The GERDA experiment: results and perspectives

The Germanium Detector Array, GERDA, at Laboratori Nazionali del Gran Sasso (Italy), is designed to search for Majorana neutrinos via neutrinoless double beta (0νββ) decay of 76Ge. GERDA completed the Phase I in 2013, after an exposure of 21.6 kg·yr and with a background of about 0.01 cts/(keVkgyr): no signal was found and a limit on the half-life of T0ν1/2 > 2.1 · 1025 yr (90% C.L.) was established. The previous claim of 0νββ observation for 76Ge is strongly disfavoured in a model independent way. The commission for GERDA Phase II is currently ongoing and about 20 kg of additional enriched Ge diodes will be deployed. Pulse- shape analysis, together with the liquid argon instrumentation will allow to reach a background level one order of magnitude lower than in Phase I. In this paper the measurement of the half-life of 0νββ decay from GERDA Phase I and the expected sensitivity for Phase II are discussed.


Introduction
The observation of neutrinoless double beta decay (0νββ) probes fundamental questions about lepton number violation and neutrino properties, indeed it would give direct information on the possible "Majorana" nature of the neutrino and could determine the absolute neutrino mass complementary to other techniques. 0νββ decay could be observed experimentally as a narrow peak at the end-point of the 2νββ decay energy spectrum, corresponding to the Q-value (Q ββ ) of the decay, given by the sum energy of the two emitted electrons. The GERDA experiment [1,2,3] searches for neutrinoless double beta decay of 76 Ge, in which 76 Ge (Z=32) would decay into 76 Se (Z=34) and two electrons. GERDA detectors are germanium semiconductors with an enrichment fraction in 76 Ge of about 86%. The crystals act as both the decay source and a 4π detector and their very good energy resolution translate in a narrow 0νββ peak at Q ββ =2039 keV.

The GERDA experiment
The GERDA experimental setup consists of an array of bare enr Ge (Ge detectors enriched in 76 Ge) semiconductors, placed in strings into a cryostat filled with liquid argon (LAr) and surrounded by an additional shield of ultra-pure water. Liquid argon is the cooling medium for the enr Ge detectors and also acts as shield against external gamma radiation from the cryostat walls. The water buffer provides the Cherenkov medium for the muon veto, attenuates the flux of the external γ radiation and absorbs neutrons. Further details about the GERDA experimental setup are reported in ref. [3]. Data acquisition of GERDA Phase I started in November, 2011 with nine p-type enr Ge semi-coaxial (HPGe) detectors (from the previous HdM and IGEX experiments) with a total mass of about 20.7 kg (17.7 kg enriched and 3 kg not enriched). Five Broad Energy GErmanium diodes 2 (BEGes), were deployed on July 2012, with total mass of about 3.6 kg. The energy scale is determined by calibrating the detectors with 228 Th sources on a weekly basis. The exposure-weighted average energy resolution (FWHM), extrapolated at Q ββ , is (4.8±0.2) keV for semi-coaxial detectors and (3.2±0.2) keV for BEGes. Events in the region of interest (in the interval Q ββ ±20 keV) were kept "blinded", i.e. not processed, until the calibration was finalized and all the selection cuts and analyses were fixed. The experimental energy spectra for the enriched and natural detectors are shown in fig. 1. The green boxes indicate the blinded window at Q ββ ±20 keV. Visible gamma peaks are from 40 K and 42 K decays and from the decay chains of 226 Ra and 232 Th. The low energy part of the spectrum is dominated by the β-decay of 39 Ar and events from 2νββ decay populate the range from 600 to 1800 keV; the half-life of 2νββ decay for 76 Ge has been measured after collecting an exposure of 5.04 kg·yr (see ref. [5]). Above 4000 keV the background is dominated by α decays of 210 Po and 226 Ra. The energy spectrum from semi-coaxial and BEGe detectors is fitted to a background model in the range between 570 and 7500 keV (for further details see ref. [6]): the background is mainly due to sources close to the detectors or on the detector surface and no peak is expected to appear in the region of interest. In this region, with the exclusion of ±5 keV around the expected position of the single escape peak from 208 Tl (2104 keV) and of the γ line from 214 Bi (2119 keV), the interpolated value for the background index (BI) is BI=1.75 +0.26 −0.24 ×10 −2 cts/(keV·kg·yr) for semi-coaxial detectors and BI=3.6 +1.3 −1.0 ×10 −2 cts/(keV·kg·yr) for the BEGe detectors. Detector signals are read out independently by a charge sensitive amplifier; the signal is then digitized by 100 MHz Flash ADCs and physical parameters like energy and risetime of the signal are reconstructed by digital filters [7]. The specific pulse shape of 0νββ events in GERDA detectors is used to discriminate them from background events. In GERDA Phase I two different methods for Pulse Shape Discrimination (PSD) have been developed, according to the different characteristics of the pulses and electric field distributions of semi-coaxial and BEGe detectors [8]. For a review of the GERDA experiment see also ref. [9].   count. The best fit value is N 0⌫ = 0, namely no excess of signal events above the background. The limit on the half-life is including the systematic uncertainty. The limit on the half-life corresponds to N 0⌫ < 3.5 counts. The systematic uncertainties weaken the limit by about 1.5 %. Given the background levels and the e ciencies of Table I, the median sensitivity for the 90 % C.L. limit is 2.4 · 10 25 yr. A Bayesian calculation [24] was also performed with the same fit described above. A flat prior distribution is taken for 1/T 0⌫ 1/2 between 0 and 10 24 yr 1 . The toolkit BAT [25] is used to perform the combined analysis on the data sets and to extract the posterior distribution for T 0⌫ 1/2 after marginalization over all nuisance parameters. The best fit is again N 0⌫ = 0 and the 90 % credible interval is T 0⌫ 1/2 > 1.9 · 10 25 yr (with folded systematic uncertainties). The corresponding median sensitivity is T 0⌫ 1/2 > 2.0 · 10 25 yr.

