1st Draft of 8/29/99 1442

2nd Draft of 9/1/99 1520 edits

3rd Draft of 10/14/99 1715 major cuts

4th draft of 10/31/99 1300, massive cuts

Neutrinos Have Mass!

John G. Learned

Department of Physics and Astronomy, University of Hawaii

....Astonishing Results
........Oscillations in the Air
........SuperK Finds the Smoking Gun
....Corroborative Evidence

........Other Hints at Oscillations
....The Importance of Neutrino Mass and Where Do We Go from Here


Astonishing Results

Over a year ago physicists working on the Super-Kamiokande project in Japan announced strong evidence for neutrino mass and jolted the world by indicating that a rethinking of the Standard Model of particle physics (which assumes that neutrinos have no weight at all) would surely follow. It was not the first time that the elusive neutrino had been reported to have weight. But the evidence this time seemed irrefutable, coming as it did from observing the decrease of atmospheric muon neutrinos with distance with strong statistical significance and apparent lack of significant systematic uncertainties. The results came from the most sensitive instrument of its kind in the world, a 50,000-m3 detector filled with 12.5 million gallons of ultra-clean water and lined with 13,000 sensitive light detectors, located deep underground in the Japanese Alps. But particle physics is not the only field that will have to rethink things. Cosmology and astrophysics have their fair share of recalculating to do to accommodate neutrino mass. Such mass may have influence from the generation of an excess of matter over anti-matter in the Big Bang, to the accounting for the mass of the universe, since we can now infer that neutrinos must weigh in total at least as much as all the visible stars, to the generation of heavy elements in supernova explosions.

Now, one and a half years after this profound announcement that neutrinos appear to change identities -or oscillate- and thus have weight, the K2K Long Baseline Neutrino Oscillation Experiment has taken the first step towards its verification, with a few events in hand but not enough to say anything definitive yet. Meanwhile, as more SuperK data is collected and analysis refined, the noose becomes tighter and the conclusions of neutrino mass and oscillations more inescapable. What does this mean for particle physics? Are we any closer to solving the mysteries of the Universe such as its origin and future? What road blocks lie ahead?

Oscillations in the Air

As with most stories in the cosmic ray business, there is a long history. The experimental tale begins with the first observations of natural neutrinos in 1967 in the world's deepest mines in South Africa and in the Kolar Gold Fields in India. At that time the instruments measured a rate a little lower than expected, but nobody made much of that and neutrino flux calculations made by others soon agreed with the data.

The second round of experiments began after the enthusiasm in the late '70's for the simple GUT SU(5), which made a prediction for proton decay lifetime at an experimentally accessible level. The first really large instrument was the IMB detector, in a salt mine in Cleveland Ohio. The experimental technique was simple in the extreme: fill a tank with ultra pure and hence transparent water, and surround it with light detectors looking inwards. When a neutrino interacts in the water producing secondaries, or when a charged particle enters the tank from the surrounding rock, these particles travel at close to the speed of light. Yet the speed of light in water is the speed of light in vacuum, so the particles outstrip their disturbance of the medium, as does a jet making a sonic boom by exceeding the speed of sound in flight and a boat leaving an expanding wake. Thus do the particles produce the characteristic "Cherenkov radiation", which projects onto the detector wall as a transient (nanosecond) ring of very blue light. The location, timing and amplitude of the sensor signals allows one to reconstruct the track direction. Moreover, as illustrated in Figure 2, some neutrino events can be uniquely discriminated, as between muon events which make crisp rings, and electron events which make fuzzy rings (electrons being much less massive, scatter a great deal more than muons).

The ratio of muon to electron neutrino events turns out to be a rather simple quantity to calculate, as illustrated in Figure 3, and not susceptible to much uncertainty. When the neutrinos interact in our deep tanks after traversing the earth, we expect two muons to appear for every electron. What was found however, was nearly an equal number.

Soon after beginning operations in 1982 the IMB group found that there were not as many muon decays following neutrino interactions as they had expected. Muon neutrino interactions in the water usually give a second 2.2 microsecond delayed light pulse. The deficit found caused much debate amongst the IMB physicists, including of course consideration of neutrino oscillations as the cause. But there were many other possible explanations at that time, both systematics and possible physics. So, the collaboration reported the result in a publication, but in a very understated way, so as to get it into the record, but not to incite the community with grand claims which were not then supportable.

