Discovery of neutrino oscillations

Transcription

1 INSTITUTE OF PHYSICS PUBLISHING Rep. Prog. Phys. 69 (2006) REPORTS ON PROGRESS IN PHYSICS doi: / /69/6/r01 Discovery of neutrino oscillations Takaaki Kajita Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa-no-ha 5-1-5, Kashiwa, Chiba , Japan Received 26 November 2002, in final form 6 February 2006 Published 8 May 2006 Online at stacks.iop.org/ropp/69/1607 Abstract Neutrinos are very special particles. Studies of these particles have played a crucial role in the understanding of the laws of elementary particles and their interactions. Until recently, there was no evidence that neutrinos have masses, and therefore the standard model in elementary particle physics assumed that neutrinos are massless. Small but non-zero masses of neutrinos have been discovered by studying neutrinos produced by cosmic ray interactions in the atmosphere. The small neutrino masses have profound implications for our understanding of particle physics and the universe. This paper discusses the discovery of neutrino masses. (Some figures in this article are in colour only in the electronic version) /06/ $ IOP Publishing Ltd Printed in the UK 1607

2 1608 T Kajita Contents Page 1. Introduction Atmospheric neutrinos Early indication of neutrino oscillations Discovery of neutrino oscillations in Super-Kamiokande From the discovery to studies More data Detecting tau neutrinos Observing oscillation Long baseline neutrino oscillation experiments Future directions Summary 1634 Acknowledgments 1634 References 1634

3 Discovery of neutrino oscillations Introduction In June 1998, at the 18th International Conference on Neutrino Physics and Astrophysics (Neutrino 98) held in Takayama, Japan, about 400 neutrino physicists heard that data from an underground neutrino detector, which is called Super-Kamiokande, showed evidence of the oscillation of atmospheric neutrinos [1, 2]. This was truly a new discovery in elementary particle physics. Since that moment, physicists working in neutrino physics, or more broadly in elementary particle physics, have been very excited about the research on neutrinos. A neutrino is a particle introduced by Pauli in 1930 [3] in order to secure energy, momentum and spin conservation in nuclear beta decays. Neutrinos are one of the most abundant particles in the Universe. They are, however, very difficult to observe. They have no electric charge, hence they do not feel any electromagnetic force. Likewise, they do not feel the strong nuclear force by which nucleons are bound to a nucleus. Neutrinos feel only a weak force, which is indeed very weak. The consequences are very significant. If a neutrino is produced, it travels straight into any matter as if it is travelling in a vacuum. It seldom interacts with matter. For example, a neutrino produced in the Earth s atmosphere can easily travel through the whole Earth. The probability of a neutrino thus produced interacting somewhere within the Earth is about 0.001%. Thus, % of them penetrate through the Earth and continue travelling in the Universe. It is, however, important to note that the probability of neutrino interaction in matter is not exactly zero. Physicists realized that it is possible to observe neutrinos. If the probability of a neutrino interacting within the Earth while travelling through it is 0.001%, the probability of a neutrino interaction in a 1.28 m thick particle detector (with the same density as the Earth) is 0.001% (1.28/ ) = %, namely one per trillion. This number suggests that it must be possible to observe the interaction of a neutrino, if the total number of neutrinos passing through the detector is one trillion, i.e ! Tremendously large numbers of neutrinos are produced in various places in the Earth and in the Universe. For example, nuclear power reactors produce large numbers of neutrinos as the by-product of nuclear fissions in reactors. It is also possible to produce neutrinos using beams of high energy protons, which are generated by large accelerators. Indeed, the existence of neutrinos was first confirmed by observing interactions of neutrinos produced by a nuclear power reactor in the mid-1950s [4]. Following this in the early 1960s, neutrinos produced by beams of high energy protons were also observed [5]. Since it has been extremely difficult to observe neutrinos through their interactions with matter, the details of the properties of neutrinos have not been known. However, even in the early 1960s, it was known that the interaction of a neutrino produced by a nuclear power reactor only produced an electron, or more exactly, a positively charged electron (positron, e + ). On the other hand, the interaction of a neutrino produced by a beam of high energy protons only produced a muon, a particle similar to but about 200 times heavier than an electron. From these observations, people realized that there are two types of neutrinos; they are called electron-neutrinos (ν e ) and muon-neutrinos (ν µ ). An electron-neutrino produces an electron when it interacts with matter. Likewise, the interaction of a muon-neutrino produced a muon. The pairing of the two particles, namely (electron and electronneutrino) and (muon and muon-neutrino), was well established by various experimental and theoretical works. Since this pairing looked so promising, many people thought that there must be yet another type of neutrino, when the tau particle was discovered in the late 1970s. A tau is also similar to an electron, but is nearly 20 times heavier than a muon, or 4000 times heavier than an electron. The tau neutrino (ν τ ) was discovered recently as expected [6].

