Evidence for oscillation of atmospheric neutrinos
The Super-Kamiokande Collaboration

Y.Fukudaa, T.Hayakawaa, E.Ichiharaa , K.Inouea, K.Ishiharaa, H.Ishinoa , Y.Itowa, T.Kajitaa,a , S.Kasugaa , K.Kobayashia , Y.Kobayashia , Y.Koshioa , M.Miuraa , M.Nakahataa ,J.KamedaaS.Nakayama , A.Okadaa, K.Okumuraa, N.Sakuraia , M.Shiozawaa, Y.Suzukia, Y.Takeuchia, Y.Totsukaa,b , E.Kearnsb , M.D.Messierb , K.Scholbergb , J.L.Stoneb , L.R.Sulakb ,S.Yamadaa,b M.Earlb , A.Habig
cdC.W.Walter, M.Goldhaber, T.Barszczak,d D.Casperd , dW.Gajewskid , d P.G.Halversoned;3 , J.Hsud , edddW.R.Kropp , L.R. Price , F.Reines , M.Smy , H.W.Sobel , M.R.Vagins , K.S.Ganezer , W.E.Keig ,g , J.W.Flanaganh;y A.Kibayashih , J.G.Learnedh , S.Matsunoh , V.J.Stengerh ,R.W.Ellsworthh f , S.Tasakai
D.Takemori , T.Ishii , J.Kanzakii , T.Kobayashii, S.Minei , K.Nakamurai , K.Nishikawai, Y.Oyamai,
A.Sakaii , M.Sakudai, O.Sasakii , S.Echigoj , M.Kohamaj , A.T.Suzukij , T.J.Hainesk;d E.Blaufussl,l , R.Svobodal , M.L.Chenm , Z.Connerm;z J.A.Goodmanm , G.W.Sullivanm , J.Hilln ,B.K.Kiml, R.Sanford
nC.K.Jung , K.Martensn, C.Maugern, C.McGrewn, E.Sharkeyn, B.Virenn, C.Yanagisawan, W.Dokio ,o , H.Okazawao , C.Sajio , M.Takahatao , Y.Nagashimap , M.Takitap , T.Yamaguchip ,K.Miyanoprrrr
M.Yoshidar , S.B.Kimq , M.Etoh, K.Fujita, A.Hasegawa, rT.Hasegawar ,rS.Hatakeyamas r , T.Iwamoto
,
r
r
r
t
M.Koga , T.Maruyama , H.Ogawa , J.Shirai , A.Suzuki , F.Tsushima , M.Koshiba , M.Nemoto ,u , Y.Hayatou;x , Y.Kanayau , K.Kaneyukiu , Y.Watanabeu , D.Kielczewskav;d ,K.Nishijimat, T.Futagamiw
R.A.Doyle, J.S.Georgew , A.L.Stachyraw , L.L.Waiw;33 , R.J.Wilkesw , K.K.YoungwaInstitute for Cosmic Ray Research, University of Tokyo, Tanashi, Tokyo 188-8502, Japanb Department of Physics, Boston University, Boston, MA 02215, USAc Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USAd Department of Physics and Astronomy, University of California, Irvine, Irvine, CA 92697-4575, USAe Department of Physics, California State University, Dominguez Hills, Carson, CA 90747, USAf Department of Physics, George Mason University, Fairfax, VA 22030, USAg Department of Physics, Gifu University, Gifu, Gifu 501-1193, Japanh Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USAi Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki
305-0801, Japanj Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japank Physics Division, P-23, Los Alamos National Laboratory, Los Alamos, NM 87544, USA.
l Physics Department, Louisiana State University, Baton Rouge, LA 70803, USAm Department of Physics, University of Maryland, College Park, MD 20742, USAn Department of Physics and Astronomy, State University of New York, Stony Brook, NY 11794-3800, USAo Department of Physics, Niigata University, Niigata, Niigata 950-2181, Japanp Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japanq Department of Physics, Seoul National University, Seoul 151-742, Korear Department of Physics, Tohoku University, Sendai, Miyagi 980-8578, Japans The University of Tokyo, Tokyo 113-0033, Japant Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japanu Department of Physics, Tokyo Institute for Technology, Meguro, Tokyo 152-8551, Japanv Institute of Experimental Physics, Warsaw University, 00-681 Warsaw, Poland
w Department of Physics, University of Washington, Seattle, WA 98195-1560, USA

