Draft of 8/29/99 1442
2nd Draft of 9/1/99 1520
Neutrinos Have Mass!
John G. Learned
Department of Physics and Astronomy, University of Hawaii
Neutrinos are Real
I still recall when I first heard about neutrinos as a student, that they seemed to be some sort of fiction, perhaps just an excuse for not facing up to some fundamental problems in physics. Mysterious particles that have no mass and go through everything, but which saved conservation of energy and momentum (and as I found out later, also angular momentum) seemed to be a dodge. Like ghosts or angels perhaps, some convenient but incredible rationalization. Well, these many long years later I am addicted to the study of these bizarre will-o-the-wisps, which we now record by the thousands per year, and we squeeze those traces for clues to the structure of elementary particles and use them to try to see to the heart of the universe. Neutrinos it seems are indeed "for real", as real as anything else. We can make a beam of them at an accelerator, let it pass through large amounts of material, such as the earth for 275 kilometers between Tsukuba and Kamioka in Japan, and see occasional neutrinos manifest themselves in a detector at the right time, with expected energies and directions... just no doubt they came from the place they were intentionally created. More dramatically, from the observation of a burst of neutrinos from Supernova 1987A in the IMB and Kamioka detectors, we know (as had been predicted for thirty years) that neutrinos do carry off most of the energy in the gravitational collapse of old and tired massive stars. And those neutrinos fly straight through the universe at very close to the speed of light and can be sensed here on earth, telling us things about the inner last moments of a star which we could learn no other way.
One should not fail to mention that of course neutrinos have been detected since 1955 when Reines and Cowan first astounded the physics world by recording a few neutrinos from the gale of low energy (and hard to catch) neutrinos emanating from a nuclear reactor at the secret Atomic Energy Commission Savannah River laboratories. These were the same neutrinos as Pauli had first invoked to save sacred laws of physics in 1930, and subsequently put into a calculable model of the so called "weak interactions" (which cause, for example, the "beta decay" of a neutron into a proton, an electron and an electron anti-neutrino) by Fermi in 1936.
In 1961 this was followed up by making an artificial neutrino beam at the Brookhaven National Laboratory (another product of the cold war), where Schwartz and colleagues found that there were more than one kind of neutrino. They identified the muon neutrino as well as the muon as resulting from the decay of unstable but plentiful particles called pions. As it happens the muon seems to be nothing more than the 200 times heavier sibling of the electron (except that the muon decays in about 2 microseconds, into two neutrinos and an electron, and apparently the electrons have nowhere to go so they are stable as probably are the neutrinos).
Still later Pearl, working at SLAC in 1975 uncovered the third charged lepton, named the tau particle or sometimes called the tauon (see box). This creature was even heavier, at nearly twice the mass of the proton, and 2600 times the mass of the electron, and it fell apart swiftly (in typically 290 femto-seconds). By examining the remnant detritous of tau decay people could soon confirm that something was missing: most probably a third type of neutrino, the tau neutrino, had slipped away when a tau decayed. At present, nobody has directly detected a tau neutrino because we know of no way to make a useable beam of tau neutrinos, and even so the interactions of tau neutrinos are devilishly hard to distinguish from other neutrino interactions. (However, rumors have it that an experiment at Fermilab may soon be able to stake the claim of the first direct detection of the tau neutrino... we wish them success).
Masses, the Biggest Hassle in Particle Physics
As indicated in the box to the [left] a picture of the fundamental fermions, the building blocks of which all matter is composed, has been revealed to us in the last 25 years or so as consisting of three "generations" or "flavors" or "families" as they are variously called. Each seems to be just a heavier version of the lightest (up and down quarks, and electron and electron-neutrino leptons), and we know of no reason for their existence. It seems the universe as we see it would work just fine without these heavier particles. [Aside from putting a few physicists out of work, the most notable consequence of a lack of the heavier generations might be in modified explosions of supernovae, to which we owe our very existence for the production and distribution of heavy elements. The lack of heavier generations would make the cooling of the Big Bang slower as well, with implications upon light element abundance. I have never seen a paper exploring this hypothetical situation, but it seems to me to fly against the popular trend of invoking much of the properties of the universe to be just so, else we would not be here, under the banner of the slippery Anthropic Principle. It is a moot question in any case, as we are stuck with the heavy ephemeral particles and the headaches they bring us physicists who want to make a nice tidy model.]
