e

Physics Letters B 566 (2003) 35–44

www.elsevier.com/locate/np

Atmospheric neutrino oscillations from upward throughgoingmuon multiple scattering in MACRO

MACRO Collaboration

M. Ambrosiol, R. Antolini g, D. Bakarib,q, A. Baldinim, G.C. Barbarinol, B.C. Barishd,G. Battistonif,1, Y. Becherinib, R. Bellottia, C. Bemporadm, P. Bernardinij,H. Bilokonf, C. Bloisef, C. Bowerh, M. Brigidaa, S. Bussinor, F. Cafagnaa,

M. Calicchioa, D. Campanal, M. Carbonif, R. Carusoi, S. Cecchinib,2, F. Ceim,V. Chiarellaf, T. Chiarusib, B.C. Choudharyd, S. Coutuk,3, M. Cozzib, G. De Cataldoa,

H. Dekhissib,q, C. De Marzoa, I. De Mitri j, J. Derkaouib,q, M. De Vincenzir,A. Di Credicog, C. Favuzzia, C. Fortif, P. Fuscoa, G. Giacomellib, G. Gianninim,4,N. Gigliettoa, M. Giorgini b, M. Grassim, A. Grillo g, C. Gustavinog, A. Habigc,5,

K. Hansonk, R. Heinzh, E. Iaroccif, E. Katsavounidisd,6, I. Katsavounidisd,7,E. Kearnsc, H. Kim d, A. Kumarb,8, S. Kyriazopouloud, E. Lamannan,9, C. Lanee,D.S. Levink, P. Liparin, M.J. Longok, F. Loparcoa, F. Maaroufib,q, G. Mancarellaj,

G. Mandriolib, S. Manzoorb,10, A. Margiottab, A. Marini f, D. Martelloj,A. Marzari-Chiesap, M.N. Mazziottaa, D.G. Michaeld, S. Mikheyevd,g, P. Monacellii ,

T. Montarulia, M. Montenop, S. Mufsonh, J. Musserh, D. Nicolòm, R. Noltyd,C. Orthc, G. Osterial, O. Palamarag, V. Pateraf, L. Patriziib, R. Pazzim, C.W. Peckd,

L. Perronej, S. Petrerai, V. Popab,11, A. Rainòa, J. Reynoldsong, F. Rongaf,A. Rrhiouab,q, C. Satrianon,12, E. Scapparoneg,∗, K. Scholbergc,6, A. Sciubbaf,13,

P. Serrab, M. Sioli b,∗, G. Sirrib, M. Sittap,14, P. Spinellia, M. Spinettif, M. Spuriob,R. Steinberge, J.L. Stonec, L.R. Sulakc, A. Surdoj, G. Tarlèk, V. Togob, M. Vakili o,15,

C.W. Walterc, R. Webbo

a Dipartimento di Fisica dell’Università di Bari and INFN, 70126 Bari, Italyb Dipartimento di Fisica dell’Università di Bologna and INFN, 40126 Bologna, Italy

c Physics Department, Boston University, Boston, MA 02215, USAd California Institute of Technology, Pasadena, CA 91125, USA

e Department of Physics, Drexel University, Philadelphia, PA 19104, USAf Laboratori Nazionali di Frascati dell’INFN, 00044 Frascati (Roma), Italy

g Laboratori Nazionali del Gran Sasso dell’INFN, 67010 Assergi (L’Aquila), Italyh Departments of Physics and of Astronomy, Indiana University, Bloomington, IN 47405, USA

i Dipartimento di Fisica dell’Università dell’Aquila and INFN, 67100 L’Aquila, Italyj Dipartimento di Fisica dell’Università di Lecce and INFN, 73100 Lecce, Italyk Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA

0370-2693/03/$ – see front matter 2003 Published by Elsevier B.V.doi:10.1016/S0370-2693(03)00806-2

