# Status of the GERDA Experiment at the Laboratori Nazionali del Gran Sasso

Authors: R. Brugnera; A. Garfagnini
Journal: Advances in High Energy Physics
 (2013)

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## Abstract

The Germanium Detector Array (Gerda) is a low background experiment at the Laboratori Nazionali del Gran Sasso (LNGS) of the INFN designed to search for the rare neutrinoless double beta decay (0νββ) of 76Ge. In its first phase, high purity germanium diodes inherited from the former Heidelberg-Moscow and Igex experiments are operated “bare” and immersed in liquid argon, with an overall background environment of 10−2 cts/(keV·kg·yr), a factor of ten better than its predecessors. Measurements on two-neutrino double beta decay (2νββ) giving T1/22ν=(1.88±0.10)×1021yr and recently published background model and pulse shape performances of the detectors are discussed in the paper. A new result on 0νββ has been recently published with a half-life limit on 0νββ decay T1/20ν>2.1×1025yr (90% C.L.). A second phase of the experiment is scheduled to start during the year 2014, after a major upgrade shutdown. Thanks to the increased detector mass with new designed diodes and to the introduction of liquid argon instrumentation techniques, the experiment aims to reduce further the expected background to about 10−3 cts/(keV·kg·yr) and to improve the 0νββ sensitivity to about T1/20ν>1.5×1026yr (90% C.L.).


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## Body

## 1. Introduction

Double beta decay is the simultaneous beta decay of two neutrons in a nucleus. It is a second-order weak process, predicted by the standard model:(A,Z)→(A,Z+2)+2e-+2ν¯e. The process (2νββ) has been experimentally observed in even-even nuclei and can be detected only when its single beta decay is energetically forbidden or strongly suppressed because of a large change of spin. Typical half-lives are very large and lie between 7×1018 yr and 2×1024 yr [1–6]. Extensions of the standard model (SM) predict that also neutrinoless double beta decay, (A,Z)→(A,Z+2)+2e-, could occur (0νββ). Its observation implies that the lepton number is violated by two units. It would prove that neutrinos have a Majorana mass component, and consequently they are their own antiparticle. With the further assumption that 0νββ decay is mediated by the exchange of light Majorana neutrinos, an effective neutrino mass can be evaluated through the use of predictions for the nuclear matrix element and the phase space factor. For recent reviews on 0νββ, see [7–10].The Gerda [11] experiment in Europe and Majorana [12, 13] in the USA, at different stages of development and using different experimental approaches, are the current state-of-the-art experiments to search for 0νββ in 76Ge using germanium detectors. The process has a clear signature with a monoenergetic line in the observed energy spectrum at Qββ=2039.061±0.007keV [14], corresponding to the sum of the two electrons energies. Two previous experiments, Heidelberg-Moscow (HdM) and Igex, have studied double beta decay in germanium and set limits on the 0νββ half-life: T1/20ν>1.9×1025 yr [15] and T1/20ν>1.6×1025 yr [16–18], respectively. Part of the HdM collaboration claimed evidence for a peak at Qββ which corresponds to a half-life central value of T1/20ν=1.19-0.23+0.37×1025 yr [19]. The result was later refined with pulse shape discrimination (PSD) analysis techniques giving a half-life T1/20ν=2.23-0.31+0.44×1025 yr [20]. Due to various inconsistencies in the analysis pointed out in [7], only the first claim will be considered in the following.The data taking of the Gerda experiment has been organized in two phases. During Phase I, the experiment aims to scrutinize the HdM claim, using high purity germanium detectors coming from the HdM and Igex collaborations (about 18 kg of total mass) and operating in a environment with a lower background. The sensitivity will be improved by an order of magnitude during the Phase II with the help of an additional set of new detectors (increasing the mass by about 20kg) and a higher background suppression thanks to liquid argon (LAr) instrumentation and enhanced PSD of the new detectors.In the following sections, after an introduction to the experimental setup, the Phase I results will be reviewed: the first2νββ half-life measurement, a detailed study of the Gerda background decomposition model, and the detector performances with respect to PSD techniques. Finally, the recent 0νββ half-life measurement is discussed and the implications of the limit with respect to those determined in 76Ge [19] and with 136Xe based experiments [21, 22] are illustrated.


## 2. TheGerda Detector

The Gerda [11] experiment, at the Laboratori Nazionali del Gran Sasso (LNGS) of INFN, operates bare germanium diodes made of isotopically modified material, enriched to about 86% in 76Ge, in a LAr cryogenic bath, without their usual vacuum cryostats. The experiment aims to pursue very low backgrounds thanks to ultrapure shielding against environmental radiation. An artist view of the detector is given in Figure 1. The germanium detectors are suspended in strings into the cryostat. The 64 m3 of LAr are used both as a coolant and shield. The stainless steel cryostat vessel is covered, from the inside, with copper lining to reduce gamma radiation from the cryostat walls. The vessel is surrounded by a large tank filled with high purity water (590 m3) which further shields the inner volumes from the experimental hall radiation (absorbing γs and moderating neutrons). Moreover it provides a sensitive medium for the muon system which operates as a Cherenkov muon veto.Figure 1
Artist view of the Gerda experiment. The following components are labeled in the picture: (1) the germanium array strings (not to scale), (2) the LAr cryostat, (3) the internal copper shield, (4) the instrumented water tank, and (5) the clean room with the lock insertion system (6). From [11].On top of the Gerda building, just above the cryostat neck, a ISO class 7 clean room has been installed and is used as a working environment within which a nitrogen fluxed glove box is used to manipulate the detectors before inserting them into the cryostat. The detectors are arranged in strings, each supporting three semicoaxial or five broad energy germanium (BEGe) detectors and are lowered into the cryostat through a two-arm lock which separates the clean room from the cryostat. The detector strings are surrounded by a 60 μm thick copper cylinder (called minishroud) with dimensions such that the detector outer surface is placed at few mm from the copper walls. A larger enclosure—a 30 μm thick copper cylinder—with a 75 cm diameter is built around all detector strings.All detectors are read out with charge sensitive preamplifiers (called CC2 [23]) operated in LAr at about 30 cm for the top of the detector array. The CC2, located inside a copper box providing electromagnetic shielding, drives 20 m long signal cables from the cold LAr region to the room temperature DAQ electronics through custom made feedthroughs. The analog signals are digitized by 100 MHz FADCs. The raw data, saved in binary format, is converted to a standardized format defined by MGDO (Majorana-Gerda Data Objects) [24], a software library jointly developed by the Gerda and Majorana collaborations that contains general-purpose interfaces and analysis tools supporting digital processing of experimental or simulated signals. The MGDO data objects are stored as Root files [25], named Tier1. The Gelatio software framework [26] provides independent and customizable modules which are applied to the Tier1 waveforms producing several observables (pulse amplitude, rise time, average baseline, etc.) which are stored in new Root files (Tier2) and are used for both data and Monte Carlo.Eight reprocessed semicoaxial germanium detectors, inherited from the previous HdM and Igex experiments, were deployed on November 9, 2011, together with three detectors with natural isotopic abundance. In July 2012, two of the semicoaxial diodes with natural isotopic abundance were replaced by five enriched BEGe detectors. The latter follow the Phase II design of Gerda and were recently characterized by the collaboration with the HEROICA [27] infrastructure at HADES (Belgium).Further information on the detectors properties used in Gerda Phase I are available here [28], while details on the detector design, construction, and first results on the commissioning phase can be found here [11].


### 2.1. Germanium Detectors

In Gerda two types of germanium detectors are used: semicoaxial and BEGe. A sketch of both reporting their typical geometrical dimensions, electrodes, grooves, and weighting potentials [29] is shown in Figure 2. The semicoaxial germanium detectors used in Phase I are standard p-type detectors, with a n+ conductive lithium layer (~1 mm) separated from the boron implanted p+ contact by a groove. In normal DC coupled readout, the p+ surface (~1 μm) is connected to a charge sensitive amplifier and the n+ surface is biased with up to +4600 V. For Phase II new detectors will be used of BEGe type. The detector has a cylindrical shape, a small boron-implanted p+ electrode is placed on one of the flat surfaces. The lithium-diffused n+ electrode, covers the rest of the outer surface and it is separated from the p+ electrode by a circular groove. The positive bias is applied to the n+ electrode, while the p+ electrode (signal read-out electrode) is grounded. The main characteristic of this detector is the small area p+ electrode. This implies a lower capacitive noise and so an improved energy resolution in a wide range with respect to the standard semicoaxial detectors. Moreover this geometrical configuration in conjunction with an ad hoc impurities profile inside the detector permits to obtain enhanced PSD capabilities.Cross-section of a semicoaxial detector (a) and a BEGe detector (b). Then+ electrode is drawn in black and the p+ electrode in gray; the thicknesses are not to scale. The two electrodes are separated by an insulating groove. The weighting potential [29] inside the detectors is indicated through a color map. For the BEGE also the readout with a charge sensitive amplifier is shown. From [32].
(a)
(b)


