Observation of high energy atmospheric neutrinos with the Antarctic...

PHYSICAL REVIEW D 66, 012005 ~2002!

Observation of high energy atmospheric neutrinos with the Antarctic muonand neutrino detector array

J. Ahrens,9 E. Andres,14 X. Bai,1 G. Barouch,11 S. W. Barwick,8 R. C. Bay,7 T. Becka,9 K.-H. Becker,2 D. Bertrand,3

F. Binon,3 A. Biron,4 J. Booth,8 O. Botner,13 A. Bouchta,4,* O. Bouhali,3 M. M. Boyce,11 S. Carius,5 A. Chen,11 D. Chirkin,7

J. Conrad,13 J. Cooley,11 C. G. S. Costa,3 D. F. Cowen,10 E. Dalberg,14,† C. De Clercq,15 T. DeYoung,11,‡ P. Desiati,11

J.-P. Dewulf,3 P. Doksus,11 J. Edsjo,14 P. Ekstrom,14 T. Feser,9 J.-M. Frere,3 T. K. Gaisser,1 M. Gaug,4,§ A. Goldschmidt,6

A. Hallgren,13 F. Halzen,11 K. Hanson,10 R. Hardtke,11 T. Hauschildt,4 M. Hellwig,9 H. Heukenkamp,4 G. C. Hill,11

P. O. Hulth,14 S. Hundertmark,8 J. Jacobsen,6 A. Karle,11 J. Kim,8 B. Koci,11 L. Kopke,9 M. Kowalski,4 J. I. Lamoureux,6

H. Leich,4 M. Leuthold,4 P. Lindahl,5 I. Liubarsky,11 P. Loaiza,13 D. M. Lowder,7,i J. Madsen,12 P. Marciniewski,13,¶

H. S. Matis,6 C. P. McParland,6 T. C. Miller,1,** , Y. Minaeva,14 P. Miocinovic,7 P. C. Mock,8,†† R. Morse,11 T. Neunhoffer,9

P. Niessen,4,15 D. R. Nygren,6 H. Ogelman,11 Ph. Olbrechts,15 C. Perez de los Heros,13 A. C. Pohl,5 R. Porrata,8,‡‡

P. B. Price,7 G. T. Przybylski,6 K. Rawlins,11 C. Reed,8,§§ W. Rhode,2 M. Ribordy,4 S. Richter,11 J. Rodrı´guez Martino,14

P. Romenesko,11 D. Ross,8 H.-G. Sander,9 T. Schmidt,4 D. Schneider,11 R. Schwarz,11 A. Silvestri,2,4 M. Solarz,7

G. M. Spiczak,12 C. Spiering,4 N. Starinsky,11,i i D. Steele,11 P. Steffen,4 R. G. Stokstad,6 O. Streicher,4 P. Sudhoff,4

K.-H. Sulanke,4 I. Taboada,10 L. Thollander,14 T. Thon,4 S. Tilav,1 M. Vander Donckt,3 C. Walck,14 C. Weinheimer,9

C. H. Wiebusch,4,* C. Wiedeman,14 R. Wischnewski,4 H. Wissing,4 K. Woschnagg,7 W. Wu,8 G. Yodh,8 and S. Young8

~AMANDA Collaboration!1Bartol Research Institute, University of Delaware, Newark, Delaware 19716

2Fachbereich 8 Physik, BUGH Wuppertal, D-42097 Wuppertal, Germany3UniversiteLibre de Bruxelles, Science Faculty CP230, Boulevard du Triomphe, B-1050 Brussels, Belgium

4DESY-Zeuthen, D-15735 Zeuthen, Germany5Department of Technology, Kalmar University, S-39182 Kalmar, Sweden

6Lawrence Berkeley National Laboratory, Berkeley, California 947207Department of Physics, University of California, Berkeley, California 94720

8Department of Physics and Astronomy, University of California, Irvine, California 926979Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany

10Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 1910411Department of Physics, University of Wisconsin, Madison, Wisconsin 5370612Physics Department, University of Wisconsin, River Falls, Wisconsin 54022

13Division of High Energy Physics, Uppsala University, S-75121 Uppsala, Sweden14Department of Physics, Stockholm University, SCFAB, SE-10691 Stockholm, Sweden

15Vrije Universiteit Brussel, Dienst ELEM, B-1050 Brussel, Belgium~Received 1 February 2002; published 31 July 2002!

The Antarctic muon and neutrino detector array~AMANDA ! began collecting data with ten strings in 1997.Results from the first year of operation are presented. Neutrinos coming through the Earth from the NorthernHemisphere are identified by secondary muons moving upward through the array. Cosmic rays in the atmo-sphere generate a background of downward moving muons, which are about 106 times more abundant than theupward moving muons. Over 130 days of exposure, we observed a total of about 300 neutrino events. In thesame period, a background of 1.053109 cosmic ray muon events was recorded. The observed neutrino flux isconsistent with atmospheric neutrino predictions. Monte Carlo simulations indicate that 90% of these events liein the energy range 66 GeV to 3.4 TeV. The observation of atmospheric neutrinos consistent with expectationsestablishes AMANDA-B10 as a working neutrino telescope.

DOI: 10.1103/PhysRevD.66.012005 PACS number~s!: 95.85.Ry, 95.55.Vj, 96.40.Tv

*Now at CERN, CH-1211, Gene`ve 23, Switzerland.†Now at Defense Research Establishment~FOA!, S-17290 Stockholm, Sweden.‡Now at Santa Cruz Institute for Particle Physics, University of California—Santa Cruz, Santa Cruz, CA 95064.§Now at IFAE, 08193 Barcelona, Spain.i Now at MontaVista Software, 1237 E. Arques Ave., Sunnyvale, CA 94085.¶Now at The Svedberg Laboratory, S-75121 Uppsala, Sweden.** Now at Johns Hopkins University, Applied Physics Laboratory, Laurel, MD 20723.††Now at Optical Networks Research, JDS Uniphase, 100 Willowbrook Rd., Freehold, NJ 07728-2879.‡‡Now at L-174, Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, CA 94550.§§Now at Dept. of Physics, Massachussetts Institute of Technology, Cambridge, MA.i i Now at SNO Institute, Lively, ON, Canada P3Y 1M3.

0556-2821/2002/66~1!/012005~20!/$20.00 ©2002 The American Physical Society66 012005-1

oh

nten

oig

thrahlth

eb

roTinony. Tune—thsuc

oeues-rifthrvc

da-osiona

aa

ic

pcuw0

udithatin

ep

us-of-assix

e

allyod-

atedtheuleof

sionelyion,so-in

hngingsed

ry-

the

esthe

J. AHRENSet al. PHYSICAL REVIEW D 66, 012005 ~2002!

I. INTRODUCTION

Energetic cosmic ray particles entering the Earth’s atmsphere generate a steady flux of secondary particles sucelectrons, muons and neutrinos. The electronic componecosmic rays is quickly absorbed. High energy muons petrate the Earth’s surface for several kilometers, while atmspheric neutrinos can easily pass the Earth up to very henergies. Interactions of hadronic particles, similar toones that create the atmospheric neutrino flux, will geneneutrinos at sites where cosmic rays are generated and wthey interact as they travel through the Universe. The goaobserving neutrinos of astrophysical origin determinesdesign and the size of neutrino telescopes.

The primary channel through which neutrino telescopdetect neutrinos above energies of a few tens of GeV isobserving the Cherenkov light from secondary muons pduced innm-nucleon interactions in or near the telescope.ensure that the observed muons are produced by neutrthe Earth is used as a filter and only upward moving muare selected. A neutrino telescope consists of an arraphotosensors embedded deeply in a transparent mediumtracks of high energy muons—which can travel many hdreds of meters, or even kilometers, through water or iccan be reconstructed with reasonable precision even wicoarsely instrumented detector, provided the medium isficiently transparent. A location deep below the surfaserves to minimize the flux of cosmic-ray muons.

In this paper we demonstrate the observation of atmspheric muon neutrinos with the Antarctic muon and ntrino detector array~AMANDA !. These neutrinos constituta convenient flux of fairly well known strength, angular ditribution, and energy spectrum, which can be used to vethe response of the detector. The paper will focus onmethods of data analysis and the comparison of obsedata with simulations. After a brief description of the detetor, the data and the methods of simulation are introduceSec. III and the general methods of event reconstructiondescribed in Sec. IV. Two AMANDA working groups analyzed the data in parallel. The methods and results of banalyses are described in Secs. V and VI. After a discusof systematic uncertainties in Sec. VII we present the firesults and conclusions.

II. THE AMANDA DETECTOR

The AMANDA detector uses the 2.8 km thick ice sheetthe South Pole as a neutrino target, Cherenkov mediumcosmic ray flux attenuator. The detector consists of vertstrings of optical modules~OMs!—photomultiplier tubessealed in glass pressure vessels—frozen into the ice at deof 1500–2000 m below the surface. Figure 1 shows therent configuration of the AMANDA detector. The shalloarray, AMANDA-A, was deployed at depths of 800 to 100m in 1993–1994 in an exploratory phase of the project. Sties of the optical properties of the ice carried out wAMANDA-A showed a high concentration of air bubblesthese depths, leading to strong scattering of light and makaccurate track reconstruction impossible. Therefore, a de

01200

-asof--h

eteereofe

sy-

oos,sofhe-

af-e

--

yeed-inre

thnl

tndal

thsr-

-

ger

array of ten strings with 302 OMs was deployed in the atral summers of 1995–1996 and 1996–1997 at depths1500–2000 m. This detector is referred to as AMANDAB10, and is shown in the center of Fig. 1. The detector waugmented by three additional strings in 1997–1998 andin 1999–2000, forming the AMANDA-II array.