4 1610 T Kajita A remarkable feature of neutrinos is their masses. As an example, we consider beta decay of tritium, i.e. 3 H. A 3 H decays to a 3 He, a e and an anti-electron-neutrino ( ν e ). If the mass of the neutrino is heavy, one naively expects that the maximum energy of the observed electron is lower than that in the case of a massless neutrino. All the experiments which observed the energy spectrum of the electrons very accurately showed that the mass of the neutrino is consistent with zero within the experimental resolutions. These results suggested that neutrinos could be massless. Indeed, the standard model of elementary particle physics has been formulated assuming that the mass of the neutrinos is exactly zero. The standard model of particle physics is the theory of the strong, weak and electromagnetic interactions of elementary particles. It has been extraordinary successful in explaining all the existing data from recent particle physics experiments that have been carried out using high energy accelerators. On the other hand, it has also been recognized that there is no strong theoretical base that postulates a vanishing neutrino mass. Therefore, there have been continuing experimental activities to search for a non-zero neutrino mass. One of the methods is to study neutrino oscillations, a phenomenon that a neutrino produced in a definite type (for example, ν µ ) is to be observed in a different type (for example, ν τ ) after travelling some distance. Neutrinos may not be exactly massless. In quantum mechanics, it is possible that a type of neutrino (for example ν µ ) does not have a unique mass. Instead, it is generally possible that it (for example, ν µ ) is a mixture of several (probably three) mass states with definite masses. In this case, neutrino oscillations occur, where the original type of neutrino (for example ν µ ) changes to a different neutrino type (for example ν τ ) after travelling some distance [7, 8]. After travelling even further this type of the neutrino becomes the original one (for example, ν µ ). This way, the type of the neutrino oscillates, and therefore this phenomenon is called neutrino oscillation. The probability that a neutrino of one original type (for example, ν µ ) will be observed as a different type (for example, ν τ ) after travelling a distance of L with the energy of E ν is a function of the neutrino mass (or more exactly the difference of the neutrino masses squared ( m 2 ), namely m 2 νj m2 νi, where m νi and m νj are the masses of the ith and jth mass states of definite masses). Therefore, by measuring neutrino oscillation probability as a function of neutrino flight length or neutrino energy, it is possible to get information on the neutrino mass. When a massive ν µ propagates, is it possible that the neutrino type is completely changed to ν τ at a specific flight length L? The answer is yes, only if ν µ contains both ν 2 and ν 3 mass states in equal amounts. This is a special case. In general, the fraction of the ν 2 and ν 3 components in ν µ is not equal. The fraction of the ν 2 and ν 3 components in ν µ is mathematically expressed by introducing a mixing angle θ. If ν µ is composed of ν 2 only, the mixing angle θ is 0.Ifν µ is composed of ν 2 and ν 3 with an equal fraction, the mixing angle θ is 45.If ν µ is composed of ν 3 only, the mixing angle θ is 90.Ifθ is 45, the initial type of neutrino (for example ν µ ) will completely oscillate to the other type of neutrino (for example ν τ ) when the neutrino travels a specific distance L. If θ is not 45, there is always the probability of observing initial neutrino type whatever L is. If θ is either 0 or 90 s, the type of neutrino to be observed at any distance L is always identical to the initial neutrino type. In summary, assuming neutrino oscillation is purely between ν µ and ν τ, the probability of a ν µ surviving as ν µ after travelling some distance L is expressed as P(ν µ ν µ ) = 1 sin 2 2θ sin 2 ( 1.27 m 2 L E ν ). (1) The ν µ which disappeared has now oscillated to ν τ. Neutrino oscillation is a very powerful method to study small neutrino masses. For simplicity, we assume that m 2 νi m2 νj. Thus, we assume that neutrino oscillation experiments approximately measure the neutrino mass itself, since m 2 νj m2 νi is approximately equal to

5 Discovery of neutrino oscillations 1611 m 2 νj. For example, if the neutrino mass m νj is 1 ev/c 2 (namely, about times lighter than an electron, which is the lightest matter particle except for the neutrino), the length where the initial ν µ with the energy of 1 GeV will be most oscillated to ν τ for the first time is 1.24 km. This length is proportional to the neutrino energy and inversely proportional to the neutrino mass squared. Therefore if the energy of ν µ is 10 GeV, the corresponding length is 12.4 km. If the neutrino mass m νj is 0.1 ev, the corresponding length for 1 GeV neutrinos is 124 km. This way, by observing the length at which neutrinos with known energy change their type, one can determine the neutrino mass, or more exactly the difference in the neutrino masses squared. Motivated by the prediction of neutrino oscillations and by the importance of neutrino masses, there were many neutrino oscillation experiments starting from around the 1980s. Most of them used neutrinos produced by accelerators and reactors. No convincing evidence for neutrino oscillations was discovered. These accelerator experiments typically had a neutrino energy of around 1 GeV and a neutrino flight length of about 1 km. The reactor experiments had a typical neutrino flight length of less than 100 m and a typical neutrino energy of a few megaelectronvolts. Therefore these experiments had a typical sensitivity in m 2 larger than 0.1 to 1 (ev/c 2 ) 2. Later, we sometimes write the unit of mass as ev rather than ev/c 2 for simplicity. Therefore, m 2 = 1 (ev/c 2 ) 2 is then written as m 2 = 1eV 2. Equation (1) indicates that if one wants to observe small neutrino masses, one needs to observe neutrinos that travel long distances. One such example is neutrinos that are generated by cosmic ray interactions in the atmosphere. The flight length of the neutrinos ranges up to km, the diameter of the Earth. Indeed, the small neutrino mass was discovered by the study of these neutrinos. 2. Atmospheric neutrinos A cosmic ray is a radiation of high energy particles arriving at the Earth from the Universe. These cosmic ray particles are mostly high energy protons, about 5% are helium nuclei and a still smaller fraction of heavier nuclei. (Electrons and photons are also a part of the cosmic rays, but since these components have nothing to do with neutrino production, these particles will not be mentioned later.) The energy spectrum of these particles extends to very high energies, although the flux of these particles decreases rapidly with increasing energy. These particles, once they enter into the Earth s atmosphere, interact with the nuclei (most of which are nitrogen or oxygen) in high altitude atmosphere. Typically, in these high energy nuclear interactions, many π mesons, and less abundantly K mesons, are produced. Since these mesons are unstable, they decay into other particles. For example, a π + decays into a muon (µ + ) and a ν µ. The produced muon (µ + ) is also unstable and decays into a positron (e + ), an anti-ν µ and a ν e. A similar decay process occurs for π and K mesons. In this manner, neutrinos are produced when a cosmic ray particle enters the atmosphere: figure 1, which shows schematically the production of neutrinos in the atmosphere. These neutrinos are called atmospheric neutrinos. If we study the processes of neutrino production, we find that 2 ν µ plus anti-ν µ and 1 ν e (or anti-ν e ) are produced for every charged pion decay. Since the energies of these neutrinos are almost equal, one finds that the flux ratio of (ν µ + anti-ν µ ) and (ν e + anti-ν e ) should be approximately 2. This ratio is calculated to be very close to 2 by detailed calculations of the neutrino flux. The accuracy of the calculated ratio is estimated to be about a few per cent. It turned out that this flux ratio is a very good indicator for neutrino oscillations, since if neutrinos oscillate, this ratio should deviate from the predicted ratio. Indeed the first serious indication for neutrino oscillation was obtained by the study of this ratio, as described later. Later in this paper, both neutrinos and anti-neutrinos are called neutrinos for simplicity.

