EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN{EP/2001{028March 29, 2001

MEASUREMENT OF THE �� POLARIZATION IN �� CHARGED

CURRENT INTERACTIONS IN THE NOMAD EXPERIMENT

NOMAD Collaboration

P. Astier1) D. Autiero2) A. Baldisseri3) M. Baldo-Ceolin4) M. Banner1) G. Bassompierre5)

N. Besson3) I. Bird2;6) B. Blumenfeld7) F. Bobisut4) J. Bouchez3) S. Boyd8) A. Bueno9;10)

S. Bunyatov11) L. Camilleri2) A. Cardini12) P.W. Cattaneo13) V. Cavasinni14)

A. Cervera-Villanueva2;15) A. Chukanov11) G. Collazuol4) G. Conforto2;16) C. Conta13)

M. Contalbrigo4) R. Cousins12) D. Daniels9) H. Degaudenzi6) T. Del Prete14) A. De Santo2)

T. Dignan9) L. Di Lella2) E. do Couto e Silva2) J. Dumarchez1) M. Ellis8) T. Fazio5)

G.J. Feldman9) R. Ferrari13) D. Ferr�ere2) V. Flaminio14) M. Fraternali13) J.-M. Gaillard5)

E. Gangler2;1) A. Geiser17;2) D. Geppert17) D. Gibin4) S. Gninenko2;18) A. Godley8)

J.-J. Gomez-Cadenas2;15) J. Gosset3) C. G�o�ling17) M. Gouan�ere5) A. Grant2) G. Graziani19)

A. Guglielmi4) C. Hagner3) J. Hernando15) D. Hubbard9) P. Hurst9) N. Hyett20) E. Iacopini19)

C. Joseph6) F. Juget6) M. Kirsanov18) O. Klimov11) J. Kokkonen2) A. Kovzelev18;13)

A. Krasnoperov5;11) D. Kustov11) V. Kuznetsov11;2) S. Lacaprara4) C. Lachaud1) B. Laki�c21)

A. Lanza13) L. La Rotonda22) M. Laveder4) A. Letessier-Selvon1) J.-M. Levy1) L. Linssen2)

A. Ljubi�ci�c21) J. Long7) A. Lupi19) A. Marchionni19) F. Martelli16) X. M�echain3)

J.-P. Mendiburu5) J.-P. Meyer3) M. Mezzetto4) S.R. Mishra9;23) G.F. Moorhead20)

D. Naumov11) P. N�ed�elec5) Yu. Nefedov11) C. Nguyen-Mau6) D. Orestano24) F. Pastore24)

L.S. Peak8) E. Pennacchio16) H. Pessard5) R. Petti2;13) A. Placci2) G. Polesello13)

D. Pollmann17) A. Polyarush18) B. Popov11;1) C. Poulsen20) J. Rico10) P. Riemann17)

C. Roda2;14) A. Rubbia2;10) F. Salvatore13) K. Schahmaneche1) B. Schmidt17;2) T. Schmidt17)

M. Sevior20) D. Sillou5) F.J.P. Soler2;8) G. Sozzi6) D. Steele7;6) U. Stiegler2) M. Stip�cevi�c21)

Th. Stolarczyk3) M. Tareb-Reyes6) G.N. Taylor20) V. Tereshchenko11) A. Toropin18)

A.-M. Touchard1) S.N. Tovey2;20) M.-T. Tran6) E. Tsesmelis2) J. Ulrichs8) L. Vacavant6)

M. Valdata-Nappi22;�) V. Valuev11;12) F. Vannucci1) K.E. Varvell8) M. Veltri16) V. Vercesi13)

G. Vidal-Sitjes2) J.-M. Vieira6) T. Vinogradova12) F.V. Weber9;2) T. Weisse17) F.F. Wilson2)

L.J. Winton20) B.D. Yabsley8) H. Zaccone3) K. Zuber17) P. Zuccon4)

ABSTRACT

We present a measurement of the polarization of �� hyperons produced in �� chargedcurrent interactions. The full data sample from the NOMAD experiment has beenanalyzed using the same V 0 identi�cation procedure and analysis method reportedin a previous paper [1] for the case of � hyperons. The �� polarization has beenmeasured for the �rst time in a neutrino experiment. The polarization vector isfound to be compatible with zero.

