study of the cherenkov signal in teo bolometers: towards ... 0 dbd could occur without implying a...

Universita degli Studi dell’Aquila

Facolta di scienze Matematiche, Fisiche eNaturali

Dottorato di Ricerca in Fisica, XXVII Ciclo

Study of the Cherenkov signal in TeO2

bolometers: towards next-generationneutrinoless double beta decay

experiments

SSD FIS/04

Dottorando

Nicola Casali

Coordinatore Scuola diDottorato:Prof. Michele NardoneTutor:Prof. Luigi Pilo

Relatore:Dr. Marco Vignati

Relatore Interno:Prof. Sergio Petrera

A.A. 2014 / 2015

Contents

1 Hints of new physics in neutrino field 9

1.1 The Standard Model Neutrino . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2 The Neutrino oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2.1 The Neutrino beyond Standard Model . . . . . . . . . . . . . . . . 11

1.2.2 Unsolved problems in neutrino physics . . . . . . . . . . . . . . . . 12

1.3 The Majorana Neutrino . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.4 Double Beta Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.4.1 Double Beta Decay with neutrinos . . . . . . . . . . . . . . . . . . 17

1.4.2 Double Beta Decay without neutrinos . . . . . . . . . . . . . . . . 19

1.5 The Experimental Search for the 0νDBD . . . . . . . . . . . . . . . . . . 22

1.6 Two different approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.6.1 Source≡Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.6.2 Source 6=Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2 The Bolometric Technique 29

2.1 TeO2 Bolometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.1.1 The absorber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.1.2 The resolution: the most important bolometric performance . . . . 30

2.1.3 The TeO2 choise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.1.4 The sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.1.5 Detector operation . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2 CUORICINO: the first large bolometric array . . . . . . . . . . . . . . . . 35

2.2.1 CUORICINO α background . . . . . . . . . . . . . . . . . . . . . . 36

2.3 Cuore-0: the α background reduction . . . . . . . . . . . . . . . . . . . . . 37

2.4 CUORE projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.5 An Inverted Hierarchy Explorer . . . . . . . . . . . . . . . . . . . . . . . . 41

2.6 The Cherenkov effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.6.1 The Cherenkov effect in TeO2 crystal . . . . . . . . . . . . . . . . 45

2.6.2 Light trapping and surface effects of the crystal . . . . . . . . . . . 48

2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3

4 Contents

3 Litrani: a general purpose Monte Carlo program simulating light prop-agation in isotropic or anisotropic media 51

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.2 Optical Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.2.1 Revetment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.3 Volume detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.4 Surface detector: photomultiplier . . . . . . . . . . . . . . . . . . . . . . . 53

3.5 Particles, gammas and optical photons sources . . . . . . . . . . . . . . . 53

3.6 Monte Carlo Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4 The Cherenkov emission of TeO2 crystal at room temperature 55

4.1 Study of the Cherenkov emission with cosmic muons . . . . . . . . . . . . 55

4.1.1 Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.1.2 Light Yield components . . . . . . . . . . . . . . . . . . . . . . . . 56

4.1.3 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.1.4 Results from the angular scan . . . . . . . . . . . . . . . . . . . . . 58

4.1.5 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . 60

4.2 Absolute light yield measurement with 22Na . . . . . . . . . . . . . . . . . 63

4.2.1 Calibration of the photo-multipliers . . . . . . . . . . . . . . . . . 63

4.2.2 Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.2.3 Light yield measurement result . . . . . . . . . . . . . . . . . . . . 66

4.2.4 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . 68

4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5 The Cherenkov emission of the TeO2 bolometers 73

5.1 Low temperature light detector . . . . . . . . . . . . . . . . . . . . . . . . 73

5.2 Cherenkov light measurement with Germanium light detector . . . . . . . 74

5.2.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.2.2 First level data analysis . . . . . . . . . . . . . . . . . . . . . . . . 75

5.2.3 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.2.4 The synchronization algorithm . . . . . . . . . . . . . . . . . . . . 78

5.2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.2.6 Light Yield optimization . . . . . . . . . . . . . . . . . . . . . . . . 81

5.3 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.3.1 Monte Carlo approximations and cross-checks . . . . . . . . . . . . 85

5.4 Study of the Monte Carlo output . . . . . . . . . . . . . . . . . . . . . . . 87

5.5 Light collection optimization exploiting the Monte Carlo output . . . . . . 88

5.5.1 Surface roughness and light emission from Cuore crystal . . . . . . 89

5.5.2 Increasing the light collection efficiency . . . . . . . . . . . . . . . 90

5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Contents 5

6 High sensitive light detector 936.1 Transition Edge Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 936.2 Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 946.3 First level data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 966.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 966.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7 Conclusions and perspectives 997.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997.2 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

6 Contents

Introduction

The elementary particle physics has recently obtained an extraordinary experimentalvalidation of the theoretical model built in the last one hundred years, known as theThe Standard Model of particle physics (SM). The prediction and the observation of theHiggs boson at the Large Hadron Collider (LHC) is the end point of a theoretical modeland experimental research program that is able to explain and reproduce all the (known)elementary particles interaction; an impressive demonstration of the human capabilityto understand the Nature.

Despite these huge progresses a large number of questions still remain unanswered:the nature of Dark Energy (DE), Dark Matter (DM) and Neutrino (ν), which constituteour universe for about 95.3% is, to date, covered by a thick of mystery.Concerning the neutrino, it has always been source of surprises for the physicist com-munity, starting from its theorization from the evidence that it is a massive particle.This last result cannot be easily explained by the SM, and suggests the existence of newphysics beyond the Standard model.The most consolidated model to explain the neutrino mass is the so called see-saw modelthat can be realized if neutrino is a Majorana particle.

The most sensitive process that can confirm the Majorana nature of neutrino is arare nuclear transition named Neutrinoless Double Beta Decay, that eventually can seta value for its absolute mass scale. None of the past experiments was able to provide aconvincing evidence of the 0νDBD, therefore only lower limits on its half-life (of the orderof 1025 years) were set. The search for such a rare transition with an enhanced sensitivity,requires the development of large mass experiments with essentially zero-background inthe energy region of decay. The most sensitive experiment that will search for the0νDBD of 130Te will be the CUORE experiment, exploiting an array composed by 988TeO2 bolometer for a total detector mass of about 1 ton. Despite the effort exploitedby the CUORE collaboration in the last 10 years to reduce all background components,the CUORE experiment will be likely affected by an α background which will limit itssensitivity.

This Ph.D thesis is devoted to demonstrate that the α background of bolometricexperiment based on the TeO2 crystal can be rejected tagging the Cherenkov radiationproduced only by electrons and not by αs. For this purpose, I performed and analyzedseveral light yield measurements on TeO2 crystals that will be presented and discussedin this thesis.

After a brief overview of the scenario in which CUORE and this Ph.D thesis wereborn (chapter 1), I will explain the working principles of bolometers and analize thepast, present and future experiments composed by TeO2 bolometer arrays (chapter 2).

7

8 Contents

In chapter 2 the expected Cherenkov signal produced by the charged particle interactionswithin TeO2 crystal will be presented. In chapter 3 I will give a brief overview of theMonte Carlo used to simulate the optical photons propagation in the several experimentalset-up used to study the light yield of the TeO2 crystal. These measurements will beexplained and analyzed in chapter 4 and 5 and compared with the Monte Carlo output.In chapter 5 an optimization of the experimental set-up used to measure the light yieldof the CUORE TeO2 crystal will be presented, based on the results of a simulation.In chapter 6 a further measurement performed in collaboration with the Max PlanckInstitute exploiting the TES technology will be presented. Finally, in chapter 7 I willdiscuss the conclusion and perspectives concerning this Ph.D work.

Chapter 1

Hints of new physics in neutrinofield

When the existence of neutrino was theorized by Pauli, Pauli itself was worried thisneutral and massless particle would never been observed.On the contrary, three different families of neutrinos were detected and discovered inthe last 80 years. Moreover the neutrino flavour oscillation measured during the last 15years proves that this particle is not massless, opening the door to new physics beyondthe Standard Model.

Despite these giant progresses in the neutrino field, many fundamental questions stillremain unanswered: its nature, the absolute mass value and the mass hierarchy.The easiest experimental method to approach these problems involves a rare nuclearprocess, the so-called neutrinoless double beta decay (0νDBD).

The detection of 0νDBD would demonstrate the Majorana nature of neutrinos and,thanks to the measurement of the process half-life, could give indications about theabsolute value of their mass and about their mass hierarchy. Recent theories state that0νDBD could occur without implying a Majorana component of neutrinos, providedthat other (more exotic) scenarios are considered. Despite the theoretical reason at thebasis of the process, it is clear that its detection would pave the way for new physics.For this reason, the study of 0νDBD is still among the priorities in the particle physicsresearch field.

In this chapter a brief review of the neutrino properties will be reported in order tointroduce the study of the neutrinoless double beta decay.

1.1 The Standard Model Neutrino

In 1914 James Chadwick in his study of the β decay pointed out that the electronsemitted by the nuclei had a continuous energy spectrum. Since the electron and thedaughter nucleus were the only visible decay products, this reaction was considered atwo-bodies decay; in that case the energies of the final states are fixed by the energyconservation law and the electron energy spectrum was expected to be monoenergetic. Inorder to protect this fundamental Nature’s law, Pauli in 1930 introduced a new neutralparticle (massless with spin 1/2) as further decay product. Afterwards, in his study ofthe β decay Fermi named this particle neutrino [1] to distinguish it from the neutron

9

10 Chapter 1. Hints of new physics in neutrino field

that had been discovered in the same period by Chadwick. The β decay was recognizedas a three bodies reaction, recovering the energy conservation law:

n→ p+ e− + νe

The first experimental evidence for the existence of the neutrino came from Cowan eReines in 1956 [2]. They observed the reactions induced by anti-neutrinos on protons:

p+ νe → n+ e+

In 1957 Goldhaber made a clever experiment able to measure its helicity [3] (definedas h = ~σ·~p

|~p| , where ~σ and ~p are the neutrino spin and momentum, respectively). Theexistence of two other neutrino families, νµ and ντ , was discovered respectively atBrookhaven National Laboratory in 1957 [4] and at Fermilab in 2001 [5].The measurements performed at the electron-positron collider LEP at CERN showedthat there are only 3 active light neutrino families [6].

According to the Standard Model of particle physics, each one of these massless neu-trinos is paired with a charged lepton in a weak iso-doublet: for electron and electronicneutrino:

ψ =

(νee

)(an identical weak iso-doublet can be written for muon and tau leptons). Each weakiso-doublet can be described as the sum of two components with positive and negative

chirality (the right-handed and left-handed projection operators are PR;L = 1±γ52 ):

ψ = ψL + ψR =

((νe)LeL

)+

((νe)ReR

).

The field (νe)R is never observed in the weak interactions and for this reason it is notincluded in the electroweak field theory. Leptons are described only by the left-handeddoublet and right-handed singlet:

lL =

((νe)LeL

)Y=−1

; (eR)Y=−2

where Y is the weak hyper-charge (the same representation is applied to the muonand tau leptons). It is possible to summarize all the properties of the standard modelneutrinos with the following table:

Flavor Mass Spin Helicity Chirality

νe νµ ντ 0 -1/2 -1 -1νe νµ ντ 0 +1/2 +1 +1

Table 1.1: Standard model neutrinos.

The existence of the (νe)R field is an open issue, it can be not existent at all, or be onlysensitive to an interaction more weak than the electroweak one, for example the gravity;anyhow it’s not taken into account in the SM.

1.2. The Neutrino oscillation 11

1.2 The Neutrino oscillation

Despite the success of SM in the description (and prediction) of all known neutrinos weakinteractions, an effect measured for the first time by Raymond Davis wasn’t explainedfor a long time. This effect is known as the Solar neutrino problem.

In order to test the Standard Solar Model (SSM), Davis performed an experimentin the Homestake mine using a radiochemical detector from 1967 until 1994. The ex-periment was based on the reaction νe +37 Cl → e− +37 Ar, induced by solar νe. Davisfound out that only one third of the neutrinos expected from model predictions weredetected [7] but, since the neutrino flux strongly depends on parameters that can not beeasily measured (like the internal temperature of the Sun), this result was not consideredas so remarkable.

Unexpectedly, the deficit in the solar ν flux measured by Davis was confirmed afew years later by other experiments like SAGE and GALLEX that, using 71Ga insteadof 37Cl, could achieve a much lower energy threshold with respect to the Homestakedetector [8, 9, 10].

The Solar neutrino problem was solved in 2001 by SNO, which was sensitive toall neutrino interactions: charged current interactions, neutral current interactions andelastic scattering [11, 12]. In this way, it was possible to access the total neutrino flux,which was found to be compatible with the SSM expectations. Moreover, the simulta-neous measurement of the νe flux component demonstrated that the deficit was due tothe oscillation of electron neutrinos in other neutrino flavors, that could not be detectedby previous experiments. This oscillation phenomenon was completely unexpected andhad not explanation in the SM.

1.2.1 The Neutrino beyond Standard Model

Flavor oscillations can occur only if neutrinos are massive particles and if there is adifference between flavor eigenstates and mass eigenstates, i.e., a difference betweenstates that take part in the weak interactions and states that determine the particlepropagation.

The easiest way to describe neutrino oscillations is to relate the three flavor eigen-states |να〉 where α = e, µ, τ with three mass eigenstates |νi〉, i = 1, 2, 3, by introduc-ing an unitary 3×3 mixing matrix U, known as the Pontecorvo-Maki-Nakagawa-Sakata(PMNS) matrix:

|να〉 =∑i

U∗αi |νi〉

The most common parametrization for the PMNS matrix involves three Euler angles(θ12, θ23 and θ13) and three phases [13]:

U =

c12c13 s12c13 s13e−iδ

−s12c23 − c12s23s13eiδ c12c23 − s12s23s13eiδ s23c13

s12s23 − c12s23s13eiδ −c12s23 − s12c23s13eiδ c23c13

·1 0 0

0 eiα21/2 0

0 0 eiα31/2


where sij and cij refer to sin(θij) and cos(θij), δ is a CP violating phase, and α21,31

are two Majorana phases that are observables only if neutrinos have a Majorana masscomponent.

The discovery of neutrino oscillations implies that the off-diagonal elements of thePMNS matrix are non-vanishing. This means that a neutrino produced in a given flavoreigenstate |να〉 can be detected in a different one |νβ〉 with a probability:

P (|να〉 → |νβ〉) = | 〈νβ|να〉 |2 =3∑j=1

∣∣∣∣U∗αjUβje−im2jL

2E

∣∣∣∣2 (1.1)

where E is the energy of the neutrino and L is the travel length, which for relativisticparticles coincides with the time elapsed from the production to the detection.

In the simple approximation of two-neutrino oscillations, the above formula can besimplified as follows:

P (|να〉 → |νβ〉) = sin2(2θ)sin2(

1.27× ∆m2

[eV 2]

L

[m]

[MeV ]

E

)(1.2)

According to equation 1.2, the oscillation probability is maximal for large mixing angles(θ = π/4) and vanishes for θ = 0. In addition, it depends on the difference between thesquared masses of the two neutrinos, ∆m2 = m2

1 −m22. In the hypothesis of mass-less

neutrinos, or neutrinos with the same mass, oscillations could not occur.The study of solar neutrino oscillations provided a measurement for the so-called solar

mixing angle (θ12) and solar mass-squared difference (∆m212); later on, a measurement

of the same parameter was carried on by the KamLAND experiment, that studied theflux of electron antineutrinos produced by nuclear reactors [14, 15]. The KamLANDresults were source of great interest because they showed for the first time the neutrinosurvival probability as a function of L/E.

The phenomenon of oscillation was observed also for atmospheric neutrinos, i.e. neu-trinos produced by cosmic rays interactions in the atmosphere. This study was performedby the SuperKamiokande detector, that found a large asymmetry between neutrinos pro-duced in the upper atmosphere and neutrinos that, after being produced on the otherside of the Earth, had to travel across the planet before reaching the detector [16]. Thisbehavior, lead to the measurement of a second mixing angle (θ23) and mass-squareddifference (∆m2

23).The third mixing angle (θ13) was recently measured by the accelerator experiment

T2K [17], as well as reactor experiments Daya-Bay [18], Reno [19] and Double-CHOOZ [20,21]. In Ref. [22] the data coming from solar, atmospheric, accelerator and reactor ex-periments are global fitted, and the values of the oscillation parameters are summarizedin Table 1.2.

1.2.2 Unsolved problems in neutrino physics

The study of the neutrino oscillation allowed to improve considerably our knowledge ofneutrino properties, nevertheless some important aspects about neutrino physics are still

1.2. The Neutrino oscillation 13

Parameter Best Fit 1 σ range

∆m212/10−5 eV2 (NH or IH) 7.54 7.32 - 7.80

∆m223/10−3 eV2 (NH) 2.43 2.33 - 2.49

∆m223/10−3 eV2 (IH) 2.42 2.31 - 2.49

sin2(θ12)/10−1 (NH or IH) 3.07 2.91 - 3.25

sin2(θ23)/10−1 (NH) 3.86 3.65 - 4.10

sin2(θ23)/10−1 (IH) 3.92 3.70 - 4.31

sin2(θ13)/10−2 (NH) 2.41 2.16 - 2.63

sin2(θ13)/10−2 (IH) 2.44 2.19 - 2.67

δ/π (NH) 1.08 0.78 - 1.36

δ/π (IH) 1.09 0.83 - 1.47

Table 1.2: Mass-mixing parameters resulting from the global 3ν oscillation analysis reportedin [22]. The scenarios of normal hierarchy (NH) and inverse hierarchy (IH) are treated separately(see next section).

unsolved.The first one is the neutrino mass hierarchy: it is not possible to know from the datacollected up to now if m1 is heavier or lighter than m3. Two possible scenarios, whichare sketched in Figure 1.1, have to be considered:

• In the first one, the so called “normal hierarchy”, the mass eigenstate (m3) is muchheavier with respect to the closely-spaced mass states m1 and m2.

• In the “inverted hierarchy” scenario, on the contrary, m3 is the lightest state andlies well below m1 and m2.

A last possibility must be taken into account: if the absolute value of the smaller neutrinomass is larger with respect to ∆m2

23 (atmospheric mass splitting), all the mass eigenstatesare almost degenerate, despite of their hierarchy.

The mass hierarchy problem could be solved by exploiting the Mikheyev-Smirnov-Wolfenstein (MSW) mechanism, i.e., the effect of transformation of one neutrino flavorinto another one when traveling across a medium with varying density. This matter-enhanced mixing, that affects the sign of the mass difference, is due to the fact thatin normal matter there is a larger density of e−, but not of µ or τ . The study of theMSW effect in solar neutrinos allowed to determine the sign of ∆m2

12, thus resolvingthe mass hierarchy between m1 and m2. The recent measurement of a non vanishingθ13 opened the doors for the study of matter effects also on the Earth, exploiting theenhancement (suppression) of νe appearance in the case of normal (inverted) hierarchy.Unfortunately, this kind of effect is expected to be very small for running acceleratorexperiments, like T2K, due to their short baseline (less then 300 km). For this reason,next generation experiments are in construction phase (like for example NOνA, with abaseline of 810 km) or under feasibility studies.

The second open question concerns the absolute mass scale of neutrinos, that cannotbe probed by oscillations experiments. This issue can be addressed via cosmological


ν3

∆m2

23

ν1

ν2

∆m2

12

??

νµ ντ

eν ντνµ

eν νµ ντ

(a) normal hierarchy

ν1

ν2

∆m2

12

∆m2

23

ν3

??

eν ντνµ

eν νµ ντ

νµ ντ

(b) inverted hierarchy

Figure 1.1: Two possible neutrino mass hierarchies. The contribution of each flavor (e, µ, τ) tothe mass eigenstate is represented by the colored band.

observations or beta decay measurements. Cosmological observations are sensitive tothe sum of the neutrino masses:

mcosmological =∑

mν (1.3)

A conservative upper limit of mcosmological < 0.58 eV at 95% C.L. can be obtainedcombining the most recent data of WMAP with measurement of the distribution ofgalaxies and of the Hubble constant [23]. However, this limit is strongly dependent onthe cosmological model and parameters that were used for the analysis.An accurate measurement of the β decay spectrum could provide the absolute value ofthe electron neutrino mass, which is responsible for the distortion of the energy spectrumin the region of the β endpoint.The quantity that can be measured by experiments devoted to β decay studies is:

mβ =∑|Uei|2mi (1.4)

The most stringent limit on mβ, given by the combination of the Troitsk and Mainzexperiments on the decay of Tritium, is mβ < 2 eV at 95% C.L. [24]. Next generationexperiments, that are extensively reviewed in [25], will investigate the kinematics of β-decaying isotopes (3H, 187Re and 163Ho) using different technological approaches, in theattempt to improve the sensitivity on mβ of one order of magnitude.

Very stringent limits on neutrino masses and on its mass hierarchy could be obtainedmeasuring the 0νDBD half-life. It should be pointed out, however, that these results arevalid only if neutrinos have a Majorana mass component.

1.3. The Majorana Neutrino 15

Indeed, the last important open question concerns the nature of neutrino: the exten-sions of the SM that were proposed to account for a neutrino mass require a discussionon the intrinsic nature of this particle and on the mechanism that introduces its mass.In the next section, a simplified theoretical discussion on these topics is reported.

1.3 The Majorana Neutrino

The experimental evidences about neutrinos oscillation confirmed that they are massiveparticles. In the SM the masses of the charged leptons are originated by the spontaneoussymmetry breaking produced by the Higgs field. In principle it is possible to assign aDirac mass term also to the neutrino using the same procedure adopted for the chargedleptons; the only problem of this theoretical approach is that a Dirac mass term of theorder of 1 eV (more or less the current limit on the absolute neutrino mass) would requirea Yukawa coupling of the order of ≤ 10−12, which seems unlikely.

An alternative way to introduce the neutrino mass is exploiting the Majorana the-ory [26]: he realized that in the specific case of neutral particles, particle and antiparticleare identical because one cannot distinguish them by any kind of charge:

ψ = ψC (1.5)

whereψC = Cψ (1.6)

and C is the charge-conjugation transformation. More precisely the two neutrinos thatpartecipate to the weak interaction, νL and νR, can be considered as two differents chi-rality states of the same particle, the Majorana neutrino (νM ). However, if the neutrinosare Majorana then they violate the conservation of lepton number, a phenomenon thathas never been experimentally observed.

