Revision of May 6, 1998

Study of the atmospheric neutrino ux in the multi-GeV energy range
The Super-Kamiokande Collaboration
Y.Fukudaa , T.Hayakawaa, E.Ichiharaa, K.Inouea , K.Ishiharaa, H.Ishinoa , Y.Itowa , T.Kajitaa,
J.Kamedaa, S.Kasugaa, K.Kobayashia, Y.Kobayashia, Y.Koshioa, K.Martensa;1 , M.Miuraa ,M.Nakahataa, S.Nakayamaa, A.Okadaa, M.Oketaa, K.Okumuraa, M.Otaa , N.Sakuraia, M.Shiozawaa,
Y.Suzukia , Y.Takeuchia, Y.Totsukaa , S.Yamadaa , M.Earlb, A.Habigb , E.Kearnsb, S.B.Kimb; 2 ,M.D.Messierb , K.Scholbergb, J.L.Stoneb , L.R.Sulakb , C.W.Walterb , M.Goldhaberc , T.Barszczakd,
W.Gajewskid, P.G.Halversond;3 , J.Hsud, W.R.Kroppd, L.R. Priced, F.Reinesd , H.W.Sobeld ,M.R.Vaginsd, K.S.Ganezere, W.E.Keige , R.W.Ellsworthf , S.Tasakag , J.W.Flanaganh;4 , A.Kibayashih,
J.G.Learnedh, S.Matsunoh , V.Stengerh, D.Takemorih, T.Ishiii , J.Kanzakii, T.Kobayashii,
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 , R.Sanfordl , R.Svobodal , M.L.Chenm , Z.Connerm;5
J.A.Goodmanm , G.W.Sullivanm , M.Morin; 6 , J.Hillo , C.K.Jungo, C.Maugero, C.McGrewo , E.Sharkeyo,
B.Vireno , C.Yanagisawao, W.Dokip , T.Ishizukap; 7 , Y.Kitaguchip, H.Kogap, K.Miyanop, H.Okazawap,
C.Sajip , M.Takahatap, A.Kusanoq , Y.Nagashimaq , M.Takitaq , T.Yamaguchiq , M.Yoshidaq , M.Etohr ,K.Fujitar , A.Hasegawar , T.Hasegawar, S.Hatakeyamar , T.Iwamotor , T.Kinebuchir , M.Kogar ,T.Maruyamar , H.Ogawar, A.Suzukir , F.Tsushimar , M.Koshibas, M.Nemotot , K.Nishijimat ,T.Futagamiu, Y.Hayatou;8 , Y.Kanayau, K.Kaneyukiu, Y.Watanabeu , D.Kielczewskav;d;9 , R.Doylew ,J.Georgew , A.Stachyraw , L.Waiw , J.Wilkesw , 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, Miyagi University of Education, Sendai, Miyagi 980-0845, Japano Department of Physics and Astronomy, State University of New York, Stony Brook, NY 11794-3800, USAp Department of Physics, Niigata University, Niigata, Niigata 950-2181, Japanq Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japanr 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
1 Present address: Department of Physics and Astronomy, State University of New York, Stony Brook
2 Present address: Department of Physics, Seoul National University, Seoul 151-742, Korea
3 Present address: NASA, JPL, Pasadena, CA 91109, USA
4 Present address: Accelerator Laboratory, High Energy Accelerator Research Organization (KEK)
5 Present address: Enrico Fermi Institute, University of Chicago, Chicago, IL 60637 USA
6 Present address: Institute for Cosmic Ray Research, University of Tokyo
7 Present address: Dept. of System Engineering, Shizuoka University Hamakita, Shizuoka 432-8561, Japan
8 Present address: Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK)
9 Supported by the Polish Committee for Scienti c Research.

1

Abstract
The atmospheric neutrino ux ratio  =e and its zenith angle dependence have been measured in themulti-GeV energy range using an exposure of 25.5 kiloton-years of the Super-Kamiokande detector. By
comparing the data to a detailed Monte Carlo simulation, the ratio (=e)DATA =(=e)MC was measured
to be 0:66  0:06(stat:)  0:08(sys:). In addition, a strong distortion in the shape of the event zenith angle
distribution was observed. The ratio of the number of upward to downward -like events was found to:07
be 0.52+0,0:06(stat:)  0:01(sys:), with an expected value of 0:98  0:03(stat:)  0:02(sys:), while the sameratio for the e-like events was consistent with unity.