36 MACRO Collaboration / Physics Letters B 566 (2003) 35–44

upwarde muonangular

bove the

l Dipartimento di Fisica dell’Università di Napoli and INFN, 80125 Napoli, Italym Dipartimento di Fisica dell’Università di Pisa and INFN, 56010 Pisa, Italy

n Dipartimento di Fisica dell’Università di Roma “La Sapienza” and INFN, 00185 Roma, Italyo Physics Department, Texas A&M University, College Station, TX 77843, USA

p Dipartimento di Fisica Sperimentale dell’Università di Torino and INFN, 10125 Torino, Italyq L.P.T.P, Faculty of Sciences, University Mohamed I, B.P. 524, Oujda, Morocco

r Dipartimento di Fisica dell’Università di Roma Tre and INFN Sezione Roma Tre, 00146 Roma, Italy

Received 12 May 2003; received in revised form 23 May 2003; accepted 26 May 2003

Editor: L. Montanet

Abstract

The energy of atmospheric neutrinos detected by MACRO was estimated using multiple Coulomb scattering ofthroughgoing muons. This analysis allows a test of atmospheric neutrino oscillations, relying on the distortion of thenergy distribution. These results have been combined with those coming from the upward throughgoing muondistribution only. Both analyses are independent of the neutrino flux normalization and provide strong evidence, a4σ level, in favour of neutrino oscillations. 2003 Published by Elsevier B.V.

PACS: 14.60.Lm; 14.60.Pq; 25.30.Mr

fores

ity,

nt,

9,

a,

nia.

85

er-

ardstonon-theantno

te-rdeds

e the, up-ned

intionareith

re-o-y

thes-

1. Introduction

The results obtained by experiments lookingneutrinos coming from natural or artificial far sourc

* Corresponding authors.E-mail addresses: scapparone@bo.infn.it (E. Scapparone),

sioli@bo.infn.it (M. Sioli).1 Also INFN Milano, 20133 Milano, Italy.2 Also IASF/CNR, Sez. di Bologna, Italy.3 Also Department of Physics, Pennsylvania State Univers

University Park, PA 16801, USA.4 Also Università di Trieste and INFN, 34100 Trieste, Italy.5 Also University of Minnesota, Duluth Physics Departme

Duluth, MN 55812, USA.6 Also Department of Physics, MIT, Cambridge, MA 0213

USA.7 Also Intervideo Inc., Torrance, CA 90505, USA.8 Also Department of Physics, SLIET, Longowal, India.9 Also Dipartimento di Fisica dell’Università della Calabri

Rende (Cosenza), Italy.10 Also RPD, PINSTECH, P.O. Nilore, Islamabad, Pakistan.11 Also Institute for Space Sciences, 76900 Bucharest, Roma12 Also Università della Basilicata, 85100 Potenza, Italy.13 Also Dipartimento di Energetica, Università di Roma, 001

Roma, Italy.14 Also Dipartimento di Scienze e Tecnologie Avanzate, Univ

sità del Piemonte Orientale, Alessandria, Italy.15 Also Resonance Photonics, Markham, Ontario, Canada.

gave the first indication of physics beyond the standmodel. Neutrino flavor changing is in fact the mostraightforward explanation for electron and muneutrino disappearance and for the evidence of nelectron neutrinos from the sun. In this scenario,study of atmospheric neutrinos plays an importrole to improve our understanding of the neutrioscillation mechanism.

The MACRO detector studied [1–3] three cagories of events as shown in Fig. 1: (1) upwathroughgoing muons, (2) upward semicontainmuons, and (3+ 4) upward stopping muons pludownward semicontained muons. The (3+ 4) cate-gories cannot be separated experimentally, becausevents have only one time measurement. Howeverward stopping muons and downward semicontaimuons have similar parent neutrino energy.

An atmospheric muon neutrino deficit was foundall of the three categories and an angular distribudistortion was found in category (1). Such resultsexplained by the neutrino oscillation hypothesis wparameters�m2 = 2.5 × 10−3 eV2 and sin2 2θ = 1,in good agreement with the Super-Kamiokandesults [4]. A detailed study of the upward throughging muon angular distribution by MACRO [3] and bSuper-Kamiokande [5] allowed the exclusion at99% C.L. of the muon neutrino into sterile neutrino o

MACRO Collaboration / Physics Letters B 566 (2003) 35–44 37

of

ino

e

no

ntsto

nceionmergyofinhee,ultsereve

uon

edhe

erbersoflups

edck

andtheow

lti-theofe-s

ode

ngter-

ts.ngctingcale

nd

onileer

tum

Fig. 1. Cross section of the MACRO detector and topologiesevents induced by neutrino interactions.

cillation mechanism, compared to the muon neutrinto the tau neutrino.