In this scenario, the neutrino mass could be accommodated in a simple way by meansof the so called see-saw mechanism [27]. This mechanism can be realized in severaldifferent ways; the simplest one is the type I see-saw mechanism with two independentMajorana neutrinos, a left-handed one and a right-handed one. The most general massterm in the lagrangian density can be written as sum of Dirac and Majorana mass terms:

L = LD + LML + LMR (1.7)

that is

L = −mDνRνL −1

2mLν

CL νL −

1

2mRν

CRνR + H.C. (1.8)

Writing the neutrino fields as two-dimensional spinors, the following mass matrix canbe obtained

L = −1

2

(νCL νR

)( mL mD

mD mR

)(νLνCR

)+ H.C.

which for mD = 0 is a pure Majorana lagrangian and for mL = mR = 0 and real mD

represents the Dirac case. The mass term mL is forbidden by the SM because it is not


an invariant under SU(2)L ⊗ U(1)Y transformations, the mass matrix becomes(0 mD

mD mR

)Since the mass of νL and νCR is not defined, one has to introduce two mass eigenstates,νm and νM (with eigenvalues m and M respectively) and a mixing matrix U such that:(

νLνCR

)= U ·

(νmνM

)and UTV U =

(m 00 M

)The resulting lagrangian density will be:

L = −1

2

(mνCmνm +MνCMνM

)+ H.C. (1.9)

In other words, the Lagrangian describing massive neutrinos (Eq. 1.3) has resulted intwo Majorana neutrinos. The mass term mR has no constraint in the SM and can be in amuch larger mass scale with respect to the one of the electroweak interaction. Assuminginstead a neutrino Yukawa coupling of the order of the charged fermion coupling, mD

lies in the same mass range of the other charged leptons. In the hypothesis mD mR,the first one of the two neutrinos has a small mass m ' m2

D/mR and a predominantlynegative chirality (the neutrino that partecipates to the weak intaractions). The secondone has a large mass M ' mR and predominantly positive chirality.

It is common to refer to this field with the name sterile neutrino, as it does not couplewith the neutral current as the active one. A heavy sterile neutrino corresponds to alight active one (and vice-versa), explaining why the mass of active neutrinos has sucha small value. As a final remark, it should be pointed out that the reason why the see-saw mechanism is so appealing, does not reside only in the possibility to explain smallneutrino masses. For example, the existence of heavy Majorana neutrinos that havedifferent decay rates in lepton and anti-lepton could have interesting applications in thebranch of physics that tries to explain the baryon asymmetry through the leptogenesis,as explained in [28, 29].

In the last decades, a large number of processes that can probe the Majorana natureof neutrino have been proposed. The most sensitive is by far the neutrinoless doublebeta decay that will be widely discussed in the next section.

1.4 Double Beta Decay

The Double Beta Decay (DBD) is a transition among isobaric isotopes in which thenuclear charge Z changes by two units. It can occur through the following modes:

(A,Z)→ (A,Z + 2) + 2e− + 2ve (β−β−)

(A,Z)→ (A,Z − 2) + 2e+ + 2ve (β+β+)

(A,Z) + 2e− → (A,Z − 2) + 2ve (EC − EC)

(A,Z) + e− → (A,Z − 2) + e+ + 2ve (EC − β+)

1.4. Double Beta Decay 17

but, since the β−β− decay provides the largest experimental sensitivity, the attentionwill be focused on this process.

1.4.1 Double Beta Decay with neutrinos

The Double Beta Decay with two neutrinos emission (2νDBD) is a Standard Modelallowed decay and it does not violate the total lepton number. Predicted by MariaGoeppert-Mayer in 1935 [30], it was observed for the first time in 1987. This transition,indeed, is extremely suppressed with respect to the single beta decay: typical half-livesare of the order of 1018 ÷ 1021 years, which are among the longest observed in Nature.

In order to detect such a rare transition, only emitters for which the single betadecay is forbidden are under study. The existence of this kind of isotopes is due to thepairing energy term (δp) visible in the the semi-empirical mass formula (evaluated partlyon liquid drop model of nucleus and partly on empirical measurements):

Ebinding = c1A− c2A2/3 − c3(A/2− Z)2

A− 3

5

e2Z(Z − 1)

4πε0A1/3+ δp (1.10)

where A is the total number of nucleons, Z the number of protons and ci are coefficientsthat can be extrapolated by measurements of the nuclei masses. The pairing energy canbe empirically parametrized as:

δp =

−ap ·A−1/2 A even - Z even nuclei0 A odd nuclei

+ap ·A−1/2 A even - Z odd nuclei

with ap ≈ 12 MeV. This means that the pairing energy vanishes for odd A, resulting ina single parabola, while for even A two parabola separated by 2δp appear (Figure 1.2).The isotopes characterized by an even number of nucleons are then the only candidatesfor DBD searches, as for them the beta decay is energetically forbidden.

The half-life of the process is given by the following equation:

1

T 2ν1/2

= G2ν(Q,Z)∣∣M2ν

∣∣2 (1.11)

where G2ν is a phase-space factor, which depends on the Q-value of the decay and onthe charge of the final state nucleus and M2ν is the nuclear matrix element (NME),containing all the nuclear structure effects. As explained in the next section, severalmethods based on different approximations have been developed for the calculation ofthe NME. However, these methods are characterized by large uncertainties and thecomparison among them is still a delicate issue.

The most interesting isotopes are reported in Table 1.3 with a summary of theirfeatures in terms of isotopic abundance and Q-value for DBD.


ZZ+2Z-2

E

EE EE

E

Suppressed ~1021

Z-1 Z+2

Odd Mass

Number

Atomic Number

Nu

clea

r M

ass

(a) odd A

EE

EE

N,Z even

N,Z odd

ZZ+2Z-2 Z-1 Z+2

Even Mass

Number

Atomic Number

Nu

cle

ar

Mass

(b) even A

Figure 1.2: Nuclear binding energy for odd (left) and even (right) atomic number ofnucleons A.

Parent Abundance Q−value T2ν1/2

Rosman ‘98 Audi ‘03 MeasuredIsotope [atomic %] [keV] [years]48Ca 0.187 4274 4.4+0.6

−0.5 × 1019

76Ge 7.61 2039 (1.5 ± 0.1)×1021

82Se 8.73 2995.5 (0.92 ± 0.07)×1020

96Zr 2.8 3347.7 (2.3 ± 0.2)×1019

100Mo 9.63 3035 (7.1 ± 0.4)×1018

116Cd 7.49 2809 (2.8 ± 0.2)×1019

128Te 31.74 867.9 (1.9 ± 0.4)×1024

130Te 34.08 2530.3 6.8+1.2−1.1 × 1020

136Xe 8.87 2462 (2.11 ± 0.21)×1021

150Nd 5.60 3367.7 (8.2 ± 0.9)×1018

Table 1.3: Isotopic abundance (atomic %) and Q-values reported in Rosman ‘98 [31] and Audi‘03 [32] respectively. The values of T2ν

1/2 are taken from the average values reported in refer-

ence [33], except for T2ν1/2 (136Xe ) which is taken by [34].


1.4.2 Double Beta Decay without neutrinos

If the neutrino is a Majorana particle, the double beta decay can occur without theemission of the two neutrinos (0νDBD) as proposed by Furry in 1937 [35]:

(A,Z)→ (A,Z + 2) + 2e− (1.12)

This decay is forbidden by the SM because of the non conservation of the leptonic number(∆L = 2) and, up to now, has never been observed. The differences between the 2νDBDand 0νDBD are summarized by the Feynman graphs reported in Figure 1.3.

−ν

ν

n

n p

p

e

e

−

W

W

(a) 2νDBD

νΜ

n

n p

p

e

eW

W

x

(b) 0νDBD

Figure 1.3: Feynman graph for 2-neutrinos (a) and neutrinoless (b) double beta decay.

The right-handed antineutrino emitted in one of the two vertex is absorbed as a left-handed neutrino in the second one: this can happen only if ν = ν (Majorana nature ofneutrino) and the emitted ν has a left-handed component (proportional to mν).This means that the amplitude of the 0νDBD must be proportional to effective Majoranamass 〈mββ〉 defined as

〈mββ〉 =

∣∣∣∣∣∣∑j

mjU2ej

∣∣∣∣∣∣ =∣∣u2e1eiα1m1 + u2e2e

iα2m2 + u2e3m3

∣∣ (1.13)

and the half-life of the reaction can be obtained just modifying the equation 1.11 in sucha way to account for 〈mββ〉:

1

T 0ν1/2

= G0ν(Q,Z)∣∣M0ν

∣∣2(〈mββ〉me

)2

(1.14)

where G0ν(Q,Z) is a known integral over the phase space, Q = Mi −Mf − 2me is the

Q-value of the process,∣∣M0ν

∣∣2 is the nuclear matrix element and me is the electron mass.An experimental measurement of T 0ν

1/2 allows to measure the effective Majorana mass


of the neutrino. Up to now the 0νDBD has never been observed, therefore only lowerlimits on T 0ν

1/2 (upper limits on 〈mee〉) have been set. The most recent limits are listedin Table 1.4.

DBD Reaction T0ν1/2 Reference

[years]48Ca →48Ti > 1.4 ×1022 [36]76Ge →76Se > 3.0 ×1025 [37]82Se →82Kr > 1 ×1023 [38]96Zr →96Mo > 1.0 ×1021 [39]

100Mo →100Ru > 4.6 ×1023 [38]116Cd →116Sn > 1.7 ×1023 [40]130Te →130Xe > 2.8 ×1024 [41]136Xe →136Ba > 3.4 ×1025 [42]150Nd →150Sm > 1.8 ×1022 [43]

Table 1.4: 90% C.L. limits on T 0ν1/2. The limit on T0ν

1/2(76Ge) comes from the combined fit of

the GERDA, HDM and IGEX spectra, the one on T0ν1/2(136Xe) is obtained by the combination

of the limits from KamLAND-Zen and EXO-200.

The possible values of 〈mββ〉 as a function of the lightest neutrino mass (m1 or m3,according to the mass hierarchy) are reported in Fig. 1.4 from Ref. [44]. It should behighlighted that, even if the oscillations parameters were known with low uncertainty,the colored bands would still have an intrinsic width due to the the unknown phases inthe neutrino mixing matrix. The areas of the graph delimited by the dotted red lines rep-resent the mass regions that have already been excluded by cosmological measurementsand by 0νDBD experiments.

The goal of the next generation double beta decay experiments is to achieve a sensi-tivity on 〈mββ〉 of 10−1÷ 10−2 eV in order to explore the region of 〈mββ〉 correspondingto the inverse neutrino mass hierarchy. This can be done with a drastical improvementof the experimental sensitivity on T 0ν

1/2 and a better accuracy in the calculation of the

Nuclear Factor of Merit (FN = G0ν(Q,Z)∣∣M0ν

∣∣2). Improving the experimental sensitiv-ity is the aim of this Ph.D work, and will be widely discussed in the following chapters.The calculation of

∣∣M0ν∣∣2 is a very delicate issue, because it shows a strong dependence

on the structure of the involved nuclei.

The problem related to the evaluation of the nuclear matrix elements (NME) thatconnect the initial and final state is that it is a many-body problem that cannot beanalytically solved.Two main methods were used to perform NME calculations: the Quasi Particle RandomPhase Approximation (QRPA) [45, 46] and the Interacting Shell Model [47]. The QRPAaccounts for a large number of single particle states but in a limited number of con-figurations. On the contrary, the ISM handles only a few single-particle orbitals but itcalculates all the possible correlations between them. In the last years, a large effort was


Figure 1.4: Possible values of 〈mββ〉 as a function of the lightest neutrino mass for the direct(NS) and inverse (IS) hierarchy scenarios.

|ν0

|M

0

1

2

3

4

5

6

7

8

9

Ca48

Ge76

Se82

Zr96

Mo100

Cd116

Sn124

Te128

Te130

Xe136

Nd150

IBM

QRPA-T

QRPA-J

ISM

PHFB

GCM

Figure 1.5: NME values calculated with different techniques for each isotope. The central markfor each NME range indicates only the mean values of the range. The error bars show the fullextent of each range.


made to reduce the relevant discrepancies between the results provided by the differentmethods and new competitive techniques were developed. Among them, it is worthy tomention the Interacting Boson Model [48], the Generating Coordinate Method [49] andthe Projected Hartree-Fock-Bogoliubov model [50]. In Fig. 1.5, a schematic view of theNME calculated using different methods is reported. It is evident that an uncertainty ofa factor 3 due to the NME calculations has to be considered, in particular when studyingthe isotope of interest for this Ph.D work: the 130Te.

1.5 The Experimental Search for the 0νDBD

The energy released in a nuclear decay, i.e. the Q-value of the reaction, can be calculatedas the mass difference between the mother nucleus (Mm) and the particles in the finalstate (the daughter nucleus Md and the emitted particles). This energy is shared withthe decay products; for the 2νDBD the Q-value results:

Q2νββ = Mm −Md − 2me (1.15)

and a part of the decay energy is carried away by neutrinos, giving rise to a continuumenergy spectrum for the electrons. On the contrary, in the 0νDBD all the energy isshared between the two electrons, producing the monochromatic peak at the Q-valueof the transition. When the two electrons are detected together the differences in theexperimental signature between the two decay is shown in Fig. 1.6. Despite the clear ex-

2.0

1.5

1.0

0.5

0.0

1.00.80.60.40.20.0

Ke/Q

30

20

10

0

x10-6

1.101.000.90

Ke/Q

Figure 1.6: Sum of the energies of the two electrons emitted in the decay. Dotted line: 2νDBD;continuous line: 0νDBD. The ratio between the two peaks is not normalized, as the 0νDBD hasnever been observed.

perimental signature of 0νDBD, its very long half-life sets stringent requirements on the

1.5. The Experimental Search for the 0νDBD 23

features of the detectors. First of all the experiment must be located deep undergroundto be shielded against cosmic rays.

The second requirement is the materials selection for the maximization of the ra-diochemical purity. Indeed the natural radioactivity coming from the contamination of232Th or 238U chains has an half-life of the order of 109÷1010 y, 1014 times more intensethan the 0νDBD decay half-life.

The third requirement is a high energy resolution. Even if one could build a detec-tor with zero background in the 0νDBD region, however, he would have to deal withthe irreducible background produced by the 2νDBD. This kind of background can besuppressed choosing isotopes with large Q-value for DBD and using detectors with anexcellent energy resolution ∆E. Indeed, the fraction F2ν of 2νDBD events that fall inthe energy region of 0νDBD scales as:

F 2ν ∝ ∆E6

Q5ββ

A further advantage of a large transition energy resides in the suppression of the γnatural background, which drops above the 2615 keV line produced by 208Tl decay.

Finally, a competitive 0νDBD experiment requires a large mass of DBD emitters.This goal can be achieved using detectors whose mass can be scaled up and by choosingisotopes whose isotopic abundance is naturally high (like 130Te) or can be enriched withreasonable costs.

Besides, the recent work carried out by R. G. H. Robertson shows that no isotopeis preferred from the theoretical point of view [51]: thanks to an inverse correlationbetween the phase space and the square of the nuclear matrix elements, all the DBDcandidates are expected to have approximately the same decay rate per unit mass. Forthis reason, the isotope choice should be roughly based on the previous technical criteria.

All these considerations can be summarized introducing a parameter called sensi-tivity (S), which is the half-life corresponding to the minimum number of signal eventsdetectable over a background fluctuation at a given significance level, expressed in num-ber of gaussian standard deviations nσ:

S0ν =ln(2)

nσεNa

η · I.A.A

√M · tB ·∆E (1.16)

where Na is Avogadro’s number and:

• η and I.A. are the stoichiometric coefficient and the isotopic abundance of the DBDemitter, respectively;

• A is the compound molecular mass;

• ε, ∆E and B are the efficiency, the FWHM energy resolution (in keV) and thebackground rate (in counts/(keV kg y)) of the detector in the energy region ofinterest;


• M is the mass of the detector (in kg);

• T is the measurement time (in years)

Unfortunately, none of the available technologies allows to design a detector that optimizesimultaneously all the parameters that play an important role in the sensitivity equation.In the next section, a brief overview of the techniques used in the past years and proposedfor next generation experiments is reported.

1.6 Two different approaches

Several 0νDBD experiments have been carried out in the past exploiting different tech-niques, but none of them was able to provide an observation of the process (except fora controversial claim that will be discussed in this section). These searches were basedon two different experimental approaches.

In the first one, the 0νDBD emitter constitutes the active part of the detector(source ≡ detector). In this way, a very high efficiency on the process and an highenergy resolution can be achieved but, since the two electrons are detected as a singleenergy release, the information on the event topology is lost, opening the door to ahigher background.

In the second approach, on the contrary, the source is a passive component sur-rounded by active detectors. The main advantage of this technique consists in thecapability of measuring the energy and the angular distribution of individual electrons,providing a higher background discrimination power. However, a rather poor efficiency(and often energy resolution) must be taken into account when choosing this detectiontechnique.

1.6.1 Source≡Detector

The best limit on the 0νDBD half-life has been obtained so far by the Heidelberg-Moscowexperiment (HDM), that studied the 0νDBD of 76Ge. The detector was made of 5 high-purity Ge diodes enriched to 86% in 76Ge, and was operated between 1999 and 2003 inthe Laboratori Nazionali del Gran Sasso (LNGS, Italy), for a total exposure of 71.7 kg·y.The low background achieved in the energy region of interest (0.12 counts/(keV kg y)), aswell as the excellent energy resolution provided by Ge diodes (about 4 keV at the Q-valueof 76Ge), allowed to reach a lower limit on T 0ν

1/2(76Ge) > 1.9× 1025 years at 90 % C.L.,

corresponding to an upper bound on the effective Majorana mass of 〈mee〉 < 0.35 eV [52].Some members of the collaboration re-analyzed the data of the experiment and claimedan evidence for the 76Ge 0νDBD. In their last paper, the claim was strengthened bypulse shape analysis and a value of T 0ν

1/2(76Ge) = (2.23+0.44

−0.31) × 1025 years was inferred,

corresponding to 〈mee〉 = 0.30+0.02−0.03 eV [53].

The GERmanium Detector Array (GERDA [54]) is currently taking data at Lab-oratori Nazionali del Gran Sasso (Italy). High purity Germanium detectors, enrichedto about 86% in 76Ge, were reprocessed from the HDM experiment and International

1.6. Two different approaches 25

Germanium Experiment (IGEX [55]) and mounted in copper supports inside a 64 m3

cryostat filled with ultra pure liquid Argon (LAr), which serves as a cooling medium forthe detector operation as well as passive shield and active veto (see Fig. 1.7).

Figure 1.7: Pictorial view of the GERDA detector. Figure provided courtesy of the GERDACollaboration.

These detectors, whose total mass is 17.67 kg, have been operated from November2011 until May 2013 (GERDA Phase-I and Phase-II), featuring a FWHM energy res-olution of 4.2 ÷ 5.7 keV in Phase-I and 2.6 ÷ 4.0 keV in Phase-II at the Q-value ofthe decay (depending on the detector). No indication of a peak at the 0νDBD Q-valueis detected [37]: the resulting limit on 0νDBD half-life is T 0ν

1/2(76Ge) > 2.1 × 1025 y

(90% C.L.).This limit is consistent with the one obtained by the HDM and IGEX experiments andthe combinations of the three values, yields to T 0ν

1/2(76Ge) > 3.0 × 1025 y (90% C.L.).

The conclusion of these experiments, that in principle could rule out definitively thedetection claim, has been recently challenged by Klapdor and Krivosheina [56], showingthat the debate on this issue is far from the end.

A different experimental approach was followed by the Cuoricino collaboration, thatstudied the 0νDBD decay of 130Te by means of a 40.7 kg array of TeO2 bolometers.This experiment (that will be extensively described in the next chapter) was operatedat LNGS from 2003 to 2008 and reached a lower limit on 130Te half-life of T 0ν

1/2(130Te) >

2.8×1024 years at 90% C.L., corresponding to an upper bound on the effective Majoranamass of 〈mee〉 < 0.30÷0.71 eV [41]. Unfortunately, due to the large uncertainties on thenuclear matrix elements, Cuoricino was not able to probe the Heidelberg-Moscow claim.


1.6.2 Source6=Detector

Important results in the study of the 0νDBD of several isotopes, like 100Mo, 96Zr, 130Te,150Nd and 48Ca, were obtained by the Neutrino Ettore Majorana Observatory (NEMO3),a tracking experiment located in the Modane Underground Laboratory in France. Fordetectors like NEMO3, in which the source is deposited on thin foils and placed withina drift chamber (for tracking) and plastic scintillator blocks (for calorimetry), it is verydifficult to achieve a large mass of emitters. However, having the source separated fromthe detector allows to measure other important quantities, like the energy of individualelectrons, their angular distribution, the event vertex coordinates in the source plan andso on. The analysis of 5797 h of data collected with NEMO3 provided new limits on the0νDBD of 100Mo (T 0ν

1/2(100Mo) > 3.1× 1023 years, 90% C.L.) and of 82Se (T 0ν

1/2(82Se) >

1.4 × 1023 years, 90% C.L.), corresponding to 〈mee〉 < 0.8 ÷ 1.2 eV and 〈mee〉 < 1.5 ÷3.1 eV, respectively (see Figure 1.8).

0

2000

4000

6000

8000

10000

12000

0 0.5 1 1.5 2 2.5 3

E2e (MeV)

S/B = 40

NEMO 3 (Phase I)

Nu

mb

er

of

ev

en

ts/0

.05

Me

V

Mo100

219,000 ββ events

7.369 kg.y

(a) 100Mo 2νDBD

0

20

40

60

80

100

120

140

160

180

0 0.5 1 1.5 2 2.5 3

S/B = 4

NEMO 3 (Phase I)

Nu

mb

er

of

ev

en

ts/0

.05

Me

V Se82

0.993 kg.y

eventsββ2,750

E2e (MeV)

(b) 82Se 2νDBD

Figure 1.8: 2νDBD spectra of 100Mo (left) and 82Se (right) measured by NEMO 3. The blackdots represent the data, the solid line is the 2νDBD spectrum expected from simulations andthe shaded histogram is the subtracted background. Pictures taken from [38].

The KamLAND-Zen experiment searches for the 136Xe → 136Ba 0νDBD. The de-tector, sketched in Figure 1.9, was build by modifying the previous KamLAND set-upwith the insertion of a balloon to hold the dissolved Xenon (389 kg in the first phase and1 ton in a projected second phase) [57]. Despite the poor resolution (16% at 1 MeV),KamLAND-Zen plans to reach a high sensitivity thanks to the large source mass and thegood knowledge of the detector and background sources. Unfortunately, in the first com-missioning runs an unexpectedly large background rate was observed. This background,most likely due to metastable 110mAg, is currently being removed through a purificationcampaign, whose beginning marked the end of the first phase of KamLAND-Zen.The large exposure collected in the first phase of KamLAND-Zen (89.5 kg·yr), whichis the largest exposure for a DBD emitter to date, allowed to set a lower limit of

1.6. Two different approaches 27

T 0ν1/2(

136Xe) > 1.9× 1025 y at 90% C.L. [42].

Inner Balloon(3.08 m diameter)

Photomultiplier Tube

Outer Balloon(13 m diameter)

Buffer Oil

ChimneyCorrugated Tube

Suspending Film Strap

Film Pipe

Xe-LS 13 ton(300 kg Xe)

Outer LS1 kton

136

ThO W Calibration Point2

Figure 1.9: Pictorial view of the KamLAND-Zen detector. Figure provided courtesy of theKamLAND-Zen Collaboration.

Another experiment devoted to the search of 136Xe 0νDBD is the next EnrichedXenon Observatory (n-EXO), whose detection technique is based on the simultaneousmeasurement of the scintillation and ionization signals produced in a liquid Xenon timeprojection chamber. Interesting physics results were already obtained by EXO-200, a200 kg TPC installed in early 2010 and filled with un-enriched liquid Xenon at the endof the same year. The first background run performed with enriched 136Xe started atthe beginning of 2011 and provided the first measurement of the 136Xe 2νDBD aftera few months of data taking [34]. EXO-200 collected an exposure of 32.5 kg·y with abackground of ∼1.5×10−3 counts/(keV kg y) in the ±1σ energy region of interest. Nosignal was detected, providing a limit on the half life of 136Xe of T 0ν

1/2(136Xe) > 1.6×1025 y

at 90% C.L., that corresponds to 〈mee〉 < 140÷ 380 meV [58].

