Results on neutrinoless double beta decay of 76Ge from GERDA Phase I

The Germanium Detector Array (GERDA) experiment is searching for the neutrinoless double beta (0νββ) decay of 76Ge by operating bare germanium diodes in liquid argon. GERDA is located at the Gran Sasso National Laboratory (LNGS) in Italy. During Phase I, a total exposure of 21.6 kg yrand a background index of 0.01 cts/(keVkg yr) were reached. No signal was observed and a lower limit of T0ν1/2 > 2.1 · 1025 yr(90% C.L.) is derived for the half life of the 0νββ decay of 76Ge.


Introduction
Neutrino accompanied double beta (2νββ) decay is a second order weak process predicted by the Standard Model of particle physics. This decay has been observed for several isotopes and the experimentally determined half-lives lie in the range of 10 19 to 10 24 years [1,2].
Neutrinoless double beta (0νββ) decay is a process that violates lepton number conservation by two units, and its observation would indicate physics beyond the Standard Model [3,4,5]. Furthermore, it would prove that neutrinos have a Majorana mass component. This process has not been observed so far and the half-life limits set on 0νββ decay for 76 Ge lie in the range of (1.6 − 1.9) × 10 25 years [6,7,8]. In 2004, part of the HdM collaboration claimed an observation of 0νββ decay [9], reporting a half-life of T 0ν 1/2 = (1.19 +0.37 −0.23 ) × 10 25 years. The experimental signature of 0νββ decay is a monoenergetic peak of the sum electron kinetic energy at the Qvalue of the decay, Q ββ = 2039 keV, above the continuous energy spectrum of the 2νββ decay.
The GERDA experiment is introduced in section 2. The results from GERDA Phase I are summarised in the following sections. The measurement of the half-life of 2νββ decay, the modelling of the background energy spectrum and the background discrimination methods are discussed in sections 3, 4 and 5, respectively. The result on the search of 0νββ decay is presented in section 6. The status of the ongoing transition to Phase II is presented in section 7.

The GERDA experiment
The GERDA experiment searches for the 0νββ decay of 76 Ge [10]. The experiment is located at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy. GERDA operates bare germanium diodes inside liquid argon (LAr) which serves as a coolant and as shielding. The array of germanium detectors is suspended inside a stainless steel cryostat filled with 64 m 3 of LAr. The cryostat is located inside a water tank that contains 590 m 3 of high purity water, moderating  (1), the LAr cryostat (2), the internal copper shield (3), the water tank (4), the clean room (5) and the lock system (6) are indicated. Taken from [10]. ambient neutrons and gamma radiation. The water tank is instrumented with 66 photomultiplier tubes (PMTs) and operates as aČerenkov muon veto reducing the cosmic induced background index to less than 10 −3 cts/(keV kg yr) [11]. The rate of events coincident between the germanium detectors and the GERDA muon veto system is (9.3 ± 0.4) × 10 −5 /s [12]. The detector strings are lowered into the cryostat from the clean room, located above the GERDA tank. An artist's view of the experimental setup is shown in figure 1.
Two types of detectors were used during GERDA Phase I. Eight p-type high purity germanium (HPGe) semi-coaxial detectors from the HdM [6] and IGEX [7] experiments were refurbished and used as the main GERDA Phase I detectors. They have an n+ conductive lithium layer and a boron implanted p+ contact, separated by a groove. They are enriched to ∼86% in 76 Ge and have a total mass of 17 kg. Additionally, 30 enriched p-type broad energy germanium (BEGe) detectors were produced and will be used in Phase II of the experiment [13,14]. Five of them were already deployed in GERDA during Phase I. Their total mass is 3.6 kg.
The data collected during Phase I, from November 2011 until May 2013, correspond to 492 days and a total exposure of 21.6 kg yr. The average duty cycle is 88%. The data were divided into three datasets. The golden coaxial dataset with an exposure of 17.9 kg yr contains all data taken with the enriched semi-coaxial detectors with the exception of a short period of approximately 30 days. This was due to increased activity after the insertion of the five BEGe detectors. This dataset, referred to as silver coaxial dataset, corresponds to 1.3 kg yr. The BEGe dataset consists of data taken with the BEGe detectors and has an exposure of 2.4 kg yr.
Regular calibration runs were taken on a weekly basis, using a 228 Th source, in order to determine the energy scale of the individual detectors. The energy shift between successive calibrations is less than 1 keV at Q ββ . This is due to gain drifts of the readout chain [10]. The mean exposure-weighted energy resolutions for the GERDA detectors are 4.8 ± 0.2 keV for the semi-coaxial detectors and 3.2 ± 0.2 keV for the BEGe detectors.