A lot of progress has also been made in model building in the few severeal decades, in that we have a patchwork "standard model" of elementary interactions, which does subsume the strong, electromagnetic and weak forces (yet ignoring gravity, the weakest while most immediately evident as a long range force to us humans), and which theory seems at least if not to be elegantly compact or calculable, not to be wrong (a little reminiscent of Ptolemaic theory). Indeed some of the successes of the standard model are awesome, in terms of ability to calculate the rates of certain reactions, or the magnetic moment of the muon, for example. Overall however, the standard model is a kind of a Rube Goldberg sort of affair, with a large number of quantities which have to be inserted from experiment, very unsatisfactorily (and unlike the beautiful simplicity of mechanics, thermodynamics and electromagnetism at the classical scale, and atomic physics at the quantum scale). The standard model has no explanation for three (only) generations of particles, no explanation of particle mixing, and perhaps worst of all makes no predictions of masses. Masses, by which we mean the m you put in F = m a, and which by the equivalence principle result in the weight of stuff in the gravity of earth, seem to be a most fundamental attribute of matter. Indeed we see that such is the case via Father Einstein's E = m c2, so that the mass of the particle tells us the energy needed to make it, or the energy which will be released when it decays.
One of the peculiarities of elementary particles is that the famous remark of former President Reagan about the Redwood trees, "seen one, you've seen 'em all", is actually true about these most basic building blocks of the infinitely varied universe. All the astounding varieties of material forms with which we are surrounded, on up in scale to the multitudinous patterns of galaxies, everything built of absolutely interchangeable units, like children's Lego blocks (though with even less variety!). The only thing we need to know about an electron, for example, is that it has spin one half, partakes of the electro-weak interaction (and gravity) and not the strong interaction, has an electric charge equal and opposite to the proton, and that it has a mass of 1/2000 of the proton. Of the 1080 or so electrons in the visible universe, you could not tell any one from any other... the ultimate clones. Of these quantities, mass seems the most strange in some way, as it alone is measured in a not simple number. (Need caveat here about coupling constants....).
Now, for 25 years or so particle physicists have been flirting with the possibility of a "grand unified theory" (or GUT), which would nicely condense and extend the standard model into an understanding of the unification of forces (though still leaving out gravity for the time being). Even more bold initiatives have gone forward incorporating gravity. Some people think that these new geometrical models, the final dream of Father Albert, may indeed synthesize all our fundamental physics understanding. But it has not yet coalesced, and nobody knows if it will succeed. Anyway, in such models, one imagines that the present standard model and all we know about elementary particles will drop out as an approximation at ordinary energies.
Whatever the model, one sees in Figure 1 that the masses of all the charged fundamental fermions (quarks and charged leptons), lie within a rough band in energy, ranging from ½ MeV for the electron to 180 GeV for the top quark, a factor of 360,000. Up to now we have not discussed the carriers of the forces, which are so-called bosons, indivisible particles with integer spin. The photon (light, radio waves, x-rays and gamma rays) carries the electrmagnetic force, the gluon the strong force holding quarks in protons and neutrons, gravitons for gravity, and the W and Z particles the weak interaction. The only ones with mass, peculiarly, are the W and Z at roughly 85 and 96 times the proton mass, and about half the top quark mass.