### 2.2. Data Taking

The data taking started on November 9, 2011, and finished on May 21, 2013. A total exposure of 21.60 kg·yr was collected, subdivided into 19.20 kg·yr from the semicoaxial detectors and 2.40 kg·yr from the BEGe detectors. Table 1 shows the different exposures used in the analyses explained in the following sections, while Table 2 illustrates how the exposure, for the different analyses, is then subdivided into various data sets. The reason to divide the exposure of the semicoaxial detectors into two different data sets (GOLD-coax and SILVER-coax) is due to the fact that for approximately 30 days after the BEGe detectors deployment the background counting rate increased a lot. All the quoted numbers for the exposures are calculated from the total detector mass. In the analyses the isotopic abundance of the 76Ge and the active mass are properly taken into account. The abundances ranges vary from 86% to 88% while the active volume fractions, that is, the ratio between active detector mass and total detector mass, from 83% to 92%.Table 1
List of the various analyses illustrated in the paper with the corresponding exposures and data taking time periods.
Period
Exposure   kg·yr
Analysis
From
To
09/11/2011
21/03/2012
5.04
2νββ
09/11/2011
3/03/2013
18.50
Background decomposition
09/11/2011
21/05/2013
21.60
PSD analysis
09/11/2011
21/05/2013
21.60
0νββTable 2
Data sets, the detectors used and their exposure are listed for the data used for the background decomposition, PSD and 0νββ analyses.
Data set
Detectors
Exposure
Background
0νββ analysis
decomposition
PSD analysis
kg·yr
S
U
M-coax
all enriched semicoaxial
16.70
19.20
G
O
L
D-coax
all enriched semicoaxial
15.40
17.90
S
I
L
V
E
R-coax
all enriched semicoaxial
1.30
1.30
S
U
M-bege
all enriched BEGe
1.80
2.40
G
O
L
D-nat
GTF 112
3.13
3.98The energy scale of the individual detectors was determined with228Th sources once every one or two weeks. The energy resolution was stable over the entire data acquisition period. At the Qββ point, the exposure-averaged values are (4.8±0.2) keV for semicoaxial and (3.2±0.2) keV for BEGe, respectively. The differences between reconstructed peak positions and the ones from the calibration curves are smaller than 0.3 keV.


### 2.3. Background Sources

In the experiments dedicated to the search of0νββ events the level of the background is given in terms of the so-called background index (BI), that is, the background counts per keV, per kg, and per year in the region of interest (ROI) around Qββ. In order to achieve its sensitivity goals, in Phase I Gerda has to confine the BI at the level of 10-2 cts/(keV·kg·yr) and down to 10-3 cts/(keV·kg·yr) in Phase II.The sources of background can be classified by the location of the radioactive isotope: backgrounds internal to the germanium diode and external backgrounds.The backgrounds internal to the germanium diode are generated during the diode production above ground. There the germanium is exposed to hadronic radiation, especially neutrons. These cause spallation in the material and hence a variety of isotopes are produced. Most important for the neutrinoless double beta decay are the decays of68Ge and 60Co since Q values above Qββ = 2039 keV occur in the chain, and the lifetimes are in the range of years. The cosmogenic production of 60Co in a germanium detector is about 4 atoms/(kg·d) above ground [30], while the production rate of 68Ge in 76Ge is about 1 atom/(kg·d) [30]. The final internal background contamination for the semicoaxial detector was estimated to be 10-2 cts/(keV·kg·yr) mainly due to 60Co activity. For the BEGe detectors all the various steps from the enrichment of the material to the diode production were realized minimizing the time exposure on the surface.The external backgrounds consist of photons from primordial decay chains, neutrons, and muon induced background. The cryostat and the water tank were designed in order to suppress the contribution from 2.615 MeV photons from208Tl decays (coming from the rock in LNGS Hall A and cryostat material), from neutrons (coming from spontaneous fission mainly by the 238U isotope, from (α, n) reactions in the concrete and the rock and from muon interactions). For all these background components the BI is reduced to a level of 10-4 cts/(keV·kg·yr). The LAr contains the 42Ar isotope, electrons from the 42K decays, the progeny of 42Ar, have energies up to 3.5 MeV, well above the Qββ. Beta decays of 39Ar have a Q value of 565 keV and do not contribute to the background for neutrinoless double beta decay. In LAr also some 222Rn impurities can be present. The experience of many low background experiments shows that surface contaminations are often larger than bulk activities; the main isotopes are 232Th and 210Pb. Another important source of contamination is the holder material of the diodes: simulations show that the fraction of decays depositing energy in the interval 2.0 to 2.8 MeV is similar to the case of surface contaminations.


### 2.4. Background Rejection Techniques

In order to achieve the goal of one or two orders of magnitude reduction in backgrounds relative to previous experiments, a very careful selection of materials was made during Phase I. This selection was carried out by using state-of-the-art screening techniques: gamma ray spectroscopy with high purity germanium spectrometers in underground laboratories, gas counting with ultralow background proportional counters and mass spectrometry with inductively coupled plasma mass spectrometers (ICP-MS). To reduce the background further active techniques have to be used.(i)
Anticoincidence between different detectors in the setup: this method relies on the fact that0νββ events are single site events (SSE), while large part of the background can deposit its energy in many distant locations inside one detector and also in different detectors (multisite events, MSE).(ii)
PSD analysis: again, the nonlocalized energy deposition for background events is explored (for further details see Section3.3).(iii)
Scintillation light detection: ionizing radiation that creates background signals in the diode with energies close toQββ typically has energies greater than the one deposited in the germanium crystals. Part of this energy is dissipated in the LAr and is visible. The scintillation properties of LAr are well established: about 40,000 photons are emitted per MeV of deposited energy. Photons are emitted in the deexcitation of the Ar2* excimer with a wavelength of 128 nm. These powerful techniques will be used during Phase II of the Gerda experiment.


## 2.1. Germanium Detectors

In Gerda two types of germanium detectors are used: semicoaxial and BEGe. A sketch of both reporting their typical geometrical dimensions, electrodes, grooves, and weighting potentials [29] is shown in Figure 2. The semicoaxial germanium detectors used in Phase I are standard p-type detectors, with a n+ conductive lithium layer (~1 mm) separated from the boron implanted p+ contact by a groove. In normal DC coupled readout, the p+ surface (~1 μm) is connected to a charge sensitive amplifier and the n+ surface is biased with up to +4600 V. For Phase II new detectors will be used of BEGe type. The detector has a cylindrical shape, a small boron-implanted p+ electrode is placed on one of the flat surfaces. The lithium-diffused n+ electrode, covers the rest of the outer surface and it is separated from the p+ electrode by a circular groove. The positive bias is applied to the n+ electrode, while the p+ electrode (signal read-out electrode) is grounded. The main characteristic of this detector is the small area p+ electrode. This implies a lower capacitive noise and so an improved energy resolution in a wide range with respect to the standard semicoaxial detectors. Moreover this geometrical configuration in conjunction with an ad hoc impurities profile inside the detector permits to obtain enhanced PSD capabilities.Cross-section of a semicoaxial detector (a) and a BEGe detector (b). Then+ electrode is drawn in black and the p+ electrode in gray; the thicknesses are not to scale. The two electrodes are separated by an insulating groove. The weighting potential [29] inside the detectors is indicated through a color map. For the BEGE also the readout with a charge sensitive amplifier is shown. From [32].
(a)
(b)


## 2.2. Data Taking

The data taking started on November 9, 2011, and finished on May 21, 2013. A total exposure of 21.60 kg·yr was collected, subdivided into 19.20 kg·yr from the semicoaxial detectors and 2.40 kg·yr from the BEGe detectors. Table 1 shows the different exposures used in the analyses explained in the following sections, while Table 2 illustrates how the exposure, for the different analyses, is then subdivided into various data sets. The reason to divide the exposure of the semicoaxial detectors into two different data sets (GOLD-coax and SILVER-coax) is due to the fact that for approximately 30 days after the BEGe detectors deployment the background counting rate increased a lot. All the quoted numbers for the exposures are calculated from the total detector mass. In the analyses the isotopic abundance of the 76Ge and the active mass are properly taken into account. The abundances ranges vary from 86% to 88% while the active volume fractions, that is, the ratio between active detector mass and total detector mass, from 83% to 92%.Table 1
List of the various analyses illustrated in the paper with the corresponding exposures and data taking time periods.
Period
Exposure   kg·yr
Analysis
From
To
09/11/2011
21/03/2012
5.04
2νββ
09/11/2011
3/03/2013
18.50
Background decomposition
09/11/2011
21/05/2013
21.60
PSD analysis
09/11/2011
21/05/2013
21.60
0νββTable 2
Data sets, the detectors used and their exposure are listed for the data used for the background decomposition, PSD and 0νββ analyses.
Data set
Detectors
Exposure
Background
0νββ analysis
decomposition
PSD analysis
kg·yr
S
U
M-coax
all enriched semicoaxial
16.70
19.20
G
O
L
D-coax
all enriched semicoaxial
15.40
17.90
S
I
L
V
E
R-coax
all enriched semicoaxial
1.30
1.30
S
U
M-bege
all enriched BEGe
1.80
2.40
G
O
L
D-nat
GTF 112
3.13
3.98The energy scale of the individual detectors was determined with228Th sources once every one or two weeks. The energy resolution was stable over the entire data acquisition period. At the Qββ point, the exposure-averaged values are (4.8±0.2) keV for semicoaxial and (3.2±0.2) keV for BEGe, respectively. The differences between reconstructed peak positions and the ones from the calibration curves are smaller than 0.3 keV.


