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Nuclear Instruments and Methods in Physics Research A 512 (2003) 539–545

*Corresp

Universit"a

80126 Napo

E-mail a1Now at

0168-9002/$

doi:10.1016

Momentum measurement by the angular method inthe Emulsion Cloud Chamber

M. De Serioa, M. Ievaa, S. Simonea, M. Giorginib, M. Siolib, G. Sirrib,S. Buontempoc, N. D’Ambrosioc, G. De Lellisc,*, G. De Rosac, S. Manganoc,1,P. Migliozzic, C. Pistilloc, L. Scotto Lavinac, V. Tioukovc, P. Righinid, G. Rosad,

E. Barbutoe, C. Bozzae, C. Sirignanoe

aUniversit "a di Bari and INFN, Bari, ItalybUniversit "a di Bologna and INFN, Bologna, ItalycUniversit "a ‘‘Federico II’’, and INFN, Napoli, ItalydUniversit "a ‘‘La Sapienza’’ and INFN, Roma, Italy

eUniversit "a and INFN, Salerno, Italy

Received 18 December 2002; received in revised form 23 April 2003; accepted 12 May 2003

Abstract

We present the first automated momentum measurement in an Emulsion Cloud Chamber, consisting of multiple

sandwiches of lead plates and nuclear emulsion sheets. The measurement is based on the detection of the multiple

Coulomb scattering analysed by the so-called angular method. A 3X0 chamber was exposed to 2, 3 and 4 GeV=c p�: Apion momentum resolution of 36% at 4 GeV=c; 35% at 3 GeV=c and 28% for 2 GeV=c was achieved.

r 2003 Elsevier B.V. All rights reserved.

PACS: 29.30.Ep; 29.40.Rg

Keywords: Emulsion Cloud Chamber; Momentum measurement

1. Introduction

The Emulsion Cloud Chamber (ECC) consistsof multiple sandwiches of nuclear emulsion sheetsand plates of lead or other passive material. Thenuclear emulsion sheets provide tracking with sub-micron resolution. Combining low- and high-Z

onding author. Dipartimento di Scienze Fisiche,

‘‘Federico II’’ di Napoli, Via Cintia, edificio G,

li, Italy. Tel.: +39-081-676333; fax: +39-081-676246.

ddress: giovanni.de.lellis@cern.ch (G. De Lellis).

ETH, Zurich, Switzerland.

- see front matter r 2003 Elsevier B.V. All rights reserve

/S0168-9002(03)02016-3

materials, the ECC provides a means to controlthe development of cascade showers in thedetector, unlike homogeneous emulsion stacks.The ECC technique was first introduced in 1951 tostudy high-energy interactions in the cosmicradiation [1]; it was further developed in Japan[2], where it notably led to the observation of thefirst naked charm particle—known as the ‘‘Xparticle’’ [3]—in 1971.Together with automatic emulsion scanning [4],

the ECC allows massive detectors to be con-structed for neutrino physics. In particular, it has

d.

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pion beam

6018560 (µm)

emulsions

BASE BASELEAD LEAD

emulsions

1000

Fig. 1. Schematic structure of an ECC cell.

2FoMos PLC, 77 Leningradsky str., Moscow, Russia.3See, for instance, http://lhcb-vd.web.cern.ch/lhcb-vd/

vertexdetector/00000070.htm.

M. De Serio et al. / Nuclear Instruments and Methods in Physics Research A 512 (2003) 539–545540

been used in the DONUT experiment at FNAL [5]and it will be used as the target of the OPERAexperiment aiming at the search for nm-ntoscillations on the long-baseline neutrino beamfrom CERN to Gran Sasso [6]. We present here astudy of ECC performance, with lead as passivematerial, for momentum measurements. Themomentum is measured from the analysis ofMultiple Coulomb Scattering (MCS) along theparticle trajectory.The paper is organised as follows: Section 2 is

devoted to the description of the experimental set-up of the test beam; in Section 3, the principle ofthe method is described; the emulsion scanning isreported in Section 4; and in Section 5 we presentour conclusions.