Introduction
Cosmic ray interactions in the atmosphere produce neutrinos. The avor ratio of the atmospheric neutrinoux, ( +  )=(e + e ) has been calculated to an accuracy of better than 5% in the range from 0.1 GeV
to higher than 10 GeV[1, 2]. The calculated ux ratio has a value of about two for energies <1 GeVand increases with increasing neutrino energy. For neutrino energies higher than a few GeV, the uxesof upward and downward going neutrinos are expected to be nearly equal; geomagnetic eld e ects on
atmospheric neutrinos in this energy regime are expected to be small because the primary cosmic rays
that produce these neutrinos have rigidities exceeding the geomagnetic cuto rigidity (10 GeV/Ze).
The avor ratio of the atmospheric neutrino ux has been studied by several massive undergrounddetectors. In these experiments, the ratio of the number of -like to the number of e-like neutrino
interactions observed in the detector was compared with Monte Carlo (MC) simulation; i.e., the ratioR  (=e)DATA =(=e)MC was measured to study the atmospheric neutrino avor ratio ( + )=(e +e ).
In the measurement of R, uncertainties in the neutrino ux and cross sections cancel. The expectedvalue for R is unity if there is agreement between the experiment and the theoretical prediction. Threeexperiments { Kamiokande [3], IMB-3 [4] and Soudan-2 [5] { observed an R smaller than unity in theenergy region E <
 1 GeV, although two experiments { Frejus [6] and NUSEX [7] { reported no deviationfrom unity with smaller data samples. Super-Kamiokande [8] recently reported a small R for Evis < 1.33
GeV. The measured small values of R suggest the possibility of neutrino oscillations.
The value of R in the \multi-GeV" (E > 1 GeV) energy region has been studied by fewer experiments.
Kamiokande [9] observed a value of R smaller than unity, as well as a dependence of this ratio on thezenith angle. Since there is a large di erence in the neutrino path-length between upward-going ( 10,000km) and downward-going neutrinos ( 20 km), a zenith angle dependence of R can be interpreted asadditional evidence for neutrino oscillations. IMB-3 has reported a result in a similar energy range [10],but its smaller data sample neither con rmed nor ruled out the Kamiokande results.
In this paper, the atmospheric neutrino measurement in the multi-GeV energy range from the SuperKamiokande detector is presented. With an analyzed ducial volume exposure of 25.5 kiloton-years, R
and the zenith angle dependence of the ux in this region were measured with much higher statistics
than previous experiments. In addition to higher statistics, due to the much larger dimensions of thedetector, Super-Kamiokande can contain multi-GeV muon events, making possible for the rst time ameasurement of the momentum spectrum of -like events up to 8 GeV/c.
Super-Kamiokande is a cylindrical 50 kiloton ring imaging water Cherenkov detector. The detector
consists of an inner detector volume completely surrounded by an outer detector layer. The two detectors
are optically separated by a pair of opaque sheets which enclose a dead region 55 cm in thickness. The
inner detector is 36.2 m high and 33.8 m in diameter; these dimensions are sucient to contain muonsof momentum up to 8 GeV/c. The inner detector is lined with 11,146 50 cm diameter photomultipliertubes (PMT). The photocathode coverage of the inner wall surface is 40%. The outer layer of water is
2.6 , 2.75 m thick and is instrumented with 1885 outward facing 20 cm diameter PMTs. To maximize
light collection, a re ective surface of Tyvek covers the walls of the outer detector, and each PMT istted with a 60 cm  60 cm plate of wavelength shifter. The outer detector is used to reduce backgroundentering from the surrounding rock and to identify penetrating muons. The trigger required at least 29
2inner detector PMT hits, corresponding to the mean number of hit PMTs for a  5.7 MeV electron. The
atmospheric neutrino data reduction was applied to  4  108 raw input triggers from 414 live days of
exposure.