Considering a two flavor neutrino oscillation, thprobability for aνµ to oscillate toντ is given by:

(1)Pνµ→ντ = sin2 2θ sin2(

1.27Lν�m2

Eν

),

whereLν (km) is the distance between the neutriproduction and interaction points andEν (GeV) isthe neutrino energy. The different categories of evequoted above have median energy from 4 GeV50 GeV, which provides evidence of the dependeon neutrino energies, as required by the oscillathypothesis. In this Letter we address for the first tithe estimate of the upward throughgoing muon eneby using multiple scattering. The implementationthis method to the MACRO data is discussedSection 2. Two different analysis were performed. Tfirst one, using the tracking system in digital modis described in Section 3. Section 4 shows the resobtained with the streamer tube in drift mode, whelectronic readout of the hit time was used to improthe position resolution and thereby the range of menergies that could be estimated.

2. The muon energy estimate

The MACRO detector was extensively describin [7]. The detector consisted of a lower half (tlower detector) and an upper half (theAttico). Thelower detector had 10 horizontal planes of streamtubes separated by either crushed rock absor(60 g/cm2) or (at its top and bottom) a planescintillator counters. TheAttico had 4 horizontaplanes of streamer tubes separated into two growith a plane of scintillator counters between them.

Upward throughgoing muons are mainly producin neutrino deep inelastic scattering (DIS) in the robelow the detector. The recoil hadrons are lostthe muon energy is degraded in the propagation todetector. Nevertheless, Monte Carlo simulations sha linear relation between the parent neutrino energyEν

and the muon residual energyEµ at detector level.The momentum resolution obtainable from mu

ple Coulomb scattering (MCS) measurements isresult of two different contributions: the numbersampling planesN and the space resolution of the dtectorσ0. In MACRO the number of tracking planeinterleaved with rock absorbers givesN = 8. The reso-lution of the streamer tube system used in digital mis σ0 � 1 cm and was improved toσ0 � 0.3 cm byusing the drift time. The other six horizontal trackiplanes are separated by a negligible amount of maial, and do not contribute to the MCS measuremen

In a tracking detector with equispaced trackiplanes, separated by a given absorber and neglethe energy losses, the characteristic momentum scan be written as [8]:

(2)pMCS(GeV)= 0.015∆√∆/X0

σ0,

where∆ is the distance between tracking planes aX0 is the material radiation length. Forp < pMCS,the main limitation to the momentum reconstructicomes from the number of sampling planes whfor p > pMCS the space resolution dominates. Undthe conditions quoted above the relative momenerror [8] can be written as:

(3)σp

p→ 1√

2N

38 MACRO Collaboration / Physics Letters B 566 (2003) 35–44

edntalbersand

ngrtumpac

is-

ntter

ionint)

merd inec-hesso-

te

oftheuiv-rdredn-rdpre-atala-4

er-theonsetc-1sis,an-

thisd inthenck-

ava-ith

eenfor

sed,ofbe

ingeeuonglues

e

ericy ofg

up-ara-.

for p pMCS, and

(4)σp

p→ 1√

2N

(p

pMCS

)2

,

for p pMCS. As shown in [8] the 1/p distributionapproaches a Gaussian only forN � 30; thereforethe momentum error for MACRO is not expectto have a Gaussian behaviour. The eight horizostreamer tube planes interleaved with rock absor(planes 2 to 9, from the bottom) are equispacedhave the same space resolution, hencepMACRO

MCS =2.2 GeV/c. Since about 90% of upward throughgoimuons havep > 2.2 GeV/c, the intrinsic chamberesolution dominates. The MCS-based momenestimates scale therefore as the square of the sresolutionσ0.