## 2.3. Background Sources

In the experiments dedicated to the search of0νββ events the level of the background is given in terms of the so-called background index (BI), that is, the background counts per keV, per kg, and per year in the region of interest (ROI) around Qββ. In order to achieve its sensitivity goals, in Phase I Gerda has to confine the BI at the level of 10-2 cts/(keV·kg·yr) and down to 10-3 cts/(keV·kg·yr) in Phase II.The sources of background can be classified by the location of the radioactive isotope: backgrounds internal to the germanium diode and external backgrounds.The backgrounds internal to the germanium diode are generated during the diode production above ground. There the germanium is exposed to hadronic radiation, especially neutrons. These cause spallation in the material and hence a variety of isotopes are produced. Most important for the neutrinoless double beta decay are the decays of68Ge and 60Co since Q values above Qββ = 2039 keV occur in the chain, and the lifetimes are in the range of years. The cosmogenic production of 60Co in a germanium detector is about 4 atoms/(kg·d) above ground [30], while the production rate of 68Ge in 76Ge is about 1 atom/(kg·d) [30]. The final internal background contamination for the semicoaxial detector was estimated to be 10-2 cts/(keV·kg·yr) mainly due to 60Co activity. For the BEGe detectors all the various steps from the enrichment of the material to the diode production were realized minimizing the time exposure on the surface.The external backgrounds consist of photons from primordial decay chains, neutrons, and muon induced background. The cryostat and the water tank were designed in order to suppress the contribution from 2.615 MeV photons from208Tl decays (coming from the rock in LNGS Hall A and cryostat material), from neutrons (coming from spontaneous fission mainly by the 238U isotope, from (α, n) reactions in the concrete and the rock and from muon interactions). For all these background components the BI is reduced to a level of 10-4 cts/(keV·kg·yr). The LAr contains the 42Ar isotope, electrons from the 42K decays, the progeny of 42Ar, have energies up to 3.5 MeV, well above the Qββ. Beta decays of 39Ar have a Q value of 565 keV and do not contribute to the background for neutrinoless double beta decay. In LAr also some 222Rn impurities can be present. The experience of many low background experiments shows that surface contaminations are often larger than bulk activities; the main isotopes are 232Th and 210Pb. Another important source of contamination is the holder material of the diodes: simulations show that the fraction of decays depositing energy in the interval 2.0 to 2.8 MeV is similar to the case of surface contaminations.


## 2.4. Background Rejection Techniques

In order to achieve the goal of one or two orders of magnitude reduction in backgrounds relative to previous experiments, a very careful selection of materials was made during Phase I. This selection was carried out by using state-of-the-art screening techniques: gamma ray spectroscopy with high purity germanium spectrometers in underground laboratories, gas counting with ultralow background proportional counters and mass spectrometry with inductively coupled plasma mass spectrometers (ICP-MS). To reduce the background further active techniques have to be used.(i)
Anticoincidence between different detectors in the setup: this method relies on the fact that0νββ events are single site events (SSE), while large part of the background can deposit its energy in many distant locations inside one detector and also in different detectors (multisite events, MSE).(ii)
PSD analysis: again, the nonlocalized energy deposition for background events is explored (for further details see Section3.3).(iii)
Scintillation light detection: ionizing radiation that creates background signals in the diode with energies close toQββ typically has energies greater than the one deposited in the germanium crystals. Part of this energy is dissipated in the LAr and is visible. The scintillation properties of LAr are well established: about 40,000 photons are emitted per MeV of deposited energy. Photons are emitted in the deexcitation of the Ar2* excimer with a wavelength of 128 nm. These powerful techniques will be used during Phase II of the Gerda experiment.


## 3. Results

When all the detectors of Phase I were deployed into the LAr, the experiment strategy was to maximize the exposure under stable conditions. In parallel, an effort to understand the composition of the collected data and to develop methods to suppress a large fraction of background over signal (0νββ events) has been started. In the following sections, first the determination of the 2νββ half-life [31] and afterwards the full spectrum background decomposition [28] will be described. After a discussion on the PSD methods [32] developed for background suppression, the first Gerda results on the 0νββ process [33] will be reported.


### 3.1. Determination of the Half-Life of the 2νββ Decay

The2νββ decay of atomic nuclei, with the simultaneous emission of two electrons and two antineutrinos, conserves lepton number and is allowed within the SM, regardless of the nature of the neutrino. It is characterized by an extremely low decay rate because it is a second-order process. So far it is the rarest decay ever observed in laboratory experiments. The measurement of the 2νββ half-life (T1/22ν) is of some interest. Indeed it has been suggested [34–41] that, within the same model framework, the evaluation of the nuclear matrix element for the 2νββ decay (M2ν) from T1/22ν measurements could set some constraints on M0ν. Moreover, M2ν can be compared with the predictions based on charge exchange experiments [42, 43]. An agreement between those two evaluations will increase the knowledge of the reaction mechanisms and the nuclear structure aspects involved in 2νββ.The data set considered for the2νββ analysis was taken between November 9, 2011, and March 21, 2012, corresponding to an exposure of 5.04 kg·yr. The collected data were processed following the steps already described in Section 2. The 2νββ analysis was performed in the energy range between 600 and 1800 keV. Below 600 keV indeed the Gerda energy spectrum is largely dominated by 39Ar decay. From Monte Carlo simulations, the probability of 2νββ decay fully contained in the active volume of the detectors and producing a total energy release between 600 and 1800 keV is about 63.5%. The probability of releasing energy in the region above 1800 keV is less than 0.02%: therefore the energy region above 1800 keV gives no information on the 2νββ process. The total number of events in the selected energy window is 8796. The experimental spectra of the diodes were analyzed following a binned maximum likelihood approach described in [44]. The analysis region was divided into 40 bins, of 30 keV each. A global model was fitted to the observed energy spectra. It includes the 76Ge 2νββ decay and three main background components: 42K, 214Bi, and 40K. The presence of such background sources was established by the observation of their characteristic γ lines in the energy spectra: 1525 keV from 42K keV, 1460 keV from 40K, and 609 keV and 1764 keV due to 214Bi. The 2νββ decay half-life is common in the fit to the six semicoaxial detector spectra. The intensities of the background components are independent for each detector. The shapes of the energy spectra for the signal and the three backgrounds contamination are obtained from the Monte Carlo simulation, separately calculated for each detector. The simulation is performed using the Mage code [45] based on Geant 4 [46, 47]. The spectrum of the two electrons emitted in the 76Ge 2νββ decay follows the distribution of [3] as implemented in the DECAY0 [48] code. The 42K activity is uniformly distributed in the LAr volume. The actual position of the 40K and 214Bi emitters is not known very well: in the Monte Carlo simulation a “close source” assumption was made. The spectral fit was performed using the Bayesian Analysis Toolkit (BAT) [49]. Well-chosen prior probability density functions (PDF) were given for T1/22ν, for the active volume fractions and 76Ge isotopic abundances of the germanium diodes. Figure 3 shows the data together with the best fit model (black histogram) with its 68% uncertainties. The best fit model returns 8797.0 events in comparison to 8796 data events, with the following components: 76Ge 2νββ (79%), 42K (14.1%), 218Bi (3.8%), and 40K (2.1%). The signal-to-background ratio in the region 600–1800 keV is around 4 to 1, much better than that for any past experiment observing the 76Ge 2νββ decay. The best half-life estimate, having marginalized over all nuisance parameters, gives
(1)T1/22ν=(1.84-0.08fit+0.09-0.06syst+0.11)×1021yr.(a) shows the experimental data (black markers) and the best fit model (black histogram) for the sum of the semicoaxial detectors in linear scale and (b) in logarithmic scale. Individual components are shown with colored histograms. The shaded band covers the 68% probability range for the model expectation. (c) gives the ratio between experimental data and the prediction of the best fit model. The smallest intervals containing the 68%, 95%, and 99.9% probability for the expectation are shown in green, yellow, and red regions, respectively. From [31].
(a)
(b)
(c)The first error comes from the statistics and the marginalization of the nuisance parameters, while the second relates to the systematic uncertainties. Active masses and76Ge isotopic abundances drive the uncertainties coming from the fit procedure, while the dominant systematic uncertainties are due to the background model.A compilation of the76Ge T1/22ν results from earlier experiments plotted versus the publication year, nine experimental measurements and two weighted averages, is shown in Figure 4. A trend toward longer T1/22ν values is clearly seen. The effect is probably related to the signal-to-background ratio increase over the years. This also explains why the total Gerda uncertainty is comparable to what was obtained by HdM in spite of the much smaller exposure. From the present Gerda result and using the improved electron wave functions reported in [50], it is possible to calculate the nuclear matrix element for the 76Ge 2νββ decay: M2ν = 0.133-0.005+0.004 MeV-1. The value is consistent with 76Ge M2ν extracted from the charge exchange reactions (d,2He) and (3He, t) [42, 43].Figure 4
Experimental results forT1/22ν of 76Ge versus publication year. The plot includes results from the experiments ITEP-YPI [55], PNL-USC [56], PNL-USC-ITEP-YPI [57, 58], Heildelberg-Moscow (HdM) [15, 59], and Igex [17, 18] as well as reanalysis of the HdM data by Dörr and Klapdor-Kleingrothaus [60] (HdM-K) and by Bakalyarov et al. [61] (HdM-B). Recommended values coming from a global analysis are also shown (NNDC [62], Barabash [2]). From [31].


