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PHYSICAL REVIEW LETTERS

Evidence for the Appearance of Atmospheric Tau Neutrinos in Super-Kamiokande
K. Abe,1,27 Y. Hayato,1,27 T. Iida,1 K. Iyogi,1 J. Kameda,1,27 Y. Koshio,1,27 Y. Kozuma,1 Ll. Marti,1 M. Miura,1,27
S. Moriyama,1,27 M. Nakahata,1,27 S. Nakayama,1,27 Y. Obayashi,1,27 H. Sekiya,1,27 M. Shiozawa,1,27 Y. Suzuki,1,27
A. Takeda,1,27 Y. Takenaga,1 K. Ueno,1 K. Ueshima,1 S. Yamada,1 T. Yokozawa,1 C. Ishihara,2 H. Kaji,2 T. Kajita,2,27
K. Kaneyuki,2,27,* K. P. Lee,2 T. McLachlan,2 K. Okumura,2 Y. Shimizu,2 N. Tanimoto,2 L. Labarga,3 E. Kearns,4,27
M. Litos,4 J. L. Raaf,4 J. L. Stone,4,27 L. R. Sulak,4 M. Goldhaber,5,* K. Bays,6 W. R. Kropp,6 S. Mine,6 C. Regis,6A. Renshaw,6 M. B. Smy,6,27 H. W. Sobel,6,27 K. S. Ganezer,7 J. Hill,7 W. E. Keig,7 J. S. Jang,8,† J. Y. Kim,8 I. T. Lim,8J. B. Albert,9 K. Scholberg,9,27 C. W. Walter,9,27 R. Wendell,9 T. M. Wongjirad,9 T. Ishizuka,10 S. Tasaka,11 J. G. Learned,12
S. Matsuno,12 S. N. Smith,12 T. Hasegawa,13 T. Ishida,13 T. Ishii,13 T. Kobayashi,13 T. Nakadaira,13 K. Nakamura,13,27
K. Nishikawa,13 Y. Oyama,13 K. Sakashita,13 T. Sekiguchi,13 T. Tsukamoto,13 A. T. Suzuki,14 Y. Takeuchi,14,27 M. Ikeda,15
A. Minamino,15 T. Nakaya,15,27 Y. Fukuda,16 Y. Itow,17,18 G. Mitsuka,17 T. Tanaka,17 C. K. Jung,19 G. D. Lopez,19
I. Taylor,19 C. Yanagisawa,19 H. Ishino,20 A. Kibayashi,20 S. Mino,20 T. Mori,20 M. Sakuda,20 H. Toyota,20 Y. Kuno,21
M. Yoshida,21 S. B. Kim,22 B. S. Yang,22 H. Okazawa,23 Y. Choi,24 K. Nishijima,25 M. Koshiba,26 M. Yokoyama,26,27
Y. Totsuka,26,* K. Martens,27 J. Schuemann,27 M. R. Vagins,27,6 S. Chen,28 Y. Heng,28 Z. Yang,28 H. Zhang,28
D. Kielczewska,29 P. Mijakowski,30 K. Connolly,31 M. Dziomba,31 E. Thrane,31,‡ and R. J. Wilkes31(Super-Kamiokande Collaboration)
2

