Measurement of the half-life of the two-neutrino double beta decay of 76Ge with the Gerda experiment

TLDR: The first 5.04 kg yr of data collected in Phase I of the experiment have been analyzed to measure the half-life of the neutrino-accompanied double beta decay of 76Ge as mentioned in this paper.

Abstract: The primary goal of the GERmanium Detector Array (GERDA) experiment at the Laboratori Nazionali del Gran Sasso of INFN is the search for the neutrinoless double beta decay of 76Ge. High-purity germanium detectors made from material enriched in 76Ge are operated directly immersed in liquid argon, allowing for a substantial reduction of the background with respect to predecessor experiments. The first 5.04 kg yr of data collected in Phase I of the experiment have been analyzed to measure the half-life of the neutrino-accompanied double beta decay of 76Ge. The observed spectrum in the energy range between 600 and 1800 keV is dominated by the double beta decay of 76Ge. The half-life extracted from GERDA data is T2ν1/2 = (1.84+0.14−0.10) × 1021 yr.

Figures

Table 2. Summary table of the systematic uncertainties on T 2ν 1/2 which are taken into account for this work and which are not included in the fitting procedure.

Figure 2. Energy spectrum of the six enrGe detectors. The 39Ar β decay dominates the counting rate at low energies up to its Qβ-value of 565 keV. The energy range which is considered for the 2νββ analysis and a few prominent γ lines are also shown.

Figure 3. Upper and middle panels: Experimental data (markers) and the best fit model (black histogram) for the sum of the six detectors together (linear and logarithmic scale). Individual contributions from 2νββ decay (red), 42K (blue), 40K (purple) and 214Bi (green) are shown separately. The shaded band covers the 68% probability range for the data calculated from the expected event counts of the best fit model. Lower panel: ratio between experimental data and the prediction of the best fit model. The green, yellow and red regions are the smallest intervals containing 68%, 95% and 99.9% probability for the ratio assuming the best fit parameters, respectively [26].

Figure 4. Experimental results for T 2ν 1/2 of 76Ge vs. publication year. The plot includes results from the experiments ITEP-YPI [33], PNL-USC (natGe) [34] PNL-USC-ITEP-YPI [35, 36], Heidelberg-Moscow (HdM) [11, 17] and Igex [12, 16], as well as the re-analysis of the HdM data by Klapdor-Kleingrothaus et al [31] (HdM-K) and by Bakalyarov et al [37] (HdM-B). The NNDC-recommended value [38] and the global weighted average evaluated by Barabash [2] are also shown.

Table 1. Summary table of the six enriched detectors used in this work. For each detector, the total mass, the active mass and the isotopic abundance of 76Ge are given. The uncertainties reported for the active masses are the uncorrelated (first) and correlated (second) errors. The last column reports the T 2ν 1/2 which is obtained by performing the analysis on each detector individually. The uncertainty on T 2ν 1/2 is the fit uncertainty only.

Figure 1. Artist’s view of the Gerda experiment. The detector array is not to scale.

Full text

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Year:2013
Measurementofthehalf-lifeofthetwo-neutrinodoublebetadecayofGe-76
withtheGerdaexperiment
GERDACollaboration;Baudis,L;Benato,G;Ferella,AD;Froborg,Francis;Guthikonda,KK;
Tarka,M;Walter,M;etal
Abstract:TheprimarygoaloftheGERmaniumDetectorArray(GERDA)experimentattheLaboratori
NazionalidelGranSassoofINFNisthesearchfortheneutrinolessdoublebetadecayof76Ge.High-
puritygermaniumdetectorsmadefrommaterialenrichedin76Geareoperateddirectlyimmersedinliquid
argon,allowingforasubstantialreductionofthebackgroundwithrespecttopredecessorexperiments.
Therst5.04kgyrofdatacollectedinPhaseIoftheexperimenthavebeenanalyzedtomeasurethe
half-lifeoftheneutrino-accompanieddoublebetadecayof76Ge. Theobservedspectrumintheenergy
rangebetween600and1800keVisdominatedbythedoublebetadecayof76Ge.Thehalf-lifeextracted
fromGERDAdataisT2฀1/2=(1.84+0.14−0.10)×1021yr.
DOI:https://doi.org/10.1088/0954-3899/40/3/035110
PostedattheZurichOpenRepositoryandArchive,UniversityofZurich
ZORAURL:https://doi.org/10.5167/uzh-75716
JournalArticle
Originallypublishedat:
GERDACollaboration;Baudis,L;Benato,G;Ferella,AD;Froborg,Francis;Guthikonda,KK;Tarka,
M;Walter,M;etal(2013).Measurementofthehalf-lifeofthetwo-neutrinodoublebetadecayofGe-76
withtheGerdaexperiment.JournalofPhysicsG:NuclearandParticlePhysics,40(3):035110.
DOI:https://doi.org/10.1088/0954-3899/40/3/035110