We present an analysis of atmospheric neutrino data from a 33.0 kiloton-year (535-day)
exposure of the Super{Kamiokande detector. The data exhibit a zenith angle dependentde cit of muon neutrinos which is inconsistent with expectations based on calculations of
the atmospheric neutrino ux. Experimental biases and uncertainties in the predictionof neutrino uxes and cross sections are unable to explain our observation. The data
are consistent, however, with two- avor  $  oscillations with sin 2 > 0:82 and
5 2 100 < 1m < 6 2 100 eV at 90% con dence level.
2

4

2

3

2

1

Atmospheric neutrinos are produced as decay
products in hadronic showers resulting from collisions of cosmic rays with nuclei in the upper atmosphere. Production of electron and muon neutrinos is dominated by the processes + ! + + 
followed by + ! e+ +  + e (and their charge
conjugates) giving an expected ratio ( =e ) of
the ux of  +  to the ux of e + e of about
two. The  =e ratio has been calculated in detailwith an uncertainty of less than 5% over a broad
range of energies from 0.1 GeV to 10 GeV [1,2].
The  =e ux ratio is measured in deep underground experiments by observing nal-state leptons produced via charged-current interactions ofneutrinos on nuclei,  + N ! l + X . The avor of
the nal state lepton is used to identify the avorof the incoming neutrino.
The measurements are reported as R (=e)DAT A =(=e)MC , where  and e are the number of muon-like (-like) and electron-like (e-like)events observed in the detector for both data andMonte Carlo simulation. This ratio largely cancels
experimental and theoretical uncertainties, especially the uncertainty in the absolute ux. R = 1 is
expected if the physics in the Monte Carlo simulation accurately models the data. Measurements ofsigni cantly small values of R have been reportedby the deep underground water Cherenkov detectors Kamiokande [3,4], IMB [5], and recently bySuper{Kamiokande [6,7]. Although measurementsof R by early iron-calorimeter experiments Frejus[8] and NUSEX [9] with smaller data samples wereconsistent with expectations, the Soudan-2 ironcalorimeter experiment has reported observationof a small value of R [10].
Neutrino oscillations have been suggested to explain measurements of small values of R. For a
two-neutrino oscillation hypothesis, the probability for a neutrino produced in avor state a to beobserved in avor state b after traveling a distanceL through a vacuum is: 1:271m2 (eV2 )L(km) 
Pa!b = sin2 2 sin2
; (1)E (GeV)
where E is the neutrino energy,  is the mixing
angle between the avor
eigenstates and the mass
eigenstates, and 1m2 is the mass-squared di erence of the neutrino mass eigenstates. For detectors near the surface of the Earth, the neutrino
ight distance, and thus the oscillation probability, is a function of the zenith angle of the neutrino direction. Vertically downward-going neutri-

nos travel about 15 km while vertically upwardgoing neutrinos travel about 13,000 km before interacting in the detector. The broad energy spectrum and this range of neutrino ight distances
makes measurements of atmospheric neutrinos sensitive
to2 neutrino oscillations with 1m2 down to0
4
10 eV . The zenith angle dependence of R measured by the Kamiokande experiment at high energies has been cited as evidence for neutrino oscillations [4].
We present our analysis of 33.0 kiloton-years(535 days) of atmospheric neutrino data fromSuper{Kamiokande. In addition to measurementsof small values of R both above and below 1 GeV,
we observed a signi cant zenith angle dependentde cit of -like events. While no combination of
known uncertainties in the experimental measurement or predictions of atmospheric neutrino uxes
is able to explain our data, a two-neutrino oscillation model of  $ x , where x may be  ora new, non-interacting \sterile" neutrino, is consistent with the observed avor ratios and zenith
angle distributions over the entire energy region.
Super{Kamiokande is a 50 kiloton water Cherenkov detector instrumented with 11,146 photomultiplier tubes (PMTs) facing an inner 22.5 kiloton
ducial volume of ultra-pure water. Interaction
kinematics are reconstructed using the time andcharge of each PMT signal. The inner volume issurrounded by a 2 meter thick outer detector instrumented with 1885 outward-facing PMTs. The
outer detector is used to veto entering particles andto tag exiting tracks.
Super{Kamiokande has collected a total of 4353
fully-contained (FC) events and 301 partiallycontained (PC) events in a 33.0 kiloton-year exposure. FC events deposit all of their Cherenkov
light in the inner detector while PC events haveexiting tracks which deposit some Cherenkov lightin the outer detector. For this analysis, the neutrino interaction vertex was required to have beenreconstructed within the 22.5 kiloton ducial volume, de ned to be > 2 m from the PMT wall.
FC events were separated into those with a single visible Cherenkov ring and those with multiple Cherenkov rings. For the analysis of FC
events, only single-ring events were used. Singlering events were identi ed as e-like or -like basedon a likelihood analysis of light detected aroundthe Cherenkov cone. The FC events were separated into \sub-GeV" (Evis < 1330 MeV) and\multi-GeV" (Evis > 1330 MeV) samples, where2Evis is de ned to be the energy of an electron that