In AMANDA B10, an optical module consists of a singl8 in. Hamamatsu R5912-2 photomultiplier tube~PMT!housed in a glass pressure vessel. The PMT is opticcoupled to the glass housing by a transparent gel. Each mule is connected to electronics on the surface by a dedicelectrical cable, which supplies high voltage and carriesanode signal of the PMT. For each event, the optical modis read out by a peak-sensing ADC and a TDC capableregistering up to eight separate pulses. The overall preciof measurement of photon arrival times is approximat5 ns. Details of deployment, electronics and data acquisitcalibration, and the measurements of geometry, timing relution, and the optical properties of the ice can be found@1,2#.

The optical properties of the polar ice in whicAMANDA is embedded have been studied in detail, usiboth light emitters located on the strings and the downgomuon flux itself. These studies@3# have shown that the ice inot perfectly homogeneous, but rather that it can be dividinto several horizontal layers which were laid down by vaing climatological conditions in the past@4#. Different con-centrations of dust in these layers lead to a modulation of

FIG. 1. The present AMANDA detector. This paper describdata taken with the ten inner strings shown in expanded view inbottom center.

5-2

wat0ox

thg

ictima

chliderrag

Mtera

eg

bigenra

ofntsrloro-to

ric

n-es:

ithteic

ntede-s 75

oforo-sesesea-gh

the

800the

mo-

asnd

c-s

heteicar

Aers

.

OBSERVATION OF HIGH ENERGY ATMOSPHERIC . . . PHYSICAL REVIEW D 66, 012005 ~2002!

scattering and absorption lengths of light in the ice, as shoin Fig. 2. The average absorption length is about 110 mwavelength of 400 nm at the depth of the AMANDA-B1array, and the average effective scattering length is apprmately 20 m.

III. DATA AND SIMULATION

The data analyzed in this paper were recorded duringaustral winter of 1997, from April to November. Subtractindowntime for detector maintenance, removing runs in whthe detector behaved abnormally and correcting for deadin the data acquisition system, the effective livetime w130.1 days.

Triggering was done via a majority logic system, whidemanded that 16 or more OMs report signals within a sing window of 2ms. When this condition was met, a triggveto was imposed and the entire array read out. Thetrigger rate of the array was on average 75 Hz, producintotal data set of 1.053109 events.

Random noise was observed at a rate of 300 Hz for Oon the inner four strings and 1.5 kHz for tubes on the ousix, the difference being due to different levels of concenttion of radioactive potassium in the pressure vessels~detailson noise rates can be found in Ref.@5#!. A typical event hasa duration of 4.5ms, including the muon transit time and thlight diffusion times, so random noise contributed on averaone PMT signal per event.

Almost all of the events recorded were produceddowngoing muons originating in cosmic ray showers. Trgers from atmospheric neutrinos contribute only a few tof events per day, a rate small compared to the event

FIG. 2. Variation of the optical properties with depth. The effetive scattering coefficient at a wavelength of 532 nm is shown afunction of depth. Thez axis is pointing upwards and denotes tvertical distance from the origin of the detector coordinate syslocated at a depth of 1730 m. The shaded areas on the side indlayers of constant scattering coefficient as used in the Monte Csimulation.

01200

na

i-

e

he

s

-

wa

sr-

e

y-ste

from cosmic ray muons, as shown in Fig. 3. The main taskAMANDA data analysis is to separate these neutrino evefrom the background of cosmic-ray muons. Monte Ca~MC! simulations of the detector response to muons pduced by neutrinos or by cosmic rays were undertakendevelop techniques of background rejection.

Downgoing muons were generated by atmospheshower simulations of isotropic protons withBASIEV @6# orprotons and heavier nuclei withCORSIKA using the QGSJETgenerator@7,8#, and tracked to the detector with the muopropagation codeMUDEDX @9,10#. Two other muon propagation codes were used to check for systematic differencPROPMU @11# with a 30% lower rate andMMC @12# with aslightly higher rate. A total of 0.93108 events were simu-lated. Most characteristics of the events generated wBASIEV were found to be similar to the more accuraCORSIKA-based simulation. For the latter, the primary cosmray flux as described by Wiebel-Sooth and Biermann@13#was used. The curvature of the Earth has been implemein CORSIKA to correctly describe the muon flux at large znith angles. The event rate based on this Monte Carlo waHz and compares reasonably well with the observed rate100 Hz~after deadtime correction!. The detector response tmuons was modeled by calculating the photon fields pduced by continuous and stochastic muonic energy los@14#, and simulating the response of the hardware to thphotons@15,16#. Upgoing muons were generated by a propgation of atmospheric neutrinos, which were tracked throuthe Earth and allowed to interact in the ice in or arounddetector or in the bedrock below@17,18#. Muons that weregenerated in the bedrock were propagated usingPROPMU@11#until they reached the rock-ice boundary at the depth of 2m. The muons were then propagated through the ice insame way as those from cosmic ray showers. The atspheric neutrino flux was taken from Lipari@19#.

The Cherenkov photon propagation through the ice wmodeled to create multidimensional tables of density a

a

matelo

FIG. 3. The zenith angle distribution of simulated AMANDtriggers per 130.1 days of lifetime. The solid line represents triggfrom downgoing cosmic ray muons generated byCORSIKA. Thedashed line shows triggers produced by atmospheric neutrinos

5-3

.ckwucothto

,pndlaonctioerctsthsix

spetaedetr

r-ineritythea

Othwisccereal0ivmh

asas

sonist

ion

-ne

ere.m-eu-

thetheles

om

rerms.d,ata

eby

ntsre-r ofreata

tolyseslongofrylarsrebe

ali-nelsOnaly-s inicsto

thetalhs,and

theoverin

II,an-


arrival time probability distributions of the photon fluxThese photon fields were calculated for pure muon traand for cascades of charged particles. A real muon trackmodeled as a superposition of the photon fields of a pmuon track and the stochastic energy losses based oncades. The photon fields were calculated out to 400 m frthe emission point, taking into account the orientation ofOM with respect to the muon or cascade. In the detecsimulation, the ice was modeled as 16 discrete layersindicated by the shaded areas in Fig. 2. The spectral proties of the photomultiplier sensitivity, the glass, the gel, amost importantly, the ice itself were included in the simution of the photon propagation. The probability of photdetection depends on the Fresnel reflectance at all interfatransmittances of various parts, and quantum and collecefficiencies of the PMT. The relevant physical paramethave been measured in the laboratory, so that the spesensitivity of the OM could be evaluated. Two types of OMdiffering in the type of pressure vessel, were used inconstruction of AMANDA-B10. The inner four string~AMANDA-B4 ! use Billings housings while the outer sstrings use Benthos housings.~Benthos Inc. and Billings In-dustries are the manufacturers of the glass pressure vesBenthos and Billings are registered trademarks of the restive companies.! The two types of housing have differenoptical properties. The Benthos OMs have an effective qutum efficiency of 21% at a wavelength of 395 nm for planwave photons incident normal to the PMT photocathoNinety percent of the detected photons are in the specrange of 345–560 nm.

An additional sensitivity effect arises from the ice surounding the OMs. The deployment of OMs requires meltand refreezing of columns of ice, called ‘‘hole ice’’ hereaftThis cycle results in the formation of bubbles in the vicinof the modules, which increase scattering and affectssensitivity of the optical modules in ways that are not undstood in detail. Since the total volume of hole ice is smcompared to bulk ice in the detector~columns of 60 cm di-ameter, compared to 30 m spacing between strings!, its effecton optical properties can be treated as a correction to theangular sensitivity. The increased scattering of photons inhole ice has been simulated and compared to data takenlaser measurementsin situ to assess the magnitude of theffect. This comparison provides an OM sensitivity corretion that reduces the relative efficiency in the forward diretion, but enhances it in the sideways and backward dirtions. The sensitivity in the backward hemisphe(90° –180°) relative to the sensitivity integrated overangles (0° –180°) of the optical sensor increases from 2to 27%, due to this correction, while the average relatsensitivity in the forward direction (0° –90°) drops fro80% to 73%. In other words, an OM becomes a somewmore isotropic sensor.

The effective angular sensitivity of the OMs was alsosessed using the flux of downgoing atmospheric muonstest beam illuminating both the 295 downward facing OMand the 7 upward facing OMs. We assumed that the respof the upward facing OMs to light from downward muonsequivalent to the response of the downward facing OMs

01200

sasreas-mer

aser-,

-

es,nsral,e

els.c-

n--.al

g.

er-ll

Meith

--c-

l%e

at

-a

se

o

light from upward moving muons. Based on this assumptwe derived a modified angular response function~later re-ferred to asANGSENS!, which resulted in a effective reduction of the absolute OM sensitivity in forward direction. Ithis model the effective relative sensitivity is 67% in thforward hemisphere, and 33% in the backward hemisphThis correction will be used to estimate the effect of systeatic uncertainties in the angular response on the final ntrino analysis.

The simulation of the hardware response includedmodeling of gains and thresholds and random noise atlevels measured for each OM. The transit times of the caband the shapes of the photomultiplier pulses, ranging fr170 to 360 ns full width at half maximum~FWHM!, wereincluded in the trigger simulation. Multi-photon pulses wesimulated as superimposed single photoelectron wavefoIn all, some 83105 seconds of cosmic rays were simulatecorresponding to 7% of the events contained in the 1997 dset.

