Probing Majorana neutrinos with double-β decay

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Science  27 Sep 2019:
Vol. 365, Issue 6460, pp. 1445-1448
DOI: 10.1126/science.aav8613

Looking for an exotic decay

Neutrinos—elementary fermionic particles with no electrical charge—defy the standard model of particle physics by having a tiny, but nonzero mass. One explanation for their properties is that they are Majorana fermions, which are particles equal to their antiparticles. If neutrinos were Majorana fermions, a process called neutrinoless double-β decay would become possible: an unstable nucleus could decay by turning two of its neutrons into protons with the emission of two electrons but no antineutrinos. The GERDA Collaboration searched for this decay in a particular isotope of germanium. Housed deep underground to reduce the background signal, the experiment did not detect the elusive process but did place improved boundaries on its half-life.

Science, this issue p. 1445


A discovery that neutrinos are Majorana fermions would have profound implications for particle physics and cosmology. The Majorana character of neutrinos would make possible the neutrinoless double-β (0νββ) decay, a matter-creating process without the balancing emission of antimatter. The GERDA Collaboration searches for the 0νββ decay of 76Ge by operating bare germanium detectors in an active liquid argon shield. With a total exposure of 82.4 kg⋅year, we observe no signal and derive a lower half-life limit of T1/2 > 0.9 × 1026 years (90% C.L.). Our T1/2 sensitivity, assuming no signal, is 1.1 × 1026 years. Combining the latter with those from other 0νββ decay searches yields a sensitivity to the effective Majorana neutrino mass of 0.07 to 0.16 electron volts.

Neutrinos were discovered in 1956 (1), but only at the turn of the millennium was it experimentally proven that the three known neutrino types (flavors) να (α = e, μ, τ) can convert into one another (24). These flavor oscillations are possible only if neutrinos have nonzero mass, which is currently the only established contradiction to the standard model (SM) of particle physics. From tritium β decay experiments (5, 6) and cosmological observations (7), we know that their masses are very small—less than 10−5 of the electron mass. Neutrinos are the only fundamental spin-½ particles (fermions) without electric charge. As a consequence, they might be Majorana fermions (8)—particles identical to their antiparticles. This is a key ingredient of some explanations for why matter is so much more abundant than antimatter in today’s Universe and why neutrinos are so much lighter than the other elementary particles (9).

Majorana neutrinos would lead to nuclear decays that violate lepton number conservation and are therefore forbidden in the SM of particle physics. The so-called neutrinoless double-β (0νββ) decay simultaneously transforms two neutrons inside a nucleus into two protons with an emission of two electrons (Fig. 1). The SM-allowed double-β (2νββ) decay occurs with an emission of two electrons and two antineutrinos. In the 0νββ decay, the two electrons together carry the available decay energy (Qββ) and the resulting monoenergetic signal is the chief experimental signature. A positive detection of this process would imply the first observation of a matter-creating process, without the balancing emission of antimatter, and would establish the Majorana nature of neutrinos (10, 11).

Fig. 1 The concept of active background suppression.

GERDA searches for the 0νββ decay 76Ge → 76Se + 2e, Qββ = 2039 keV, with high-purity Ge detectors enriched in 76Ge that are operated in liquid argon (LAr). (i) Artist’s view of the 0νββ decay of a nucleus by an emission of two electrons (β particles). (ii to iv) Three BEGe detectors, out of the 40 Ge detectors of the GERDA detector array (table S1 and fig. S2), immersed in LAr (bluish cylinder). Events from 0νββ decays would deposit energy Qββ within a few cubic millimeters in a single detector (ii). Events with coincident LAr scintillation light or with multiple interactions in the Ge detector [e.g., from Compton scattering (iii)] are classified as background events. The special detector design with a small readout electrode (fig. S1) enhances drift time differences between different trajectories (black dashed lines) of the charges (holes) generated by the energy depositions. The color code (see fig. S1 for color bar) indicates the electrical signal strength at the respective location. Hence, single- and multi-site events can be identified efficiently by the time profile of their electronic signal. Similarly, α decays at the readout electrode show unique signal characteristics (iv).

We report here on the search for the 0νββ decay 76Ge → 76Se + 2e [Qββ = 2039.061 ± 0.007 keV (12)] with the Germanium Detector Array (GERDA). Unlike previous experiments, GERDA surpasses the sensitivity for a 0νββ decay half-life of T1/2 ~ 1026 years (90% C.L.) and operates in a background-free regime such that the expected number of background events is less than 1 in the energy region of interest at the final exposure (13); here the sensitivity is defined as the median limit expected from many repetitions of the experiment assuming no signal. This achievement, together with the excellent energy resolution of Ge detectors, is crucial in reaching a regime where it would be possible to detect a nonzero signal for the decay.