When you look at a stellar spectrum, that is a graph showing the strength of the colors from a star, it looks to be a terrible mess, peaks in chaotic abundance. However, beginning in the last century people found patterns characteristic of each element (eg. the famous phenomenological Balmer formula) and the these patterns led to atomic theory (as well as allowing us to determine that the material of distant stars is the same as here, and even to discern relative atomic abundances in those stars). One hopes for a Balmer formula for elementary particle masses, but we do not have such as yet. Nonetheless, we see the general scheme, the nearness of the W and Z to the heavy quark masses, so we suspect that this mass scale will fall out somehow from a forthcoming GUT. As we have seen in the past in atomic and nuclear physics, the patterns of atomic and nuclear levels can be rather complicated upon first inspection, only getting to their final values after corrections upon corrections from the simplest picture (due to complications such as spin and relativity).
We also know of a large mass scale, at around 1019 times the proton mass, known as the Planck mass. A particle of this mass would be a little black hole, and surely the usual laws of quantum mechanics will need modifying. At somewhat less than this energy (mass) scale we have reason to believe that the other forces of nature would all become of equal strength. The general picture is that after the start of the Big Bang the temperature was so high that all particles existed in a fantastic cosmic chowder, with particles in equal abundances and interacting with equal strengths. As expansion and cooling took place the forces took on their present various strengths and the heavier particles decayed leaving ultimately only protons, neutrons, electrons, photons and neutrinos. Within the context of the present standard model we have evidence that the weak, electromagnetic and strong forces appear to converge at an energy (or equivalent temperature) of order of 1014-16 proton masses, and this is known as the GUT scale. So, somehow, in descending from the GUT scale, the particle masses must get sorted out.
Neutrino Masses are Important
Ever since Pauli's proposal for the neutrino's existence it was known that neutrino masses were not large. Direct 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, 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.
Since, there was no evidence to suggest a non-zero neutrino mass at all until recently, it has thus been assumed that the neutrino mass was precisely zero in the standard model. As we shall shortly discuss, the atmospheric neutrino evidence of the last year suggests almost inescapably that at least one neutrino has mass, of the order of 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.
Note that even small neutrino masses are of cosmological importance. 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!
Yet this total neutrino mass seems not enough to provide the missing dark matter, which may be twenty to one hundred times the mass of all the stars and neutrinos. Since the oscillations measurements provide only mass differences, it could be that all the masses are rather close together, say at 2 eV. Then indeed neutrino mass would dominate the universe. This seems at present the unlikely solution, but we cannot rule it out. The betting would be for the masses to be nearer the lower limits, close to the differences. As illustrated in Figure 1, this would leave the third generation neutrino with about 0.07 eV, the second generation neutrino with of the order of at least 2 x 10-5 eV, and by extrapolation, the first neutrino mass at something of the order of 10-(7-9) eV.
So finally we are in a position to see why the most likely neutrino masses pose such a quandry for theory. Zero mass would have been simple, and would somehow have dropped out of the hoped for GUT. Now we are coming towards a strange situation where the neutrino masses may be as far below the charged fermion masses as are the latter below the unification mass, twelve to fourteen orders of magnitude down. Fortunately this is exactly what was predicted in some rather general considerations made nearly thirty years ago, and known as the "see-saw" model. Unfortunately this is rather more of a scaling argument than a theory, but nonetheless encouraging, pointing the finger at unification for understanding the tiny neutrino masses.
Mixing Particles Up
Quantum mechanics presents a strange view of our world on the sub-microscopic scale. There are lots of phenomena which seem weird to us from our vantage point of typically ten orders of magnitude or so larger than the quantized orbits of electrons in atoms. Every beginning physics student suffers from the mind-boggling particle-wave duality. But that is what we have to work with... this is not reality, it is our model of reality and it works very well quantitatively, and has resulted in much of our modern world, most notably the ubiquitous computer and communications technologies. One of these quantum mechanical peculiarities is particle mixing, and the related lovely phenomenon of neutrino oscillations.