IV. EVENT RECONSTRUCTION

The reconstruction of muon events in AMANDA is donoffline, in several stages. First, the data are ‘‘cleaned’’removing unstable PMTs and spurious PMT signals~or‘‘hits’’ ! due to electronic or PMT noise. The cleaned eveare then passed through a fast filtering algorithm, whichduces the background of downgoing muons by one ordemagnitude. This reduction allows the application of mosophisticated reconstruction algorithms to the remaining dset.

Because of the complexity of the task, and in orderincrease the robustness of the results, two separate anaof the 1997 data set were undertaken. Both proceeded athe general lines described above, but differ in the detailsimplementation. The preliminary stages, which are vesimilar in both analyses, are described here. The particuof each analysis will be described in Secs. V and VI. A modetailed description of the reconstruction procedure willpublished elsewhere@20#.

A. Cleaning and filtering

The first step in reconstructing events is to clean and cbrate the data recorded by the detector. Unstable chan~OMs! are identified and removed on a run-to-run basis.average, 260 of the 302 OMs deployed are used in the anses. The recorded times of the hits are corrected for delaythe cables leading from the OMs to the surface electronand for the amplitude-dependent time required for a pulsecross the discriminator threshold. Hits are removed fromevent if they are identified as being due to instrumennoise, either by their low amplitudes or short pulse lengtor because they are isolated in space by more than 80 mtime by more than 500 ns from the other hits recorded inevent. Pulses with short duration, measured as the timethreshold~TOT!, are often related to electronic cross-talkthe signal cables or the surface electronics. In analysisTOT cuts are applied to individual channels beyond the stdard cleaning common to both analyses~see Sec. VI!.

5-4

s

a

o

dfoe

lteo

ertoth

tckgehais.b-atase

ren

ndh

fze

exth

wgis

fwck

re-up-nethe

tedanon

rinoblespa-am-

aleheeedpli-


Following the cleaning and the calibration, a ‘‘line fit’’ icalculated for each event. This fit is a simplex2 minimiza-tion of the apparent photon flux direction, for which an anlytic solution can be calculated quickly@21# ~see also@1#!. Itcontains no details of Cherenkov radiation or propagation

light in the ice. Hits arriving at timet i at PMT i located atr iW

are projected onto a line. The minimization ofx25( i(rW i

2rW02vW lf•t i)2 gives a solution forrW0 and a velocityvW lf . The

results of this fit—at the first stage the directionvW lf /uvW lfu, atlater stages the absolute value of the velocity—are usefilter the data set. Approximately 80–90 % of the data,which the line fit solution is steeply downgoing, are rejectat this stage.

B. Maximum likelihood reconstruction

After the data have been passed through the fast fitracks are reconstructed using a maximum likelihomethod. The observed photon arrival times do not followsimple Gaussian distribution attributable to electronic jittinstead, a tail of delayed photons is observed. The phocan be delayed predominantly by scattering in the icecauses them to travel on paths longer than the length ofstraight line inclined at the Cherenkov angle to the traAlso, photons emitted by scattered secondary electronserated along the track will have emission angles other tthe muon Cherenkov angle. These effects generate a dbution of arrival times with a long tail of delayed photons

We construct a probability distribution function descriing the expected distribution of arrival times, and calculthe likelihoodLtime of a given reconstruction hypothesisthe product of the probabilities of the observed arrival timin each hit OM:

Ltime5)i 51

Nhit

p~ t res( i )ud'

( i ) ,uori( i )! ~1!

where t res5tobs2tCher is the time residual~the delay of theobserved hit time relative to that expected for unscattepropagation of Cherenkov photons emitted by the muo!,andd' anduori are the distance of the OM from the track athe orientation of the module with respect to the track. Tprobability distribution functionp includes the effects oscattering and absorption in the bulk ice and in the refroice around the modules. The functional form ofp is based ona solution to a transport equation of the photon flux frommonochromatic point source in a scattering medium@22,23#.The free parameters of this function are then fit to thepected time profiles that are obtained by a simulation ofphoton propagation from muons in the ice@14,22#. Varyingthe track parameters of the reconstruction hypothesis,find the maximum of the likelihood function, correspondinto the best track fit for the event. The result of the fitdescribed by five parameters: three (x,y,z) to determine areference point, and two (u,f) for the zenith and azimuth othe track direction. Figure 4 shows an event display of tupgoing muon events together with the reconstructed tra

01200

-

f

tord

r,da;nsathe.n-n

tri-

e

s

d

e

n

a

-e

e

os.

C. Quality parameters

The set of apparently upgoing tracks provided by theconstruction procedure exceeds the expected number ofgoing tracks from atmospheric neutrino interactions by oto three orders of magnitude, depending on the details ofreconstruction algorithm~see Secs. V and VI!. In order toreject the large number of ‘‘fake events’’—events generaby a downgoing muon or cascade, but seemingly havingupgoing structure—we impose additional requirementsthe reconstructed events to obtain a relatively pure neutsample. These requirements consist of cuts on observaderived from the reconstruction and on topological eventrameters. Below, we describe the most relevant of the pareters used.

FIG. 4. Event display of an upgoing muon event. The gray scindicates the flow of time, with early hits at the bottom and tlatest hits at the top of the array. The arrival times match the spof light. The sizes of the circles correspond to the measured amtudes.

5-5

-

s

e

ite

wine

ph

ecnteon

thcuecacoluo

lfyisen

stonrouh

ticorss

two

k tor

onck-mvent


1. Reduced likelihood, L

In analogy to a reducedx2, we define a reduced likelihood

L52 lnLtime

Nhit25~2!

whereNhit25, the number of recorded hits in the event lethe five track fit parameters, is the number of degreesfreedom. A smallerL corresponds to a higher quality of thfit.

2. Number of direct hits, Ndir

The number of direct hits is defined as the number of hwith time delayst res smaller than a certain value. We ustime intervals of @215 ns,125 ns# and @215 ns,175 ns#, and denote the corresponding parameters asNdir

(25)

and Ndir(75) , respectively. The negative extent of the windo

allows for jitter in PMT rise times and for small errorsgeometry and calibration, while the positive side includthese effects as well as delays due to scattering of thetons. Events with many direct hits~i.e. , only slightly delayedphotons! are likely to be well reconstructed.

3. Track length, Ldir

The track length is defined by projecting each of the dirhits onto the reconstructed track, and measuring the distabetween the first and the last hit. A cut on this paramerejects events with a small lever arm for the reconstructiDirect hits with time residuals of@215 ns,175 ns# areused for the measurement of the track length. Cuts onabsolute length, as well as zenith angle dependent~which take into account the cylindrical shape of the dettor! have been used. The requirement of a minimum trlength corresponds to imposing a muon energy threshFor example, a track length of 100 m translates into a menergy threshold of about 25 GeV.

4. Smoothness, S

The ‘‘smoothness’’ parameter is a check on the seconsistency of the fitted track. It measures the constanclight output along the track. Highly variable apparent emsion of light usually indicates that the track either has becompletely misreconstructed or that an underlaying muoCherenkov light was obscured by a very bright stochalight emission, which usually leads to poor reconstructiThe smoothness parameter was inspired by the KolmogoSmirnov test of the consistency of two distributions; in ocase the consistency of the observed hit pattern with thepothesis of constant light emission by a muon.

Figure 5 shows two events to illustrate the characterisof the smoothness parameter. One event is a long uniftrack, which was well reconstructed. The other event ibackground event which displays a very poor smoothnes

The simplest definition of the smoothness is given by

01200

sof

s

so-

tcer.

ets-kd.n

-of-nicic.v-ry-

sma.

S5max~ uSj u!, where Sj5j 21

N212

l j

l N. ~3!

Figure 6 illustrates the smoothness parameter for theevents displayed in Fig. 5. Herel j is the distance along thetrack between the points of closest approach of the tracthe first and thej th hit modules, with the hits taken in ordeof their projected position on the track.N is the total number

FIG. 5. Two muon events: The upgoing muon event shownthe left has a smooth distribution of hits along the track. The tralike hit topology of this event can be used to distinguish it frobackground events. The event on the right is a background ewith a poor smoothness value.

5-6

o

igth

mtr

dsalitrdda

intio

on

s

in

eu

th,

isre

thes

thea-

ticer-

d to

at-

inoight-twouts,the

lev-ck-lua-

thee-

i-fit

to a

ylike-

omero-thecon-

in

e

svia

d onbe

s inical

thecuts,theof

muore

aeal


of hits. Tracks with hits clustered at the beginning or endthe track haveSj approaching11 or 21, leading toS51.High quality tracks such as the event on the left side of F5, with S close to zero, have hits equally spaced alongtrack.

5. Sphericity

Treating the hit modules as point masses, we can fortensor of inertia for each event, describing the spatial disbution of the hits. Diagonalizing the tensor of inertia yielas eigenvaluesI i the moments of inertia about the principaxes of rotation. For a long, cylindrical distribution of hmodules, two moments will be much larger than the thiWe can reject spherical events, such as those producemuon bremsstrahlung, by requiring that the normalized mnitude of the smallest moment,I 1 /(I i , be small.

D. Principal methods of the analyses

The two analyses of the data diverge after the filterstage, following different approaches to event reconstrucand background rejection.

Analysis I uses an improved likelihood function baseda more detailed description of the photon response@22#, fol-lowed by a set of stepwise tightened cuts. Analysis II useBayesian reconstruction@24# in which the likelihood is mul-tiplied by a zenith angle dependent prior function, resultin a strong rejection of downgoing background.