The GERDA experimental design was guided by the requirement to reduce interfering signals from naturally occurring radioactivity and from cosmic rays to negligible levels. The Ge detectors are made from high-purity (99.9999%) Ge material that is enriched in the 76Ge isotope from the natural abundance of 7.8% to more than 85%. The Ge detectors act as both the source and detector for the 0νββ decay, as illustrated in Fig. 1. In total, GERDA deploys 37 enriched detectors with two different geometries [coaxial and broad-energy Ge (BEGe) detectors; see fig. S1] and with a total mass of 35.6 kg as bare crystals in 63 m3 of liquid argon (LAr). The LAr serves as high-purity shielding against radiation from radioactive decays, and it also provides cooling for the Ge diodes. Moreover, the LAr—as a result of its scintillation property—acts as a veto system to discard events originating from background radiation, which simultaneously deposit energy inside the Ge detectors and the adjacent LAr. The scintillation light is detected by 16 photomultipliers and wavelength-shifting fibers connected to silicon photomultipliers. A water tank encloses the LAr cryostat to further attenuate γ radiation and neutrons from the experimental environment. It also serves as a water Cherenkov detector to identify cosmic-ray muons and their secondary shower particles that could mimic signal events. GERDA is operated deep underground, at the Gran Sasso National Laboratories (LNGS) of INFN in Italy, at a depth of 3500 m water equivalent to reduce the cosmic ray muon flux by six orders of magnitude with respect to Earth’s surface. Detailed descriptions of phases I and II of the experiment can be found in (14, 15).

The signals of the Ge detectors are read out by low radioactive charge–sensitive amplifiers, digitized at a sampling rate of 100 MHz and stored for off-line analysis. Weekly calibrations with 228Th sources are performed to monitor the energy scale and resolution, as well as to define and monitor the analysis cuts. The derived energy resolution, full width at half maximum (FWHM), at Qββ is 3.6 ± 0.1 keV for the coaxial detectors and 3.0 ± 0.1 keV for the BEGe detectors, both corresponding to σ/Qββ < 10−3 (σ = FWHM/2.35).

During physics data taking, all Ge and LAr scintillation channels are read out if one or more Ge diodes detect a signal above a preset trigger threshold. Multiple detector hits are discarded as background events. Similarly, events are classified as background (Fig. 1) if at least one photoelectron is detected in the LAr within ~6 μs around the Ge detector signal—that is, ~5 times the lifetime of the argon excimer observed in GERDA. Random coincidences lead to a loss of potential 0νββ signals of 2.3 ± 0.1%. All events with a muon trigger preceding a Ge trigger by less than 10 μs are rejected with a signal loss of <0.1%. Background events from γ radiation often lead to multiple interactions separated in space but within the same detector. The time structure of the recorded signal allows us to reject this background as well as events occurring at the surface of a detector from α or β decays (Fig. 1, pulse shape discrimination, PSD). More than 95% of the background is rejected by the LAr veto and PSD (Fig. 2), whereas 69% of the 0νββ decay events would be kept for the coaxial detectors and 86% for the BEGe detectors. Relative to (16), the Phase II exposure has been more than doubled while improving both energy resolution (by 10%) and background rate (by ~80%) in the coaxial detectors and maintaining the excellent energy resolution of the BEGe detectors throughout the run; the result is a doubling of the sensitivity to more than 1026 years.

Fig. 2 GERDA Phase II energy spectra (53.9 kg⋅year).

Enriched coaxial and BEGe data are displayed in a combined spectrum after indicated cuts. Main contributions to the spectra are labeled. The insets display the analysis window for coaxial and BEGe detectors separately, including the background rates (solid blue lines). No event reconstructs within Qββ ± 2σ. The dashed blue curves depict the 90% C.L. limit for a 0νββ signal of T1/20ν=0.9×1026years derived from the likelihood analysis of all GERDA datasets.

