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Establishing atmospheric neutrino oscillations with Super-Kamiokande
Available online at www.sciencedirect.com
ScienceDirect Nuclear Physics B 908 (2016) 14–29 www.elsevier.com/locate/nuclphysb
Establishing atmospheric neutrino oscillations with Super-Kamiokande T. Kajita a,d , E. Kearns b,d,∗ , M. Shiozawa c,d for the Super-Kamiokande Collaboration a Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiawa, Chiba,
277-8582, Japan b Department of Physics, Boston University, Boston, MA 02215, USA c Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan d Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for
Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan Received 21 February 2016; received in revised form 5 April 2016; accepted 11 April 2016 Available online 16 April 2016 Editor: Tommy Ohlsson
Abstract In this article we review the discovery of atmospheric neutrino oscillation by the Super-Kamiokande experiment. This review outlines the sequence of observations and their associated publications that solved the atmospheric neutrino anomaly and established the existence of neutrino oscillations with nearly maximal mixing of muon neutrinos and tau neutrinos. We also discuss subsequent and ongoing studies that use atmospheric neutrinos to continue to reveal the nature of the neutrino. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3 .
1. Introduction The Super-Kamiokande experiment [1] commenced data taking on April 1, 1996, prepared for a broad range of inquiry in particle physics including the search for nucleon decay and the study of neutrinos from cosmic rays, nuclear reactions in the sun, and core collapse supernovae. Based * Corresponding author at: Department of Physics, Boston University, Boston, MA 02215, USA.
E-mail address: [email protected] (E. Kearns). http://dx.doi.org/10.1016/j.nuclphysb.2016.04.017 0550-3213/Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3 .
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Fig. 1. The Super-Kamiokande detector, in cutaway, showing the inner and outer detector, partially filled with water. The detector dome contains front–end electronics and calibration devices such as the electron LINAC (tower is shown). Also shown are access drifts, the control room, and water purification system.
on unresolved indications in prior experiments, there were two immediate goals for neutrino studies: solving the “solar neutrino puzzle” [2] and resolving the “atmospheric neutrino anomaly” [3–6]. It was already anticipated that neutrino oscillations [7,8] could play a role in explaining the existing data. The Super-Kamiokande detector was designed to be large enough and have sufficient sensitivity to provide definitive results on these topics. The Super-Kamiokande detector design [9] was influenced by the successes of the first generation experiment, Kamiokande [10], with which it shares its name. Super-Kamiokande (also referred to as Super-K or SK) was constructed in the same lead and zinc mine operated by the Kamioka Mining Company as its predecessor. In addition to increased fiducial mass, 22.5 kiloton versus 1 kiloton for Kamiokande, the photon collection coverage was increased from 20% to 40% with second-generation 50-cm PMTs [11] with improved time resolution of 2.2 ns and improved single photoelectron response. The outer detector veto region was increased to a thickness of 2 meters and highly instrumented by the U.S. group with PMTs recovered from the IMB experiment [12], a competing first generation water Cherenkov experiment that operated contemporaneously with Kamiokande. The high level of light collection and veto shielding, combined with an advanced water purification system that ensured good water clarity and low levels of radioactive background, allowed the experiment to lower the threshold for solar neutrino detection to 5 MeV (and lower, in later upgrades of the detector). Several advanced calibration systems [13] were implemented including an electron LINAC. For atmospheric neutrinos, the large detector mass resulted in roughly 3800 atmospheric neutrino events per year with excellent separation of muons from electrons, improved energy resolution, higher efficiency for counting decay electrons, and better performance for resolving multiple Cherenkov rings [14] compared to the first generation experiments Kamiokande and IMB. Fig. 1 shows an artist’s rendering of the detector. The Super-Kamiokande detector has gone through several operating stages in its twenty year history. Most of the work in establishing atmospheric neutrino oscillation used data from
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1489 live days during the first running period from 1996 to 2001, now referred to as SuperKamiokande I. During 2001 the detector was drained to perform maintenance such as replacing failed PMTs. During refilling, a terrible accident occurred where a single PMT imploded, causing an underwater chain reaction that destroyed nearly half of the PMTs in the detector. Once the mechanism that caused the accident was understood, protective shells were designed to prevent another chain reaction. The detector was rebuilt in two stages. The remaining PMTs, around 5200 of the original 11,100, were redistributed to cover the inner detector with a uniform 20% photocoverage. Replacement PMTs to fully recover the outer detector were installed by the U.S. group. This configuration is referred to as Super-Kamiokande II, and took data from 2002 to 2005, for 799 live days. This much time was needed for the manufacture of another 6000 50-cm PMTs. One challenge for Super-Kamiokande II was to retune the detector simulation and event reconstruction to accommodate the new configuration with half of the phototubes and new reflective surfaces in the protective shells. We were able to retain good results, with only slightly degraded performance for atmospheric neutrinos [15] and proton decay, but had to accept a higher minimum energy of 7 MeV for solar neutrinos. In 2005, the detector was drained again and the photocoverage was restored to 40% by July 2006. The detector took data in this configuration, Super-K III, for two years (518 live days) and has remained filled with water since. In August 2008, the front–end electronics system was completely replaced for better performance providing improved deadtimeless operation for detecting muon decay electrons and higher dynamic range for better energy resolution. The data acquisition system was also upgraded to one based on a software trigger, an improvement that allowed wide search windows for subsequent events that enabled the detection of the 2.2 MeV gamma ray from neutron capture on hydrogen [16,17]. The configuration with upgraded electronics and DAQ, known as Super-K IV, has been in operation for more than 2100 live days at the time of this writing. The total analyzed exposure for atmospheric neutrinos and proton decay over all SK periods is in excess of 300 kt-years. 2. The atmospheric neutrino anomaly The first sign of the atmospheric neutrino anomaly was found in the relative number of muon neutrinos to electron neutrinos in Kamiokande [3] and IMB [18,4]. Muon neutrinos were expected to be roughly twice as abundant as electron neutrinos, since atmospheric neutrinos mainly come from a π → μ decay chain, but the studies found more equal numbers. To cancel systematic uncertainties, it became conventional to present the double ratio: Nμ /Ne data R= , (1) Nμ /Ne MC where a significant deviation from unity was considered anomalous. Besides new physics, some pedestrian origins for the anomalous ratio were considered, such as poor understanding of the neutrino flux, neutrino cross section, or the performance of water Cherenkov detectors. The atmospheric neutrino flux was well-studied by several authors with independent calculations (for a review, see Ref. [19]); the consensus was that the double ratio was uncertain to no more than 5%. Cross sections were of special interest because the underground detectors Frejus [20] and NUSEX [21], that had iron as the neutrino target did not observe an anomalous double ratio, although with a large statistical error. As for the performance of water Cherenkov analysis, one unique contribution was a dedicated beam test of charged particles sent into a 1-kiloton tank at KEK [22]. This experiment demonstrated that electrons and muons were well separated by the applied particle identification algorithms and data and simulation were in good agreement. Fig. 2
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Fig. 2. The double-ratio of muon to electron neutrino rates for the atmospheric neutrino measurements that characterized the atmospheric neutrino anomaly. Square data points represent iron tracking detectors, circles represent water Cherenkov detectors [21,6,5,20,23].
