013-12-23 10:13 - 2014-01-24 11:40 1391948117 - 1392132830 2014-02-09 13:15 - 2014-02-11 16:33 1393402571 - 1393460265 2014-02-26 09:16 - 2014-02-27 01:17 1402076995 - 1402307475 2014-06-06 19:49 - 2014-06-09 11:51 1404487311 - 1404732194 2014-07-04 17:21 - 2014-07-07 13:23 1410157906 - 1410316390 2014-09-08 08:31 - 2014-09-10 04:33 1418217485 - 1418303967 2014-12-10 14:18 - 2014-12-11 14:19 1419031269 - 1419261752 2014-12-20 00:21 - 2014-12-22 16:22 1428237748 - 1428446229 2015-04-05 14:42 - 2015-04-08 00:37 1430654922 - 1430745723 2015-05-03 14:08 - 2015-05-04 15:22 1431423055 - 1431699833 2015-05-12 11:30 - 2015-05-15 16:23 1432371152 - 1432584994 2015-05-23 10:52 - 2015-05-25 22:16 1433303164 - 1433404044 2015-06-03 05:46 - 2015-06.04 09:47 1434048193 - 1434405676 2015-06-11 20:43 - 2015-06-16 00:01 bad 1435748355 - 1435935634 2015-07-01 12:59 - 2015-07-03 17:00 run 1436597955 - 1436864133 2015-07-11 08:59 - 2015-07-14 10:55 all periods 1437402478 - 1437748158 2015-07-20 16:27 - 2015-07-24 16:29 1438920732 - 1439233296 2015-08-07 06:12 - 2015-08-10 21:01 1440448630 - 1440563910 2015-08-24 22:37 - 2015-08-26 06:38 1441182888 - 1441398981 2015-09-02 10:34 - 2015-09-04 22:36 1441929422 - 1442015902 2015-09-11 01:57 - 2015-09-12 01:58 1442534222 - 1442764702 2015-09-18 01:57 - 2015-09-20 17:58 1443247354 - 1443463434 2015-09-26 08:02 - 2015-09-28 20:03 1443726867 - 1444058147 2015-10-01 21:14 - 2015-10-05 17:15 1445557094 - 1445614774 2015-10-23 01:38 - 2015-10-23 17:39 1446394080 - 1448007572 2015-11-01 17:08 - 2015-11-20 09:19 1448583816 - 1448627095 2015-11-27 01:23 - 2015-11-27 13:24 1449774946 - 1449832626 2015-12-10 20:15 - 2015-12-11 12:17 1450350946 - 1450465814 2015-12-17 12:15 - 2015-12-18 20:10 1450710534 - 1450802412 2015-12-21 16:08 - 2015-12-22 17:40 1451214534 - 1455702588 2015-12-27 12:08 - 2016-02-27 10:49 1457959078 - 1458333570 2016-03-14 13:37 - 2016-03-18 21:39 1460781084 - 1465826265 2016-04-16 06:31 - 2016-06-13 15:57 bad detec- 1, 4, 19, 25, 26, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 46, 48, 58, 60, 62, 63 tors

List of Figures

1.1 2ν2β half-lives of 116Cd measured with several experiments ...... 8

2.1 Scheme of the two possible neutrino mass orderings...... 11

2.2 Predicted two-sigma values of the effective neutrino Majorana mass mββ versus the lightest neutrino mass in the case of normal ordering and inverted ordering. . . . . 12 2.3 The leading-order Feynman diagrams for the β−-decay and the β+-decay...... 13 2.4 Nuclear masses for nuclei with A = 101 and A = 106 as a function of Z...... 14 2.5 Feynman diagrams of the 2ν2β−-decay and the 0ν2β−-decay...... 17 2.6 The 2ν2β-decay nuclear matrix elements extracted from the average and recom- mended half-life values...... 20 2.7 0ν2β-decay nuclear matrix elements calculated with the IBM-2, QRPA-T¨uand ISM models...... 22 2.8 Electron sum energy spectra for the 2ν2β and the 0ν2β-decay...... 23