Data reduction
Atmospheric neutrino events have two basic topologies which determine the data reduction stream. If
all of the visible energy is contained within the inner detector, the event is called \fully contained"(FC). An event for which some of the produced particles deposit visible energy in the outer detector
is called \partially contained" (PC). More precisely, a clustering algorithm is applied to the hits in theouter detector:  10 hits are required in an outer detector cluster for an event to be classi ed as PC, or< 10 hits to be classi ed as FC. Figure 1 shows the distribution of the number of hits in an outer detector
cluster for atmospheric neutrino interactions. The separation between FC and PC events is clearly seen.
For both topologies, the interaction vertex is required to be inside the 22.5 kton ducial volume, de ned
as the volume 2 m from the inner detector PMT planes.
For the multi-GeV FC event sample, the reduction and reconstruction chains have already been
described in detail in another paper [8]. The multi-GeV FC data di ered from the sub-GeV FC data onlyin that we required Evis >1.33 GeV. The total number of multi-GeV FC events in the ducial volume
was 792.
According to Monte Carlo estimates, the PC data is a 980.3% pure sample of charged current (CC) +  scattering events. PC events are typically characterized by a single muon with energy sucientto escape the inner detector. The data reduction for PC events di ered signi cantly from the reduction
for FC events, mainly due to the presence of additional hits in the outer detector. Because of these extra
hits from the exiting muon, a simple criterion based on the number of hit outer detector tubes could
not be used to reject cosmic ray background. Several automated data reduction criteria were used toeliminate background in the PC sample before a nal reduction by physicist scanners based on a visualdisplay of the event data.
(i) Low energy events with fewer than 1000 total p.e. were removed, corresponding to muons (electrons) with momentum less than 310(110) MeV/c. By de nition, an exiting (PC) particle must havereached the outer detector from the inner ducial volume, and so must have had a minimum track lengthof about 2.5 meters (corresponding to muons with > 700 MeV/c momentum).
(ii) The time distribution and spatial clustering of hits in the inner and outer detectors were used in
the next reduction step. Events for which the width of the time distribution of hits in the outer detector
exceeded 240 nanoseconds were rejected, as well as events with two or more spatial clusters of outerdetector hits. These cuts eliminated many through-going muons, which typically left two well separated
clusters in the outer detector. Muons which clipped the edges of the detector were eliminated based
upon the topology of the outer detector cluster. Cosmic ray muons which entered and stopped in the
inner volume of the detector were eliminated by excluding events with a relatively small number of innerdetector photoelectrons near the outer detector cluster (1000 p.e. within 2 m). This cut did not remove
PC neutrino events because PC events produced large numbers of photoelectrons in the region where theparticle exited.
(iii) In the next step, a simple vertex t and charge weighted direction estimate were used. A
requirement of  10 hits in the outer detector within 8 meters of the back-extrapolated entrance point
was imposed. The remaining background after this cut consisted of muons which left few or no entrance
hits in the outer detector. These events were rejected by requiring the angle subtended by the earliest
inner detector PMT hit, the vertex, and the back-extrapolated entrance point to be > 37. Remaining
corner clipping muons were rejected by requiring a tted vertex at least 1.5 meters away from the cornersof the inner detector volume. A through-going muon tter was also applied to reject events with a wellt muon track greater than 30 meters long.
(iv) A precise automatic tting algorithm was applied to further reject entering events, again requiring
10 hits in the outer detector within 8 meters of the more accurately back-extrapolated entrance point.
3

At this stage, a minimum requirement of 3000 total p.e. was applied. This requirement corresponded to
350 MeV of visible energy, well below that of any exiting muon. It was estimated that 0.1% of the PC
events in the ducial volume were eliminated by this requirement. After this step, 758 events remainedin the full detector volume.
(v) The remaining events were scanned with an interactive graphical event display to eliminate theremaining background. There were two independent scans of the data, with Monte Carlo events interspersed randomly and in proportion to livetime. Scanners were asked to classify each event as a neutrino(FC or PC), or various types of known background. Most (>85%) of the events eliminated by scanningwere entering events (through-going or stopping muons). A third and nal scan was used to resolve
disputes between the rst two independent scans. Blind scanning of Monte Carlo events mixed in withthe data showed that the scanning eciency was 99% in the ducial volume.
Applying the same reduction steps to Monte Carlo generated atmospheric neutrino events yielded an
overall data reduction eciency of 885% for interactions in the ducial volume. Ineciency accruedat the few percent level in each automated reduction stage. After the visual scan, 352 (230) PC events
remained in the full ( ducial) detector volume.
The vertex resolution for the FC single-ring -like (e-like) events was estimated to be 23 (42) cm andfor PC events it was estimated to be 104 cm.