2. Beam exposure

The ECC used here is made of 19 cells, each ofthem consisting of a 1 mm lead plate followed by a305 mm thick Emulsion Sheet (ES). One ES ismade up of two 60 mm thick emulsion layers oneither side of a 185 mm plastic base. Fig. 1 showsthe schematic structure of an ECC cell. Thetransverse size is 10� 12 cm2:In the past, emulsions were poured by hand,

following procedures developed over many yearsof experience. The very large productionðOð105Þ m2Þ for the OPERA experiment makesmanual procedures unaffordable. Therefore, filmproducing companies have started the develop-ment of industrial nuclear emulsion as for X-ray

films. In order to reduce the cost required for thelarge quantities which are envisaged, industrialnuclear emulsions are also characterised by a geldilution of a factor up to 3 larger than, forexample, the emulsions used in the CHORUSexperiment at CERN [7], so far the largestapplication of the nuclear emulsion technique.The dilution is limited by the need for a sufficientgrain density along the particle tracks (about 30grains per 100 mm).For this work, nuclear emulsions produced by

the FoMos2 company with a dilution factor ofthree (with respect to the CHORUS emulsions [7])were used. Accidental grains randomly distributedin the emulsion volume (the so-called fog)constitute a background, which in the emulsionsused for this work is below 6–8 grains perð10 mmÞ3:Emulsion and lead sandwiches were packed into

a ‘‘brick’’, by means of a plastic box keeping themwell stuck and light-protected. The brick wasexposed to the p� beam at the CERN PS in the T9experimental area. Data were taken at pionenergies of 2, 3 and 4 GeV=c: The uncertainty onthe beam energy is of the order of 1%, well belowthe achievable performances. At these energies, theT9 pion beam has a large electron contaminationranging from about 30% at 2 GeV=c to 20% at4 GeV=c3. In order to avoid irradiation of theemulsion layers by the electron-generated showers

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M. De Serio et al. / Nuclear Instruments and Methods in Physics Research A 512 (2003) 539–545 541

above an acceptable track density, we placedabout 2:5 cm of lead ðB5X0Þ upstream of the lastfocusing magnet. This reduced to the per-mil levelthe electron contamination as monitored byCherenkov detectors so that its effect becomescompletely negligible (our basic plots are based onhundreds of tracks).Before each exposure, we rotated the brick by

about 100 mrad (well above the beam angularspread), in order to separate the tracks belongingto exposures at different beam momenta. Acoincidence of three scintillating counters wasused to monitor the incident flux and set theexposure time to obtain the desired sample. Therecorded track density is about 10 tracks=mm2 at 3and 4 GeV=c; and 5 tracks=mm2 at 2 GeV=c:

3. Measurement method

The momentum measurement of charged parti-cles in emulsion through the detection of multiplescattering is a technique that has been used sincethe early days of the emulsion technique [8].Originally it was performed by tedious manualmeasurements whereas today it can be fullyautomated. There are essentially two methods:the ‘‘position’’ (sometimes called ‘‘sagitta’’) meth-od and the ‘‘angular’’ method. They measure thedeviations of the trajectory from a straight line onthe basis of position or angle measurements,respectively. The use of one method rather thanthe other depends on the accuracy needed and onthe spatial and angular resolution achievable. Inour case, the deposition of two emulsion layers oneither side of the plastic base allows a precisemeasurement of the angle (with an error of about3 mrad) by the so-called ‘‘base angle’’ which isobtained by connecting the emulsion grains closestto the plastic base. This measurement does notdepend on the precise knowledge of the relativepositions of the different emulsion sheets. There-fore, we used the angular method. The automaticemulsion scanning was performed with the NewTrack Selector (NTS) developed in Japan [4].The angular reference of the tracks is crucial for

the measurement. Instead of using ‘‘absolute’’scattering angles it is better to use ‘‘relative’’ ones,

where ‘‘relative’’ means with respect to a referencetrack. The use of relative angles allows systematiceffects to be cancelled. We use as reference trackthe average trajectory of as many tracks aspossible (several hundred in practice) since thistrajectory behaves like an infinite momentum trackand therefore the momentum contribution to theangular deviations is negligible.Let Wi be the relative angle (one per plane

projection) of a given track in the ith emulsionsheet ðiAf1;y; 19gÞ and

DWik ¼ Wiþk � Wi

the scattering angle after crossing k cells. Thescattering-angle distribution is peaked at zero witha shape which can be approximated by a Gaussianwith a standard deviation given by [9]

