Particle physics

Neutrino deficit challenges conservation laws

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SuperKamiokande is a modern wonder of the world: 50,000 m3 of purified water surrounded by giant phototubes looking out for Cerenkov radiation, the shock waves of light left behind by ‘superluminal’ particles. (I speak here not of the hypothetical and dubious tachyons, but of ordinary particles boosted to high energy, which outrace light through water even though their speed is less than that of light in a vacuum.) The giant instrumented aquarium has proved to be a superb detector of the rare interactions of neutrinos. At a conference last monthFootnote 1, the SuperKamiokande group reported an anomaly in their observations of neutrino interactions that has considerable implications for fundamental physics(E. Kearns, Boston Univ.). The anomaly is in the relative number of electron-type and muon-type neutrinos found in cosmic rays. The observation greatly strengthens earlier hints in the same direction1,2,3,4,5. It threatens cherished conservation laws, and calls into question the completeness of the Standard Model of particle physics.

Figure 1: Inside the SuperKamiokande detector.

Deep underground, a vast volume of water is surrounded by photomultiplier tubes, which detect flashes from high-energy neutrino interactions. An observed lack of muon-type neutrinos from the atmosphere appears to overturn the laws of lepton-number conservation. (Details of SuperKamiokande can be found at

Let me first define the matter at stake. A wide range of experimental results can be explained by the postulate that there are conservation laws for three different classes of fundamental particle: the laws of conservation of electron number, muon number and tau number. Known collectively as the laws of lepton-number conservation, these laws make very similar, very simple statements about what sorts of particle interactions do or do not occur.

Electrons, for example, are assigned electron number +1, and their antiparticles, positrons, are assigned electron number -1. Electron neutrinos, νe, have electron number +1, and the corresponding antineutrinos ν̄eelectron number -1. All other particles have electron number 0. In any reaction we have yet observed, the sum of all the particles' electron numbers in the initial state is equal to that in the final state. The laws of muon (μ) and tau (τ) number conservation follow exactly the same pattern.

The idea that electron and muon numbers are separately conserved was postulated6 to explain why certain types of particle decay, notably μ→ eγ, in fact never occur (e is an electron; γ is a photon). The ‘two-neutrino’ experiment7, eventually rewarded by a Nobel prize, tested this very idea. It showed that neutrinos produced in the decay of pi mesons, π→μνμ, were able to induce the reaction ν̄μp →nμ+ but not ν̄μp →ne+ (p is a proton; n is a neutron). The idea has since been tested in a variety of ways, and is now embedded in the Standard Model of particle physics.

The laws of lepton-number conservation greatly resemble, in their formulation and use, the dozens of atom-number conservation laws — one for each type of chemical element — in allowed chemical reactions. These laws are what defeat the dreams of alchemy, and they have served chemistry well; but nuclear physics shows that they are only approximate. SuperKamiokande may be teaching us a similar lesson for the elemental leptons.

So what has SuperKamiokande seen? When energetic cosmic rays strike the atmosphere they typically produce many charged pi mesons, which in turn decay into states containing muon neutrinos or antineutrinos. The muons themselves then decay, usually into a muon neutrino, an electron and an electron antineutrino; and there are several other processes that produce neutrinos of both types.

Although the details are complicated, a great deal is known experimentally about cosmic-ray showers, and essentially all the basic underlying processes have been studied in great detail. As a result, one can estimate the ratio of muon to electron neutrinos with considerable confidence8 — it is close to 2:1. But experimenters at SuperKamiokande find far fewer muon neutrinos and antineutrinos than were predicted. The observed ratio is about 1:1.

If the theoretical estimates were correctly reckoned, and the experimental results correctly interpreted, what could account for the seeming contradiction? To many physicists, the most interesting possibility is that neutrinos of one type ‘oscillate’ into neutrinos of another type. Indeed, if many of the mu-type neutrinos making their way from the atmosphere to the SuperKamiokande detector oscillate into tau-type neutrinos, which are more difficult to detect, the observations could be explained. Of course, that would violate the conservation of both muon and tau lepton numbers.