Measurement of the half-life of the two-neutrino
double beta decay of
76
Ge with the Gerda
experiment
The Gerda Collaboration
M Agostini
14
, M Allardt
3
, E Andreotti
5,18
,
A M Bakalyarov
12
, M Balata
1
, I Barabanov
10
,
M Barnab´e Heider
14
‡, N Barros
3
, L Baudis
19
, C Bauer
6
,
N Becerici-Schmidt
13
, E Bellotti
7,8
, S Belogurov
11,10
,
S T Belyaev
12
, G Benato
19
, A Bettini
15,16
, L Bezrukov
10
,
T Bode
14
, V Brudanin
4
, R Brugnera
15,16
, D Budj´aˇs
14
,
A Caldwell
13
, C Cattadori
8
, A Chernogorov
11
,
F Cossavella
13
, E V Demidova
11
, A Denisov
10
, A Domula
3
,
V Egorov
4
, R Falkenstein
18
, A D Ferella
19
, K Freund
18
,
F Froborg
19
, N Frodyma
2
, A Gangapshev
10,6
,
A Garfagnini
15,16
, S Gazzana
6
, P Grabmayr
18
,
V Gurentsov
10
, K Gusev
4,12,14
, K K Guthikonda
19
,
W Hampel
6
, A Hegai
18
, M Heisel
6
, S Hemmer
15,16
,
G Heusser
6
, W Hofmann
6
, M Hult
5
, L V Inzhechik
10
§,
L Ioannucci
1
, J Janicsk´o Cs´athy
14
, J Jochum
18
, M Junker
1
,
S Kianovsky
10
, I V Kirpichnikov
11
, A Kirsch
6
,
A Klimenko
4,10,6
, K T Kn¨opfle
6
, O Kochetov
4
,
V N Kornoukhov
11,10
, V Kusminov
10
, M Laubenstein
1
,
A Lazzaro
14
, V I Lebedev
12
, B Lehnert
3
, H Y Liao
13
,
M Lindner
6
, I Lippi
16
, X Liu
17
, A Lubashevskiy
6
,
B Lubsandorzhiev
10
, G Lutter
5
, A A Mach ad o
6
,
B Majorovits
13
, W Maneschg
6
, I Nemch en ok
4
, S Nisi
1
,
C O’Shaughnessy
13
, L Pandola
1
k, K Pel czar
2
, L Peraro
15,16
,
A Pullia
9
, S Riboldi
9
, F Ritter
18
¶, C Sada
15,16
, M Salathe
6
,
C Schmitt
18
, S Sch¨onert
14
, J Schreiner
6
, O Schulz
13
,
B Schw in gen h eu er
6
, E Shevchik
4
, M Shirchenko
12,4
,
H Simgen
6
, A Smolnikov
6
, L Stanco
16
, H Strecker
6
,
M Tarka
19
, C A Ur
16
, A A Vasenko
11
, O Volynets
13
,
K von Sturm
18
, M Walter
19
, A Wegmann
6
, M Wojcik
2
,
E Yanovich
10
, P Zavarise
1
+
, I Zhitnikov
4
, S V Zhukov
12
,
D Zinatulina
4
, K Zuber
3
and G Zuzel
2
1
INFN Laboratori Nazionali del Gran Sasso, LNGS, Assergi, Italy
2
Institute of Physics, Jagiellonian Un iversity, Cracow, Poland
‡ Present Address: CEGEP St-Hyacinthe, Qu´ebec, Canada
§ Moscow Institute of Physics and Technology, Russia
k Corresponding Author
¶ Present Address: Robert Bosch GmbH, Reutlingen, Germany
+
University of L’Aquila, Dipartimento di Fisica, L ’A q uila , Italy
arXiv:1212.3210v1 [nucl-ex] 13 Dec 2012