Measurement of the 2νββ decay half-life
The measurement of the half-life of the neutrino accompanied double beta decay of 76 Ge by GERDA corresponds to an exposure of 5.04 kg yr [15]. The observed energy spectrum between 600 and 1800 keV is dominated by the neutrino accompanied double beta decay of 76 Ge. The signal-to-background ratio in this energy range is on average 4:1. A global model was fitted to the observed energy spectra above the cosmogenic 39 Ar background, which dominates the energy spectrum below 565 keV. The model contains the 2νββ decay of 76 Ge and three independent background contributions from 42 K, uniformly distributed in liquid argon, as well as 214 Bi and  Upper and middle panels: experimental data (markers) and the best fit model (black histogram) in linear and logarithmic scale. Individual components are shown with coloured histograms. The shaded band covers the 68% probability range for the data, calculated from the expected counts of the best fit model. Lower panel: ratio between the experimental data and the best fit model, shown with the smallest intervals containing 68%, 95% and 99.9% probability for the ratio assuming the best fit parameters. Taken from [15].   [15]. 40 K from close sources. The presence of these sources is established by the observation of their characteristic gamma lines. Possible contributions from other background components were included in the systematic uncertainties. The spectral fit has 32 free parameters, the 2νββ half-life, the detector masses and enrichment fractions and the background contributions. The experimental energy spectrum together with the best fit model and the individual spectral contributions are shown in figure 2. The ratio between experimental data and the prediction of the best fit model is shown in the lower panel. The green, yellow and red regions are the smallest intervals containing 68%, 95% and 99.9% probability for the ratio, respectively, assuming the best fit parameters.
After marginalising over all nuisance parameters, the best half-life estimate is T 2ν 1/2 = (1.84 +0.14 −0.10 )×10 21 yr. This result is shown in figure 3, together with previous publications and two weighted averages. The value reported by GERDA is longer than the previous measurements. There is a tendency towards higher values for more recent measurements. This is probably related to the improved signal-to-background ratio, which reduces the relevance of background