Combining the data obtained in the first phase of KamLAND-Zen with the onesprovided by EXO-200 results in T 0ν

1/2(136Xe) > 3.4× 1025 y at 90% C.L.

Using a representative range of matrix elements, a limit of 〈mee〉 < 120 ÷ 250 meV forthe effective Majorana mass can be obtained [42]. This value, in principle, excludes thedetection claim reported by part of the Heidelberg-Moscow collaboration at more than97.5% C.L.


1.7 Conclusion

In this chapter we explained why the search for the 0νDBD is a priority for particlephysics, and the information that the detection of this rare decay could provide; the largenumber of experiments devoted to this search testifies the importance that this processbe detected. In the next chapter the attention will be focused on the experimental searchfor the neutrinoless double beta decay of 130Te performed with TeO2 bolometers. Tothis purpose the bolometric technique and the past, present and future of the TeO2

bolometric arrays will be presented.

Chapter 2

The Bolometric Technique

As mentioned in the previous chapter an important study of the 0νDBD of 130Te wasperformed by the CUORICINO experiment exploiting the bolometric technique. TheCUORE-0 detector is now in data taking, and in 2015 the CUORE experiment will start.With an active mass of about 750 kg, it will be the largest bolometric experiment evermade and in 5 years of live time it is expected to reach a sensitivity on the effectivemajorana mass of about 50÷ 130 meV.In this chapter these three experiments will be presented, and the bolometric techniqueexplained. In addition, a proposal to increase the experimental sensitivity of TeO2

bolometers will be presented and discussed.

2.1 TeO2 Bolometer

The most commonly used particle detectors measure the energy released in the form ofionization or scintillation.

heat sink

weak thermal

coupling

absorber

energy

release

sensor

Figure 2.1: Schematic representation of a bolometer: absorber, sensor, thermal coupling andheatsink.

The energy that can be collected measuring these channels, however, constitutes only

29

30 Chapter 2. The Bolometric Technique

a very small fraction of the total energy, as the largest fraction is converted in latticevibration and escape detection seriously worsening the energy resolution. This limitationof the energy resolution of “standard” detectors can easily be overcome by using adetector that can measure the phonons produced by an interaction: a bolometer, i.e. acalorimeter working at cryogenic temperature (about 10÷ 100 mK).

A schematic picture of a bolometer is shown in Fig. 2.1 where two fundamentalcomponents can be recognized: the absorber and the sensor. When a particle interactswithin the absorber characterized by a heat capacity C, the temperature of the absorberitself increases proportionally to the energy released. The heat accumulated in thisprocess is then dissipated in the heat sink through a weak thermal conductance (G),restoring the initial temperature of the absorber. This temperature variation of theabsorber due to the energy deposit ∆E can be written as:

∆T (t) =∆E

Cexp

(− tτ

)(2.1)

where τ = C/G depends on both the heat capacity of the absorber and the conductanceto the heat sink.The temperature signal generated by the interaction is converted into a readable elec-trical signal by means of a proper sensor, as described below.

2.1.1 The absorber

From the equation 2.1 it’s easy to understand why bolometers can work only at cryogenictemperatures: to have a detectable temperature variation one needs a very low heatcapacity of the absorber. This can be achieved operating as absorber a dielectric anddiamagnetic crystal at cryogenic temperatures.For these materials, indeed, the electrons contribution to the specific heat (that scalesas T) can be neglected and the only contribution to the thermal capacitance comes fromthe lattice, and it is described by the Debye law (that scales as T3):

cl(T ) =12

5π4NakB

(T

ΘD

)3

T < ΘD (2.2)

where Na, kB and ΘD are the Avogadro number, the Boltzmann constant and the Debyetemperature respectively.

For a 750 g TeO2 crystal (the one used by the CUORE collaboration), a thermalcapacitance C = 10−9 J/K is obtained at T = 10 mK, providing a temperature increaseof 100 µK for an energy deposit of 1 MeV.

2.1.2 The resolution: the most important bolometric performance

In theory, the energy resolution of a bolometric detector is dominated by the thermalbath temperature fluctuations: the energy exchange between the thermal bath and the

2.1. TeO2 Bolometer 31

bolometer. The nuclei or the electrons of the material convert the energy deposit intovibrational excitations of the lattice (phonons). Assuming that an energy deposition Eproduces N phonons, each one with energy ε = kBT , one can write:

E = N · ε = C(T ) · T (2.3)

If the phonons are produced according to the Poisson statistics, their fluctuation causesan energy spread described by:

σE =√N · ε =

√kBC(T )T 2 (2.4)

Using the same parameters reported above for a typical TeO2 bolometer, the expectedenergy spread would be of the order of 10 eV, well below the measured resolution, of afew keV (see section 2.2.1).

In order to explain this discrepancy, a deeper analysis of the energy release processesthat occur before the conversion in phonons is needed (for a detailed description seeRef. [59]). These processes involve two different channels in which the energy can betransferred to the absorber: the electronic and the nuclear channel. The particle interac-tion with the electrons of the absorber (electronic channel) produces electron-hole pairsthat spread quickly from the interaction point in the rest of the detector. These carriersreach a quasi-equilibrium condition by interacting with each other and start transferringenergy to the lattice as vibrational excitations. In this channel, many phenomena cangive rise to a worsening of the energy resolution, like trapping of the carriers in impuritysites or lattice defects, radiative recombinations of electron-hole pairs or non radiativerecombinations on very long time scales. On the other hand, when the particle interactswith the nuclei of the absorber (nuclear channel), part of the energy could be trappedin the structural defects of the lattice. This phenomenon, almost negligible for electronsand gammas, can worsen the energy resolution of αs up to several hundreds of eV foran energy deposition of 1 MeV.

The fraction of energy that leaves the crystal without being detected, as well as theone stored in stable or metastable states, are almost irreducible sources of resolutionworsening that have to be accounted in the selection of the absorber.

2.1.3 The TeO2 choise

The absorbers used in the 0νDBD experiments are crystals grown starting from theisotope of interest (as the TeO2 crystal used for the study of 0νDBD of the 130Te),in this way the detector and the source of the experiment coincide, providing a highefficiency (of about 80% [60]) on the decay. However, it is not always possible to grown aradio-pure crystal based on 0νDBD emitters that shows good mechanical and bolometricperformances (as for example a good energy resolution). Besides, the natural isotopicabundance or the enrichment cost must be taken into account for the 0νDBD isotopechoice.

The TeO2 crystals were chosen because of their excellent mechanical properties, thehigh Debye temperature and the capability to survive to stresses produced by thermal


contractions; in addition, these crystals have always been extensively used for acousto-optic applications, providing a lot of expertise on their growth. These properties makethem the best candidates as bolometers for the 0νDBD search:

• they represent the crystals with the best bolometric performances (excellent energyresolution of 5 keV FWHM at 2.5 MeV) and reproducibility;

• they can achieve very high radio-purity level;

• the natural isotopic abundance of 130Te is about 34% (the highest among the0νDBD emitters); an hypothetical enrichment of 130Te up to 90% is about threetimes cheaper than other 0νDBD emitters (as 100Mo or 82Se).

The only problem of TeO2 bolometers is the inability to operate any kind of particle dis-crimination, that cause an higher background to the experiment that uses this detector.This delicate issue will be widely discussed in the next sections where a possible solutionwill be presented.

2.1.4 The sensor

The temperature variations in the absorber are converted into electrical signals by meansof devices whose resistance shows a steep dependence on the temperature. In order tocompare the different sensors that have been developed in the last years, it is useful tointroduce the logarithmic sensitivity A:

A =

∣∣∣∣d logR(T )

d log T

∣∣∣∣ (2.5)

The sensitivity relates the temperature variation of the absorber to the resistance vari-ation of the sensor:

dR

R= A

dT

T(2.6)

The larger the sensitivity, the better the response of the device. The temperature sensorsused in the CUORICINO, CUORE-0 and CUORE detectors are Neutron Transmuta-tion Doped (NTD) Germanium thermistors operated in the Variable Range Hoppingregime [61, 62, 63]. If compared to other devices, like the transition edge sensors (TES),NTD Ge thermistors show a rather poor sensitivity (ANTD ∼ 10, a factor 10 less withrespect to TES).The reasons why they were chosen are the wide temperature range in which they canoperate without significant changes in the response, as well as the ease in assemblyand the simple electronic read-out. NTD Germanium thermistors can be built by dop-ing uniformly Ge wafers to a level just below the metal-insulator transition. Indeed,semiconductors at cryogenic temperatures would behave as insulators and no electricalconduction would be possible. On the contrary, the lattice impurities induced by thedoping process create new energy levels slightly above the valence band or below theconduction one (depending on the type of dopant). The conduction for such a doped Ge

2.1. TeO2 Bolometer 33

thermistor occurs when electrons “hop” (tunnel) between dopant atoms. This quantumeffect depends on the absorption/emission of the required energy difference via phonons.Since at low temperatures the number of high energy phonons is very low, electrons cantravel to far impurity sites that have energy close to the Fermi one. In this situation,called “variable range hopping regime”, the thermistor resistance strongly depends onthe temperature:

R(T ) = R0 exp

(T0T

)γ(2.7)

The thermistors used in the CUORE-0 experiment come from two different samples forwhich γ ∼ 1/2, T0 ∼ 4.342 K and R0 ∼ 1.378 Ohm for the first one and T0 ∼ 4.170 Kand R0 ∼ 1.549 Ohm for the second one.

2.1.5 Detector operation

The resistance variation of the thermistor, reported in equation 2.7, can be convertedinto a readable voltage signal ∆V by polarizing the thermistor with a simple bias circuitreported in Fig. 2.2. A voltage generator VBIAS is connected to the thermistor via 2

+VBIAS

RL/2

Rbol(T)Ibol Vbol(T)

RL/2

Figure 2.2: Scheme of the bias circuit used for the thermistor readout

load resistors (RL/2+RL/2), whose resistance is chosen large enough to provide a smallsteady current across the thermistor: Ibol = Vbias/(RL + Rbol) ∼ Vbias/RL. For theread-out of the CUORE-0 thermistors, whose resistances are of the order of 20÷50 MΩ,load resistors of 54 GΩ are used. During the bolometer operation, the bias current thatflows across the thermistor dissipates a power P = RbolI

2bol. The power dissipation in

the thermistor increases its temperature (Tbol = T0 + PG), thus diminishing its resistance.

If the dissipated power is negligible, the V-I curve follows a Ohmic behavior and theworking resistance of the thermistor (i.e. the resistance measured during normal opera-tion) is very similar to the base resistance (resistance measured with Vbias ∼ 0).


VBIAS

Vbol

IbolWorking Point

(WP)

Load Curve (LC)

Load Line

Inversion Point

(IP )

VBIAS

RL

Figure 2.3: Relationship between the bias current Ibol and the voltage across the thermistorVbol.

Time [s]0 1 2 3 4 5

Vol

tage

[m

V]

200

220

240

260

280

300

320

340

360

Figure 2.4: Bolometric pulse produced by an interaction in a TeO2 crystal after theamplification stage.

For larger values of Ibol the temperature rise due to the power dissipation becomes ap-preciable and the slope of the V-I curve begins to increase until an inversion point isreached. A further increase of the bias current produces a decrease of the sensor voltage(see Figure 2.3), for the so-called electrothermal feedback effect.In CUORE-0 a new automated bias voltage scanning algorithm was implemented to lo-cate the optimal working point that maximizes the signal-to-noise ratio (SNR). However,both the signal amplitude and the noise of each channel can vary during the measure-

2.2. CUORICINO: the first large bolometric array 35

ments, that usually last several weeks or months, demanding for a further tuning of theworking conditions. To conclude this section, we report in Figure 2.4 a typical bolometricpulse.

2.2 CUORICINO: the first large bolometric array

The CUORICINO experiment was composed by 62 TeO2 bolometers: 44 of them were5 × 5 × 5 cm3 crystals arranged in 11 floors of 4 crystals each, the remaining 18 were3×3×6 cm3 crystals, 2 of them were enriched in 130Te and 2 of them in 128Te, arrangedin 2 floors of 9 crystals each (see Figure 2.5).Each absorber was equipped with a NTD Ge thermistor and a heater, a simple resistorthat produces a fixed pulse at constant time intervals in the detector, allowing for sta-bility checks. Both the sensors and the heaters were glued using 9 Araldit Rapid spotswith diameter of roughly 0.7 mm. The choice of 9 spots (instead of a more practice veilof glue) was made to avoid crystal breaks due to the different thermal contractions ofTeO2 and Ge while cooling the detector.

The crystals were enclosed in an oxygen-free high thermal conductivity (OFHC)copper structure, used as mechanical support as well as thermal bath for the detectoroperation. The weak thermal conductance between absorber and heat bath was realizedby means of small teflon pieces that, in addition, could compensate for the differentthermal contractions of TeO2 and copper. The 13 floors were stacked in a tower, operatedin the 3He/4He dilution cryostat located in the Hall A of LNGS from 2003 to 2008.

(a) 5×5×5 cm3 crystals (b) 3×3×6 cm3 crystals

Figure 2.5: TeO2 crystals with NTD Ge thermistors fixed in copper structures by meansof teflon pieces.

With an average signal efficiency of 82.8± 1.1% and an average FWHM energy reso-lution of 6.3±2.5 keV at 2615 keV for the 5×5×5 cm3 crystals,1 CUORICINO, besides

1Similar results were obtained with the smaller crystals, that featured an average signal efficiency of


proving the feasibility of a large mass bolometric experiment, allowed to reach the mostcompetitive limits on 130Te 0νDBD half-life.Cuoricino, indeed, collecting a total exposure of 19.75 kg·y in 130Te measured a lowerlimit of T 0ν

1/2(130Te) > 2.8 × 1024 years at 90% C.L. [41] and obtained many important

physics results, like those reported in [64, 65]. Moreover, being the first large bolometricarray operated, it allowed to characterize the main background sources for this kind ofexperiments. Given the importance of this topic a summary of the background analysisreported by the CUORICINO collaboration is presented in the next section; more detailscan be found in [66, 67].

2.2.1 CUORICINO α background

The sources of background for a bolometric experiment can be divided in two categories:particles coming from the laboratory environment and particles coming from radioactivecontaminations of the detector itself.

The first contribution consists of muons, neutrons and natural environmental ra-dioactivity. With an average depth of about 3650 m.w.e., the LNGS features a totalmuon intensity of (2.58± 0.3)× 10−8 µcm−2s−1 [68], a flux of neutrons with energy be-low 10 MeV of about 4× 10−6 n cm−2 s−1 [69], and an integral γ-ray flux below 3 MeVof about 0.73 γ cm−2 s−1 [70, 66]. All these sources of background can be reduced bymeans of proper vetoes and shields, or during the off-line analysis, as explained later.

The second contribution, i.e. contaminations coming from the crystals, their me-chanical support or the cryostat are by far more dangerous, as they can not be easilyshielded.The background spectrum measured by CUORICINO is reported in Figure 2.6. This

Energy [keV]1000 2000 3000 4000 5000 6000 7000

Rat

e [c

ount

s / (

keV

*kg*

y)]

-210

-110

1

10

210

Figure 2.6: Single-hit background spectrum (black) and calibration spectrum (red) measuredby the Cuoricino detector. The 232Th calibration spectrum is normalized to the 208Tl activityof the background spectrum at the 2615 keV peak.

spectrum, to which one refers as single-hit, was obtained selecting events in which only

79.7 ± 1.4% and an average FWHM energy resolution of 9.9 ± 4.2 keV at 2615 keV

2.3. Cuore-0: the α background reduction 37

one crystal was hit within a coincidence time window of 100 ms. Indeed, since the twoelectrons emitted in 0νDBD are expected to release their entire energy inside a singledetector with an efficiency of about 86%, the anti-coincidence operation of the arrayprovides an efficient background suppression. The single-hit spectrum can be divided intwo regions:

• the region dominated by β/γ events, i.e. the region below the 2615 keV 208Tlline; here several peaks due to contaminants like 214Bi or 60Co can be recognized.However, due to the relatively large 0νDBD Q-value of 130Te, only the multi-Compton events of 208Tl can be considered as a dangerous contribution to thebackground.

• the region dominated by the α events, i.e. over the 2615 keV 208Tl line; hereseveral structures can be recognized. Most of them can be seen in both single anddouble hit spectra and have a large low energy tail. The last feature allowed tounderstand that these peaks can not be ascribed entirely to internal contaminationsof the crystals, otherwise the α and the nuclear recoil emitted in the decay wouldhave released their entire energy inside the detector, giving rise to a monochromaticpeak at the Q-value of the transition.

The background in the α region was attributed to surface contaminations in 238U and232Th (and their daughters) of the crystals and of the copper structure that supportsthe array except for the 3249 keV, 4083 keV, 5304 keV and 5407 keV peaks, due to bulkcontaminations in 190Pt, 232Th, 210Pb and 210Po respectively. Thanks to the geometryof the detector, the surface contaminations of the crystals can be studied plotting thecoincidence spectra between close detectors. In a fraction of decays, indeed, the αparticle (or with lower probability the nuclear recoil) escapes the source crystal and isdetected in a facing one. The energy depositions within the two detectors are recordedas a coincidence event whose total energy yields the Q-value of the alpha transition;these events are rejected in the off-line analysis. However, if the α particle emitted inthe decay is absorbed in an inert material (such as copper) and not in another crystal,there are no ways to tag the event as an α interaction. Loosing a variable part of theirenergy in the source crystal, these events give rise to a flat continuum extending from theQ-value down to lower energies, contaminating also the 0νDBD region. Nevertheless, thestudy of the CUORICINO background showed that, given the surface contaminationsof the TeO2 crystals, only a minor fraction of the flat distribution between 3 ÷ 4 MeV(see Figure 2.6) could be explained. The remaining (80 ± 10)% of this continuum wasindeed attributed to degraded αs (namely αs that release only part of their energy inthe crystal) coming from the surface of the copper structure.

2.3 Cuore-0: the α background reduction

Since the analysis of the Cuoricino background indicated that the most worrisome back-ground in the 0νDBD region comes from α surface contaminations of the copper struc-ture, the CUORE collaboration performed an extensive R&D activity devoted to the


suppression of this contribution of about one order of magnitude, whose summary canbe found in reference [71]. This work involved a new design of the bolometric towers(to minimize the inert material) as well as the development of cleaning, assembly andstorage techniques specific for each material that will constitute the detector of CUORE.

A first CUORE tower, named CUORE-0, composed by 52 TeO2 bolometers 5× 5×5 cm3 arranged in a copper structure (see Fig. 2.7), was assembled by means of a ded-icated procedure in order to minimize the risk of recontaminations induced by externalagents both during their construction and their storage [72] and is now in data-takingin the ex-CUORICINO cryostat.

Figure 2.7: CUORE-0 detector: 52 TeO2 bolometers were arranged in a copper structure andare now operated in a 3He/4He dilution cryostat located in the Hall A of LNGS.

The procedures used in the production and assembly of the CUORE-0 detector, wereproved to be very efficient, reducing the α background of about 6 times with respectto CUORICINO (see Fig. 2.8 and Table 2.1). With a total background in the 0νDBDregion of interest (ROI) of (0.063± 0.006) counts/(keV kg y), CUORE-0 will be able toovercome the CUORICINO sensitivity in less than 1 year of live time [73].The γ-ray background in the 0νDBD region is predominantly Compton-scattered 2615 keVγ-rays originating from 208Tl in the cryostat. Since CUORE-0 is hosted in the same cryo-

2.4. CUORE projection 39

stat used for CUORICINO, the γ-ray background is expected to be similar. The γ-raybackground is estimated as the difference between overall background in the ROI andthe degraded α background in the continuum (2.7 ÷ 3.9 MeV). The measured γ-raybackgrounds of CUORE-0 and CUORICINO are indeed compatible, consistent with thehypothesis that the background in the ROI is composed of γ-ray from the cryostat anddegraded α particles.

Energy [keV]

1000 2000 3000 4000 5000 6000 7000

Even

t R

ate

[counts

/keV

/kg/y

]

210

110

1

10

Cuoricino

CUORE0

CUORE0 Preliminaryyr⋅Exposure: 18.1 kg

Figure 2.8: Comparison between the CUORICINO (black line) and CUORE-0 (red dots) back-ground energy spectra.

0νDBD region [2700-3900] keVcounts/(keV kg y) counts/(keV kg y)

CUORICINO 0.153± 0.006 0.110± 0.001

CUORE-0 0.063± 0.006 0.020± 0.001

Table 2.1: Comparison between the CUORICINO and CUORE-0 average flat background (incounts/(keV kg y) in the 0νDBD window and in the region between 2.7 and 3.9 MeV (notefficiency corrected).

The reduction of the background to about 0.09 counts/(keV kg y) in both regions mea-sured by CUORE-0 demonstrated that the hypothesis that the ROI is affected also bythe flat α background produced by the degraded α particles is correct and that thecleaning, assembly and storage techniques developed by the CUORE collaboration areable to achieve an α background level of 0.02 counts/(keV kg y), 6 times lower thanCUORICINO one.

2.4 CUORE projection

The Cryogenic Underground Observatory for Rare Events (CUORE [74]), will be com-posed by 19 CUORE-0 like towers (988 TeO2 crystals 5 × 5 × 5 cm3) and hosted in a


custom 3He/4He dilution cryostat located in the hall-A of the underground LNGS.All the 19 towers are now assembled and the cryostat has reached for the first time thebase temperature (8 mK) in september 2014, the data taking will start in autumn 2015.

Detector suspensionsupport

Dilution unit

Pulse tubehead

Pulse tuberemote motor

Accessports

Pb

Pb

Pb

CUORE

detector

Figure 2.9: The CUORE detector will be made of 19 CUORE-0 like towers and is now inbuilding phase at LNGS.

Compared to CUORE-0, the larger array of CUORE affords obviously a larger activemass, more powerful time coincidence analysis and more effective self-shielding fromexternal backgrounds, particularly those originating from the copper thermal shields orcryostat. With this stronger background rejection and the already demonstrated reduc-tion of surface contamination, the CUORE background goal of 0.01 counts/(keV kg y)in the ROI is expected to be within reach. The projected half-life sensitivity to 130Te0νDBD is 9.5× 1025 y (90% C.L.) with 5 years of live time, reaching an effective Majo-

2.5. An Inverted Hierarchy Explorer 41

rana neutrino mass sensitivity of 0.05 to 0.13 eV, for the first time touching the invertedhierarchy region of neutrino mass (see Fig. 2.10).

[eV]lightestm-410 -310 -210 -110 1

[eV

]ββ

m

-410

-310

-210

-110

1Cuoricino exclusion 90% C.L.

GERDA exclusion 90% C.L. Ge claim76

KamLAND-Zen and EXO-200 exclusion 90% C.L.

CUORE 90% C.L. sensitivity

>0223 m∆

<0223 m∆

Figure 2.10: CUORE projected sensitivity to 〈mββ〉 (90% C.L.); 〈mββ〉 is a function of thelightest neutrino mass for the direct (red) and inverse (green) hierarchy scenarios.