1
Kamioka Observatory, Institute for Cosmic Ray Research, University of Tokyo, Kamioka, Gifu 506-1205, Japan
Research Center for Cosmic Neutrinos, Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan3
Department of Theoretical Physics, University Autonoma Madrid, 28049 Madrid, Spain
4
Department of Physics, Boston University, Boston, Massachusetts 02215, USA
5
Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
6
Department of Physics and Astronomy, University of California Irvine, Irvine, California 92697-4575, USA
7
Department of Physics, California State University, Dominguez Hills, Carson, California 90747, USA
8
Department of Physics, Chonnam National University, Kwangju 500-757, Korea
9
Department of Physics, Duke University, Durham, North Carolina 27708, USA
10
Junior College, Fukuoka Institute of Technology, Fukuoka 811-0214, Japan
11
Information and Multimedia Center, Gifu University, Gifu, Gifu 501-1193, Japan
12
Department of Physics and Astronomy, University of Hawaii, Honolulu, Hawaii 96822, USA
13High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
14
Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan
15
Department of Physics, Kyoto University, Kyoto, Kyoto 606-8502, Japan
16
Department of Physics, Miyagi University of Education, Sendai, Miyagi 980-0845, Japan
17
Solar Terrestrial Environment Laboratory, Nagoya University, Nagoya, Aichi 464-8602, Japan
18
Kobayashi-Maskawa Institute for the Origin of Particle and the Universe, Nagoya University, Nagoya, Aichi 464-8602, Japan
19
Department of Physics and Astronomy, State University of New York, Stony Brook, New York 11794-3800, USA
20
Department of Physics, Okayama University, Okayama, Okayama 700-8530, Japan
21
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
22
Department of Physics, Seoul National University, Seoul 151-742, Korea
23
Department of Informatics in Social Welfare, Shizuoka University of Welfare, Yaizu, Shizuoka 425-8611, Japan
24
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
25
Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan
26
The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
27
Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japan
28
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
29
Institute of Experimental Physics, Warsaw University, 00-681 Warsaw, Poland
30
National Centre For Nuclear Research, 00-681 Warsaw, Poland
31
Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA(Received 5 June 2012; published 2 May 2013)

Super-Kamiokande atmospheric neutrino data were fit with an unbinned maximum likelihood method
to search for the appearance of tau leptons resulting from the interactions of oscillation-generated tau
neutrinos in the detector. Relative to the expectation of unity, the tau normalization is found to be 1:42 
0:35ðstatÞþ0:14
0:12 ðsystÞ excluding the no-tau-appearance hypothesis, for which the normalization would be0031-9007=13=110(18)=181802(7)181802-1

Ó 2013 American Physical Society

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zero, at the 3:8 level. We estimate that 180:1  44:3ðstatÞþ17:8
15:2 ðsystÞ tau leptons were produced in the22.5 kton fiducial volume of the detector by tau neutrinos during the 2806 day running period. In future
analyses, this large sample of selected tau events will allow the study of charged current tau neutrino
interaction physics with oscillation produced tau neutrinos.
DOI: 10.1103/PhysRevLett.110.181802