summarizes measurements by several experiments leading up to and including the first Super-K measurements. The first ever paper by the Super-Kamiokande collaboration directly addressed the issue of the double ratio [24] with the first 414 live days (25.5 kt-years) of data. This paper restricted itself to the sub-GeV energy range, defined as visible energy less than 1.33 GeV, matching the Kamiokande definition. This energy range for events fully-contained in the inner detector is also the hunting ground for proton decay. The paper documented two independent end-to-end analyses [25,26], one mostly by the former Kamiokande institutions and one mostly by the former IMB institutions. The two analyses used different flux models, different cross section calculations, and independent data reduction and reconstruction. The two analyses were compared in detail and found to have high overlap in event selection and particle identification. The measured double ratio was: R = 0.61 ± 0.03stat. ± 0.05sys. , as shown in Fig. 2. The paper concluded that “it would be difficult to explain the observed deviation in R from expectation in terms of unresolved mistakes in experimental analysis.” The analysis also demonstrated that the double ratio was independent of fiducial position, thereby eliminating entering cosmogenic background, such as neutrons, as playing a role. The “sub-GeV paper” published the double ratio as a function of zenith angle and no significant distortion was observed, only a tilt towards longer baselines. Zenith angle dependence for low energy atmospheric neutrino events is somewhat washed out due to poor angular correlation between the neutrino and the outgoing lepton. Furthermore, the eventual value for m2 resulted in a significant oscillation probability for sub-GeV atmospheric neutrinos arriving from all directions. For the oscillation length that nature handed us, 500 km/GeV, higher energy neutrinos dramatically revealed the effect of neutrino oscillation. This was first seen in the final analysis by Kamiokande [27], which showed an intriguing dependence of the double ratio on zenith angle for higher energy events. The second Super-Kamiokande paper published was based on fully-contained events with visible energy greater than 1.33 GeV (“multi-GeV”) as well as partially-contained (PC) events [28]. Partially contained events have a neutrino interaction in the fiducial volume but a particle exits into the outer detector. The particle is typically a high energy muon from a charged current muon neutrino interaction. The signature of an exit point in the outer detector provides an event sample that is 98% pure CC νμ . In this paper we continued to report numbers for the double ratio [29], but now the most striking feature was a zenith angle distortion of the double ratio. The source of the distortion, a deficit of μ-like events, can be seen directly in the zenith distributions shown in Fig. 3, where the event counts are compared with expectation. With this paper, it became clear that the atmospheric neutrino anomaly was mainly associated with muon neutrinos. With a sam-
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Fig. 3. The zenith angle distribution for multi-GeV FC and partially-contained events from the first 414 days of SuperKamiokande data. The markers represent the events counted by Super-Kamiokande, the boxes represent the expected event counts.
ple of roughly 400 single-ring μ-like plus PC events, an up-down asymmetry of greater than 5σ was observed. Although no oscillation analysis was performed, inspection of the zenith distribution shows fully-contained Multi-GeV μ-like plus PC events, i.e. high energy muon neutrinos, were detected at half the expected rate if they traveled long distances. This implied muon neutrino disappearance with nearly maximal mixing. The Multi-GeV e-like sample agreed with expectation, suggesting that electron neutrinos were not measurably affected by neutrino oscillations at these energies. 3. Evidence for atmospheric neutrino oscillation The sub-GeV and multi-GeV paper served as the foundation for a full interpretation of atmospheric neutrino oscillation [30,31]. Our journal paper was titled “Evidence for oscillation of atmospheric neutrinos” [32] and went on to become one of the most highly cited particle physics papers in history. At that time the guidelines connecting the statistical significance to the wording of the title were not well established; today this paper might be titled “Observation of”. The subGeV double-ratio, as well as the multi-GeV up-down asymmetry, deviated from unity by more than 5σ , and a clear preference for the neutrino oscillation hypothesis was inferred. For this paper, the exposure was increased to 535 days or 33.0 kt-years. In addition to reporting updated values for the double-ratio and the up-down asymmetry, we sub-divided the single-ring sub-GeV, single-ring multi-GeV, and partially contained event samples and performed a combined fit over 70 bins to the two-flavor oscillation hypothesis: Pa→b = sin2 2θ sin 2 1.27
m2 L , Eν
(2)
where L is measured in kilometers, the neutrino energy Eν is measured in GeV, and m2 is found in units of eV2 . This gives the probability that a neutrino of energy Eν , produced in flavor state a, is detected in flavor state b after traveling a distance L through vacuum. Both νμ → νe and νμ → ντ were considered, with the latter statistically favored by several standard deviations. In the case of νμ → ντ oscillation, the experimental signature is a disappearance of muon neutrino interactions, because the most oscillated tau neutrinos have energy below the threshold of 3.5 GeV, and those that are over threshold generally do not produce the clean single ring events required by this analysis for lepton flavor identification.
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Fig. 4. The confidence intervals for νμ → ντ oscillations. The left plot is based on the 1998 analysis of 33.0 kt-yr of Super-K data [32], and is plotted as a function of sin2 2θ with m2 on a logarithmic scale. The right plot contains the 90% confidence interval from a 2015 (preliminary) SK atmospheric oscillation analysis, plotted as m2 versus sin2 θ23 . This interval assumes normal hierarchy, and is compared to final results from MINOS and recent results from T2K. The bold inset square region on the left plot approximates the interval from the right plot for SK atmospheric neutrinos.
The result of the fit is shown in the left panel of Fig. 4 as confidence interval contours. The Super-Kamiokande measurement found lower values of m2 than were suggested by Kamiokande [27], favoring a mass splitting of a few times 10−3 eV2 . The Kamiokande interval now seems to be on the high side for m2 , but is probably consistent at the few percent level. As a historical note, some of the subsequent long-baseline experiments, designed as this story was unfolding, were optimized for larger values of m2 and hoped to take advantage of a modest amount of ντ appearance. The lower values favored by nature made the task more difficult for experiments such as MINOS and OPERA. OPERA has now reported five ντ events [33] over an expected background of 0.25 events based on four years of running from 2008 to 2012. The first long-baseline experiment, K2K [34], exposed the Super-K detector to a beam of neutrinos produced 250 km away at KEK. The K2K experiment detected 58 single-ring μ-like events compared to an expectation of 158 events with an energy spectrum and fitted parameters consistent with those measured by Super-K [35]. This provided confirmation of atmospheric neutrino oscillation using a man-made neutrino source. Subsequent measurements by long-baseline experiments such as MINOS [36] and T2K [37] are now more precise, consistent with the latest SK atmospheric measurements, and consistent with the original 1998 result from Super-K. The right panel in Fig. 4 shows the confidence intervals from the analysis of SK I-through-IV atmospheric neutrino data in 2015 overlayed with results from MINOS and T2K. The next two Super-Kamiokande papers [38,39] used the upward-going muon sample as an independent confirmation of the oscillation effect. The upward-going muon data sample is not just statistically independent, it also has many distinct experimental aspects that differentiate it from the fully-contained and partially-contained analyses [40,41]. Upward-going muons are the result of muon neutrino interactions in the rock below and around the detector. The observed particle is the high energy muon that reaches the detector. The muon retains the direction of the neutrino with good accuracy, but the neutrino energy may only be inferred from a parent distribution. For muons that stop in the detector, the mean parent neutrino energy is roughly 10 GeV;
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Fig. 5. The flux of through-going (upper data points and histograms) and stopping (lower data points and histograms) neutrino induced upward-going muons measured by Super-Kamiokande. The solid histograms give the expected flux, the dashed histograms are the result of a fit to neutrino oscillations.