2.5 An Inverted Hierarchy Explorer

The next generation bolometric experiments aim to explore the inverted neutrino masshierarchy region at effective Majorana mass mββ of about 10÷ 20 meV. This sensitivitycan be achieved decreasing the background level up to 0.001 counts/(keV kg y) andsimultaneously increasing the number of 0νDBD emitters.However, as shown in the previus section, the α background level cannot be reduced be-low 0.01 counts/(keV kg y) although the most advanced cleaning techniques have beenused. Besides, the CUORE cryogenics system cools a total of 7 ton of material (about1 ton comes from the detector and the rest from the shielding) to 10 mK base tempera-ture; the construction of a cryostat able to cool down an ipotetical 2 ton bolometer arrayand its shielding (a total of 12÷14 ton) is beyond our current technological capabilities.This means that the increase in the number of 0νDBD emitter can be made only usingcrystals grown with enriched material and the reduction of the α background can bemade using a new type of bolometer able to perform a particle discrimination, in orderto eliminate the α background and achieve the goal of 0.001 counts/(keV kg y) [75].


The most common approach used by next generation bolometric experiments is toexploit the scintillating bolometric technique in order to perform an active backgroundrejection [76].

A scintillating bolometer is a crystal that, beside working as calorimeter at cryogenictemperatures, also emits scintillation light; the Light Yield (LY) produced in the particleinteraction is strongly dependent on the particle itself: for a fixed energy released in thebolometer the LY of a β/γ particle is very different from an α one.To detect the emitted light, an addictional detector must be faced to the main bolometer:this light detector is another bolometer, consisting of a thin germanium/silicon wafer asabsorber and a thermal sensor of the same type as the one used for the main bolometer(see Fig. 2.11).

Thermal Sensor !

Absorber!

Ther

mal

Bat

h !

L!

Energy Release!

Thermal Sensor!

Light Detector!

Light!

Figure 2.11: Schematic representation of a scintillating bolometer: the main bolometer and thelight detector.

The LUCIFER [77] and LUMINEU [78] experiments want to exploit this technique tostudy the 0νDBD of 82Se using ZnSe scintillating bolometers and the 0νDBD of 100Mousing ZnMoO4 scintillating bolometers respectively.

According to the present understanding of TeO2 crystals, they do not scintillate atbolometric temperatures, and for this reasons they are not considered good candidatesfor a next generation bolometric experiments.

However, the many advantages offered by this material in terms of bolometric perfor-mances and the high natural isotopic abundance of 130Te with respect to other candidatenuclei have provided a strong motivation to pursue another, extremely challenging, op-tion: the active background rejection technique can be applied to the TeO2 bolometerexploiting, insted of the scintillation light, the Cherenkov radiation. Indeed, as proposedby Tabarelli De Fatis in Ref. [79], detecting the Cherenkov radiation produced in theTeO2 crystal only by electrons (at the low energies of the natural radioactivity) it ispossible to disentangle the β/γ interactions from the α ones.

This Ph.D thesis is devoted to study this possibility in order to demonstrate that

2.6. The Cherenkov effect 43

also the TeO2 bolometers can be exploited for a next generation bolometric experiment.Therefore, in the next section, a complete study of the Cherenkov signal that is expectedwhen a β particle interacts within the TeO2 crystal will be presented.

2.6 The Cherenkov effect

The Cherenkov effect [80] is a threshold effect that happens when a charged particlepasses through a medium with a velocity v greater than the velocity of light in thatmedium cm:

v > cm = c/n (2.8)

where n is the refractive index of the medium and c the speed of light; the thresholdcondition can be written as:

v

c= β >

1

n(2.9)

The effect raises the prompt emission of an electromagnetic radiation that, unlike fluores-cence or scintillation spectra that have characteristic spectral peaks, shows a continuouswavelength spectrum. Moreover these photons are emitted in a cone with an openingangle θC = arccos(1/(βn)) with respect to the particle direction.

The number of Cherenkov photons produced per unit path length of a particle withcharge ze and per unit wavelength interval of the photons is:

dN2

dxdλ=

2παz2

λ2

(1− 1

β2n2 (λ)

)(2.10)

where α is the fine-structure constant, λ the wavelength of the Cherenkov photons andn(λ) the refractive index of the material.

Typically the wavelength range for which the Cherenkov photons give an impor-tant energy contribution starts from the ultra violet up to the near infrared: at higherwavelength (x-ray) the refractive index approaches 1 and the Cherenkov threshold isno more satisfied also for ultra relativistic particles; al lower wavelength (medium in-frared) the number and the energy of the Cherenkov photons decreases at a level thatcan be neglected. Moreover many materials exhibit a cut-off in the transmission spec-trum, for which photons with a wavelength λ < λcut−off do not propagate inside themedium. They are absorbed by the material itself decreasing the amount of the mea-surable Cherenkov photons.

As shown in eq. 2.10 all the properties of the emitted Cherenkov photons are functionsof the optical parameters of the material; therefore in order to evaluate the number andthe wavelength spectrum of the emitted Cherenkov photons in TeO2 crystal the refractiveindex n(λ) and the absorption length δ(λ) will be studied.

TeO2 crystal optical properties: refractive index and absorption length

The TeO2 crystal is a birefringent material, this means that the refractive index dependson the polarization and on the propagation direction of light.


m]µWavelength [0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ref

ract

ive

inde

x

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

oe

Figure 2.12: Ordinary and extraordinary refractive indices of TeO2 crystal as function of wave-length at T=300 K.

The ordinary and extraordinary refractive indices (no and ne, respectively) are shown inFig. 2.12. Both the refractive indeces are described by the Sellmeier equation [81], thatis an empirical relationship between refractive index and wavelength for a transparentmedium:

n(λ)2 − 1 =Aλ2

λ2 − λ21+

Bλ2

λ2 − λ22(2.11)

The Sellmeier parameters for the TeO2 crystal are shown in Tab. 2.2.

A λ1 [µm] B λ2 [µm]

no 2.584 0.1342 1.157 0.2638

ne 2.823 0.1342 1.542 0.2631

Table 2.2: Coefficients of the Sellmeier equations for the TeO2 crystal [82].

As TeO2 crystals are currently produced for acousto-optic devices, special attentionis given in literature only to those optical properties connected to this application. Thestudy of optical characteristics as transmission and reflection near and above the fun-damental absorption edge at low temperatures was carried out only till 80 K [83] andexperimental results [83, 82] do not allow for a definitive interpretation of electronicband structure for TeO2 crystal. It is also missing from the literature a detailed studyof the agreement between calculated electronic structure [84] and optical transmissionmeasurements.

Preliminary optical transmission measurements were performed on pure TeO2 slicesusing a Perkin Elmer Lambda 900 spectrophotometer and a Leybold RDK10-320 (Tmin=12 K)cryostat. The results around the fundamental absorption edge are shown in Fig. 2.13;


Wavelength [nm]290 295 300 305 310 315 320 325 330 335 340

Abs

orpt

ion

leng

th [

cm]

0

10

20

30

40

50

60

70

80T = 300 K

T = 150 K

T = 80 K

T = 50 K

T = 15 K

(T=300K)cut-offλ

(T<15K)cut-offλ

Figure 2.13: Absorption length (δ(λ)) for different temperatures around the fundamental ab-sorption edge.

for wavelengths grater than 350 nm the absorption length approaches a value of about80 cm, irrespective of the temperature. The absorbance spectra show a temperaturedependence typical of an indirect band structure, and the shift in the λcut−off due tothe temperature variation reaches an asymptotic value for T < 50 K. This suggests thatfor temperatures below 15 K it is possible to assume an absorbance spectrum like theone measuered at 15 K. The λcut−off results to be about 325 nm at room temperatureand about 305 nm for T < 15 K.

Also the refractive index shows a temperature dependence, but as for the absorptionlength no reference is available in literature. Nevertheless the variation is expected tofollow the absorption length one (a shift of about 20 nm toward lower wavelengths). But,unlike the absorption length, the temperature dependence of the refractive index weaklyaffects the number of Cherenkov photons emitted. Indeed, the expected refractive indexvariation decreases the number of Cherenkov photons by less than 1%, therefore can beneglected.

2.6.1 The Cherenkov effect in TeO2 crystal

Using the refractive index and the absorpion lenght it is possible to evaluate the numberand the wavelength spectrum of the emitted Cherenkov photons per unit path length ofthe charged particle.First of all, an estimation of the Cherenkov threshold must be made: using, for example,the value of no(400 nm) = 2.44 the corresponding threshold for Cherenkov emission isabout 50 keV for electrons and about 400 MeV for alpha particles (see Eq. 2.6). In thisexample the number of Cherenkov photons produced by an e− of about 2.5 MeV for mmpath length is evaluated. Equation 2.10 multiplied by the photons absorption probability


after 1 mm path from the emission points e− 1 mm

δ(λ) , integrated between 0.2÷1.0 µm, gives:

dN

dx=

∫ 1 µm

0.2 µm

2παz2

λ2

(1− 1

β2n2 (λ)

)· e−

1 mmδ(λ) dλ ≈ 84.1 photons/mm (2.12)

Using the extraordinary refractive index the dN/dx value is about 86.5 photons/mm,3% more.At cryogenic temperature the λcut−off decreases to about 20 nm; this effect increases thenumber of the emitted Cherenkov photons up to 92.9 photons/mm (95.5 photons/mmusing the extraordinary refractive index). The room temperature spectrum comparedwith the low temperature one is shown in Fig. 2.14.

m]µWavelength [0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

m)]

µ [

phot

ons

/ (m

m

λdx

ddN

0

50

100

150

200

250

300

350

400

450: T < 15 K

2Cherenkov spectrum in TeO

: T = 300 K2

Cherenkov spectrum in TeO

: T < 15 K2


: T = 300 K2


Figure 2.14: Emission spectrum of the Cherenkov photons in TeO2 crystal at room temperatureand at cryogenic temperature (T < 15 K). These spectra are evaluated using an electron of about2.5 MeV for 1 mm path length.

The evaluation of the spectrum and of the number of Cherenkov photons was per-formed taking into account photons up to 1000 nm, well beyond the visible range(700 nm). This means that the estimation reproduces all the photons that are in the sen-sibility range of the conventional light detectors working at room temperature (PMT orSiPM). For light detectors operated at cryogenic temperature (as for example germaniumlight detector 5.1) the sensibility wavelength range is larger that the room temperatureones: in principle they can be sensible also to photons in the near infrared wavelengthrange (700÷1000 nm) and beyond. The NIR was chosen as end point of the wavelengthspectrum of Cherenkov photons because most of the optical properties needed for thesimulation of the optical photons propagation are available up to 1000 nm. An estima-tion of the approximation made can be done comparing the total energy emitted by the


Cherenkov radiation with the approximated one, thanks to the following equation:

dN

dxdε=αz2

hc

(1− 1

β2n2 (ε)

)≈ 37

(1− 1

β2n2 (ε)

)[photons ·mm−1 · eV−1)

](2.13)

This equation shows that the number of Cherenkov photons has an approximately flatenergy spectrum; the total energy emitted can be obtained integrating between 0 and4.27 eV (that corresponds to 290 nm; see Fig. 2.14) the equation 2.13 multiplied by thephotons energy (ε) gives:

E

dx=

∫ 4.27 eV

0 eV

dN

dxdεεdε ≈

∫ 4.27 eV

0 eV37

(1− 1

β2n2 (ε)

)εdε ≈ 280

[eV ·mm−1

](2.14)

As shown in Fig. 2.15, the wavelength range used (1.24 ÷ 4.27 eV → 290 ÷ 1000 nm)takes into account the 93% (260 eV ·mm−1) of the total energy emitted by the Cherenkoveffect, enough for the purpose of the simulation of the cryogenic measurements.

[eV]ε0 0.5 1 1.5 2 2.5 3 3.5 4

[eV

/ (m

m e

V)]

εdx

ddE

0

20

40

60

80

100

120

140

=290nmλ=1000nmλ

93% of the Cherenkov Energy

Figure 2.15: Energy emitted by the Cherenkov effect in TeO2 crystal at cryogenic temperature(T < 15 K). This function is evaluated using an electron of about 2.5 MeV for 1 mm path length.

The TeO2 stopping power for electrons is shown in Fig. 2.16: an electron with akinetic energy of about 2.5 MeV travels about 3 mm, this correspond to an averagenumber of Cherenkov photons equal to ∼ 280 and an energy of about 780 eV.In Ref. [79] the number of Cherenkov photons expected at the 0νDBD Q-value is about125 ÷ 135, a very different value with respect to the one obtained here. This is due tothe fact that only photons in the range 350÷600 nm are taken into account; if the equa-tion 2.12 is integrated between 350÷600 nm an average value of about 134 is obtained,in agreement with [79].


Electron kinetic energy [MeV]-210 -110 1 10 210 310

/ g]

2S

topp

ing

Pow

er [M

eV c

m

-210

-110

1

10

210Total stopping power

Radiative stopping power

Collision stopping power

Figure 2.16: Collision, radiative and total stopping power for electrons in TeO2 crystal. Thecrystal density is 6.04 g/cm3, corresponding to an average energy loss of about 1 MeV each 1.2mm (for an electron with a kinetic energy in the range 2÷ 3 MeV.)

2.6.2 Light trapping and surface effects of the crystal

Unfortunately the number of photons able to come out from the TeO2 crystal will be quitesmaller than 280; this is due to the light trapping that happens when an optical photontravels from a medium with a higher refractive index to one with a lower refractive index.In the interface region between the two media the photons propagation is described, foran ideal crystal with perfectly smooth faces, by Snell’s law:

n1 sin(θ1) = n2 sin(θ2) (2.15)

where n1 and n2 are the refractive index of the two materials and θ1 and θ2 are re-spectively the angles of the incident photon and of the refracted photon respect to thenormal of the boundary plane. The eq. 2.15 can be rewritten as:

sin(θ2) =n1n2

sin(θ1) (2.16)

If n1 > n2 and the angle of incidence is large enough, the light is completely reflectedby the boundary, a phenomenon known as total internal reflection. The largest possibleangle of incidence which still results in a trasmitted ray is called the critical angle:

θCrit = arcsin

(n1n2

sin(90)

)= arcsin

(n1n2

)(2.17)

In this case the trasmitted ray travels along the boundary between the two media; if theincident angle is grater than θCrit the photon is totally reflected inside the medium.

In the case of TeO2 crystal surrounded by vacuum (as the real one) θCrit = 19.1 ÷26.9 degrees (for photons with wavelength 300÷ 1000 nm using the ordinary refractive

2.7. Conclusion 49

index; for the extraordinary one θCrit = 17.4 ÷ 25.2 degrees). This small critical angleadded to the high symmetry of the cubic shape of the crystal leads to a high probabilitythat photons are internally reflected an indefinitely large number of times, i.e. theyremain trapped inside the crystal until absorption.

Fortunately, this trapping effect can be partially overcome thanks to the roughnessof the crystal surface that can randomly change the incident angle increasing the exitprobability of the photons. These two competitive effects rule the light yield of thecrystal.

Figure 2.17: A TeO2 crystal comes from samples of the CUORE batches, it is possible to notethe different roughness of the crystal faces.

The CUORE TeO2 crystals are cubes of 5 × 5 × 5 cm3 with translucent faces, twoof these (opposite) have a better polishing quality, close to optical polishing grade, theremaining four faces are rough: all the surface treatments are optimized to eliminate orminimize radioactive contaminations.

2.7 Conclusion

In this section the problem of the continuos α background measured in the TeO2 bolome-ter arrays as CUORICINO and CUORE-0 was presented; this background reaches the


unreducible limit of 0.02 counts/(keV kg y) in CUORE-0, where the best cleaning tech-nique and the ultimate assembly line of the CUORE experiment have been used. Theα particle discrimination is the last possibility to remove completely this backgroundcomponent from the TeO2 detectors arrays.

The way to performe this particle identification is detecting the Cherenkov radiationemitted by the β/γ interactions that, taken into account the Cherenkov photon up to1 µm, should have a total energy of about 780 eV at the Q-value of the 0νDBD decay(for temperatures below to 15 K).

In my Ph.D work I tested this possibility performing several test measurements atroom temperature and at cryogenic temperature, in order to asses the nature and theamount of the TeO2 crystal light yield. In the following sections these measurementswill be described and the result discussed and compared with a Monte Carlo simulationbased on the Litrani and Geant4 codes.

Chapter 3

Litrani: a general purpose MonteCarlo program simulating light

propagation in isotropic oranisotropic media

Before discussing the room temperature and cryogenic measurements on TeO2 lightyield a brief introduction on the Litrani software [85] will be made. For what concernsGeant4 [86, 87] one assumes that being a widely used and common simulation softwareit doesn’t need a detailed presentation.

3.1 Introduction

Litrani is a general purpose Monte Carlo program, built upon ROOT, to simulate lightpropagation in any type of set-up which may be represented by the shapes providedby the geometry of ROOT. The geometry of LITRANI is flat: it is not possible toplace a volume inside an other volume. Each shape may be made of a different materi-als. Dielectric constant, absorption length and diffusion length of materials may dependupon wavelength. Dielectric constant and absorption length may be anisotropic. Eachplane face of a volume may be either partially or totally in contact with another face ofanother volume, or covered with some wrapping having defined characteristics of absorp-tion, reflection and diffusion. When in contact with another face of another volume, thepossibility exists to have a thin slice of width d and refractive index n between the twofaces. The program has various sources of light: spontaneous photons, photons comingfrom an optical fibre, photons generated by the crossing of particles, photons generatedby the crossing of gamma rays of energy of 0.1 to 1 MeV or photons generated by an highenergy electromagnetic shower. The time and wavelength spectra of emitted photonsmay reproduce any scintillation spectrum. As detectors, one can have phototubes, APD,or any general type of surface or volume detectors. The aim is to follow each photonuntil it is absorbed or detected. Quantities of interest to be delivered by the programare the proportion of photons detected, and the time distribution for the arrival of these,or the various ways photons may be lost. The program takes into account the variationof the physical parameters as a function of the wavelength.

51

52 Chapter 3. Litrani: a general purpose Monte Carlo program simulating lightpropagation in isotropic or anisotropic media

3.2 Optical Material

The optical photons propagation inside an optical material can be simulated by Litraniusing essentially two parameters: the refractive index and the absorption length. Theinteraction with the lateral surfaces of the material can be simulated also in the case ofunpolished surface: the normal to the surface at the point hit by the photon is randomlytilted (with respect to the true normal of the surface) by an angle θ, which is generatedaccording to a distribution sin(θ)dθdφ, between 0 and θ∗. The parameter θ∗ is a functionof the surface roughness. Unfortunately there are some restrictions for the simulation ofunpolished surface:

• the use of grinded (unpolished) surface is only allowed for the faces of a shapecontaining an isotropic material. For an anisotropic material, Litrani gives up,because in the case of anisotropy, angle of reflection is not necessarily equal to theincident angle and this double diffusion effect cannot be parameterized efficiently.

• even if one declares a face to be grinded, the part of this face which is in contactwith another face of another shape is never treated as grinded by Litrani. Onlythe part of the face which is not in contact with another face (be it covered by arevetment or not) is treated as grinded

• another restriction is that one has not the right to declare as depolished a facehaving a revetment without slice (of air or something else) between the face andthe revetment.

However, bear in mind that this parameterization of the surface roughness is rathersimplified.

The TeO2 crystal is simulated in Litrani using this class, but as shown in section 2.6the TeO2 crystal is an anisotropic material and the 5 × 5 × 5 cm3 CUORE bolometershave four unpolished faces, this means that we cannot simulate all the surface effect thatcause the diffusion of the optical photons; one of the two effects must be neglected. Thedifference between the two refractive indices in the range 300÷1000 nm is 9÷6 %, thisproduces a difference in the Cherenkov photons emission of about 3 % and a variationin the critical angle of about 2 (as shown in section 2.6.1 and 2.6.2). These effects canbe neglected considering that the light yield variation produced by the diffusion effectof the surface roughness is expected to be greater than 50 %. For this reasons the TeO2

crystal is assumed to be isotropic with a refractive index equal to the ordinary one anda sourface roughness for the 5 × 5 × 5 cm3 crystal corrisponding to 20 degrees. Thisvalue has been evaluated from the comparison between the data and the simulations (seesection 5.3).

3.2.1 Revetment

An optical material or a portion of it can be covered with a revetment that can bea reflector, a diffuser or an absorber. Litrani allows to simulate all of them using as

3.3. Volume detector 53

input the real and imaginary part of the refractive index of the revetment. Litrani takesinto account also the possibility to simulate a slice of intermediate material between theoptical material and the revetment as for example air.

3.3 Volume detector

An optical material can be defined as “SENSIBLE”, this means that the material isconsidered to be the sensitive part of a detector: a photon that is absorbed inside thisshape is considered to be “SEEN” by the detector. Thanks to this option it is possibleto simulate the germanium light detector operation (see section 5.1).

3.4 Surface detector: photomultiplier

In Litrani it is possible to simulate a surface detector as one of the faces or subfacesof a shape. In that case, the photon is detected if it reaches the face or the subfaceof the shape, under these two conditions: acceptance angle of the photon and cathodeefficiency.

A phototube is a special case of a surface detector, with the following restrictions:the associated shape is a cylinder, there is a condition of cathode efficiency, there arenot conditions about acceptance angle; the length of the cylinder is the length fromits entrance window to the photocathode. In this way it is also possible to simulatethe interactions of optical photons with the window of the photomultiplier defining itsrefractive index and absorption length.

3.5 Particles, gammas and optical photons sources

The generation of a beam of particles can be done defining the starting position anddirection of emission of the particle. Every position and direction is given in the localcoordinate system of a shape which can be selected among all shapes of the set-up. Ingeneral, the surface of emission of the beam will be outside the reference shape.It is forbidden to emit the beam from within a shape which emits light when crossedby particles. So if the reference shape is made of a material for which it is defined thedE/dx it is not possible place the beam cradle inside this shape nor on one of its face,but strictly outside. It is possible to activate or deactivate the emission of Cherenkovlight by the particle.The generation and interaction of gamma ray is implemented in Litrani with an ap-proximate validity range of up to 1 MeV. There are two approximations made in theimplementation of this interaction:

• coherent scattering is not included

• scattered electrons are not simulated. Care should be taken when simulating gam-mas which have sufficient energy to eject electrons which will have a non-negligible

54 Chapter 3. Litrani: a general purpose Monte Carlo program simulating lightpropagation in isotropic or anisotropic media

path length. Non-negligible will depend on the application simulated, as well asthe materials involved and the homogeneity of the detector.

Pair creation is not implemented, entailing a maximum validity range of about 1.022 MeV.Therefore it is easy to simulate in Litrani the interaction of the cosmic muons withinthe crystal taking into account also the Cherenkov effect (as the simulation performedin section 4.1.5), instead it is impossible to evaluate the Cherenkov photons producedby the electrons originated by the gamma ray interactions within the crystal.For the simulation of this interaction the Geant4 code was used: the simulation wasdivided in two parts, in the first part the total amount of Cherenkov photons for eachinteraction is evaluated with Geant4, in the second part the propagation of the Cherenkovphotons inside the experimental set-up is reproduced by means of Litrani, which allowsto create optical photons with a certain wavelength inside the optical material (as thesimulation performed in sections 4.2.4, 5.3).