PACS numbers: 14.60.Pq, 95.55.Vj

It is now well known that neutrinos undergo flavor
oscillations. The flavor states of the neutrino measured
through the weak interaction are quantum mechanicalmixtures of neutrino mass states. As observed in the quark
sector, this mixture results in oscillations of detected flavor
states. Evidence exists for this effect in atmospheric neutrinos [1,2], solar neutrinos [3–7], reactor experiments [8],and long-baseline oscillation experiments [9–11]. In 2011,
the T2K [12], MINOS [13], and Double Chooz [14] experiments showed the first indications of full three-flavor oscillations. In 2012 the Daya Bay [15] and RENO [16]experiments reported the first precision measurements ofthe 13 mixing angle which drives three-flavor oscillation.
Definitive proof of flavor oscillation requires unambiguous appearance of the charged current interaction of aneutrino not in the original source. In the dominant oscillation for  at GeV energies,  !  oscillations,observing the resulting  lepton is quite difficult. This isbecause producing a tau lepton requires a neutrino ofenergy greater than a threshold of 3.5 GeV. Long-baseline
experiments tuned to the neutrino oscillation maximum fortheir distances tend to have the bulk of their neutrinos
below this energy. Furthermore, the tau lepton immediately
decays to final states with an electron, muon, or mesons
plus a tau neutrino so the tau lepton itself cannot be easily
seen. Nevertheless, the OPERA Collaboration was recently
able to show evidence for a single reconstructed eventin their emulsion consistent with tau appearance [17].
The Super-Kamiokande (Super-K) Collaboration first published a search for tau appearance in atmospheric neutrinos
in 2006 [18]. Since the atmospheric neutrino flux extends
to energies well above 10 GeV, and spans a wide range ofbaselines, we expect to see tau leptons produced in the
Super-K detector. However, these events must be distinguished from other high-energy atmospheric neutrino
interactions. Further comparisons of these techniques canbe found in Ref. [19] and prospects for future detectors canbe found in Ref. [20].
This Letter reports a result from a new search utilizing
the Super-Kamiokande experiment. This analysis
addresses the question of whether the atmospheric data
are consistent with the lack of oscillation-generated  orwhether they are necessary to explain the observations.
Super-K is a 50 000 ton water Cherenkov detector [21]with 22.5 kton of fiducial volume. It consists of two concentric detectors: an inner detector with 11 129 inwardlooking 20 in. photodetectors and an outer detector with
1885 outward-facing 8 in. photodetectors which acts as aveto. Its large target mass makes it well suited to look forthe rare appearance of tau neutrinos from oscillations. The
typical energy of atmospheric neutrinos is about 1 GeV.
Because of the previously noted energy threshold, aboutone  charged current event per kton-yr should be produced in the Super-K detector.
Super-K has been in operation for approximately
15 years and has had several running configurations indicated by the labeling SK-I (1996-2001), SK-II (20022005), SK-III (2006-2008), and SK-IV (2008-2012). The
previously reported Super-K result [18] was based on thedata from SK-I alone. Since that time the analysis has been
improved to increase its sensitivity and the data set has
used has been expanded to also include SK-II and SK-III,thereby almost doubling its size. As the total data set
covers the period between 1996 and 2008, it comprises
2806 days of live time.
In order to predict the rate of both the tau signal andatmospheric background, a full Monte Carlo (MC) simulation is used both to predict the neutrino interactions
inside the detector and to model the response of Super-K
itself. Three-dimensional neutrino fluxes for  and e
produced in atmospheric showers are taken from the flux
calculation of Honda et al. [22]. The fluxes are oscillatedwith a custom code [23] which takes into account all
relevant path lengths, energies, and matter effects using
our current knowledge of three-flavor neutrino oscillation
parameters. The oscillation parameters used are [24–26]
m232 ¼2:1103 eV2 , m221 ¼7:6105 eV2 , sin2 223 ¼
1:0, sin2 212 ¼ 0:84, CP ¼ 0. The Super-K best fit valueof m232 from Refs. [24,25] was used in order to make useof the full set of systematic errors which were previously
evaluated around this point. However, the difference inresults between using this value and that of recent more
precise values reported in the literature [27] is found to be
negligible due to the wide range of L and E sampled by theatmospheric neutrinos. For the values of 13 , recent Daya
Bay [15] and RENO [16] results are combined in aweighted average and we use sin2 213 ¼ 0:099. The interactions of the  , e , and oscillation-produced  ’s with
the nuclei of water molecules inside the Super-K detector
are modeled with the NEUT [2,28] neutrino interaction
code. Finally, a GEANT3 [29] based detector MC is used
to simulate Super-K itself. More detailed descriptions of
this software can be found in Ref. [2].
For the purposes of this analysis it is important tounderstand some details of the neutrino interaction model.
The NEUT code models the known neutrino-nucleon