for muons that penetrate the detector it is roughly 100 GeV. Reconstructing this sample of events required quite different techniques than used for the fully-contained sample. Event reconstruction relied on fitting long muon tracks and rejecting the vast majority of downward-going cosmic ray muons. Fig. 5 shows the flux of both stopping and through-going upward muons measured as a function of zenith angle from directly upward-going to the horizontal. The upper data points and histograms are for through-going muons, which are more numerous because the high energy muon may originate far from the detector or penetrate far past it; stopping muons have an extra acceptance requirement that the muon stop in the detector. In both cases, a minimum muon length of 7 meters in the inner detector is required. The stopping upward-going muons have a parent neutrino energy spectrum that is similar to partially contained events. The signs of maximal mixing are present here as the stopping upward-going muons are depleted by half due to rapid averaging of the oscillation probability. The higher energy through-going muons reveal only a subtle, but statistically significant shift in shape as the neutrino baseline varies from 13,000 km to 500 km. In later analyses, the through-going upward muon sample is further divided into a subsample of showering muons with a parent neutrino energy of 1 TeV [42]. This sample which exhibits no evidence of neutrino oscillation even at the longest baselines. Although the Super-Kamiokande upward-going muon papers were published several months later, the data analyses were prepared as preliminary results and were included in the presentation at the Neutrino 1998 Conference in Takayama announcing the discovery of neutrino oscillations [43]. At around the same time, the MACRO experiment also published [44] an upward-going muon zenith spectrum with similar characteristics to the Super-K spectrum, also favoring m2 values of a few times 10−3 eV2 . The iron-based Soudan 2 experiment published an atmospheric neutrino analysis with an anomalous double-ratio [45], as shown in Fig. 2. Somewhat later, Soudan 2 published an oscillation study using events with good resolution in L/E [46], and with best fit interval in agreement with Super-Kamiokande. By the year 2000 the predominant interpretation of atmospheric neutrino oscillation as being due to maximal mixing of νμ and ντ was widely ac-
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cepted, with Super-Kamiokande providing the most precise results, limiting sin2 2θ to be greater than about 0.9 at the 90% C.L. In parallel to the work on atmospheric neutrinos, a thorough set of studies by SuperKamiokande of solar neutrinos also favored nearly maximal mixing of electron neutrinos, eliminating several other possibilities such as vacuum oscillations driven by small m2 and a small mixing angle solution driven by resonant conversion in the sun. Super-Kamiokande detects solar neutrinos by their elastic scattering off atomic electrons at a rate of roughly 15 per day. A large sample of solar neutrinos had been collected down to a threshold of 6.5 MeV and the flux was clearly much lower than allowed by the standard solar model [47]. By 2001, the SK solar neutrino analysis was performed on a 1258 day exposure yielding more than 18,000 solar neutrino events with energy greater than 5.0 MeV [48,49]. The preference for maximal mixing was due to the non-observation of large spectral distortion due to oscillation and matter effects in the Sun, and the non-observation of any sizeable day-night asymmetry due to matter effects in the Earth. In 2001, new evidence for solar neutrino oscillation was discovered by comparing the results of solar neutrino elastic scattering off electrons in Super-Kamiokande [48] and the SNO charged current event rate on deuterium [50]. The SNO experiment continued with a series of measurements based on three distinct phases of detector operation [51]. SNO counted too few charged current solar neutrino interactions, but counted the expected number of neutral current solar neutrino interactions. This was direct evidence that the disappearance of electron neutrinos was the origin of solar neutrino deficits [52]. That neutrino oscillations solved another long-standing puzzle encouraged follow-up experiments such as K2K [34], MINOS [53], KamLAND [54], and OPERA [55], all of which had already been proposed before either atmospheric or solar neutrino oscillations were firmly established. The Super-Kamiokande I running period concluded with an exposure of 1489 live days of data (92 kt-yr) containing 12180 fully-contained events, 911 PC events, 458 stopping upward-going muons, and 1856 through-going upward-going muons. We used 180 bins from these data sets and considered 39 systematic parameters to perform a single fit to two-flavor neutrino oscillations. The best fit region, 1.5 × 10−3 < m2 < 3.4 × 10−3 eV2 with sin2 2θ > 0.92 is shown in bold in Fig. 6. Also shown are the confidence interval from six distinct subsamples which demonstrate the consistent indications from a wide range of atmospheric neutrino event categories. A lengthy Physical Review D paper [14] documented this analysis and included details about the SK detector response, performance of the data reduction and reconstruction, and comparisons to multiple atmospheric neutrino flux calculations and neutrino interaction cross section models. 4. Nature of the oscillation phenomenon Because atmospheric neutrino oscillation was strictly a disappearance phenomenon, there remained some alternative interpretations to νμ → ντ mixing that required some consideration. Oscillation to a sterile state could give roughly the same deficit of muon neutrinos. However, the sterile neutrino oscillation is predicted to be suppressed at high energies due to the interference of forward scattering diagrams as the neutrinos pass through the matter [56]. Further, neutral current interactions would disappear. Based on these signatures, the Super-K atmospheric data disfavors sterile neutrinos. We found that muon neutrino disappearance to tau neutrinos was preferred over disappearance to a sterile state [57,58] largely because the zenith angle distortions of higher energy samples such as PC and upward-going muons would have been suppressed, but were not. Rejecting the possibility that sterile neutrino oscillation was taking place instead of oscillation
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Fig. 6. The 90% confidence level regions for six atmospheric neutrino samples individually fit for a two-flavor atmospheric neutrino oscillation. The small bold region is the interval with all subsamples simultaneously fit.
Fig. 7. A scan in χ 2 for oscillation frequency proportional to LE −n . The oscillation frequency due to neutrino mass has an index of n = 1, which is the index that best fits the Super-K atmospheric neutrino data.
between the active muon and tau neutrinos was refined [59–62] and eventually excluded by more than 7σ . Later, the allowable admixture of a sterile state in 4-neutrino models was limited to be very small using the data taken through SK-IV [63]. Other hypotheses that could result in neutrino disappearance, such as neutrino decay, decoherence, or Lorentz violation effects were also rejected as the sole source of the muon neutrino deficit due to their poor fit to the data [64,62]. This is illustrated in Fig. 7, summarizing the χ 2 difference as a function of the oscillation frequency L × E −n with n being a free parameter. Alternate models of neutrino disappearance may be found that have n = 1, however the Super-K data favors L/E, i.e. n = 1.