W0ðmradÞ ¼13:6

bpðGeV=cÞ

ffiffiffiffiffiffix

X0

r; ð1Þ

where p is the particle momentum and X0 is theradiation length of the traversed material ofthickness x: In our case the scattering is dominatedby the lead since the radiation length of emulsionlayers and plastic base is larger by more than oneorder of magnitude than that of lead. Moreover, inthe following analysis, what matters is thetraversed material before and after the measure-ment and therefore X0C5:6 mm: Note that theangular deviations in the two projections can beconsidered as uncorrelated since the track slopesare sufficiently small (less than 150 mrad).The observed RMS of the scattering angle

distribution for a given cell depth k in the brickis defined as the RMS of all N scattering angles:

/W2obsSk ¼X

i

ðDWikÞ2=N:

Out of the 19 emulsion sheets of the brick, themaximum number of useful sheets for the MCSdetection is 17, since at least two scattering anglesare needed for the RMS calculation of the angulardeviations. The maximum available thickness thuscorresponds to 3X0:The observed RMS can be written as

/W2obsS ¼ /W2scSþ e2;

where Wsc is the scattering angle and e is themeasurement error. For small thickness of the

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Ncell

sca

tteri

ng a

ngle

θ(m

rad)

0

5

10

15

5 10 15

Fig. 2. Scattering angle (dots) as a function of the number of

cells traversed for one track. The triangles give the scattering

angles of the best-fit trajectory with error bars.

2.232 / 6P1 2.065P2 4.313

Ncellθ R

MS (

mra

d)

4

6

8

10

0 2 4 6 8

Fig. 3. The RMS of the scattering angle as a function of the

number of cells traversed for all tracks of the 2 GeV=c beam.

The result of the fit is given by the function f ðxÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4:3132 þ ð 13:6

2:065Þ2ðx=5:6Þ

q:

M. De Serio et al. / Nuclear Instruments and Methods in Physics Research A 512 (2003) 539–545542

passive material, the number of scattering mea-surements is large, which turns into a smallstatistical error in the determination of thescattering angle. In order to increase the sensitivityto high-momentum tracks, it is mandatory to havea good statistical error at the thickness where theMCS starts dominating rather than the resolution.After having obtained the RMS values for all

cell depths k; the reconstruction program gener-ates Monte Carlo trajectories according to themeasured angular resolution and for different trialmomenta. For each trial momentum, 100 attemptsare made to obtain the error for the w2 analysis aswell. Indeed, the momentum is obtained after theminimisation of the w2: Fig. 2 gives an example ofthe observed RMS of the angular deflections(circles) as a function of the cell depth togetherwith the minimum w2 trajectory (triangles): a giventrack is shown in the plot.

4. Emulsion analysis and results

The emulsion scanning was performed by meansof automatic scanning systems developed inNagoya [4]. The beam was uniformly distributed

on the emulsion surface. For each momentum, thebeam angle is centred at about 7100 mrad in oneprojection and 0 in the other, while the beam width(sigma of the distribution) is about 10 mrad:Since no electronic detector has been used to

produce position predictions of the particle tracksin the emulsion and the emulsions themselves aretime-insensitive, a wide-angle scanning in a largearea (about 3 cm2) of the first emulsion sheet wasperformed in order to pick up all tracks in thatarea. The measured tracks are then extrapolated tothe next emulsion sheet and used as predictions forfurther scanning. The scanning area is, therefore,reduced according to the angular resolution and tothe position accuracy. Large deflection angles arethus ruled out by the track-finding algorithm.A crucial step is the intercalibration of con-

secutive emulsion sheets. This is done by matchingtrack patterns using sets of tracks in two con-secutive emulsion sheets. To avoid random coin-cidences and thus to obtain a clean set ofintercalibration tracks in each emulsion sheet,tracks on the tail of the angular beam distributionare used.

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Entries 180 8.192 / 4

Constant 59.14Mean 0.4935Sigma 0.1429

1/p(GeV/c)

Entries 335 10.91 / 3

Constant 157.9Mean 0.3746Sigma 0.1311

1/p(GeV/c)

Entries 241 7.194 / 4

Constant 87.99Mean 0.2490Sigma 0.8934E-01

1/p(GeV/c)

0

50

0 0.5 1

0

100

0 0.5 1

0

50

0 0.5 1

Fig. 4. Measured 1=p distribution for 2, 3 and 4 GeV=c pions. The fitting distribution function is Gaussian.