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interactions including quasielastic scattering, single meson
production, coherent pion production, and deep-inelastic
scattering (DIS). All  and e interactions are simulated.
Additionally, charged-current (CC)  interactions are
simulated and added to the sample using weighting basedon the oscillation probabilities. Neutral current (NC) interactions are assumed to be unaffected by oscillations. The
 CC cross sections are calculated following the samemodels as those used for  and e with the appropriate
lepton mass terms. In the case of single and coherent pion
production lepton mass corrections not included in theoriginal models are also employed [30,31]. Tau leptons
are decayed using TAUOLA (version 2.6) [32]. Since the
distribution of decay particles depends on the polarizationof the tau lepton, a polarization model from Ref. [33] isincorporated into NEUT. At the relevant neutrino energies
selected by this analysis, the CC interactions contain a highpercentage of DIS (46%) with the portion of CC events
induced by the  signal interactions alone containing
56% DIS. In the calculation of the cross sections of DIS,
the GRV94 [34] parton distribution functions are used, andadditional corrections to make the DIS cross sections
match smoothly with the resonance region as developed
by Bodek and Yang are also applied [35]. More details of
the DIS implementation can be found in Ref. [2].
The signature of oscillation-induced tau neutrinos in theatmospheric flux is the detection of the decay of tau leptons
in the Super-K detector. As the leptonic decays of the tau
look on the whole very similar to normal CC DIS interactions from  and e , an analysis is developed whichattempts to select the hadronic decays.
In order to select the tau events, we first identify highenergy events contained in the inner detector by requiringthat there is no appreciable activity in the outer detector,
the interaction is in the fiducial volume (the distance to thenearest wall >200 cm), and the event has more than
1.3 GeV of visible energy. The selection efficiencies forthis set of cuts are 81% for the  CC signal and 23% for the
background events, respectively.
The presence of the extra pions from hadronic tau decay
which come from a heavy object can statistically separate
the signal from the normal  and e CC and NC background. In order to further separate the signal from thebackground, a set of variables which show differentiation
between the two samples is used as the inputs to a feedforward neural network (NN). The NN is configured using
the TMVA package [36] with seven inputs nodes, one hidden
layer with 10 nodes, and one output node. Exclusive training and testing samples are selected from the MC sets toavoid bias and test for overtraining.
The variables used are (a) the log base 10 of the total
visible energy of the event, (b) the particle identification of
the maximum energy ring in the event, (c) the number ofdecay electron candidates in the event, (d) the maximum
distance between the primary interaction and any decay

electron found from a pion or muon decay, (e) the clusteredsphericity of the event in the center of mass system, (f) the
number of possible Cherenkov ring fragments, and finally(g) the fraction of total number of photoelectrons in theevents carried by the first ring. The agreement between
downward-going data and MC simulations (where notau signal is expected) for the NN output along with theoverlaid expected tau signal is shown in Fig. 1. See
Supplemental Material [37] for the additional agreement
between the data and MC simulations of the seven input
variables to the NN.
All of the oscillation-induced tau neutrinos will comefrom below due to differing path lengths in the earth. Inorder avoid encoding such up-down biases into the network, and to select events based solely on their topology,
the training is performed by weighting the oscillation
probabilities of all events based on their energies alone,
not their direction. In this way, all oscillation probabilities
are correct on average, but upward-going and downwardgoing events are treated the same in the training process.
This technique has the added benefit of not setting theweights of the down-going signal events to zero, thus
preserving MC statistics. The training is performed suchthat a NN output which is near 1.0 signifies that the event istaulike, while events near 0.0 are nontaulike. After training,
the NN is found to efficiently separate the tau appearance
signal from the background of other atmospheric neutrino
interactions.
When acting on the events passing the preselection cuts,
75% of the signal events (60% total efficiency) and only
26% of the background events (6% total efficiency) remain
when events with a NN output of greater than 0.5 areconsidered. In this ‘‘taulike’’ sample, NC backgroundmakes up 26% of the sample and is an important remaining
background. Table I further displays the fractional breakdown of the interaction modes in the sample. In order toextract maximum information from the event samples,
instead of cutting on the NN output, the output of the NN

300

200

100

0

0

0.2

0.4

0.6

0.8

1

Neural Network Output

FIG. 1. The separation of signal and background by the neuralnetwork. The downward-going data (points) are overlaid withthe downward-going atmospheric MC simulations (solid line).
Also shown is the tau signal MC simulation (shaded). The tau
signal is normalized for equal statistics.