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Fig. 8. The ratio of data to MC events (in the absence of neutrino oscillation) as a function of the reconstructed L/E, together with the best-fit 3-flavor expectation for neutrino oscillation and two alternative hypotheses with similar shape. The dashed (blue) and dotted (green) lines show the best-fit expectations for neutrino decay and neutrino decoherence, respectively. This is a preliminary result based on 220 kt-yrs of SK-I through SK-IV data. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
With alternatives eliminated, νμ → ντ oscillations caused by massive neutrinos was clearly the preferred hypothesis to explain the atmospheric neutrino data. Massive neutrinos also explained solar neutrino observations. Although neutrino mass technically requires physics beyond the Standard Model, the new physics including neutrino mass is readily formulated. The quantum mechanics of neutrino oscillation made several other predictions that remained to be tested. The first two that we tested using atmospheric neutrinos were observation of the oscillation probability pattern and tau neutrino appearance. An expectation for massive neutrino oscillation is that the shape of the oscillation pattern should be truly oscillatory with a frequency proportional to L/E, as seen in Eqn. (2). For most atmospheric neutrino events, the baseline distance L and the neutrino energy E are not well determined, due to uncertainty in the direction, the production height in the atmosphere, or the energy transfer to the outgoing lepton. A specialized analysis was developed [65] that minimized these effects by selecting events with good resolution in L/E largely by excluding low energy events and events near the horizon. In addition, we used multi-ring events and distinguished PC events that stopped in the outer detector from higher energy ones that completely exited. Using this high resolution sample, we took the ratio of the observed event rate to expectation and found evidence for a dip in the rate of muon neutrinos near 500 GeV/km that was greater than the 50% deficit found at higher values of L/E due to maximal mixing and averaging of rapid oscillations. To characterize the significance of the dip, we compared standard neutrino oscillation due to massive neutrinos to two alternate models, neutrino decay and neutrino decoherence. These predict a more smooth transition to 50% survival at large values of L/E. The significance of the dip was more than 3σ using SK-I [66]. The analysis was extended to include SK-II [67] and later SK-III and SK-IV [68]. Our most recent result, using SK-I through SK-IV data and a 3-flavor oscillation formula is reproduced in Fig. 8 and favors the observation of the neutrino oscillation minimum by greater than 4σ . Because atmospheric neutrinos have an energy spectrum that extends to very high energies, we expect charged current tau neutrino interactions in the event sample. The CC ντ threshold is approximately 3 GeV, so the number of τ events would be relatively small and mixed with the
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Fig. 9. The zenith distribution for events that are considered tau-like by a neural network identification, for a data sample from SK-I+II+III. The fitted tau signal is shown in gray.
difficult to classify multi-ring multi-GeV events. Even quasielastic events were expected to have many Cherenkov rings due to interactions of the recoiling nucleon as well as hadronic decays of the tau. We performed searches [69,70] for τ appearance in the multi-GeV multi-ring sample, focusing on upward-going events as neutrinos with energy above tau-threshold require longer pathlengths to have an appreciable probability of oscillation. As of our latest search [71], we see greater than 3σ evidence for tau neutrinos appearing in our sample. The excess over no tau appearance can be seen in Fig. 9, where the gray bands are the fitted component of tau candidates passing a neural network identification. 5. Current research with atmospheric neutrinos The measurements described above established the nature of atmospheric neutrino oscillations, which have contributed to the modern paradigm for neutrino oscillation. The paradigm is that the three active neutrino species mix [7,8] based on a 3 × 3 unitary matrix that may be expanded in the following convention: ⎛ ⎞⎛ ⎞⎛ ⎞ 1 s13 e−iδ c13 c12 s12 ⎠ ⎝ −s12 c12 ⎠. c23 s23 ⎠ ⎝ 1 (3) UP MNS = ⎝ iδ −s23 c23 1 −s23 e c13 Here, abbreviations cij = cos θij and sij = sin θij are used and Majorana phases, unobservable in neutrino oscillation experiments, are not shown. Because the mass splitting for atmospheric and solar neutrinos differ by two orders of magnitude and θ13 is small, atmospheric neutrino oscillation is dominated by the first rotation matrix and solar neutrino oscillation is dominated by the last rotation matrix in Eqn. (3). Although atmospheric neutrino mixing is mostly governed by θ23 , there should be an admixture of νμ ↔ νe as a result of solar terms and the interference between the atmospheric and solar terms proportional to the non-zero θ13 . Contemporary atmospheric neutrino oscillation studies by Super-K are done in a three-flavor framework [72–77]. Our current research program is to use the enormous data set from Super-Kamiokande I through IV, shown in 19 different subsamples in Fig. 10, to reveal information about undetermined quantities such as the neutrino mass ordering, whether θ23 is greater than or less than 45◦ , and the value of the CP violating phase, δCP .
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Fig. 10. Zenith angle and momentum distributions for atmospheric neutrino subsamples used for recent analyses by Super-Kamiokande to study subleading effects, preferences for mass hierarchy and δCP , as well as searches for astrophysical sources such as dark matter annihilation.
In addition to trying to determine or more precisely measure the parameters of the three-flavor paradigm, we find atmospheric neutrinos to be fertile ground for searching for exotic phenomena; the range of energies and baselines are very large, upward-going neutrinos pass through matter of various density, and two flavors of neutrinos and antineutrinos are present in the flux. On top of the standard neutrino oscillations, we have searched for deviations and subleading effects from sterile neutrinos [63], mass-varying neutrinos [78,79], non-standard interactions [80–82], and Lorentz violation [83]. We searched for, but did not find any differences in the oscillation between neutrinos and antineutrinos [84], relying on statistical difference in the response of the atmospheric sample. And we have made comprehensive measurements of the flux of atmospheric neutrinos [85,86] in order to test the underlying cosmic ray physics such as variations of flux with the level of solar activity and azimuthal asymmetry due to geomagnetic cutoff (also known as the East–West effect, first observed in atmospheric neutrinos by SK-I [87]). Acknowledgements The work described in this Review was the result of years of effort by numerous members of the Super-Kamiokande collaboration, students in particular. The bibliography of this review mentions the many papers and Ph.D. theses that were directly related to the atmospheric neutrino oscillation discovery and subsequent measurement. However, those represent only half of the Atmospheric Neutrino and Proton Decay working group, which has been led by the authors of this review. The students and researchers who worked on proton decay and neutrino astrophysics also
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contributed to the data reduction, event reconstruction, detector simulation, and calibration that were essential for establishing atmospheric neutrino oscillations. Furthermore, the high quality of Super-Kamiokande data could not have been achieved without the efforts of the Low Energy group who played an equal role in simulating, calibrating, and operating the detector, not to mention establishing neutrino oscillation in solar neutrinos. All Super-Kamiokande Ph.D. theses are available online at the Kamioka Neutrino Observatory website.1 We gratefully acknowledge the cooperation of the Kamioka Mining and Smelting Company. The Super-Kamiokande experiment was built and has been operated with funding from the Japanese Ministry of Education, Science, Sports and Culture, and the United States Department of Energy. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
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ScienceDirect Nuclear Physics B 908 (2016) 14–29 www.elsevier.com/locate/nuclphysb
Establishing atmospheric neutrino oscillations with Super-Kamiokande T. Kajita a,d , E. Kearns b,d,∗ , M. Shiozawa c,d for the Super-Kamiokande Collaboration a Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiawa, Chiba,
277-8582, Japan b Department of Physics, Boston University, Boston, MA 02215, USA c Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan d Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for
Advanced Study, University of Tokyo, Kashiwa, Chiba 277-8582, Japan Received 21 February 2016; received in revised form 5 April 2016; accepted 11 April 2016 Available online 16 April 2016 Editor: Tommy Ohlsson
Abstract In this article we review the discovery of atmospheric neutrino oscillation by the Super-Kamiokande experiment. This review outlines the sequence of observations and their associated publications that solved the atmospheric neutrino anomaly and established the existence of neutrino oscillations with nearly maximal mixing of muon neutrinos and tau neutrinos. We also discuss subsequent and ongoing studies that use atmospheric neutrinos to continue to reveal the nature of the neutrino. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3 .