Flavor ratio
For the  =e ratio in the multi-GeV region, we used FC single-ring events with Evis > 1.33 GeV and PC
events. In Table 1, the numbers of observed events are summarized along with the corresponding Monte
Carlo predictions. For FC events, lepton avor was determined by the particle identi cation method
described in Ref.[8]. According to Table 1, the PC events comprise a 98% pure charged-current (CC) sample; therefore we classify all PC events as -like. FC -like (e-like) events were a 99% (84%) pure CC
 (CC e ) sample. The relatively low purity of the e-like sample was due to the incompleteness of theseparation of the electromagnetic shower events from CC and neutral-current (NC) interactions which
produced single and multiple pions.
From these data, the ratio RFC +PC  (=e)DATA =(=e)MC for the multi-GeV region was obtained:
R = 0:66  0:06(stat:)  0:08(sys:);where e is the number of FC e-like events and  is the sum of the numbers of FC and PC -like events.
The same ratio for FC events only is RFC = 0.64  0.07  0.10. This result is consistent with theprevious results from Kamiokande [9] in the same energy range and is also consistent with the results inthe lower energy region obtained by Kamiokande [3] IMB-3 [4], Soudan-2 [5] and Super-Kamiokande [8].
It is signi cantly smaller than unity.
The systematic uncertainty in RFC +PC came from several sources: 5% from uncertainty in the atmospheric ux ratio ( +   )=(e +  e ), 4.3% from the uncertainties in the CC neutrino cross section andnuclear e ects in H2 O targets, 4.1% from corresponding uncertainties for NC interactions, 1.6% from theuncertainty of the cosmic ray primary energy spectrum, 1% from hadron tracking simulation, 6% fromthe single and multi-ring separation for FC events, 4% from energy scale determination and 0.5% fromenergy resolution uncertainty, 3% from PC reduction eciency, 3% from particle type misidenti cation,
2% from the vertex reconstruction, 1% from uncertainty in the separation between FC and PC events,and 3% from Monte Carlo statistical uncertainty. In addition, uncertainties on R from event sample
contamination included: 1% from cosmic muons, less than 0.1% from the neutron-induced background,and less than 0.5% from \ asher" events (Ref.[8]). Adding all of these uncertainties in quadrature, weestimated the total systematic uncertainty on R to be 12%.
Fig. 2 shows RFC +PC as a function of the distance of the reconstructed vertex to the nearest innerdetector wall DWALL. From this gure, there is no evidence for neutron, gamma-ray, or cosmic ray
muon background which could change R near the edges of the ducial volume. By scanning FC andPC events, it was determined that the high R value of the bin nearest to DWALL=0 was mostly due
4to a contamination of cosmic ray muon background which entered into the inner detector through lessecient regions of the outer detector. However, the high R value (by 2 standard deviations) at the binjust inside the ducial volume was due to a relative de cit of e-like events by 2.0 sigma (34% de cit) anda 1.1 sigma excess of FC -like and PC events (16% excess). Scanning of events in this bin showed noevidence for background contamination.
For FC events, lepton energy was reconstructed with 4% uncertainty (3% uncertainty from the estimated energy resolution and 2.5% uncertainty from the absolute energy calibration). Fig. 3 showsreconstructed momentum distributions for : (a) FC e-like events, (b) FC -like events and (c) RFC asa function of momentum. The values of 2 /d.o.f. for comparison of the shapes of the MC and data
distributions were 4.4/6 and 1.4/3 for the e-like and -like distributions respectively. (c) was consistent
with a at distribution within the statistical uncertainty (2 /d.o.f. was about 2.3/3). For the PC events,
only a minimum energy for the muon is measurable. Fig. 4 shows the minimum momentum (PMIN )distribution assuming that the exiting particle is a muon. The shape is consistent with the Monte Carloprediction (2 /d.o.f. = 3.7/5). The mean neutrino energies of our sample were approximately 5 GeV, 3
GeV, 15 GeV and 9 GeV for FC e-like, FC -like, PC, and FC -like+PC respectively.
Data
FC events
single ringe-like-likemulti ring
total

Monte Carlo
total e CC(q.e.)  CC(q.e.)