Measurement of the half-life of the two-neutrino ββ deca y of
76
Ge with Gerda 2
3
Institut f¨ur Kern- und Teilchenphysik, Technische Universit¨at Dresden,
Dresden, Germany
4
Joint Institute for Nuclear Research, Dubna, Russia
5
Institute for Reference Materials and Measurements, Geel, Be lgium
6
Max-Planck-Institut f¨ur Kernphysik, Heidelberg, Germany
7
Dipartimento di Fisica, Universit`a Milano Bico c ca, Milano, Italy
8
INFN Milano Bicocca, Milano, Italy
9
Dipartimento di Fisica, Universit`a degli Studi di Milano e INFN M ila no,
Milano, Italy
10
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow,
Russia
11
Institute for Theoretical and Experimental Physics, Moscow, Russia
12
National Research Centre “Kurchatov Institute”, Moscow, Russia
13
Max-Planck-Institut f¨ur Physik, M¨unchen, Germany
14
Physik Department and Excellence Cluster Universe, Technische Universit¨at
M¨unchen, Germany
15
Dipartimento di Fisica e Astronomia dell’Universit`a di Padova, Padova, Italy
16
INFN Padova, Padova, Italy
17
Shanghai Jiaotong University, Shanghai, China
18
Physikalisches Institut, Eberhard Karls Universit¨at T¨ubingen, T¨ubingen,
Germany
19
Physik Institut der Universit¨at Z¨urich, Z¨urich, Switzerla nd
E-mail: pandola@lngs.infn.it
Abstract. The primary goa l of the GERmanium Detector Array (Gerda)
expe riment at the Laboratori Nazionali del Gran Sasso of INFN is the search
for the neutrinoless double beta decay of
76
Ge. High-purity germanium detectors
made from material enriched in
76
Ge are operated directly immersed in liquid
argon, allowing for a substantial reduction of the background with respect to
predecessor experiments. The first 5.04 kg·yr of data collecte d in Pha se I of
the experiment have been analyzed to measure the half-life of the neutrino-
accompanied double beta decay of
76
Ge. The observed spectrum in the energy
range between 600 and 1800 keV is dominated by the double beta decay of
76
Ge.
The half-life extracted from Gerda data is T
2ν
1/2
= (1.84
+0.14
−0.10
) · 10
21
yr.
PACS numbers: 23.40.-s, 07.85.Fv
Submitted to: J. Phys. G: Nucl. Part. Phys.

Measurement of the half-life of the two-neutrino ββ deca y of
76
Ge with Gerda 3
1. Introduction and scope
Neutrinoless double beta (0νββ) decay of atomic nuclei (A,Z) → ( A, Z + 2) +2e
−
is a
forbidden process in the Standard Model (SM) of particle physics because it violat es
lepton number by two units. An observation of such a decay would demonstrate
lepton number violation in nature and would prove that neutrinos have a Majorana
component. For recent reviews, see [
1]. The two-neutrino double beta (2νββ) decay
of atomic nuclei,
(A, Z) → ( A, Z + 2) + 2e
−
+ 2
−
ν
e
,
with the simultaneous emission of two electrons and two anti-neutrinos, conserves lep-
ton number and is allowed within the SM, independent of the nature of the neutrino.
Being a higher-order process, it is characterized by an extremely low decay rate: so
far it is the rarest decay observed in laboratory experiments. It is observable for a
few even-eve n nuc l ei and was detected to-date for eleven nuclides; the corresponding
half-lives are in the range of 7 · 10
18
− 2 · 10
24
yr [
2, 3, 4].
The meas ur em ent of the half-life of the 2νββ decay (T
2ν
1/2
) is of substantial in-
terest. For example, model pre di c t ion s of the 0νββ half-life require the eval u at i on
of nuclear matrix elements. These calculations are complicated and have large un-
certainties. They are different from those required for the 2νββ decay, but it has
been suggested [
5, 6] that, within the same model framework , some constraints on the
0νββ matrix elements NME
0ν
can be derived from the knowledge of the 2νββ nuclear
matrix elements NME
2ν
. Al so, the nuclear matrix element NME
2ν
which is extracted
from the measurement of the half-life of the 2νββ decay can be directly comp ar ed
with the predictions based on charge exchange experiments [
7, 8]. A good agreeme nt
would indicate that the reaction mechanisms and the nuclear structure aspects that
are involved in the 2νββ decay are well understood.
The GERmanium Detector Array (Gerda) exp e ri me nt at the Laboratori Nazion-
ali del Gran Sasso of INFN searches for the 0νββ decay of
76
Ge. High-purity germa-
nium detectors isotopically enriched in
76
Ge are operated bare and immersed in liquid
argon in order to greatly red uc e the environmental background. As a first r es ul t of
this ongoing resear ch, the p r es ent paper reports a precise measurement of the half-life
of the 2νββ decay of
76
Ge. The data used in this work encompasses an exposure of
5.04 kg·yr, taken between November 2011 and March 2012.
2. The Gerda experimental setu p
A brief outline of the components of the Gerda detector that are most relevant for
this work is given below; a detailed description can be found in [9, 10].
The Gerda experimental setup is shown in figure
1. At the core of the setup
there is an array of high-purity germanium detectors (HPGe). They are operated bare
in liquid argon (LAr) which acts both as a coolant and as a shield against the resid-
ual environmental background. The array confi gur at i on c ons i st s of eleven germanium
detectors: eight are made from isotopically modified germanium (
enr
Ge), enriched to
about 86% in
76
Ge, and three are made from natural germanium (
nat
Ge), with a total