1. Introduction The Super-Kamiokande experiment [1] commenced data taking on April 1, 1996, prepared for a broad range of inquiry in particle physics including the search for nucleon decay and the study of neutrinos from cosmic rays, nuclear reactions in the sun, and core collapse supernovae. Based * Corresponding author at: Department of Physics, Boston University, Boston, MA 02215, USA.
E-mail address: [email protected] (E. Kearns). http://dx.doi.org/10.1016/j.nuclphysb.2016.04.017 0550-3213/Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3 .
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Fig. 1. The Super-Kamiokande detector, in cutaway, showing the inner and outer detector, partially filled with water. The detector dome contains front–end electronics and calibration devices such as the electron LINAC (tower is shown). Also shown are access drifts, the control room, and water purification system.
on unresolved indications in prior experiments, there were two immediate goals for neutrino studies: solving the “solar neutrino puzzle” [2] and resolving the “atmospheric neutrino anomaly” [3–6]. It was already anticipated that neutrino oscillations [7,8] could play a role in explaining the existing data. The Super-Kamiokande detector was designed to be large enough and have sufficient sensitivity to provide definitive results on these topics. The Super-Kamiokande detector design [9] was influenced by the successes of the first generation experiment, Kamiokande [10], with which it shares its name. Super-Kamiokande (also referred to as Super-K or SK) was constructed in the same lead and zinc mine operated by the Kamioka Mining Company as its predecessor. In addition to increased fiducial mass, 22.5 kiloton versus 1 kiloton for Kamiokande, the photon collection coverage was increased from 20% to 40% with second-generation 50-cm PMTs [11] with improved time resolution of 2.2 ns and improved single photoelectron response. The outer detector veto region was increased to a thickness of 2 meters and highly instrumented by the U.S. group with PMTs recovered from the IMB experiment [12], a competing first generation water Cherenkov experiment that operated contemporaneously with Kamiokande. The high level of light collection and veto shielding, combined with an advanced water purification system that ensured good water clarity and low levels of radioactive background, allowed the experiment to lower the threshold for solar neutrino detection to 5 MeV (and lower, in later upgrades of the detector). Several advanced calibration systems [13] were implemented including an electron LINAC. For atmospheric neutrinos, the large detector mass resulted in roughly 3800 atmospheric neutrino events per year with excellent separation of muons from electrons, improved energy resolution, higher efficiency for counting decay electrons, and better performance for resolving multiple Cherenkov rings [14] compared to the first generation experiments Kamiokande and IMB. Fig. 1 shows an artist’s rendering of the detector. The Super-Kamiokande detector has gone through several operating stages in its twenty year history. Most of the work in establishing atmospheric neutrino oscillation used data from
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1489 live days during the first running period from 1996 to 2001, now referred to as SuperKamiokande I. During 2001 the detector was drained to perform maintenance such as replacing failed PMTs. During refilling, a terrible accident occurred where a single PMT imploded, causing an underwater chain reaction that destroyed nearly half of the PMTs in the detector. Once the mechanism that caused the accident was understood, protective shells were designed to prevent another chain reaction. The detector was rebuilt in two stages. The remaining PMTs, around 5200 of the original 11,100, were redistributed to cover the inner detector with a uniform 20% photocoverage. Replacement PMTs to fully recover the outer detector were installed by the U.S. group. This configuration is referred to as Super-Kamiokande II, and took data from 2002 to 2005, for 799 live days. This much time was needed for the manufacture of another 6000 50-cm PMTs. One challenge for Super-Kamiokande II was to retune the detector simulation and event reconstruction to accommodate the new configuration with half of the phototubes and new reflective surfaces in the protective shells. We were able to retain good results, with only slightly degraded performance for atmospheric neutrinos [15] and proton decay, but had to accept a higher minimum energy of 7 MeV for solar neutrinos. In 2005, the detector was drained again and the photocoverage was restored to 40% by July 2006. The detector took data in this configuration, Super-K III, for two years (518 live days) and has remained filled with water since. In August 2008, the front–end electronics system was completely replaced for better performance providing improved deadtimeless operation for detecting muon decay electrons and higher dynamic range for better energy resolution. The data acquisition system was also upgraded to one based on a software trigger, an improvement that allowed wide search windows for subsequent events that enabled the detection of the 2.2 MeV gamma ray from neutron capture on hydrogen [16,17]. The configuration with upgraded electronics and DAQ, known as Super-K IV, has been in operation for more than 2100 live days at the time of this writing. The total analyzed exposure for atmospheric neutrinos and proton decay over all SK periods is in excess of 300 kt-years. 2. The atmospheric neutrino anomaly The first sign of the atmospheric neutrino anomaly was found in the relative number of muon neutrinos to electron neutrinos in Kamiokande [3] and IMB [18,4]. Muon neutrinos were expected to be roughly twice as abundant as electron neutrinos, since atmospheric neutrinos mainly come from a π → μ decay chain, but the studies found more equal numbers. To cancel systematic uncertainties, it became conventional to present the double ratio: Nμ /Ne data R= , (1) Nμ /Ne MC where a significant deviation from unity was considered anomalous. Besides new physics, some pedestrian origins for the anomalous ratio were considered, such as poor understanding of the neutrino flux, neutrino cross section, or the performance of water Cherenkov detectors. The atmospheric neutrino flux was well-studied by several authors with independent calculations (for a review, see Ref. [19]); the consensus was that the double ratio was uncertain to no more than 5%. Cross sections were of special interest because the underground detectors Frejus [20] and NUSEX [21], that had iron as the neutrino target did not observe an anomalous double ratio, although with a large statistical error. As for the performance of water Cherenkov analysis, one unique contribution was a dedicated beam test of charged particles sent into a 1-kiloton tank at KEK [22]. This experiment demonstrated that electrons and muons were well separated by the applied particle identification algorithms and data and simulation were in good agreement. Fig. 2
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Fig. 2. The double-ratio of muon to electron neutrino rates for the atmospheric neutrino measurements that characterized the atmospheric neutrino anomaly. Square data points represent iron tracking detectors, circles represent water Cherenkov detectors [21,6,5,20,23].