DISCUSSION
The Gerda data show no indication of a peak at Q , i.e. the claim for the observation of 0⌫ decay in 76 Ge is not supported. Taking T 0⌫ 1/2 from Ref. [11], 5.9 ± 1.4 decays are expected (see note [26]) in E = ±2 E and 2.0 ± 0.3 background events after the PSD cuts, as shown in Fig. 1. This can be compared with three events de- Figure 2. Energy spectrum from all enr Ge detectors before (filled) and after (open) the PSD selection.
In the upper panel the expectation based on the central value of the half-life estimated by ref. [12] is also shown (red), together with the 90% C.L. limit estimated by GERDA Phase I (blue). In the lower panel the energy window used for the backgrund interpolation is indicated. Plot from ref. [4].

Results on 0νββ decay of 76 Ge
After the collection of an exposure of 21.6 kg·yr from GERDA Phase I, a limit on the half-life of 0νββ decay in 76 Ge was established [4]. Phase I data were divided into three different sets: data from the BEGe detectors ("BEGe" set), data from semi-coaxial detectors in the time period when the BEGe detectors were deployed ("silver" set) and remaining data from semi-coaxial detectors ("golden" set). "Unblinded" data showed a flat background in the region of interest, with seven events observed while 5.1±0.5 were expected from background interpolation. After the PSD was applied, three events from the semi-coaxial detectors and the one from the BEGe detector were classified as background. No event remains in the energy window Q ββ ±σ E and the corresponding BI becomes 10 −2 cts/(keV·kg·yr). The observed spectrum was fitted with a profile likelihood fit; the fitted function contains three constant terms for the background (for the three data sets) and a Gaussian peak, centered at Q ββ and with standard deviation according to the energy resolution. The four corresponding parameters of the function were the three terms for the background and 1/T 0ν 1/2 . The limit on the half-life is T 0ν 1/2 > 2.1 · 10 25 yr (90% C.L.) and the best fit value for the number of 0νββ events is N 0ν =0. The corresponding limit on the number of signal events is N 0ν < 3.5 counts. The median sensitivity for the 90% C.L. limit, given the background levels and the efficiencies, is T 0ν 1/2 > 2.4 · 10 25 yr. The systematic uncertainties due to detector parameters, selection efficiency, energy resolution and energy scale, were folded into the half-life estimation; they weaken the limit by about 1.5%. A Bayesian analysis [10] was also performed (using the BAT toolkit [11]) with the same fit and a flat prior distribution for 1/T 0ν 1/2 between 0 and 10 −24 yr −1 . The corresponding result for the limit is T 0ν 1/2 > 1.9 · 10 25 yr, with a median sensitivity of T 0ν 1/2 > 2.0 · 10 25 yr. The GERDA result does not support the previous claim of 0νββ decay observation in 76 Ge [12]. The Bayes factor, i.e. the ratio between the probability that the observed data D are produced according to the model H 1 (0νββ with half-life T 0ν 1/2 from ref. [12]) and the probability that they are produced according to the model H 0 (only background), is P(D|H 1 )/P(D|H 0 ) = 0.024. In fig. 2 the "unblinded" spectrum is shown, together with the likelihood fit and the expectation based on the claim from ref. [12]. A combined profile likelihood fit, when GERDA data are combined with data from the HdM [13] and IGEX [14] experiments, gives again N 0ν = 0 as best fit and T 0ν 1/2 > 3.0 · 10 25 yr (90% C.L.). Considering this limit, the phase-space factor for the 76 Ge [15] and the nuclear matrix element calculations reported in refs. from [16] to [22] (scaling the different g A and R A parameters according to ref. [23]), the derived upper limits on the effective electron neutrino mass range between 0.2 and 0.4 eV. A Bayesian analysis gives the same limit and a Bayes factor equal to P(D|H 1 )/P(D|H 0 ) = 2·10 −4 .

Phase II upgrades
The main goal of GERDA Phase II is to increase the sensitivity with respect to Phase I, by lowering the background level and increasing the total collected exposure. The background level will be reduced thanks to the implementation of a LAr scintillation veto and the procurement of 30 additional enriched BEGe detectors, to achieve a total mass of about 40 kg. The scintillation veto consists of the detection of the 128 nm scintillation light generated in liquid argon by radioactive background decays or cosmic muons, accompanied with the emission of gamma particles which eventually excite the argon. A curtain made of light-guiding fibers surrounding the detector strings will collect the light, eventually read out by Silicon Photo-Multipliers (SiPMs) on the top of the array. In addition, light will be also directly detected by PMTs coated by wavelength shifter and placed on top and bottom of the detector array. Residual background contamination will be rejected by the Pulse Shape Discrimination, as described in ref. [8]. The expected background index for GERDA Phase II, when the combination of LAr veto and Pulse Shape Discrimination is used, is of the order of 10 −3 cts/(keV·kg·yr). The commissioning of the Phase II upgrade of GERDA is presently ongoing. The sensitivity of GERDA as a function of the total collected exposure is shown in fig. 3. With the increased total mass of enriched germanium an exposure of 100 kg·yr will be reached in about 3 years. The corresponding sensitivity on the half-life of 0νββ decay is T 0ν 1/2 1.4 · 10 26 yr.