(To be published in Nuclear Physics B)

1) LPNHE, Univ. of Paris VI and VII, Paris, France2) CERN, Geneva, Switzerland3) DAPNIA, CEA Saclay, France4) Univ. of Padova and INFN, Padova, Italy5) LAPP, Annecy, France6) University of Lausanne, Lausanne, Switzerland7) Johns Hopkins Univ., Baltimore, MD, USA8) Univ. of Sydney, Sydney, Australia9) Harvard Univ., Cambridge, MA, USA

10) ETH Z�urich, Z�urich, Switzerland11) JINR, Dubna, Russia12) UCLA, Los Angeles, CA, USA13) Univ. of Pavia and INFN, Pavia, Italy14) Univ. of Pisa and INFN, Pisa, Italy15) IFIC, Valencia, Spain16) Univ. of Urbino, Urbino, and INFN Florence, Italy17) Dortmund Univ., Dortmund, Germany18) Inst. Nucl. Research, INR Moscow, Russia19) Univ. of Florence and INFN, Florence, Italy20) University of Melbourne, Melbourne, Australia21) Rudjer Bo�skovi�c Institute, Zagreb, Croatia22) Univ. of Calabria and INFN, Cosenza, Italy23) Univ. of South Carolina, Columbia, SC, USA24) Roma Tre University and INFN, Rome, Italy�) Now at Univ. of Perugia and INFN, Perugia, Italy

1

1 Introduction

The spin structure of hadrons has been extensively studied both experimentally andtheoretically over the past two decades. Measuring parton spin distributions in di�erentoctet baryons can shed light on many phenomena in non-perturbative QCD, such as SU(3)symmetry breaking, baryon spin content, avor asymmetry in the baryon sea, which wereevoked in connection with the proton spin puzzle [2]. Despite some achievements in this�eld, our current knowledge of the nucleon sea-quark spin distributions and the spincontent of the other hyperons is still very poor. One way to learn about the quark spindistributions of unstable hadrons is to measure the polarized quark fragmentation function�Dh

q (z) of the quark q into the hadron h, where z is the fraction of the total hadronicenergy carried by the hadron in the laboratory system.

Among various hadrons produced in deep inelastic scattering (DIS) � and �� hy-perons are unique because of their parity violating decays into a pair of charged hadrons(�! p�� and ��! �p�+ respectively) which can be e�ciently reconstructed and identi-�ed.

The � (��) polarization is measured by the asymmetry in the angular distribu-tion of the protons (antiprotons) or pions in the parity violating decay process �! p��

(��! �p�+). In the � (��) rest frame the angular distribution of the decay protons (pions)is given by:

1

N

dN

d=

1

4�(1 + �P � k); (1)

where P is the � (��) polarization vector, � = 0:642� 0:013 [3] is the decay asymmetryparameter and k is the unit vector along the direction of the outgoing positive decayparticle (the proton in case of � and the �+ in case of ��).

To probe the polarized quark distribution in a hadron �qh(xBj), where xBj is thestandard Bjorken variable, a source of polarized quarks is required. Of the many meansof obtaining polarized quarks [4, 5], neutrino and antineutrino DIS are exceptional due totheir 100% natural polarization. Moreover, weak interactions provide a source of polarizedquarks of speci�c avour, which makes the measurement of � and �� polarizations in(anti)neutrino DIS an ideal tool to investigate di�erent spin transfer mechanisms and tocheck various models of the baryon spin content.

Di�erent physical mechanisms are responsible for the � and �� polarization in thefragmentation regions de�ned by positive and negative values of xF = 2p�L=W . A polar-ization of the strange sea in the nucleon [6] can manifest itself through a polarization of �and �� hyperons produced in the target fragmentation region (xF < 0) in (anti)neutrinoDIS process. Measurements of the polarization of the � and �� hyperons produced in thecurrent fragmentation region (xF > 0) in (anti)neutrino DIS can provide informationon the polarized fragmentation functions of quarks and antiquarks into a given hyperon(h = � or ��) [7, 8, 9]. The longitudinal polarization of a hyperon h produced in neutrinoDIS in the current fragmentation region, assuming no polarization transfer from the other(anti)quarks fragmenting into this hyperon, is given by:

P h� = �

[d(xBj) + !s(xBj)] �Dhu(z) � (1� yBj)