Not long thereafter the Kamioka group came on line with a smaller but deeper and more sensitive detector located in Japan. Soon the Kamiokande group had not only found the same result, but had gone further and developed some sophisticated algorithms for distinguishing muon and electron events, as did IMB around the same time but without as much discrimination power.

The situation began to change towards the end of life of the old Kamiokande detector when eventually enough statistics had been accumulated to publish an angular distribution of muon neutrino interactions in the detector, but where the muons leave the tank. Still the evidence was weak, because the statistics were not good enough to rule out no angular variation, but it certainly appeared suggestive. People outside physics are often curious as to why some results are accepted at face value and yet others are held at arms length, despite apparent statistical strength: five standard deviations are often not enough! Without diverging into a philosophical treatise here, I find it interesting how there appears to be some community wisdom which goes beyond mere numbers. Major new results, paradigm shifts as some call them, require extraordinary evidence, not entirely quantifiable. We do not need much to convince us about, say, a better measurement of the mass of some particle. But something like the claim of neutrino oscillations and hence neutrino mass, demands gold plated evidence.

SuperK Finds the Smoking Gun

The Super-Kamiokande instrument is an awesome piece of technology. One cannot appreciate its size from pictures, such as the one shown in Figure 4. It is a vast hall carved from hard rock in the old zinc mine near Mozumi, about 100 m from the predecessor Kamiokande instrument (now being rejuvenated into the 1000 ton liquid scintillator KamLAND). SuperK is housed in a huge stainless steel tank, welded in place, and containing a concentric structure, as illustrated in Figure 5, which supports 11,142 twenty inch photomultiplier tubes (PMTs) looking inwards and 1,800 eight inch photomultipliers with wavelength shifting light collecting collars (recycled from the IMB experiment) looking outwards into the 2 m thick veto region. This fiducial volume, taken as the region 2 m inside the PMTs is 22,000 tons. This may be compared with the old Kamiokande at 600 tons, and IMB at 3,000 tons. It is indeed a big jump in collecting power, but perhaps the most important difference is in the ability to contain muon events. Muons travel distances of about 5 m per GeV of kinetic energy in water. The old Kamiokande instrument could only record with any efficiency muons up to about 1 GeV, while with the same geometry scaled up, the Super-Kamiokande instrument can record muon events up to several GeV, since it is nearly 50 m across the long diagonal. As it happens this gain was crucial.

In early June 1998 at the NEUTRINO98 meeting in Takayama, Japan (just over the mountain range from Kamioka), we announced the results from analysis of the first two years of data accumulated in Super-Kamiokande. Here we show the updated results as of summer 1999, with 848 days of live time analyzed, in Figures 6 and 7. The most compelling data are for events in which we have single electron or muon events produced by neutrinos, and which secondary particles are completely contained within the fiducial volume. We record this type of event at about once per 10 hours of data recording.

In Figure 6 we show the asymmetry between upward going and downward going events, electrons and muons, a nice quantity as systematic errors cancel out and some results are interpretable without calculation. The electron events are up-down symmetric, as demanded by geometry in the absence of oscillations or other unexpected phenomena. For the muons, on the other hand, there exists a dramatic asymmetry which corresponds to a deficit of nearly one half for the upcoming muons, and which tells us straight away that the oscillations must be most surprisingly nearly maximal. The shape of the asymmetry versus momentum is just what one would expect for oscillations: the dashed curve comes from simulations with oscillations. This plot alone eliminates some hypotheses which could not be eliminated prior to SuperK. Of course, this up-down asymmetry by itself still may leave one nervous: how come it turns out that the geometry of the earth is so well matched to eliciting this maximal deviation from expectations, are we being fooled somehow?

In the next plot, Figure 7, we show the angular distributions of muon and electron events, for two energy groupings. This plot may be the one which has been most convincing to many in the particle physics community, since it shows really dramatic evidence that indeed the `trouble' is with the muons, and that the onset of the deviation is smooth and not confined to the upcoming muons. A fit to the hypothesis of oscillations is also shown here, and again it fits beautifully to the presence of maximal oscillations with a mass squared difference of 0.0035 eV2 with an error of about a factor of two. One can see that the null hypothesis is statistically rejected at such a high level that the probability of this being a fluctuation is not worth discussion.