The idea of neutrino oscillations goes back a long way9,10, having been proposed not long after oscillations between different types of K meson were first observed, during the childhood of particle physics. In this view, different kinds of neutrino are like different polarization states of light. In empty space, a given polarization state of light will be maintained as it propagates. But as light passes through a crystal, or any optically active material, one polarization will oscillate into another. Very similar mathematics governs the propagation of neutrinos, so oscillations among the different types would indicate that empty space is ‘leptonically active‘.

The question of whether neutrino oscillations occur is closely connected to the question of whether neutrinos have mass. Indeed, the oscillations are attributed to what are called off-diagonal masses. Whereas ordinary masses, in quantum mechanics, cause the phase of the wavefunction of a particle to oscillate in time, off-diagonal masses cause not only its phase but also its direction (polarization, for example, or neutrino type) to oscillate.

This connection to mass is central to the deeper theory of neutrino oscillations. For one thing, it allows us to quantify the observed effect. If the SuperKamiokande observations do indicate neutrino oscillations, then the value of the off-diagonal masses responsible is of the order of 10−2 electron volts. This is more than six orders of magnitude smaller than the mass of the electron, which itself is by far the smallest mass appearing in the Standard Model. So the oscillation would only represent a tiny correction to the Standard Model, visible only because a very small oscillation per unit length gets multiplied by the long distance neutrinos can travel between interactions. It does not so much challenge the Standard Model as supplement it.

Most theoretical physicists would welcome such tiny, but non-zero, neutrino masses as an encouraging sign that our ambitious ideas about unification and symmetry beyond the Standard Model may be on the right track. The existence of off-diagonal mass terms for quarks has long been established, and if one attempts to treat quarks and leptons symmetrically — as one must in all modern unification schemes — it is hard to avoid such terms for neutrinos. Furthermore, the most complete and beautiful unification schemes, which view all the quarks and leptons as facets of a single symmetrical entity, require the existence of an additional, heavy, neutral particle. This so-called right-handed neutrino mixes with ordinary (left-handed) neutrinos in a way that induces tiny masses for the latter. These tiny masses are expected, though with considerable uncertainty, to be roughly the size of those claimed by SuperKamiokande.

The new, firm reports of an anomaly in the cosmic-ray neutrinos will be sharpened — or compromised — by additional observations in coming months. Decisive would be observations that the lost muon neutrinos still exist in another form: this might be verified by studying so-called neutral current interactions, which are largely insensitive to the change.

Finally, we should note that the atmospheric neutrino anomaly occurs in the context of two other claimed neutrino deficits, similar in form but quite different in important details: long-standing claims, from several experiments, of a deficit of electron neutrinos from the Sun11, and recent observations by an accelerator team at Los Alamos12. These various reports neither confirm nor directly contradict one another — with three different neutrinos and several possible mass terms coming into play, there is room for several distinct oscillation phenomena on different energy and length scales. It seems probable that the separate laws of lepton-number conservation will soon fall.


  1. 1.

    *Santa Barbara Neutrino Conference, 2-6 December 1997;


  1. 1

    Hirata, K. al. Phys. Lett. 205, 416–420 (1988); 280, 146-152 (1992).

  2. 2

    Casper, al. Phys. Rev. Lett. 66, 2561–2564 (1991).

  3. 3

    Becker-Szendy, al. Phys. Rev. D 46, 3720–3724 (1992).

  4. 4

    Fukuda, al. Phys. Lett. 335, 237–245 (1994).

  5. 5

    Allison, W. W. al. Phys. Lett. 391, 491–500 (1997).

  6. 6

    Feinberg, G. Phys. Rev. 110, 1482–1483 (1958).

  7. 7

    Danby, al. Phys. Rev. Lett. 9, 36–44 (1962).

  8. 8

    Gaisser, T. al. Phys. Rev. D 54, 5578–5584 (1996).

  9. 9

    Pontecorvo, B. Zh. Eksper. Theoret. Fiz. 34, 247-249 (1958); Sov. Phys. JETP 7, 172–173 (1958).

  10. 10

    Maki, al. Prog. Theor. Phys. 28, 870–876 (1962).

  11. 11

    Bahcall, J. & Krastev, P. Phys. Rev. D 53, 4211–4225 (1997).

  12. 12

    Athanassopoulos, al. Phys. Rev. Lett. 77, 3082–3085 (1996).

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