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TABLE I. The fractional breakdown of interaction modes ofboth the expected signal (CC  ) and background for the SK-I
period. For fitting purposes the entire sample is used in theanalysis, but the NN enhanced (NN > 0:5) and depleted(NN < 0:5) signal selections are shown here to demonstrate
the effect of signal and background separation. For each sample,
the number of selected SK-I MC events is shown scaled by the1489 days of SK-I live time. The fractional breakdown byinteraction mode of each sample is shown in parentheses.
Interaction mode
CC e
CC 
CC 
NC

NN < 0:5

NN > 0:5

All781.4 (0.40)
1070.2 (0.55)
12.4 (0.01)
95.2 (0.05)

381.3 (0.46)
200.2 (0.24)
37.2 (0.04)
209.3 (0.25)

1162.7 (0.42)
1270.4 (0.46)
49.7 (0.02)
304.4 (0.11)

is combined with the zenith direction of the event into a
probability distribution functions (PDF) and is used tojointly fit the tau and background components.
An example of the two-dimensional distributions of theNN output versus the direction of the detected events used
to discriminate signal from background is shown in Fig. 2.
Distributions for both oscillation-generated taus on the left
and other atmospheric background on the right are shown.
The vertical axes of these two-dimensional distributions
contain the output of the NN and reflects how taulike theevent is (NN output near 1.0 taulike, 0.0 nontaulike). The
horizontal axis is the cosine of the reconstructed zenith
angle of the event which is determined by an energyweighted sum of the ring directions in the event. The tau
events (left-hand panel) are indicated as taulike by the NN
and come from below [cosðÞ near 1:0] as expected. In
contrast, other atmospheric neutrinos (right-hand panel)are primarily nontaulike and come from both above andbelow. In fact, it can be seen that these events are depleted
in the upward-going direction due to their oscillation into
(mostly noninteracting) tau neutrinos. By varying the relative normalization of the two distributions, both the

Background PDF

Neural Network Output

Neural Network Output

Signal PDF
1
0.8
0.6
0.4
0.2
0
-1

-0.5

0

0.5

Cosine of the Zenith Angle

1

1
0.8
0.6
0.4
0.2
0
-1

-0.5

0

0.5

1

Cosine of the Zenith Angle

FIG. 2. Histograms of the PDFs of both tau signal (left) andatmospheric background (right). The vertical axis is the output of
the NN, the horizontal axis the cosine of the event zenith
direction. Upward-going events are to the left, downward-going
events to the right. The tau signal appears in the upward-going
taulike region.

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amount of tau appearance and the overall background levelcan be adjusted.
PDFs for each run period for both signal and backgroundare built out of two-dimensional histograms prepared from
the MC simulations, with the probability density following
the normalized bin contents. Then, an unbinned likelihood
fit of the data is done to the sum of the signal and background PDFs varying the normalization between them. It isnecessary to perform an unbinned fit as statistics of bins in
the full two-dimensional space would be quite low. The
result of the fit is a normalization factor on the signal andthe background which tells us how many tau interactions
are needed to be consistent with our data set. Separate
PDFs are produced for SK-I, -II, and -III, and each data
set is fit to its appropriate MC set. The data sets are fit bothindividually for each run period and jointly together.
Although the technique employed here is more sophisticated than that of Ref. [18], it is also more sensitive tosome systematic errors since large numbers of background
events remain in the nonsignal regions of the fitting space
which were previously removed by cuts. By training the
NN to recognize tau interactions, the NN also learns toeffectively separate quasielastic from multi-pi and DIS
interactions in the background samples. This is because
the DIS events tend to have many extra pions in them, andthus look more like the tau signal. The DIS portion of theinteractions thus forms a large part of the background in
the signal region and we therefore explicitly take into
account uncertainties in the DIS normalization in the fit.
The average neutrino energy in the DIS interactions in
our sample is 14 GeV and the cross section is not known tobetter than the 10% level at that energy. We also know thatthe application of the Bodek-Yang corrections [35] tends tosuppress our DIS interactions at higher energies by about
5%. For this reason, the DIS error is introduced into the fit
as a 10% Gaussian error constraint. After the fit is completed it is found that the amount of DIS is increased fromits nominal value by 10% at the best fit point. If the fit isperformed with no constraint on the DIS fraction at all,then the DIS fraction fits 14% higher than the nominal
value.
The fit is performed on each data period separately, andis also performed jointly with all data periods being fit at
the same time. In the case of finding the exact normalization as predicted by the MC simulations, these factors
would be 1.0. When the data periods are fit together, thetau normalization is found to be 1:42  0:35ðstatÞ withthe background normalization 0:94  0:02ðstatÞ. When fit
separately, the tau normalizations are found to be
1:27  0:49ðstatÞ, 1:47  0:62ðstatÞ, and 2:16  0:78ðstatÞ
for SK-I, SK-II, and SK-III, respectively.
It is also instructive to examine the results of the combined fit graphically. Binned projections of the fitted results
can illustrate the quality and features of the fit. Figure 3
shows the projections in zenith for both taulike (NN output