Finally, in Figure 8 we show a plot of the allowed regions for the oscillation parameters between muon neutrinos and tau neutrinos. As the contour lines indicate, the mass squared difference lies in the range of 0.002 - 0.007 eV2, and the mixing is very nearly maximal.

Corroborative Evidence

Another detector in a mine, the Soudan II instrument in Minnesota (built to search for nucleon decay as were IMB and Kamiokande) has weighed in during the last few years with evidence of a low value of the ratio of muon to electron events, and is completely consistent with the old IMB and Kamiokande data. Unfortunately the statistics are not good enough to see the angular distribution, but at least the results dismiss the hypothesis that there is something uniquely peculiar about a water target. Also, the Soudan instrument has a veto shield lining the mine cavity, and helps one to understand perhaps the reasons for the earlier and smaller European instruments failure to detect the anomaly.

There is also supportive evidence for the SuperK contained data, from the through-going muons which originate from neutrinos of about 100 times higher energies, and comprise a nice consistency check even thought they do not constrain the oscillations parameters as severely. There is similar data from other experiments, such as MACRO, and the older experiments Kamioka and IMB. IMB published a limit which would rule out the present oscillations solution, based upon the ratio of stopping to through-going muons. This result depends upon the flux of atmospheric neutrinos at around 10 GeV (stopping) and 100 GeV (through going), as well as detector response. Reanalysis of those results is underway, but it appears that the problem will probably disappear because of updated Monte Carlo models (the sensitivity to which is a strong drawback for this test). In any case, the analysis of the now world-dominating data set of throughgoing muons and entering-stopping muons in SuperK yields completely consistent results with the contained event data discussed above.

But, is it really neutrino oscillations, one may well ask? As in much exploratory science, we must proceed here like Sherlock Holmes, eliminating all hypotheses until (hopefully) we are left with only one, however initially seemingly unlikely. In fact we have done this, carefully examining such things as potential detector biases, cross sections, neutrino flux ratio calculations, and even some rather wild physics possibilities. Nothing we have tried even comes close to fitting the evidence, except oscillations. There is only one marginally viable alternative of which I am aware, a `strawman' for which I am partially to blame (ref) (nobody I know would put money upon it).

This does give one the flavor of how we are tightening the noose on the phenomenon we have encountered. We still worry, of course, that there might be some trick eluding us and that we have not got the interpretation quite right, or that something more bizarre is lurking in the data. Still, in the year and a half since we made the announcement at NEUTRINO98, the data and analysis have only become more reassuring that we are on the right track. There are some concerns, at least to me, in the very lowest energy electron neutrino data, below 400 MeV, where the events do not fit expectations very well (including possible rate variations). This is just where the geomagnetic effects are large, so most likely that is the cause, but one wonders if some physics might be hiding there. We can only await better neutrino flux calculations (now underway) and more statistics. In any case that low energy regime has no effect upon our main conclusions about muon neutrino oscillations.

There is not room to go into detail here, but one big question has been as to whether the muon neutrino oscillating partner was the tau neutrino, the electron neutrino (or both), or even worse, some new "sterile" neutrino. Our data does indicate that the muon neutrino couples at most only a little (less than a few percent) to the electron neutrino for the oscillations we see. A hypothetical sterile neutrino would not interact with ordinary matter at all. We are now finding evidence that the sterile neutrino hypothesis does not work very well for explaining our data. Sterile neutrinos are not totally dead yet (and only in this context), but you should not put any money on them. In fact, every test we have made so far is completely consistent with the oscillating partner of the muon neutrino being the tau neutrino.

Other Hints at Oscillations

Due to space limitations this article cannot include a full discussion of the grandfather of neutrino "problems", the solar neutrino deficit (see Bahcall article...). Oscillations seem the likely solution but we need more solar data from SuperK and most importantly data from the now operating SNO instrument, and two other detectors under construction, GALLEX and KamLAND, to nail down the answer (we hope).