394
218
176
398
792

411.6 155.4(70.1) 239.7(125.6) 16.6
182.7 154.1(69.9)
12.9(1.7) 15.6
229.0
1.2(0.2) 226.8(123.9) 0.9
433.7 129.2(9.0)
237.2(8.6) 67.1
845.2 284.5(79.0) 477.0(134.3) 83.7

PC events
total

230

287.7

4.4(0.8)

281.5(51.6)

NC

1.9

Table 1: Summary of the multi-GeV event sample compared with the Monte Carlo estimation for 25.5ktyrs of detector exposure using the calculated ux from Ref.[1]. Monte Carlo statistics have beennormalized to the live time of the experimental data. \q.e." refers to quasi-elastic events.
A second FC event analysis using a completely independent analysis chain was also performed. The
reduction and reconstruction steps were identical to those performed for the sub-GeV \Analysis B" FC
data sample described in Ref.[8]. For Analysis B, which did not include a PC event selection, the multiGeV sample comprised events with 1:33 GeV< Evis < 5 GeV. The total number of multi-GeV FC eventsin the ducial volume was 602. Among the FC multi-GeV single-ring events, 100 events were classi ed as
e-like and 109 events were classi ed as -like. Based on an independent Monte Carlo sample [8] of 10.2
years of equivalent exposure, the predicted numbers of FC e-like and -like events were 91.6 and 141.1,:11
respectively. The independent analysis result was RFC = 0:71+0,0:09  0:07.
Di erences between the two analyses were consistent with estimated eciencies and resolutions. Although approximately the same live time was analyzed, there were fewer events in the nal Analysis B
sample due to the upper energy cut and a tighter single-ring selection. The Analysis B result con rmedthat the value of R was smaller than unity.
5

Zenith angle dependence
The angular correlation between the neutrino direction and the produced charged lepton direction for
multi-GeV neutrinos is 15 , 20 (RMS). Therefore the zenith angle distribution of the leptons re ects
that of the neutrinos.
Fig. 5 shows the cos  distribution for (a) FC e-like events, (b) FC -like +PC events, (c) FC -likeevents and (d) PC events, where  is the zenith angle of the particle direction, and cos  = ,1(+1)
corresponds to upward-going (downward-going). The neutrino ux calculation has a 20% uncertainty
in absolute ux; therefore we compared only the shape of the zenith angle distribution for data andMonte Carlo. The 2 values for the shape analysis were : 2 /d.o.f. = 4.5/4, 27.3/4, 20.0/4 and 16.0/4,
for Figs. 5 (a) through (d) respectively. For e-like events, the data were consistent with Monte Carlo, butfor -like events, there was an obvious discrepancy. Fig. 6 shows R as a function of zenith angle. The
value of 2 /d.o.f. with respect to a at line through the mean is about 8.2/4. Fig. 5 and Fig. 6 showthat there is a signi cant de cit in the number of upward-going -like events relative to the number ofdownward-going ones. The ratio of the number Nup of upward-going (,1 < cos  < ,0:2) events to thenumber Ndown of downward-going (0:2 < cos  < 1) events is shown in Table 2. Horizontal-going events(,0:2 < cos  < 0:2) were excluded. A signi cant de cit was present in Nup =Ndown for both FC -likeand PC events. The value of Nup =Ndown for e-like events was consistent with expectations. The statisticalsigni cance of the asymmetry for -like data was 5.7. These results con rmed the Kamiokande results[9] with smaller statistical uncertainty.10
Several sources of systematic uncertainty on the up/down ratio were considered. First, the up/down
ratios for e-like events, -like events and (=e)MC for the two calculated uxes [1, 2] were compared.
Both calculations predicted up/down ratios very close to unity. The predicted Nup =Ndown ratio di eredbetween the two calculations by 2% and <1% for the e-like and -like events, respectively, and theup/down ratio of (=e)MC di ered by <2% between the two calculations. These two calculations do
not assume the existence of a 1 km mountain over the Super-Kamiokande detector; the rock reduces theneutrino ux due to muons which are stopped before they can decay in ight. We estimated the e ectof the presence of rock on the predicted ux: Nup =Ndown was increased by about 2% and 1.5% for e-likeand -like events respectively. The presence of rock changed the up/down ratio of (=e)MC by less than
1%. We did not expect any other signi cant sources of systematic uncertainty in the predicted up/down
ratio. The total up/down systematic uncertainty in the Monte Carlo is shown in Table 2.
We estimated that the detector PMT gain was 3% higher for down-going particles than for up-goingparticles by studying decay electrons from stopping cosmic ray muons [8]. This gain asymmetry caused
 2.2% and  3.5% uncertainty in the up/down ratio for the e-like and FC -like events, respectively.
However, the gain asymmetry caused less than 0.1% uncertainty in the up/down ratio for the PC events
due to the looseness of the energy cut in the selection of the PC events. The gain asymmetry caused
a 0.6% uncertainty on the up/down ratio of (=e)DATA . A contamination of non-neutrino backgroundsuch as down-going cosmic muons could have directional correlation. The maximum contribution to theuncertainty in the up/down ratio from contamination was estimated to be  0.5%,  2.0% and  2.1%
for the e-like events, -like events, and (=e)DATA , respectively. From these studies, the total systematic
uncertainties in the up/down ratios for the data were estimated and are shown in Table 2. The total
systematic uncertainty in the up/down ratio of RFC +PC = (RFC +PC )up =(RFC +PC )down was 3%, which
was much smaller than the statistical uncertainty.
The validity of the present analysis can be tested by measuring the azimuth angle distribution of theincoming neutrinos, which is insensitive to a possible in uence from neutrino oscillations. The shape of theazimuth angle distributions agreed with the Monte Carlo predictions which were nearly at. The shapecomparison 2 /d.o.f. values were 9.1/7, 3.3/7 and 3.7/7 for e-like, FC -like and PC events, respectively.
Therefore, the only observed directional distortion was for the -like zenith angle distribution.
:34
For Analysis B, the up/down ratio for e-like events was 1.17+0,0:270.01 for data and 0.940.08 for:13
10 From Fig. 3 of Ref. [9], the Kamiokande Nup =Ndown value for the multi-GeV -like (e-like) data was 0.58+0
,0:11
+0
:
39
(1.38,0:30 ).