Since the outset, GERDA has adopted a rigorous blind analysis strategy to ensure an unbiased search for 0νββ decays. Events with a reconstructed energy of Qββ ± 25 keV are blinded (i.e., removed from the data stream) until the data selection is fixed. Figure 2 displays the energy spectra corresponding to 53.9 kg⋅year Phase II exposure before and after analysis cuts, including a PSD method for coaxial detectors that was not used in prior work (15). At low energies, the spectrum after analysis cuts is dominated by 2νββ decays. The insets in Fig. 2 display separately the event distribution of the coaxial detector and BEGe detector datasets in the analysis window 1930 to 2190 keV. After unblinding, only three events in the coaxial dataset and four events in the BEGe dataset remain in the analysis window (17). GERDA thus reaches an unprecedented low background rate of 5.72.6+4.1×104 counts/(keV⋅kg⋅year) for the coaxial detectors and 5.62.4+3.4×104 counts/(keV⋅kg⋅year) for the BEGe detectors.

An unbinned maximum likelihood fit is carried out simultaneously in the different datasets (see table S3), including those from GERDA Phase I (18). In total, 82.4 kg⋅year have been scrutinized for a 0νββ signal so far. The fit function (13) comprises flat distributions for the background, independent for each dataset, and Gaussian distributions for a possible 0νββ signal: The mean is Qββ, the resolutions are taken from calibration data individually for each set, and the normalizations are calculated from the target half-life T1/2. A null signal maximizes the likelihood. Confidence intervals are evaluated in both the frequentist and Bayesian frameworks (15). The frequentist analysis is based on the profile likelihood method, and systematic uncertainties are included as nuisance parameters with Gaussian pull terms. The derived limit of T1/2 > 0.9 × 1026 years (90% C.L.) is compatible with the sensitivity (assuming no signal) of 1.1 × 1026 years; this is an improvement over previous experiments, which had sensitivities of less than 1026 years. The weaker limit is a consequence of an event in the signal region at 2042.1 keV, 2.4 standard deviations (σ) away from Qββ. The statistical analysis attributes it to background. Statistical analysis including Bayesian inference is detailed in (15).

Table 1 compares our results with those of other 0νββ decay searches. The T1/2 sensitivities of other experiments are at most half of ours despite sometimes higher exposures; this is caused by GERDA’s lower background and superior energy resolution (15). Several physical processes beyond the SM can produce 0νββ decay. Here, we focus on the paradigm of the mixing of three light Majorana neutrinos. In this context, the half-life can be converted into a 0νββ decay strength that has the dimension of mass, denoted the effective Majorana mass (19), mββ=|i=13Uei2mi|(1)Nuclear structure details enter the decay rate, and uncertainties in the nuclear structure calculations result in a spread of mββ values for a given T1/2 by typically a factor of 2 to 3 (20). Some reported half-life limits L deviate by almost a factor of 2 from the associated sensitivity S, indicating significant underfluctuation (CUORE, KamLAND-Zen) or upward fluctuation (EXO-200). To overcome this possible behavior of frequentist limits, we used the sensitivity to extract the constraints on mββ shown in Table 1. For GERDA, the median limit is mββ < 0.1 to 0.23 eV. Combining it with the sensitivities of the other searches (15), the bound tightens to mββ < 0.07 to 0.16 eV (90% C.L.), very similar to the bound deduced by KamLAND-Zen from their T1/2 limit (21).

Table 1 Comparison of present and prior experiments.

Lower half-life limits L(T1/2) and sensitivities S(T1/2), both at 90% C.L., reported by recent 0νββ decay searches with indicated deployed isotope masses Mi and FWHM energy resolutions. Sensitivities S(T1/2) have been converted into upper limits of effective Majorana masses mββ using the nuclear matrix elements quoted in (20).

View this table:

Figure 3 shows the dependence of the effective Majorana mass mββ as a function of the lightest neutrino mass mlight = min(mi), the cosmological observable of the sum of neutrino masses, Σ = ∑imi, and the effective neutrino mass, mβ=i|Uei2|mi2(2)—that is, the mass observable in single beta decays. The allowed parameter space is classified according to the ordering of the neutrino mass eigenstates as normal (Δm312>0) or inverted (Δm312<0). The overlap region is called quasi-degenerate; here, the mass splittings are small relative to the absolute mass scale. The latest oscillation data prefer normal ordering at the 3σ level (22). Figure 3 shows that our extracted limits of mββ disfavor a large fraction of the parameter space of quasi-degenerate Majorana neutrino masses. The combined limit of mββ = 0.16 eV corresponds to constraints on mlight < 0.15 to 0.44 eV, Σ < 0.46 to 1.3 eV, and mβ < 0.16 to 0.44 eV. Direct measurements of mβ yield a limit of ~2.3 eV (5, 6). In the coming years, the KATRIN tritium decay experiment will increase the sensitivity to ~0.2 eV (23). The sum of the neutrino masses influences the evolution and structure of the Universe. In the framework of the 6 + 1–parameter cosmological SM, the latest Planck data on the anisotropy of the cosmic microwave radiation along with baryonic acoustic oscillation data provide limits as low as Σ < 0.12 eV (95% C.L.) (24). Extended models relax these limits to <0.37 eV for one additional parameter, and to <0.66 eV for five additional parameters (7).

