Another year, another more strict exclusion of neutrinoless double beta decay. The latest result doubles the duration of the exclusion from the last paper from GERDA, discussed here in a post made in the summer of 2015.

The universe is roughly 1.4*10^9 years old, so the current limit from GERDA means that no more than one in 3.8*10^16 of hadrons that could have done so have actually experienced neutrinoless double beta decay since the formation of the universe. According to the new paper cite below:

A good definition of mββ appears on page 2 of a 2015 paper on the topic together with some other very standard definitions of some other key terms:

We use mi (i = 1, 2, 3) to denote the masses of the neutrino mass eigenstates νi . We denote with 1 and 2 the eigenstates that are closest in mass; moreover, we take m2 > m1, so that ∆m2 21 is always positive, while the sign of ∆m2 31 discriminates between the normal (NH) and inverted (IH) hierarchies, for ∆m2 31 > or < 0, respectively. The neutrino mass eigenstates are related to the flavour eigenstates να (α = e, µ, τ ) through να = P i Uαiνi , where Uαi are the elements of the neutrino mixing matrix U, parameterized by the three mixing angles (θ12, θ23, θ13), one Dirac (δ) and two Majorana (α21, α31) CP-violating phases. Oscillation phenomena are insensitive to the two Majorana phases, that however affect lepton number-violating processes like 0ν2β decay. The different probes of the absolute scale of neutrino masses are sensitive to different combinations of the mass eigenvalues and of the elements of the mixing matrix. β decay experiments measure the squared effective electron neutrino mass m2 β ≡ P i |Uei| 2 m^2 i , while 0ν2β searches are sensitive to the effective Majorana mass mββ ≡ P i Uei^2 mi , where φ2 ≡ α21 and φ3 ≡ α31 − 2δ. Finally, cosmological observations probe, at least in a first approximation, the sum of neutrino masses Mν ≡ P i mi = m1 + m2 + m3.At this blog, I usually refer to "the neutrino mixing matrix U" as the PMNS matrix.

The quantity mββ is equal to the weighted average of the three neutrino mass eigenstates based upon the relative likelihood of an electron neutrino being in each of the mass eigenstates. This works out to approximately 0.6724 * Mv1+ 0.2916 * Mv2 + 0.0225 * Mv3, which the sum of the row of PMNS entries doesn't quite add to 1.0 as it should due to experimental uncertainties in the value of the respective entries. As I noted earlier this year the range of the three neutrino masses that would be consistent with experimental data is approximately as follows (with the location of each mass within the range being highly correlated with the other two and the sum):

Mv1 0-7.6 meV

Mv2 8.42-16.1 meV

Mv3 56.92-66.2 meV

For pro forma values of 1 meV, 10 meV and 58 meV, the value of mββ is (to spurious accuracy) equal to 4.8934. Put in more easily compatible terms mββ = 0.005 eV. So, GERDA and other neutrinoless double beta decay experiments need to be about 30 times more precise before they have any hope of meaningfully determine the Majorana neutrino mass of the neutrinos from neutrinoless double beta decay.

In fact, cosmology data and neutrino oscillation data implies that it is very likely that mββ <0.15, so the experimental data don't yet rule out a Majorana neutrino.

But, GERDA's sensitivity is expected to increase by a factor of five over the remainder of its current experimental run over the next few years, and the combination of GERDA's results with other experiments also tweaks down the upper threshold. So, we may be just a few years away from being able to resolve the Majorana v. Dirac neutrino mass debate (or at least, from being able to rule out the most straightforward Majorana neutrino mass models).

The Standard Model of particle physics cannot explain the dominance of matter over anti-matter in our Universe. In many model extensions this is a very natural consequence of neutrinos being their own anti-particles (Majorana particles) which implies that a lepton number violating radioactive decay named neutrinoless double beta (0νββ) decay should exist. The detection of this extremely rare hypothetical process requires utmost suppression of any kind of backgrounds.

The GERDA collaboration searches for 0νββ decay of 76Ge (76Ge→76Se+2e−) by operating bare detectors made from germanium with enriched 76Ge fraction in liquid argon. Here, we report on first data of GERDA Phase II. A background level of ≈10−3 cts/(keV⋅kg⋅yr) has been achieved which is the world-best if weighted by the narrow energy-signal region of germanium detectors. Combining Phase I and II datawe find no signal and deduce a new lower limit for the half-life of 5.3⋅10^25 yr at 90 % C.L.Our sensitivity of 4.0⋅10^25 yr is competitive with the one of experiments with significantly larger isotope mass.

GERDA is the first 0νββ experiment that will be background-free up to its design exposure. This progress relies on a novel active veto system, the superior germanium detector energy resolution and the improved background recognition of our new detectors. The unique discovery potential of an essentially background-free search for 0νββ decay motivates a larger germanium experiment with higher sensitivity.

M. Agostini, et al., "Background free search for neutrinoless double beta decay with GERDA Phase II" (March 2, 2017).

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