6 1612 T Kajita Figure 1. Production of neutrinos by cosmic ray interactions with an air nucleus in the atmosphere. The typical height of the neutrino production is 15 km above the ground. Flux E ν 2(m -2 sec -1 sr -1 GeV) Honda flux Bartol flux Fluka flux E ν (GeV) Figure 2. Calculated energy spectrum of the atmospheric neutrino flux by three independent groups [9 11]. Since the energy spectrum is very soft, we multiply the fluxes by E 2. Figure 2 shows the energy spectrum of the atmospheric neutrino flux calculated by three independent groups. The primary cosmic ray flux falls rapidly with increasing energy; the flux decreases with the energy by approximately E 2.7. Therefore the calculated neutrino energy spectrum rapidly decreases with increasing energy. Figure 3 shows the calculated (ν µ + ν µ )/(ν e + ν e ) flux ratio as a function of neutrino energy. It is clear that the ratio is approximately 2 below about 1 GeV, where most of the muons produced by the pion decays are expected to decay before reaching the ground. Above this energy, the ratio increases. It is also clear that the ratio is calculated very accurately, since the results from three independent calculations agree well. Another important feature of the atmospheric neutrino flux is the up down symmetry. The neutrino thus produced that enters the Earth at a point pos in with a zenith angle θ in should exit the Earth at a point pos out with a zenith angle θ out. Obviously, θ in and θ out are related by

7 Discovery of neutrino oscillations 1613 Flux ratio Honda flux Bartol flux Fluka flux 2 ν µ +ν µ /ν e +ν e E ν (GeV) Figure 3. Calculated (ν µ + ν µ )/(ν e + ν e ) ratio of the atmospheric neutrino flux as a function of the neutrino energy by three independent groups [9 11]. θ out = 180 θ in. Since the cosmic ray enters the atmosphere with approximately the same rate at every position in the Earth, there must be a neutrino that enters the Earth at a point pos out with a zenith angle θ out, and exits the Earth at a point pos in with a zenith angle θ in. These two processes occur at the same rate as far as the cosmic ray rates in both positions are equal. Thus one can conclude that the flux is up down symmetric. This prediction is very robust. As we will discuss later, the comparison of the up down asymmetry of the experimental data and the prediction gave compelling first evidence of neutrino oscillations. Figure 4 shows the calculated zenith angle dependence of the atmospheric neutrino flux for several neutrino energy ranges. As expected, above about 1 GeV, the flux is up down symmetric. Below this energy, the flux is not exactly up down symmetric. This is due to the geomagnetic field. Low energy cosmic ray particles, typically below 10 GeV are bent significantly by the geomagnetic field and only cosmic ray particles above certain energy, which depend on the position in the Earth and on the direction of the cosmic ray particles, can enter the atmosphere. The flux of the low-energy, downward going neutrinos depends on the local geomagnetic field above the detector. On the other hand, for the flux of the low-energy, upward going neutrinos, the geomagnetic field effect is more or less averaged out by integrating over the whole Earth. 3. Early indication of neutrino oscillations The observation of atmospheric neutrinos started in the mid-1960s. Two experiments that were carried out in extremely deep mines in India [12] and South Africa [13] successfully observed muons produced by atmospheric ν µ interactions. In the 1970s, Grand Unified Theories of elementary particles were proposed [14, 15]. These theories predicted that the strong, electromagnetic and weak forces are unified at the very high energy of GeV. According to the Grand Unified Theories, a proton (and a neutron as well), which is the fundamental constituent of matter, is not absolutely stable and