3.6 Monte Carlo Results

The results of the simulations are focused on the proportion of optical photons seenby the detectors. For the photons that are absorbed it is possible to know where andwhen this happens, if they have been absorbed by the material itself or by the revetmentand their path length; the same quantities are accessible for the photons seen by thedetectors. For these, also the incident angle with the detector can be known.

Chapter 4

The Cherenkov emission of TeO2crystal at room temperature

As show in chapter 2 the identification of the Cherenkov radiation produced by the β/γparticles can be a powerful tool to disentangle these interactions from the α ones.In order to quantify the amount and the nature of the photons emitted by the TeO2

crystals, two different measurements at room temperature were performed:

• in the first one a TeO2 crystal 5× 2.5× 2.5 cm3 crossed by cosmic muons was usedto set the nature of the light detected: Cherenkov emission or scintillation.

• in the second one a TeO2 crystal 5× 5× 5 cm3 hit by 511 keV γ rays was used tomeasure the absolute LY of the crystal.

In this chapter these two measurements will be presented, and the results comparedwith a Monte Carlo simulation developed to explain and predict the light emitted bythe TeO2 crystals.

4.1 Study of the Cherenkov emission with cosmic muons

The first important issue in the study of TeO2 light yield is the assessment and themeasurement of the Cherenkov contribution in the Light Yield (LY) of the crystal, andits discrimination from a possible scintillation emission. The differences between thesetwo processes are well known: scintillation light is isotropically emitted and usuallyshows a time development with an exponential decay typical of the material, Cherenkovlight is instead promptly emitted when a charged particle crosses the material, moreoverthe Cherenkov photons are emitted in a cone with an opening angle θC = arccos(1/(βn))with respect to the particle direction. As it was already demonstrated in Ref. [88, 89, 90,91, 92] the study of the signal shape and of the directionality of the light yield representsa useful tool to disentangle these two components.

4.1.1 Experimental Set-up

In order to exploit these differences for the TeO2 crystals the experimental setup shownin Fig. 4.2 was built. A 5 × 2.5 × 2.5 cm3 crystal (see Fig. 4.1 left) placed inside a

55

56 Chapter 4. The Cherenkov emission of TeO2 crystal at room temperature

black box was read-out on the two small opposite faces with two photo-multiplier tubes(PMTs) XP2970 1.

[nm]λ100 200 300 400 500 600 700 800 900 1000

Qua

ntum

Effi

cien

cy [%

]

0

5

10

15

20

25

30

Figure 4.1: Left: the 5 × 2.5 × 2.5 cm3 TeO2 crystal; all the surfaces are polished. Right:photo-cathode quantum efficiency of the PMTs (Photoninis XP2970 data-sheet available athttp://www.photonis.com/en/ism.php).

This PMT model has an extended sensitivity (see Fig. 4.1 right) in the UV regionwhere the production of Cherenkov photons is expected to be large. The two faces ofthe crystal read-out with the PMTs are polished and optically coupled with the PMTswindows in order to maximize the light transmission to the photocathode. The box wasfree to rotate in the XY plane giving the possibility of changing the angle ϕ betweenthe longest crystal axis and the horizontal direction in the range ±40 degrees.

The Cherenkov photons are emitted in a cone with an opening angle θc = arccos(1/(βn))with respect to the particle direction. Therefore the Cherenkov light transmission to aPMT is expected to be at a maximum when the crystal is parallel to the Cherenkov pho-ton direction. Since the TeO2 refractive index in the band of the detected light is about2.44, for an angle ϕM = 90 − θc = 24, PMT-Left is expected to see the maximumamount of Cherenkov light which, instead, reaches PMT-Right for ϕ = − 24. Inorder to select vertical muons in cosmic rays, the trigger signal to the data acquisitionwas provided by the coincidence of two 2 cm thick, 4 × 7 cm2 scintillator fingers placedabove and below the crystal. The distance between the scintillators was of about 50 cmand the trigger rate was about 0.1 Hz.

4.1.2 Light Yield components

The light produced by the cosmic muons interactions and exiting from a face of thecrystal can be separated into two components: one that is independent from the anglebetween the muon and the crystal and another one that is produced with a directionalityand for which the probability of exiting from a face of the crystal is a function of theangle ϕ. The first one (A) can be scintillation light or Cherenkov light diffused by theinternal reflections on the crystal faces loosing its initial directionality, the second one

110-stages, UV-Sensitive, 29 mm diameter, datashet at http://www.photonis.com/en/ism.php

4.1. Study of the Cherenkov emission with cosmic muons 57

Top Scintillator

x

y

ϕ

Bottom Scintillator

PMT-Right

PMT-Left

Muon

θc

TeO2

∼ -26− o

Figure 4.2: Experimental set-up.

(B(ϕ)) is expected to be entirely due to the Cherenkov photons. The total light exitingon the two lateral faces of the crystal will result:

L(ϕ) =α

cosϕ(AL +BL(ϕ)) (4.1)

R(ϕ) =β

cosϕ(AR +BR(ϕ)) (4.2)

with α and β being two parameters that take into account possible non-equalizations ofthe PMT responses while 1/cosϕ is proportional to the path length of the muon withinthe crystal. Because of symmetry reasons, one expects:

AL = AR = A (4.3)

BL(ϕ) = BR(−ϕ) = B(ϕ) (4.4)

For ϕ = 0 it follows:

L(0) = α (A+B(0)) = αk (4.5)

R(0) = β (A+B(0)) = βk (4.6)

Defining L(ϕ) and R(ϕ) as the responses equalized at ϕ = 0, it follows:

L(ϕ) =L(ϕ)cosϕ

L(0)=

1

k(A+B(ϕ)) (4.7)

R(ϕ) =R(ϕ)cosϕ

R(0)=

1

k(A+B(−ϕ)) . (4.8)


4.1.3 Data analysis

The waveforms of the signals provided by the two PMTs are acquired and analyzedoff-line. The average waveform of PMT-Right obtained for a thousand muon events andfor ϕ = 0 is shown in Fig. 4.3.

Time (ns)140 160 180 200 220 240

Am

plitu

de (

mV

)

-35

-30

-25

-20

-15

-10

-5

0

Entries 2683Constant 1671MPV 2.199

Integrated charge (pC)0 5 10 15 20 25 300

50

100

150

200

250

300Entries 2683Constant 1671MPV 2.199

Figure 4.3: Left: average signal shape of thousand muon events acquired by PMT-Right; thesmall bounces after the maximum position are due to a non perfect impedance matching betweenthe PMT and the oscilloscope. Right: example of the charge spectrum obtained integrating eventby event in a 15 ns wide time window around the maximum (Voltage·s/Ohm=C).

The signals show a rise and a decay time of the order of few nanoseconds. Thisvery fast behavior is a first indication that an important component of the light is dueto Cherenkov emission. In order to evaluate the charge produced by the PMT, thewaveforms are integrated, event by event, in a 15 ns wide time window around themaximum signal amplitude. An example of a charge spectrum obtained by the PMT-Right for ϕ = 0 is shown in Fig. 4.3-right. The fit of the charge spectrum with aLandau function returns the average charge and thus an evaluation of the light yield(see Fig. 4.3-right).

The effect of the electronics noise is computed by integrating the same waveformsin a 15 ns time interval before the signal pulse. The width of the pedestals resulted tobe about the 4% of the FWHM of the charge distribution of the signal. Therefore, theeffect of the electronics noise is negligible.

4.1.4 Results from the angular scan

The light reaching the two PMTs is collected for several crystal grades and the depen-dence of L(ϕ) and R(ϕ) on the angle ϕ are shown in Fig. 4.4.

The two sides show the same behavior. Analyzing the case of PMT-Left it is possibleto note that the detected light, corrected for the path length of the muon within thecrystal, is small and weakly dependent on the angle for ϕ far from ϕM . It shows amarked increase as long as ϕ approaches the value of ϕM where the transmission of theCherenkov light is expected to have a maximum. At angles much larger than ϕM adecrease of the amount of light reaching PMT-Left is also visible. A symmetric analysis


Angle-50 -40 -30 -20 -10 0 10 20 30 40 50

Nor

mal

ized

Res

pons

e

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

PMT Left

PMT Right

'M'M

Figure 4.4: Behavior of the LY responses corrected for the muon path length; the dotted linerepresent the expected maximum position for PMT-Left and PMT-Right normalized response.

applies to PMT-Right. This dependence on ϕ of the signals on the two sides of the crystalis a clear indication that a good fraction of the light is due to Cherenkov photons. Inorder to understand the nature of the flat component, the average waveforms of PMT-Right obtained for ϕ = ϕM and ϕ = −ϕM are reported in Fig. 4.5.

Time (ns)140 160 180 200 220 240

Ampl

itude

(mV)

-70

-60

-50

-40

-30

-20

-10

0

PMT Right for -ϕm

PMT Right for ϕm

Figure 4.5: Comparison between the average waveforms of the signals provided by PMT-Rightas obtained for ϕ = ϕM and ϕ = −ϕM .


Although the amplitudes are different, the signal shapes are the same. In particular,even for ϕ = ϕM , where Cherenkov photons cannot directly reach PMT-Right, the signalis very fast and shows a rise and a decay time of the order of few nanoseconds and doesnot show any slow or exponential tail. This indicates that also the flat component islikely due to Cherenkov light able to reach the PMTs by means of internal diffusion.

4.1.5 Monte Carlo Simulation

In order to confirm that the flat component is produced by the Cherenkov effect, andaccordingly no scintillation component contributes to the LY of the TeO2 crystal, aMonte Carlo simulation based on Litrani software (see chapter 3) was performed. Theexperimental set-up shown in Fig. 4.2 has been reproduced. The crystal has their sixlateral surfaces polished, for this reason a small value of θ∗ = 2 degrees was assumed(see Section 3.2 for a detailed explanation of the surface roughness parameterization per-formed by Litrani); nevertheless the simulation results for values of 0 ≤ θ∗ ≤ 10 degreesare compatible each other. The trigger system is not included in the simulation as ithas no influence on the measured data. A muon beam with an energy of 4 GeV (themean energy of muons at sea level) crossing the TeO2 was simulated: for each angle inthe range −40÷+40 degrees with steps of 10 degrees 50 muons are propagated.

In this simulation the only contribution to the LY of the TeO2 crystal came fromthe Cherenkov photons produced in the interaction of the muon within the crystal, noscintillation process is supposed to take place. The average number of photons seenby the PMT-Right NR(ϕ) and PMT-Left NL(ϕ) as function of the incident angle areshown in Fig. 4.6. The number of photons expected at angles far from ϕM (-24 degrees

ϕAngle -50 -40 -30 -20 -10 0 10 20 30 40 50

Num

ber

of p

hoto

ns

0

10

20

30

40

50

60

Figure 4.6: The average number of photons seen by the two PMTs: in black NR(ϕ) and in grayNL(ϕ).

for NR(ϕ) and 24 degrees for NL(ϕ)) should be almost zero. On the contrary, in Fig. 4.6


one can see that a considerable number of photons was detected even at disadvantageousangles for the light transmission to a PMT.This means that, although the Cherenkov photons are emitted in a cone with an openingangle θc with respect to the particle direction, the photons are reflected by the lateralsurface of the crystal. This interaction produces a flat component in the light yield,independent from the angle between the muon and the crystal. In order to comparethe data and the simulation results NR(ϕ) and NL(ϕ) are normalized for the number ofphotons seen at ϕ = 0 and corrected for the muon path lengh 1/cosϕ. The comparison

ϕAngle -50 -40 -30 -20 -10 0 10 20 30 40 50

Nor

mal

ized

Res

pons

e

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

'M'M

Figure 4.7: Behavior of the responses corrected for the muon path length: comparison betweendata (triangles) and simulation (bullets) for R(ϕ) (black) and L(ϕ) (gray).

between data and simulation (Fig. 4.7) shows that the LY of the TeO2 crystal canbe ascribed only to the Cherenkov radiation: the trend of R(ϕ) near the maximumposition (ϕM ∼ −24 degrees) is compatible with the measured one, confirming that thedirectional component B(ϕ) produced by the Cherenkov photons is very well reproducedby the simulation; also, at angles far from ϕM , where the contribution of B(ϕ) is almostzero and the flat component is dominant, the simulation reproduces the data; the sameconsiderations are valid for L(ϕ). Pointing out that the only interaction simulated ableto produces optical photons is the Cherenkov effect, it can be concluded that the LY ofthe TeO2 crystal can be totally explained with the only contribution of the Cherenkovphotons.This is also proven by the study of the charge asymmetry ∆(ϕ), the ratio between theisotropic component of the LY and the one that depends on ϕ; it is defined as:

∆(ϕ) =L(ϕ)−R(ϕ)

L(ϕ) +R(ϕ)=

B(ϕ)−B(−ϕ)

2A+B(ϕ) +B(−ϕ)(4.9)

For ϕ ' ϕM the angle-dependent component of the light reaches its maximum (Bmax)


ϕAngle -50 -40 -30 -20 -10 0 10 20 30 40 50

∆C

harg

e As

ymm

etry

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

'M'M

Figure 4.8: Behavior of the charge asymmetry ∆ as a function of the angle ϕ: comparisonbetween data (triangle) and simulation (bullet). The dotted line represent the positions wherethe angle-dependent component of the light reaches its maximum Bmax = B(ϕM ) and, on theother hand, B(−ϕM ) = 0

and, on the other hand, B(−ϕM ) = 0. Therefore:

∆(±ϕM ) = ± Bmax2A+Bmax

(4.10)

From the analysis of the data shown in Fig. 4.8 it results that ∆(−ϕM ) ' −0.45 and∆(ϕM ) ' 0.55 that means two values for A = 0.41Bmax and A = 0.61Bmax. Accordingto the average of the measurements, the ratio between the component of the detectedlight that depends on the angle ϕ and the total one is 0.66. A compatible result canbe obtained from the analysis of the simulated charge asymmetry (see Fig. 4.8). Theagreement between measured and simulated charge asymmetry confirms that the flat orisotropic component of the TeO2 LY is produced by the Cherenkov photons reflectedby the lateral surface of the crystal; any contribution due to scintillation light wouldincrease this component, mismatching simulations and data. This demonstrates thatthe contribution of an hypothetical scintillation process in the light yield of the TeO2

crystals is to be discarded.

4.2. Absolute light yield measurement with 22Na 63

4.2 Absolute light yield measurement with 22Na

In the previous section we demonstrated that the LY of the TeO2 crystal is entirely dueto the Cherenkov radiation. In order to completely characterize the light emission of thecrystal at room temperature an absolute measurement of the light yield is required.

In this section the evaluation of the number of Cherenkov photons emitted by thecrystal and the study of the effect on the light collection of wrapping the crystal with adiffusive material will be shown. The TeO2 crystal used to performe this measurementscomes from samples of the CUORE batches used to check the radiopurity and the bolo-metric performances during the production [93], and therefore is identical to the crystalsthat were mounted in CUORE.

4.2.1 Calibration of the photo-multipliers

A first step, needed to measure the absolute light yield of the crystal, is the calibrationof the PMT response. In particular, the evaluation of the charge provided for a singlephoto-electron (p.e.) is required.

[nm]λ100 200 300 400 500 600 700 800

Qua

ntum

Effi

cien

cy [%

]

0

5

10

15

20

25

30

Figure 4.9: Photo-cathode quantum efficiency of the PMTs (Hamamatsu R1924A data-sheetavailable at http://www.hamamatsu.com).

The chosen PMTs are two Hamamatsu R1924A PMTs: the 22 mm diameter windowin borosilicate glass provides these PMTs with a quantum efficiency larger than 10%between 300 nm and 550 nm, with a peak of about 25% around 400 nm (see Fig. 4.9),the same wavelengths range where the Cherenkov light signal is maximum. The PMTswere operated at 1200 V with a nominal gain of about 107. The signals provided by thePMTs were acquired by an oscilloscope with a bandwidth of 300 MHz and a samplingfrequency of 10 GS/s.In order to perform the PMTs calibration, the light produced by a blue LED was sent


to the PMT by means of an optical fiber. A rectangular electric pulse, 60 ns wide, wasused to drive the LED and to simultaneously trigger the oscilloscope acquisition. Adiaphragm placed upstream of the optical fiber allowed to regulate the amount of lightreaching the PMT window. With the diaphragm wide open the average PMT waveformshown in Fig. 4.10-left is obtained. The Fig. 4.10-right also shows the charge spectrum

Time (ns)0

Ampl

itude

(V)

-0.2

-0.15

-0.1

-0.05

0

500 1000

Mean 1.022Sigma 61.01

PMT response (pC)-200 0 200 400 600 8000

20

40

60

80

100

120

140

160

180

Mean 678.4Sigma 74.5

BEFORE TRIGGER

AFTER TRIGGER

Cou

nts/

35 p

C 200

Figure 4.10: Left: average waveform of the PMT signal illuminated by the LED with a wideopen diaphragm. Right: charge spectrum of the pedestal and of the signal, with superimposedGaussian fit, obtained by integrating event by event the LED signals (Voltage·s/Ohm=C).

obtained by integrating event by event the charge produced by the PMT in a 1 µs timewindow before the trigger and after the trigger. A Gaussian fit to the distributions allowsto extract the values of the fluctuations due to the electronics σe (before the trigger)and the total one σt (after the trigger). The value of the fluctuation of the charge signalσs can be obtained as:

σs =√σ2t − σ2e (4.11)

and results to be σs = 43±2 pC. In the hypothesis that σs is mainly due to the statisticalvariation of the total number of photoelectrons (np.e.) and that this number follows aPoisson distribution the value of np.e. can be calculated as:

np.e. =

(µ

σstat

)2

(4.12)

being µ = 687 ± 1 pC the average value of signal charge spectrum (Fig. 4.10-right). Itresults that, in this configuration, np.e. is 242± 30, so that, the charge produced by eachsingle p.e. (µ/np.e.) is about 2.8± 0.3 pC.To check the obtained results, a direct measurement of the charge produced by a singlephoto-electron was performed. The diaphragm was almost completely closed in order toreduce the amount of photons reaching the PMT. In some events, one or, very rarely,more than one peaks as the one shown in Fig. 4.11 are visible. Very likely these peaks aresignals produced by a single photon converted in an electron on the PMT photo-cathode.In order to check this hypothesis the distribution of the number of peaks per event isstudied. For each acquired waveform the number of times the signal exceeds a threshold


Time (ns)0 20 40 60 80 100

Ampl

itude

(V)

-0.1

-0.08

-0.06

-0.04

-0.02

0

Figure 4.11: Example of a peak visible in the configuration with almost closed diaphragm.Oscillations are due to a non perfect impedance matching between the PMT and the oscilloscope.

is analyzed. The threshold value is optimized by studying the behavior of the noisebefore the trigger. A time distance of at least 15 ns was required between two peaksin order to avoid multiple counting of the same signal due to the oscillations after thefirst peak (see Fig. 4.11). As it is shown in Fig. 4.12-left this quantity follows a Poisson

Number of photo-electrons0 2 4 6 8 101

10

210

310

410

510

Poisson distribution with mean value 0.25

Entri

es

MeanSigma

Charge (pC)-2 -1 0 1 2 3 4 5 61

10

210

310

2.88 1.04

Cou

nts/

0.1

pC

Figure 4.12: Left: distribution of the number of peaks per event with superimposed a poissonianfit. Right: spectrum of the charge integrated in a 10 ns time gate around the peak in theconfiguration with almost closed diaphragm with a superimposed Gaussian fit.

distribution as the number of photo-electrons is expected to. Moreover, a Gaussian fit tothe distribution of the charge integrated in a 10 ns time gate around the peak (2 ns beforeand 8 ns after the maximum amplitude) returns a value of 2.88±1.04 pC (Fig. 4.12-right)that is in very good agreement with the one found with the open diaphragm.

It is therefore possible to conclude that these peaks are signals due to single photo-


electrons and to confirm that 2.88 pC is the corresponding charge. The same calibrationperformed on the opposite PMT gives a value of about 2.70 pC.

4.2.2 Experimental Set-up

In order to measure the absolute light yield of the crystal the set-up shown in Fig. 4.13was prepared: the 5× 5× 5 cm3 crystal of TeO2 was placed in a light tight box, in orderto cross check the obtained results, the crystal was read out on two opposite opticalfaces (see section 2.6) by the two PMTs operated in the same configuration used for thecalibration measurement 2. The two LY values measured by the two PMTs are thereforeexpected to be equal. The idea is to measure the number of photo-electrons provided by

Figure 4.13: The experimental set-up.

the PMT for a given value of energy released in the crystal. A 22Na source was placedon one side of the black box, exposed towards a plastic scintillator. The signal of thescintillator PMT was sent to the oscilloscope, used as trigger and acquired. The sourcein use emits two back-to-back 511 keV photons, and, simultaneously, a 1274 keV photon,uncorrelated in space. Given the geometry of the system, in the triggered events one ofthe two 511 keV photons always reaches the TeO2 crystal.In order to select events where only the 511 keV photon reaches the crystal the thresholdon the trigger signal was tuned to select the events where the 1274 keV photon hits thetrigger scintillator. From the comparison of the results obtained in runs with and withoutthe 22Na source we evaluated that about 10% of triggers were due to noise in the triggerPMT.

4.2.3 Light yield measurement result

Two different measurements are performed using this set-up, the first one with the nakedcrystal, the second one with the wrapped crystal. In the wrapped configuration all thecrystal faces except for two holes faced to the PMTs were wrapped with Polytetrafluo-roethylene (PTFE) in order to maximize the amount of light collection in the PMTs.The response spectra of the TeO2 crystal obtained in the two runs are shown in Fig. 4.18

21200 V, gain 107, acquired by an oscilloscope with a bandwidth of 300 MHz and a sampling frequencyof 10 GS/s


with a superimposed double Gaussian fit. They present a narrow peak around 0, a largepeak around 1 photo-electron and a small tail for higher values.

-4 0 4 8 12 16 20

1

10

210

310

410

Charge (pC)

Cou

nts/

0.1

pC

-4 0 4 8 12 16 20

1

10

210

310

410

Charge (pC)

Cou

nts/

0.1

pC

Figure 4.14: Example of a charge spectrum of TeO2 crystal obtained with 22Na source inthe “naked” run (left) and in the “wrapped” run. The two visible Gaussian fits were used todetermine the number of events with 0 and 1 p.e.

Time (ns)-10 0 20 40 60 800

50

100

150

200

250

300

350

400

Coun

ts/ns

Figure 4.15: Measured distributions of the arrival time of the Cherenkov photons on the PMTwithout (grey) and with (white) wrapping on the crystal.

Since the number of produced photo-electrons is expected to follow a Poisson distribu-tion, if P(k) is the probability of detecting k photo-electrons, the average number µ ofcollected photo-electrons is given by:

µ =P (1)

P (0)(4.13)


where P (0) and P (1) are evaluated from the results of the fit, after subtracting the noisecontribution. The values of µ were calculated for the two PMTs and were found to be:µL = 0.015± 0.003 and µR = 0.016± 0.003.For the wrapped configuration the average number of photo-electrons were found to beµL = 0.036 ± 0.002 and µR = 0.036 ± 0.002. The use of the PTFE on all faces of thecrystal is able to increase by a factor 2.4 the number of photo-electrons detected. Animportant aspect is that the signal arrival time distribution shows a large tail on highvalues when the crystal is wrapped. This confirms that the light yield increase is due tophotons that are reflected and diffused by the wrapping and travel up to 30÷40 ns beforereaching the PMT instead of exiting the crystal from the lateral faces (see Fig. 4.15).This means that these photons travel up to 340÷ 450 cm inside the crystal, a value thatis compatible with the absorption length of TeO2 that for a 400 nm wavelength photonis about 80 cm (4÷ 5 attenuation length).