6

e-like

Nup

76
data
(FC+PC) 102
-like (FC)
45
(PC)
57
e-like67.6
Monte Carlo(FC+PC) 189.2
-like (FC)
86.7
(PC)
102.5

Ndown

90
195
96
99
66.8
193.5
88.4
105.1

Nup =Ndown:140.84 +0,0:12 0.02:07
0.52 +0,0:06 0.01:09
0.47 +0,0:08 0.02:10
0.58 +0,0:09 0.01

1.01 0.06 0.03
0.98 0.03 0.02
0.98 0.05 0.02
0.98 0.05 0.02

Nup ,Ndown
Nup +Ndown,0.084  0.077  0.01
,0.313  0.055  0.01
,0.362  0.079  0.02
,0.269  0.078  0.01
0.006  0.029  0.01
,0.013  0.017  0.01
,0.010  0.025  0.01
,0.013  0.023  0.01

Table 2: Summary of upward-going and downward-going events. Upward-going (downward-going) events
are those with zenith angle ,1 < cos  < ,0:2 (0:2 < cos  < 1). The Nup =Ndown ratios are shownin the third column with their statistical and systematic uncertainties. Also shown in the last column
are the up-down asymmetry (Nup , Ndown)=(Nup + Ndown) values with their statistical and systematic
uncertainties.
:11
Monte Carlo; the up/down ratio for -like events was 0.38+0,0:090.01 for data and 0.990.06 for Monte
Carlo. The Analysis B result con rmed the signi cant up/down asymmetry for -like events.
Several studies were undertaken to evaluate whether it is possible to reproduce the observed distortionof the FC multi-GeV -like zenith angle distribution (in the absence of neutrino oscillations) by assuming various kinds of possible angular-dependent systematic biases. Angular-dependent muon detectioneciency, energy and track reconstruction were considered; in all cases investigated, consistency between
Monte Carlo and data for -like events could only be attained by assuming unrealistically large systematic errors. From these studies, we conclude that an angular dependent systematic e ect is unlikely tobe responsible for the distortion of the -like zenith angle distribution.