In quantum mechanics one describes the state of a particle as a wave function. What constitutes this wave has been the source of endless debate, but it is the square of this wave function which tells us the probability of something happening. I do not want to present a discourse on quantum mechanics here, but simply to say that Schrodinger's famous equation tells us how to propagate that wave in space and time, which is to say how a particle moves. Now it is the case that a quantum mechanical state can be the sum of several states in which the system could be. Let us suppose that the muon neutrino (defined by that produced by pion decay into a muon and muon antineutrino) is actually the sum of two different states of the underlying neutrino mass states (which are nearest to what one intuitively thinks of as the "real" particle). This seems very odd, but is perfectly allowable, and probably the case with both neutrinos and quarks.
These quantum mechanical waves have a definite frequency, determined by the total energy of the neutrino (including rest mass, if any). The result of a differing mass will be beats between the two component waves, just as one hears beats between two tuning forks of nearby pitches. The beat frequency goes as the mass difference between the states. Due to relativity, the beats are like the ticking of a clock in a fast space ship as we all learned about in studying Father Albert's relativity. Clocks in fast passing space ships appear to be slowed to us, and so also does the beat frequency between neutrino mass states as they fly along. The slowing factor is just the energy divided by the average mass. Hence the net result is that the beating, or oscillation, will be observed by us as proportional to the difference of the square of the masses, times the time (or distance), divided by the neutrino energy. The parameter of distance over energy, L/E, is thus key to searching for neutrino oscillations, and hence indications of finite neutrino mass. The formulae are illustrated in the box and accompanying figures.
Quarks Do It Too
It has been know for several decades that the quarks are also "mixed up". Since the masses are huge in comparison to neutrinos, and generally the heavier particles fall apart right away, we do not see oscillations phenomenon. We do see one instance though, in the mysterious system involving neutral kaons (which are now known to be composed of d and s quarks), in which oscillation are observed. In making sense of the decay patterns of the quarks people were driven to making a matrix called the Cabibbo-Kobayashi-Maskawa (CKM) matrix, which describes the tilting of the quarks physical mass states versus their weak interaction states. This is a pretty strange business, but much as we described for neutrinos above. Let me emphasize that we have no top-down theoretical model which gives us this phenomenological (and compact) description of the coupling of the quarks. One of the characteristics of this matrix is that the angles are relatively small. (For years I have asked my model building bretheren about guidance for where to seek neutrino oscillations and the answer has until quite recently been to look for small angles such as seen in the quarks.)
Another feature of the CKM matrix is what is called "CP violation". This is a long story which cannot be retold here (ref), but the essence is that there are some decays in the kaon system and now seen in the b quarks (whence all the activity in building b factories at SLAC, KEK and elsewhere), which imply terms in the CKM matrix which are "complex quantities". The latter means that they involve an internal angle as well as a magnitude. The consequence of such terms is decays which violate microscopic time reversal invariance. [This has nothing to do with the arrow of time in our lives.] The operations of C for charge inversion, P for parity or mirror reversal and T for time reversal, when combined into CPT are thought to hold under extremely broad circumstances. Thus if CP is violated, then for CPT to hold, T must be violated as well. Basically this has to do with matter/antimatter symmetry. If you had a telephone and could call someone in another galaxy which you did not know was made of matter or anti-matter could you tell them how to make an experiment which would discern the difference? If CP is violated you could do so, and this is the case. CP violation is also a necessary ingredient, according to the Sakharov criteria, for the generation of the net preponderance (by only 1/2 ppb) of matter over anti-matter in the Big Bang, whence we owe our existence, so this arcane issue has much more grand implications than just a peculiarity of largely irrelevant (to our daily lives anyway) heavy quark decays (as well as being a foot hold perhaps towards a unifying theory).