A most peculiar result came from an experiment at Los Alamos in 1990, in which they detected a few events which appeared to be due to muon neutrinos oscillating into electron neutrinos, from a stopping proton beam, and thus at quite low energies (30 MeV) and small distances (30 m), but a tiny fraction of the throughgoing neutrino flux. Another experiment with mostly but not entirely overlapping regions of sensitivity, KARMEN (at the Rutherford laboratory in England), has not found any supporting evidence, yet has not ruled out the LSND results. If correct, the LSND result would have tremendous implications. Nobody has been able to make a simple model incorporating oscillations from atmospheric neutrinos, solar neutrinos and the LSND results. If the LSND group is right we will need more neutrino types or some other dramatic physics.

The Importance of Neutrino Masses and Where do we go from Here?

Ever since Pauli's proposal for the neutrino's existence it was known that neutrino masses were not large. Direct laboratory attempts at measuring the masses, such as by time of flight or most sensitively by looking for the upper limit of electron energies in beta decay (which upper limit would have the neutrino mass subtracted), have only given us upper bounds which now are about 3 eV for electron neutrinos (less than one hundred thousandth of the electron mass), and somewhat poorer limits on the others (which are even harder to measure). Cosmology reinforces this by telling us that since neutrinos in staggering numbers are left from the Big Bang (about 2 billion for every proton), the total mass of all the neutrino types (electron, muon and tau, neutrino and anti-neutrino) cannot exceed about 12 eV or the universe would have collapsed already. On the other hand, since the number of neutrinos left from the Big Bang must be close to the number of photons we measure in the cosmic background radiation (as seen in the marvelous COBE results of a few years ago), and since we know roughly how much matter there is in all the stars we can see, we can calculate that at minimum the neutrino mass in the universe is approximately as much, or more, than all the stars one sees! Neutrinos with mass, it appears cannot be the long sought non-baryonic dark matter, but they may play important roles in astrophysics from the origin of the excess of matter over anti-matter, to processes having to do with the generation of the heavy elements in supernovae.

Since, there was no widely accepted evidence to suggest a non-zero neutrino mass until recently, it has thus been assumed that the neutrino mass was precisely zero in the construction of Standard Model of elementary particle physics, an ugly but functional patchwork. As we have discussed, the atmospheric neutrino evidence of the last year suggests that at least one neutrino has mass, of the order of 0.05 - 0.07 eV at minimum. Taken that neutrino oscillations are the probable solution to the solar neutrino problem as well, this would demand that at least two neutrinos have mass. Thus most reasonably all three possess some mass. There is a huge theoretical difference between some mass, even if small, than zero. The central problem for particle physics is illustrated by Figure 1, where one sees that the charged fermion masses all cluster at roughly the same distance on s log plot above the neutrino masses as they are below the anticipated scale for the unification of all forces. The challenge to model builders is to account for this huge scale jump. The second problem is to account for why the neutrinos are so much more mixed than the quarks, certainly not the simplest expectation.

The future for neutrino studies seems bright, with new experiments building and more being proposed. One of the more interesting prospects is intense pure beams from muon factories. After clarification of the neutrino mixing situation in the next few years, the medium range push seems to be clearly towards looking for CP violations with neutrinos. Cosmic experiments can explore in other directions and to the highest energies.

In summary, we have evidence for a whole new sector of interesting particle behavior the implications of which are deep for particle physics and cosmology. It is in keeping with the tradition of exploratory science that the results now discussed came from the exploration for proton decay. And while the physics seems very different, there is a deep relationship, hopefully pointing us along the way towards a unified theory. For us experimentalists, every day one can look forward to the possibility of finding something which will be of great importance in the history of science, surprises just lurking in the data, ripe for plucking by the ready mind. In particle physics it does not get any better than this.


1) Fermion masses

2) Muon and electron hit patterns

3) Schematic of cosmic Rays hitting the atmosphere and making neutrinos.

4) Picture of SK inner tank with boat during filling.

5) SK schematic, cross section of mountain.

6) Up-Down asymmetry versus momentum,

7) Angular distribution.

8) dm2 versus s22th.

copyright 1999, John G. Learned