We have measured signi cantly small values of
Several sources of systematic uncertainties in thesemeasurements have been considered. Cosmic ray
induced interactions in the rock surrounding thedetector have been suggested as a source of e-like
contamination from neutrons, which could produce small R values [11], but these backgrounds
have been shown to be insigni cant for large water
Cherenkov detectors [12]. In particular, Super{
Kamiokande has 4.7 meters of water surrounding
the ducial volume; this distance corresponds toroughly 5 hadronic interaction lengths and 13 radiation lengths. Distributions of event vertices exhibit no excess of e-like events close to the ducial
boundary [6,7].
The prediction of the ratio of the  ux to thee ux is dominated by the well-understood decay chain of mesons and contributes less than 5%
to the uncertainty in R. Di erent neutrino ux
Data Monte Carlomodels vary by about 620% in the prediction of
sub-GeVabsolute rates, but the ratio is robust [13]. Uncersingle-ring
2389 2622.6
tainties in R due to a di erence in cross sections
e-like1231 1049.1
for e and  have been studied [14]; however, lep-like1158 1573.6
ton universality prevents any signi cant di erence
multi-ring
911 980.7
total
3300 3603.3
in cross-sections at energies much above the muon
R = 0:63 6 0:03 (stat:) 6 0:05 (sys:) mass and thus errors in cross-sections could not
produce a small value of R in the multi-GeV enmulti-GeV
single-ring
520 531.7
ergy range. Particle identi cation was estimated toe-like290 236.0
be > 98% ecient for both -like and e-like events
-like230 295.7
based on Monte Carlo studies. Particle identi multi-ring
533 560.1
cation was also tested in Super{Kamiokande on
total
1053 1091.8
Michel electrons and stopping cosmic-ray muonspartially-contained 301 371.6
andthe -like and e-like events used in this analyRF C P C = 0:65 6 0:05 (stat:) 6 0:08 (sys:)
sis are clearly separated [6]. The particle identi cation programs in use have also been tested using
TABLE I. Summary of the sub-GeV, multi-GeV beams of electrons and muons incident on a waterand PC event samples compared with the Monte Carlo Cherenkov detector at KEK [15]. The data haveprediction based on the neutrino ux calculation of been analyzed independently by two groups, makRef. [2].
ing the possibility of signi cant biases in data selection or event reconstruction algorithms remote[6,7]. Other explanations for the small value of R,
such as contributions from nucleon decays [16], canbe discounted as they would not contribute to thezenith angle e ects described below.
We estimate the probability that the observed
=e ratios could be due to statistical uctuation isless than 0.001% for sub-GeV R and less than 1%
for multi-GeV R.
The -like data exhibit a strong asymmetry inzenith angle (2) while no signi cant asymmetry
is observed in the e-like data [7]. The asymme-

would produce the observed amount of Cherenkov
light. Evis = 1330 MeV corresponds to p  1400
MeV=c.
In a full-detector Monte Carlo simulation, 88%(96%) of the sub-GeV e-like (-like) events were e( ) charged-current interactions and 84% (99%)
of the multi-GeV e-like (-like) events were e ( )charged-current interactions. PC events were estimated to be 98%  charged-current interactions;hence, all PC events were classi ed as -like, andno single-ring requirement was made. Table I summarizes the number of observed events for bothdata and Monte Carlo as well as the R values forthe sub-GeV and multi-GeV samples. Further details of the detector, data selection and event reconstruction used in this analysis are given elsewhere [6,7].

R in both the sub-GeV and multi-GeV samples.