### 3.2. Background Decomposition

The characteristic signature of the 0νββ process is the presence of a peak at Qββ. All other parts of the energy spectrum are to be considered as background. It is obvious that a good knowledge of the background composition is rather important in order to extract a possible signal or in case of no signal events to obtain a lower limit on T1/20ν. Background decomposition is also useful to derive a strategy for background suppression. A comprehensive analysis of the background decomposition of the data was made using 18.50 kg·yr over a total collected exposure of 21.60 kg·yr. That exposure was subdivided into three data sets: GOLD-coax with 15.40 kg·yr, SILVER-coax with 1.30 kg·yr, and BEGe with 1.80 kg·yr.It is worth reminding that a 40 keV energy window between 2019 keV and 2049 keV remained blinded up to the collection of 20 kg·yr; afterwards it was partially unblinded, with the opening of a 30 keV region for the semicoaxial detectors and a 32 keV wide window for the BEGe detectors, respectively. The energy widths of the final blind windows (10 keV for semicoaxial detectors and 8 keV for BEGe detectors) are dictated by the different energy resolution of the two types of detectors. The partial unblinding was done in order to test the background model predictions.The energy spectra obtained from enriched semicoaxial, enriched BEGe, and natural abundance semicoaxial detectors are shown in Figure5, respectively. The low energy part up to 565 keV is dominated by cosmogenic 39Ar β-decay in all spectra, with differences in shape between semicoaxial and BEGe type detectors due to geometry and of n+ dead layer thickness variations among the diodes. Between 600 keV and 1500 keV the enriched detectors spectra show an enhanced continuous spectrum due to 2νββ decay. γ-lines from the decays of 40K and 42K can be identified in all spectra. The enriched detectors spectra contain also lines coming from 208Tl, 214Bi (visible in Figure 5), 60Co, 214Pb, and 228Ac (not visible in Figure 5) decays. A peak-like structure around 5.3 MeV is visible in the enriched semicoaxial diodes spectra and partially also in that of the natural one. Such feature can be attributed to the 210Po decay in the detector p+ surfaces. Additional peak-like structures at energies of 4.7 MeV, 5.4 MeV, and 5.9 MeV are identified as indicated in Figure 5. They are attributed to 226Ra, 222Rn, and 218Po α decays on the detector p+ surface, respectively.Spectra obtained using all the enriched semicoaxial (a), BEGe (b), and nonenriched (c) detectors. The blinding window of 40 keV around theQββ is indicated with the green band. The bars in the color of the histogram around the green band represent the 200 keV region from which the BI of the dataset is computed. From [28].
(a)
(b)
(c)Background components clearly identified in the energy spectra (see the previous discussion) or that were known to be present near the detectors from the material screening were simulated using the Mage code. The expected BIs due to the neutron and muon fluxes at the LNGS underground laboratories have been estimated to be of the order of 10-5 cts/(keV·kg·yr) [51] and 10-4 cts/(keV·kg·yr) [52] and were not considered in the analysis.The energy spectrum between 570 keV and 1500 keV can be explained in terms of the same background components described in the Section3.1. The events in the 3.5 MeV to 7.5 MeV energy region are expected to come from α emitting isotopes in the 226Ra decay chain, which can be broken at 210Pb and at 210Po due to their long half-lives of 22.3 yr and 138.4 days, respectively. An analysis of the time distribution of the collected events demonstrates the presence of the 210Po isotope. The event rate distribution is well described by an exponentially decreasing plus a constant rate model: the half-life is 138.4±0.4 days, in nice agreement with the literature value for the half-life of  210Po. In Figure 6 the energy spectrum between 3.5 MeV and 7.5 MeV is shown (black markers) together with the best fit model (black histogram). The spectrum is well described assuming the presence of 210Po on the surface of the diodes and also of 226Ra and its short lived daughter nuclei (222Rn, 218Po) on the p+ surface and in LAr. In order to describe the data, different layer thicknesses of the p+ surface were taken into account (from 300 to 600 nm). In the other panel the ratio of data and model are shown; the colored bands give the smallest interval probability for the model expectation.(a) shows the best fit model (black histogram) and the observed spectrum (black dots) for theGOLD-coax data set. The other curves represent the individual components of the model. (b) shows the data over model ratio (empty points) and the smallest intervals containing 68% (green), 95% (yellow), and 99.9% (red) probability for the model expectation. From [28].
(a)
(b)The best fit model and the single background components together with the observed data spectrum from 570 keV to 1650 keV and from 1650 keV to 3750 keV is shown in Figure7. The best fit model around the Qββ for the GOLD-coax data is shown in Figure 8. The spectral shape of the model is flat around Qββ, and no peaks are predicted in the blinded regions. The predicted BI around Qββ is 1.85-0.09+0.08×10-2 cts/(keV·kg·yr). The main background contributions come from 214Bi and 228Th in the detector assembly, 42K homogeneously distributed in LAr and finally from α emitters. The predicted BI nicely agrees with the same quantity derived from the data interpolation in the energy intervals 1930–2019 keV, 2059–2099 keV, 2109–2114 keV, and 2124–2190 keV for a total width of 200 keV: 1.75-0.24+0.26×10-2 cts/(keV·kg·yr). This BI evaluation window excludes the central 40 keV window around Qββ and the regions within ±5 keV of the single escape peak from 208Tl at 2104 keV and the 214Bi γ line at 2119 keV. The model discussed here gives a satisfactory description of the spectrum without any medium distance and distant contaminations. It is called minimum model. It is also possible to build a model with a fair description of the data leaving the possibility to have contamination sources at medium and long distances. The main difference between the two models is the number of events deposited on the p+ surface of the detectors. This last model is called maximum model (see Figure 8(b)). The predicted BI of the maximum model is 2.19-0.12+0.19×10-2 cts/(keV·kg·yr), not very far from the minimum model estimation. To conclude we have to say that all contaminations expected from material screening are seen in the background spectra and are taken into account in the models.(a) shows the background decomposition (black histogram) and the observed spectrum (black dots) using the best fit minimum model for theGOLD-coax data set in the energy range from 570 keV to 1650 keV. The lower panel shows the data over model ratio (empty points) and the smallest intervals containing 68% (green), 95% (yellow), and 99.9% (red) probability for the model expectation. (b) shows the same for the energy range from 1650 keV to 3750 keV. From [28].
(a)
(b)Experimental spectrum with minimum (a) model aroundQββ for the GOLD-coax data set. (a) shows the individual contributions of the considered background sources (colored curves) and the model prediction (black curve). The events colored in gray were used in the analysis, while the light gray shaded (unblinded data, UB data) ones have not been used in the analysis. The lower panel shows the best fit model fitted with a constant. In the fit, the peak areas predicted by the model and the 40 keV blinding window are not considered. (b) shows the same experimental spectrum compared with maximum model around Qββ for the GOLD-coax data set. From [28].
(a)
(b)As mentioned, the 40 keV blinded region was partially unblinded leaving a central 10 keV for semicoaxial detectors (8 keV for BEGe detectors) window still blind. In total 13 events were observed in the unblinded 30 keV window of theGOLD-coax data set. The predictions in this window were 8.6 events for the first model and 10.3 for the second one. The agreement between predictions and observed number of events in the unblinded region is rather good.


