The Latest Neutrinoless Double-β Decay Experiment Results
The world's new most probing search ever for neutrinoless double-β decay (a decay with violates conservation of lepton number and does not occur in the Standard Model if neutrinos are not Majorana neutrinos) at GERDA has yet to see any sign of this decay.
GERDA established a minimum Ge76 half-life for these decays of 1.8 × 10^26 yr, and a maximum sum of the three neutrino masses in a three Majorana mass neutrino model of 180 meV at a 90% confidence interval (with a best fit limit of about 130 meV).
The latest limits from GERDA are strong that those any other experiment at the moment, although Xenon and Tellurium based neutrinoless double-β decay experiments strongly corroborate the new GERDA result and make it more robust. Combining the limits slightly improves the limitation, but only slightly in excess of the best result.
The current result implies that there is less than one neutrinoless double-β decay per 2.3 kg of Ge76 per year, if it happens as all.
How do these results compare to other things we know?
The age of the Universe is approximately 13.8 billion years (i.e. 10^9 years) ± about 1.5%.
The sum of the three neutrino masses is more than about 50-60 meV in a normal ordering and more than about 100-140 meV in an inverse ordering (based on neutrino oscillation data), with cosmology data favoring three generations of neutrinos that have masses under about 1-10 eV, and a sum of the three neutrino masses of under about 130-180 meV at 90%-95% confidence level, with a best fit value that is under the 100 meV that is the minimum sum of the three neutrino masses in an inverse ordering. The cosmology bound on absolute neutrino masses is indifferent to their mass ordering.
There is a model dependent linear relationship between half life and the sum of the three neutrino masses if the masses are Majorana.
Therefore, Majorana neutrino hypothesis is ruled out (in a model dependent way with conventional assumptions) in both a normal ordering of neutrino masses (which is observationally favored) or an inverse ordering of neutrino masses, at a Ge76 half-life of T1/2 > 6 × 10^27 yr (a 67% tightening of the limits) Majorana neutrino masses with an inverse ordering are ruled out at a Ge76 half-life of T1/2 > 1.3 × 10^26 yr (a 28% tightening of the limits).
Several experiments which can resolve the question of the nature of the neutrino mass (subject to widely accepted conventional model assumptions about neutrinoless double-β decay in a Majorana neutrino mass model) are underway.
An answer to the nature of the neutrino mass is probably achievable in the next three to ten years with currently planned experiments.
For what it is worth, my conjecture and prediction (a long standing one) is that neutrinos have a normal mass ordering, that neutrinoless double-β decay does not occur, and that neutrinos do not have Majorana mass.
Of course, if there are three Majorana mass neutrinos with a normal mass ordering (probably the most widely held prediction in the field), the non-detection of neutrinoless double-β decay to date is perfectly consistent with the data as well. But models in which neutrinoless double-β decay occurs more often than with the conventional Majorana neutrino mass models are already ruled out experimentally.
Likewise, my long standing conjecture and prediction proton decay and flavor changing neutral currents at tree level, does not occur, and that neither lepton number nor baryon number are violated outside of sphaleron interactions (which may or may not actually exist).
An experimental test of the existence of extremely high energy small volume sphaleron interactions (which conserve baryon number minus lepton number, but not baryon number and lepton number separately) is at least decades, and at least two generations of particle accelerator experiments, away from an experimental test.
 There would be one neutrinoless double-β decay per 10^10 Ge76 atoms in the entire life of the universe, if it happens at all. One mole of Ge76 has a mass of 75.9214026(18) grams and contains about 6*10^23 atoms (Avogardo's number).
More technical details and citations are below the fold.
The new paper is as follows:
[Submitted on 13 Sep 2020]Final Results of GERDA on the Search for Neutrinoless Double-β Decay
The GERmanium Detector Array (GERDA) experiment searched for the lepton-number-violating neutrinoless double-β (0νββ) decay of 76Ge, whose discovery would have far-reaching implications in cosmology and particle physics. By operating bare germanium diodes, enriched in 76Ge, in an active liquid argon shield, GERDA achieved an unprecedently low background index of 5.2 × 10−4 counts/(keV kg yr) in the signal region and met the design goal to collect an exposure of 100 kg yr in a background-free regime.