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300

400

Events

300
200
200
100
100

Taulike
500-1

-0.5

Up-going
0cos(θ)

0.5

1

0

0.2

0.4

0.6

0.8

1

0.8

1

NN output

600

Events

400
400

300
200

200
100

Nontaulike
0
-1

-0.5

Down-going0cos(θ )

0.5

1

0

0

0.2

0.4

0.6

NN output

FIG. 3 (color online). Fit results showing projections in the
NN output and zenith angle distribution for taulike (NN > 0:5),
upward-going [cosðÞ > 0:1], nontaulike (NN < 0:5), anddownward-going [cosðÞ < 0:1] events for both the twodimensional PDFs and data. The PDFs and data sets have beencombined from SK-I through SK-III in this figure. The fitted tau
signal is shown in gray.

>0:5) and nontaulike (NN output <0:5) events, along withthe projections in NN output for both upward-going[cosðÞ > 0:1] and downward-going [ cosðÞ < 0:1] events.
In these plots the PDFs have been rescaled to the fitted
normalization values. The fitted tau signal is shown in gray.
Good agreement is seen in all distributions. As expected,
tau events are observed as an excess of taulike events in the
upward-going direction. In these plots the PDFs and data
sets from all of the run periods have been combined
together.
There are 28 uncertainties which are a subset of thoseused in the Super-K three-flavor atmospheric neutrino
analysis. A more detailed description of them can be foundin Ref. [24]. The systematic errors for the analysis are
divided into two sets. The first set, which describes errors
on the tau expectation itself, plays no role in comparing
the fitted observed number of events with the no-tauappearance hypothesis and does not affect the significanceof this quoted result. However, this set is used to quote
an error on the expected number of events and includes
uncertainties in the  cross section and any uncertainty
that would increase both the signal and the background in a
way that does not change the significance of the reported
result. Detector biases on selection and fitting are includedin these uncertainties but are quite small compared to thetau cross-section error, the largest being a 5% error on thedetector energy scale. The error on the tau cross section
was made by a comparison of NEUT [28] with several othermodels, looking in particular at the differences between
NEUT and the cross-section model by Hagiwara et al. [33].