2�u(xBj)��Dh

�d(z) + !�Dh

�s (z)�

[d(xBj) + !s(xBj)]Dhu(z) + (1� yBj)2�u(xBj)

hDh

�d(z) + !Dh

�s (z)i ; (2)

where ! = tan2 �C (�C is the Cabibbo angle). A measurement of the � polarization inthe current fragmentation region in �� charged current (CC) DIS provides an estimate of

the spin transfer coe�cient C�u = �D�u (z)=D

�u (z) because of the dominant contribution

2

from the �rst term in both the numerator and denominator of Eq. (2). However an inter-pretation of the �� polarization in the current fragmentation region in �� CC DIS is morecomplicated since the two terms in both the numerator and denominator of Eq. (2) couldbe of comparable size.

In order to reduce the number of independent fragmentation functions the authorsof [7] made the following assumptions:

D�q (z) = D�

u (z) = D�d (z) = D

���u (z) = D

���d (z) (3)

and

�D�q (z) = �D�

u (z) = �D�d (z) = �D

���u (z) = �D

���d (z): (4)

The relations (3) and (4) simplify the interpretation of the results of the � and �� polar-ization measurements in (anti)neutrino DIS. However, these relations may not be validif a sizable fraction of � and �� hyperons is produced via resonance or heavier hyperondecays.

The NOMAD experiment [10] has collected 1:3 � 106 �� CC events and has ob-served an unprecedented number of � and �� decays. A detailed paper devoted to the �polarization measurement in the NOMAD experiment has been published recently [1]. Wepresent here the �rst measurement of the polarization of �� hyperons produced in �� CCinteractions.

2 Event selection and V 0 identi�cation

The measurement of charged tracks produced in neutrino interactions in the NO-MAD detector is performed with a set of drift chambers [11] located inside a dipole magnetwith a �eld of 0.4 Tesla.

A �� decay appears in the detector as a V 0-like vertex: two tracks of opposite chargeemerging from a common vertex separated from the primary neutrino interaction vertex(see Fig. 1). A V 0-like signature is expected also for � and K0

s decays and for photonconversions.

The data are compared to the results of a Monte Carlo (MC) simulation basedon LEPTO 6.1 [12] and JETSET 7.4 [13] generators for neutrino interactions and on aGEANT [14] based program for the detector response. In our MC simulation �� hyperonsare not polarized.

The selection procedure for the �� CC event sample used in this analysis has beendescribed in [1].

Since the NOMAD detector is unable to distinguish (anti)protons from pions in themomentum range relevant to this analysis, our V 0 identi�cation procedure relies on thekinematic properties of a V 0 decay.

For the V 0 identi�cation a kinematic �t method has been used as described in refer-ence [1]. This �t has been performed for three decay hypotheses: K0

s ! �+��, �! p��,��! �p�+ and for the hypothesis of a photon conversion ! e+e�. The output of thekinematic �ts applied to a given V 0 vertex consists of four �2

V 0. The di�erent regions inthe four-dimensional �2

V 0 space populated by particles identi�ed as �, �� and K0s have been

selected.Identi�ed V 0's are of two types:

{ uniquely identi�ed V 0's, which, in the four-dimensional �2V 0 space described above,

populate regions corresponding to the decay of di�erent particles;

3

Figure 1: A reconstructed data event containing 2 V 0 vertices identi�ed as � and �� decaysby our identi�cation procedure. The scale on this plot is given by the size of the vertexboxes (3� 3 cm2).

{ ambiguously identi�ed V 0's, which populate overlapping kinematic regions wherethe decays of di�erent particles are simultaneously present.

The treatment of ambiguities aims at selecting a given V 0 decay with the highest e�ciencyand the lowest background contamination from other V 0 types. Our identi�cation strategyconsists of two steps:

1) we select a sample of uniquely identi�ed �� hyperons which has a purity of 91%;

2) we allow ourselves an additional 7% contribution from a subsample of ambiguouslyidenti�ed �� particles resolving the ambiguities between �� and K0

s in favour of max-imal purity.

This approach provides an optimum compromise between high statistics and well under-stood background contamination.