Oscillations in the Air
So, finally to the story of the experimental evidence. Actually, as with everything in the cosmic ray business, there is a long history, which in this case is a little interesting. The tale begins with the first observations of natural neutrinos in 1967 in the wrold's deepest mines in South Africa by Reines and colleagues, and in the Kolar Gold Fields in India by Miyake, Wolfendale and collaborators. (In fact the first observation was twenty years to the day before SN1987A). At that time the instruments measured a rate a little lower than expected, but nobody made much of that and the 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 of 1030± 2 years. Since 1000 tons of material has 6 x 1032 nucleons, one just needs a large vat of matter to watch carefully for a year or so. The first large instrument was the IMB detector, in a salt mine in Cleveland Ohio. The technique was simple in the extreme: fill a tank with ultra pure water (pure for optical transparency), and surround it with light detectors looking inwards. The detectors of choice are large glass photomultiplier tubes, immersed in the water and connected by cables to the electronics nearby. 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 ¾ 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 charateristic "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 identified, 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).
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, such as an experimental inefficiency in the detection of the muon decay signal, possible problems with the neutrino flux calculations, possible problems with interaction cross section calculations, explanation as an excess electrons from proton decay or extra-terrestrial neutrinos, etc. 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 at then supportable.
Not long thereafter the Kamioka group came on line with a smaller but deeper and more sensitive detector in Japan. Having one of the graduate students from IMB working for them, they knew the details of the IMB peculiar results (and they had IMB computer code). 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 accuracy.
The ratio of muon to electron neutrino events turns out to be a rather simple quantity to calculate, and not susceptible to much uncertainty. The reason is as follows, and as illustrated in Figure 3: cosmic rays with a few GeV of kinetic energy, entering the atmosphere strike nuclei of nitrogen or oxygen and make a spray of secondary particles, most of which are pions. The pions (nearly equal numbers of positive and negative) decay into a muon and muon neutrino (positive and negative, neutrino and anti-neutrino). As it happens the muon gets most of the energy of the decay. At energies lower than around 10 GeV, most of the muons decay after flying some distance in the air. (At higher energies they penetrate into the ground, and the highest energy muons go event to the greatest depths of any mines). The muons decay results in an electron (or positron) and two neutrinos (one neutrino, one anti-neutrino), and conveniently the energy is roughly shared between particles. Hence on average, for each charged pion produced by the incoming cosmic ray there result two muon neutrinos and one electron type neutrino (and the same for anti-neutrinos). So 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.
The Kamiokande group, having found a low ratio began claiming to have discovered neutrino oscillations. This claim was heard by the community, but not taken very seriously, since there were other more prosaic possibilities. First, the statistics were not overwhelming in the 80's. Next there was the possibility of some problem with the water Cherenkov detection technique, since the peculiar evidence, which came to be known as the "atmospheric neutrino anomaly", was not found in several smaller instruments in Europe (Frejus and NUSEX) which detectors were of the style more typical of accelerator based instruments, being of a linear design of layers of plates and electronic track sensing. Most importantly the target material was not water but iron, so this suggested some peculiarity in the water as a target.
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. Kamiokande had a veto layer around the outside (which IMB did not), and this facilitated a clean sample of "partially contained" events, as they are called. Now since the neutrinos coming from the other side of the world have had more time to begin oscillating, one may hope for an angular variation of the sample and this is just what was seen by Kamiokande, a deficit in the apparent rate of upcoming muon neutrinos. Yet, still the evidence was weak, because the statistics were not good enough to rule out no angular variation, but it certainly appeared suggestive. Also, people wondered why the oscillation length should turn out to be just about one earth radius, a strange coincidence but now which made people suspicious of some undiscovered experimental bias.
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 sigmas are 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. 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.
Another detector in a mine, the Soudan II instrumentin 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 European instruments failure to detect the anomaly. So, this is the situation up to about 1996, when SuperK began operations: the atmospheric neutrino anomaly had been around for more than ten years, with roots going back even further, but one could not pin the blame only upon neutrino oscillations with enough evidence to convince the community. Indeed, this author was unconvinced personally that oscillations were the solution, though many in the Kamiokande group were sure.