8 1614 T Kajita Figure 4. Calculated zenith angle dependence of the atmospheric neutrino flux for several neutrino energy ranges by three independent groups [9 11]. While there is an enhancement of the flux near the horizon, the up down symmetry is predicted in the energy range above a few GeVs. should decay within a certain life time. The predicted life time of a proton and a neutron was about years according to the Grand Unified Theories at that time. This means that it is possible to observe about 300 proton decays (or 600 proton plus neutron decays) if one watches 1000 tons of matter for a year, since 1000 tons of matter contain about of protons plus neutrons and since typical matter contains approximately the same number of protons and neutrons. Motivated by this prediction, several proton decay experiments whose detector masses ranged from about 100 to 3000 tons were started in the early 1980s. Unfortunately, these experiments did not show any signal of proton decay. However, the experiments made observations of hundreds of atmospheric neutrino interactions in the detectors. (Hereafter, we call observed atmospheric neutrino interactions events.) For proton decay experiments, atmospheric neutrino interactions are considered to be serious background for proton decays, since a neutrino arrives at the detector without showing any evidence of incidence and may interact with a nucleon, producing visible secondary particles. This signal is similar to that of proton decay, since the signal of the proton decay is also characterized by the sudden appearance of secondary particles somewhere in the detector material. The proton decay signal and atmospheric neutrino background can only be separated by studying the details of the secondary particles. For this reason, these experiments had to study the details of the neutrino interactions. One of these experiments in particular, whose name was Kamiokande, used water as the source of protons (or as the target of neutrino interactions) together with specially produced huge photomultiplier tubes to study the details of proton decay. Figure 5 shows the inside of the Kamiokande detector. When a proton decay or a neutrino interaction occurs inside water, secondary particles are produced. Some of these particles propagate in water with initial speed faster than the velocity

9 Discovery of neutrino oscillations 1615 Figure 5. Inside the Kamiokande detector. The detector had a cylindrical steel tank which contained 3000 tons of pure water. Inside this tank, about 1000 photomultiplier tubes each of whose diameter was 50 cm, were used. The outside of the tank was also filled with water of about 1500 tons, thus the total mass of the detector was 4500 tons. This photo was taken when the Kamiokande detector was upgraded to Kamiokande-II between 1984 and of light in water (but less than that of light in vacuum). If a charged particle propagates in a medium with a speed exceeding that of the light in the medium, these particles emit light (photons), called Cherenkov radiation. The direction of the radiated photons is about 42 away from the direction of the charged particle, if the particle propagates with almost the speed of light in vacuum. Therefore, if one observes the Cherenkov radiation on a wall perpendicular to the particle direction, the image of the radiation shows a ring shape (figure 6). The Cherenkov radiation is a very faint light. However these photons can be observed through the photomultiplier tubes. The number of photons to be observed through the photomultiplier tubes is, of course, proportional to the surface area of the tubes. Therefore, the larger the surface area, the more the information on the particles. For this reason, the Kamiokande, which used 1000 of the largest photomultiplier tubes ever produced, was able to get detailed information on the particles produced by the neutrino interactions. The total mass of the Kamiokande detector was 4500 tons and the central 1000 tons was the fiduciary volume of the neutrino interactions. Only this volume was used for the analysis of the atmospheric neutrino events. One important piece of information on the particles produced by neutrino interactions (or by proton decays) is the type of particles produced. In general, it is possible to separate the particle types into showering and non-showering. An electron produced in the detector by a neutrino interaction propagates in the water producing an electromagnetic shower: an electron propagating in the water (or in any other medium) emits a high energy photon, this photon in the water (or in any other medium) is soon converted to a pair of an electron and a positron,

10 1616 T Kajita Figure 6. If a particle propagates in a medium with the velocity exceeding that of light in the medium, Cherenkov radiation is generated. In the water, if the velocity of the particle is very close to that of light in the vacuum, the Cherenkov photons are radiated in a direction 42 away from the particle direction. which emit high energy photons. Thus the number of electrons and positrons increases making an electromagnetic shower. On the other hand, a muon produced by a neutrino interaction propagates in water in almost a straight manner losing energy slowly. A muon does not produce an electromagnetic shower. The ring image of the Cherenkov radiation due initially to an electron is the summation of the ring images of many electrons and positrons in the electromagnetic shower and shows a fuzzy ring pattern. On the other hand, the ring image due to a muon is only produced by a muon and shows a clearer ring pattern. Therefore, it is possible to separate Cherenkov rings due to a muon and an electron. For this reason, the showering and non-showering Cherenkov rings are sometimes called electron-like (or e-like ) and muon-like (or µ-like ), respectively. How well can one separate Cherenkov rings produced by an electron and a muon? It depends on the amount of information one can get from the ring image, and therefore depends on the number of Cherenkov photons one can observe. The Kamiokande was an ideal detector to carry out this analysis owing to the use of huge photomultiplier tubes. The number of photoelectrons for 1 GeV electrons and muons was about 3000, which is large enough for the efficient identification of electrons and muons. In 1988, the Kamiokande reported the results of the number of non-showering (µ-like) and showering (e-like) events [16]. A muon is produced by a ν µ interaction, and an electron by a ν e interaction. Therefore, counting the number of µ-like and e-like events simply corresponds to counting the number of ν µ and ν e interactions. In order to estimate the expected signal that should be compared with actual data, a Monte Carlo simulation technique is commonly used. In the Monte Carlo simulation, simulated data are generated based on details of known physical processes as well as the detector performance. Then the data and the results from the simulation are compared in order to obtain scientific results. If the data and the simulated