The r.m.s. of the lateral displacement of a relativtic muon crossing a layer of material with depthXis proportional to the inverse of muon momentumpµ[9]:

(5)σMCSproj � X√

3

13.6 MeV

pµβc

√X

X0

(1+ 0.038 ln

X

X0

).

In MACRO,X � 25X0/cosΘ, giving on the verticalσMCS

proj � (10 cm)/Eµ(GeV). Therefore, a saturatiopoint above 10 GeV requires a space resolution bethan 1 cm. An improvement in the space resolutincreases the maximum energy value (saturation poabove which the MCS method is not effective [10].

Consequently we decided to improve the streatube resolution: in the second analysis, describeSection 4, we took advantage of the QTP-TDC eltronics, developed for magnetic monopole searc[7]. In this case, we obtained an improved space relution,σx ∼ 0.3 cm [11], which allowed us to estimathe muon energy up toEµ � 40 GeV.

For both analyses, we used the whole sampleupward throughgoing muon events collected withcomplete apparatus in a period of data taking eqalent to 5.5 years of live time. We studied upwamuon events selected by the time-of-flight measuby planes of scintillators combined with the stadard MACRO tracking algorithm. The original upwathroughgoing muon data set has been describedviously [3]. To make a comparison between real dand expectation we performed a Monte Carlo simution using the Bartol neutrino flux [12] and the GRV9

e

DIS parton distributions [13] for deep-inelastic scatting. For low energy neutrino interactions we usedcross sections given in [14]. The energy loss for mupropagating through rock is taken from Lohmannal. [15] while the muon simulation inside the detetor was performed with GMACRO (the GEANT 3.2based detector simulation). For the second analywhere the streamer system is used in drift mode,other simulation chain has been implemented. Incase neutrino interactions are randomly distributea rock semi-sphere below the detector. Muons aretransported to the detector using the FLUKA99 paage [6]. A Monte Carlo statistics corresponding tolive time of � 2700 years was produced (500 equilent experiments). This simulation was compared wthat used in [1,3], obtaining a satisfactory result.

3. The first analysis: streamer tubes in digitalmode

Because of MCS in thelower detector, with thisanalysis we expect a measurable deflection betwthe incoming and the outgoing track directionsmuons with energies smaller than∼ 10 GeV. This cor-responds to an effective arm-lever of∼ 4 m betweenthelower detector and theAttico [7].

The eight lowest streamer tube planes were uthrough a track refit, to estimate the directionthe incoming muon. The five upper streamer tuplanes in thelower detector and the fourAttico planeswere used to estimate the direction of the outgomuon. The distancerw between the intercepts of thtwo tracks in thez = 0 plane, and the differenc�Φ between the two slopes depend on the menergy Eµ. We divided the upward throughgoinmuons in three subsamples, according to the vaof rw and �Φ: sampleL = Low energy, if rw >

3 cm and�Φ > 0.3◦; H = High energy if rw �3 cm and�Φ � 0.3◦. The remaining events werclassified asM = Medium energy. These cuts wereoptimized using two large samples of real atmosphmuons: (i) downward throughgoing (average energ∼ 300 GeV [16]), and (ii) downward going stoppinmuons (average energy of∼ 1 GeV).

The aforementioned cuts were applied on theward throughgoing muons (crossing the whole apptus,lower detector + Attico), both real and simulated

MACRO Collaboration / Physics Letters B 566 (2003) 35–44 39

[1]we

g-

tedwith

m-

eu-Sec-ysisthehector

o-p-

thestya-

eaduteS-

ROas3.0ve.estromrythe

ns:uousata

ace

Ningta.

ta isrgy

gyithtoiththerkedthe

aytheer-s-c-of

to

They were selected from the same analysis chainand had the same data format. From the simulationexpect 430 events: 178 ofLow energy, with〈Eν〉 =11 GeV, 59 ofMedium energy, with〈Eν〉 = 33 GeVand 193 ofHigh energy, with〈Eν〉 = 72 GeV. Fromthe real data, 316 events were selected: 101 ofLow, 51of Medium and 164 ofHigh energy.