4.2.4 Monte Carlo simulation

In order to evaluate the absolute light yield of the TeO2 crystal at the low energies of thenatural radioactivity, a detailed simulation of 511 keV γ interactions within the crystaland of the readout system was developed and compared with the measured data.As explained in section 3.5 Litrani is not able to simulate the Cherenkov radiationproduced by the low energies γ interactions.

Entries 20000Mean 0.2695

Energy [MeV]0 0.1 0.2 0.3 0.4 0.5

coun

ts /

2 ke

V

-110

1

10

210

310

410


Events with no interactions

Figure 4.16: Simulation: spectrum of the energy deposited by the 511 keV photons in the TeO2

crystal.

For this reason the simulation was divided in two parts: in the first part the total amountof Cherenkov photons for each γ interaction is evaluated by means of Geant4, in thesecond part the propagation of the Cherenkov photons inside the different componentsof the experimental set-up is reproduced by means of Litrani.


Thanks to Geant4 it is possible to know the path and the kinetic energy of all electronsexcited by the γ interactions within the crystal. Applying the equation 2.12 to all theseelectrons it is possible to evaluate the total amount of Cherenkov photons produced inthe 511 keV γ interactions.The simulation starts with the emission of 2·104 γs with a total energy energy of 511 keV,from a point-like source located 5 mm from the TeO2 crystal with an isotropic angulardistribution inside the solid angle covered by the trigger scintillator (see Fig. 4.13).The energy deposition in the TeO2 crystal for each interaction is shown in Fig. 4.16.According to the simulation, given the geometry, in about 31% of triggered events the511 keV photon crossing the TeO2 crystal does not interact with it and the averageenergy released within the crystal is about 0.269 MeV. For each interaction within thecrystal (13733 events), the total number of Cherenkov photons with a wavelength in therange 300÷ 1000 nm is evaluated and its distribution is shown in Fig. 4.17.

Entries 13733

Mean 14.16

Number of Cherenkov photons0 10 20 30 40 50

coun

ts /

1 ph

oton

1

10

210

310

Entries 13733

Mean 14.16

Figure 4.17: Simulation: distribution of the number of Cherenkov photons produced per inter-action within the TEO crystal.

Fig. 4.17 shows that:

• in 12.1% of the interactions the photons emitted are equal to zero because theCherenkov threshold for an electron in TeO2 crystal is about 50 keV (see sec-tion 2.6.1);

• the peak around 30 photons is due to photo-electric effect within the crystal, i. eall the photon energy transferred to a single electron;

• the shoulder between 10 and 20 photon is instead due to single or multiple Comptonscattering.

By means of Litrani the Cherenkov photons are thus simulated inside the experimentalset-up reproduced coherently with the one shown in Fig. 4.13. As discussed in section 3.2


and section 3.4 also the diffusion effect produced by the unpolished lateral surface andthe PMTs quantum efficiencies were taken into account.The number of photons detected by the PMTs, i. e. photo-electrons, for the nakedset-up was found to be µ = 0.015± 0.002 and µ = 0.034± 0.002 for the wrapped one, ingood agreement with the measured ones.


N photons detected-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

s si

mul

ated

γN

1

10

210

310

410



N photons detected-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

s si

mul

ated

γN

1

10

210

310

410


Figure 4.18: Simulation: number of photons detected by the PMT-Left in the “naked” config-uration (left) and in the “wrapped” one. The number of γ interactions in which 0 photons aredetected, it is corrected taken into account the trigger efficiency (the 31% of γ-rays that do notinteract with the crystal.)

The values of θ∗ (the quantity that parametrizes the crystal surface roughness in Litrani)for which the simulation reproduces the acquired data are in the range 10÷ 40 degreesaccording to the fact that the four lateral surfaces of the CUORE TeO2 crystal areunpolished (see Fig. 4.19).

[deg]θ0 10 20 30 40 50 60

Ligh

t Yie

ld [p

.e.]

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Figure 4.19: Simulation: average number of photo-electrons detected by the PMTs as functionof the surface roughness. The green dotted lines represent the range values of θ∗ that reproducethe measured light yield.

Also the simulation results show (see Fig. 4.20) that, thanks to the reflection on thewrapping, several photons that would have been lost are instead driven toward the

4.3. Conclusions 71

PMTs and are detected after having traveled for up to 30 ns (about 3.4 meters insidethe crystal). The simulated distributions of the time of arrival for the naked and wrappedset-up show smaller tails for large time values with respect to the data shown in Fig. 4.15:probably this can be explained with an instrumental time jitter of the PMT trigger thatwas not accounted for in the simulation.


Time [ns]-10 0 10 20 30 40 50 60 70 80

N p

hoto

ns /

ns

0

50

100

150

200

250

300


Figure 4.20: Simulation: distributions of the arrival time of the Cherenkov photons on the PMTwithout (grey) and with (white) wrapping on the crystal.

4.3 Conclusions

The two measurements shown in this chapter demonstrate the existence of a light emis-sion from the TeO2 crystals. This light signal can be totally explained taking into accountonly the photons produced by the Cherenkov effect. No scintillation light contributionwas measured in agreement with the Monte Carlo simulation that discards the existenceof this type of contribution to the crystal light yield.For a 5 × 5 × 5 cm3 CUORE crystal this light yield at room temperature is 0.015 ÷0.016 photo-electrons for an average energy deposition of about 270 keV. By means ofthe Monte Carlo simulation it was possible to demonstrate that this light yield derivesfrom a number of primary Cherenkov photons (produced inside the crystal) equal to52 photons/MeV (evaluated in the wavelength range between 300 and 1000 nm and foran average energy deposition of about 270 keV). The effect of a reflective and diffusivewrapping was studied. The most promising result was obtained by covering all lateralfaces with PTFE, that allowed to increase the number of photons reaching the PMTsby a factor 2.4.

Chapter 5

The Cherenkov emission of theTeO2 bolometers

In the previous chapter the nature and the value of the LY at room temperature forthe TeO2 crystals was measured. In this chapter the study of the TeO2 LY at 10 mKwill be shown. These measurements were performed in the CUORE/LUCIFER R&Dcryostat [94], placed in the Hall C of Laboratori Nazionali del Gran Sasso. Also in thischapter the data obtained will be compared with the Monte Carlo results.

5.1 Low temperature light detector

The development of an high efficiency and high resolution light detector able to work atcryogenic temperature (∼ 10 mK) is today an open issue. Besides the efficiency and res-olution requirements, they must satisfy very high radiopurity level and high scalability.Up to now the more affordable technology in terms of cost and scalability is the bolo-metric one, even if in terms of resolution the best performances are obtained with thetransition edge sensor (TES) technology, as in the CRESST dark matter experiment [95].

A bolometric light detector can be realized using an opaque semiconductor: in thatcase it is sensitive over an extremely wide range of photon wavelengths and satisfies thevery stringent radiopurity requirements of rare event searches. Their overall quantumefficiency can be as good as the one of photodiodes, providing at the same time an higherenergy resolution. Moreover, they are much easier to operate at cryogenic temperatures.The LUCIFER collaboration [96] chose this technology to detect the light emitted bytheir scintillating bolometers: the final detector will be a disk-shaped pure Ge crystal( 44 mm × 180 µm) grown by UMICORE using Czochralski technique, etched on oneside and polished on the other one. A SiO2 layer is deposited on the side that facesthe scintillating bolometer to increase the light collection efficiency. Its temperaturevariation is detected via a 3× 1.5× 0.4 mm3 NTD Ge thermistor, thermally coupled tothe etched side of the crystal with 6 epoxidic glue spots of about 600 µm diameter and50 µm height [97].

73

74 Chapter 5. The Cherenkov emission of the TeO2 bolometers

5.2 Cherenkov light measurement with Germanium lightdetector

In this section the results of several R&D measurements facing a Ge light detector (GeLD) to a TeO2 crystal will be presented. The used Ge LDs are developed for the LU-CIFER R&D on scintillating bolometers. The results are compared with a dedicatedMonte Carlo simulation of the Cherenkov photons creation and propagation in the ex-perimental set-up. Several cross-checks between simulation and data will also shown.

5.2.1 Experimental set-up

The TeO2 crystal operated as bolometer comes from samples of the CUORE batchesused to check the radiopurity and the bolometric performances during the production[93], and therefore is identical to the CUORE crystals. All faces are surrounded bythe VM 2002 light reflector except for an optical one that is monitored by a 5 cm indiameter, 300 µm thick germanium light detector (LD). The temperature sensor of theTeO2 crystal was a NTD Ge thermistor of 3×3×1 mm3, thermally coupled to the crystalsurface by means of 9 epoxy glue spots of about 0.6 mm diameter and 50 µm height.The LD was equipped with a NTD Ge thermistor of 3×1.5×0.4 mm3. The detectors areheld in a copper structure by means of teflon (PTFE) supports (see Fig. 5.1), anchoredto the mixing chamber of the CUORE/LUCIFER R&D dilution refrigerator.

Figure 5.1: The TeO2 crystal in the copper holder, surrounded by a 3M VM 2002 light reflectorand monitored by the germanium bolometric light detector.

Both the TeO2 crystal and the Ge LD have also an heater glued on top, this device is usedto inject a calibrated pulse in the bolometer in order to correct gain instabilities [98].The voltage signals, amplified and filtered by means of an anti-aliasing 6-pole activeBessel filter (120 dB/decade), were acquired by a NI PXI-6284 18-bits ADC with asampling frequency of 1 kHz for the TeO2 crystal and 2 kHz for the Ge LD . The Bessel

5.2. Cherenkov light measurement with Germanium light detector 75

cut-off frequency could be adjusted according to the signal bandwidth and to the noisecontributions. For these test, the Bessel cutoff is set at 120 Hz for the LD and at 16 Hzfor the TeO2. Further details on the cryogenic facility and the electronic read-out canbe found in Refs. [99, 100, 94].

The trigger is software generated on each bolometer: if the amplitude of a TeO2

pulse or a LD pulse exceeds a given threshold for a given amount of time, waveforms 5 slong on the TeO2 and 250 ms long on the LD are saved on disk. In addition, whenevera TeO2 pulse was triggered, a 250 ms window length was acquired on the LD detectortoo, irrespective of its trigger. This second condition on the LD trigger system wasintroduced because the expected Cherenkov light signal is very small, comparable withthe LD noise (hundred of eV). These very small light pulses, overwhelmed by the noise,would not be acquired using the software trigger. Exploiting the time coincidence withthe TeO2 signals, the second trigger prevents the loss of the Cherenkov light signals.To calibrate the TeO2 and to generate events in the 0νDBD region, the setup waspermanently exposed to a 232Th γ-source placed just outside the cryostat. The LD isexposed to a permanent 55Fe source, providing 5.9 and 6.5 keV calibration X-rays.

5.2.2 First level data analysis

For each acquired signal the amplitude of the pulse is evaluated with the optimum filteralgorithm (OF) [101, 102]. This algorithm is able to evaluate the amplitude of the pulsemaximizing the signal to noise ratio in the frequency domain. In order to use the OFone starts with the assumption that the acquired pulse can be written as:

p(t) = b+A · S(t− t0) + n(t) (5.1)

where b is the baseline value, obtained averaging the pre-trigger interval, A the pulseamplitude, S(t) the theoretical response function of the detector and n(t) stochasticnoise. The parameter t0 must be introduced to account for any possible jitter betweenthe observed signal and S(t). If the theoretical response function of the detector isunknown, S(t) can be evaluated by averaging a large number of pulses, so that thecontributions from the random noise averages to zero.The transfer function H(ω) that maximizes the signal to noise ratio can be written as:

H(ω) = kS∗(ω)

N(ω)eiωtM (5.2)

where S(ω) is the Fourier transform of S(t), N(ω) is the noise power spectrum, k isa normalization constant and tM is the time at which S(t) is maximum. It can beobserved that one is implicitly assuming that the pulse shape is independent of am-plitude. This approximation, which is not exactly true, is compensated by applying anon-linear calibration function. N(ω) is evaluated averaging the Fourier transform ofwaveforms without signal (noise waveforms) acquired at regular time intervals all overthe measurement.

Each acquired signal p(t) is Fourier transformed and then multiplied by H(ω). Then,(p(ω) · H(ω)) is transformed back into the time domain, where the maximum value of


the OF output gives the pulse amplitude (see Fig. 5.2). Since the maximum value couldfall between discrete data samples, a parabolic interpolation is used to obtain a moreprecise evaluation of the amplitude.

Time [s]0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Am

plitu

de [

mV

]

0

20

40

60

80

100

120

140

160

2Avg. pulse - TeO

originalfiltered

Time [s]0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

Am

plitu

de [

mV

]

0

5

10

15

20

25

30

35

Avg. pulse - Ge LDoriginalfiltered

Frequency [Hz]1 10 210

/Hz

2m

V

-910

-810

-710

-610

-510

-410

-310

-210

-110

1

2Noise - TeOoriginalfilterednorm. avg. pulse

Frequency [Hz]10 210 310

/Hz

2m

V

-1210

-1110

-1010

-910

-810

-710

-610

-510

-410

-310

-210

Noise - Ge LDoriginalfilterednorm. avg. pulse

Figure 5.2: Up-Left: TeO2 average pulse evaluated on the 232Th γ interactions (black). Thesame pulse filtered with the OF technique is reported (red). Up-Right: LD average pulse eval-uated on the 55Fe X-rays (black). The same pulse filtered with the OF technique is reported(red). Down-Left: TeO2 average noise power spectrum (black); the same power spectrum afterthe filter (red); average signal power spectrum (green). Down-Right: LD average noise powerspectrum (black); the same power spectrum after the filter (red); average signal power spectrum(green).

5.2.3 Data analysis

The energy spectra acquired by the TeO2 bolometer and by the Ge LD in 6.86 days ofdata taking are shown respectively in Fig. 5.3 and in Fig. 5.4. The peak around 5400 keVis due to the α-decay of 210Po, a natural contamination of the TeO2 crystal, observedalso in CUORE-0. The remaining peaks are γs from the 232Th source, except for thepeak at 1461 keV, which is a γ from 40K contamination of the cryostat. Both the single(SE) and double escape (DE) peaks of the 2615 keV from 208Tl are visible.The energy resolution at the 2615 keV 208Tl peak from the thorium source is 11.5 keVFWHM, worse than the 5.7 keV FWHM obtained averaging all the CUORE-0 bolome-ters. This might be due to the slightly higher temperature of this test or to the different


hHeat__1Entries 16211

Mean 730.9

RMS 622.5

Energy [keV]0 1000 2000 3000 4000 5000 6000

coun

ts /

5 ke

V

1

10

210hHeat__1

Entries 16211

Mean 730.9

RMS 622.5

Th Calibration: 6.86 days232

Po210 α

Tl208

Pb212 511

Tl208 Ac228

Ac228

K40

2615 DE2615 SE

Figure 5.3: Energy spectrum acquired by the TeO2 crystal. All the labeled peaks are γs, exceptfor the single and double escape peaks of the 2615 keV γ from 208Tl, which are β + β+ + γ andβ + β+ events, respectively, and for the events around 5.4 MeV, which are generated by theα-decay of 210Po in the crystal.

Energy [keV]0 1 2 3 4 5 6 7 8

coun

ts /

0.00

8 ke

V

1

10

210

310

Fe Calibration: 6.86 days55

: 6.86 days2

Events triggered by TeO

Fe55Smeared auger electron from

5.9 keV X-ray

6.4 keV X-ray

Figure 5.4: Energy spectrum acquired by the Ge light detector. The two X-ray peaks and thesmeared auger electron come from the 55Fe source faced on the top of the LD. A huge numberof events acquired on the LD thanks to the TeO2 trigger (gray histogram) are below 0.5 keV.Random coincidences between the TeO2 trigger and the LD iron source can also be seen.


assembly, but it does not affect the results since the attention is focused on the light sig-nal. On the LD energy spectrum, besides the two X-rays used for the energy calibration,the smeared auger electrons output from the 55Fe source are also visible. The energyresolution at the iron peaks and at the baseline is 135 and 72 eV RMS, respectively.

5.2.4 The synchronization algorithm

In Fig. 5.5 it is shown a typical LD event triggered by a 2615 keV γ from 208Tl thatinteracts within the TeO2 bolometer: as expected the light signal is overwhelmed by thenoise of the detector, therefore no pulse is visible on the LD acquired window.

Time [s]0 1 2 3 4 5

Am

plitu

de [

mV

]

0

20

40

60

80

100

120

140

Time [s]0 0.05 0.1 0.15 0.2 0.25

Am

plitu

de [

mV

]

-1

-0.5

0

0.5

1

1.5

Figure 5.5: Left: 208Tl event on the TeO2 bolometer. Right: the correspondent acquired windowon the LD. In black the original pulses and in red the filtered ones.

This means that an algorithm which associates the energy of the event with the maximumof the acquired window fails because it could pick up a noise fluctuation as signal: theamplitude evaluated will be the maximum value of the noise pedestal instead of the realsignal amplitude. To prevent this, an algorithm to optimize the energy threshold of lightdetectors was developed [103]: it is based on the observation that the amplitude of thelight signal must be estimated from the value of the filtered waveform at a fixed timedelay with respect to the signal in the TeO2 bolometer. In this way the noise pedestalis eliminated. The amplitude measured is the real signal amplitude, smeared by thenoise distribution, which is a Gaussian centered at zero amplitude. Events in concidencebetween the two bolometers are needed to evaluate this characteristic time delay.

With the TeO2 bolometer this can be done averaging the LD waveforms acquired bythe TeO2 trigger: the noise contribution will be drastically reduced and the Cherenkovsignal pulse appears as it is shown in Fig. 5.6. Using this pulse it is possible to evaluate itsdelay with respect to the signal in the TeO2 bolometer. When the time delay is known thesynchronization algorithm can be applied to the LD waveforms and the real Cherenkovlight energy as function of the energy released in the TeO2 crystal can be obtained. InFig. 5.7 the two results obtained using the two different amplitude evaluation algorithmsare shown:

• the wrong one, which associates the energy of the event with the maximum of the


Time [s]0 0.05 0.1 0.15 0.2 0.25

Am

plitu

de [

mV

]

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35 Average Cherenkov pulse

OF of average Cherenkov pulse

Figure 5.6: Average pulse performed on the LD waveforms with energy below 1 keV triggeredby TeO2 β/γ events with an energy release between 1 and 2.64 MeV (3102 events). The greenline represents the time value for which the amplitude of the pulse is maximum.

acquired window (Fig. 5.7-left)

• the correct one, which associates the energy of the event with the amplitude ofthe filtered waveform at a fixed time delay with respect to the signal in the TeO2

bolometer (Fig. 5.7-right)

These two scatter plots summarize all the points discussed above.

Energy [keV]0 1000 2000 3000 4000 5000 6000

Max

imum

Lig

ht E

nerg

y [k

eV]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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Figure 5.7: Left: the maximum of the filtered LD waveforms is shown as function of the energyreleased in TeO2 bolometer. Right: the amplitude of the filtered LD waveforms evaluated at thecharacteristic time delay is shown as function of the energy released in TeO2 bolometer.


5.2.5 Results

The scatter plot obtained with the synchronization algorithm can be now analized (seeFig. 5.8): the distribution of the light corresponding to each peak in Fig. 5.3 (blue dots inthe scatter plot) is fitted with a Gaussian, the mean of which is overlaid onto the figure;an example of the Gaussian fit for the light detected at the 208Tl photopeak it is shown inFig 5.9. The mean light from the α-decay of 210Po is found to be< Lα >= −3.9±14.5 eV,i.e. compatible with zero.

Energy [keV]0 1000 2000 3000 4000 5000 6000

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S1_LvsH

/ ndf 2χ 8.358 / 7 [keV] thE 63± 283

Yield [eV/MeV] 2.0± 45.2

/ ndf 2

χ 8.358 / 7

p0 0.002443± -0.01279

p1 2.004e-06± 4.518e-05

/ ndf 2

χ 8.358 / 7

p0 0.002443± -0.01279

p1 2.004e-06± 4.518e-05

/ ndf 2

χ 8.358 / 7

p0 0.002443± -0.01279

p1 2.004e-06± 4.518e-05

Figure 5.8: Detected light versus calibrated heat in the TeO2 bolometer for all the acquiredevents (gray) and for the events belonging to the peaks labeled in Fig 5.3 (blue). The mean lightis clearly energy dependent for the γ peaks (red circles below 3 MeV) and compatible with zerofor the α-decay of the 210Po (pink circle at 5.4 MeV).

The mean light from the γ peaks is fitted with a line:

< Lβ/γ >= LY · (Energy − Eth) (5.3)

with Eth = 283±63 keV and LY = 45±2 eV/MeV. The standard deviations of the lightdistributions are found compatible with the baseline noise of the LD, which thereforeappears as the dominant source of fluctuation, hiding any possible dependence on theposition of the interaction in the TeO2 crystal or statistical fluctuations of the numberof photons. The light from the double escape peak is compatible with the light fromγs, indicating that the fitted line can be used to predict the amount of light detectablefrom 0νDBD events. One computes 101.4± 3.4 eV of light for a β/γ event with 0νDBD


energy: the amount of detected light at the 0νDBD is small, at the same level of the LDnoise, and does not allow to perform an event by event rejection of the α background.

Entries 417

Mean 0.1062

RMS 0.0791

/ ndf 2χ 8.002 / 8

Constant 6.3± 102.6 µ 0.0040± 0.1064

σ 0.00296± 0.07956

Light energy [keV]-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

coun

ts /

0.05

keV

0

20

40

60

80

100

Figure 5.9: The distribution of the light detected at the 208Tl peak fitted with a Gaussian.

5.2.6 Light Yield optimization

In order to increase the light collection efficiency, different modifications to the setupwere tested:

• the VM 2002 light reflector was changed to aluminum foils. Aluminum is expectedto have higher reflectivity in the UV (300 ÷ 400 nm) band, the region where theCherenkov emission is more intense. Despite of that, the amount of light detectedis 25% less than in the case of VM 2002;

• the VM 2002, which is a specular light reflector, was removed and the crystalwrapped with teflon tape, which is a light diffusor. The amount of light detectedis compatible with the VM 2002 measurement;

• the LD was changed to an identical one, but the side faced to the TeO2 was coatedwith 60 nm of SiO2. It has been demonstrated, in fact, that in the red/infraredband this layer enhances the light absorption by up to 20% [104, 105]. In thisset-up, however, the amount of light detected does not change significantly;

• a second LD was added, monitoring opposite faces with two different light detec-tors. The amount of light detected from each LD is found to be the 50% of theamount detected with a single LD. This causes an overall decrease of the signal tonoise ratio, because each LD adds its own noise;


• the crystal was replaced with a cylindrical one, 4 cm in diameter and in height.Again the amount of light detected does not change.

Summarizing, none of the above trials succeeded in providing a significant increase ofthe light collection efficiency, indicating that most of the light is absorbed by the TeO2

crystal. The setup providing the highest light signal, around 100 eV at the 0νDBD,consists in a single LD with the crystal surrounded by the VM 2002 reflector or wrappedwith teflon tape.