M. De Serio et al. / Nuclear Instruments and Methods in Physics Research A 512 (2003) 539–545 543

The above procedure (intercalibration and pre-diction scanning) is iterated up to plate 19 to defineparticle trajectories as made of 19 consecutiveemulsion segments. The RMS of the angulardifference distribution of the tracks of 2 GeV=c

pions is shown in Fig. 3, where the RMS value isplotted as a function of the number of cellstraversed. Fitting the curve with the function

f ðxÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2 þ ð13:6=pÞ2ðx=5:6Þ

q; where p is

expressed in GeV=c; x in mm and s in mrad, weobtain both a statistical measurement of theaverage beam momentum p and the angularaccuracy e ¼ s=

ffiffiffi2

pof the base track. The factorffiffiffi

2p

provides the correction for the single-platemeasurement accuracy, which thus gives3:0570:05 mrad: The estimate of the beam mo-mentum at this stage is purely statistical; in otherwords it is obtained from a large statistics of tracksand it is not our goal. At this stage we use thestatistics accumulated to estimate the single-plateresolution s=

ffiffiffi2

pto be used in the track-by-track

momentum measurement.Samples of 180, 335 and 241 tracks were

followed up along 19 cells for the 2, 3 and

4 GeV=c beams, respectively. We used the angularresolution measured as described above and theangular method described in Section 3 to extractthe scattering angle and therefore the momentum.Fig. 4 shows the scattering-angle distributionsscaled to give 1=p for 2, 3 and 4 GeV=c pions.These distributions are Gaussian with standarddeviations of 28%, 35% and 36% for 2, 3 and4 GeV=c pions, respectively. This gives also themomentum accuracy since Dp=p ¼ Dy0=y0:The momentum is proportional to the inverse of

the RMS of the angular deviations (see Eq. (1))and has a distribution which can be parameterisedas

f ðxÞ ¼a0 exp½�ðð1=xÞ � ð1=a1ÞÞ

21=a22x2

; ð2Þ

where ai ðiAf0; 1; 2gÞ are the parameters of thefunction. Fig. 5 shows the momentum distributionfor 2, 3 and 4 GeV=c pions with superimposed thefitted function. None of the parameters of thisfitting function can be identified with the resolu-tion and therefore, as already mentioned, themomentum resolution is obtained from the

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Entries 180 10.03 / 4

P1 332.8P2 1.960P3 0.1651

P (GeV/c)

Entries 335 7.623 / 12

P1 468.1P2 2.847P3 -0.1490

P (GeV/c)

Entries 241 5.193 / 11

P1 939.3P2 4.196P3 0.1044

P (GeV/c)

0

100

0 2 4 6 8

0

50

0 5 10 15

0

50

0 5 10 15 20 25

Fig. 5. Measured momentum distribution for 2, 3 and 4 GeV=c pions. The fitting distribution function is shown in Eq. (2) and the

parameters are listed according to the order defined in the equation itself.

M. De Serio et al. / Nuclear Instruments and Methods in Physics Research A 512 (2003) 539–545544

variance of the Gaussian function fitting thescattering angle.The error on the momentum measurement is

therefore not symmetric. For 2 GeV=c data themeasurement thus gives p ¼ 2:0þ0:8�0:4; for 3 GeV=c

it gives p ¼ 2:7þ1:4�0:7; while for 4 GeV=c we obtainp ¼ 4:0þ2:3�1:0:Similar results have also been obtained with a

neural network approach based on the JETNET3.0 package [10].

5. Conclusions

In the past, measurements of particle momen-tum with the ECC technique were performed bymeans of tedious and time-consuming manualmeasurements.The achievable resolution was lim-ited by the number of reference tracks measurablein a reasonable time; therefore, the accuracyachievable was not satisfactory even when usingthick ECCs.We have reported here the first automated

measurement of particle momentum in an ECC

by means of the angular method. The result showsthat the technique works well and proves thevalidity of the method in automated mode.The measurement was conducted using an ECC

with 3X0 thickness only. The achieved resolutionranges from 28% at 2 GeV=c to 36% at 4 GeV=c:This is an encouraging result for future ECCexperiments, where the measurement will becarried out over a considerably larger ECCthickness and a better angular resolution isenvisaged.

Acknowledgements

We gratefully acknowledge G. Romano and P.Strolin for their careful reading of the manuscript.

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