Fig. 3 Constraints of the parameter space for mββ in the scenario of three light Majorana neutrinos.

Constraints are shown, left to right, as function of the lightest neutrino mass mlight, the sum of neutrino masses Σ, and the effective neutrino mass mβ. Contours follow from a scan of the Majorana phases with the central oscillation parameters from NuFIT 4.0 (22). The blue horizontal band shows the upper limits on mββ obtained by GERDA; the gray band shows those from combining sensitivities of all leading experiments in the field (see Table 1). Vertical lines denote Σ = 0.12 eV and Σ = 0.66 eV, a stringent limit from cosmology (24) and an extended model bound (7), as well as mβ = 0.23 eV, the 5-year sensitivity of the KATRIN experiment (23). Hatching denotes the excluded parameter space.

Currently, there are no tensions among the three mass observables. A discovery of 0νββ decay close to the current experimental half-life sensitivity should have counterpart signals in tritium β decay and in cosmology, provided that the paradigm of three light Majorana neutrinos holds. In case of discrepancies with the other mass observables, a 0νββ signal would point to other lepton number–violating processes. Within the framework of three light Majorana neutrinos and the cosmological SM, and in the absence of a 0νββ decay at or close to the current sensitivity, the KATRIN experiment would not observe a signal. Conversely, a positive measurement of mβ > 0.44 eV in KATRIN would point to Dirac neutrinos or to an incomplete understanding of the nuclear physics (20) of 0νββ decay. It also would require extensions to the current minimal cosmological model. Instead, if the cosmological limit on Σ holds, 0νββ decay experiments would have to probe a mass range mββ < 0.05 eV, which requires a half-life sensitivity of 1027 years and above for a 76Ge-based experiment.

The leading performance of GERDA in terms of background suppression, energy resolution, and sensitivity opens the way to LEGEND, a next-generation Ge experiment with sensitivity to half-lives of 1027 years and beyond. A first-phase 200-kg 76Ge experiment, LEGEND-200 (25), is in preparation at LNGS.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S12

Tables S1 to S7

References (3159)

References and Notes

  1. See supplementary materials.
  2. Three intervals ±5 keV wide at 2104 keV and 2119 keV, the position of known γ lines, and Qββ are excluded for the calculation of the background rate. The limit calculation, however, includes the interval Qββ ± 5 keV.
  3. The unitary 3 × 3 matrix Uαi relates neutrino flavor states να (α = e, μ, τ) and mass eigenstates νi (i = 1, 2, 3). The absolute neutrino masses are still unknown, but two squared neutrino mass differences Δm212 and |Δm312|, (Δmij2=mi2mj2), are known with increasing precision from neutrino oscillation experiments (22).
Acknowledgments: The GERDA Collaboration thanks the directors and the staff of the LNGS for their continuous strong support of the GERDA experiment. Funding: The GERDA experiment is supported financially by the German Federal Ministry for Education and Research (BMBF), the German Research Foundation (DFG) via the Excellence Cluster Universe and the SFB1258, the Italian Istituto Nazionale di Fisica Nucleare (INFN), the Max Planck Society (MPG), the Polish National Science Center (NCN) under grant UMO-2016/21/B/ST2/01094, the Foundation for Polish Science (TEAM/2016-2/2017), the Russian Foundation for Basic Research (RFBR), and the Swiss National Science Foundation (SNF). The institutions also acknowledge internal financial support. This project has received funding or support from the European Union’s Horizon 2020 research and innovation program under Marie Sklodowska-Curie grant agreements 690575 and 674896, respectively. Author contributions: All authors contributed to the publication, being differently involved in the design and construction of the detector system, in its operation, and in the acquisition and analysis of data. All authors approved the final version of the manuscript. In line with collaboration policy, the authors are listed alphabetically. Competing interests: The authors declare no competing financial interests. Data and materials availability: All data generated during this analysis and shown in Fig. 2, Fig. 3, and figs. S3 to S12 are available as png, pdf, and root/txt files from the GERDA repository (26) at Zenodo. For further information, contact the GERDA Collaboration (
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