+3

try is de ned as A = (U 0 D)=(U + D) where
U is the number of upward-going events (01 <cos 2 < 00:2) and D is the number of downwardgoing events (0:2 < cos 2 < 1). The asymmetry isbin. NMC is the weighted sum of Monte Carloevents:X
L
NMC = DAT A 2
w:(3)
LM C MC events
LDAT A and LMC are the data and Monte Carlolive-times. For each Monte Carlo event, the weight
w is given by:
w = (1 + )(Ei =E0 ) (1 + s;m cos 2) 2
2fe; (sin2 2; 1m2 ; (1 + )L=E )8(1 0 s=2)
sub-GeV e-like>>> (1 + s =2)>
sub-GeV -like<2 > (1 0 m =2)  N multi-GeV e-like>(1 + m=2)(1 0 2 NPC ) multi-GeV -like>>:(1 + m=2)(1 + 2 ):PC(4)Ei is the average neutrino energy in the ith momentum bin; E0 is an arbitrary reference energy(taken to be 2 GeV); s (m) is the up-down uncertainty of the event rate in the sub-GeV (multiGeV) energy range; NP C is the total number ofMonte Carlo PC events; N is the total numberof Monte Carlo FC multi-GeV muons. The factor fe; weights an event accounting for the initial
neutrino uxes (in the case of  $ e ), oscillation parameters and L=E . The meaning of theMonte Carlo t parameters, and j ( s , m,
 , , , s , m ) and their assigned uncertainties,j , are summarized in Table II. The over-all normalization, , was allowed to vary freely. The uncertainty in the Monte Carlo L=E ratio () was
conservatively estimated based on the uncertainty
in absolute energy scale, uncertainty in neutrinolepton angular and energy correlations, and theuncertainty in production height. The oscillation
simulations used pro les of neutrino production
heights calculated in Ref. [18], which account forthe competing factors of production, propagation,and decay of muons and mesons through the atmosphere. For  $ e , e ects of matter on neutrino
propagation through the Earth were included following Ref. [20,21]. Due to the small number of
events expected from  -production, the e ects of appearance and decay were neglected in simulations2 of  $ 2 . A global scan wasmade on a(sin 2; log 1m ) grid minimizing 2 with respect
to , s, m, , , , s and m at each point.
The best- t to  $  oscillations, 22min =65:2=67 DOF, was obtained at (sin 2 =expected to be near zero independent of ux model
for E > 1 GeV, above which e ects due to the
Earth's magnetic eld on cosmic rays are small.
Based on a comparison of results from our fullMonte Carlo simulation using di erent ux models [1,2] as inputs, treatment of geomagnetic e ects
results in an uncertainty of roughly 60:02 in the
expected asymmetry of e-like and -like sub-GeV
events and less than 60:01 for multi-GeV events.
Studies of decay electrons from stopping muons
show at most a 60:6% up-down di erence in Cherenkov light detection [17].
Figure 1 shows A as a function of momentum forboth e-like and -like events. In the present data,
the asymmetry as a function of momentum for elike events is consistent with expectations, whilethe -like asymmetry at low momentum is consistent with zero but signi cantly deviates from expectation at higher momentum. The average angle
between the nal state lepton direction
and the incomingneutrino direction is 55 at p = 400 MeV/c
and 20 at 1.5 GeV/c. At the lower momenta in
Fig. 1, the possible asymmetry of the neutrino ux
is largely washed out. We have found no detector
bias di erentiating e-like and -like events that
could explain an asymmetry in -like events but
not in e-like events [7].
Considering multi-GeV (FC+PC) muons alone,
the measured asymmetry, A = 00:296 6 0:048 6
0:01 deviates from zero by more than 6 standard
deviations.
We have examined the hypotheses of two- avor
 $ e and  $  oscillation models using a
2 comparison of data and Monte Carlo, allowing all important Monte Carlo parameters to varyweighted by their expected uncertainties.
The data were binned by particle type, momentum, and cos 2. A 2 is de ned as:
XX
2 =(NDAT A 0 NM C )2=2 + 2j =j2 ; (2)2cos ;pj

where the sum is over ve bins equally spaced
in cos 2 and seven momentum bins for both e-likeevents and -like plus PC events (70 bins total).
The statistical error, , accounts for both data
statistics and the weighted Monte Carlo statistics.
NDAT A is the measured number of events in each4