Background modelling for GERDA Phase I
A good understanding of the background is important in order to extract a possible 0νββ signal or to obtain a limit on the half-life of the process in case no signal events are observed. A background model was developed, prior to the 0νββ analysis, to describe the observed energy spectrum using data corresponding to an exposure of 18.5 kg yr [12]. The model contains several contributions that are either expected after material screening or established through the observation of characteristic structures in the energy spectrum. The energy spectra for the enriched semi-coaxial detectors, the BEGe detectors and one non-enriched detector are shown in figure 4. The low energy part, up to 565 keV, is dominated by the beta decay of cosmogenic 39 Ar. Between 600 and 1500 keV the spectra of the enriched detectors are dominated by the 2νββ decay of 76 Ge. Gamma lines from the decays of 40 K and 42 K can be identified in all spectra. Gamma lines from 60 Co, 208 Tl, 214 Bi, 214 Pb and 228 Ac are visible in the spectra of the enriched semi-coaxial detectors. A peak-like structure around 5.3 MeV in the spectrum of the enriched semi-coaxial detectors can be attributed to the decay of 210 Po on the detector p+ surfaces. Further peak-like structures at energies of 4.7, 5.4 and 5.9 MeV can be attributed to the alpha decays of 226 Ra, 222 Rn and 218 Po on the detector p+ surface, respectively. A 40 keV window around Q ββ was kept blinded during the analysis.
The background model was obtained by fitting the simulated spectra of different contributions to the measured energy spectrum using a Bayesian approach. The high energy part of the spectrum between 3.5 and 7.5 MeV, above the Q-value of 42 K, was analysed first, providing a best fit for the alpha induced spectrum. This result was used along with other contributions to establish a model covering the energy range from 570 to 7500 keV. The main contributions at Q ββ come from 42 K (uniform in LAr), 60 Co (in germanium and on the detector assembly), 214 Bi (on the detector assembly and p+ surface), 208 Tl (on the detector assembly), as well as alpha events from surface contamination and 222 Rn in LAr. Figure 5 shows the best fit model in black, together with the observed counts and the individual background contributions considered in the high energy alpha fit, for the golden coaxial dataset. Figure 6 shows the best fit model in black, together with the observed counts and the individual background contributions considered in the global fit, for the golden coaxial dataset. In the lower panels, the ratios of data and model are shown together with the smallest intervals of 68%, 95% and 99.9% probability for the model expectation.  Figure 5. Experimental data (markers) and the best alpha model fit (black line) for the golden coaxial dataset. The lower panel shows the ratio between data and model, as well as the 68%, 95% and 99.9% probabilities for the ratios assuming the best fit parameters. Taken from [12].  Figure 6. Experimental data (markers) and the best fit minimum model (black line) for the golden coaxial dataset. Individual background contributions are shown separately. In the legend, "inGe", "H" and "P", refer to contributions from the germanium detectors, the holders and the p+ surface, respectively. The lower panels show the ratio between data and model, as well as the 68%, 95% and 99.9% probabilities for the ratios assuming the best fit parameters. Taken from [12].
Two models were constructed for the background description, a minimal model consisting of well-motivated contributions (see figure 6) and a maximum model consisting of various additional contributions. They are shown in figure 7 together with the experimentally observed counts for the golden coaxial dataset. Both models show a good agreement with the data and their p-values do not favour one model over the other.
A partial unblinding was performed in order to confirm the validity of the background model. A 10 keV window for the semi-coaxial detectors and an 8 keV window for the BEGe detectors around Q ββ remained blinded for the 0νββ analysis. The partially unblinded data are shown in light grey in figure 7. The agreement of the model with the data after the partial unblinding is satisfactory. It is important to note that the spectrum between 1930 and 2190 keV can be modelled with a flat background, shown in the lower panels of figure 7. The background index at the region of interest is (17.6 − 23.8) × 10 −3 cts/keV kg yr before applying any pulse shape discrimination algorithms.

Pulse shape discrimination analysis
The experimental sensitivity can be improved by analysing the pulse shapes of the detector signals with the aim of rejecting background events. Pulse shape discrimination (PSD) is therefore used to separate single-site (SSE) from multi-site (MSE) events. The signature of   a double beta decay is a SSE, i.e. the energy is deposited in a single location in the detector. On the other hand, MSEs, e.g. from multiple Compton scattering, deposit energy in well separated locations in the detector.
Different PSD techniques were used for the semi-coaxial and the BEGe detectors [16]. This is due to the different geometries and, hence, different electric field distributions of the detectors. The cross sections of a semi-coaxial and a BEGe detector, along with the corresponding weighting potentials, are shown in figure 8. For the semi-coaxial detectors a neural network approach was utilised, where the rising part of the charge pulse was used for the network analysis. For the BEGe detectors a mono-parametric A/E method was implemented, where A corresponds to the maximum of the current pulse and E is the reconstructed energy. For MSEs, the current pulses of the charges from different locations will have different drift times and, hence, more time-separated current pulses. Therefore, for the same total energy, E, the maximum amplitude,  has a 0⌫ acceptance of 90% while it rejects approximately half of the background around Q . The A/E method has an e ciency of 92% and rejects 80% of the background events around Q . On 2⌫ events, the methods have an e ciency of 85% and 91% for the semi-coaxial and BEGe detectors, respectively.

Results on neutrinoless double beta decay
The combined energy spectrum from all enriched germanium detectors around the region of interest after unblinding is shown in figure 7. The filled histogram shows the counts after the PSD selection.
In the lower panel, the energy region used for the background interpolation is shown. After opening the blinded window, no excess of events was found above the expected background. Two analyses were performed to derive the lower limit for the half-life of 0⌫ of 76 Ge. The baseline analysis was a frequentist analysis, where a profile likelihood fit was performed to the datasets using a common half-life. The best fit corresponded to zero counts and an upper limit of 3.5 counts. The derived lower limit for the half-life of 0⌫ is T 0⌫ 1/2 > 2.1 ⇥ 10 25 yr at 90% confidence level, including the systematic uncertainty. A second Bayesian analysis was performed, using a flat prior on the inverse half-life in the 0 10 24 yr 1 range. The best fit was again zero counts corresponding to a lower limit of T 0⌫ 1/2 > 1.9 ⇥ 10 25 yr at 90% credible interval. A combination of the GERDA result with the results from IGEX and HdM experiments gave a lower limit of T 0⌫ 1/2 > 3 ⇥ 10 25 yr at 90% confidence level.  has a 0⌫ acceptance of 90% while it rejects approximately half of the background around Q . The A/E method has an e ciency of 92% and rejects 80% of the background events around Q . On 2⌫ events, the methods have an e ciency of 85% and 91% for the semi-coaxial and BEGe detectors, respectively.