5.3 Monte Carlo simulation

As indicated in Ref. [79] and evaluated in section 2.6.1, the produced Cherenkov lightamounts to about 780 eV, a much higher value than what was detected. In order tounderstand the disagreement between the expected signal and the measured one a MonteCarlo simulation was performed. As discussed in section 4.2.4 the simulation was splitin two parts: the total number of Cherenkov photons was evaluated using Geant4, thepropagation of these photons inside the different components of the experimental set-upis reproduced by means of Litrani.The simulated energy spectrum produced by the 208Tl, 40K and 228Ac γ interactionswithin the TeO2 crystal is shown in Fig. 5.10.

histototEntries 900Mean 0.8821RMS 0.7043

Energy [MeV]0 0.5 1 1.5 2 2.5

Cou

nts

/ 3 k

eV

1

10

210

310

410histotot

Entries 900Mean 0.8821RMS 0.7043

Tl208

2615 SE

2615 DE

K40 Ac228

511

Figure 5.10: Spectrum of the energy deposited by the 2615 keV, 1460 keV and 911 keV (208Tl,40K and 228Ac respectively) photons in the TeO2 crystal as obtained from the Monte Carlosimulation (Geant4). In addition to the photopeaks we can see the SE, DE and the 511 keVpeak.

Selecting, for example, the events in the 208Tl photopeak it is possible to know the kineticenergy and the path of all electrons and positrons produced in these interaction; usingthe equation 2.12 it is possible to evaluate the number of Cherenkov photons produced

5.3. Monte Carlo simulation 83


Number of Cherenkov photons100 150 200 250 300 350 400

coun

ts /

1 ph

oton

0

10

20

30

40

50 Entries 3168Mean 261.7RMS 39.68

Figure 5.11: Number of Cherenkov photons produced by the 2615 keV γ interactions that havereleased all their energy in the crystal.

by each e± particle with a kinetic energy greater than 50 keV (see Fig. 5.11).The six most intense peaks are chosen to compare the light detected in the data with theone predicted by the simulation: using the same procedure carried out for the 208Tl, thenumber of Cherenkov photons are evaluated for the remaining five peaks (see Fig. 5.10).

Once the number of Cherenkov photons produced is known, it is possible to simulatetheir propagation in the experimental set-up with Litrani; the optical properties of thegermanium and VM 2002 reflective foil are shown in Fig. 5.12.

[nm]λ300 400 500 600 700 800

Ref

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ive

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x

3.5

4

4.5

5

5.5

6

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orpt

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cm]

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-510

[nm]λ300 400 500 600 700 800 900 1000

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10A

bsor

ptio

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ngth

[cm

]

0

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0.6

0.8

1

-610×

Figure 5.12: Left: germanium optical properties from Ref. [106], red dots for the real part ofthe refractive index and blue dots for the absorption length. Right: VM 2002 optical propertiesfrom Ref. [85], red dots for the real part of the refractive index and blue dots for the absorptionlength. The refractive index less than 1 for the VM 2002 means that the incident photon istotally reflected.

For each peak 100 interactions are simulated; the total number of Cherenkov photons


and their wavelength distribution for the 208Tl photopeak are shown in Fig. 5.13. TheCherenkov energy emitted can be obtained integrating this distribution (Fig. 5.13-right):the average energy emitted for interaction is equal to 744.4 eV.


Number of Cherenkov photons100 150 200 250 300 350 400

coun

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30 p

hoto

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0

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4

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Entries 26638

[nm]λ300 400 500 600 700 800 900 1000

Num

ber

of p

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ns /

5 nm

0

100

200

300

400

500

600

Entries 26638

Figure 5.13: Distribution of the number of Cherenkov photons (left) and their wavelengthdistribution (right) produced in one hundred 208Tl γ interactions simulated by means of Litrani.The distribution of the number of Cherenkov photons is randomly generated according to thedistribution shown in Fig. 5.11, their wavelength distribution is randomly generated accordingto the distribution shown in Fig. 2.14.

Each Cherenkov photon is propagated through the materials until it is absorbed:if it is absorbed inside the Germanium disk it is considered as detected. The numberof photons detected and their wavelength distribution for the 208Tl peak are shown inFig. 5.14.


Number of Cherenkov photons0 20 40 60 80 100

coun

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2 ph

oton

s

0

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Entries 4876

[nm]λ300 400 500 600 700 800 900 1000

Num

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5 nm

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50

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70Entries 4876

Figure 5.14: Distribution of the number of Cherenkov photons (left) and their wavelength dis-tribution (right) absorbed by the germanium disc in one hundred 208Tl γ interactions simulatedby means of Litrani. The reduction of photons detected by the LD between 300÷ 400 nm is dueto the low reflectance efficiency of the VM 2002 reflective foil in that wavelengths range. Therefractive index less than 1 for the VM 2002 means that an incident photon is totally reflected

The total Cherenkov energy absorbed by the LD can be evaluated integrating thespectrum of Fig. 5.14, that results to have an average value of 117.8 eV for interaction.The same procedure is applied to the other five peaks: the results compared with the

5.3. Monte Carlo simulation 85

measured data are shown in Fig. 5.15. The simulation well reproduces the experimentaldata and confirms that the Cherenkov light detected is only 18% of the produced one:60% of the Cherenkov photons are absorbed by the TeO2 crystal, 22% absorbed by thereflective foil and by the LD copper frame.

The values of θ∗ used for the simulation of the surface roughness of the 4 lateral facesof the crystal is 20 degrees in agreement with the simulation performed in section 4.2.4.The Monte Carlo results are fairly dependent by this last parameter and a detailed studyof the light emitted as function of θ∗ will be shown in the next sections, but first twocross-check on the simulation will be presented.

Energy [keV]0 500 1000 1500 2000 2500 3000

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V]

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30Energy [keV]

0 500 1000 1500 2000 2500 3000

Ligh

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rgy

[eV

]

0

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80

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120 Data

MC

Figure 5.15: Measured (filled black circles) and simulated (empty black circles) energy releasein the Ge LD. The red dots represent the ratio between data and Monte Carlo.

5.3.1 Monte Carlo approximations and cross-checks

In addition to the approximation discussed in section 3.2 about the TeO2 crystal refrac-tive index other approximations have been made: the refractive index and the absorptionlength of the Germanium disk [106] and the real and imaginary part of the refractiveindex of the VM 2002 reflective foil [85] have been found in literature only at roomtemperature. To test the validity of the Monte Carlo two cross-checks have been made.First, from the set-up shown in Fig. 5.1 the reflective foil has been removed, and themeasurement described in section 5.2.1 has been repeated, but using the naked crystal


(see Fig. 5.16-left).

Energy [keV]0 500 1000 1500 2000 2500 3000

Dat

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V]

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0 500 1000 1500 2000 2500 3000

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[eV

]

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60Data

MC

Figure 5.16: Left: the naked TeO2 crystal in the copper holder. Right: measured (filled blackcircles) and simulated (empty black circles) energy release in the Ge LD. The red dots representthe ratio between data and Monte Carlo

As expected the mean light from the α-decay of 210Po is found to be again compat-ible with zero (< Lα >= −48 ± 37 eV), the mean light detected for the γ peakssmaller. Performing the previous fit (see Eq. 5.3) we obtained Eth = 335 ± 310 keVand LY = 17 ± 3 eV/MeV. This means that the VM 2002 reflective foil increases thelight collection efficiency of the set-up by a factor ∼ 2.6.

A new simulation using the same procedure shown in section 5.3 was performed;the only difference in the Monte Carlo is the absence of VM 2002 reflective foil. TheCherenkov energies detected for the six most intense peaks compared with the measuredones are shown in Fig. 5.16-right; also the results obtained with this set-up can bereproduced by the Monte Carlo.The second cross-check can be made considering the measurement performed in Ref [107]where a smaller TeO2 crystal was used to study for the first time the Cherenkov emissionof TeO2 bolometer (a 3.0 × 2.4 × 2.8 cm3 TeO2 crystal doped with natural samarium).The light detected at the 208Tl line was found to be 195± 7 eV; reproducing that set-up(TeO2 crystal surround by VM 2002 reflactive foil monitoring with a Germanium disk66 mm diameter 1 mm thick covered with a 600 A layer of SiO2 operated as bolometer)the simulated energy detected is 204 eV, in agreement with the measured one. Theseresults are a further evidence that, despite the approximations performed, the MonteCarlo simulation developed in this work is able to reproduce and predict the Cherenkovlight yield of TeO2 bolometers.

5.4. Study of the Monte Carlo output 87

5.4 Study of the Monte Carlo output

In this section the Monte Carlo output will be analysed in detail in order to understandwhy the detected Cherenkov light is so smaller than the produced one. One starts withthe study of the light propagation in the naked set-up (crystal + germanium disk);only the case of the 208Tl interaction will be studied, for the other γ interactions theconclusions are exactly the same. The propagation of the Cherenkov photons emittedfrom the interaction of one hundred 208Tl γs is simulated. For this study the numberof Cherenkov photons emitted for interaction is fixed to 262 (equal to the mean of thedistribution shown in Fig. 5.11). The photons able to exit from the six crystal facesare 66% of the total, about 174 photons for interaction, as it is shown in Fig. 5.17, theremaining 34%, about 88 photons for interaction, are trapped inside the crystal andabsorbed.

gEntries 6Mean 3.656RMS 1.742

Crystal faces1 2 3 4 5 6

Ave

rage

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g ph

oton

s

0

5

10

15

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25

30

35

40

gEntries 6Mean 3.656RMS 1.742

Figure 5.17: Average number of photons exiting from the six crystal faces: the faces 1-2-3-4 arethe rough ones, 5-6 are the polished ones.

A first important information is that the two opposite polished surfaces (5 and 6 inFig. 5.17) allow the photons to come out more easily than the rough ones. Neverthelesswithout the diffusion effect produced by the 4 unpolished lateral faces, the light emittedis quite small (as will be shown in the next section).Only 23.6 photons of the 34 photons exiting from the top crystal face reach the LDplate: this happens because the empty space between the top face of the crystal and theLD (1.2 cm spaced) allows 10.4 photons to leave the set-up immediately after exitingfrom the crystal. The photons that reach the LD plate can be absorbed or reflectedby the germanium disk and by its copper holder; if they are reflected back towards thecrystal they can be reabsorbed into the crystal or leave the set-up. As the germaniumreflectivity between 300 ÷ 1000 nm is in the range 59 ÷ 40% and the TeO2 one is in


the range 16 ÷ 14% (for incident angle < 40 degrees) one can easily understand whythe photons absorbed by the light detector are only about 12.6 compared to the 23.6incident photons: the germanium disk reflects half of the incident photons. It is possibleto evaluate a light collection efficiency for the germanium LD in the naked setup equalto 53% (12.6/23.6).

In the wrapped set-up the VM 2002 reflective foil is applied all around the crystaland the empty space between the crystal face and Ge light detector: the photons canexit only from the top face (one of the two polished faces) of the crystal. The trappedphotons increase from 34% to 55% of the total ones, about 144.4 photons for interaction;46.8 photons for interaction are absorbed by the reflective foil, but the number of photonable to reach the LD plane (1.2 cm away from the top crystal face) goes from 23.6 to70.8 (an increase by a factor ∼ 3).

These 70.8 photons that reach the LD plate can be absorbed or reflected by thegermanium disk and by its copper holder; if they are reflected back towards the crystalthey can be reabsorbed into the crystal or reflected back towards the LD plate and soon until they are totally absorbed by the crystal or by the LD o by the reflective foil.As before, the germanium and TeO2 reflectivity explains why the photons absorbed bythe Ge LD are 48.8 and the photons absorbed by the crystal go from 55% to 60% of thetotal ones (the values obtained in the simulation shown in section 5.3). The germaniumLD collection efficiency for the wrapped set-up goes from 53% to 69% (48.8/70.8): thephotons reflected by the LD in the first interaction do not leave the set-up and haveanother possibility to hit the germanium disk and be absorbed.

In view of these considerations it is possible to understand why all the trials toincrease the light collection efficiency have not been successful: the absorption on theTeO2 crystal and the reflectivity of the germanium disk do not allow to collect morethan the 19% of the Cherenkov photons produced in the γ interactions. This explainsthe reason why the only test in which more than 110 eV were detected was the testperformed with the smaller TeO2 crystal for which the self light absorption is smaller.

5.5 Light collection optimization exploiting the Monte Carlooutput

In the previous sections we have demonstrated that the MC simulation developed inthis Ph.D work is able to reproduce the light yield measured using several experimentalconfigurations and operating the TeO2 crystal at room temperature and cryogenic tem-perature.In this section a study of this MC will be presented in order to try to increase the lightemitted and the light detected of a 5 × 5 × 5 cm3 TeO2 crystal operated at cryogenictemperature.

5.5. Light collection optimization exploiting the Monte Carlo output 89

5.5.1 Surface roughness and light emission from Cuore crystal

As mentioned in section 2.2.1 the surface treatment of the CUORE crystals is optimizedto maximize the surface radio-purity of the crystal. The result of this surface cleaning isthat two opposite faces have a better polishing quality, close to optical polishing grade,the remaining four faces are rough (see section 2.6.2). No attention was paid to optimizethe light yield of the crystal. This means that the surface roughness of the four lateralfaces can be increased in order to maximize the light yield as said in section 2.6.2.Thanks to the MC simulation it is possible to study this issue.

The attention was focused on the wrapped set-up: the VM 2002 reflective foil isapplied all around the crystal and the empty space between the crystal face and Ge lightdetector (1.2 cm spaced); in this configuration the photons can exit only from the oneof the two polished faces and reach the light detector directly or after being reflected bythe VM 2002 foil. As performed in section 5.4 one hundred 208Tl γs were simulated, foreach one 262 Cherenkov photons were emitted; for each value of the surface roughnessthese photons (262 photons × 100 208Tl γs) were propagated in the experimental set-up.The result of this surface roughness scan is shown in Fig. 5.18, where the increase inthe light emitted with the increase of the surface roughness of the crystal faces is clearlyvisible.

[deg]θ0 10 20 30 40 50 60 70 80 90

Ave

rage

num

ber

of e

xitin

g ph

oton

s

0

10

20

30

40

50

60

70

80

90

100

Figure 5.18: The average number of photons for interaction that reach the LD plane (1.2 cmfrom the crystal face) as function of the roughness of the four later crystal faces. The red dottedline represent the value of θ∗ that reproduced the data shown in chapter 5 and the two greendotted line the range value of θ∗ that reproduce the data shown in section 4.2.3.

In Fig. 5.18 we also report the value of θ∗ that reproduces the cryogenic data (reddotted line), that results compatible with the range of values of θ∗ (the area of the graphdelimited by the dotted green lines) that reproduces the room temperature data.

Assuming that the MC is able to reproduce correctly the surface interaction of theCherenkov photons, the simulation suggests that the light yield can be maximized in-


creasing the roughness of the lateral faces of the crystal: the light yield can be increasedby about 35%. Obviously this is an important information for the optimization of theTeO2 light yield and we will see the impact on the light collected by the LD in the nextsections.

Finally, we studied if the number of photons reaching the LD increases assumingthat also the two opposite polished faces of the TeO2 crystal be rough: the results arecompatible with the ones shown in Fig. 5.18, suggesting that no additional advantagecan be obtained. Moreover, all the four lateral faces must be rough: increasing theroughness of only 1, 2 or 3 crystal faces, one cannot increase the light yield at the samelevel of one shown in Fig. 5.18.

5.5.2 Increasing the light collection efficiency

The germanium light detector used in the setup of Fig. 5.1 and 5.16 is not optimized tobe faced to a CUORE TeO2 crystal: the shape, the size and the mechanical couplingbetween the TeO2 copper holder and the germanium holder can be improved in order tomaximize the light collection. Also this issue has been studied exploiting the MC.

Heat Energy [keV]0 500 1000 1500 2000 2500 3000

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]

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140

160

180

200 / ndf 2χ 70.23 / 4 [keV] thE 18± 327


/ ndf 2χ 70.23 / 4 [keV] thE 18± 327


Figure 5.19: Simulation: trend of the Cherenkov energy detected in the optimized set-up asa function of the energy released in the TeO2 bolometer. The high value of the fit χ2/ndf canbe explained recognizing that the first order polynomial function is just a first approximation ofthe real trend of the Cherenkov energy as function of the γ interaction in TeO2 bolometer, asexplained in the text.

Obviously the shape and the size of the germanium light detector must match the TeO2

face ones: for this reason the new light detector that was simulated is a 5×5 cm2 and 300µm thick germanium slab. The distance between the crystal face and the germaniumslab does not seem to produce a significant increase in the light collection efficiency inthe range 1.2 ÷ 0.2 cm. For simplicity, it was set to 1 cm (a further decreasing of thedistance does not increase the light collected and would complicate unnecessarily the

5.5. Light collection optimization exploiting the Monte Carlo output 91

mechanical assembly of the detectors). Using the same procedure adopted in section 5.3it was possible to evaluate the expected Cherenkov energy for the six most intensepeaks of TeO2 spectrum (511 keV, 228Ac, 40K, SE, DE and 208Tl) in the new optimizedexperimental set-up: the mean light from the γ peaks was fitted with a line (see Eq. 5.3)and an Eth = 327±18 keV and a LY = 72±1 eV/MeV (see Fig. 5.19) was obtained. Theoptimized set-up should be able to increase the TeO2 LY of about 58% (see section 5.2.4),this means an expected Cherenkov energy at the 0νDBD Q-value of 159.7± 1.8 eV.

Moreover, from Fig. 5.19, we can recognize that the first order polynomial functionis just a first approximation of the real trend of the Cherenkov energy as function of theγ interaction in TeO2 bolometer. For example, the events that produced the DE peak(1593 keV) are e−+e+ interactions that produced an average Cherenkov energy slightlygreater than a γ interaction with energy 1593 keV; similarly, the events that producedthe SE peak (2104 keV) are e−+e++γ(511 keV) and, as expected, the Cherenkov energyobtained is equal to the one obtained for the DE peak plus the Cherenkov energy obtainedfor the 511 keV gamma interaction, and result slightly smaller than a γ interaction withenergy 2104 keV. Also for the 2615 keV peak a small deviation from the linear trendseems present. Therefore, given this consideration, the high value of the fit χ2/ndfwas expected. However, the linear trend of the Cherenkov energy can be assumed as areasonable approximation for the purpose of this work.

As a last test of the simulation, one can try to change the LD absorber materialfrom germanium to silicon (see Fig. 5.20): the slightly smaller reflectivity for wavelengthgreater than 500 nm can increase the light collection efficiency of the detector. Never-theless the total Cherenkov energy collected is compatible with the one detected usingthe germanium.

[nm]λ300 400 500 600 700 800

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Figure 5.20: Red dots: real part of the refractive index (n); blue dots imaginary part of therefractive index (k) from Ref. [106].

In Tab. 5.1 the results of the study of the simulation output are summarized, to-


gether with the number of photons absorbed by the materials that make up the detectorconfiguration discussed in these sections.

Simulated Simulated Absorbed Absorbed Hitting AbsorbedSet-up Photons by TeO2 by VM 2002 the LD by LD

TeO2 naked 262 88 0 23.6 12.6

TeO2 VM 2002 262 144.4 (+13.1) 46.8 (+8.9) 70.8 48.8

TeO2 VM 2002 optimized 262 120.3 (+13.3) 45.9 (+8.6) 95.8 73.9

Table 5.1: Summary of the results obtained in the study of the simulation: the number ofsimulated and absorbed photons are evaluated averaging one hundred 208Tl γ interactions withinthe crystal. The numbers in brackets represent the number of photons that, after hitting thelight detector are reflected and absorbed by TeO2 crystal or reflective foils.

5.6 Conclusions

In this chapter we demonstrated that the Cherenkov signal emitted by the β/γ inter-actions in TeO2 bolometer can be detected using a cryogenic light detector. The lightdetected at the 130Te Q-value is around 100 eV, no light is detected from α interactions,further confirming the nature of the light emission. The Cherenkov signal is howeversmall at the same level of the noise of the bolometric light detector used, and does notallow an event by event discrimination of the background. Several tests were performedin order to increase the Cherenkov signal, nevertheless they did not produce a significantincrease of the light detected.

A detailed Monte Carlo simulation was developed to understand why this trials didnot succed and why the Cherenkov signal is only 100 eV compared to the 740 eV emittedinside the crystal. The simulation results confirmed that the light yield measured is thecorrect one if one takes into account the optical properties of the set-up materials andthe trapping effect produced by the high refractive index of the TeO2 crystal. TheMonte Carlo also suggests a possible way to increase the LY of the crystal: the onlyway seems to increase the surface roughness of the lateral crystal faces. In such a way,and optimizing the germanium shape, a LY of about LY = 72 ± 1 eV/MeV can beachieved. The Cherenkov signal at the 0νDBD Q-value is expected to be about 160 eV.Nevertheless also in this case, an event by event discrimination would not be possiblebecause of the poor resolution of the bolometric light detector used (70 eV).

Chapter 6

High sensitive light detector

The results shown in the previous chapter demonstrate that to achieve an event by eventdiscrimination of the β/γ interactions from α ones in a TeO2 bolometer two requirementsmust be satisfied:

• the lateral crystal faces have to be grinded, to increase the Cherenkov photons exitprobability;

• the light detector facing the TeO2 bolometer has to have an energy resolution ofthe baseline of about 20 eV (σ) and a high absorption efficiency for the Cherenkovphotons wavelenghts.

These requirements were satisfied by the last cryogenic test run performed in the frame-work of this PhD thesis. The lateral surface of the cylindrical crystal (40 mm in diameterand height, 285 g) tested in section 5.2.6 is mechanically roughened, the crystal is sur-rounded with VM 2002 reflective foil and faced to a cryogenic light detector read outby a Transition Edge Sensor (TES). This measurement was performed in collaborationwith the Max Planck Institute for Physics in Munich, Germany. Their high experienceaccumulated in the development of high sensitive light detectors exploiting the TEStechnology allowed to perform the measurement with the so far highest discriminationpower between α and β/γ particles achieved by the Cherenkov light detection.

6.1 Transition Edge Sensor

As explained in section 2.1.4 the temperature variation of a bolometric absorber canbe converted into electrical signals by means of devices whose resistance shows a steepdependence on the temperature: in addition to the NTD, also the Transition Edge Sensor(TES) is extensively used as bolometric temperature sensor.

A TES is a thermometer made from a superconducting film operated in betweenthe normal conducting and superconducting phase: in this configuration a small rise intemperature ∆T causes a steep (true only in linear regime) rise of the resistance ∆R(see Fig. 6.1). The circuit is laid-out as a parallel circuit biased with a constant currentI0. In the branch parallel to the thermometer film RT there is a superconducting coil LI(input coil) as well as two identical shunt resistances each with half the value of RS . Theinput coil LI is inductively coupled to a Superconducting Quantum Interference Device

93

94 Chapter 6. High sensitive light detector

signal: μK

operating points (OP)

I0

I0

LI

Figure 6.1: Transition curve of a W-TES. A stabilization of the termometer in its transitionOP allows to detect tiny excursions in temperature ∆T by measuring the change in resistence.The readout scheme used to convert the charge ∆R in a voltage signal is shown on the rightside [108].