TheL andH events were further divided accordinto their zenith angleΘ: events from the vertical direction −1.0< cosΘ < −0.8, and events with cosΘ >

−0.8. For each event topology the number of detecand expected events were determined and ordereddecreasing value of the〈Lν 〉/〈Eν〉 (〈Lν〉 = averagevalue of neutrino path length). The relative systeatic uncertainty on each of the five〈Lν 〉/〈Eν〉 valuesis 12.5%, coming from the uncertainties on the ntrino spectrum and angular shape (discussed intion 4.3), from the detector related effects and analcuts. This includes the number of planes used forrefit, the definition of the cuts, the fluctuations in tstreamer tube and scintillator efficiencies, and deteacceptance uncertainties.

We evaluatedχ2 for the hypothesis of no neutrinoscillations using the five〈Lν 〉/〈Eν〉 bins, plus the additional point from the analysis of semi contained uward going events (IU) [2] (upgoing neutrinos wi〈Eν〉 ∼ 4 GeV). We found that the distribution agrewith the no oscillation hypothesis with a probabililower than 2%). For two-flavor oscillations with parmeters�m2 = 2.5×10−3 eV 2 and sin2 2θ = 1 we geta probability of 45%.

4. The second analysis: streamer tubes in driftmode

The performance of the streamer tube system, rout in drift mode, is described in [11]. Here an absolmuon energy calibration was performed at the PT9 and SPS-X7 beams, where a slice of the MACdetector was reproduced. The MCS information whandled by a neural network, based on JETNET[17], calibrated with the muon beams quoted aboThe neural network (NN) output obtained using tbeam data, was compared with that expected fthe Monte Carlo simulation, obtaining a satisfactoagreement [11]. The application of such analysis to

Fig. 2. Neural network (NN) output for down-throughgoing muoreal data (black squares) and Monte Carlo expectations (continline). NN output for downward going stopping muons: real d(empty circle) and Monte Carlo expectations (dotted line).

MACRO data resulted in an improvement of the spresolution fromσx � 1 cm toσx � 0.3 cm.

Fig. 2 shows the Monte Carlo prediction for Ndownward throughgoing muons and downward gostopping muons compared with experimental daA nice agreement between simulation and real dafound for both categories, representing a large eneinterval.

The result of the neural network output enercalibration shows that NN output is almost linear wlog10(Eµ), increasing with the muon energy upEµ � 40 GeV, where a saturation effect occurs. Wrespect to the approach used in [11] few details ofneural network were optimized: the neural netwotraining and the energy calibration was performseparately for events with hits in the upper part ofdetector (Attico).

Although smeared by the energy carried awby hadrons and by energy loss in the rock,detected neutrino induced muons still carry on avage � 40% of the original neutrino energy. By uing the full Monte Carlo simulation quoted in Setion 2, we calibrated the NN output as a functionlog10(Eν ): the calibrated NN output is linear up

40 MACRO Collaboration / Physics Letters B 566 (2003) 35–44

dealRO

rgy.li--n-

ede)ousob-tora-in-chthe

ata94.

atgletedredmeth

ysisding, inntehitsof

tedithg

eame

tricrialnt offor00

ralourame

heub-

Fig. 3. Neutrino energy resolution that can be obtained with an iresidual muon energy resolution (dotted line) and with the MACenergy estimate (continuous line).

log10(Eν(GeV))� 2.15. We may write:

δ log10(Eν)= log10(e)δ lnEν

(6)= log10(e)δEν

Eν

,

whereδ log10(Eν) is the difference between the log10of the real and of the reconstructed neutrino eneTaking into account that the NN output was cabrated as a function of log10(Eν), the energy resolution δEν/Eν was obtained by plotting the quatity δ log10(Eν)/ log10(e), equivalent toδ ln(Eν). InFig. 3 we show the resolution that could be obtainwith an ideal muon energy resolution (dotted linand that obtained with the present analysis (continuline). The precision of the neutrino energy estimatetained with an ideal muon energy resolution detecis δEν/Eν � 70%, while with the present methodresolution ofδEν/Eν � 150% is obtained. The asymmetry present in both curves comes from neutrinoteractions occurring far from the detector, for whia large fraction of the muon energy is lost duringtransport.