SuperK Finds the Smoking Gun
The SuperKamiokande 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 the 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 a big jump in collecting power, but there is more than just mass as it turns out. 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 SuperKamiokande 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, 7 and 8. 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. This is a nice quantity to plot since by using the ratio many potential systematic errors will cancel out, and moreover one does not need and fancy calculation to see the trend of the data. Simply one sees that as a function of the recorded electron momentum there seems to be not much, if anything, going on. The events are up-down symmetric, as demanded by geometry in the absence of oscillations or other unexpected phenomena. (We should mention that this asymmetry is a little spoiled by the not very symmetric effects of the earth's magnetic field, which bends the cosmic ray trajectories coming into the atmosphere, and even bends the muon tracks. However, the effect is mostly at the lowest energies, below about 400 MeV/c, and fortunately not a problem for the phenomenon we do see, as follows). For the muons, on the other hand, the departure from expectations is dramatic, with a large asymmetry setting in at low momentum, and plateauing at about one third, which corresponds to a deficit of nearly one half for the upcoming muons, and telling us straight away that the oscillations must be most surprisingly nearly maximal. This indeed is what one would expect for oscillations, and as indicated by the dashed curve, such a hypothesis does fit the data. This eliminates some hypotheses which could not be eliminated earlier, for example, that the ratio of events was not deficient in muons but excessive in electrons, as might have arisen from an extraterrestrial source of electron neutrinos, or even from electrons coming from some weird nucleon decay mode. Of course, this evidence 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 plot the data in terms of the L/E of each event. Now the flight distance L is determined by the measured zenith angle of the events, which is not the angle of the neutrino arrival (varying by 30 degrees or more near the lower end, though better at the higher energies), and neither is the detected energy E the neutrino energy, being half on average. So, sadly, one cannot expect to see real oscillations on such a plot as the wiggles are all smoothed over, but since we span such a large range in energy (few hundred MeV to tens of GeV) and distance (from 10 km to 13,000 km), the reach in L/E> spans nearly five decades, a range not achievable elsewhere (eg., at accelerators). One sees that indeed, as expected from the earlier plots, the data divided by expectations does follow a ski slope form, going from no oscillations at small L/E, to saturated oscillations at large L/E. From this plot, by looking at the region of the drop in L/E> one can determine the mass squared difference, and looking at the value (once again of the plateau, one can determine the mixing angle, again maximal. The dashed curve as before indicates the fitted oscillation hypothesis. A point which has not been widely noted is that this plot shows the statistically most dramatic departure from the expectations of no oscillations (amounting to about 20 sigma equivalent), as compared to other projections. Giving the highest contrast, this points at L/E> being the correct physics variable for the phenomena under scrutiny.
The Pieces Fall Together
But, is it oscillations, one may well ask? Indeed what has been shown above is sufficient to "explain" the anomaly, but perhaps not unique. Could there be another explanation? As in much exploratory science, we must proceed here like Sherlock Holmes, eliminating all hypotheses until we are left with only one, however initially seemingly unlikely (hopefully). 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, and I am partially to blame for it (ref). This is a model which has one of the neutrino mass states decaying and giving an L/E> plot as shown above. We set up this model as a "strawman" intending to eliminate it, but found to our surprise that it could just barely survive, so we published it. I do not much like the model as it involves neutrino mass, oscillations and decay, and certainly must be disfavored by Occam's Razor, but it is still a possibility (though nobody 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 since we made the announcement at NEUTRINO98, the data and analysis have only become more reasurring 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 to see. (In any case that low energy regime has no effect upon our main conclusions about muon neutrino oscillations.)
There is supportive evidence for the SuperK contained data, from the through-going muons which originate from neutrinos af 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).
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. First of all, our data indicates 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 (and indeed might be in a parallel universe where parity is violated the other way than in our universe). Anyway, 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.
