V OLUME

81, N UMBER 8 PHYSICAL REVIEW LETTERS 2 4 A

UGUST

1998

s; n

m

y n

e

d of the ﬂux of n

m

1 n

m

to the ﬂux of n

e

1 n

e

of about 2. The n

m

y n

e

ratio has been calculated in detail

with an uncertainty of less than 5% over a broad range of

energies from 0.1 to 10 GeV [1,2].

The n

m

y n

e

ﬂux ratio is measured in deep underground

experiments by observing ﬁnal state leptons produced via

charged-current interactions of neutrinos on nuclei, n1

N ! l 1 X . The ﬂavor of the ﬁnal state lepton is used to

identify the ﬂavor of the incoming neutrino.

The measurements are reported as R ;s m y e d

DATA

y

s m y e d

MC

, where m and e are the number of muon-

like s m - like d and electronlike s e - like d events observed

in the detector for both data and Monte Carlo simu-

lations. This ratio largely cancels experimental and theo-

retical uncertainties, especially the uncertainty in the

absolute ﬂux. R  1 is expected if the physics in the

Monte Carlo simulation accurately models the data.

Measurements of signiﬁcantly small values of R have

been reported by the deep underground water Cherenkov

detectors Kamiokande [3,4], IMB [5], and recently by

Super-Kamiokande [6,7]. Although measurements of R

by early iron-calorimeter experiments Fréjus [8] and NU-

SEX [9] with smaller data samples were consistent with

expectations, the Soudan-2 iron-calorimeter experiment

has reported observation of 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 pro-

duced in ﬂavor state a to be observed in ﬂavor state b after

traveling a distance L through a vacuum is

P

a ! b

 sin

2

2 u sin

2

µ

1.27 D m

2

s eV

2

d L s km d

E

n

s GeV d

∂

, (1)

where E

n

is the neutrino energy, u is the mixing angle

between the ﬂavor eigenstates and the mass eigenstates,

and D m

2

is the mass squared difference of the neutrino

mass eigenstates. For detectors near the surface of the

Earth, the neutrino ﬂight distance, and thus the oscilla-

tion probability, is a function of the zenith angle of the

neutrino direction. Vertically downward-going neutrinos

travel about 15 km, while vertically upward-going neutri-

nos travel about 13 000 km before interacting in the detec-

tor. The broad energy spectrum and this range of neutrino

ﬂight distances make measurements of atmospheric neu-

trinos sensitive to neutrino oscillations with D m

2

down to

10

2 4

eV

2

. 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 kton yr (535 days) of

atmospheric neutrino data from Super-Kamiokande. In

addition to measurements of small values of R both above

and below , 1 GeV, we observed a signiﬁcant zenith angle

dependent deﬁcit of m - like events. While no combination

of known uncertainties in the experimental measurement

or predictions of atmospheric neutrino ﬂuxes is able to

explain our data, a two-neutrino oscillation model of

n

m

$ n

x

, where n

x

may be n

t

or a new, noninteracting

“sterile” neutrino, is consistent with the observed ﬂavor

ratios and zenith angle distributions over the entire energy

region.

Super-Kamiokande is a 50 kton water Cherenkov detec-

tor instrumented with 11 146 photomultiplier tubes (PMTs)

facing an inner 22.5 kton ﬁducial volume of ultrapure wa-

ter. Interaction kinematics are reconstructed using the time

and charge of each PMT signal. The inner volume is sur-

rounded by a , 2m thick outer detector instrumented with

1885 outward-facing PMTs. The outer detector is used to

veto entering particles and to tag exiting tracks.

Super-Kamiokande has collected a total of 4353 fully

contained (FC) events and 301 partially contained (PC)

events in a 33.0 kton yr exposure. FC events deposit all

of their Cherenkov light in the inner detector while PC

events have exiting tracks which deposit some Cherenkov

light in the outer detector. For this analysis, the neutrino

interaction vertex was required to have been reconstructed

within the 22.5 kton ﬁducial volume, deﬁned to be . 2m

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. Single-ring events were identiﬁed as c - like or m - like

based on a likelihood analysis of light detected around

the Cherenkov cone. The FC events were separated into

“sub-GEV” s E

vis

, 1330 MeV d and “multi-GeV” s E

vis

.

1330 MeV d samples, where E

vis

is deﬁned to be the energy

of an electron that would produce the observed amount

of Cherenkov light. E

vis

 1330 MeV corresponds to

p

m

, 1400 MeV y c .

In a full-detector Monte Carlo simulation, 88% (96%) of

the sub-GeV e - like s m - like d events were n

e

s n

m

d charged-

current interactions and 84% (99%) of the multi-GeV

e - like s m - like d events were n

e

s n

m

d charged-current (CC)

interactions. PC events were estimated to be 98% n

m

charged-current interactions; hence, all PC events were

classiﬁed as m - like, and no single-ring requirement was

made. Table I summarizes the number of observed events

for both data and Monte Carlo as well as the R values for

the 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].

We have measured signiﬁcantly small values of R

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

sources of systematic uncertainties in these measurements

have been considered. Cosmic ray induced interactions in

the rock surrounding the detector 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 insigniﬁcant for large water Cherenkov

detectors [12]. In particular, Super-Kamiokande has 4.7 m

of water surrounding the ﬁducial volume; this distance

corresponds to roughly 5 hadronic interaction lengths

and 13 radiation lengths. Distributions of event vertices

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