(SQUID) (see Fig. 6.1). A change of RT causes a change of the current branching ratio;the resulting change of the magnetic field in the coil causes a change in the input flux tothe SQUID. The SQUID acts as a “cold preamplifier” and transforms the flux variationin a voltage signal, the final recorded voltage pulse.

6.2 Experimental Set-up

The TeO2 crystal is a cylinder of 40 mm in diameter and height, and the lateral surfaceis mechanically roughened; despite its cylindrical shape favours total internal reflection,i.e. a smaller light yield than a cubic or parallelepiped crystal of comparable mass, thisTeO2 crystal was chosen because its shape fits exactly the mechanical assembly and theexperimental volume of the cryostat that hosted the detector.

To measure the temperature variation of the TeO2 crystal a composite detectordesign [109] was used: a small 20 × 10 × 1.5 mm3 cadmium tungstate carrier crystalis equipped with a TES. The TES consists of a thin tungsten film (200 nm) which isproduced in a dedicated evaporation process. The carrier was attached onto one of thepolished flat surfaces of the TeO2 by vacuum grease. A direct evaporation of the W-TESonto the TeO2 was not possible due to the low melting point of the crystal.The other polished face of the crystal is facing a cryogenic light detector of the CRESST-II type [110], which consists of a thin sapphire disc (d=460 m) with a diameter of 40 mm.Since pure sapphire is transparent a 1 µm thick layer of silicon is deposited chemically

6.2. Experimental Set-up 95

Figure 6.2: On the left hand side the TeO2 crystal surrounded by a reflective foil and mounted inits copper holder is shown. The light detector, also mounted in a copper structure is visible on theright hand side. The temperature sensors can be identified on the surface of both detectors. Incase of TeO2 a composite detector approach was used: a small CdWO4 carrier crystal containingthe TES is glued onto the large TeO2.

on the surface of the sapphire disc (silicon on sapphire, i. e. SOS). A W-TES optimizedfo the purpose of light detection is used to measure the temperature variation of theSOS detector.

The detectors are held in a copper structure by means of bronze clamps and sur-rounded by VM 2002 reflective foil (see Fig. 6.2). The measurement was carried out in adilution refrigerator located in the test facility of the Max-Planck-Institute for Physicslocated deep underground at LNGS.

The readout of the TES is realized via a commercial dc-SQUID electronics. Forrecording thermometer pulses, the output voltage of the SQUID electronics is split intotwo branches. In one branch the pulse is shaped and AC-coupled to a trigger unit, whilein the other branch the signal is passed through an 8-pole antialiasing low-pass filterand then DC-coupled to a 16-bit transient digitizer. The hardware triggered signalsare sampled in a 409 ms window with a sampling rate of 10 kHz. The TeO2 and lightdetector channels are read out together, indipendent of which detector triggered. A moredetailed description of the DAQ, the control of detector stability as well as the pulseheight evaluation is given in Ref. [111, 112].

To calibrate the TeO2 and to generate events in the 0νDBD region, the setup waspermanently exposed to a 232Th and 40K γ-sources. In addition, a degraded 238U α-source was faced to the crystal in order to produce α interactions in the 0νDBD energyregion. In such way it was possible to study the discrimination power between α and β/γparticles in the 0νDBD energy region. The LD is exposed to a 55Fe source, providing5.9 and 6.5 keV X-rays used for means of calibration.


6.3 First level data analysis

The amplitude of the acquired signals are evaluated fitting the pulses with a templatepulse. The template pulse is constructed averaging a set of (order 100) pulses from the2615 keV 208Tl line for the TeO2 crystal and from their Cherenkov light signals for thelight detector. Both pulses from TeO2 and light detector are fitted simultaneously. Freeparameters in the fit are the two baselines, the two pulse amplitudes, and a commontime shift relative to the trigger.

The TeO2 energy resolution at the 2615 keV 208Tl peak is 24 keV FWHM, worse thanany ones obtained with NDTs. Being the first test performed with a W-TES coupled toa TeO2 crystal, the reason why the resolution is so poor is under study; nevertheless thisdoes not affect the results since the attention is focused on the light signal. The energyresolution of the light detector at the iron peaks is about 257 eV FWHM, the RMS ofthe baseline is about 24 eV.

6.4 Results

The Cherenkov light detected in the LD as function of the energy deposited in theTeO2 crystal is shown in Fig. 6.3; in the scatter plot two different popolutions can beidentified: the β/γ events, for which the light detected is clearly energy dependent,and the α events, produced by the degraded 238U α-source for which the average lightdetected is < Lα >= 3.2± 1.3 eV, i.e. compatible with zero.

The mean light of the γ peaks was fitted with a line (see Eq. 5.3:

< Lβ/γ >= LY · (Energy − Eth) (6.1)

with Eth = 140± 30 keV and LY = 53.9± 1.3 eV/MeV. One computes 128.7± 1.7 eV oflight for a β/γ event with the same energy of the 0νDBD one. The standard deviationsof the light distributions are found compatible with the baseline noise of the LD, whichtherefore appears again as the dominant source of fluctuation, hiding any possible de-pendence on the position of the interaction in the TeO2 crystal or statistical fluctuationsof the number of photons. Given the Cherenkov signal at the 0νDBD and the LD noise,this set-up allows one to perform an event by event rejection of the α background.

The discrimination power (DP) achieved between α and β/γ events can be studiedexploiting the α events produced by the 238U degraded α-source and the β/γ eventsproduced by the 208Tl γs in the energy region between 2400 ÷ 2800 keV. In order toperform this analysis, the scatter plot shown in Fig. 6.4-left is evaluated.The light yield in this plot is defined as the direct energy detected in the light detectorin eV per one MeV of deposited energy in the TeO2 crystal. Now, the two distributionsare clearly identifiable.

A way to quantify the theoretical DP between two symmetric distributions can begiven by

DP =µα − µβ/γ√σ2α + σ2β/γ

(6.2)

6.4. Results 97

Energy [keV]0 1000 2000 3000 4000 5000

Lig

ht e

nerg

y [e

V]

-100

-50

0

50

100

150

200

S1_LvsH

/ ndf 2χ 5.735 / 3

p0 1.867± -7.032

p1 0.001326± 0.05384

/ ndf 2χ 5.735 / 3

p0 1.867± -7.032

p1 0.001326± 0.05384

/ ndf 2χ 5.735 / 3

p0 1.867± -7.032

p1 0.001326± 0.05384

/ ndf 2χ 5.735 / 3

[keV] thE 30± 140


Figure 6.3: Detected light versus deposited energy in the TeO2 bolometer for all the acquiredevents (gray) and for the events belonging to the peaks of 208Tl (583 keV, SE and 2615 keV),228Ac (911 keV) and 40K (1461 keV) (blue). The mean light is clearly energy dependent for the γpeaks (red circles below 3 MeV) and compatible with zero for the 238U degraded α-source (pinkcircle centered at 3.2 MeV, the x-axis error band represent the energy range of the degradedα-particles).

Energy [keV]0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Ligh

t Yie

ld [e

V/M

eV]

-150

-100

-50

0

50

100

150

200

250 / ndf 2χ 20.86 / 12

Prob 0.05248

αA 1.88± 13.45

αµ 2.391± -1.004

σ 0.387± 9.319 γ/βA 5.91± 82.95

γ/βµ 0.5± 49.2

Light Yield [eV/MeV]-40 -20 0 20 40 60 80

coun

ts /

6

0

10

20

30

40

50

60

70

80

90 / ndf 2χ 20.86 / 12

Prob 0.05248

αA 1.88± 13.45

αµ 2.391± -1.004

σ 0.387± 9.319 γ/βA 5.91± 82.95

γ/βµ 0.5± 49.2

Figure 6.4: Left: scatter plot of the light yield detected for all events (α and β/γ): it is definedas the intrinsic energy detected in the light detector in eV per one MeV of deposited energyin the TeO2 crystal. Right: light yield distribution in the energy interval from 2400 keV to2800 keV. The distribution is fitted with two Gaussians with the same standard deviation. TheDP achieved using equation 6.3 is 3.8.


Since the standard deviation of the α (LD noise) and β/γ distributions are measured tobe the same, the DP function becomes:

DP =µα − µβ/γ√

2σ(6.3)

and results to be 3.8, as shown in Fig. 6.4-right.

6.5 Conclusion

In this chapter we demonstrated that the active background rejection in TeO2 bolometerexploiting the Cherenkov signal can be done. Using a sensitive light detector (about24 eV RMS) equipped with TES a separation of 3.8 σ between the α and β/γ eventswas achieved (in the energy range from 2400 keV to 2800 keV, around the Q-value of130Te).

Chapter 7

Conclusions and perspectives

7.1 Conclusions

Next generation bolometric experiments aim to reach a sensitivity on the effective majo-rana mass mββ of about 10÷20 meV in order to explore the inverse neutrino mass hierar-chy. To achieve this ambitious goal it is mandatory to reach a background level in the ROI≤ 0.001 counts/(keV kg y). The projections for the background budget of the CUOREexperiment are 0.01 counts/(keV kg y) from the α particles and 0.001 counts/(keV kgy) from the β/γ ones. Therefore, an active rejection of the α background is mandatoryto allow also to the TeO2 bolometric arrays the exploration of the inverted hierarchy ofneutrino mass.

In this Ph.D work the possibility to operate such a discrimination exploiting theCherenkov radiation produced by β/γ particles was investigated.

Two measurements were performed at room temperature to assess the nature andthe amount of the Cherenkov light yield and to exclude any scintillation contribution.These measurements demonstrated the existence of a light emission from TeO2 crystalsand, with the help of a Monte Carlo simulation, that their light yield are compatiblewith the expected number of Cherenkov photons produced in the particle interactionswithin the crystal.

Several cryogenic measurements were performed at Laboratori Nazionali del GranSasso to evaluate the light yield of a 5 × 5 × 5 cm3 CUORE TeO2 crystal operated asbolometer monitored with a germanium light detector equipped with NTD. The bestresult was obtained wrapping the crystal with VM 2002 reflective foil, and an averageCherenkov light of about 100 eV at the Q-value of the 0νDBD of 130Te was detected.However, the signal is at the same level of the noise of the bolometric light detectorused (72 eV RMS). An event by event discrimination of the background could not berealized. The Monte Carlo simulation developed is able to reproduce the observed datain the several set-up configurations.

Besides, the MC suggested that increasing the lateral surface roughness of the TeO2

crystal and optimazing the shape of the germanium LD it is possible to increase theCherenkov signal detectable. The Cherenkov light at the Q-value of the 0νDBD usingsuch a optimized set-up is expected to be about 157 eV. Nevertheless, even in this casethe signal to noise ratio would be too low to operate an event by event rejection of the αbackground. Indeed, to achieve a complete rejection of the α background a light detectorwith a signal to noise ratio (S/N) higher or equal to 5 is necessary.

99

100 Chapter 7. Conclusions and perspectives

An additional test performed in collaboration with the Max Planck Institute demon-strated this statement: facing a cryogenic light detector equipped with W-TES to acylindrical TeO2 crystal a S/N > 5 was achieved. With a baseline RMS of about 24 eVand a Cherenkov signal of about 128 eV (S/N ' 5.3) this detector allows to perform anevent by event rejection of the α background. The discrimination power between α andβ/γ events achieved is about 3.8 σ. In Fig. 7.1 it is shown how the CUORE sensitivity

Signal/Noise of light detector0 1 2 3 4 5 6 7 8

y]

26 [

10ββν

90%

CL

sen

sitiv

ity to

0

1

1.5

2

2.5

3

/ keV kg ysα0.01

/ keV kg ysγ0.001

Figure 7.1: 90% C.L. sensitivity to the half-life of 130Te as a function of the signal to noise ratioof the light detectors, under the reasonable hypothesis of an α background index in CUORE of0.01 counts/(keV kg y). The sensitivity of the experiment without light detectors corresponds toS/N = 0. When S/N > 5 the α background is hidden by the unreducible background predictedfrom γ interactions, amounting to 0.001 counts/(keV kg y), and the sensitivity is maximal. Theperformance of the light detectors equipped with NTDs, S/N = 1.4, is clearly too low.

would increase, performing the α particle discrimination: the increase in the sensitivityis a function of the S/N of the light detector. The signal to noise ratio achieved withthe germanium light detector equipped with NTD is able (to date) only to increase bya factor ∼1.5 the sensitivity of the experiment.

Instead, exploiting the TES technology which is able to reach baseline resolution ofabout 24 eV, and reminding that the Cherenkov signal detected from a TeO2 crystal is100 eV and that from simulation it seems that this signal can be increased up to 157 eV,the active background rejection is expected to be within reach.

Therefore, one can state that the active α background rejection in CUORE crystal ispossible, provided that one has a light detector with a noise RMS less than 20÷ 30 eV.

To date, the only technology that can reach this very high resolution level is theTES one, but it has for sure a scalability problem due to the limited number of SQUIDchannels that can be operated and to the challenge of manufacturing W-TES on a massproduction scale. The NTD technology is more affordable and scalable up to thousandchannels (as demonstrated by CUORE) but the resolution is worse by a factor 2 ÷ 3

7.1. Conclusions 101

than the required one.

Recently, an alternative technology was investigated in Ref. [113], where a light sensorbased on the Neganov-Luke effect was exploited to detect the Cherenkov light outputfrom a small TeO2 crystal. Despite the promising results obtained the scalability of thistechnology has not yet been demonstrated.

The conclusion is that a R&D activity focused on the improvement of the resolu-tion and/or scalability of the current cryogenic light detectors, or the development of anew one, is mandatory to achieve the complete rejection of the α background in TeO2

bolometers.

When these detectors will be available, they can be used to monitor 988 TeO2 bolome-ters 5× 5× 5 cm3 enriched to 90% with the ββ emitting isotope. This next generationexperiment could reach a half-life sensitivity to 130Te 0νDBD of 7 × 1026 y (90% C.L.)with 5 years of live time, corresponding to an effective Majorana neutrino mass sensi-tivity of 7÷ 18 eV, that is the end point of the inverted neutrino mass hierarchy region(see Fig. 7.2).

[eV]lightestm-410 -310 -210 -110 1

[eV

]ββ

m

-410

-310

-210

-110

1Cuoricino exclusion 90% C.L.

GERDA exclusion 90% C.L. Ge claim76

KamLAND-Zen and EXO-200 exclusion 90% C.L.

CUORE 90% C.L. sensitivity

>0223 m∆

<0223 m∆

CUORE NEXT: 90% isotopic enrichment in 130Te with Cherenkov tag (90% C.L. )

Figure 7.2: CUORE NEXT: 988 TeO2 bolometers 5 × 5 × 5 cm3 enriched to 90% with 130Teand with an active α background rejection thanks to the Cherenkov signal tag: the projectionsensitivity to 〈mββ〉 is 7÷ 18 meV (90% C.L.).


7.2 Perspectives

Simultaneously to the R&D activities focused on the improvements of the light detectorsperformances, an additional study can be made using the current light detector. Indeed,after the demonstration of the existence of a detectable Cherenkov signal exiting fromthe CUORE TeO2 bolometer (thanks to this PhD work), it is possible to asses the natureof the background contaminations measured by the CUORE0 experiment. Exploitingthe Cherenkov signal emitted by β/γ particle it is possible to measure the hypotheticalcomponent of the β/γ background hidden by the 0.02 counts/(keV Kg y) detected byCUORE0.

The question is: what is the exposure (expressed in kg·y) for a TeO2 detector arrayfor which it is possible to identify the percentage of the β/γ contribution in the αbackground region (2.7÷ 3.9 MeV) with an error of the order of 10%?

Heat energy [keV]2800 3000 3200 3400 3600 3800

Che

renk

ov e

nerg

y [e

V]

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0

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150

200

Cherenkov energy [eV]-50 0 50 100 150 200

Cou

nts

/ 20

eV

0

5

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Heat energy [keV]2800 3000 3200 3400 3600 3800

Che

renk

ov e

nerg

y [e

V]

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-100

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200

300

400

Cherenkov energy [eV]-300 -200 -100 0 100 200 300 400

Cou

nts

/ 20

eV

0

2

4

6

8

10

Figure 7.3: Example of two simulated experiments. The top graphs refer to an experiment withan exposure of 2 kg·y and a light energy resolution of 10 eV: on the left the simulated events (thered dots are β/γs and the blue dots are αs) are shown in the light versus heat scatter plot; on theright the bi-dimensional fit for the α (blue) and β/γ (red) interactions is shown. The percentageof beta gamma background simulated is 20% and the one fitted is 18.6 ± 5.9%. The bottomgraphs refer to an experiment with an exposure of 2 kg·y and a light energy resolution of 100 eV.The percentage of beta gamma background simulated is 20% an the one fitted is 31± 15%.

One can answer this question performing a Toy Monte Carlo: several experimentsare simulated according to the statements described below. The number of background

7.2. Perspectives 103

events simulated for each experiment varies according to a poisson distribution with meanvalue 0.02 · 1200 · exposure (1200 keV is the width of the studied energy region). Theirenergy distribution is flat from 2700 to 3900 keV. For the percentage of β/γ events (δ)an average Cherenkov energy equal to the one measured in section 5.2.1 (Eth = 283 keVand LY = 45 eV/MeV) was detected, with a standard deviation depending on thedetector noise. Instead, for the percentage of α events, (1− δ), zero Cherenkov light wasdetected with a standard deviation still depending on the detector noise. This results ina bi-dimensional probability dentity function (pdf), flat in the heat energy variable, andGaussian in the light energy variable; for the β/γ events the mean value of the gaussiandistribution is energy dependent (according to the Cherekov light trend). The result ofeach simulated experiment was fitted using this pdf (the fit is unbinned), with one onlyfree parameter: the percentage δ of β/γ events.

The input parameters that are scanned in the several Toy Monte Carlo are theexposure and the standard deviation of the detected light, i. e. the light detectorbaseline RMS (or equivalently its energy resolution σ).

An example of two simulated experiments is shown in Fig. 7.3 using two differentlight detector energy resolutions.

component [%]γ/β0 20 40 60 80 100

Err

or [

%]

3

4

5

6

7

8

component %γ/β0 20 40 60 80 100

Err

or [

%]

2

4

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12

component %γ/β0 20 40 60 80 100

Err

or [

%]

-5

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20

25

30

component %γ/β0 20 40 60 80 100

Err

or [

%]

0

10

20

30

40

50

60

70

80

90

Figure 7.4: Median (blue dots) and RMS (error bands) values of the error distribution ofthe δ parameter (percentage of β/γ component) obtained using a total exposure of 2 kg·y andassuming 4 different light detector resolutions: 10 eV top-left, 50 eV top-right, 100 eV bottom-left, 300 eV dottom-right. Each point in the four graphs has been evaluated over a sample of1000 experiments.


For each input parameters (exposure and light detector resolution) several percent-ages of β/γ components were tested; and for each percentage value, 1000 experimentswere simulated. The distribution of the fitted parameter δ (percentage of β/γ compo-nent) has a mean value compatible with the simulated one, and its RMS is compatiblewith the mean value of the error distribution evaluated by the fit (as expected). Sincethe interest is focused on the error with which η can be estimated, the results of the toyMC are presented in term of the error distribution of δ obtained by the fit: its medianvalue and its RMS, as shown in Fig 7.4.

Therefore, to identify the percentage of the β/γ contribution in the α backgroundregion with an error of the order of 10%, one needs of 2 kg·y exposure and a light detectorwith an energy resolution of the order of 50 eV.

Increasing the exposure up to 3 kg·y and using the LD resolution obtained in sec-tion 5.2.1 the result shown in Fig. 7.5 was obtained: this means that, assembling amini-tower composed by 12 CUORE-like TeO2 crystals, monitored by 12 germaniumlight detectors and a live time of 4 months it is possible to identify (using the exist-ing technologies) the β/γ contribution in the background of TeO2 bolometric detectorarrays.

This can be a very useful information to approach in the correct way the invertedneutrino mass hierarchy exploration. Indeed the projection of a β/γ contribution equalto 0.001 counts/(keV kg y) was never demonstrated by any detector.

component [%]γ/β0 20 40 60 80 100

Err

or [

%]

0

2

4

6

8

10

12

Figure 7.5: Median (blue dots) and RMS (error bands) values of the error distribution of the δparameter (percentage of β/γ component) obtained using a total exposure of 3 kg·y and assuminga light detector resolutions of 70 eV. Each point in the graph has been evaluated over a sampleof 1000 experiments.

Ringraziamenti

Siamo arrivati alla fine, la parte che probabilmente risulta essere la piu facile e difficileal tempo stesso. Ringraziare infatti tutte le persone che mi hanno aiutato a realizzarequesto lavoro non sara semplice dal momento che il sostegno dato non e stato soloscientifico ma morale ed affettivo.

Iniziamo con Stefano. Grazie ai suoi metodi di insegnamento estremamente singolariho imparato a costruire un bolometro e farlo funzionare correttamente, senza contareche tutto cio che so sulla criogenia viene da lui. Quindi grazie Stefano, anche se magarinon lo sospetti nemmeno, sei diventato una persona importartante per me, ed i momentipassati insieme rievocano in me un piacevole ricordo.

Poi viene Luca, abbiamo imparato molte cose e abbiamo lavorato davvero tanto,insieme. Le nostre chiaccherate rendevano i momenti di pausa al gran sasso, i pienid’elio, le giornate intere in camera pulita ad assemblare rivelatori, i venerdi sera passatia condensare, piacevoli e leggeri. Sei diventato per me un ottimo amico e collega, unapersona che sicuramente restera nel mio cuore.

Poi il turno di Marco, Fabio, Claudia e Silvio: siete stati dei punti di riferimentofondamentali senza i quali non avrei mai raggiunto questo traguardo. Grazie per avermisostenuto sempre e per avermi dato la forza necessaria per vincere i momenti piu difficili,tipo quelli in cui Stefano puntava i piedi e non voleva sentir parlare di effetto Cherenkov.

In ultimo, ma non per importanza, Karoline, Davide e Ioan: senza il loro fondamen-tale aiuto molti risultati non avrebbero mai visto la luce del sole. Quindi vi ringrazioper il vostro aiuto e per aver contribuito con tanta dedizione ad alcune delle misurepresentate in questo lavoro.

Per ultimi ho lasciato i ringraziamenti piu difficili, infatti distinguere dove finiscel’essere colleghi ed inizia l’essere amici e davvero impossibile per Emanuele (Pappo),Gabriele (Pipi), Valeria, Marco (Garatto), Francesco (Cicciocio’), Roberta (Robby),Laura (Lauretta), Martina (Marti’), Filippo (Fili’), Ilaria (Ila) e Michela (Michi). Avetereso questi anni indimenticabili, imprevedibili, a volte surreali. Momenti che nessunopotra mai togliermi dal cuore e che ricordero per sempre come bellissimi. Vi voglio bene.

Concludiamo con i ringraziamenti sobri: grazie a YouTube, senza la sue canzoni nonsarei mai resistito giornate intere chiuso in Sala C; grazie ai ristoranti di Assergi e din-torni, la cena, grazie alla vostra cucina, era il momento piu atteso della giornata. Grazieinoltre a tutti i tecnici dell’officina meccanica del Gran Sasso, la loro professionalita estata fondamentale per la realizzazione di tutte le componenti in rame usate per i mieimontaggi. Infine un grazie a Mario e Domenico per la loro ospitalita.

105

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