Rare backgrounds due to unsimulated instrumentalfects, such as cross-talk between signal channels andstable voltage supply, were identified in the course ofanalyses. These effects either produced spurious triggersmore often, spurious hits that caused the event to be mconstructed. Different but comparably efficient techniqu

FIG. 6. Illustration of the smoothness parameter, which copares the observed distribution of hits to that predicted for a memitting Cherenkov light. In the simplest formulation, shown hethe prediction is given as a straight line. A large deviation fromstraight line~0. 68! is found for the event on the right in Fig. 5. Thhigh quality track-like event on the left in Fig. 5 displays a smdeviation~0.09!.

01200

f

.e

ai-

.by

g-

gn

a

g

f-n-

eor,e-s

were developed to treat these backgrounds. In analysis Ievent topology is inspected; if the spatial pattern of hit OMis inconsistent with the reconstructed muon trajectory,event is rejected. Analysis II attempts to remove the anomlous hits or triggers through identification of characteriscorrelations in signal amplitudes and times, which considably reduces the rate of these misreconstructions.

At this stage the data set in each analysis is reduceseveral thousand events out of the original 1.053109, but thedata are still background dominated. The prediction formospheric neutrinos is about 500 at this point.

For the final selection of a nearly pure sample of neutrinduced events, cuts on characteristic observables are tened until the remaining background disappears. Theanalyses use different techniques to choose their final cbut obtain comparable efficiencies. Further details ofanalyses can be found in Refs.@25–27#.

V. ANALYSIS I

In this analysis the data were processed through threeels of initial cuts, designed to reduce the number of baground events to a manageable size for the final cut evation. After a first filtering based on the line fit~level 1!, cutson the zenith angle, the number of direct photons, andlikelihood of the fitted track obtained by the maximum liklihood reconstruction were applied~level 2!.

A. Removal of cascade-like events and detector artifacts

A third filter level used the results of an iterative likelhood reconstruction with varying track initializations, abased on the hit probabilities@see Eq.~4!# and a reconstruc-tion to the hypothesis of a high energy cascade, e.g., duebright seconday muon bremsstrahlung interaction.

The first two levels of filtering consisted of relativelweak cuts on basic parameters like the zenith angle andlihood. They reduced the data set to about 43105 events. Atthis stage, residual unsimulated instrumental features becapparent, e.g., comparatively high amplitude cross-talk pduced when a downgoing muon emits a bright shower incenter of the detector. Such events are predominantly restructed as moving vertically upward and can be identifiedthe distribution of the center of gravity~COG! of hits. Itsvertical component (zCOG) shows unpredicted peaks in thmiddle and the bottom of the detector@see also Fig. 14~top!,demonstrating the effect for analysis II#, while the horizontalcomponents (xCOG and yCOG) show an enhancement of hittowards the outer strings. These strings are read outtwisted pair cables, as opposed to the coaxial cables usethe inner strings. The twisted pair cables were found tomore susceptible to cross-talk signals. Note that variationthe optical parameters of the ice due to past climatologepisodes also produce some vertical structure.

We developed additional COG cuts on the topology ofevents in order to remove these backgrounds. Thesewhich depend on the reconstructed zenith angle, usetrack lengthsLdir and the normalized smallest eigenvaluesthe tensor of inertia (I 1 /(I i).

-n,

l

5-7

-

onin

da-a-


FIG. 7. Characteristic distributions of the center of gravity~COG! of events. The figures on theleft show the distribution of the depthzCOG ver-sus the reconstructed zenith angle. The figuresthe right show the horizontal location of eventsthe xCOG-yCOG plane of events with 0 m,zCOG

,50 m. The positions of the strings are markeby stars. Top: Experimental data before appliction of the COG cuts. Middle: Experimental datafter application of the COG cuts. Bottom: Expectation from the BG simulation after cuts.

r oforl

onthhech

anp

b

t b

attheit

sto

firstoton

to-r

to

or-ch

rob-t is

-

nd

Figure 7 shows the different components of the centegravity of the hits and the reconstructed zenith angle beand after application of the COG cuts, and the Monte Caprediction for fake upward events stemming from misrecstructed downgoing muons. The cuts remove most ofunsimulated background—in particular that far from thorizon—and bring experiment and simulation into mubetter agreement.

In order to verify the signal passing rates, these cutsthose from the previous levels were applied to a subsamof unfiltered ~i.e., downgoing! events but with the zenithangle dependence of the cuts reversed, thus using the adant cosmic ray muons as stand-ins for upgoing muons.

In all, these three levels of filtering reduced the data sea factor of approximately 105 ~see Table II!.

B. Multi-photoelectron likelihood and hit likelihood

Before the final cut optimization the last, most elaborreconstruction was applied, combining the likelihoods forarrival time of the first of muliple photons in a PMT with thlikelihoods for PMTs to have been hit or have not been h

The probability densitiesp(t res( i )ud'

( i ) ,uori( i )) @see Eq.~1!,

Sec. IV B# describe only the arrival times of single photonDensity functions for the multi-photoelectron case haveinclude the effect of repeatedly sampling the distribution

01200

freo-e

dle

un-

y

ee

.

.of

photon arrival times. For several detected photons, theof them is usually less scattered than the average ph~which defines the single photoelectron case!. Therefore theleading edge of a PMT pulse composed of multiple phoelectrons ~MPE! will be systematically shifted to earlietimes compared to a single photoelectron. TheMPE likeli-hoodLtime

MPE @22# uses the recorded amplitude informationmodel this shift.

In the reconstructions mentioned so far, the timing infmation from hit PMTs was used. However, a PMT whiwasnot hit also delivers information. Thehit likelihood Lhitdoes not depend on the arrival times but represents the pability that the track produced the observed hit pattern. Iconstructed from the probability densitiesphit(d'

( i ) ,uori( i )) that

a given PMTi was hit if it was in fact hit, and the probabilities @12phit(d'

( j ) ,uori( j ))# that a given PMTj was not hit if it

was not hit:

Lhit5)i 51

Nhit

phit~d'( i ) ,uori

( i )! )i 5Nhit11

NOM

~12phit~d'( i ) ,uori

( i )!! ~4!

where the first product runs over all hit PMTs and the secoover all non-hit PMTs.

The likelihood combining these two probabilities is

5-8

omt,

ucr

orly

utiou

wnonimeletr

at

ntrin

icckeact

er

aerthgnethtteme

ngh

veomFonsto

am

ter

ro

ls:ltalandates


L5LtimeMPE

•Lhit . ~5!

A cut on the reconstructed zenith angle obtained frfitting with L leaves less than 104 events in the data sedefined as level 4 in Fig. 8.

C. Final separation of the neutrino sample

For the final stage of filtering, a method~CUTEVAL! wasdeveloped to select and optimize the cuts taking into accocorrelations between the cut parameters. A detailed destion of this method can be found in@27#. The principle ofCUTEVAL is to numerically optimize the ratio of signal tAbackground by variation of the selection of cut parameteas well as the actual cut values. Parameters are used onthey improve the efficiency of separation over optimized con all other already included parameters. A first optimizatwas based purely on Monte Carlo simulations, with simlated atmospheric neutrinos for signal and simulated dogoing muons forming the background. This optimizatiyielded four such independent parameters. Two other optzations involved experimental data. In both cases, expmental data have been defined as the background sampone case, the signal was represented by atmospheric neuMonte Carlo simulations, in the other by experimental dsubjected to zenith angle inverted cuts~i.e., to downwardevents passing the quality cuts, but being ‘‘good’’ evewith respect to the upper hemisphere instead—like neutcandidates—with respect to the lower hemisphere!. Theselatter optimizations yielded two additional parameters, whrejected a small contribution of residual unsimulated bagrounds: coincident muons from simultaneous independair showers and events accompanied by instrumental artifsuch as cross-talk. After application of these two cutssimulated and experimental data, the distributions of obsables agree to a satisfactory precision.

Once the minimal set of parameters is found, the optimcut values can be represented as a function of the numbbackground eventsNBG passing the cuts. The result is a pathrough the cut parameter space which yields the best siefficiency for any desired purity of the signal, characterizby NBG. Using this representation, one can calculatenumber of events passing the cuts as a function of the fiNBG for signal and for background Monte Carlo prograFigure 8~top! shows this dependence for simulations as was for experimental data, withNBG varying from trigger levelto a level that leaves only a few events in the data set. Oobserves that the actual background expectation falls roulinearly as the fittedNBG is reduced. Below values of a fewhundred events the signal is expected to dominate the esample. The experimental curve follows the expectation frthe sum of background and signal Monte Carlo program.large NBG, the observed event rate follows the backgrouexpectation. At smallerNBG, the experimental shape turnover into the signal expectation and follows it nicely downthe sample of events with highest quality~the smallest valuesof NBG!. For a moderate background contamination ofNBG510, one gets a total of 223 neutrino candidates. The par

01200

ntip-

s,if

sn--

i-ri-. Ininoa

so

h-ntts

ov-

lof

alded

.ll

ely

nt

rd

-

eters and cut values as obtained by theCUTEVAL procedureare summarized in Table I.

Figure 8 ~bottom! translates the background parameNBG into an event quality parameterQ, defined asQ[ ln(N0 /NBG)5 ln(1.05•109/NBG). The plot shows the ratios

FIG. 8. The fitted background parameterNBG . Top: Number ofevents versusNBG . Smaller values ofNBG correspond to hardecuts. BelowNBG51500 theCUTEVAL parametrization was used tcalculate the cut values corresponding toNBG . For larger values ofNBG the data points correspond to the cuts from the filter leveLevel 4 ~see Sec. V B!, level 3, level 2, level 1, and trigger leve~Table II!. Bottom: Ratios of events passing in the experimendata compared to various Monte Carlo expectations for signalbackground as a function of event quality. The dashed line indicthe final cuts.