3.1 Overview of the LNGS underground laboratory...... 29 3.2 Setup of the COBRA experiment at the LNGS...... 30 3.3 Demonstrator and XDEM detector layer...... 30 3.4 Overview of the main components of the DAQ chain and the experimental infras- tructure of the COBRA setup...... 32 3.5 Schematic drawing of the electrode configuration for coplanar grid detectors used by COBRA...... 35 3.6 Simulated weighting potentials for the CA and the NCA for a plane in the middle of the detector ...... 36

4.1 Typical pulse shape of a SSE...... 41 4.2 Pulse shapes for an event close to the lateral surface with an outlying CA strip, a central event and an event close to the lateral surface with an outlying NCA strip. 41 4.3 Typical pulse shape of a MSE and the corresponding derivative of the difference pulse. 42 4.4 CA, NCA and difference pulse as well as current pulse of a SSE and a MSE with nearly equal energy...... 44 4.5 228Th calibration spectrum with highlighted FEP, SEP and DEP...... 45 4.6 Schematic drawing of a SEP event and a DEP event...... 46 4.7 228Th calibration spectra for different A/E-cut values...... 48 4.8 Normalized sensitivity and efficiency for signal and background events in the DEP, SEP and FEP...... 50 88 List of Figures

4.9 Influence of the calculation method and the smoothing window size on the A/E distribution of DEP events...... 51 4.10 Average cut efficiencies for different A/E calculation methods and smoothing win- dow sizes...... 52 4.11 A/E distributions of DEP events for five different detectors...... 53

4.12 Distribution of the (A/E)90% and (A/E)opt cut values of all running detectors. . . 53 4.13 A/E distribution of DEP events with the fit function used by GERDA...... 54 4.14 A/E distribution of DEP events with a fit function using two EMG distributions. . 55 4.15 A/E distribution of DEP events with a two-sigma-Gaussian fit...... 56 4.16 A/E distribution of DEP events of detector 23 and 43 for two different smoothing window sizes...... 57 4.17 A/E distributions for five different detectors after the A/E calibration...... 58

4.18 Distribution of the (A/E)90% and (A/E)opt cut values of all running detectors after the A/E calibration...... 59 4.19 A/E calibration parameter for all calibration runs between 2014 and 2016 for de- tector 19 and detector 42...... 60

5.1 Prominent background contributions highlighted in an energy-depth plot...... 62 5.2 Count rate for all 64 detectors between end of 2011 and fall 2016 as a heat map. . 63 5.3 Interaction depth of events during a hot pixel time period of detector 60 and a corresponding pulse...... 65 5.4 Rate for all detectors within six weeks in 2015 with a failure of the Nitrogen flushing. 65 5.5 Rate for all detectors within six months with several failures of the Nitrogen flushing. 66 5.6 Illustration of natural decay chains starting at 232Th and 238U...... 67 5.7 Energy spectrum of the data set with bad run periods and for the data set without bad run periods...... 67 5.8 Energy spectrum of bad run periods for all events and only for MSEs, where γ-lines are highlighted...... 68 5.9 Count rate for all 64 detectors between end of 2011 and fall 2016 as a heat map after the removal of hot pixels and bad run periods...... 69 5.10 Energy spectrum for layer three detectors compared to the data set without bad run periods and bad detectors...... 70 5.11 Energy spectrum for events in the depth region 0.7 < z < 0.97 and 0.2 < z < 0.7. . 70 5.12 Energy spectra of the complete data set without data partitioning for the previous and the new cut combination...... 73 5.13 Energy spectra of the complete data set after data partitioning for the previous and the new cut combination...... 74 5.14 Energy spectra of the complete data set after data partitioning for the previous and the new cut combination with the low z-cut...... 75 List of Tables

2.1 Possible 2β−-nuclides and their Q-values...... 18 − 0ν 2.2 2β -nuclides with Q-values, average half-lives, best present limits on T1/2 and a selection of investigating experiments...... 18

3.1 2β-decay nuclides that are naturally abundant in CdZnTe...... 27 3.2 Properties of CdZnTe compared to other semiconductor materials...... 33

4.1 Sensitivity and efficiency for the A/E cut-values (A/E)90% = 0.75 and (A/E)opt = 0.78 in different energy regions (DEP, SEP and FEP)...... 50