summarizes measurements by several experiments leading up to and including the first Super-K measurements. The first ever paper by the Super-Kamiokande collaboration directly addressed the issue of the double ratio [24] with the first 414 live days (25.5 kt-years) of data. This paper restricted itself to the sub-GeV energy range, defined as visible energy less than 1.33 GeV, matching the Kamiokande definition. This energy range for events fully-contained in the inner detector is also the hunting ground for proton decay. The paper documented two independent end-to-end analyses [25,26], one mostly by the former Kamiokande institutions and one mostly by the former IMB institutions. The two analyses used different flux models, different cross section calculations, and independent data reduction and reconstruction. The two analyses were compared in detail and found to have high overlap in event selection and particle identification. The measured double ratio was: R = 0.61 ± 0.03stat. ± 0.05sys. , as shown in Fig. 2. The paper concluded that “it would be difficult to explain the observed deviation in R from expectation in terms of unresolved mistakes in experimental analysis.” The analysis also demonstrated that the double ratio was independent of fiducial position, thereby eliminating entering cosmogenic background, such as neutrons, as playing a role. The “sub-GeV paper” published the double ratio as a function of zenith angle and no significant distortion was observed, only a tilt towards longer baselines. Zenith angle dependence for low energy atmospheric neutrino events is somewhat washed out due to poor angular correlation between the neutrino and the outgoing lepton. Furthermore, the eventual value for m2 resulted in a significant oscillation probability for sub-GeV atmospheric neutrinos arriving from all directions. For the oscillation length that nature handed us, 500 km/GeV, higher energy neutrinos dramatically revealed the effect of neutrino oscillation. This was first seen in the final analysis by Kamiokande [27], which showed an intriguing dependence of the double ratio on zenith angle for higher energy events. The second Super-Kamiokande paper published was based on fully-contained events with visible energy greater than 1.33 GeV (“multi-GeV”) as well as partially-contained (PC) events [28]. Partially contained events have a neutrino interaction in the fiducial volume but a particle exits into the outer detector. The particle is typically a high energy muon from a charged current muon neutrino interaction. The signature of an exit point in the outer detector provides an event sample that is 98% pure CC νμ . In this paper we continued to report numbers for the double ratio [29], but now the most striking feature was a zenith angle distortion of the double ratio. The source of the distortion, a deficit of μ-like events, can be seen directly in the zenith distributions shown in Fig. 3, where the event counts are compared with expectation. With this paper, it became clear that the atmospheric neutrino anomaly was mainly associated with muon neutrinos. With a sam-
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Fig. 3. The zenith angle distribution for multi-GeV FC and partially-contained events from the first 414 days of SuperKamiokande data. The markers represent the events counted by Super-Kamiokande, the boxes represent the expected event counts.
ple of roughly 400 single-ring μ-like plus PC events, an up-down asymmetry of greater than 5σ was observed. Although no oscillation analysis was performed, inspection of the zenith distribution shows fully-contained Multi-GeV μ-like plus PC events, i.e. high energy muon neutrinos, were detected at half the expected rate if they traveled long distances. This implied muon neutrino disappearance with nearly maximal mixing. The Multi-GeV e-like sample agreed with expectation, suggesting that electron neutrinos were not measurably affected by neutrino oscillations at these energies. 3. Evidence for atmospheric neutrino oscillation The sub-GeV and multi-GeV paper served as the foundation for a full interpretation of atmospheric neutrino oscillation [30,31]. Our journal paper was titled “Evidence for oscillation of atmospheric neutrinos” [32] and went on to become one of the most highly cited particle physics papers in history. At that time the guidelines connecting the statistical significance to the wording of the title were not well established; today this paper might be titled “Observation of”. The subGeV double-ratio, as well as the multi-GeV up-down asymmetry, deviated from unity by more than 5σ , and a clear preference for the neutrino oscillation hypothesis was inferred. For this paper, the exposure was increased to 535 days or 33.0 kt-years. In addition to reporting updated values for the double-ratio and the up-down asymmetry, we sub-divided the single-ring sub-GeV, single-ring multi-GeV, and partially contained event samples and performed a combined fit over 70 bins to the two-flavor oscillation hypothesis: Pa→b = sin2 2θ sin 2 1.27
m2 L , Eν
(2)
where L is measured in kilometers, the neutrino energy Eν is measured in GeV, and m2 is found in units of eV2 . This gives the probability that a neutrino of energy Eν , produced in flavor state a, is detected in flavor state b after traveling a distance L through vacuum. Both νμ → νe and νμ → ντ were considered, with the latter statistically favored by several standard deviations. In the case of νμ → ντ oscillation, the experimental signature is a disappearance of muon neutrino interactions, because the most oscillated tau neutrinos have energy below the threshold of 3.5 GeV, and those that are over threshold generally do not produce the clean single ring events required by this analysis for lepton flavor identification.
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Fig. 4. The confidence intervals for νμ → ντ oscillations. The left plot is based on the 1998 analysis of 33.0 kt-yr of Super-K data [32], and is plotted as a function of sin2 2θ with m2 on a logarithmic scale. The right plot contains the 90% confidence interval from a 2015 (preliminary) SK atmospheric oscillation analysis, plotted as m2 versus sin2 θ23 . This interval assumes normal hierarchy, and is compared to final results from MINOS and recent results from T2K. The bold inset square region on the left plot approximates the interval from the right plot for SK atmospheric neutrinos.
The result of the fit is shown in the left panel of Fig. 4 as confidence interval contours. The Super-Kamiokande measurement found lower values of m2 than were suggested by Kamiokande [27], favoring a mass splitting of a few times 10−3 eV2 . The Kamiokande interval now seems to be on the high side for m2 , but is probably consistent at the few percent level. As a historical note, some of the subsequent long-baseline experiments, designed as this story was unfolding, were optimized for larger values of m2 and hoped to take advantage of a modest amount of ντ appearance. The lower values favored by nature made the task more difficult for experiments such as MINOS and OPERA. OPERA has now reported five ντ events [33] over an expected background of 0.25 events based on four years of running from 2008 to 2012. The first long-baseline experiment, K2K [34], exposed the Super-K detector to a beam of neutrinos produced 250 km away at KEK. The K2K experiment detected 58 single-ring μ-like events compared to an expectation of 158 events with an energy spectrum and fitted parameters consistent with those measured by Super-K [35]. This provided confirmation of atmospheric neutrino oscillation using a man-made neutrino source. Subsequent measurements by long-baseline experiments such as MINOS [36] and T2K [37] are now more precise, consistent with the latest SK atmospheric measurements, and consistent with the original 1998 result from Super-K. The right panel in Fig. 4 shows the confidence intervals from the analysis of SK I-through-IV atmospheric neutrino data in 2015 overlayed with results from MINOS and T2K. The next two Super-Kamiokande papers [38,39] used the upward-going muon sample as an independent confirmation of the oscillation effect. The upward-going muon data sample is not just statistically independent, it also has many distinct experimental aspects that differentiate it from the fully-contained and partially-contained analyses [40,41]. Upward-going muons are the result of muon neutrino interactions in the rock below and around the detector. The observed particle is the high energy muon that reaches the detector. The muon retains the direction of the neutrino with good accuracy, but the neutrino energy may only be inferred from a parent distribution. For muons that stop in the detector, the mean parent neutrino energy is roughly 10 GeV;
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Fig. 5. The flux of through-going (upper data points and histograms) and stopping (lower data points and histograms) neutrino induced upward-going muons measured by Super-Kamiokande. The solid histograms give the expected flux, the dashed histograms are the result of a fit to neutrino oscillations.