### 3.3. Pulse Shape Discrimination Analysis

Signal events have a different topology with respect to a large part of the background events. Due to the limited range of the electrons in germanium (a few mm), the two0νββ electrons release their energy in a well-localized space area inside the detectors. This type of events is SSE. The background in the region of interest is largely due to γs. The latter often interact more than once in the detector at points separated by several centimeters. This type of events is MSE. This different topology is usually registered in the rising part of the recorded signal and the distinction can be facilitated by the particular electric field inside the detector. The procedure of selecting SSE from MSE is called PSD analysis. In Gerda, two different PSD methods were used: one optimized for the BEGe detectors and the other for the semicoaxial diodes.In the case of the BEGe we consider two measured quantities: the energyE of the event (proportional to the maximum of the charge pulse) and then the maximum (A) of the current pulse. The current is measured differentiating the charge pulse. Then the ratio A/E is built and used as a PSD variable [53, 54].The physical justification of such a variable is easy to understand looking to Figure2. The weighting potential sharply rises in the small region around the p+ contact; for that reason, in a single interaction, mainly holes contribute to the induced signal on the readout electrode. Single interactions in different places of the detectors produce charge pulses which differ only from the collection time and the total released energy. If the energy release happens in different places of the BEGe (as for a γ interaction) the output pulse will be the convolution of all the different energy deposition and contain this information in the shape of its rising edge.An application of this simple idea is shown in Figure9. In Figure 9(a) a charge pulse trace for a SSE event is shown with its current pulse superimposed. For a SSE in the bulk detector an almost Gaussian distribution of A/E is expected with a width dominated by the noise of the readout electronics. The situation for a MSE event is depicted in Figure 9(b): for the same total energy E, the maximum current amplitude will be smaller due to the various energy depositions in different places of the detector and at different times. Examples of p+ electrode and n+ surface events are shown in the bottom right and left plots of Figure 9, respectively.Examples of pulse traces taken from SSE data (a), MSE (b),p+ electrode event (c), and n+ surface event (d). The pulse traces are normalized in order to have the maximum of the charge pulse equal to one, current pulses have equal integrals. From [32].
(a)
(b)
(c)
(d)TheA/E method performance was determined using calibration data. A 228Th calibration spectrum contains a line at 2614.5 keV from 214Tl decays, a double escape peak (DEP) at 1592.5 keV dominated by SSE, while the full energy peak (FEP) at 1620.7 keV or the single escape peak (SEP) at 2103.5 keV are dominated by MSE. (If a γ ray has sufficiently high energy (several MeV), the results of pair production are evident in the electron spectrum. If the two annihilation γs leave the detector, only the electron and positron energies are deposited. The net effect is to add a peak to the spectrum, called double escape peak, located at an energy of ~1.02 MeV below the full energy peak. The full energy peak corresponds to the total energy of the primary γ. If instead only one annihilation γ escapes from the detector another peak is added, called single energy peak, which now appears at an energy of ~0.511 MeV below the full energy peak.) Further checks come from the use of the 2νββ events which are genuine SSE distributed homogeneously in the detector. If one determines the mean value of the A/E distribution using DEP from calibration data, then it is possible to rescale the A/E of any event by that mean value. In this manner, the A/E distribution of all SSE (whatever is their origin) will be centered at 1; MSE and n+ surface events will populate the region below 1 while p+ electrode events the region above 1.AnA/E distribution plotted versus energy is shown in Figure 10. The red lines correspond to A/E< 0.965 (“low A/E cut”) and A/E> 1.07 (“high A/E cut”), respectively. The low A/E cut has the aim to reject MSE and n+ events; its value is chosen to minimize at values below 1% the efficiency loss of the A/E Gaussian function for energy above 1 MeV. The high A/E cut rejects p+ events; its value is twice larger than the low cut due to the much lower number and better separation of p+ electrode events.Figure 10
A
/
E versus energy for the BEGe data set. The accepted region is that inside the two red lines (low cut at A/E = 0.965, high cut at A/E = 1.07). The blinded region is given by the green band. From [32].With the aforementioned cut values, the efficiency of theA/E method for 0νββ events is 0.92±0.02 as given by DEP events from calibration data and cross-checked by the use of 2νββ events. The A/E method rejects about 80% of the background events at Qββ. Figure 11 shows the BEGe data energy spectrum before and after the PSD cuts. With an exposure of 2.4 kg·yr, seven out of 40 events in the 400 keV wide region around Qββ are kept. The BI for BEGe detectors in this interval is reduced from (0.042±0.007) to (0.007-0.002+0.004) cts/(keV·kg·yr).Figure 11
Energy spectrum of the BEGe data set. The gray histogram shows the data before PSD cut and the blue one after PSD cut. The inset shows the regionQββ, with the 8 keV blinded region in green. From [32].For semicoaxial detectors the situation is more complicated. The weighting potential (see Figure2(a)) also peaks at the p+ contact but the gradient is lower and hence a larger part of the volume, with respect to the BEGe, is important for the charge pulse. For an interaction which happens in the bulk of the detector, both electrons and holes contribute. All these complications make the semicoaxial less good in PSD with respect to the BEGe. Simulated current pulse shapes for SSE taken in various positions starting from the outer n+ surface and going towards the bore hole (n+ surface) along a radial line at the midplane of the detector are shown in Figure 12. The pulse shape behaviour is rather complicated so a simple A/E variable cannot efficiently discriminate between SSE and MSE.Figure 12
Simulated current pulse shapes for SSE in a semicoaxial detector taken at various places inside the diode. The places vary from the outern+ surface towards the bore hole (n+ surface) along a radial line at the midplane of the detector. From [32].For the semicoaxial detectors a PSD analysis based on neural network was applied. The selected algorithm called TMlpANN (present inside the TMVA [63] toolkit implemented in Root) is based on multilayer perceptron. Two hidden layers, with 50 neurons each, are used.The rising part of the charge pulse is used for this neural network analysis. The input parameters are the times when the pulses reach 1, 3, 5,…, 99% height. The time, at which 50% of the charge of the pulse have been seen, serves as a reference. Due to the 100 MHz sampling frequency, a linear interpolation is required between two consecutive time bins in order to determine the corresponding time points. For the training calibration data are used. The output of the neural network is a number between 0 for background and 1 for signal like events. The cut values are chosen in order to have detector per detector a DEP survival probability fixed at 90%. All possible deviations from 90% were taken into account (energy dependence, volume effect due to the different distribution of DEP and 0νββ events, etc.) and combined quadratically. The final result for the 0νββ efficiency of the neural network is 0.90-0.09+0.05. About 45% of the events in a 230 keV window around Qββ are classified as background and rejected.The energy spectrum collected by the semicoaxial detectors before and after the neural network PSD selection is shown in Figure13.Figure 13
Energy spectrum of semicoaxial detectors without (empty histogram) and with (black histogram) neural network PSD selection. From [32].


### 3.4. Limit on the Half-Life of the 0νββ Decay Process in 76Ge

The total exposure useful for the 0νββ analysis was of 21.60 kg·yr of enrGe detectors collected from November 9, 2011, to May 21, 2013 (492.3 live days). The collected data were processed following the steps described in Section 2. The deposited energy is reconstructed by a digital filter with semi-Gaussian shaping. Events generated by discharges or due to electromagnetic noise are rejected by a set of quality cuts. The analysis cuts applied to the data were the following.(i)
Only events with an energy deposition in a single detector were accepted (anticoincidence cut). AroundQββ 15% of the background events are rejected, with no loss for 0νββ events.(ii)
Events in the germanium detectors in coincidence within 8μs with a signal from the muon veto are rejected (muon veto cut). This leads to a further rejection of ~7% of events.(iii)
Events which are preceded or followed by another event in the same detector within less than 1 ms are excluded. In this manner possible events coming from the decay chain214Bi-214Po are rejected (anti-“BiPo” cut). Less than 1% of the events around the Qββ are affected by this cut.(iv)
To the remaining events, the PSD cut is applied as explained in the Section3.3.As mentioned in Section 2.3, there was a blinded region around the Qββ in order to prevent from possible analysis bias. This region was open and analyzed only after the background model and all the analysis cuts (especially PSD) were frozen.Figure14 shows the energy spectrum around the region of interest with and without PSD selection. No excess of events were observed over a flat background distribution. Seven events were seen in the range Qββ±5 keV before the PSD cuts, while 5.1 were expected. Only 3 events survived (classified as SSE) after PSD cuts and no event remained in Qββ±σE. To derive the number of signal counts N0ν a profile likelihood fit of the spectrum was performed. The fit function was given by the sum of a constant term for the background and of a Gaussian for the signal events. The profile likelihood ratio was limited to the region T1/20ν>0. The best fit was obtained for N0ν = 0, that is, no excess of signal events above background. The lower limit on the half-life is
(2)T1/20ν>2.1×1025yr@90%C.L.
including systematic uncertainties. This limit corresponds to N0ν< 3.47 events. The median sensitivity was 2.4 ×1025yr, taking into account the number of events after PSD, the efficiency, and the exposure. A Bayesian calculation using a flat prior distribution for 1/T1/20ν from 0 to 10-24/yr gives T1/20ν>1.9×1025 yr @ 90%C.I.(a): Energy spectrum for the sum of allenrGe detectors in the range 2020–2060 keV, without PSD (empty histogram) and with PSD (black histogram). The red dashed curve is the expectation based on the central value of [19]; the blue curve is instead based on the 90% upper limit derived by Gerda, T1/20ν = 2.1 ×1025 yr. (b): Energy spectrum in the range 1880–2240 keV; the vertical dashed lines indicate the interval 1930–2190 keV used for the background estimation. From [33].
(a)
(b)As discussed before, the data collected by Gerda do not show any peak at Qββ and do not support the claim described in [19]. Taking the T1/20ν from [19], 5.8 signal events are expected to be observed in Gerda in an energy interval of ±σE with 2.0 background events after the PSD cut. In the same energy range, no events are observed. The model (H1) with the value of T1/20ν and its associated error as given from [19] gives a worse fit than the background only model (H0): the Bayes factor, that is, the ratio of the posterior probabilities of the two models, is P(H1)/P(H0) = 0.024.The Gerda result is consistent with the negative results from Igex and HdM. A combined profile likelihood fit including all these three negative results gives as best fit N0ν = 0 and a 90% probability limit:
(3)T1/20ν>3.0×1025yr@90%C.L.A Bayesian analysis gives the same limit with a Bayes factor of2×10-4 strongly disfavoring the claim. Figure 15 shows the limits set on 76Ge T1/20ν as determined by Gerda alone and combining Gerda with HdM and Igex and on 136Xe T1/20ν as obtained by KamLAND-Zen and EXO-200 separately and combined. While the Gerda result can be compared directly with the claim of [19], in order to compare the results obtained on 136Xe with the claimed signal, the assumption that the main underlying mechanism mediating 0νββ is the exchange of light Majorana neutrinos has to be made. In this case the ratio of the half-lives of the 0νββ decay in 136Xe and 76Ge is proportional to the square of the nuclear matrix ratio M0ν(76Ge)/M0ν(136Xe), which has to be derived by theoretical calculations. The lines in the shaded band of Figure 15 are the predictions from the nuclear matrix calculations reported in [64]. The spread of the predictions on the nuclear matrix elements comes from various different approximations. It is possible, through the help of a chosen set of nuclear matrix, to make a combination of all null results from 76Ge and 136Xe experiments. Taking, to be conservative, the nuclear matrix element model which gives the lowest M0ν(136Xe)/M0ν(76Ge) ratio, a Bayesian analysis gives a Bayes factor of 0.40 for KamLAND-Zen and 0.23 for EXO-200, to be compared to the Gerda alone result of 0.024. Putting all these experiment together, the Bayes factor becomes 0.0022. It is important to note that other theoretical calculations might lead to even smaller ratios and so weaker exclusions.Figure 15
Limits at 90% C.L. onT1/20ν for 76Ge (Gerda Phase I alone and Gerda Phase I, Igex and HdM combined together [33]) and for 136Xe [21, 22]. The signal claim for 76Ge from [19] is also shown. The lines in the shaded gray band are the predictions for the correlation between the half-lives obtained in 136Xe and in 76Ge using a selection of different nuclear matrix element calculations taken from [64]. From [33].The result of (3) can be translated into the following effective electron neutrino mass mββ< 0.2−0.4 eV having used the phase space factors from [50] and the nuclear matrix elements calculations cited in [64].