11 Discovery of neutrino oscillations 1617 Table 1. The numbers of e-like and µ-like events observed in Kamiokande in 1988 are compared with the prediction that did not include neutrino oscillations [16]. The detector exposure was 2.87 kiloton year. Only single-cherenkov-ring events were used. About 90% of them were estimated to be due to charged-current ν e and ν µ interactions for e-like and µ-like events, respectively. Data Prediction e-like events µ-like events results do not agree, it could be due to a new physics effect not yet included in the Monte Carlo simulation. As discussed earlier, the ν µ -over-ν e ratio of the flux is accurately predicted. Therefore, the measurement of the ν µ -over-ν e event-ratio should agree with the Monte Carlo prediction. However, the observed data showed significant difference from the prediction, as shown in table 1. One easily notices that the number of e-like events of the data (93 ± 9.6, where the error shows the statistical error) agrees with the prediction within the statistical error of the data. However, the observed number of µ-like events (85 ± 9.2) was much smaller than the predicted number of events. Many researchers thought that this result could not be right, since the ν µ over ν e flux ratio is calculated to a high precision. One can, in principle, explain the data if one assumes neutrino oscillation, since, for example, if ν µ oscillate to ν τ with a large mixing angle, it is possible to explain this down to 50% disappearance of the ν µ events. Atmospheric neutrinos arriving at a detector near the surface of the Earth have flight lengths ranging from about 10 km to km and also the energies of these neutrinos have a certain spread. Therefore, depending on the actual value of the flight length and the energy of the neutrino, ν µ could oscillate to ν τ or oscillate back to ν µ. As a result, only the average feature of the neutrino oscillations could be observed and therefore one can expect at most 50% disappearance. However, at that time, it was commonly believed that the mixing angle between neutrinos must be small since the corresponding mixing angle between the quarks is known to be small. Therefore, for many researchers, it was unbelievable that the mixing angle between neutrinos is very large. Indeed, this was unbelievable to the Kamiokande collaboration as well. Therefore, many checks were done before the publication. The first indication of the deficit of ν µ events was already obtained in the fall of 1986, when a detailed particle identification programme was applied to the single-cherenkov-ring events in the data. For about a year, various details of the analysis were studied to confirm or exclude the initial suggestion. For example, one can imagine that ν µ events were dropped during the data reduction processes for some unknown reasons. Therefore, an independent data selection program was written and an independent data sample was selected from the raw data. No additional neutrino event was found, confirming that the data selection did not have any problem. After one year of such detailed studies, it was concluded that there was no serious mistake in the analysis. Kamiokande concluded in the paper in 1988 that We are unable to explain the data as the result of systematic detector effects or uncertainties in the atmospheric neutrino fluxes. Some as-yet-unaccounted-for physics such as neutrino oscillations might explain the data [16]. This was the beginning of the serious interest in atmospheric neutrinos. It took 10 years to conclude that the observed deficit of ν µ events was due to neutrino oscillations. In spite of the large and statistically significant deficit of the number of ν µ events, the experimental confirmation of this result was not obtained for a few years. There were three other experiments that observed a significant number of atmospheric neutrino events. Two of them used a significantly different technique to detect charged particles produced by neutrino interaction. These experiments directly observed tracks of charged particles

12 1618 T Kajita using a large number of particle counters interleaved with steel plates for the target of the neutrino interactions. Another experiment, called IMB, used the same detection technique as Kamiokande. It had about a factor of three larger fiducial mass, but used smaller 20 cm diameter photomultiplier tubes. In the 1980s, there was no supporting evidence for the ν µ deficit from the other experiments. In the meantime, Kamiokande increased the data statistics. It also improved the Monte Carlo simulation using a more precise neutrino flux model, and data analysis. However the deficit of µ-like events remained (see, for example, [17]). In 1991 and subsequently in 1992, the other water Cherenkov experiment, IMB [18], published the results on the ν µ over ν e ratio of the atmospheric neutrino flux. In the 1991 paper, there was an indication of the ν µ deficit, but the significance of the deficit was not conclusive. IMB, in the subsequent paper published in 1992, doubled the data statistics and showed the statistically significant deficit. Also, the Kamiokande published a second paper in 1992 on this topic including the results of neutrino oscillation analysis [19]. In that analysis, both ν µ ν τ and ν µ ν e were allowed, because the small µ/e ratio can occur for both oscillation channels. However, in both cases, it was clear that a large mixing angle is needed to explain the data in terms of neutrino oscillations. The researchers got more serious after these results, since two independent experiments showed a significant deficit of ν µ events. However, two other experiments that used different target material (steel) and different detection technology (tracking detectors), although with lower statistics, did not observe any evidence for ν µ deficit. Further support for the ν µ deficit came from a newer experiment called Soudan-2. It used thin steel plates for the target of the neutrino interactions, and used very good particle counters to detect the tracks of the charged particles. In 1997, Soudan-2 [20] observed a deficit of ν µ events while the statistics were limited. In the subsequent papers of the Soudan-2 experiment, the deficit got more compelling with the improved data statistics. The observed ν µ deficit or equivalently the small ν µ /ν e flux ratio was called atmospheric neutrino anomaly. More and more researchers showed interest in the the atmospheric neutrino anomaly with time. However, many researchers still did not seriously think that the observed deficit was due to neutrino oscillations. This was due to the fact that the observed effect was only a deviation of the ν µ over ν e flux ratio from the prediction. Many researchers thought that there must be some explanation for the data other than neutrino oscillations with a very large mixing angle. Indeed, the deficit of ν µ events from Kamiokande and IMB did not show any strong zenith angle and momentum dependence. Soon after submitting the first paper on the atmospheric ν µ deficit in 1988, Kamiokande started to select atmospheric ν µ events with energies in the multi-gev range from the raw data recorded on thousands of tapes. (In an earlier analysis, the atmospheric neutrino events selected for the search for proton decay were used. Hence the energy range covered was about 1 GeV or less.) A multi-gev ν µ interaction typically produces a multi-gev muon. These multi-gev muons produced in the detector typically penetrate through the detector, thus reaching the surrounding rock. The Kamiokande, in the second phase, had an anti-counter that surrounded the inner detector completely. Neutrino interactions occurring inside the inner detector and an exiting muon can be identified by a signal in the anti-counter. These events are sometimes called partially-contained neutrino events. Since muons are essentially the only charged particles that can propagate in water for more than a few metres, most of the partially contained neutrino events are ν µ interactions. Kamiokande searched for these events because if the ν µ deficit observed in the sub-gev to the GeV range is due to neutrino oscillations, the deficit should also be observed in the higher energy range, since there is a well known relation in the neutrino oscillation probability