5-9

irect’’rs


TABLE I. Final quality parameters and cuts obtained from the cut evaluation procedure. The ‘‘dtime interval for variablesNdir , Ldir , andSdir is @215 ns,175 ns#. The first four rows show cut parameteobtained by all~Monte Carlo and experimental! searches; the last two rows show two additional~weaker!cuts, which were found to remove unsimulated backgrounds.

Parameter Cut Explanation

uSu ,0.28 See Sec. IV C 4uSPhitu/(umpe290°) ,0.01 Tightens the requirement on the smoothness for

tracksclose to the horizon where background is high

(Ndir22)•Ldir .750 m Lever arm of the track times the number ofsupporting points

log(Lup/Ldown) ,27.7 Ratio of the likelihoods of the bestupgoing and best downgoing hypotheses

C(mpe,lf) ,35° Space angle between the results from themulti-photon

likelihood reconstruction and the line fit. This cuteffectively removes cross-talk features.

A(Sdir)21(Sdir

Phit)2 ,0.55 Parameter combining the two smoothnessdefinitions~here calculated using only direct hits!.

This cut effectively removes coincident muonevents from independent air showers.

oia

ue

ic

wev-ee, i

heentla-

ntstedthea-

hef

of events from the upper figure as a function ofQ. At higherqualities (Q.17), the ratio of observed events to the atmspheric neutrino simulation flattens out with a further vartion of only 30%. The value atQ517 is approximately 0.6for the standard Monte Carlo program~chosen in Fig. 8, top!and approximately unity for theANGSENSMonte Carlo pro-gram ~chosen in Fig. 8, bottom!.

Table II lists the cut efficiencies for the atmospheric netrino simulation~with and without the implementation of thangular sensitivity fitted modelANGSENS of the OMs—seeSecs. III and VII!, the background simulation of atmosphermuons from air showers~without ANGSENS! and the experi-mental data. Again, the experimental numbers agreewith the background simulation up to the first two filter leels. Later, the Monte Carlo program underestimates theperimental passing rates slightly. The last row shows thepected numbers of events for the last stage of filtering. Ifaddition, the effect of neutrino oscillations~see Sec. VII! is

01200

--

-

ll

x-x-n

included, the atmospheric neutrino simulation including tANGSENS model predicts 224 events, in closest agreemwith the experiment. However, the 5% effect due to osciltions is smaller than our systematic uncertainty~see Sec.VII !.

D. Characteristics of the neutrino candidates

1. Time distribution

Figure 9 shows the cumulative number of neutrino eveas well as the cumulative number of event triggers plotversus the day number in 1997. One can observe thatneutrino events follow the number of triggers, albeit withsmall deficit during the Antarctic winter. This deficit is consistent with statistical fluctuations.~Actually, seasonal varia-tions slightly decrease the downward muon rate during tAntarctic winter @28# and should result in a 10% deficit otriggers with respect to upward neutrino events.!

etectorrely

TABLE II. The cut efficiencies for the atmospheric neutrino Monte Carlo~MC! prediction, the atmo-spheric muon background Monte Carlo prediction, and the experimental data for 130 days of dlifetime. Efficiencies are given for filter levels L1 to L4. L4 is the final selection. All errors are pustatistical. The final background prediction of 7 events has been normalized at trigger level.

Filter level Atm.n Atm. n MC Atm. m MC ExperimentalMC ANGSENS ~Background! data

Events at trigger level 8978 5759 9.033108 1.053109

Efficiency at level 1 0.34 0.37 0.431021 0.531021



Efficiency after final cuts 0.431021 0.431021 0.631028 0.231026

No. of events 36264 23766 765 223passing final cuts normalized

5-10

2tiosnt

u39

t

s

in

-

rloeri-ape.

cutheides

oferi-ta-the

g.d at-

it

ec.tedvi-ting

ig.thepern-

nd

antheer

eamsti-

eednd

ck-nd

in

oro

macfigta


2. Zenith angle distribution

Figure 10 shows the zenith angle distribution of the 2neutrino candidates compared to the Monte Carlo predicfor atmospheric neutrinos@17# and the few remaining eventpredicted by background simulations. Note that the MoCarlo prediction is normalized to experiment.~The totalnumber of events is 362 for the atmospheric neutrino simlation and 223 for experiment, i.e., there is a deficit ofpercent in the absolute number of events.! There is goodagreement between the prediction and the experiment inshape of the angular distribution.

3. Characteristic distributions and visual inspection

Four methods were used to evaluate the effectivenesthe analysis and the level of residual backgrounds:~a! N

FIG. 9. The integrated exposure of the AMANDA detector1997. The figure shows the cumulative number of triggers~uppercurve! and the number of observed neutrino events~lower curve!versus the day number. The intervals with zero gradient correspto periods where the detector was not operating stably; data fthese periods were excluded from the analysis.

FIG. 10. Zenith angle distribution of the experimental data copared to simulated atmospheric neutrinos and a simulated bground of downgoing muons produced by cosmic rays. In thisure the Monte Carlo prediction is normalized to the experimendata. The error bars report only statistical errors.

01200

3n

e

-

he

of

21 cuts, ~b! unbiased variables, ~c! low level distributions,and ~d! visual inspection.

~a! The N21 test evaluates theN final cuts one by oneand yields an estimate of the background contaminationthe final sample. One applies all but one of the final cuts~theone in the selected variable!, and plots the data in this variable. In the signal region of this variable~defined by the laterapplied cut! shapes of experiment and signal Monte Caprogram should agree. In the background region, the expmental data should approach the expected background shFigure 11 shows four of these distributions. The appliedis shown by a dotted line. All four cuts satisfy the test: tshape of the distributions agree reasonably well on both sof the applied cuts. TwoN21 distribution from analysis IIare shown in Fig. 19.

~b! An obvious test is the investigation of distributionsunbiased variables~i.e., variables to which no cuts havbeen applied! in the final neutrino sample. Here, the expemental distributions follow the Monte Carlo signal expections nicely. Some deviations are observed, especially innumber of OMs hit and the velocityv lf obtained from theline fit ~see Sec. IV A!. However, as can be seen from Fi20, part of these disagreements disappear if the standarmospheric neutrino MC program is replaced by theANGSENS

MC version.~c! In order to account for possible pathologicallow level

features in the data sample~especially cross-talk!, we ~i! in-vestigated basic pulse amplitude and pulse width~TOT! dis-tributions and~ii ! re-fitted all events after the cross-talk hcleaning procedure applied in analysis II~which is tighterthan the standard cross-talk cleaning introduced in SIV A !. Both these distributions and that for the recalculazenith angles show no significant deviation from the preous ones. No cross-talk features are found in the resulneutrino sample.

~d! Finally, avisual inspectionof the full neutrino samplewas performed, by visually displaying each event like in F4. The visual inspection gives consistent results withother methods of background estimation and yields an uplimit on the background contamination of muons from radom coincident air showers~see below!.

E. Background estimation

The results of four independent methods of backgrouestimation are summarized in Table III.

First, the background Monte Carlo program itself givesestimate. It yields 7 events if rates are normalized totrigger level~see Table II!. Because the passing rates diffslightly between the experiment~higher! and the backgroundMonte Carlo program~lower!, we made the conservativchoice to renormalize the background Monte Carlo progrto the level 3 experimental passing rate. This gives an emate of about 16 background events in our final sample.

From theN21 distributions we obtained an alternativapproximation of the residual background. We re-normalizboth signal and background MC events in the backgrouregion to fit the number of experimental events in the baground region. The number of re-normalized backgrou

ndm

-k--l

5-11

st

rethth

aer

. 14ve

alatis-eu-er-

of

13entted

mep-ichntem

ex-the

sstein

pte

-

aleous

in


MC events in the signal region is then a background emate. This estimate was performedN times ~once for eachN21 distribution!. The average over allN estimations yields14 background events. Note that this averaging procedureasonable only for the case of independent cuts. Withmethod by which we have chosen the cut parameters,condition is satisfied to first approximation.

We have found that cross-talk hits are related to the chacteristic triple-peak structure in the distribution of the vtical component of the center of gravity of hits (zCOG) which

FIG. 11. Two distributions of variables used as cut parameterthe last filter level~see Table I for an explanation of the variable!.In both cases, all final cuts with the exception of the variable plothave been applied. The cuts on the displayed parameters arecated by the dashed vertical lines. Arrows indicate the acceparameter space.

01200

i-

iseis

r--

has been discussed in Sec. V A—see Fig. 7 and also Fig~top!. Since there are remaining cross talk hits which hasurvived the standard cleaning~see Sec. IV A!, this distribu-tion was studied in detail. As shown in Fig. 12, the finexperimental sample of neutrino candidates shows no sttically significant excess with respect to the atmospheric ntrino Monte Carlo prediction in the regions of the charactistic peaks. Therefore, an upper limit on this special classbackground was derived and yields,35 events.

The visual inspection of the neutrino sample yieldsevents. Seven of them show the signature of coincidmuons from independent air showers; i.e., two well separaspatial concentrations of hits, each with a downward tiflow but with the lower group appearing earlier than the uper one. Taking into account the scanning efficiencies whwere determined by scanning signal and background MoCarlo events, an upper limit of 23 events is obtained frovisual inspection.

Combining the results from the above methods, thepected background is estimated to amount to 4 to 10% of223 experimental events.

in

ddi-d

FIG. 12. Distributions ofzCOG for the experiment and atmospheric neutrino signal Monte Carlo programMC standardandMCbulk icedenote two different ice models. The first includes verticice layers in accordance with Fig. 2; the second uses homogenice.