Conclusions
The atmospheric neutrino data in the multi-GeV energy range collected from the Super-Kamiokande
detector for the rst 414 livetime-days are presented in this paper. The mean value of R was signi cantly
smaller than unity, RFC +PC = 0:66  0:06(stat:)  0:08(sys:). In addition, a strong deviation fromexpectation in the shape of the -like event zenith angle distribution was observed. The observed up/down:07
asymmetry of the -like events, Nup =Ndown = 0.52 +0,0:06  0.01, deviated from an expected up/downsymmetry, whereas the e-like distribution was consistent with the expected up/down symmetry. Two
independent analyses yielded consistent results on these e ects. While the zenith angle dependence of the
-like data cannot be explained by any plausible systematic detector e ect considered, the relative de citof upward-going -like events from neutrinos that traveled a long distance suggests the disappearance of via neutrino oscillations.
We gratefully acknowledge the cooperation of the Kamioka Mining and Smelting Company. The
Super-Kamiokande experiment has been built and operated from funding by the Japanese Ministry of
Education, Science, Sports and Culture, and the United States Department of Energy.

7References[1] M.Honda et al., Phys. Rev. D52(1995) 4985 ;M.Honda et al, Phys. Lett. B248 (1990) 193.
[2] G. Barr et al, Phys. Rev. D39(1989) 3532 ;V. Agrawal et al, Phys. Rev. D53(1996) 1314 ;T.K. Gaisser and T. Stanev, Proc. 24th Int. Cosmic Ray Conf.(Rome) Vol.1 (1995) 694.
[3] K.S.Hirata et al., Phys. Lett. B205(1988) 416 ;K.S.Hirata et al., Phys. Lett. B280(1992) 146.
[4] R. Becker-Szendy et al., Phys. Rev. D46(1992) 3720;
D. Casper et al., Phys. Rev. Lett. 66(1991) 2561.
[5] W.W.M Allison et al.. Phys. Lett. B391(1997) 491.
[6] K. Daum et al., Z. Phys. C66(1995) 417.
[7] M. Aglietta et al., Europhys. Lett. 8(1989) 611.
[8] Y. Fukuda et al., the Super-Kamiokande Collaboration, Measurement of a small atmospheric neutrino  =e ratio, Phys. Lett. B (1998), accepted for publication.
[9] Y. Fukuda et al., Phys. Lett. B335(1994) 237.
[10] R.Clark et al., Phys. Rev. Lett. 79(1997) 345.

8

Number of Events

10

4

10

3

10

2

Fully Contained
Partially Contained

10

1
0

20

40

60

80

Number of Hits in Outer Detector Cluster
Figure 1: Distribution of the number of hits within a 500 ns window in an outer detector cluster foratmospheric neutrino Monte Carlo (histogram) and data (points). The Monte Carlo is normalized to theexperimental livetime in this and subsequent plots. The separation between FC and PC events is madeat 10 hits.

92(µ/e)data/(µ/e)MC

fiducial volume
1.5

1

0.5

0
0

5

10

15

DWALL (m)Figure 2: RFC +PC as a function of DWALL , the distance between the event vertex and the nearest
inner detector wall. The region DWALL > 2 m is the ducial volume. Error bars show the statisticaluncertainties of the data and Monte Carlo.

10Number of Events

102(a) FC e-like2(b) FC µ-like

10

Number of Events

1
10

10

1

(µ/e)data/(µ/e)MC

(c) R

1

0
1

10

10

2

Momentum (GeV/c)

Figure 3: Reconstructed momentum distributions for : (a) FC e-like events, (b) FC -like events and(c) RFC as a function of momentum. The histograms with shaded error bars show the Monte Carlopredictions with their statistical uncertainties.

11

Number of Events

10

2

10

1
1

10

10

2

PMIN (GeV/c)
Figure 4: Minimum momentum (PMIN ) distribution for PC events. PMIN is estimated from the reconstructed track length from the vertex to the outer detector. The histogram with shaded error bars shows
the Monte Carlo prediction with its statistical uncertainties.

12

200
(a) FC e-like

Number of Events

Number of Events

100
80
60
40
20

(b) FC µ-like + PC
150
100

50

0
(c) FC µ-like

100

Number of Events

Number of Events

0

75
50
25

(d) PC

100

0

75
50
25
0

-1

0

1

-1

cosΘ

0

1

cosΘ

Figure 5: Zenith angle distributions for: (a) FC e-like events, (b) FC -like and PC events, (c) FC -likeevents and (d) PC events. cos  = 1 means down-going. The histograms with the shaded error bars show
the Monte Carlo predictions with their statistical uncertainties.

13

(µ/e)data/(µ/e)MC

1.5

1

0.5

0
-1

0

1

cosΘ
Figure 6: Zenith angle dependence of RFC+PC . Error bars show the statistical uncertainties of the data
and Monte Carlo.

14