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Another comparison between cross-section models wasrecently completed by the authors of Ref. [20] and gave
similar results. As noted above, this 25% error does notcontribute to the reported significance of this Letter.
However, future analysis using this high statistics data set
employing full simultaneous treatment of all relevant systematic errors can measure this cross section and constrain
its uncertainty using the Super-K data itself.
The second class of errors includes those that would
affect the observed signal but not the background, orotherwise would cause the significance of the measured
normalization to change when doing the fit. There are fivesuch errors, all expressed as ratios: upward to downward
neutrino flux, horizontal to vertical neutrino flux, kaon topion originated neutrino flux, NC to CC cross section, andthe upward to downward detector energy scale difference.
In the current analysis the dominant error on the signal was
the NC/CC ratio changing the fitted number of events ofabout 7% due to the relatively large percentage of NC
background in the signal region.
Also included in the errors which can change the measured results and significance are those due to variations in
the known oscillation parameters. For this study they arevaried within the 1 limits of a combined SK-I þ SK-II þ
SK-III atmospheric oscillation analysis result assuming
the normal hierarchy [25]. The m232 is varied between
1:92  103 and 2:22  103 eV2 , sin2 223 is varied
between 0.93 and 1.0. The 13 values are varied within
our combined Daya Bay [15] and RENO [16] results ofsin2 213 ¼ 0:099  0:014. The use of nonzero 13 results
in a 13% reduction of the fitted normalization as threeflavor oscillations produce high energy upward-going electron neutrinos which add to the upward-going background,thus decreasing the needed number of tau neutrinos toexplain the signal region. However, the variation in 13
around this central value results in less than a 1% change inthe fit result. For this analysis, we set the value of CP tozero. Varying the value of CP results in, at most, a 1.3%
difference in the number of fitted taus, and we neglect thisuncertainty. The systematic errors are summarized inTable II.
Including and combining the observed (þ 9:6  8:6%)
and expected (þ 28:4  30:0%) systematic uncertainties
TABLE II. Summary of systematic uncertainties for both the
expected and observed number of  events. The errors for eachcategory including that of the oscillation parameters have been
added in quadrature.
Systematics uncertainties for  normalizationþ%%Super-K atmospheric  oscillation errors
28 error terms (expected events)
5 error terms (observed events)
Tau neutrino cross section (expected events)
Oscillation parameters (observed events)

13.4
7.9
25.0
5.4

14.7
8.5
25.0
1.3

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separately, the fitted value of the tau normalization is
1:42  0:35ðstatÞþ0:14
0:12 ðsystÞ. After rescaling the MC by all
fitting factors and correcting for efficiency, the observed
number of fitted events over the entire running period is
calculated to be 180:1  44:3ðstatÞþ17:8
15:2 ðsystÞ events. This
is to be compared to an expectation of 120:2þ34:2
34:8 ðsystÞ
interactions in the fiducial volume if no fitting factors areapplied. Identifying this large statistics sample opens thepossibility to study charged current tau neutrino interaction
physics with oscillation produced tau neutrinos.
The observed number of events is converted to thesignificance level at which we can reject the no-tauappearance hypothesis. The measured signal normalization(1.42 and its associated statistical and systematic errors) is
compared with the case of no  appearance, which would
have a normalization of zero. An asymmetric Gaussian
centered at 1.42 is prepared and the integral of the PDF
below zero is calculated. The p value is 6:2  105 , whichcorresponds to a significance level of 3:8. A significanceof 2:7 is expected for the nominal expected signal. The
larger measured significance is a consequence of the factthat more signal was measured than expected. The DIS
fraction is fit with a 10% increase over its nominal value,
and is correlated with the tau normalization. Because ofthis, not only is the fitted tau normalization lower than it
would be without this error, but the error on the tau
normalization is larger than it would otherwise be due tothe presence of the correlated DIS error, thus slightly
reducing the measured significance. It should be notedthat if the inverted hierarchy is chosen instead of thenormal one when calculating the oscillation probabilities,
the expected number of 13 -induced upward-going electrons is reduced, approximately in half, resulting in asomewhat higher fitted value (1.56) and a correspondingly
higher significance.
In summary, we find that the Super-Kamiokande atmospheric neutrino data are best described by neutrino oscillations that include tau neutrino appearance in addition tothe overwhelming signature of muon neutrino disappearance. By a neural network analysis on the zenith angle
distribution of multi-GeV contained events, we have demonstrated this at a significance of 3:8.
We gratefully acknowledge the cooperation of the
Kamioka Mining and Smelting Company. The SuperKamiokande experiment has been built and operated
from funding by the Japanese Ministry of Education,
Culture, Sports, Science and Technology, the U.S.
Department of Energy, and the U.S. National Science
Foundation.

*Deceased.
†
Present address: GIST College, Gwangju Institute of
Science and Technology, Gwangju 500-712, Korea.

‡

week ending
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Present address: Department of Physics and Astronomy,
University of Minnesota, Minneapolis, MN 55455,
USA.
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