13 Discovery of neutrino oscillations 1619 as a function of neutrino energies (see equation (1)). Furthermore and more importantly, if the observed ν µ deficit was due to neutrino oscillations, the deficit must depend on the neutrino flight length, and therefore on the zenith angle. However, in the energy range below about 1 GeV, the correlation of the neutrino direction with the muon direction is rather poor and most of the zenith angle dependence in the neutrino direction is washed out if one observes the muon direction only. The poor angular correlation can be understood easily if one recalls that the nucleon mass is about 940 MeV/c 2. Namely, for neutrinos with energy below the nucleon mass, neutrino interaction with the nucleon has a propensity to collide with a very heavy object resulting in more or less isotropic particle distribution in the final state. The angular correlation gets substantially better with increasing neutrino energy, and the zenith angle distribution for muons should represent the neutrino zenith angle distribution fairly well for multi-gev neutrino events. As discussed in the previous section, the flux is predicted to be up down symmetric for a simple geometrical reason. On the other hand, if the neutrino oscillation length is about 1000 km for the neutrinos considered here, one expects that the ν µ deficit should be observed in the upward going directions, since the neutrino flight length is much less or much more than 1000 km for downward going and upward going neutrinos, respectively. This could be a very important measurement, since the observed up down asymmetry cannot happen for the nonoscillated neutrino flux. Only neutrino oscillations can explain the asymmetry. Furthermore, if neutrino oscillations are between ν µ and ν τ, the zenith angle dependent deficit can only be observed in the ν µ events. If this is observed, no explanation can be possible within the standard, zero mass neutrinos. Finally, it is possible to estimate the neutrino mass squared by identifying the zenith angle, and therefore the neutrino flight length, where the ν µ deficit becomes significant. It was not particularly difficult to select these multi-gev ν µ events. However, since the flux of the atmospheric neutrinos decreases rapidly as the energy increases, the event rate for such events was only about 20 per year in Kamiokande. It took several more years to collect a statistically meaningful number of such events. Finally, in 1994, Kamiokande reported the multi-gev atmospheric neutrino data [21]. The µ-like data showed a deficit of events in the upward going direction, while the downward going µ-like events did not show such a deficit. Furthermore, the corresponding distribution for e-like events did not show any evidence of the deficit of upward going events, which is in good agreement with the prediction. (In fact, the Kamiokande multi-gev e-like data showed some excess of upward-going e-like events. But it was not statistically significant.) Figure 7 shows the observed zenith angle distributions for multi-gev neutrino events in Kamiokande. The probability that the observed up down asymmetry in the ν µ events could be due to a statistical fluctuation was less than 1%. In other words, the observed up down asymmetry deviated from the prediction by 2.8 standard deviations. It was a very interesting observation, which showed for the first time that the ν µ deficit depends on the neutrino flight length as predicted by neutrino oscillations. However, the statistical significance was not strong enough to be conclusive. Experimental data with adequate statistics were awaited. 4. Discovery of neutrino oscillations in Super-Kamiokande The Super-Kamiokande detector is a larger version of the Kamiokande detector. It is a cylindrical detector 41.4 m high and 39.3 m in diameter, and has the total mass of tons. It is the largest neutrino detector that can study details of neutrino events in the GeV energy range. Like Kamiokande, the Super-Kamiokande detector consists of two parts: the inner detector that studies the details of neutrino interactions and the outer detector that identifies

14 1620 T Kajita number of events cos Θ (a) cos Θ (b) Figure 7. Zenith angle distributions for multi-gev (a) e-like and (b) µ-like events observed in the Kamiokande. shows the zenith angle, cos Q = 1 and 1 represent events whose direction is vertically down-going and up-going respectively. Dots with error bars show the data. Solid histograms show the prediction without neutrino oscillations. Dashed histograms show the best fit to the data including neutrino oscillations. Since there is a large uncertainty in the total number of predicted events, the prediction is normalized by the total number of observed events. Figure 8. Inside the Super-Kamiokande detector. This photo was taken in January 1996 during the construction of the detector. The detector was filled with pure water. Each dot seen on the wall shows a 50 cm diameter photomultiplier tube. About photomultiplier tubes are used for the inner detector. The outer detector is equipped with about cm diameter photomultiplier tubes. the exiting and incoming particles. The fiducial mass is the central tons, and is about 20 times larger than that of Kamiokande. Figure 8 shows the inside of the Super-Kamiokande detector. Due to the larger fiducial mass, Super-Kamiokande can observe the neutrino events approximately 20 times faster than Kamiokande. Furthermore, the images of the Cherenkov rings observed by the photomultiplier tubes make it possible to study the details of the events. Figure 9 shows the charged-current ν e and ν µ interactions with a visible single Cherenkov ring observed in Super-Kamiokande. This feature turned out to be particularly useful for studying neutrino oscillations in detail. The Super-Kamiokande collaboration is an international collaboration from Japan, United States of America, Korea and Poland. Many people from the Kamiokande and IMB

15 Discovery of neutrino oscillations 1621 Super-Kamiokande Run 3003 Event :10:50:45 Inner: 2004 hits, 4749 pe Outer: 2 hits, 1 pe (in-time) Trigger ID: 0x03 D wall: cm FC e-like, p = MeV/c Time(ns) < > Times (ns) Super-Kamiokande Run 3011 Event :07:44:11 Inner: 811 hits, 2338 pe Outer: 0 hits, 0 pe (in-time) Trigger ID: 0x03 D wall: cm FC mu-like, p = MeV/c Time(ns) < > Times (ns) Figure 9. Candidates for charged-current ν e (top) and ν µ (bottom) interactions with a visible single Cherenkov ring observed in Super-Kamiokande. The cylindrical detector is opened flat. The colours indicate the timing of the photon detection and the size of the circles indicates the pulse height for each photomultiplier tube.

