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Testing the Neutrino Hierarchy

by John G. Cramer

Alternate View Column AV-187
Keywords:  neutrino, oscillations, hierarchy, electron, mu, tau, masses, GERDA, Majorana Demonstrator
Published in the March-April-2017 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 11/10/2016 and is copyrighted ©2016 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

    In this AV column, my eleventh discussing neutrinos, I want to describe two new underground experiments that seek to determine the hierarchy in mass of the three neutrino flavors. To begin this discussion, however, I will need to delve into some of the intricacies of neutrino physics.

    At its deepest roots, all the matter and energy in our world reside in a dozen or so fundamental particles, quarks, leptons, and bosons, which are the building blocks of our universe. The leptons are further divided into the electrically charged electron, muon, and tau and the three charge-neutral neutrinos. The three flavors of neutrinos, ne, nm, and nt, are nature's most elusive and peculiar particles.

    The three neutrino flavors each have ½ unit of spin angular momentum and zero electric charge, and they interact with other particles only through gravity and the weak interaction. The electron neutrino (ne), produced by the Sun in its hydrogen-to-helium fusion cycle, interacts so weakly with matter that it can pass through a light year of lead without an interaction. We do not even notice the 600 trillion neutrinos from the Sun that are passing through our bodies in the second it takes to read this line.

    Neutrinos are exclusively "left handed" particles, with matter neutrinos always spinning only clockwise when viewed head-on. This preference for left over right leads to the strong violation of parity (mirror image) symmetry present in weak interactions. There are speculations that if the missing right-handed neutrinos exist at all, they are unobserved because they have a huge mass that is near the grand unification scale of around 1026 electron volts.

    Physicists usually discuss the mass of the neutrino in units of electron-volts or in milli-electron-volts. An electron-volt (or eV) is the kinetic energy that an electron gains in passing through one volt of potential, and a milli-electron-volt (or meV) is one thousandth of an eV. In mass terms, 1 eV is equivalent to 1.783 × 10-36 kilograms.

    Cosmology sets limits on how large neutrino masses can be. The universe contains huge quantities of neutrinos of all three flavors that were produced in the hot early stages of the Big Bang. These can contribute significantly to the overall mass of the universe. Cosmic microwave background measurements imply that the summed masses of the three neutrino flavors must total no more than about 300 meV and could be much smaller.

    One peculiarity of neutrinos is that they oscillate, changing flavors as they travel through space. When two or more quantum states like neutrinos cannot be distinguished by observation, quantum mechanics tells us that a peculiar thing happens: they mix to form new states of matter that are distinguishable. In the case of the three neutrino flavors, the mixing produces amplitudes for the three distinguishable states that are created together each time a neutrino is emitted. Because the states will have differing rest masses, for a given kinetic energy they will travel through space with slightly different speeds. Because of the speed differences, their flavor amplitudes will "slip" and change their relative phase along the path. The flavor amplitudes may cancel or may reinforce, depending on location. The result is flavor-changing along the flight path. For example, a neutrino emitted from the Sun at some points along its flight path will be primarily an electron-neutrino (ne), at other points will be primarily a mu-neutrino (nm), and at intermediate points will be a mixture of the two. This phenomenon is called neutrino oscillation, and it has been observed in several recent solar neutrino detection experiments and also in higher energy atmospheric cosmic ray experiments.

    The solar neutrino oscillation experiments indicate that the squares of the masses of two of the neutrino flavors must differ by about 5 × 10-5 eV2, while cosmic ray atmospheric neutrino oscillation experiments indicate that the squares of the masses of another two of the neutrino flavors must differ by about 3 × 10-3 eV2. These values are taken to mean that there must be a mass-energy gap of about 5 meV between one pair of adjacent neutrino flavor masses and a mass-energy gap of about a 48 meV between the other pair of adjacent neutrino flavor masses. These gaps imply that at least one of the neutrino flavors must have a mass of 0.053 eV or more. The question is, in what order do the masses of the three flavors fall? Is the big 48 meV gap lower or higher than the smaller 5 meV gap? Is the neutrino that interacts mainly with tau leptons more or less massive than the one that interacts mainly with electrons? Placing the electron-coupled neutrino at the lowest mass with the small gap just above it is called the normal hierarchy, while placing the tau-coupled neutrino at the lowest mass with the large gap just above it is called the inverted hierarchy. The charged tau-lepton is much heavier than the muon, which is in turn heavier than the electron, but that does not mean that their neutrino cousins must follow the same ordering. The standard model of particle physics provides us with no guidance as to which of these hierarchies we should expect, so it become a matter that must be tested by experiment.