Measurement of the half-life of the two-neutrino ββ deca y of
76
Ge with Gerda 4
Figure 1. Artist’s view of the Gerda experiment. The detector array is not to
scale.
mass of 17.67 kg and 7.59 kg, respectively. The enriched det e ct or s come from the
former Heidelberg-Moscow (HdM) [
11] and Igex [12] experiments. They underwent
specific refurbishing processes before operation in Gerda [
13, 14]. The germanium
detectors are mounted in strings with typically three diodes each. Signals are ampli-
fied by low noise, low radioactivity charge sensitive preamplifiers [
15] with 30 MHz
bandwidth operated inside the LAr. They are digitized by a 14-bit 100 MHz contin-
uously ru n ni n g ADC (FADC) equipped with anti-aliasing bandwidth filters. In the
offline an al y si s the waveforms are digitally processed to reconstruct the event energy.
The dete ct or array is surrounded by 64 m
3
of 5.0-grade LAr, contained in a vac-
uum insulated cryostat made of st ai n le ss steel, lined on the inner side by a 3 to 6 c m
thick layer of copper. The cryostat is in turn placed at the centre of a 580 m
3
volume
of ultra-pure water equipped with 66 photomultiplier tubes to veto the residual cosmic
ray muons by the detection of Cherenkov light. The large water volume also serves as
a shi e ld to moderate and capture neutrons produced by natural r adi oac ti v i ty and in
muon-induced hadronic showers.
The energy scale is set by using calibration curves, parametrized as second- ord er
polynomials, derived for each detector by calibration runs taken with
228
Th sources.
The stability of the energy scale is monitored by performing such calibration runs e v -
ery one or two weeks. Moreover, the stability of the system is continuously monitored
by using ad hoc charge pulses generated by a spectr osc opy pulser that ar e regularly
injected in the input of the charge sensitive preamplifier.
All Gerda detectors but two exhibit a reverse current of the order of tens of
pA. The two problematic detect or s showed an increase of leakage current soon after
the beginning of their operati on ; therefore their bias high voltage had to be reduced
and finally completely removed. These two detectors do n ot c ontribute to the present

Frequently asked questions

Q1. What are the contributions in this paper?

The first 5.04 kg yr of data collected in Phase I of the experiment have been analyzed to measure the half-life of the neutrino-accompanied double beta decay of 76Ge this paper. 

Q2. What are the future works in this paper?

The uncertainty of the Gerda result can be further reduced in the future by accumulating more exposure and by performing a new and more precise measurement of the active mass of the detectors. Large data sets will reduce also the uncertainty due to the fit model, as background components can be better characterized and constrained by the ( non- ) observation of γ lines. 

Q3. What is the reason for the Monte Carlo uncertainty?

In this particular application the Monte Carlo uncertainty is mainly due to the propagation of the external γ-rays: the 2νββ-decay electrons generated in the germanium detectors have a sub-cm range and they usually deposit their entire kinetic energy, apart from small losses due to the escape of Bremsstrahlung or fluorescence photons. 