1:0; 1m2 = 2:2 2 21003 eV2) inside the physical region (0  sin 2  1). The best- t values of the Monte Carlo parameters (summarizedin Table II) were all within their expected errors. The global minimum occurred
slightly out2 2 = 1:05; 1m2 =side the 0physicalregionat(sin
2:2 2 10 3 eV2; 2min = 64:8=67 DOF). The contours of the 68%, 90%2 and 99% con dence intervals are located at min + 2:6; 5:0; and 9:6 basedon the minimum inside the physical region [19].
These 2contours are shown in Fig. 2. The region
near  minimum is rather at and has many local
minima so that inside the 68% interval the best- t
1m2 is not well constrained.
Outside the 99% allowed region the 2 increases rapidly. We obtained
2 = 135=69 DOF, when calculated at sin2 2 = 0,
1m2 = 0 (i.e. assuming no oscillations).
For the test of  $ e oscillations, we obtained2a relatively poor2 t; 2min 0=3 87:82 =67 DOF,
at (sin 2 = 0:93; 1m = 3:2210 eV ). The expected asymmetry of the multi-GeV e-like events
for the best- t  $ e oscillation hypothesis,
A = 0:205, di ers from the measured asymmetry,A = 00:036 6 0:067 6 0:02, by 3.4 standard deviations. We conclude that the  $ e hypothesis is
not favored.

The zenith angle distributions for the FC andPC samples are shown in Fig. 3. The data arecompared to the Monte Carlo expectation (no oscillations, hatched region) and the best- t expectation for  $  oscillations (bold line).
We also estimated the oscillation parametersconsidering the R measurement and the zenith angle shape separately. The 90% con dence level
allowedregions for each case overlapped at 1 21003 < 1m2 < 4 2 1003 eV2 for sin2 2 = 1.
As a cross-check of the above analyses, we havereconstructed the best estimate of the ratio L=Efor each event. The neutrino energy is estimatedby applying a correction to the nal state lepton
momentum. Typically, nal state leptons withp  100 MeV/c carry 65% of the incoming neutrino energy increasing to 85% at p = 1 GeV/c.
The neutrino ight distance L is estimated following Ref. [18] using the estimated neutrino energy
and the reconstructed lepton direction and avor.
Figure 4 shows the ratio of FC data to Monte Carlofor e-like and -like events with p > 400 MeV/c asa function of L=E , compared to the expectationfor  $  oscillations with our best- t parameters. The e-like data show no signi cant variationin L=E , while the -like events show a signi cantde cit at large L=E . At large L=E , the  havepresumably undergone numerous oscillations andhave averaged out to roughly half the initial rate.
The asymmetry A of the e-like events in thepresent data is consistent with expectations without neutrino oscillations and two- avor e $ 
oscillations are not favored. This is in agreementwith recent results from the CHOOZ experiment[22]. The LSND experiment has reported the appearance of e in a beam of  produced by stopped
pions [23]. The LSND results do not contradict thepresent results if they are observing small mixing
angles. With the best- t parameters for  $ 
oscillations, we expect a total of only 15-20 eventsfrom  charged-current interactions in the data
sample. Using the current sample, oscillations between  and  are indistinguishable from oscillations between  and a non-interacting \sterile"
neutrino.
Figure 2 shows the Super{Kamiokande results
overlaid with the allowed region obtained by
the Kamiokande experiment [4]. The Super{2Kamiokande region favors lower values of 1m
than allowed by the Kamiokande experiment; however the 90% contours from both experiments havea region of overlap. Preliminary studies of upward-

Monte Carlo Fit Parameters Best Fit Uncertainty
overall normalization
15:8% (*)
 E spectral index
0.006  = 0:05
-6.3% s = 8%s sub-GeV =e ratio-11.8% m = 12%m multi-GeV =e ratio relative norm. of PC to FC -1.8%  = 8%
 L=E
3.1% s = 15%
s sub-GeV up-down
2.4%  = 2:4%
m multi-GeV up-down-0.09% m = 2:7%
TABLE II. Summary of Monte Carlo t parameters.
Best- t values for  $  (1m = 2:2 2 100 eV ,sin
2 = 1:0) and estimated uncertainties are given.
3 The over-all normalization ( ) was estimated tohave a 25% uncertainty but was tted as a free parameter.
2