for muons that penetrate the detector it is roughly 100 GeV. Reconstructing this sample of events required quite different techniques than used for the fully-contained sample. Event reconstruction relied on fitting long muon tracks and rejecting the vast majority of downward-going cosmic ray muons. Fig. 5 shows the flux of both stopping and through-going upward muons measured as a function of zenith angle from directly upward-going to the horizontal. The upper data points and histograms are for through-going muons, which are more numerous because the high energy muon may originate far from the detector or penetrate far past it; stopping muons have an extra acceptance requirement that the muon stop in the detector. In both cases, a minimum muon length of 7 meters in the inner detector is required. The stopping upward-going muons have a parent neutrino energy spectrum that is similar to partially contained events. The signs of maximal mixing are present here as the stopping upward-going muons are depleted by half due to rapid averaging of the oscillation probability. The higher energy through-going muons reveal only a subtle, but statistically significant shift in shape as the neutrino baseline varies from 13,000 km to 500 km. In later analyses, the through-going upward muon sample is further divided into a subsample of showering muons with a parent neutrino energy of 1 TeV [42]. This sample which exhibits no evidence of neutrino oscillation even at the longest baselines. Although the Super-Kamiokande upward-going muon papers were published several months later, the data analyses were prepared as preliminary results and were included in the presentation at the Neutrino 1998 Conference in Takayama announcing the discovery of neutrino oscillations [43]. At around the same time, the MACRO experiment also published [44] an upward-going muon zenith spectrum with similar characteristics to the Super-K spectrum, also favoring m2 values of a few times 10−3 eV2 . The iron-based Soudan 2 experiment published an atmospheric neutrino analysis with an anomalous double-ratio [45], as shown in Fig. 2. Somewhat later, Soudan 2 published an oscillation study using events with good resolution in L/E [46], and with best fit interval in agreement with Super-Kamiokande. By the year 2000 the predominant interpretation of atmospheric neutrino oscillation as being due to maximal mixing of νμ and ντ was widely ac-
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cepted, with Super-Kamiokande providing the most precise results, limiting sin2 2θ to be greater than about 0.9 at the 90% C.L. In parallel to the work on atmospheric neutrinos, a thorough set of studies by SuperKamiokande of solar neutrinos also favored nearly maximal mixing of electron neutrinos, eliminating several other possibilities such as vacuum oscillations driven by small m2 and a small mixing angle solution driven by resonant conversion in the sun. Super-Kamiokande detects solar neutrinos by their elastic scattering off atomic electrons at a rate of roughly 15 per day. A large sample of solar neutrinos had been collected down to a threshold of 6.5 MeV and the flux was clearly much lower than allowed by the standard solar model [47]. By 2001, the SK solar neutrino analysis was performed on a 1258 day exposure yielding more than 18,000 solar neutrino events with energy greater than 5.0 MeV [48,49]. The preference for maximal mixing was due to the non-observation of large spectral distortion due to oscillation and matter effects in the Sun, and the non-observation of any sizeable day-night asymmetry due to matter effects in the Earth. In 2001, new evidence for solar neutrino oscillation was discovered by comparing the results of solar neutrino elastic scattering off electrons in Super-Kamiokande [48] and the SNO charged current event rate on deuterium [50]. The SNO experiment continued with a series of measurements based on three distinct phases of detector operation [51]. SNO counted too few charged current solar neutrino interactions, but counted the expected number of neutral current solar neutrino interactions. This was direct evidence that the disappearance of electron neutrinos was the origin of solar neutrino deficits [52]. That neutrino oscillations solved another long-standing puzzle encouraged follow-up experiments such as K2K [34], MINOS [53], KamLAND [54], and OPERA [55], all of which had already been proposed before either atmospheric or solar neutrino oscillations were firmly established. The Super-Kamiokande I running period concluded with an exposure of 1489 live days of data (92 kt-yr) containing 12180 fully-contained events, 911 PC events, 458 stopping upward-going muons, and 1856 through-going upward-going muons. We used 180 bins from these data sets and considered 39 systematic parameters to perform a single fit to two-flavor neutrino oscillations. The best fit region, 1.5 × 10−3 < m2 < 3.4 × 10−3 eV2 with sin2 2θ > 0.92 is shown in bold in Fig. 6. Also shown are the confidence interval from six distinct subsamples which demonstrate the consistent indications from a wide range of atmospheric neutrino event categories. A lengthy Physical Review D paper [14] documented this analysis and included details about the SK detector response, performance of the data reduction and reconstruction, and comparisons to multiple atmospheric neutrino flux calculations and neutrino interaction cross section models. 4. Nature of the oscillation phenomenon Because atmospheric neutrino oscillation was strictly a disappearance phenomenon, there remained some alternative interpretations to νμ → ντ mixing that required some consideration. Oscillation to a sterile state could give roughly the same deficit of muon neutrinos. However, the sterile neutrino oscillation is predicted to be suppressed at high energies due to the interference of forward scattering diagrams as the neutrinos pass through the matter [56]. Further, neutral current interactions would disappear. Based on these signatures, the Super-K atmospheric data disfavors sterile neutrinos. We found that muon neutrino disappearance to tau neutrinos was preferred over disappearance to a sterile state [57,58] largely because the zenith angle distortions of higher energy samples such as PC and upward-going muons would have been suppressed, but were not. Rejecting the possibility that sterile neutrino oscillation was taking place instead of oscillation
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Fig. 6. The 90% confidence level regions for six atmospheric neutrino samples individually fit for a two-flavor atmospheric neutrino oscillation. The small bold region is the interval with all subsamples simultaneously fit.
Fig. 7. A scan in χ 2 for oscillation frequency proportional to LE −n . The oscillation frequency due to neutrino mass has an index of n = 1, which is the index that best fits the Super-K atmospheric neutrino data.
between the active muon and tau neutrinos was refined [59–62] and eventually excluded by more than 7σ . Later, the allowable admixture of a sterile state in 4-neutrino models was limited to be very small using the data taken through SK-IV [63]. Other hypotheses that could result in neutrino disappearance, such as neutrino decay, decoherence, or Lorentz violation effects were also rejected as the sole source of the muon neutrino deficit due to their poor fit to the data [64,62]. This is illustrated in Fig. 7, summarizing the χ 2 difference as a function of the oscillation frequency L × E −n with n being a free parameter. Alternate models of neutrino disappearance may be found that have n = 1, however the Super-K data favors L/E, i.e. n = 1.