4.1. Data selection

We used the 783 upward throughgoing muon dset collected in the full detector run started in 19

Table 1Data selection cuts and selection efficiencies

Cuts Number of events

Total number of upward 783throughgoing muons

Single track in the 695wire and strip views

� 4 planes with valid 347TDC hits

Track length cut 314

Θ � 60◦ 300

Table 1 describes further event selection to arrivethe sample for MCS analysis. We required a sintrack in both the wire and the strip view. We selechits belonging to the track and made of a single fitube, to associate unambiguously its QTP-TDC tiinformation. This cut is effective for muon tracks wilarge zenith angles (Θ > 30◦), while it is quite loosearound the vertical: we restricted the present analto events withΘ � 60◦. Comparisons were performebetween simulated and experimental downward gomuon data, to ensure that the selection efficiencythe used angular window, is the same in the MoCarlo and in the real data. Spurious backgroundhave been avoided by requiring a time window2 µs around the trigger time. Finally, we selecevents with at least four streamer tube planes wvalid QTP-TDC data. We fitted the drift circles usinthe same tracking developed to analyse test bmuons. A minimum path length of 200 cm in thlower detector is required for tracks hitting theAtticoand 400 cm for tracks not hitting it. These geomerequirement ensure a minimum depth of matewhere muons may experience a measurable amoumultiple scattering and a lever arm long enougha comfortable tracking. After the selection cuts 3events survived, giving an overall efficiency of 38.3%.

4.2. Qualitative tests

We used the information provided by the neunetwork to separate the neutrino events into fenergy subsamples, as shown in Table 2. The sselection was applied to simulated events.

Fig. 4 shows the zenith angle distributions of tupward throughgoing muons in the four energy s

MACRO Collaboration / Physics Letters B 566 (2003) 35–44 41

trino

nteed

a-rea

fer-the-ced

-byi-

iv-

thens,dic-

s

-

the

Table 2Subsamples selected according with the reconstructed neuenergy

Sample Energy cuts Median energy(GeV) (GeV)

Low Erecν < 30 13

Medium–Low 30<Erecν < 80 36

Medium–High 80<Erecν < 130 88

High Erecν > 130 146

samples, compared with the expectations of the MoCarlo simulation, assuming no-oscillations (dottline) and oscillations with parameters�m2 = 2.5 ×10−3 eV2 and sin2 2θ � 1 (wall boxes). The MonteCarlo including the oscillation hypothesis, with the prameters quoted above, reasonably reproduces thedata in each subsample. We point out the strong difence between the oscillations/no-oscillations hyposes at low energies, while such difference is reduby increasing the reconstructed neutrino energy.

l

Finally, we used information on the ratioLν/Eν .The distanceLν , travelled by the neutrinos from production to the interaction points, was measuredMACRO relying on the muon zenith angle determnation, with a precision�Lν/Lν ∼ 3%. The resolu-tion on the ratioLν/Eν is therefore fully dominatedby the uncertainty in the neutrino energy estimate, ging a relative error of� 150%. The ratio DATA/MonteCarlo as a function of log10(Lν/Eν), is plotted inFig. 5. The black circles are the real data overMonte Carlo predictions, assuming no oscillatiothe shaded regions represent the Monte Carlo pretions with oscillations,�m2 = 2.5 × 10−3 eV2 andsin2 2θ = 1, divided by the Monte Carlo predictionwith no oscillation.

The log10(Lν/Eν) distribution of the neutrinos detected by MACRO spans from 0.8 to 3.5. The left-pointing arrow at low log10(Lν/Eν) represents theeffect of the neural network saturation. Since

onte

Fig. 4. Number of events versus the cosine of the zenith angleΘ for four energy ranges. Black points are the real data, dotted line is the MCarlo simulation, assuming no oscillation, and dotted boxes are the Monte Carlo expectation with�m2 = 2.5 × 10−3 eV2 and sin2 2θ = 1,including a 17% error.