A MC simulation program has been used to study the purity of the overall �� sam-ple obtained by our selection criteria in �� CC interactions. This study indicates that89.6% of the selected V 0's are true �� hyperons, 5.4% are misidenti�ed K0

s mesons and5.0% are due to random track associations. The global reconstruction and identi�catione�ciency is 18.6%. A total of 649 identi�ed �� decays is found in our data, representing asigni�cantly larger number than in previous (anti)neutrino experiments performed withbubble chambers [15, 16, 17, 18, 19]. Fig. 2 shows the invariant mass distributions for �p�+

combinations before and after the V 0 identi�cation procedure.We have compared the distributions of many kinematical variables, describing the

neutrino interaction (E�, xBj , yBj), V0 production and decay (pV , p+, p

intT ), V 0 behaviour

in the hadronic jet (pT , xF , z), obtained in data and MC events. The comparison (seeFig. 3) shows that the experimental distributions of all these kinematical variables arein agreement with the MC results. However, we note that the xF distribution is shiftedtowards positive values in the data (see Fig. 3e), while it is centered around zero in theMC. A small discrepancy between data and MC may be noticed in the z distribution(Fig. 3i).

4

0

0.01

0.02

0.03

0.04

0.05

0.061.091.1

1.111.12

1.131.14

Minv (G

eV)

arbitrary units

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.161.091.1

1.111.12

1.131.14

Minv (G

eV)

arbitrary units

Figu

re2:

Norm

alizedinvarian

tmass

distribution

sin

bothdata

(points

with

errorbars)

andMC

(histogram)calcu

latedfor

V0vertices

under

theassu

mption

ofa��decay

before

(left)an

dafter

(right)the

V0iden

ti�cation

procedure.

3Polarizatio

nanalysis

For

thepolarization

analy

sisdescrib

edbelow

weuse

the\J"

reference

system

,in

which

theaxes

arede�ned

asfollow

s(in

the��rest

frame):

{thenxaxisischosen

alongtherecon

structed

W-boson

direction

(~eW);

{thenyaxisisorth

ogonalto

the��production

plan

e(de�ned

astheplan

econ

taining

both

thetarget

nucleon

(~eT)andtheW-boson

vectors):ny=~eW�~eT=j~e

W�~eTj.

{thenzaxisischosen

toform

arigh

t-handed

coord

inate

system

:nz=nx�ny .

Theexperim

ental

resolution

fortherecon

structed

cos�i=ni�k,where

kisthe

unitvector

inthedirection

oftheoutgoin

gpositive

track(�

+),isfou

ndto

beabout0:07.

Theraw

cos�idistrib

ution

sof

��hyperon

sare

a�ected

bythedetector

acceptan

ceand

therecon

struction

algorithm:

dN(cos

�i )

dcos

�i

=A(cos

�i )(1

+�Pi cos

�i );

(5)

where

A(cos

�i )isthedetector

acceptan

cefunction

which

alsodependson

otherkinem

aticvariab

les.Theangular

distrib

ution

sinthe��case

(seeFig.

4)are

lessdistorted

than

inthe

caseof

the�sam

ple(see

e.g.[1])

becau

seof

ahigh

eraverage

mom

entum

of��hyperon

sproduced

in��CCinteraction

s.Thisisdueto

baryon

numbercon

servationwhich

implies

ahigh

erW

2thresh

oldfor

��production

inneutrin

o-nucleon

DIS.

Ameth

odwhich

allowstheextraction

ofall

three

components

ofthe�( ��)polar-

izationvector

atthesam

etim

e,tak

inginto

accountboth

thedetector

acceptan

ceand

thedi�eren

cesbetw

eengen

eratedandrecon

structed

angular

variables,

has

been

devel-

oped

[1,20].

Theone-d

imension

aloption

ofthismeth

odisused

fortheanaly

sispresen

tedhere

becau

seof

thelow

statisticsof

the��sam

ple.

Theresu

ltsare

summarized

inTable1.