Results on neutrinoless double beta decay
The combined energy spectrum from all enriched germanium detectors around the region of interest after unblinding is shown in figure 7. The filled histogram shows the counts after the PSD selection.
In the lower panel, the energy region used for the background interpolation is shown. After opening the blinded window, no excess of events was found above the expected background. Two analyses were performed to derive the lower limit for the half-life of 0⌫ of 76 Ge. The baseline analysis was a frequentist analysis, where a profile likelihood fit was performed to the datasets using a common half-life. The best fit corresponded to zero counts and an upper limit of 3.5 counts. The derived lower limit for the half-life of 0⌫ is T 0⌫ 1/2 > 2.1 ⇥ 10 25 yr at 90% confidence level, including the systematic uncertainty. A second Bayesian analysis was performed, using a flat prior on the inverse half-life in the 0 10 24 yr 1 range. The best fit was again zero counts corresponding to a lower limit of T 0⌫ 1/2 > 1.9 ⇥ 10 25 yr at 90% credible interval. A combination of the GERDA result with the results from IGEX and HdM experiments gave a lower limit of T 0⌫ 1/2 > 3 ⇥ 10 25 yr at 90% confidence level.   [9] and the blue solid line is the 90% C.L. upper limit derived from the GERDA 0νββ analysis. The lower panel shows the energy region used for the background interpolation. Taken from [17].
A, will be smaller for MSEs. As a proxy of SSEs, events from the double-escape peak (DEP) at 1593 keV from the 2614 keV line of 208 Tl are used. Events in the full energy line of 212 Bi at 1621 keV are mostly MSEs and are used as the background sample. More information on pulse shapes from semi-coaxial and BEGe detectors and about the details of the analysis can be found in [16]. Figure 9 shows the result of the PSD methods applied to data for the semi-coaxial and the BEGe detectors. The events surviving the PSD selection are shown in grey. The neural network method has a 0νββ acceptance of 90% while it rejects approximately half of the background around Q ββ . The A/E method has an efficiency of 92% and rejects 80% of the background events around Q ββ . On 2νββ events, the methods have an efficiency of 85% and 91% for the semi-coaxial and BEGe detectors, respectively.