Solar Neutrinos Probably Also Do It
Due to space limitations this article cannot include a full discussion of the grandfather of neutrino "problems", the solar neutrino deficit, which has existed since Ray Davis started analyzing data from his radiochemical measurement of the rate of solar electron neutrinos detected in a gold mine in South Dakota 30 years ago. The predictions of John Bahcall and other theoreticians have always been in excess of measurements, though as the models have evolved to more sophistication over the years, the predicted rates have come down a bit. Still nobody has been able to make a solar burning model which explains the Davis experiment, or the several other experiments (including SuperK). Again there are alternative hypotheses as to what might be becoming of the neutrinos enroute from the sun to the earth, but most people are convinced that it is not a problem with the solar neutrino production model, and that oscillation are the leading suspect. SuperK records not only total solar neutrino rate, as do the radiochemical Gallium experiments (SAGE and GALLEX) and the Chlorine experiment of Davis (now Lande), but also energy distributions, and possible day/night and seasonal variations. At the moment we cannot resolve which of the four possible solutions to the solar problem are correct, and most anoyingly some of the hints are pointing in different directions (eg. as spectal upturn at high energies suggests vacuum oscillations, while some night./day excess suggests the large angle MSW solution). (See article by Bahcall, .....).
In sum we cannot reach a definitive conclusion about solar neutrinos as yet. Oscillations seem the likely solution but we need more data from Superk, and most importantly data from the now operating (as of summer 1999) SNO instrument, and two other detectors under construction, GALLEX and KamLAND, to nail down the answer (we hope).
LSND, Perhaps Now the Most Interesting Result to Check?
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. Moreover they have some apparently confirmatory evidence from the so-called in-flight data. The difficulty with the acceptance of this data by the community is that first of all when initially presented they had seemingly changed the cuts to enhance a signal that suspiciously lurked near the bottom of the detector, just where background might enter. Indeed one graduate student published a dissenting opinion upon the majority claim of oscillations. This type of experiment is well know to be particularly tricky because of working so close to an intense beam, and having backgrounds which track the putative signal. Still further data acquisition and intense scrutiny by the community has failed to identify any problem.
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. This is a most unhappy situation for the LSND collaborators, who have claimed the first observation of neutrino oscillations, but cannot meet the stiff requirements of the scientific community. A follow up experiment named Mini-BOONE will be run at higher energies at Fermilab in about 3 years. While this may settle the issue in the positive sense, should they see a signal, eliminating it may not be so easy since at higher energies there is irremoveable background (due to decays of kaons and such), and the even in the best situation the expected signal to background is small.
Scientifically, the LSND result if correct can have tremendous implications. Nobody has been able to make an oscillations model incorporating oscillations from atmospheric neutrinos, solar neutrinos and the LSND results. If the LSND group is right we are apparently going to need more neutrino types or some other dramatic physics. Thus, to my view, Mini-BOONE may be now the most important experiment on the neutrino horizon. Confirming or laying the LSND claims to rest is going to take quite a few years, pointing out once again that this business is not for the impatient!
Whither Goeth the Neutrino Hunters?
So, here we are in mid-1999, with nearly conclusive evidence that muon neutrinos oscillate with tau neutrinos, that the mass difference is around 0.05-0.07 eV, and that amazingly the mixing is maximal or very close to it. Probably, but not yet surely, the solar neutrinos oscillate, and with a smaller mass difference. I think it is now the case that particle physicists now accept the reality of oscillations and neutrino mass, with some appropriate cautions of course. What then needs to be done next?
First we need to nail the lid on the muon neutrino oscillations. The K2K experiment now underway shooting neutrinos from the KEK accelerator laboratory to SuperK, 275 km away in Japan, will most likely reinforce the SuperK results, but does not have enough energy or intensity to make much progress (my opinion). The upcoming MINOS experiment, with neutrinos from the 200 GeV machine at Fermilab being aimed at a new detector in the Soudan mine in Minesota will further confirm the SuperK results, but I despair of much progress taking place. The several things needing doing are actually seeing oscillations (an L/E> plot that has multiple peaks not just a ski slope), and even better seeing the appearance of the tau neutrino. The latter is an exceedingly tough business, as discussed earlier. At the moment the only hope for MINOS to see such tau appearance is through the addition of an (not budgeted, designed, tested, or even with precedented) 100 ton front detector made of photographic emulsions to enable seeing the 0.1 mm or so of tau flight prior to decay which would constitute the indisputable signature.