## 3.1. Determination of the Half-Life of the 2νββ Decay

The2νββ decay of atomic nuclei, with the simultaneous emission of two electrons and two antineutrinos, conserves lepton number and is allowed within the SM, regardless of the nature of the neutrino. It is characterized by an extremely low decay rate because it is a second-order process. So far it is the rarest decay ever observed in laboratory experiments. The measurement of the 2νββ half-life (T1/22ν) is of some interest. Indeed it has been suggested [34–41] that, within the same model framework, the evaluation of the nuclear matrix element for the 2νββ decay (M2ν) from T1/22ν measurements could set some constraints on M0ν. Moreover, M2ν can be compared with the predictions based on charge exchange experiments [42, 43]. An agreement between those two evaluations will increase the knowledge of the reaction mechanisms and the nuclear structure aspects involved in 2νββ.The data set considered for the2νββ analysis was taken between November 9, 2011, and March 21, 2012, corresponding to an exposure of 5.04 kg·yr. The collected data were processed following the steps already described in Section 2. The 2νββ analysis was performed in the energy range between 600 and 1800 keV. Below 600 keV indeed the Gerda energy spectrum is largely dominated by 39Ar decay. From Monte Carlo simulations, the probability of 2νββ decay fully contained in the active volume of the detectors and producing a total energy release between 600 and 1800 keV is about 63.5%. The probability of releasing energy in the region above 1800 keV is less than 0.02%: therefore the energy region above 1800 keV gives no information on the 2νββ process. The total number of events in the selected energy window is 8796. The experimental spectra of the diodes were analyzed following a binned maximum likelihood approach described in [44]. The analysis region was divided into 40 bins, of 30 keV each. A global model was fitted to the observed energy spectra. It includes the 76Ge 2νββ decay and three main background components: 42K, 214Bi, and 40K. The presence of such background sources was established by the observation of their characteristic γ lines in the energy spectra: 1525 keV from 42K keV, 1460 keV from 40K, and 609 keV and 1764 keV due to 214Bi. The 2νββ decay half-life is common in the fit to the six semicoaxial detector spectra. The intensities of the background components are independent for each detector. The shapes of the energy spectra for the signal and the three backgrounds contamination are obtained from the Monte Carlo simulation, separately calculated for each detector. The simulation is performed using the Mage code [45] based on Geant 4 [46, 47]. The spectrum of the two electrons emitted in the 76Ge 2νββ decay follows the distribution of [3] as implemented in the DECAY0 [48] code. The 42K activity is uniformly distributed in the LAr volume. The actual position of the 40K and 214Bi emitters is not known very well: in the Monte Carlo simulation a “close source” assumption was made. The spectral fit was performed using the Bayesian Analysis Toolkit (BAT) [49]. Well-chosen prior probability density functions (PDF) were given for T1/22ν, for the active volume fractions and 76Ge isotopic abundances of the germanium diodes. Figure 3 shows the data together with the best fit model (black histogram) with its 68% uncertainties. The best fit model returns 8797.0 events in comparison to 8796 data events, with the following components: 76Ge 2νββ (79%), 42K (14.1%), 218Bi (3.8%), and 40K (2.1%). The signal-to-background ratio in the region 600–1800 keV is around 4 to 1, much better than that for any past experiment observing the 76Ge 2νββ decay. The best half-life estimate, having marginalized over all nuisance parameters, gives
(1)T1/22ν=(1.84-0.08fit+0.09-0.06syst+0.11)×1021yr.(a) shows the experimental data (black markers) and the best fit model (black histogram) for the sum of the semicoaxial detectors in linear scale and (b) in logarithmic scale. Individual components are shown with colored histograms. The shaded band covers the 68% probability range for the model expectation. (c) gives the ratio between experimental data and the prediction of the best fit model. The smallest intervals containing the 68%, 95%, and 99.9% probability for the expectation are shown in green, yellow, and red regions, respectively. From [31].
(a)
(b)
(c)The first error comes from the statistics and the marginalization of the nuisance parameters, while the second relates to the systematic uncertainties. Active masses and76Ge isotopic abundances drive the uncertainties coming from the fit procedure, while the dominant systematic uncertainties are due to the background model.A compilation of the76Ge T1/22ν results from earlier experiments plotted versus the publication year, nine experimental measurements and two weighted averages, is shown in Figure 4. A trend toward longer T1/22ν values is clearly seen. The effect is probably related to the signal-to-background ratio increase over the years. This also explains why the total Gerda uncertainty is comparable to what was obtained by HdM in spite of the much smaller exposure. From the present Gerda result and using the improved electron wave functions reported in [50], it is possible to calculate the nuclear matrix element for the 76Ge 2νββ decay: M2ν = 0.133-0.005+0.004 MeV-1. The value is consistent with 76Ge M2ν extracted from the charge exchange reactions (d,2He) and (3He, t) [42, 43].Figure 4
Experimental results forT1/22ν of 76Ge versus publication year. The plot includes results from the experiments ITEP-YPI [55], PNL-USC [56], PNL-USC-ITEP-YPI [57, 58], Heildelberg-Moscow (HdM) [15, 59], and Igex [17, 18] as well as reanalysis of the HdM data by Dörr and Klapdor-Kleingrothaus [60] (HdM-K) and by Bakalyarov et al. [61] (HdM-B). Recommended values coming from a global analysis are also shown (NNDC [62], Barabash [2]). From [31].