5

0

0.05

0.1

0.15

0 100 200

Eν ,GeV

a)

0

0.05

0.1

0.15

0.2

0 10 20

pV ,GeV

b)

0

0.05

0.1

0.15

0.2

0 2 4

p+ ,GeV

c)

0

0.05

0.1

0.15

0.2

0.05 0.1

pT int ,GeV

arbi

trar

y un

its d)

0

0.05

0.1

0.15

0.2

-1 0 1

xF

e)

10-3

10-2

10-1

0 0.5 1 1.5

pT2 ,GeV 2

f)

0

0.05

0.1

0.15

0.2

0 0.5 1

xBj

g)

0

0.05

0.1

0.15

0 0.5 1

yBj

h)

0

0.05

0.1

0.15

0 0.5 1

z

i)

Figure 3: Comparison of reconstructed kinematic variables for �� CC events containingidenti�ed �� hyperons for simulated (histogram) and data (points with error bars) events: a)neutrino energy, b) �� momentum, c) momentum of the outgoing �+ from the �� decay, d)transverse component of the momentum of one of the outgoing charged tracks with respectto the V 0 direction (internal pT ), e) x-Feynman, f) square of the transverse component ofthe �� momentum with respect to the hadronic jet direction, g) x-Bjorken, h) y-Bjorken,i) fraction of the total hadronic energy carried by the �� in the laboratory system.

6

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Raw cosΘx

arbi

trar

y un

its

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Raw cosΘy

arbi

trar

y un

its

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Raw cosΘz

arbi

trar

y un

its

0

0.1

0.2

0.3

0.4

0.5

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Corrected cosΘx

arbi

trar

y un

its

0

0.1

0.2

0.3

0.4

0.5

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Corrected cosΘy

arbi

trar

y un

its

0

0.1

0.2

0.3

0.4

0.5

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Corrected cosΘz

arbi

trar

y un

its

Figure 4: Top: normalized angular distributions (cos �i) for �� hyperons in reconstructedMonte Carlo events (histogram) and in data (points with error bars). Bottom: experi-mental angular distributions corrected for detector acceptance and selection e�ects; thepolarization is given by the slope of the corresponding linear �t.

7

Table 1: �� polarization in �� CC events (the �rst error is statistical and the second issystematic).

�� PolarizationSelection Entries Px Py Pzfull sample 649 �0:07� 0:12� 0:09 0:09� 0:13� 0:10 0:10� 0:13� 0:07

xF < 0 248 0:23� 0:20� 0:15 0:04� 0:20� 0:19 �0:08� 0:21� 0:12xF > 0 401 �0:23� 0:15� 0:08 0:10� 0:17� 0:05 0:25� 0:16� 0:06

xBj < 0:2 331 �0:12� 0:17� 0:08 0:08� 0:18� 0:11 0:01� 0:17� 0:07xBj > 0:2 318 �0:03� 0:17� 0:14 0:10� 0:18� 0:10 0:20� 0:19� 0:07

Table 2: Summary of relative systematic errors on the three components of the �� polar-ization vector for the full �� sample.

Pi � energy background variation of �� spin totalreconstruction uncertainties selection criteria precession

Px 2:9 � 10�2 5:1 � 10�2 6:9 � 10�2 9:1 � 10�3 9:1 � 10�2

Py 1:0 � 10�1 9:9 � 10�3 2:1 � 10�2 4:9 � 10�3 1:0 � 10�1

Pz 7:4 � 10�3 3:7 � 10�2 5:3 � 10�2 3:3 � 10�3 6:5 � 10�2

4 Systematic errors

The following potential sources of systematic errors have been studied (see detailsin [1]):

{ uncertainty in the incoming neutrino energy determination resulting in an uncer-tainty in the reconstructed W-boson direction and, thus, leading to a poor de�nitionof the \J" reference system in which the �� polarization is measured;

{ uncertainty in the background rate caused by possible di�erences between MC anddata;

{ dependence of the �nal results on the selection criteria;

{ spin precession due to the �� travelling through the magnetic �eld of the detector.

We summarize the results of this study for the full �� sample in Table 2. The maximaldeviation with respect to the reference result is used as an estimate of the systematicuncertainty. The overall systematic errors are obtained by adding all the contributions inquadrature1). In the �� analysis the statistical errors are larger than the systematic errors.

5 Discussion

In our previous publication [1] we have reported the measurements of the � polar-ization in �� CC DIS obtained from a sample of 8087 identi�ed �! p�� decays. Let us�rst brie y recall these results.

For the longitudinal polarization we have found:

{ in the target fragmentation region P�x = �0:21� 0:04(stat)� 0:02(syst).This result is in qualitative agreement with the predictions of the model of negativelypolarized s�s pairs in the nucleon [6].

