### Out of the mouth of neutrino comes wisdom...

**... wisdom of particle physics beyond the standard model**

Decades of experimental and observational scrutiny have revealed less than a handful of phenomena outsidethe standard model, among them evidence for dark energy and dark matter, and the existence of nonzeroneutrino masses...

Massive neutrinos are special. Among all known fermions, neutrinos are the only ones not charged under the two unbroken gauge symmetries: electromagnetism and color. This implies that,unlike all known particles, neutrinos may be Majorana fermions. Majorana neutrinos would imply, for example, that neutrino masses are a consequence of a new fundamental energy scale in physics, potentially completely unrelated to the electroweak scale.Dirac neutrinos, on the other hand, would imply that U(1)B−L, or some subgroup, is a fundamental symmetry of nature, with deep consequences for our understanding of the laws of physics.If neutrinos are Majorana fermions, lepton number cannot be a conserved quantum number. Conversely, lepton number-violation indicates that massive neutrinos are Majorana fermions. Hence, the best (perhaps only) probes for the hypothesis that neutrinos are Majorana fermions are searches for lepton-number violation. By far, the most sensitive probe of lepton-number conservation is the pursuit of neutrinoless double-beta decay 0νββ

Neutrinos(authors not shown) submitted on 16 Oct 2013

**... wisdom of the spectral noncommutative paradigm**

...the Kamiokande experiments on solar neutrinos showed around 1998 that, because of neutrino oscillations, one needed a modiﬁcation of the Standard Model incorporating in the leptonic sector of the model the same type of mixing matrix already present in the quark sector...At ﬁrst our reaction to this modiﬁcation of the Standard Model was that it would certainly not ﬁt with the noncommutative geometry frameworkand hence that the previous agreement with noncommutative geometry was a mere coincidence.After about 8 years it was shown... that the only needed change (besides incorporating a right handed neutrino per generation) was to make a very simple change of sign in the grading for the anti-particle sector of the model... This not only delivered naturally the neutrino mixing, but also gave the see-saw mechanism and settled the above Fermion doubling problem.Besides yielding the Standard Model with neutrino mixing and making testable predictions..., this allowed one to hope that, instead of taking the ﬁnite geometry F from experiment, one should in fact be able to derive it from ﬁrst principles.The main intrinsic reason for crossing by a ﬁnite geometry F has to do with the value of the dimension of space-time modulo 8. We would like this KO-dimension to be 2 modulo 8 (or equivalently 10) to deﬁne the Fermionic action, since this eliminates the doubling of fermions in the Euclidean framework. In other words the need for crossing by F is to shift the KO-dimension from 4 to 2 (modulo 8).This suggested to us to classify the simplest possibilities for the ﬁnite geometry F of KO-dimension 6 (modulo 8) with the hope that the ﬁnite geometry F corresponding to the Standard Model would be one of the simplest and most natural ones. This was ﬁnally done recently([14], [15]).

**Wisdom of silence**

We are now in the very interesting situation that experimental physics may give us deep insights into the internal geometry of space time.If the neutrinoless double beta-decay would be experimentally conﬁrmed, i.e. the electron-neutrino would possess a Majorana mass, one would have to consider one of the... spectral geometries as internal space. This would exclude the case of KO-dimension zero, where Majorana masses may not exist...

Almost-Commutative Geometry, massive Neutrinos and the Orientability Axiom in KO-Dimension 6,Christoph A. Stephan, October 9th 2006

Neutrinoless double beta decay experiments constrain one combination of neutrino parameters, while cosmic surveys constrain another. This complementarity opens up an exciting range of possibilities. If neutrinos are Majorana particles, and the neutrino masses follow an inverted hierarchy, then the upcoming sets of both experiments will detect signals.The combined constraints will pin down not only the neutrino masses but also constrain one of the Majorana phases.If the hierarchy is normal, then a beta decay detection with the upcoming generation of experiments is unlikely, but cosmic surveys could constrain the sum of the masses to be relatively heavy, thereby producing a lower bound for the neutrinoless double beta decay rate, and therefore an argument for a next generation beta decay experiment. In this case as well, a combination of the phases will be constrained...In the absence of this lower ... [bound], we will never be guaranteed an answer to the question of whether neutrinos are Majorana or Dirac particles.

//last edition 30/09/2014

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