## 3.2. Background Decomposition

The characteristic signature of the 0νββ process is the presence of a peak at Qββ. All other parts of the energy spectrum are to be considered as background. It is obvious that a good knowledge of the background composition is rather important in order to extract a possible signal or in case of no signal events to obtain a lower limit on T1/20ν. Background decomposition is also useful to derive a strategy for background suppression. A comprehensive analysis of the background decomposition of the data was made using 18.50 kg·yr over a total collected exposure of 21.60 kg·yr. That exposure was subdivided into three data sets: GOLD-coax with 15.40 kg·yr, SILVER-coax with 1.30 kg·yr, and BEGe with 1.80 kg·yr.It is worth reminding that a 40 keV energy window between 2019 keV and 2049 keV remained blinded up to the collection of 20 kg·yr; afterwards it was partially unblinded, with the opening of a 30 keV region for the semicoaxial detectors and a 32 keV wide window for the BEGe detectors, respectively. The energy widths of the final blind windows (10 keV for semicoaxial detectors and 8 keV for BEGe detectors) are dictated by the different energy resolution of the two types of detectors. The partial unblinding was done in order to test the background model predictions.The energy spectra obtained from enriched semicoaxial, enriched BEGe, and natural abundance semicoaxial detectors are shown in Figure5, respectively. The low energy part up to 565 keV is dominated by cosmogenic 39Ar β-decay in all spectra, with differences in shape between semicoaxial and BEGe type detectors due to geometry and of n+ dead layer thickness variations among the diodes. Between 600 keV and 1500 keV the enriched detectors spectra show an enhanced continuous spectrum due to 2νββ decay. γ-lines from the decays of 40K and 42K can be identified in all spectra. The enriched detectors spectra contain also lines coming from 208Tl, 214Bi (visible in Figure 5), 60Co, 214Pb, and 228Ac (not visible in Figure 5) decays. A peak-like structure around 5.3 MeV is visible in the enriched semicoaxial diodes spectra and partially also in that of the natural one. Such feature can be attributed to the 210Po decay in the detector p+ surfaces. Additional peak-like structures at energies of 4.7 MeV, 5.4 MeV, and 5.9 MeV are identified as indicated in Figure 5. They are attributed to 226Ra, 222Rn, and 218Po α decays on the detector p+ surface, respectively.Spectra obtained using all the enriched semicoaxial (a), BEGe (b), and nonenriched (c) detectors. The blinding window of 40 keV around theQββ is indicated with the green band. The bars in the color of the histogram around the green band represent the 200 keV region from which the BI of the dataset is computed. From [28].
(a)
(b)
(c)Background components clearly identified in the energy spectra (see the previous discussion) or that were known to be present near the detectors from the material screening were simulated using the Mage code. The expected BIs due to the neutron and muon fluxes at the LNGS underground laboratories have been estimated to be of the order of 10-5 cts/(keV·kg·yr) [51] and 10-4 cts/(keV·kg·yr) [52] and were not considered in the analysis.The energy spectrum between 570 keV and 1500 keV can be explained in terms of the same background components described in the Section3.1. The events in the 3.5 MeV to 7.5 MeV energy region are expected to come from α emitting isotopes in the 226Ra decay chain, which can be broken at 210Pb and at 210Po due to their long half-lives of 22.3 yr and 138.4 days, respectively. An analysis of the time distribution of the collected events demonstrates the presence of the 210Po isotope. The event rate distribution is well described by an exponentially decreasing plus a constant rate model: the half-life is 138.4±0.4 days, in nice agreement with the literature value for the half-life of  210Po. In Figure 6 the energy spectrum between 3.5 MeV and 7.5 MeV is shown (black markers) together with the best fit model (black histogram). The spectrum is well described assuming the presence of 210Po on the surface of the diodes and also of 226Ra and its short lived daughter nuclei (222Rn, 218Po) on the p+ surface and in LAr. In order to describe the data, different layer thicknesses of the p+ surface were taken into account (from 300 to 600 nm). In the other panel the ratio of data and model are shown; the colored bands give the smallest interval probability for the model expectation.(a) shows the best fit model (black histogram) and the observed spectrum (black dots) for theGOLD-coax data set. The other curves represent the individual components of the model. (b) shows the data over model ratio (empty points) and the smallest intervals containing 68% (green), 95% (yellow), and 99.9% (red) probability for the model expectation. From [28].
(a)
(b)The best fit model and the single background components together with the observed data spectrum from 570 keV to 1650 keV and from 1650 keV to 3750 keV is shown in Figure7. The best fit model around the Qββ for the GOLD-coax data is shown in Figure 8. The spectral shape of the model is flat around Qββ, and no peaks are predicted in the blinded regions. The predicted BI around Qββ is 1.85-0.09+0.08×10-2 cts/(keV·kg·yr). The main background contributions come from 214Bi and 228Th in the detector assembly, 42K homogeneously distributed in LAr and finally from α emitters. The predicted BI nicely agrees with the same quantity derived from the data interpolation in the energy intervals 1930–2019 keV, 2059–2099 keV, 2109–2114 keV, and 2124–2190 keV for a total width of 200 keV: 1.75-0.24+0.26×10-2 cts/(keV·kg·yr). This BI evaluation window excludes the central 40 keV window around Qββ and the regions within ±5 keV of the single escape peak from 208Tl at 2104 keV and the 214Bi γ line at 2119 keV. The model discussed here gives a satisfactory description of the spectrum without any medium distance and distant contaminations. It is called minimum model. It is also possible to build a model with a fair description of the data leaving the possibility to have contamination sources at medium and long distances. The main difference between the two models is the number of events deposited on the p+ surface of the detectors. This last model is called maximum model (see Figure 8(b)). The predicted BI of the maximum model is 2.19-0.12+0.19×10-2 cts/(keV·kg·yr), not very far from the minimum model estimation. To conclude we have to say that all contaminations expected from material screening are seen in the background spectra and are taken into account in the models.(a) shows the background decomposition (black histogram) and the observed spectrum (black dots) using the best fit minimum model for theGOLD-coax data set in the energy range from 570 keV to 1650 keV. The lower panel shows the data over model ratio (empty points) and the smallest intervals containing 68% (green), 95% (yellow), and 99.9% (red) probability for the model expectation. (b) shows the same for the energy range from 1650 keV to 3750 keV. From [28].
(a)
(b)Experimental spectrum with minimum (a) model aroundQββ for the GOLD-coax data set. (a) shows the individual contributions of the considered background sources (colored curves) and the model prediction (black curve). The events colored in gray were used in the analysis, while the light gray shaded (unblinded data, UB data) ones have not been used in the analysis. The lower panel shows the best fit model fitted with a constant. In the fit, the peak areas predicted by the model and the 40 keV blinding window are not considered. (b) shows the same experimental spectrum compared with maximum model around Qββ for the GOLD-coax data set. From [28].
(a)
(b)As mentioned, the 40 keV blinded region was partially unblinded leaving a central 10 keV for semicoaxial detectors (8 keV for BEGe detectors) window still blind. In total 13 events were observed in the unblinded 30 keV window of theGOLD-coax data set. The predictions in this window were 8.6 events for the first model and 10.3 for the second one. The agreement between predictions and observed number of events in the unblinded region is rather good.


## 3.3. Pulse Shape Discrimination Analysis

Signal events have a different topology with respect to a large part of the background events. Due to the limited range of the electrons in germanium (a few mm), the two0νββ electrons release their energy in a well-localized space area inside the detectors. This type of events is SSE. The background in the region of interest is largely due to γs. The latter often interact more than once in the detector at points separated by several centimeters. This type of events is MSE. This different topology is usually registered in the rising part of the recorded signal and the distinction can be facilitated by the particular electric field inside the detector. The procedure of selecting SSE from MSE is called PSD analysis. In Gerda, two different PSD methods were used: one optimized for the BEGe detectors and the other for the semicoaxial diodes.In the case of the BEGe we consider two measured quantities: the energyE of the event (proportional to the maximum of the charge pulse) and then the maximum (A) of the current pulse. The current is measured differentiating the charge pulse. Then the ratio A/E is built and used as a PSD variable [53, 54].The physical justification of such a variable is easy to understand looking to Figure2. The weighting potential sharply rises in the small region around the p+ contact; for that reason, in a single interaction, mainly holes contribute to the induced signal on the readout electrode. Single interactions in different places of the detectors produce charge pulses which differ only from the collection time and the total released energy. If the energy release happens in different places of the BEGe (as for a γ interaction) the output pulse will be the convolution of all the different energy deposition and contain this information in the shape of its rising edge.An application of this simple idea is shown in Figure9. In Figure 9(a) a charge pulse trace for a SSE event is shown with its current pulse superimposed. For a SSE in the bulk detector an almost Gaussian distribution of A/E is expected with a width dominated by the noise of the readout electronics. The situation for a MSE event is depicted in Figure 9(b): for the same total energy E, the maximum current amplitude will be smaller due to the various energy depositions in different places of the detector and at different times. Examples of p+ electrode and n+ surface events are shown in the bottom right and left plots of Figure 9, respectively.Examples of pulse traces taken from SSE data (a), MSE (b),p+ electrode event (c), and n+ surface event (d). The pulse traces are normalized in order to have the maximum of the charge pulse equal to one, current pulses have equal integrals. From [32].
(a)
(b)
(c)
(d)TheA/E method performance was determined using calibration data. A 228Th calibration spectrum contains a line at 2614.5 keV from 214Tl decays, a double escape peak (DEP) at 1592.5 keV dominated by SSE, while the full energy peak (FEP) at 1620.7 keV or the single escape peak (SEP) at 2103.5 keV are dominated by MSE. (If a γ ray has sufficiently high energy (several MeV), the results of pair production are evident in the electron spectrum. If the two annihilation γs leave the detector, only the electron and positron energies are deposited. The net effect is to add a peak to the spectrum, called double escape peak, located at an energy of ~1.02 MeV below the full energy peak. The full energy peak corresponds to the total energy of the primary γ. If instead only one annihilation γ escapes from the detector another peak is added, called single energy peak, which now appears at an energy of ~0.511 MeV below the full energy peak.) Further checks come from the use of the 2νββ events which are genuine SSE distributed homogeneously in the detector. If one determines the mean value of the A/E distribution using DEP from calibration data, then it is possible to rescale the A/E of any event by that mean value. In this manner, the A/E distribution of all SSE (whatever is their origin) will be centered at 1; MSE and n+ surface events will populate the region below 1 while p+ electrode events the region above 1.AnA/E distribution plotted versus energy is shown in Figure 10. The red lines correspond to A/E< 0.965 (“low A/E cut”) and A/E> 1.07 (“high A/E cut”), respectively. The low A/E cut has the aim to reject MSE and n+ events; its value is chosen to minimize at values below 1% the efficiency loss of the A/E Gaussian function for energy above 1 MeV. The high A/E cut rejects p+ events; its value is twice larger than the low cut due to the much lower number and better separation of p+ electrode events.Figure 10
A
/
E versus energy for the BEGe data set. The accepted region is that inside the two red lines (low cut at A/E = 0.965, high cut at A/E = 1.07). The blinded region is given by the green band. From [32].With the aforementioned cut values, the efficiency of theA/E method for 0νββ events is 0.92±0.02 as given by DEP events from calibration data and cross-checked by the use of 2νββ events. The A/E method rejects about 80% of the background events at Qββ. Figure 11 shows the BEGe data energy spectrum before and after the PSD cuts. With an exposure of 2.4 kg·yr, seven out of 40 events in the 400 keV wide region around Qββ are kept. The BI for BEGe detectors in this interval is reduced from (0.042±0.007) to (0.007-0.002+0.004) cts/(keV·kg·yr).Figure 11
Energy spectrum of the BEGe data set. The gray histogram shows the data before PSD cut and the blue one after PSD cut. The inset shows the regionQββ, with the 8 keV blinded region in green. From [32].For semicoaxial detectors the situation is more complicated. The weighting potential (see Figure2(a)) also peaks at the p+ contact but the gradient is lower and hence a larger part of the volume, with respect to the BEGe, is important for the charge pulse. For an interaction which happens in the bulk of the detector, both electrons and holes contribute. All these complications make the semicoaxial less good in PSD with respect to the BEGe. Simulated current pulse shapes for SSE taken in various positions starting from the outer n+ surface and going towards the bore hole (n+ surface) along a radial line at the midplane of the detector are shown in Figure 12. The pulse shape behaviour is rather complicated so a simple A/E variable cannot efficiently discriminate between SSE and MSE.Figure 12
Simulated current pulse shapes for SSE in a semicoaxial detector taken at various places inside the diode. The places vary from the outern+ surface towards the bore hole (n+ surface) along a radial line at the midplane of the detector. From [32].For the semicoaxial detectors a PSD analysis based on neural network was applied. The selected algorithm called TMlpANN (present inside the TMVA [63] toolkit implemented in Root) is based on multilayer perceptron. Two hidden layers, with 50 neurons each, are used.The rising part of the charge pulse is used for this neural network analysis. The input parameters are the times when the pulses reach 1, 3, 5,…, 99% height. The time, at which 50% of the charge of the pulse have been seen, serves as a reference. Due to the 100 MHz sampling frequency, a linear interpolation is required between two consecutive time bins in order to determine the corresponding time points. For the training calibration data are used. The output of the neural network is a number between 0 for background and 1 for signal like events. The cut values are chosen in order to have detector per detector a DEP survival probability fixed at 90%. All possible deviations from 90% were taken into account (energy dependence, volume effect due to the different distribution of DEP and 0νββ events, etc.) and combined quadratically. The final result for the 0νββ efficiency of the neural network is 0.90-0.09+0.05. About 45% of the events in a 230 keV window around Qββ are classified as background and rejected.The energy spectrum collected by the semicoaxial detectors before and after the neural network PSD selection is shown in Figure13.Figure 13
Energy spectrum of semicoaxial detectors without (empty histogram) and with (black histogram) neural network PSD selection. From [32].