42 MACRO Collaboration / Physics Letters B 566 (2003) 35–44

areC

ties.ard

td

-sid-ructogyn

so-r-kax-1intarda-ort ise-

r-meding

ow-ionthe

he

theon.uxis-at-en-

theumri-

eu-

on--

y isom-nceticof

dsity,tor

Fig. 5. Ratio (Data/MC) as a function of the estimatedLν/Eν for theMACRO upward throughgoing muon sample. The black circlesthe real data over the MC (no oscillation), the solid line is the Massuming�m2 = 2.5×10−3 eV2 and sin2 2θ = 1 over the MC withno oscillation. The shaded region represents the MC uncertainThe last point (empty circle) is obtained from semicontained upwgoing muons.

maximum energy reconstructed by the NN isEν �140 GeV and since the minimumLν for the presenanalysis isLmin

ν � 6500 km, the minimum estimatevalue is log10(Lν/Eν)

min � 1.7. As far as the right-pointing arrow at highLν/Eν is concerned, the reconstruction of neutrino energy based on the reual muon energy, does not allow one to reconstthe ratioL/E beyond a given limit. This is due tfar neutrino interactions, originated by high enermuons, which lost a large fraction of its energy. Aideal detector with ideal muon residual energy relution, requiringEµ < 2 GeV, would select an aveage log10(Lν/Eν) = 3.2. Finally, the neural networresolution in muon energy estimate results in a mimum value log10(Lν/Eν) = 3. The dashed line atis the expectation without oscillations. The last po(empty circle) is obtained from semicontained upwgoing muon rate [2]. It is not used for the evalution of the oscillation probabilities (Section 4.3) nin the allowed region plot (Fig. 7). Good agreemenfound with the oscillations expected with the paramters quoted above.

4.3. Experimental results

To quantify the contribution of the multiple scatteing measurement in stand-alone mode, we perfora blind analysis using the Monte Carlo data, look

Table 3Real data and Monte Carlo ratiosR = Nlow/Nhigh and A =Nvert/Nhor

Ratio R′ =RMCosc R′′ = RMC

Noosc Rexp

NlowNhigh

1.00± 0.17 1.50± 0.25 0.85± 0.16

NvertNhor

1.70± 0.14 2.20± 0.17 1.48± 0.13

for the variable, based on the energy estimate, shing the maximum sensitivity to separate the oscillatfrom the no-oscillation hypothesis. We found thatbest performance is given by the ratio:

(7)R =Nlow/Nhigh,

whereNlow andNhigh are the number of events witErecν < 30 GeV andErec

ν > 130 GeV, respectively (seTable 3).

We considered systematic uncertainties due toneutrino flux calculation and neutrino cross sectiDue to the large uncertainty in the absolute fl[18–22], we use in this Letter only the angular dtribution and the ratio between different event cegories selected according to the reconstructedergy. Nevertheless, the theoretical uncertainty ofexisting neutrino flux, based on the old CR spectr[12], has to be accounted for. We varied the input pmary cosmic ray spectral indexγ in our simulationby �γ = ±0.05, obtaining a theoretical error onR,(�R/R)flux = ±13%.

Another source of systematics comes from the ntrino cross section. We looked atR varying the MonteCarlo input cross sections. The most important ctribution to the error comes from the “Low” category, since the cross section at low neutrino energmore uncertain. By comparing the cross section cputed under several hypotheses, varying for instathe structure function ([13,23]) in the deep inelasscattering, including or neglecting the contributionresonant scattering, we found(�R/R)σ = 9%. We es-timated a total theoretical error(�R

R

)theor

=√(

�R

R

)2

flux+

(�R

R

)2

σ

= 16%.

The systematic error onR reconstruction, evaluatein 6%, includes the uncertainties on absorber dendrift velocity, streamer tube efficiency and detecacceptance.

