Disappearing Atmospheric Neutrinos Don't Seem to be Turning Sterile

For some time now, we've had overwhelming evidence that a significant fraction of the muon neutrinos (ν_µ) produced by decays in cosmic-ray showers in the upper atmosphere are somehow disappearing before they can get to an underground neutrino detector. Four years of data from Super-Kamiokande, the 50-kiloton water-Cherenkov detector in Japan, have made a strong case that these missing atmospheric ν_µ's are being transformed by "neutrino oscillation" into neutrinos of some other sort. But there was no good evidence of just what sort these other neutrinos might be. (See Physics Today, August 1998, page 17.)

Now, at last, the Super-Kamiokande collaboration has published the results of its assault on this experimentally difficult question.¹ Any new evidence of neutrino oscillation and its detailed character is a subject of considerable excitement, because neutrino oscillation promises to be our first glimpse of new physics beyond the all-too-successful standard model of particle theory.

"We find," writes the collaboration, "that oscillation between ν_µ and tau neutrinos [ν_τ] suffices to explain all the results in hand." The paper rejects, at the 99% confidence level, the principal competing hypothesis--namely, that ν_µ is oscillating with a putative "sterile" neutrino species that is impervious to the normal weak interaction. (The data have long since ruled out a third possibility--that the missing atmospheric neutrinos might be turning into electron neutrinos [ν_e ].)

Why should anyone entertain something so exotic as a sterile neutrino (ν_s) in the first place, when the theorists already have three perfectly good neutrino flavors to play with: ν_µ, ν_τ, and ν_e ? In fact, the high-energy electron-positron collider data have made it quite clear that there can
be no additional neutrino varieties participating in the standard weak interactions.

That's the problem! Three neutrino flavors simply cannot suffice to explain the disparate data from all three observational regimes for which evidence of neutrino oscillation has been reported: atmospheric neutrinos, solar neutrinos, and neutrinos produced in accelerators. Suppose you have oscillation between two neutrino flavors, labeled i and j. Then the probability that a neutrino starting out as an i will have become a j after a journey of length L through empty space oscillates like sin² (L/Λ). The characteristic oscillation length Λ is proportional to E/Δm_ij², where E is the
neutrino's energy and Δm_ij² is the difference between the squares of the two neutrino masses in question. Neutrino oscillation implies unequal neutrino masses.

Because the measured oscillation parameters of the three observational regimes are so different, it is presumed that each involves a different pairing of neutrino species. But if there are only three species, one confronts an obvious algebraic constraint. By definition,

Δm²₁₂ + Δm²₂₃ + Δm²₃₁ ≡ 0.

The problem is, however, that the accelerator data, where ν_µ ↔ &nu_e is the only possible oscillation pairing, indicate a magnitude of about 1 eV² for Δm_µe² . That's orders of magnitude bigger than the mass-squared differences indicated by the solar and atmospheric neutrino oscillation data, making it impossible to satisfy the algebraic identity.

That leaves several possibilities: If one believes all the data, one almost has to invoke a fourth, sterile neutrino species taking part in either the atmospheric or solar neutrino oscillations. (Sterile neutrinos, by the way, appear in a variety of respectable theoretical schemes.) A way out might be to suggest that the data are actually describing messy three-way rather than simple pairwise oscillations. Finally, one could call the data into question. The weakest experimental link is the claimed oscillation of neutrinos within the confines of an accelerator lab. Only one group, working at the Los Alamos LAMPF accelerator, has reported such an observation (see Physics Today, August 1995, page 20). In fact, Fermilab is currently mounting an experiment called Miniboone, specifically to confirm or refute the Los Alamos result.

How did the Super-Kamiokande collaboration manage to distinguish ν_τ from a hypothetical sterile species? An unaltered ν_µ can interact with a nucleus in the detector's water in two distinct ways. First, by exchanging charge with the nucleus, the ν_µ can change into a charged muon. The emergence of the muon at the scattering site makes this so-called charged-current (CC) interaction easily visible. Alternatively, the scattering can be a "neutral-current" (NC) interaction, in which the ν_µ retains its invisible identity. NC events are much harder to identify in a water-Cherenkov detector than CC events. Lacking a muon flag, one has to rely on the emission of pions by the struck nucleus.

Almost all of the detailed evidence for atmospheric neutrino oscillation over the years has come from the anomalously anisotropic distribution of the CC events: One sees only about half as many atmospheric ν_µ's coming up through the Earth as one sees coming down from above. In the absence of neutrino oscillation, there should be almost no up/down asymmetry.

Up/Down ratio at Super-Kamiokande

Therefore, if the neutrino oscillation is, in fact, ν_µ ↔ ν_τ, the NC events should exhibit no up/down asymmetry. The probability that an atmospheric neutrino suffers an NC scattering in the detector would be unaffected by metamorphosis into ν_τ. If, on the other hand, disappearing ν_µ's are turning into ν_s's, which do not scatter at all, the NC events should exhibit the same up/down asymmetry as the CC events.

From four years of running, the Super-Kamiokande group has culled a sample of of 791 plausible NC events in which the incident neutrino direction is within about 60° of the vertical. The near equality of upward and downward events in this sample argues against the sterile-neutrino hypothesis. See the top panel of the Figure, which compares the measured up/down ratio with what's predicted by the competing hypotheses. Because the predictions depend on Δm², one should make the comparison at Δm² = 3 × 10^-3 eV².

There's yet another way of distinguishing ν_τ from ν_s in Super-Kamiokande. Passage through matter would, in general, affect neutrino oscillation, modifying its amplitude and oscillation length. That is presumably what's happening to solar (electron) neutrinos as they make their way out of the Sun. But oscillation between ν_µ and ν_τ would be an exception. Passage through the Earth would have no effect on this oscillation pairing, essentially because these two neutrino varieties have identical forward elastic-scattering amplitudes in matter.

But if the ν_µ's oscillation partner were sterile, with no scattering amplitude at all, passage through matter would modify the oscillation parameters. For typical atmospheric-neutrino energies (a few GeV), this modification would be negligible. But above 15 GeV, it would significantly suppress ν_µ ↔ ν_s oscillation for atmospheric neutrinos traveling long distances through the Earth.

Therefore the collaboration also examined two subsets of unusually high-energy CC events to see whether they exhibited any suppression of the telltale up/down asymmetry seen in the lower-energy CC data. The Figure's bottom panel shows the result for a subset of 127 vertical events with typical neutrino energies of 20 GeV. This high-energy sample turns out to be just as asymmetric as the bulk of the CC events at lower energy. That's what one expects for ν_µ ↔ ν_τ. The tau-neutrino hypothesis is similarly favored by another subset of events of even higher energy (around 100 GeV), where the CC interaction actually took place in the rock outside the detector and the resulting muon passed clean through the rock and the detector.

Combining the results from the three samples of events that have some ability to discriminate between the tau- and sterile-neutrino hypotheses, the group reports that these data exclude, at the 99% confidence level, a sterile neutrino with the oscillation amplitude and Δm² indicated by the bulk of the CC events. The tau-neutrino hypothesis, on the other hand, is quite compatible with these best-fit oscillation parameters.

If sterile neutrinos play no obvious role in the oscillation of atmospheric neutrinos, perhaps such exotics will turn up in the solar-neutrino data at the Sudbury Neutrino Observatory, which began operation last spring in a Canadian nickel mine. With all the deuterons in its core of heavy water, the SNO detector is uniquely sensitive to the neutral-current interactions of the MeV solar neutrinos (see Physics Today, July 1996, page 30).