## 3.4. Limit on the Half-Life of the 0νββ Decay Process in 76Ge

The total exposure useful for the 0νββ analysis was of 21.60 kg·yr of enrGe detectors collected from November 9, 2011, to May 21, 2013 (492.3 live days). The collected data were processed following the steps described in Section 2. The deposited energy is reconstructed by a digital filter with semi-Gaussian shaping. Events generated by discharges or due to electromagnetic noise are rejected by a set of quality cuts. The analysis cuts applied to the data were the following.(i)
Only events with an energy deposition in a single detector were accepted (anticoincidence cut). AroundQββ 15% of the background events are rejected, with no loss for 0νββ events.(ii)
Events in the germanium detectors in coincidence within 8μs with a signal from the muon veto are rejected (muon veto cut). This leads to a further rejection of ~7% of events.(iii)
Events which are preceded or followed by another event in the same detector within less than 1 ms are excluded. In this manner possible events coming from the decay chain214Bi-214Po are rejected (anti-“BiPo” cut). Less than 1% of the events around the Qββ are affected by this cut.(iv)
To the remaining events, the PSD cut is applied as explained in the Section3.3.As mentioned in Section 2.3, there was a blinded region around the Qββ in order to prevent from possible analysis bias. This region was open and analyzed only after the background model and all the analysis cuts (especially PSD) were frozen.Figure14 shows the energy spectrum around the region of interest with and without PSD selection. No excess of events were observed over a flat background distribution. Seven events were seen in the range Qββ±5 keV before the PSD cuts, while 5.1 were expected. Only 3 events survived (classified as SSE) after PSD cuts and no event remained in Qββ±σE. To derive the number of signal counts N0ν a profile likelihood fit of the spectrum was performed. The fit function was given by the sum of a constant term for the background and of a Gaussian for the signal events. The profile likelihood ratio was limited to the region T1/20ν>0. The best fit was obtained for N0ν = 0, that is, no excess of signal events above background. The lower limit on the half-life is
(2)T1/20ν>2.1×1025yr@90%C.L.
including systematic uncertainties. This limit corresponds to N0ν< 3.47 events. The median sensitivity was 2.4 ×1025yr, taking into account the number of events after PSD, the efficiency, and the exposure. A Bayesian calculation using a flat prior distribution for 1/T1/20ν from 0 to 10-24/yr gives T1/20ν>1.9×1025 yr @ 90%C.I.(a): Energy spectrum for the sum of allenrGe detectors in the range 2020–2060 keV, without PSD (empty histogram) and with PSD (black histogram). The red dashed curve is the expectation based on the central value of [19]; the blue curve is instead based on the 90% upper limit derived by Gerda, T1/20ν = 2.1 ×1025 yr. (b): Energy spectrum in the range 1880–2240 keV; the vertical dashed lines indicate the interval 1930–2190 keV used for the background estimation. From [33].
(a)
(b)As discussed before, the data collected by Gerda do not show any peak at Qββ and do not support the claim described in [19]. Taking the T1/20ν from [19], 5.8 signal events are expected to be observed in Gerda in an energy interval of ±σE with 2.0 background events after the PSD cut. In the same energy range, no events are observed. The model (H1) with the value of T1/20ν and its associated error as given from [19] gives a worse fit than the background only model (H0): the Bayes factor, that is, the ratio of the posterior probabilities of the two models, is P(H1)/P(H0) = 0.024.The Gerda result is consistent with the negative results from Igex and HdM. A combined profile likelihood fit including all these three negative results gives as best fit N0ν = 0 and a 90% probability limit:
(3)T1/20ν>3.0×1025yr@90%C.L.A Bayesian analysis gives the same limit with a Bayes factor of2×10-4 strongly disfavoring the claim. Figure 15 shows the limits set on 76Ge T1/20ν as determined by Gerda alone and combining Gerda with HdM and Igex and on 136Xe T1/20ν as obtained by KamLAND-Zen and EXO-200 separately and combined. While the Gerda result can be compared directly with the claim of [19], in order to compare the results obtained on 136Xe with the claimed signal, the assumption that the main underlying mechanism mediating 0νββ is the exchange of light Majorana neutrinos has to be made. In this case the ratio of the half-lives of the 0νββ decay in 136Xe and 76Ge is proportional to the square of the nuclear matrix ratio M0ν(76Ge)/M0ν(136Xe), which has to be derived by theoretical calculations. The lines in the shaded band of Figure 15 are the predictions from the nuclear matrix calculations reported in [64]. The spread of the predictions on the nuclear matrix elements comes from various different approximations. It is possible, through the help of a chosen set of nuclear matrix, to make a combination of all null results from 76Ge and 136Xe experiments. Taking, to be conservative, the nuclear matrix element model which gives the lowest M0ν(136Xe)/M0ν(76Ge) ratio, a Bayesian analysis gives a Bayes factor of 0.40 for KamLAND-Zen and 0.23 for EXO-200, to be compared to the Gerda alone result of 0.024. Putting all these experiment together, the Bayes factor becomes 0.0022. It is important to note that other theoretical calculations might lead to even smaller ratios and so weaker exclusions.Figure 15
Limits at 90% C.L. onT1/20ν for 76Ge (Gerda Phase I alone and Gerda Phase I, Igex and HdM combined together [33]) and for 136Xe [21, 22]. The signal claim for 76Ge from [19] is also shown. The lines in the shaded gray band are the predictions for the correlation between the half-lives obtained in 136Xe and in 76Ge using a selection of different nuclear matrix element calculations taken from [64]. From [33].The result of (3) can be translated into the following effective electron neutrino mass mββ< 0.2−0.4 eV having used the phase space factors from [50] and the nuclear matrix elements calculations cited in [64].


## 4. Outlook

As already explained in Section1, the life of the Gerda experiment has been organized in two phases. Phase I was completed in the middle of May 2013 with the results discussed in the previous sections. Phase II has the goal to improve the sensitivity by an order of magnitude, that is, to reach T1/20ν>1.5×1026 yr. For pure Majorana exchange, this higher sensitivity will constrain the effective electron neutrino mass to less than 100 meV; this value depending on the choice of the nuclear matrix elements. This improvement of a factor ten of the sensitivity will be obtained with the following strategy:(i)
a reduction of a factor ten of the BI; that is, in Phase II the goal is to reach a BI of1.0×10-3 cts/(keV·kg·yr);(ii)
adding 30 new enriched BEGe detectors (20.1 kg);(iii)
collecting an exposure of 100 kg·yr.30 new enriched BEGe detectors have been already produced by Canberra Olen and fully tested by the Gerda collaboration. In order to reach the aforementioned, very low BI various actions will be performed. Detector holders, FE electronics cards, cables, and all the foreseen material near the detectors will be accurately selected in order to satisfy the limits imposed by the BI. Active suppression methods such as PSD analysis and the readout of the scintillation light of the liquid argon will be used to further reject the background. The work for the modification of the Gerda detector will start in the fall of 2013 and it is foreseen to be completed early in 2014, after that a commissioning phase will start and the data taking could follow in the fall of 2014.


## 5. Conclusions

In the middle of 2013, the Gerda experiment has completed its Phase I data taking. After having collected an exposure of 21.6 kg·yr, no excess of 0νββ signal events around the Qββ has been observed above a flat background. A lower limit at 90% C.L. has been determined for the half-life of 76Ge: T1/20ν>2.1×1025 yr. This result strongly disfavored the long-standing claim for a 0νββ signal in 76Ge with a half-life of T1/20ν=1.19×1025 yr [19]. The Gerda experiment is now undergoing a major upgrade which will permit to increase the sensitivity by a factor of about 10 (T1/20ν>1.5×1026 yr) and give the possibility to explore further regions of the degenerate Majorana neutrino mass scale.



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