5.1 Combined cut efficiencies (signal acceptance) for the combination of z-, MSE- and LSE-cut and for z- and A/E-cut...... 71 5.2 Number of events N in the energy region 1.5 MeV< E < 2.6 MeV of the physics spec- trum after the applied cuts z+MSE+LSE or z+A/E in comparison to the simulated 2ν2β-spectrum of 116Cd...... 72

A1 Identified background enriched data periods between 2011-09-27 and 2016-09-27. . . 85

List of Acronyms

0ν2β neutrinoless double beta decay 2ν2β two neutrino double beta decay COBRA Cadmium-Zinc-Telluride 0-neutrino double-beta research apparatus BCS Bardeen–Cooper–Schrieffer BI background index Borexino Boron solar neutrino experiment BV bias voltage CA collecting anode

CANDLES CaF2 for studies of neutrino and dark matters by low energy spectrometer CdZnTe Cadmium-Zinc-Telluride CERN Conseil Europ´eenpour la recherche nucl´eaire CKM Cabibbo-Kobayashi-Maskawa CP charge conjugation parity CPG coplanar grid CSDA continuous slowing down approximation CUORE cryogenic underground observatory for rare events DAQ data acquisition DEP double escape peak EC electron capture EMG exponentially modified Gaussian EMI electromagnetic interference ERT early rise time EXO enriched Xenon experiment FADC flash analog to digital converter FEP full energy peak FWHM full width at half maximum GB grid bias GEANT4 geometry and tracking GERDA Germanium detector array IBM interacting boson model ISM interacting shell model KamLAND-Zen Kamioka liquid scintillator antineutrino detector – zero neutrino KATRIN Karlsruhe Tritium neutrino experiment LNGS laboratori nazionali del Gran Sasso LSE lateral surface event LUNA laboratory for underground nuclear astrophysics ManTiCORE multiple-analysis toolkit for the COBRA experiment MSE multi-site event MWA moving window average NCA non-collecting anode NEMO neutrino Ettore Majorana observatory NME nuclear matrix element PMNS Pontecorvo-Maki-Nakagawa-Sakata POM Polyoxymethylene PSA puse shape analysis QRPA quasiparticle random phase approximation RMS root mean square ROI region of interest ROOT an object-orientated data analysis framework, developed at CERN SEP single escape peak SSE single-site event SUSY supersymmetry TPC time projection chamber UPS uninterruptible power supply VENOM vicious evil network of Mayhem XDEM extended demonstrator Erkl¨arung

Hiermit erkl¨areich, dass ich diese Arbeit im Rahmen der Betreuung am Institut f¨urKern- und Teilchenphysik ohne unzul¨assigeHilfe Dritter verfasst und alle Quellen als solche gekennzeichnet habe.

Julia K¨uttler Dresden, M¨arz2019

Danksagung

Ein besonderer Dank gilt Prof. Dr. Kai Zuber, der es mir erm¨oglicht hat, sowohl meine Bachelor- als auch Masterarbeit in der Neutrinophysikgruppe am IKTP anzufertigen. Die Einblicke in die vielf¨altigenForschungsbereiche und die M¨oglichkeit das LNGS zu besuchen waren sehr faszinierend und lehrreich. Prof. Dr. Arno Straessner m¨ochte ich f¨urdie Begutachtung meiner Masterabeit danken. Des weiteren m¨ochte ich mich bei allen Mitgliedern der Neutrinogruppe bedanken: F¨urdie unterhaltsamen Gespr¨ache w¨ahrenddes Mittagsessens, den Tipps und Anregungen f¨urmeine Arbeit, sowie f¨urdie gute Arbeitsatmosph¨are. Ein großer Dank gilt meinem Betreuer Stefan, der mir immer mit Rat und Tat f¨urdas gelingen meiner Masterarbeit zur Seite stand. Zu guter letzt m¨ochte ich mich bei meiner Familie und meinen Freunden f¨urdie Unterst¨utzung w¨ahrenddes gesamten Studiums bedanken. Besonders danke ich dabei meinem Mann Thomas, der mich immer bei all meinen Vorhaben unterst¨utzthat.