1) Neglecting possible correlations between variations of selection criteria and resulting background un-

certainties.

8

{ in the current fragmentation region P�x = �0:09� 0:06(stat)� 0:03(syst).

This result provides a measure of the spin transfer coe�cient C�u � �P�x (seeEq. (2)).

A signi�cant transverse polarization P�y = �0:22�0:03(stat)�0:01(syst) has also been ob-served. Its dependence on the transverse momentum of the � with respect to the hadronicjet direction is in qualitative agreement with the well established behaviour observed inunpolarized hadron-hadron experiments [21].

As shown in Table 1, the observed �� polarization vector for the full data sample isconsistent with zero. If we split the �� sample into subsamples with xF > 0 and xF < 0,

we still �nd results consistent with zero. However, a negative value of P��x (xF > 0), if

con�rmed, would disagree with the expectations based on calculations [22] performed inthe framework of the naive quark model, as well as of the Burkardt-Ja�e [23] and theBigi-Gustafson-H�akkinen models [24, 25]. Similarly, a positive value of the �� longitudinalpolarization at xF < 0, if con�rmed, would not be consistent with naive expectations inthe framework of the model of negatively polarized s�s pairs in the nucleon [6].

No signi�cant transverse polarization has been found for the �� sample.As a cross-check we have measured the � (��) transverse polarization using a modi-

�cation of a bias cancelling technique adopted in hadron experiments [26]. We exploit theleft-right symmetry of our detector with respect to the neutrino beam axis, and separatelymeasure the distributions of Eq. (5) for events with primary vertex on the left (L) or onthe right (R) of this axis, replacing cos �y by � cos �y for the right half of the detector:

L =dNL

d cos �y= AL(cos �y)(1 + �Py cos �y) (6)

R =dNR

d cos �y= AR(� cos �y)(1� �Py cos �y) (7)

Using the fact that AL(cos �y) = AR(� cos �y), we de�ne an asymmetry

� =L� R

L+R= �Py cos �y

which does not depend on the detector acceptance. By �tting � to a straight line in cos �ywe extract the transverse polarization Py.

All the measurements of the transverse polarization performed with this methodare in a good agreement with the results obtained using our standard method for both� [1] and �� (Table 1) samples.

6 Conclusion

The results of the �� polarization measurements in �� CC DIS in the NOMADexperiment have been presented. A clean �� sample has been selected on the basis ofkinematic �ts performed on V 0-like decays. The method used to extract the three com-ponents of the �� polarization vector accounts for the smearing of the angular variables.While the statistics of the �� sample is limited to 649 events, the �� polarization has beenmeasured for the �rst time in a neutrino experiment. The results for the three compo-nents of the �� polarization vector as measured in the \J" reference system are compatiblewith zero: Px = �0:07 � 0:12(stat) � 0:09(syst), Py = 0:09 � 0:13(stat) � 0:10(syst),

9

Pz = 0:10�0:13(stat)�0:07(syst). In addition no evidence for the �� polarization is foundeither in the current or in the target fragmentation regions.

More precise measurements of the �� polarization in (anti)neutrino interactionscould help in clarifying the fragmentation and spin transfer mechanisms of quarks and(anti)quarks into a bound system of antiquarks. Improved experimental results on the ��polarization in �(��) DIS will be hard to obtain before more intense neutrino beams [27]become available.

Acknowledgements

We gratefully acknowledge the CERN SPS accelerator and beam-line sta� for themagni�cent performance of the neutrino beam. The experiment was supported by thefollowing funding agencies: Australian Research Council (ARC) and Department of In-dustry, Science, and Resources (DISR), Australia; Institut National de Physique Nucl�eaireet Physique des Particules (IN2P3), Commissariat �a l'Energie Atomique (CEA), France;Bundesministerium f�ur Bildung und Forschung (BMBF, contract 05 6DO52), Germany;Istituto Nazionale di Fisica Nucleare (INFN), Italy; Joint Institute for Nuclear Researchand Institute for Nuclear Research of the Russian Academy of Sciences, Russia; FondsNational Suisse de la Recherche Scienti�que, Switzerland; Department of Energy, NationalScience Foundation (grant PHY-9526278), the Sloan and the Cottrell Foundations, USA.

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