16 1622 T Kajita collaborations joined in this experiment. The Super-Kamiokande detector was designed based on the experiences in these experiments with improvements from various technological developments. The Super-Kamiokande detector started taking data in the spring of 1996 after 5 years in construction. The analysis methods for the atmospheric neutrino interactions have been known well through the studies of atmospheric neutrinos in the previous experiments. Furthermore, Super-Kamiokande developed the Monte Carlo simulation and the analysis programs based on those in Kamiokande as well as those in IMB. Therefore, Super-Kamiokande was able to produce reliable results rather quickly. However, it was realized that the analysis program must be fully automated in order to fully utilize such high statistics. In Kamiokande, the number of Cherenkov rings was determined by physicists through an interactive graphic event display. It was possible in Kamiokande since the event rate in Kamiokande was relatively low and the possible systematic effects due to the physicist s bias were likely to be much smaller than the statistical error. However, due to the much higher event rate in Super-Kamiokande, possible bias in the event scanning could be a serious source of systematic errors. In addition, it seemed to be almost impossible to scan both the data and Monte Carlo events visually. Therefore, Super-Kamiokande aimed at making the analysis fully automatic. It took more than a year to prepare the fully automatic analysis. The analysis results based on automatic analysis began to be shown outside the collaboration in the summer of By the spring of 1998, Super-Kamiokande had analysed 535 days of data, or the equivalent of 33 kiloton year detector exposure. The total number of atmospheric neutrino events was 5400, which was statistically about four times more than in Kamiokande. In June 1998, the 18th International Conference on Neutrino Physics and Astrophysics (Neutrino 98) was held in Takayama, a small, historical town near Kamioka, Japan. About 400 neutrino physicists participated in this conference. In this conference, Super-Kamiokande made an announcement of the evidence of atmospheric neutrino oscillations [1, 2]. The evidence for neutrino oscillations was obtained by several measurements. The ν µ /ν e flux ratio was measured with greater precision for both sub- and multi-gev energy ranges, showing significantly smaller ratios than the prediction in both energy ranges. However, the strongest evidence for oscillation came from the zenith angle distribution. The zenith angle distribution shown in Neutrino 98 is copied in figure 10. The left panel of figure 10 shows the zenith angle distribution for multi-gev (namely, the visible energy of an event must be larger than 1.33 GeV) e-like events, while the right panel shows that for multi-gev µ-like plus partially contained neutrino events, where partially contained events are mostly multi-gev atmospheric ν µ events with the produced muon penetrating into the outer detector. It is clear that the deficit of upward going events is observed. The statistical significance was more than six standard deviations, implying that it cannot be due to a statistical fluctuation. There must be some physical mechanism to reduce the number of ν µ interactions for neutrinos that travelled more than several hundred kilometres. On the other hand, the zenith angle distribution for e-like events did not show any statistically significant up down asymmetry. This suggests that the electron neutrinos are detected as expected independent of the neutrino flight length. That is, electron-neutrinos do not oscillate as far as the flight length is less than the diameter of the Earth. It was concluded essentially from this figure that muon neutrinos oscillate to other types of neutrinos, most likely to tau neutrinos. Furthermore, the zenith-angle distributions for upward going muons showed a deviation from the non-oscillated Monte Carlo prediction, another indication of oscillations. Upward going muons are produced by very high energy atmospheric neutrino interactions in the rock below the Super-Kamiokande detector and only the muons produced by the interactions are observed.

17 Discovery of neutrino oscillations 1623 number of events cos Θ (a) cosθ (b) Figure 10. Zenith angle distributions for multi-gev atmospheric neutrino events reported at the Neutrino 98 conference based on 535 days exposure of the Super-Kamiokande detector. The left and right panels show the distributions for e-like and µ-like events, respectively. shows the zenith angle and cos = 1 and 1 represent events whose direction is vertically down going and up going, respectively. Dots with error bars show data. Dashed and bar histograms show the predictions with and without neutrino oscillations. The µ-like events, which are mostly charged-current interactions of ν µ, showed about 50% deficit of upward going events, while the e-like events, which are mostly charged-current interactions of ν e, showed no statistically significant up down asymmetry. The data were analysed assuming ν µ ν τ neutrino oscillations. Figure 11 shows the summary of the oscillation analysis from Super-Kamiokande as well as that from the Kamiokande at the Neutrino 98 conference. Five contours of allowed neutrino oscillation parameters obtained from the Super-Kamiokande and the Kamiokande overlapped, indicating that the data were consistently explained by neutrino oscillations. This was the moment that the atmospheric neutrino anomaly was concluded to be due to neutrino oscillations. It was 10 years after the initial, serious hint for atmospheric neutrino oscillations in There were two other experiments that observed atmospheric neutrinos at that time. One was Soudan-2 which has been taking data since The data statistics were substantially improved compared with those in the earlier publications. In addition, this detector was able to determine the direction of the particles by several methods. Figure 12 shows an example of the events observed in Soudan-2. This experiment confirmed the ν µ deficit as a function of the zenith angle of the event direction [22]. Another experiment was MACRO, which was a large underground detector able to measure upward going muons as well as partially contained neutrino events. Figure 13 shows the MACRO detector. The size of the detector was 12 m 77 m 10 m (height). This experiment also observed the zenith angle dependent deficit of upward going muons and partially contained ν µ events [23, 24]. The results from these experiments were completely consistent with those from Super-Kamiokande, and therefore neutrino oscillation was quickly accepted by physicists working in this field. The observation of non-zero neutrino mass was the first evidence of physics beyond the standard model of elementary particle physics. The standard model of particle physics assumes that neutrinos have zero mass. What will be the implications for physics beyond the standard model? According to the see saw model [25, 26] of the small neutrino masses, the masses of neutrinos and the masses of quark and charged leptons are related simply by; m ν = m2 q m N, (2) where m ν, m q and m N are the masses of neutrinos, quarks and yet unobserved super heavy neutral particles, respectively. If we assume that the observed neutrino mass squared ( m 2 ) is approximately equal to the square of the heaviest mass, one can estimate the mass of the super-heavy neutral particle. One finds that the mass could be as heavy as to GeV/c 2.