3

2

2

( )

5

going stopping and through-going muons in SuperKamiokande [24] give allowed regions consistent
with the FC and PC event analysis reported inthis paper.
Both the zenith angle distribution of -likeevents and the value of R observed in this experiment signi cantly di er from the best predictionsin the absence of neutrino oscillations. While uncertainties in the ux prediction, cross sections,and experimental biases are ruled out as explanations of the observations, the present data are ingood agreement with two- avor  $  oscillations with sin2 2 > 0:82 and 5 2 1004 < 1m2 <6 2 1003 eV2 at 90% con dence level. We conclude
that the present data give evidence for neutrino oscillations.
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.

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3 Present address:

NASA, JPL, Pasadena, CA
91109,USA
y Present address: Accelerator Laboratory, HighEnergy Accelerator Research Organization (KEK)z Present address: Enrico Fermi Institute, University of Chicago, Chicago, IL 60637 USA
x Present address: Institute of Particle and Nuclear
Studies, High Energy Accelerator Research Organization (KEK)
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1

1

e-likeνµ - ντ

0.5

0

-1

10

Kamiokande

2∆m (eV )

-1
10
1

-1

1

10

10

2

2

(U-D)/(U+D)-0.5µ-like
0.5

FC

-2

10

Super-Kamiokande

PC
-3

0

68%
90%
99%

10

-0.5

-1
10

-4

-1

1

10

10

0

Momentum (GeV/c)

FIG. 1. The (U 0 D)=(U + D) asymmetry as afunction of momentum for FC e-like and -like eventsand PC events. While it is not possible to assign
a momentum to a PC event, the PC sample is estimated to have a mean neutrino energy of 15 GeV. The
Monte Carlo expectation without neutrino oscillations
is shown in the hatched region with statistical and systematic errors added in quadrature. The dashed linefor -like is the expectation for  0$  oscillations
with (sin 2 = 1:0; 1m = 2:2 2 10 eV ).
2

2

3

0.2

0.4

2

0.6

0.8

1

sin 2θ

FIG. 2. The 68%, 90% and 99% con dence intervals are shown for sin 2 and 1m for  $ 
two-neutrino oscillations based on 33.0 kiloton-yearsof Super{Kamiokande data. The 90% con dence interval obtained by the Kamiokande experiment is also
shown.
22

72

sub-GeV
250
200

250

e-likep < 0.4 GeV/c

200

multi-GeV
50

e-likep > 0.4 GeV/c40

75

e-likep < 2.5 GeV/c

60

150

150

30

45

100

100

20

30

50

50

10

15

0
200

0
300

0
100

0
125

160

µ-likep < 0.4 GeV/c

240µ-likep > 0.4 GeV/cµ-like

80

100

120

180

60

75

80

120

40

50

40

60

20

25

0
-1

-0.6 -0.2 0.2
cosΘ

0.6

1

0
-1

-0.6 -0.2 0.2
cosΘ

0.6

1

0
-1

-0.6 -0.2 0.2
cosΘ

0.6

1

0
-1

e-likep > 2.5 GeV/c

Partially Contained-0.6 -0.2 0.2
cosΘ

0.6

1

FIG. 3. Zenith angle distributions of -like and e-like events for sub-GeV and multi-GeV data sets. Upward-going particles have cos 2 < 0 and downward-going particles have cos 2 > 0. Sub-GeV data are shown
separately for p < 400 MeV=c and p > 400 MeV=c. Multi-GeV e-like distributions are shown for p < 2:5 GeV=c
and p > 2:5 GeV=c and the multi-GeV -like are shown separately for FC and PC events. The hatched region
shows the Monte Carlo expectation for no oscillations normalized to the data live-time with statistical errors.
The bold line is the best- t expectation for  $  oscillations with the overall ux normalization tted as afree parameter.

8Data / Monte Carlo

1.5

1

0.5

e-likeµ-like

0
1

10

10

2

10

3

10

4

10

5

L/Eν (km/GeV)

FIG. 4. The ratio of the number of FC data events
to FC Monte Carlo events versus reconstructed L=E .
The points show the ratio of observed data to MC expectation in the absence of oscillations. The dashedlines show the 0expected shape for  $  at
1m = 2:2 2 10 eV and sin 2 = 1.
2

3

2

2

9