TABLE III. Various estimates of the background remainingthe experimental data sample of 223 neutrino candidates.

BG estimation method Estimation

BG MC 1668N21 cuts 1464zCOG distributions ,35Visual inspection ,23

5-12

eaaohci

acinoa

ty

apb

isto

io

naonicin

ond.windon

n

-on-aig

eer

aral-sear-la-an

u-edbe

asvernlse. Incal

terre.alidof

oldthe


VI. ANALYSIS II

The second analysis follows a different approach; instof optimizing cuts to reject misreconstructed cosmic rmuons, this analysis concentrates on improving the recstruction algorithm with respect to background rejection. Tlarge downgoing muon flux implies that even a small fration of downgoing muons misreconstructed as upgoing wproduce a very large background rate. Equivalently, for eapparently upgoing event, there were many more downgomuons passing the detector than there were upgoing mueven though any single downgoing muon had only a smprobability of faking an upgoing event, the total probabilithat the event was a fake is quite high.

A. Bayesian reconstruction

This analysis of the problem motivates a Bayesianproach@24# to event reconstruction. Bayes’ theorem in proability theory states that for two assertionsA andB,

P~AuB!P~B!5P~BuA!P~A!,

whereP(AuB) is the probability of assertionA given thatBis true. IdentifyingA with a particular muon track hypothesm andB with the data recorded for an event in the detecwe have

P~mudata!5Ltime~dataum!P~m!,

where we have dropped a normalization factorP(data)which is a constant for the observed event. The functLtime is the regular likelihood function of Eq.~1!, andP(m)is the so-called prior function, the probability of a muonm5m(x,y,z,u,f) passing through the detector.

For this analysis, we have used a simple one-dimensioprior function, containing the zenith angle informationtrigger level in Fig. 3. By accounting in the reconstructifor the fact that the flux of downgoing muons from cosmrays is many orders of magnitude larger than that of upgoneutrino-induced muons, the number of downgoing muthat are misreconstructed as upgoing is greatly reduceshould be noted that the objections that are often raisedrespect to the use of Bayesian statistics in physics arerelevant to this problem: the prior function is well defineand normalized and independently known to relatively goprecision, consisting only of the fluxes of cosmic ray muoand atmospheric muon neutrinos.

B. Removal of instrumental artifacts

The Bayesian reconstruction algorithm is highly efficieat rejecting downgoing muon events. Of 2.63108 eventspassing the fast filter, only 5.83104 are reconstructed as upgoing. By contrast, the standard maximum likelihood recstruction produces about 2.43107 false upgoing reconstructions. However, less than a thousand neutrino eventspredicted by Monte Carlo program, so it is clear that a snificant number of misreconstructions remain.

Detailed inspection of the 5.83104 events reveals that thvast majority is produced by cross-talk overlaid on trigg

01200

dyn-e-llhg

ns;ll

--

r,

n

alt

gsIt

thot

ds

t

-

re-

s

from downgoing muons emitting bright stochastic light nethe detector. This cross-talk confuses the reconstructiongorithm, producing apparently upgoing tracks. Becaucross-talk is not included in the detector simulation, the chacteristics of the fakes are not predicted well by the simution, and the rate of misreconstruction is much higher thpredicted.

The cross-talk is removed by additional hit cleaning rotines developed by examination of this cross-talk enrichdata set. For example, cross-talk in many channels canidentified in scatter plots of pulse width vs amplitude,shown in Fig. 13. The pulse width is measured as time othreshold~TOT!. Real hits form the distribution shown othe left. High amplitude pulses should have large puwidth. This is not the case for cross-talk induced pulseschannels with high levels of cross-talk, an additional verti

FIG. 13. Pulse amplitude vs duration for modules on the oustrings. Normal hits lie in the distribution shown in the upper figuHigh amplitude pulses of more than a few photoelectrons are vonly if the pulse width is also large. Cross-talk induced pulseshigh amplitude are characterized by small time over thresh~TOT!. The cutoff seen at high amplitude is due to saturation ofamplitude readout electronics.

5-13

, a

nanctroteesThth

tion

truin

-ria

14

num-ts.

ctedofr aithot

cut

fitinge-

bedo-cutthisters,track

dthethe-ig.inte acell in

n-thgrts

inr-tual


band is found at high amplitudes but short pulse widthsseen in the lower figure.

Other hit cleaning algorithms use the time correlation aamplitude relationship between real and cross-talk pulsesa map of channels susceptible to cross-talk and the chanto which they are coupled. An additional instrumental effebelieved to be caused by fluctuating high voltage levels, pduces triggers with signals from most OMs on the oustrings but none on the inner four strings; some 500 of thbogus triggers were also removed from the data set.5.83104 upgoing events were again reconstructed afteradditional hit cleaning was applied. Only 4.93103 ~8.4%! ofthe events remained upgoing, compared to an expectafrom Monte Carlo program of 1855 atmospheric muevents~37.8% of the total before the additional cleaning!,and 555 atmospheric neutrino events. Figure 14~top! showsthat while there has been a significant reduction in the insmental backgrounds, an unsimulated structure still remain the center-of-gravity~COG! distribution for these remaining data events. The application of additional quality crite

FIG. 14. Top: Event center of gravity distribution after recostruction with special cross-talk cleaning algorithms applied toevents. Unsimulated background remains. Bottom: The data awith the neutrino signal after application of additional quality cu

01200

s

dndels,-reee

on

-s

brings this distribution in agreement, as shown in Fig.~bottom!.

C. Quality cuts

The improvements in the reliability of the reconstructioalgorithm described above obviated the need for large nbers of cut parameters or for careful optimization of the cuBecause the signal-to-noise ratio of the upward-reconstrudata is quite high to begin with, we have the possibilitycomparing the behavior of real and simulated data ovewide range of cut strengths to verify that the data agree wthe predictions for upgoing neutrino-induced muons, nonly in number but also in their characteristics. Using theparameters described in Sec. IV C~with the likelihood re-placed by the Bayesian posterior probability! and a require-ment that events fitted as relatively horizontal by the linefiltering algorithm not be reconstructed as steeply upgoby the full reconstruction~a requirement that suppresses rsidual cross-talk misreconstructions!, an index of event qual-ity was formed.

To do so, we rescale the six quality parameters descriabove by the cumulative distributions of the simulated atmspheric neutrino signal, and consider the six-dimensionalspace formed by the rescaled parameters. A point inspace corresponds to fixed values of the quality parameand events can be assigned to locations based on theirlength, sphericity, and so forth.

It is difficult to compare the distributions of data ansimulated up- and downgoing muons directly because ofhigh dimensionality of the space. We therefore projectspace down to a single— ‘‘quality’’ — dimension by dividing it into concentric rectangular shells, as illustrated in F15. The vertex of each shell lies on a line from the origthrough a reference set of cuts which are believed to isolafairly pure set of neutrino events. Events in the full cut spaare assigned an overall quality value, based on the shewhich they lie.

eee.

FIG. 15. Definition of event quality. Events are plottedN-dimensional cut space~two dimensions are shown here for claity!. A line is drawn from the origin~no cuts! through a selected seof cuts, and the space is divided into rectangular shells of eqwidth. Events are assigned a qualityq according to the shell inwhich they are found.

5-14

icosnt

neatct

ain

veheomcb

atisrivt

iotht-e

bwecoin

toe

u-b-set

ver,oto

inci-eld

wno-areateent

cer-rgyatao-

ityentsedineies

-

orfivee ath-

foin

nts


With this formulation we can compare the characteristof the data to simulated neutrino and cosmic-ray muevents. Figure 16 compares the number of events pasvarious levels of cuts; i.e., the integral number of eveabove a given quality. At low qualities,q<3, the data set isdominated by misreconstructed downgoing muons, datawell as the simulated background exceed the predictedtrino signal. At higher qualities, the passing rates of dclosely track the simulated neutrino events, and the predibackground contamination is very low.

We can investigate the agreement between dataMonte Carlo simulations more systematically by comparthe differential number of eventswithin individual shells,rather than the total number of events passing various leof cuts. This is done in Fig. 17, where the ratios of tnumber of events observed to those predicted from the cbined signal and background simulations are shown. Onesee that at low quality levels there is an excess in the numof misreconstructed events observed. This is mainly dueremaining cross-talk. There is also an excess, though sttically less significant, at very high quality levels, whichbelieved to be caused by slight inaccuracies in the desction of the optical parameters of the ice. Nevertheless, othe bulk of the range there is close agreement betweendata and the simulation, apart from an overall normalizatfactor of 0.58. The absolute agreement is consistent withsystematic uncertainties. It should be emphasized thatquality parameter is a convolution of all six quality parameters, and so the flat line in Fig. 17 demonstrates agreemin the correlations between cut parameters.

D. Background estimation and signal description

If we reduce the 4917 upward-reconstructed eventsrequiring a quality of at least 7 on the scale of Fig. 16,obtain a set of 204 neutrino candidates. The backgroundtamination, which is due to misreconstructed downgo

FIG. 16. Numbers of events above a certain quality level,downgoing muon Monte Carlo simulations, atmospheric neutrMonte Carlo simulations, and experimental data.