18 1624 T Kajita Figure 11. Summary slide of the presentation from Super-Kamiokande at the Neutrino 98 conference. The contours show the allowed oscillation parameters estimated based on various data samples from Super-Kamiokande and Kamiokande. It was concluded that the data from Super-Kamiokande showed evidence of neutrino oscillations. We would like to note that the mass of the heaviest quark, namely the top quark, is only about 175 GeV/c 2, which is to orders of magnitude lighter than that of the super-heavy neutral particle. Therefore, it is commonly believed that the studies of small neutrino masses are indirect studies of physics at very, very high energies. We also would like to recall that the currently estimated energy scale of the Grand Unification is GeV. It is discussed seriously that the two numbers, to GeV from the neutrino mass and GeV from the estimated energy scale of the Grand Unification, are rather close and might be related. That is, the studies of neutrino masses and related physics could be the window to study physics at the energy scale of Grand Unification. 5. From the discovery to studies The data from Super-Kamiokande in 1998 showed that about 50% of muon neutrinos disappear after travelling a long distance, and were commonly interpreted to be neutrinos oscillations. However, there were several unanswered questions, such as what are the values of the neutrino mass squared difference ( m 2 ) and the neutrino mixing angle (θ)?, are the oscillations really between ν µ and ν τ?, does the ν µ disappearance probability really oscillate as predicted by

19 Discovery of neutrino oscillations a-c matched 545 anode vs time Y X X (cm) Z (cm) 979 Figure 12. An example of an event observed in the Soudan-2 detector. A long track from a muon and a shorter, more heavily ionizing track from a recoil proton are visible. µ streamer tube planes scintillator tanks crushed rock absorber ν µ (1) (2) (3) + (4) Figure 13. A sketch of the MACRO detector (left) and the end view of the detector (right), showing various types of atmospheric neutrinos observed in MACRO. the theory of neutrino oscillation?, and is it possible to observe the same effect with different neutrino beams?. As of this writing, the answers to all these questions have been given experimentally More data Super-Kamiokande continued taking data until the summer of After that, the operation of the detector was stopped for a while to replace the dead photomultiplier tubes. After the replacement work, in November 2001 while filling the detector with pure water, the Super-Kamiokande detector had an accident, when more than half of the photomultiplier tubes were broken. It took more than a year to resume operation of the detector with the 5200 photomultiplier tubes that survived the accident. The initial phase of Super-Kamiokande

20 1626 T Kajita Number of Events Number of Events 450 Sub-GeV e-like cosθ Multi-GeV e-like cosθ Number of Events Number of Events Sub-GeV µ-like cosθ Multi-GeV µ-like + PC cosθ Figure 14. Zenith angle distributions observed in Super-Kamiokande-I during 1489 days of the detector exposure (92 kiloton year). Dots with error bars show data. Dashed and solid histograms show the predictions with and without neutrino oscillations. Sub- and multi-gevs fully contained events are defined to show the visible energy below and above 1.33 GeV, respectively. The separation at 1.33 GeV does not have any strong meaning. It was determined by a historical reason, namely Kamiokande initially selected this number to search for contained neutrino events and proton decay. is called Super-Kamiokande-I (SK-I) and the second phase after the accident is called Super- Kamiokande-II (SK-II). Many results have been presented based on the SK-I data, and therefore are described here. The total number of atmospheric neutrino events during the SK-I period was more than [27], which contain about a factor of three more statistics than the data analysed in Figure 14 shows the zenith angle distributions for these events. It is clear that the event statistics have improved significantly compared with the 1998 data, which are shown in figure 10. A determination of neutrino oscillation parameters was carried out using these events. Figure 15 shows the allowed regions of neutrino oscillation parameters ( m 2 and sin 2 2θ)at 90% confidence level (CL). There is a significant improvement in the determination of the neutrino oscillation parameters. m 2 is constrained within about ±20% and sin 2 2θ 23 is determined to an accuracy of 8% and is consistent with the maximum mixing (sin 2 2θ = 1.0). These parameters are much more accurately determined compared with those in We note that the mixing angle is very different for quarks and neutrinos. sin 2 2θ>0.92 corresponds to θ = 37 to 53, while the corresponding mixing angle between quarks is about 2.4. This difference was not expected before neutrino oscillation was discovered. Why are