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Fig. 8. The ratio of data to MC events (in the absence of neutrino oscillation) as a function of the reconstructed L/E, together with the best-fit 3-flavor expectation for neutrino oscillation and two alternative hypotheses with similar shape. The dashed (blue) and dotted (green) lines show the best-fit expectations for neutrino decay and neutrino decoherence, respectively. This is a preliminary result based on 220 kt-yrs of SK-I through SK-IV data. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
With alternatives eliminated, νμ → ντ oscillations caused by massive neutrinos was clearly the preferred hypothesis to explain the atmospheric neutrino data. Massive neutrinos also explained solar neutrino observations. Although neutrino mass technically requires physics beyond the Standard Model, the new physics including neutrino mass is readily formulated. The quantum mechanics of neutrino oscillation made several other predictions that remained to be tested. The first two that we tested using atmospheric neutrinos were observation of the oscillation probability pattern and tau neutrino appearance. An expectation for massive neutrino oscillation is that the shape of the oscillation pattern should be truly oscillatory with a frequency proportional to L/E, as seen in Eqn. (2). For most atmospheric neutrino events, the baseline distance L and the neutrino energy E are not well determined, due to uncertainty in the direction, the production height in the atmosphere, or the energy transfer to the outgoing lepton. A specialized analysis was developed [65] that minimized these effects by selecting events with good resolution in L/E largely by excluding low energy events and events near the horizon. In addition, we used multi-ring events and distinguished PC events that stopped in the outer detector from higher energy ones that completely exited. Using this high resolution sample, we took the ratio of the observed event rate to expectation and found evidence for a dip in the rate of muon neutrinos near 500 GeV/km that was greater than the 50% deficit found at higher values of L/E due to maximal mixing and averaging of rapid oscillations. To characterize the significance of the dip, we compared standard neutrino oscillation due to massive neutrinos to two alternate models, neutrino decay and neutrino decoherence. These predict a more smooth transition to 50% survival at large values of L/E. The significance of the dip was more than 3σ using SK-I [66]. The analysis was extended to include SK-II [67] and later SK-III and SK-IV [68]. Our most recent result, using SK-I through SK-IV data and a 3-flavor oscillation formula is reproduced in Fig. 8 and favors the observation of the neutrino oscillation minimum by greater than 4σ . Because atmospheric neutrinos have an energy spectrum that extends to very high energies, we expect charged current tau neutrino interactions in the event sample. The CC ντ threshold is approximately 3 GeV, so the number of τ events would be relatively small and mixed with the
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Fig. 9. The zenith distribution for events that are considered tau-like by a neural network identification, for a data sample from SK-I+II+III. The fitted tau signal is shown in gray.
difficult to classify multi-ring multi-GeV events. Even quasielastic events were expected to have many Cherenkov rings due to interactions of the recoiling nucleon as well as hadronic decays of the tau. We performed searches [69,70] for τ appearance in the multi-GeV multi-ring sample, focusing on upward-going events as neutrinos with energy above tau-threshold require longer pathlengths to have an appreciable probability of oscillation. As of our latest search [71], we see greater than 3σ evidence for tau neutrinos appearing in our sample. The excess over no tau appearance can be seen in Fig. 9, where the gray bands are the fitted component of tau candidates passing a neural network identification. 5. Current research with atmospheric neutrinos The measurements described above established the nature of atmospheric neutrino oscillations, which have contributed to the modern paradigm for neutrino oscillation. The paradigm is that the three active neutrino species mix [7,8] based on a 3 × 3 unitary matrix that may be expanded in the following convention: ⎛ ⎞⎛ ⎞⎛ ⎞ 1 s13 e−iδ c13 c12 s12 ⎠ ⎝ −s12 c12 ⎠. c23 s23 ⎠ ⎝ 1 (3) UP MNS = ⎝ iδ −s23 c23 1 −s23 e c13 Here, abbreviations cij = cos θij and sij = sin θij are used and Majorana phases, unobservable in neutrino oscillation experiments, are not shown. Because the mass splitting for atmospheric and solar neutrinos differ by two orders of magnitude and θ13 is small, atmospheric neutrino oscillation is dominated by the first rotation matrix and solar neutrino oscillation is dominated by the last rotation matrix in Eqn. (3). Although atmospheric neutrino mixing is mostly governed by θ23 , there should be an admixture of νμ ↔ νe as a result of solar terms and the interference between the atmospheric and solar terms proportional to the non-zero θ13 . Contemporary atmospheric neutrino oscillation studies by Super-K are done in a three-flavor framework [72–77]. Our current research program is to use the enormous data set from Super-Kamiokande I through IV, shown in 19 different subsamples in Fig. 10, to reveal information about undetermined quantities such as the neutrino mass ordering, whether θ23 is greater than or less than 45◦ , and the value of the CP violating phase, δCP .
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Fig. 10. Zenith angle and momentum distributions for atmospheric neutrino subsamples used for recent analyses by Super-Kamiokande to study subleading effects, preferences for mass hierarchy and δCP , as well as searches for astrophysical sources such as dark matter annihilation.
In addition to trying to determine or more precisely measure the parameters of the three-flavor paradigm, we find atmospheric neutrinos to be fertile ground for searching for exotic phenomena; the range of energies and baselines are very large, upward-going neutrinos pass through matter of various density, and two flavors of neutrinos and antineutrinos are present in the flux. On top of the standard neutrino oscillations, we have searched for deviations and subleading effects from sterile neutrinos [63], mass-varying neutrinos [78,79], non-standard interactions [80–82], and Lorentz violation [83]. We searched for, but did not find any differences in the oscillation between neutrinos and antineutrinos [84], relying on statistical difference in the response of the atmospheric sample. And we have made comprehensive measurements of the flux of atmospheric neutrinos [85,86] in order to test the underlying cosmic ray physics such as variations of flux with the level of solar activity and azimuthal asymmetry due to geomagnetic cutoff (also known as the East–West effect, first observed in atmospheric neutrinos by SK-I [87]). Acknowledgements The work described in this Review was the result of years of effort by numerous members of the Super-Kamiokande collaboration, students in particular. The bibliography of this review mentions the many papers and Ph.D. theses that were directly related to the atmospheric neutrino oscillation discovery and subsequent measurement. However, those represent only half of the Atmospheric Neutrino and Proton Decay working group, which has been led by the authors of this review. The students and researchers who worked on proton decay and neutrino astrophysics also
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contributed to the data reduction, event reconstruction, detector simulation, and calibration that were essential for establishing atmospheric neutrino oscillations. Furthermore, the high quality of Super-Kamiokande data could not have been achieved without the efforts of the Low Energy group who played an equal role in simulating, calibrating, and operating the detector, not to mention establishing neutrino oscillation in solar neutrinos. All Super-Kamiokande Ph.D. theses are available online at the Kamioka Neutrino Observatory website.1 We gratefully acknowledge the cooperation of the Kamioka Mining and Smelting Company. The Super-Kamiokande experiment was built and has been operated with funding from the Japanese Ministry of Education, Science, Sports and Culture, and the United States Department of Energy. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
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