01200

snings

asu-aed

ndg

ls

-anertois-

p-erhene

he

nt

y

n-g

muons, was estimated in three ways. The first way issimulate the downgoing muon flux, bearing in mind that ware looking at a very low tail (1028) of the total muon dis-tribution. The second way is to renormalize the signal simlation by the factor of 0.58 obtained from Fig. 17 and sutract the predicted events from the observed data~accepting the excess at extremely high qualities, howeas signal!. The third way, a cross check on the first twmethods, is to examine the data looking for fakes dueunsimulated effects such as cross-talk, independent codent downgoing muons, and so forth. All three methods yiestimates of 5–10 % contamination.

The zenith angle distribution for the 204 events is shoin Fig. 18, and compared to that for the simulation of atmspheric neutrinos. In the figure the Monte Carlo eventsnormalized to the number of observed events to facilitcomparison of the shapes of the distributions. The agreemin absolute number is consistent with the systematic untainties in the absolute sensitivity and the flux of high eneatmospheric neutrinos. The shape of the distribution of dis statistically consistent with the prediction from atmspheric neutrinos. Figure 14~bottom! shows the distributionof thezCOG parameter for the 204 events. The level 7 qualcuts have removed the remainder of the instrumental evleft after the Bayesian reconstruction with the improvcross-talk cleaning algorithm, bringing the data events in lwith the atmospheric neutrino expectations. The efficienccorresponding to the three steps of the data analysis:~1!events reconstructed upward,~2! events reconstructed upward with cross-talk cleaning, and~3! with additional level 7quality cuts are summarized in Table IV.

Figure 19 ~top! shows the smoothness distribution fevents that have passed the quality level 7 cuts for theobservables except smoothness. The vertical dashed linsmoothness;0.29 shows the value of the level 7 smoot

ro

FIG. 17. Ratio of data to Monte Carlo simulations~cosmic raymuons plus atmospheric neutrinos!. Unlike Fig. 16, the plot isdifferential—the ratio at a particular quality does not include eveat higher or lower qualities.

5-15

gonte

ha

l-

otothn

rtisereatmun-r of, as

terere

lity(

yedbythe


ness cut. This cut removes the tail of fake events leavingood agreement between remaining data and the MCarlo expectation. Figure 19~bottom! shows the same plofor the direct length variable. Again, a clear tail of fakevents is removed by requiring a direct length of greater t70 m.

VII. SYSTEMATIC UNCERTAINTIES

As a novel instrument, AMANDA poses a unique chalenge of calibration. There are no known natural sourceshigh energy neutrinos, apart from atmospheric neutrinwhose observation could be used to measure the detecresponse. Understanding the behavior of the detector isa difficult task, dependent partly on laboratory measuremeof the individual components, partly on observations of aficial light sources embedded in the ice, and partly on obvations of downgoing muons. Even with these measuments, uncertainties in various properties that systematicaffect the response of the detector persist, which prevenat this time from making a precise measurement of the atspheric neutrino flux. The primary sources of systematiccertainties, and their approximate effects on the numbeupgoing atmospheric neutrinos in the final data sample

FIG. 18. The zenith angle distribution of upward reconstrucevents. The size of the hatched boxes indicates the statistical psion of the atmospheric neutrino simulation. The Monte Carlo pdiction is normalized to the data.

01200

ate

n

ofs,r’susts-r--

llyuso-

dci--

FIG. 19. Smoothness and direct length variables where qualevel 7 cuts have been applied in all but the displayed variableN21 cuts; see also Sec. V D 3, Fig. 11!. The vertical dashed lineswith the arrow indicate the region of acceptance in the displavariable. In each case, a clear tail of fake events is removedapplication of the cut, leaving good agreement in shape betweenremaining events and the Monte Carlo expectation.

es in
TABLE IV. Event numbers for experimental data and Monte Carlo simulations for four major stagthe analysis. The errors quoted are statistical only.
Monte Carlo Monte Carlo Datadowngoingm atmosphericn

Events triggered 8.83108 8978 1.053109

Efficiency: Reconstructed upgoing 0.5531025 0.5531024

Efficiency: Reconstructed upgoing (2.160.08)31026 (6.260.06)31022 4.731026

~with cross-talk cleaning!Efficiency: Final cuts (q>7) (1.960.6)31028 (3.160.03)31022 1.931027

No. of events: Quality>7 1765 27963 204

5-16

wedli-oforehie

iviera

inulaoM

thheM

nn-dtheerby

nht

la-for

re-

isheed.-

oth

edthe

ates

isi-of

sys-rloare

iontorsrofr-

heto

ntof


determined by variation of the simulations, are listed beloAs discusssed in Secs. II and III, AMANDA is embedd

in a natural medium, which is the result of millennia of cmatological history, that has left its mark in the formlayers of particulate matter affecting the optical propertiesthe ice. Furthermore, the deployment of optical modulesquires the melting and refreezing of columns of the ice. Tcycle results in the formation of bubbles in the vicinity of thmodules, which increase scattering and affect the sensitof the optical modules in ways that are not yet fully undstood. The effects of this local hole ice are difficult to seprate from the intrinsic sensitivity of the OMs. The uncertaties in the neutrino rate are approximately 15% from the bice layer modeling in the Monte Carlo simulation, andmuch as 50% from the combined effects of the propertiesthe refrozen hole ice close to the OMs, and the intrinsic Osensitivity, and angular response.

Figure 20 shows two variables that are sensitive toabsolute OM sensitivity: the number of OMs hit and tvelocity of the line fit. The systematic effects of varying O

FIG. 20. Distributions of two variables that are affected by tOM sensitivity, comparing different signal Monte Carlos eventsthe observed data. Top: the number of OMs hit (Nch); bottom: theevent velocity for a simplified fit~line fit, v linefit).

01200

.

f-

s

ty---ksf

e

sensitivity on the hit multiplicity for analysis I are shown othe top. The peak of the multiplicity distribution for the stadard Monte Carlo events~nominal efficiency 100%—dasheline! lies at a higher value than for the data. Reducingsimulated OM sensitivity by 50% results in a peak at lowvalues than the data. The other variable strongly affectedthe OM sensitivity—the velocity of the line fit, introduced iSec. IV A!—is the apparent velocity of the observed ligfront traveling through the ice; see Fig. 20~bottom!.

As a next step, we investigated the effect of theANGSENS

OM model ~first introduced in Sec. III! on the atmosphericneutrino Monte Carlo simulation. The results of this simution gave a more consistent description of the experimentseveral variables—e.g., the hit multiplicity~the dotted line inFig. 20!—and they produced the absolute neutrino event pdiction closer to what was found in Analysis I~236.9 eventspredicted, 223 observed!. Similar effects are seen when thMonte Carlo simulation is used with analysis II, however tnumber of predicted events is 25% smaller than observThus theANGSENSmodel, while encouraging, does not completely predict the properties of observed events in banalyses.

Another uncertainty lies in the Monte Carlo routines usto propagate muons through the ice and rock surroundingdetector. A comparison of codes based on@9# and @11# indi-cates that different propagators may change the event rby some 25%.

Other factors include the simulation of the data acqution electronics and possible errors in the time calibrationsindividual modules. These effects have been studied bytematically varying relevant parameters in the Monte Casimulations. For realistic levels of variation, these effectswell below the 10% level.

Figure 21 demonstrates how the zenith angle distributdepends on different atmospheric neutrino event genera~our standard generatorNUSIM @17# and another generatoNU2MU @29#!, and also on the chosen angular sensitivitythe optical module. Neutrino flavor oscillations lead to a fu

FIG. 21. Distribution of simulated zenith angles for differeneutrino generators and also for a modified angular sensitivitythe OM.

5-17

tierirycaie

b

2Aeueth%ior

velodethe

tepe

omtivth

OC

s.os-int

on-ec-ian

ofu-

-of

tri-

an

eueuowtc

en-the

or.2°.


ther reduction of theANGSENS prediction by 5.4%~in par-ticular, close to the vertical direction!, assuming sin22u51and Dm252.531023 eV2 @30,38#. The prediction is re-duced by 11% if the largest allowedDm2 is used.

The combined effect of all these systematic uncertainis sufficiently large that simulations of a given atmospheneutrino flux can produce predictions for the event rate vaing by a factor of two. By contrast, the estimated theoretiuncertainty in the atmospheric neutrino flux, at the energprobed by these analyses, is 30%@31#. The effect of neutrinooscillations with the Super-K preferred parameters wouldless than 10% at these energies.

VIII. SYNTHESIS AND GENERAL OVERVIEW

Both analyses I and II are able to separate more thanneutrino event candidates from the 130.1 days of AMANDB10 detector lifetime in 1997. Based on atmospheric ntrino simulations we find that about 4% of the total numbof events triggered by upward moving neutrinos passedfinal selection. A total deficit in the event rate of about 35with respect to the standard neutrino Monte Carlo predictis found for both analyses. An event overlap of 102 expemental events is observed, consistent with a predicted olap of 119613 from the atmospheric neutrino Monte Carprediction. Thus, the combined sample of data proviabout 300 neutrino candidates. Both analyses estimateresidual background to be about 10% of the number of ntrino event candidates.

Figure 22 shows the energy distribution of the simulaneutrinos and the corresponding muon events. Ninetycent of all Monte Carlo signal events have muon~neutrino!energies between 48~66! GeV and 1.8~3.4! TeV. The domi-nant part of the signal events in this analysis comes frneutrino energies below 1 TeV. Figure 23 shows the effecarea as a function of the zenith angle for two ranges of

FIG. 22. Energy distributions for simulated atmospheric ntrino events which pass the final neutrino cuts. The effect of ntrino oscillations has not been taken into account. The figure shthe neutrino and muon energies at the interaction vertex andenergy of the muons at the point of closest approach to the detecenter.