When combined with the result of Phase I, no signal is observed after 127.2 kg yr of total exposure. A limit on the half-life of 0νββ decay in 76Ge is set at T1/2 > 1.8 × 10^26 yr at 90% C.L., which coincides with the sensitivity assuming no signal.
From the body text of the new paper.
A stronger limit 2.3×1026 yr (90% C.I.) is obtained assuming a priori equiprobable Majorana neutrino masses mββ (as S ∝ m2 ββ), instead of equiprobable signal strengths. . . . The T1/2 limit can be converted into an upper limit on the effective Majorana neutrino mass under the assumption that the decay is dominated by the exchange of light Majorana neutrinos. Assuming a standard value of gA = 1.27, the phase space factor and the set of nuclear matrix elements, a limit of mββ < 79 − 180 meV at 90% C.L. is obtained, which is comparable to the most stringent constraints from other isotopes.
As of 2018, the minimum sum of the three neutrino masses was about 60 meV in a normal ordering and about 100 meV in an inverted ordering. So the model dependent observational limitation on the Majorana neutrino mass inferred from the non-detection of neutrinoless double-β decay is about a factor three smaller than necessary to rule out the Majorana mass hypothesis for neutrinos (since mββ should be roughly equal to the sum of the three neutrino masses). As a 2019 paper explains:
Current running experiments like KamLAND-Zen, CUORE, CUORE-0, Cuoricino, and GERDA-II are trying to find out the lower bounds on the T 0ν 1/2 of this decay for several nucleus samples. Recent lower bound obtained by the KamLAND-Zen collaboration for sample 136Xe(xenon-136) is, T 0ν 1/2 > 1.07×10^26 yr, GERDA-II collaboration obtained the lower bound for sample 76Ge(germanium-76) is T 0ν 1/2 > 8.0 × 10^25 yr and CUORE, CUORE-0 and Cuoricino experiments collectively obtained the lower bound for sample 130T e(tellurium-130) is T 0ν 1/2 > 1.5 × 10^25 yr.
The (ββ)0ν - decay rate is proportional to the effective Majorana mass |mββ| in the three Majorana neutrino picture. The range of this effective Majorana mass is not very well understood but based on the present neutrino oscillation data, it is bounded from below |mββ|IO > 1.4 × 10^−2 eV in the case of three neutrino mass spectrum with Inverted Ordering. While for the Normal Ordering configuration of the mass spectrum the lower bound is |mββ|NO << 10^−3 eV and it can be extremely small depending on the values of the Dirac, Majorana phases and of the smallest neutrino mass. A condition is established using the recent global data on the neutrino oscillation parameters with NO(Normal Ordering) spectrum, which suggest |mββ| must exceed 10^−3 (5×10^−3 ) eV. Neutrino double beta decay experiments are trying to cover the range of |mββ| from the top and the current reachable upper limit reported by KamLAND-Zen collaboration is |mββ| < (0.061−0.165)eV. This upper limits is obtained by the KamLAND-Zen collaboration using the lower limit on the half-life of the xenon-136 sample and they have considered the uncertainties in the NMEs(Nuclear Matrix Elements) in their analysis of the relevant process.
New-generation experiments plan to look the Inverted Ordering region of parameter space and possibly work for the |mββ| ∼ 10^−2 eV energy range. Various running experiments are considered for upgradation and new experiments are also proposed to achive this goal. Some of those experiments are as fallows, MAJORANA, LEGEND(76Ge), CANDLES(48Ca), AMoRE, PandaX-III, SuperNEMO and DCBA(82Se,150 N d), ZICOS (96Zr), MOON (100Mo), COBRA (116Cd,130 T e), SNO+(130T e), NEXT and nEXO(136xE). If these planned experiments didn’t find positive responce in this energy range(10^−2 eV ), then next generation experiment will be very intersting for sterile neutrino which will correspond |mββ| ∼ 10^−3 eV or more below in the (ββ)oν-decay experiment.