The European high energy community has been slow to respond to these new developments, focussing, rather like the drunk looking for his keys under the streetlight, on searching for neutrino oscillations at very small mixing angles but unrealistically large (in my viewpoint) masses, because these experiments were possible using the existing machines and laboratory dimensions. Perhaps I am unfair, but anyway the European community has been struggling to decide where they can put effort into this new beach head for particle physics, and it appears that one or more experiments will soon be approved for operation in the Gran Sasso laboratory, 745 km distant from the accelerator
Laboratory at CERN near Geneva, Switzerland (and oddly the same distance as that for Fermilab-MINOS). As far as I know at this time, no experiment will actually be able to see oscillations and the prospects for direct tau appearance observation are not great, but the ensemble will surely tighten up the measurement of the oscillation parameters, and help start filling out the CKM mixing matrix for neutrinos.
One of my favorite prospects for a new detector is a spherical version of an instrument being developed by Tom Ypsilantis and colleagues, at CERN and in Italy, called Aqua-RICH. Ring Imaging Cherenkov detectors can be used to make effective particle identification, and have done so in many collider detectors. The Aqua-RICH idea involves scaling these techniques up to a massive water Cherenkov detector. In my favorite version this would consist of a 125 meter spherical diameter tank of ultra-pure water with pixillated PMTs looking outwards from a concentric supporting structure of half the radius to the mirrored outer sphere. The outer sphere would have PMTs as well at the interstices of the segmented mirror elements. This instrument would have the capability to detect real oscillations by identifying higher energy charged current muon neutrino interactions in which the recoil proton is also seen and identified. Aside from oscillations such an instrument would permit many other measurements, as with the previous generations of water Cherenkov detectors, including the prospect of taking nucleon decay search to the theoretically interesting range of 1035 years. Where to put such a detector is however not a solved problem. Mining seems to be too expensive, and the notion of putting it in the ocean frightens many people.
In the longer run the big push seems to me likely towards exploring the neutrino sector for evidence of CP violations. That is assuming that the LSND result goes quietly away.... if LSND is right, this could send us off into complete terra incognita. As we discussed above about the quarks, CP violation can exist in neutrinos as it does with quarks. Indeed as with the mixing angles it may be very large, so poor are our experimental constraints at present. There is reason for paying attention to this, again, aside from tipoffs to the GUT theory, and that is that presently some theoreticians claim that the early part of the Big Bang will anneal any asymmetries generated in the quark sector during cooling, and hence no hope of matter/antimatter excess from that mechanism as we thought was the case twenty years ago. One possibility for generation of the tilt between matter and antimatter comes from the neutrinos! (Indeed as far as I know it is the only currently viable suggestion). So, we must start trying to look for differences in the interactions and oscillations between neutrinos and anti-neutrinos. The reader may well imagine without prompting that this is not going to be easy. It appears that the cosmic rays may not be useful since they are of such a mixed composition. Accelerators seem to be required, and to my present understanding the best venue seems to be the new initiatives in muon accelerators where we can get quite pure beams of neutrinos or antineutrinos. Like everything else in the neutrino business this is not an endeavor for those who seek quarterly returns!
Still to my taste neutrino studies are the most exciting in particle physics and astrophysics (of course I am biased). We have evidence for a whole new sector of interesting particle behavior, the implications are vast for particle physics and cosmology. Every day one can look forward to the possibility of finding something which will be of great importance in the history of science just lurking in the data, ripe for plucking by the ready mind. In particle physics it does not get any better than this, and the fun goes on!
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, crossection of mountain.
6) Up-Down asymmetry versus momentum,
7) Angular distribution.
8) L/E> distributions.
9) dm2 versus s22th.
Box: Illustration of oscillation equations and graph of oscillating probability versus L/E.