For some time now, we’ve had overwhelming evidence that a significant fraction of the muon neutrinos (vµ ) 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-Čerenkov detector in Japan, have made a strong case that these missing atmospheric vµ ’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 vµ and tau neutrinos [vτ ] suffices to explain all the results in hand.” The paper rejects, at the 99% confidence level, the principal competing hypothesis—namely, that vµ 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 sterile neutrinos?
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: vµ , vτ , 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 , where E is the neutrino’s energy and 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,
The problem is, however, that the accelerator data, where ν µ↔ν e is the only possible oscillation pairing, indicate a magnitude of about 1 eV2 for . 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.
The search
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-Čerenkov 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.
The CC oscillation data yield a Δm 2 of about 3 × 10−3 eV2. But they are of little use for discriminating between ν τ and sterile neutrinos. Tau neutrinos do have charged-current interactions, but the charged τ leptons they produce are too heavy and too short-lived to be reliably identified in Super-Kamiokande. NC events, on the other hand, should look exactly the same for ν µ and ν τ collisions.
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 Δm 2, one should make the comparison at Δm 2 = 3 × 10−3 eV2.
Passing through matter
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 νµ↔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 Δm 2 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).
Up/down ratio observed in Super-Kamiokande for two special subsamples of atmospheric-neutrino scattering events: (a) a sample enriched in neutral-current events, as evidenced by Čerenkov signals suggestive of pions rather than muons, and (b) charged-current events of unusually high neutrino energy (typically 20 GeV), with muon tracks too energetic to stop in the detector. Horizontal lines and shading indicate the measured ratios and their errors. The blue (red) curves shows how the ratio predicted for ν µ ↔ν τ (ν µ ↔ν s) depends on Δm 2. The vertical lines indicate the best-fit value of Δm 2 from all the charged-current data.
Up/down ratio observed in Super-Kamiokande for two special subsamples of atmospheric-neutrino scattering events: (a) a sample enriched in neutral-current events, as evidenced by Čerenkov signals suggestive of pions rather than muons, and (b) charged-current events of unusually high neutrino energy (typically 20 GeV), with muon tracks too energetic to stop in the detector. Horizontal lines and shading indicate the measured ratios and their errors. The blue (red) curves shows how the ratio predicted for ν µ ↔ν τ (ν µ ↔ν s) depends on Δm 2. The vertical lines indicate the best-fit value of Δm 2 from all the charged-current data.