01200

sc-ls

e

00--

re

ni-r-

seiru-

dr-

ee

muon energy at the point of closest~POC! approach to thedetector. The effective area for muons with energies at Pbetween 100 and 1000 GeV is 3.93104 m2 at trigger leveland 2800 m2 after application of the neutrino selection cutIt should be noted that much higher effective areas are psible when searching for neutrinos from astrophysical posources@32# or from gamma ray bursts@33#.

Figure 24 shows the point spread function of the recstructed muon trajectory with respect to the true muon dirtion. Based on Monte Carlo simulations, we find a medangular resolution of muons from atmospheric neutrinos3.2° for the final sample. A more detailed study of the anglar resolution can be found in@25,34,35#. Figure 25 showsthe skyplot~equatorial coordinates! of all the candidate neutrino events found across both analyses. The distributionthe events on the skyplot is consistent with a random disbution.

IX. CONCLUSIONS

The AMANDA-B10 data from 130.1 days of livetimeduring the austral winter of 1997 have been analyzed in

--s

hetor

FIG. 23. Effective area for muons versus zenith angle. Theergy of the muons is given at the point of closest approach todetector.

FIG. 24. Monte Carlo simulation of the angular resolution fmuons that pass the final selection criteria. The median error is 3

5-18

aninneprerintuer00uo

olenteare

ineg

ce-er

Iith

or

ies:s;

er-rt-

ncil;cre-

er-n-

oft-

C.4th

ithe,u


effort to detect high energy atmospheric neutrino events,to compare their properties to expectations. Two workgroups in the collaboration, using differing reconstructiocut optimization and instrumental event rejection techniquproduced sets of 223 and 204 neutrino candidates, restively. Several methods of background estimation put thesidual event contamination from downgoing atmosphemuons and instrumental artifacts at about 10%. Taking iaccount systematic uncertainties, the observed event nbers are consistent with systematically varied atmosphneutrino Monte Carlo predictions, which are from 150–4events. The range of these predictions is dominated bycertainties in the neutrino flux, in the understanding of ph

FIG. 25. Neutrino skyplot of upgoing events as seen wAMANDA-B10 in 1997 in equatorial coordinates. In this figurneutrino events from both analyses are combined. The backgroof non-neutrino events is estimated to be less than 10%.

es

m

u-

3

a-rg,

-

01200

dg,s,ec--

com-ic

n--

ton propagation through the bulk ice and the refrozen hice, and in muon propagation and energy loss. The MoCarlo prediction suggests that 90% of the selected eventsproduced by neutrinos in the energy range of;66 GeV to3.4 TeV. The observation of atmospheric neutrinos in lwith expectations establishes AMANDA-B10 as a workinneutrino telescope. We finally note that many of the produres for signal separation simplify considerably in largdetectors. In particular, first results from AMANDA-I@36,37# demonstrate that the neutrino signal is separated wmuch higher efficiency and with fewer cuts than fAMANDA-B10.

ACKNOWLEDGMENTS

This research was supported by the following agencU.S. National Science Foundation, Office of Polar ProgramU.S. National Science Foundation, Physics Division; Univsity of Wisconsin Alumni Research Foundation; U.S. Depament of Energy; Swedish Natural Science Research CouSwedish Research Council; Swedish Polar Research Setariat; Knut and Alice Wallenberg Foundation, Sweden; Gman Ministry for Education and Research; U.S. National Eergy Research Scientific Computing Center~supported bythe Office of Energy Research of the U.S. DepartmentEnergy!; UC-Irvine AENEAS Supercomputer Facility; Deusche Forschungsgemeinschaft~DFG!. D. F. Cowen acknowl-edges the support of the NSF CAREER program andPerez de los Heros acknowledges support from the EUframework of Training and Mobility of Researchers.

nd

u-

e

s-

e

6.

@1# E. Andres et al., Astropart. Phys.13, 1 ~2000!.@2# E. Andres et al., Nature~London! 410, 441 ~2001!.@3# AMANDA Collaboration, K. Woschnagg, inProceedings of

the 26th International Cosmic Ray Conference~IUPAP, SaltLake City, UT, 1999!, Vol. 2, pp. 200–203.

@4# P. B. Price, K. Woschnagg, and D. Chrikin, Geophys. RLett. 27, 2129~2000!.

@5# J. Ahrenset al., Astropart. Phys.16, 345 ~2002!.@6# S. N. Bozievet al., INR Report P-0630~unpublished!.@7# D. Heck et al., Report FZKA 6019, Forschungszentru

Karlsruhe, Karlsruhe, Germany~unpublished!.@8# D. Heck, inSimulation and Analysis Methods for Large Ne

trino Telescopes~DESY, Zeuthen, Germany, 1998!, pp. 228–234, DESY-PROC-1999-01.

@9# W. Lohmann, R. Kopp, and R. Voss, Report CERN-85-0Geneva, Switzerland~unpublished!.

@10# R. Kopp, W. Lohmann, and R. Voss, MUDEDX: Parametriztion and Monte Carlo generation of energy loss of high enemuons~1–10000 GeV!; for astrophysicists up to 100000 GeVVersion 2.02, 1995~private communication!.

@11# P. Lipari and T. Stanev, Phys. Rev. D44, 3543~1991!.@12# W. Rhode and D. Chirkin, inProceedings of the27th Interna-

tional Cosmic Ray Conference~Copernicus Gesellschaft, Hamburg, Germany, 2001!, Vol. 3, pp. 1017–1020.

@13# B. Wiebel-Sooth and P. L. Biermann,Numerical Data and

.

,

y

Functional Relationships in Science and Technology, Landolt-Bornstein, New Series, Vol. VI 3C~Springer-Verlag, Berlin,Heidelberg, 1998!, Chap. 7.6, pp. 37–90.

@14# A. Karle, in Simulation and Analysis Methods for Large Netrino Telescopes~Ref. @8#!, pp. 174–185,DESY-PROC-1999-01.

@15# S. Hundertmark, Ph.D. thesis, Humboldt Universita¨t zu Berlin,Berlin, Germany, 1999, available at URLhttp://amanda.berkeley.edu/manuscripts/

@16# S. Hundertmark, inSimulation and Analysis Methods for LargNeutrino Telescopes~Ref. @8#!, pp. 276–286,DESY-PROC-1999-

01.@17# G. C. Hill, Astropart. Phys.6, 215 ~1997!.@18# G. C. Hill, Ph.D. thesis, University of Adelaide, Adelaide, Au

tralia, 1996.@19# P. Lipari, Astropart. Phys.1, 195 ~1993!.@20# J. Ahrenset al. ~unpublished!.@21# V. Stenger, DUMAND Internal Report HDC-1-90.@22# C. Wiebusch, inSimulation and Analysis Methods for Larg

Neutrino Telescopes~Ref. @8#!, pp. 302–316,DESY-PROC-1999-

01.@23# D. Pandel, Diploma thesis, Humboldt-University, Berlin, 199@24# G. C. Hill, in Proceedings of the27th International Cosmic

Ray Conference~Ref. @12#!, Vol. 3, pp. 1279–1282.@25# A. Biron, Ph.D. thesis, Humboldt Universtita¨t zu Berlin, Ber-

lin, Germany, 2002, available at URL

5-19

i-

m

:l

u-

e


http://amanda.berkeley.edu/manuscripts/@26# T. R. DeYoung, Ph.D. thesis, University of Wisconsin, Mad

son, 2001, available at URLhttp://amanda.berkeley.edu/manuscripts/

@27# M. Gaug, Diploma thesis, Humboldt Universita¨t zu Berlin,Berlin, Germany, 2001,DESY-THESIS-2001-022, available at URLhttp://amanda.berkeley.edu/manuscripts/.

@28# AMANDA Collaboration, A. Bouchta, inProceedings of the26th International Cosmic Ray Conference, ~Ref. @3#!, HE3.2.11.

@29# E. Dalberg, Ph.D. thesis, Stockholm University, StockholSweden, 1999, available at URLhttp://amanda.berkeley.edu/manuscripts/

@30# Super-Kamiokande Collaboration, J. Kameda, inProceedingsof the 27th International Cosmic Ray Conference~Ref. @12#!,Vol. 3, pp. 1057–1060.

@31# T. K. Gaisser, ‘‘Uncertainty in flux of Atmospheric NeutrinosImplications for Upward Muons in Amanda B10,’’ Interna

01200

,

Report 20001201, 2000.@32# J. Ahrenset al., ‘‘Search for point sources of high energy ne

trinos with the AMANDA detector.’’@33# AMANDA Collaboration, R. Hardtke and G. Barouch, inPro-

ceedings of the27th International Cosmic Ray Conferenc~Ref. @12#!, Vol. 3, pp. 1121–1124.

@34# AMANDA Collaboration, ‘‘Calibration and Survey ofAMANDA with the SPASE detectors’’~to be published!.

@35# AMANDA Collaboration, G. Spiczak, inProceedings of the27th International Cosmic Ray Conference~Ref. @12#!, Vol. 3,pp. 977–980.

@36# AMANDA Collaboration, R. Wischnewski, inProceedings ofthe27th International Cosmic Ray Conference~Ref. @12#!, Vol.3, pp. 1105–1108.

@37# AMANDA Collaboration, S. W. Barwick, inProceedings ofthe27th International Cosmic Ray Conference~Ref. @12#!, Vol.3, pp. 1105–1108.

@38# S. Fukudaet al., Phys. Rev. Lett.85, 3999~2000!.

5-20

Observation of high energy atmospheric neutrinos with the Antarctic...

Documents

Transcript of Observation of high energy atmospheric neutrinos with the Antarctic...