    How can we test which neutrino hierarchy is correct? Fortunately, there is a weak-interaction process called double beta decay that can address this question. In the table of isotopes there are a number of nuclei that are stable against single beta decay (radioactive emission of a single electron plus anti-neutrino, producing an increase in nuclear charge by one unit). A few of these can reduce their mass-energy by decay with the emission of two electrons and two (or zero) neutrinos, thereby increasing the nuclear charge by two units. Double beta decay accompanied by the emission of two neutrinos is a well established process, and measurements have established that typical half-lives for such decays are around 1021 years. The pressing experimental issue is whether the weak but competing process of double beta decay with the emission of no neutrinos exists and can be observed.

    The two-neutrino and zero-neutrino processes are easily distinguishable in a measurement of the summed energies of the two emitted electrons, because the two-neutrino decay produces a broad bump distribution in energy while the zero-neutrino decay produces a sharp energy spike. Theoretical predictions indicate that the probability of neutrino-less double beta decay should be about ten times larger for the inverted hierarchy of neutrino mass than for the standard hierarchy, because the neutrino-less double beta decay probability depends on the mass of the electron-coupled neutrino. Therefore, observation of the strength of a neutrino-less process should indicate a preference for one of the two hierarchies and should also provide needed neutrino mass information.

    The naturally-occurring semi-stable nuclei that can undergo double beta decay include 48Ca, 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te, 136Xe, 150Nd, and 238U. Of these isotopes, germanium-76 is particularly interesting because it occurs in natural germanium with a 7.83% isotopic abundance and because a pure germanium crystal is a good semiconductor that is widely used in the construction of high-resolution detectors of gamma rays and electrons. If a 76Ge nucleus decays inside such a detector, the two emitted electrons are detected with nearly 100% efficiency, and their summed kinetic energy can be measured to a resolution of 3 to 4 keV. It would be very difficult to obtain this kind of efficiency and resolution with any of the other isotopes listed above.

    Two current experiments, GERDA and Majorana Demonstrator, are now using isolated and highly shielded clusters of germanium detectors to search for the neutrino-less decay process in 76Ge. GERDA is a European collaboration operating about 35.8 kilograms of coaxial germanium detectors surrounded by liquid argon that scintillates, thereby suppressing background radioactivity. GERDA is placed beneath 1,400 meters of rock in the Grand Sasso underground laboratory (LNGS) in central Italy.

    Majorana Demonstrator is an international collaboration operating about 44.1 kilograms of point-contact germanium detectors surrounded by lead shielding and mounted 4,958 feet below the Earth's surface in the Sanford/Homestake underground laboratory (SURF), a former deep gold mine in Lead, South Dakota. Both experiments use enriched germanium for their detectors that has been brought to 87% 76Ge concentration through the use of Russian gas-centrifuge isotope separators, remnants of Cold War uranium-235 separation projects, now operating with GeF4 gas instead of UF6.

    The GERDA experiment, funded by several European government agencies, has demonstrated the excellent effectiveness of liquid argon as an active shield for their germanium detectors. The Majorana Demonstrator experiment, funded by the US Department of Energy and the National Science Foundation, has achieved remarkably low background levels in their detectors by careful and systematic elimination of the many sources of natural and cosmic-ray-induced radioactivity (particularly springs) in the materials from which the detector system is constructed.

    Both experiments are now taking data. However, both are presently operating at a level that is not likely to reach the sensitivity needed to observe and measure the strength of neutrino-less double beta decay in 78Ge. The two groups are now discussing joining forces to form a new experimental collaboration that will combine and improve on the best features of both detector systems and will have a good chance of achieving observation of neutrino-less double beta decay and produce a hierarchy test.

    I should also mention another aspect of this work. The mysterious dark matter that clusters around galaxies accounts for about 27% of the total mass of the universe. We know it is there, but we don't know what it is. Many of the searches for hypothetical dark matter candidate particles require sensitive well-shielded underground detectors. Both GERDA and Majorana Demonstrator therefore can serve double duty as dark-matter detectors while they are recording data on 76Ge double beta decay. The Majorana Demonstrator group is already preparing a publication that will use their sensitivity to dark matter particles depositing energies as low as 5 keV to set rather low upper limits on the detection of pseudo-scalar dark matter, vector dark matter, and the hypothetical 14.4-keV solar axion. As more data is gathered, these upper limits will go lower, and it is possible that such measurements might even result in an actual discovery of dark matter particles.

    In any case, there are new experiments currently operating to explore the unknown properties of the neutrinos. These can be expected to provide new information on how our peculiar universe actually works.

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or

SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at and His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: .


Majorana Demonstrator web site:

"The Majorana Demonstrator: A Search for Neutrinoless Double-beta Decay of 76Ge", The Majorana Collaboration, arXiv:1501.03089 [nucl-ex].

GERDA web site:

"Search of Neutrinoless Double Beta Decay with the GERDA Experiment", The GERDA Collaboration, Nucl. Part. Physics Procs. 273-275 (2016) 1876; arXiv:1506.03120 [nucl-ex].

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