Q4. What is the reason why the half-lives of 76Ge are longer?

The fact that the half-lives derived in the more recent works − and particularly in this one − are systematically longer is probably related to the superior signal-to-background ratio, which lessens the relevance of the background modelling and subtraction. 

Q5. How long is the half-life of 76Ge calculated?

Using phase space factors from the improved electron wave functions reported in [39], the experimental matrix element for the 2νββ decay of 76Ge calculated with the half-life of this work is NME2ν = 0.133+0.004−0.005 MeV −1. 

Q6. How many counts/day are produced by the enrGe detectors?

In fact, the low-energy spectrum is dominated by these β particles and their Bremsstrahlung photons, which account for about 1000 counts/day above 100 keV. 

Q7. What is the contribution due to the particle tracking?

The estimated contribution due to the particle tracking is based on the fact that electromagnetic physics processes provided by Geant4 for γ-rays and e± have been systematically validated at the few-percent level in the energy range which is relevant for γ-ray spectroscopy [32]. 

Q8. How many counts/day is the enrGe detectors expected to have?

Given the half-life of the 2νββ decay reported in the literature (about 1.5 ·1021 yr), the anticipated count rate of the enrGe detectors is about 100 counts/day in the entire energy range up to Qββ=2039 keV. 

Q9. How many days was the data set taken?

The data set considered for the analysis was taken between November 9, 2011, and March 21, 2012, for a total of 125.9 live days, amounting to an exposure of 5.04 kg·yr. 

Q10. What is the effect of the lack of knowledge about the source position on the 76Ge?

The impact on T 2ν1/2 due to the lack of knowledge about the source position – which affects the peak-to-Compton ratio – is accounted as a systematic uncertainty. 

Q11. Why are the background contributions not included in the fit?

Given the lack of discriminating power in the data, the background contributions other than 42K, 214Bi and 40K are not included in the fit. 

Q12. How is the uncertainty of the spectra of the Gerda spectrum evaluated?

It is evaluated by repeating the analysis with different assumptions on the position and distribution of the sources and with artificial variations (e.g. via a scaling factor) of the ratio between the full-energy peaks and the Compton continua. 

Q13. How long did the coincidence between the muon detector and the HPGe detectors take?

The time window for the coincidence between the muon detector and the HPGe detectors was set to 8 µs while that between different HPGe detectors was set to a few µs. 

Q14. What is the rare decay observed in the SM?

Being a higher-order process, it is characterized by an extremely low decay rate: so far it is the rarest decay observed in laboratory experiments. 

Q15. What is the prior pdf for the active mass fraction of each detector?

The prior pdf for the active mass fraction of each detector is modelled as a Gaussian distribution, having mean value and standard deviation according to the measurements performed in [13]. 

Q16. What is the estimate of the half-life of the 2 decay?

The best estimate of the half-life of the 2νββ decay isT 2ν1/2 = (1.84 +0.09 −0.08 fit +0.11 −0.06 syst) · 10 21 yr = (1.84+0.14 −0.10) · 10 21 yr, (2)with the fit and systematic uncertainties combined in quadrature. 

Q17. What is the contribution of 208Tl to the analysis energy window?

The flat component describes the contribution coming from 208Tl decays from the 232Th chain: given the small number of events expected in the analysis energy window, this contribution can be roughly approximated to be constant. 

Q18. What would be the important thing to know about the two-neutrino decay?

An observation of such a decay would demonstrate lepton number violation in nature and would prove that neutrinos have a Majorana component. 

Q19. How much is the uncertainty on T 2 1/2 due to the uncertainties in the standard background components?

The systematic uncertainty on T 2ν 1/2 due to the uncertainties in the spectra of the standard background components (42K, 40K, and 214Bi) is estimated to be 2.1%. 

Q20. How many events are expected from the fit model?

The best fit model has an expectation of 8797.0 events, divided as follows: 7030.1 (79.9%) from the 2νββ decay of 76Ge; 1244.6 (14.1%) from 42K; 335.5 (3.8%) from 214Bi; and 186.8 (2.1%) from 40K. 

Q21. What is the impact of the background on the extracted half-life of the enrG?

their possible impact on the extracted half-life T 2ν1/2 is included in the systematic uncertainty, as discussed in section 4.2; their cumulative contribution to the background is estimated to be of a few percent.