MACRO Collaboration / Physics Letters B 566 (2003) 35–44 43

n ofaticsts th

-ep-arlo

ianlsoes-is

yone,thela-m-ted

thetingde-rlom-nd

the

al-

a-

eWe

g

d

is

o

esults

heac-s

-

Fig. 6. Low energy events over high energy events as a functio�m2: the area between the solid lines includes a 17% system(the error is not Gaussian, see text). The hatched band represenreal data.

Fig. 6 shows the ratioR as a function of�m2,assuming maximal mixing, for the Monte Carlo simulation: the area between the two solid curves rresents the 17% systematic error. The Monte Cprediction in case of no oscillations isR′ = 1.5 ±0.25(theor.+ syst.), while for�m2 = 2.5× 10−3 eV2

and sin2 2θ = 1, R = 1.00± 0.17(theor.+ syst.). Aspointed out in [3], the ratio does not have a Gaussdistribution. The errors on the ratio are therefore anot Gaussian: they are reported just to give a crudetimates of the significance. The experimental ratioRexp = 0.85± 0.16(stat.). The one sided probabilitof measuring a value smaller than the measuredwas computed by using two different methods. Infirst one we let the Monte Carlo simulation (no osciltions) to fluctuate according to statistical and systeatic errors of the considered ratio. We then evaluathe fraction of events giving a value smaller thanmeasured one. In a more pessimistic view, rejecthe hypothesis that the lower number of eventstected by MACRO with respect to the Monte Caexpectation is due to oscillation effects, the total nuber of Monte Carlo events (sum of the numerator athe denominator in the ratios), were normalized to

e

Fig. 7. 90% C.L. allowed region in the (�m2,sin2 2θ ) plane forνµ → ντ oscillations, obtained with different data samples.

experimentally measured sum and then they werelowed to fluctuate.

The corresponding one sided probability of mesuring a value smaller thanRexp according to method1 (2) is 0.75% (1.9%) corresponding to 2.4σ (2.1σ ).Finally, we combined the information coming from thenergy estimate and from the angular distribution.considered the ratio:

(8)A=Nvert/Nhor,

whereNvert is the number of upward throughgoinmuon events with cosθ � −0.7 and Nhor is thenumber of events with cosθ � −0.4, as discussein [3]. The probability of measuring a valueA′lower thanAexp according to the method 1 (2)P(A′ < Aexp) = 0.001% (0.01%), corresponding to4.3σ (3.7σ ). It is worth noting that, combining the twindependent probabilities on the ratiosR andA, theprobability that a fluctuation of the expected valu(no oscillations) generates the experimental resis P(A′R′ < AexpRexp) = 1.3 × 10−6 (3.2 × 10−5),corresponding to 4.7σ (4σ ).

The 90% confidence level allowed regions in toscillation parameter space have been computedcording to the prescription given in [24]. Fig. 7 showthe 90% C.L. for the ratioR, the angular distribution [3] and for their combination.

44 MACRO Collaboration / Physics Letters B 566 (2003) 35–44

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5. Conclusions

Muon multiple Coulomb scattering has been usto estimate the energy of the neutrino induced upwthroughgoing muons detected by MACRO. The diffent tests performed on the data, using the estimenergy (separation in subsamples with differentergies,Lν/Eν estimates, etc.) give a consistent pture, all of them supporting the neutrino oscillatihypothesis with parameters�m2 = 2.5 × 10−3 eV2

and sin2 2θ � 1. To quantify such effect, the ratioR =Nlow/Nhigh was used, in stand-alone mode and in cobination with the angular distribution,A=Nvert/Nhor.Both of them are independent of the neutrino absoflux. The significance of the MACRO observationthe neutrino oscillations is above 4σ .

Acknowledgements

We gratefully acknowledge the support of tDirector and of the staff of the Laboratori Naziondel Gran Sasso and the invaluable assistance otechnical staff of the Institutions participating in thexperiment. We thank the Istituto Nazionale di FisNucleare (INFN), the US Department of Energy athe US National Science Foundation for their genersupport of the MACRO experiment. We thank INFICTP (Trieste), WorldLab and NATO for providinfellowships and grants (FAI) for non-Italian citizens

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