Results on neutrinoless double beta decay of 76 Ge
The combined energy spectrum from all enriched germanium detectors around the region of interest after unblinding is shown in figure 10, before (open histogram) and after (filled histogram) PSD selection. The energy region used for the background interpolation is shown in the lower panel.
After opening the blinded window, no excess of events was found above the expected background. Two analyses were performed to derive the lower limit for the half-life of 0νββ of 76 Ge. The baseline analysis was a frequentist analysis, where a profile likelihood fit was performed to the datasets using a common half-life. The fit function was the sum of a constant term for the background and a gaussian term for the signal. The best fit corresponded to  Figure 11. Limits (90% C.L.) on T 0ν 1/2 of 76 Ge and 136 Xe [20,21] compared to the signal claim for 76 Ge.
The shaded grey bands are the predictions for the correlation of the half-lives for the two isotopes according to different nuclear matrix elements calculations. Taken from [17]. zero counts and an upper limit of 3.5 counts. The derived lower limit for the half-life of 0νββ is T 0ν 1/2 > 2.1 × 10 25 yr at 90% confidence level, including the systematic uncertainty. The corresponding median sensitivity for the 90% C.L. limit is T 0ν 1/2 > 2.4 × 10 25 yr. A second, Bayesian analysis was performed, using a flat prior on the inverse half-life in the 0 − 10 −24 yr −1 range. The best fit was again zero counts corresponding to a lower limit of T 0ν 1/2 > 1.9 × 10 25 yr at 90% credible interval. The median sensitivity is T 0ν 1/2 > 2.0 × 10 25 yr. The profile likelihood fit was also extended to include the energy spectra from IGEX and HdM experiments, giving a lower limit of T 0ν 1/2 > 3.0 × 10 25 yr at 90% confidence level. Constant background for all five datasets and gaussian peaks with a common half-life were assumed.
In order to compare the GERDA result with the signal claim, a hypothesis test was performed. The expected number of counts for the background only hypothesis, H 0 , is 2 ± 0.3 in the ±σ window around Q ββ . As an alternative hypothesis, H 1 , the claimed signal corresponding to a half-life of T 0ν 1/2 = 1.19 × 10 25 yr plus a background was considered, corresponding to 5.9 ± 1.4 expected counts. In figure 10, the exposure corrected expectation according to the signal claim is shown in dotted red line together with the lower limit derived from the GERDA analysis in blue. The number of observed counts is 3. Assuming the model H 1 , the probability to obtain zero counts as the best fit from the profile likelihood analysis is 0.01. Also the Bayes factor, i.e. the ratio of the probabilities of the two models P (H 1 )/P (H 0 ), computed with the GERDA result alone as well as with the combined result is 0.024 and 2 × 10 −4 , respectively, therefore the claim is strongly disfavoured. This comparison is restricted to the result of [9] and not [18], due to inconsistencies in the latter, pointed out in [19].
A comparison to the recent limits on the half-life of 136 Xe from KamLAND-Zen [20] and EXO-200 [21] is possible, assuming that the leading mechanism is the exchange of a light Majorana neutrino. The experimental results, the claimed signal and the different NME calculations are shown in figure 11.
7. GERDA Phase II GERDA Phase II aims to improve the half-life sensitivity by another order of magnitude. The sensitivity as a function of the exposure for different background levels is shown in figure 12. An  Figure 12. Sensitivity as a function of the exposure for different background cases. The lines corresponding to the background index of Phase I and Phase II are indicated on the figure. Taken from [22]. order of magnitude improvement on the 0νββ half-life sensitivity is expected in approximately 5 years.
The size of the detector array is increased to 7 strings. The detectors are assembled in a dry nitrogen atmosphere. The new cable chain is made of selected stainless steel of low radioactivity. The Phase II cables exhibit more than a factor of 10 lower 228 Th and 226 Ra activities compared to Phase I cables.
The liquid argon will be instrumented with a scintillation background veto system. PMT arrays are installed above and below the detector array. Silicon photomultipliers coupled to wavelength shifting fibres surround the detector array. They will provide increased background reduction capability by detecting scintillation light in liquid argon. Pulse shape analysis in combination with the liquid argon veto provide a suppression factor of 5.2 × 10 3 at Q ββ for a close 228 Th source.
For Phase II, 30 new BEGe detectors were produced. A significant amount of copper and PTFE, for the detector modules, has been replaced by intrinsically radio pure silicon. The energy resolution (FWHM) of the detectors was determined with a 60 Co source to be less than 1.9 keV at 1.3 MeV in vacuum. In addition, the A/E pulse shape discrimination, described in section 5, is a robust, simple and well-understood method of background rejection that was successfully implemented during Phase I. Finally, careful handling of the detectors during manufacturing and transportation insures a very low background contribution from 60 Co and 68 Ge due to cosmogenic activation.

Conclusions
Phase I of the GERDA experiment was completed successfully and the design goals were reached. A total exposure of 21.6 kg yr was accumulated. The background index at Q ββ after pulse shape analysis was 0.01 cts/keV kg yr. A blinded analysis looking for the 0νββ decay of 76 Ge was performed. No signal was observed and the most competitive limit on the half-life of this process for 76 Ge was derived, strongly disfavouring the long standing claim of 0νββ signal observation.
The transition to GERDA Phase II is ongoing. An additional 20 kg of detector mass will be deployed. The new custom-made BEGe detectors have an excellent pulse shape discrimination capability and a subset of them was tested successfully during Phase I. A liquid argon instrumentation surrounding the detector array will be utilised for further background reduction. The background target of GERDA Phase II is 10 −3 cts/keV kg yr, which will allow