A centrality detector concept

A centrality detector concept

Sourav Tarafdar, Zvi Citron, Alexander Milov n

Department of Particle Physics and Astrophysics, Weizmann Institute of Science, 234 Herzl str., Rehovot 7610001, Israel

a r t i c l e i n f o

Article history:Received 7 June 2014Received in revised form19 August 2014Accepted 20 September 2014Available online 30 September 2014

Keywords:Heavy ionsCentralityHadron collider

a b s t r a c t

The nucleusnucleus impact parameter and collision geometry of a heavy ion collision are typicallycharacterized by assigning a collision centrality. In all present heavy ion experiments centrality ismeasured indirectly, by detecting the number of particles or the energy of the particles produced in theinteractions, typically at high rapidity. Centrality parameters are associated to the measured detectorresponse using the Glauber model. This approach suffers from systematic uncertainties related to theassumptions about the particle production mechanism and limitations of the Glauber model. In thecollider based experiments there is a unique possibility to measure centrality parameters by registeringspectator fragments remaining from the collision. This approach does not require model assumptionsand relies on the fact that spectators and participants are related via the total number of nucleons in thecolliding species. This paper describes the concept of a centrality detector for heavy ion experiment,which measures the total mass number of all fragments by measuring their deflection in the magneticfield of the collider elements.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

The field of relativistic heavy ion (HI) collisions is a rapidlydeveloping branch of modern nuclear physics whose goal is tostudy the nature of the strong force. An extensive scientificprogram carried out by several experimental collaborations atthe Super Proton Synchrotron (SPS) at CERN, the Relativistic HeavyIon Collider (RHIC) at BNL, and recently at the Large HadronCollider (LHC) at CERN has charted the creation of hot, dense,thermalized QCD medium. The study of this medium revealsproperties consistent with a Quark Gluon Plasma [1,2]. An accurateand quantitative description of these properties is key to under-standing the underlying physics of strong force interactions.

The collisional geometry of HI interactions plays a very impor-tant role in defining the physics of the collision, and it is thereforecrucial to characterize it with high precision. Ideally, the impactparameter (bimp) of the collision, the distance between the centersof colliding ions, would be used to define the collision centrality.However bimp cannot be directly measured. The number ofnucleons participating in the collision, (Npart) i.e. the number ofnucleons in both ions suffering at least one interaction with anucleon of the counterpart ion, serves as a more experimentallyaccessible ordering parameter in defining centrality. Npart isdirectly associated with the bulk particle production measuredin HI collisions. In the ion fragmentation direction the number of

charged particles and the energy they carry is found to beproportional to Npart [3]. The wounded nucleon model [4]assumes the proportionality to be linear and accurately describesthe experimental data at the SPS [5,6]. However, with increasedenergy, and considering mid-rapidity particle production thelinearity is violated. The number of participant quark modelappears to be a more complete description of the underlyingprocesses [710].

Extracting Npart from the response of the detector, typicallylocated at forward rapidity on both sides of the interaction point,varies depending on the design of the experiment and thediscretion of the collaboration. It is typically based on a MonteCarlo (MC) Glauber model [11] and involves simulating the particleproduction in the forward rapidity region and the detectorresponse. Event centrality is defined by considering the distribu-tion of the observed bulk particle production (Nch) in measuredevents. The dN=dNch distribution is divided into percentile classes,with the convention that the X% of events with the largest Nch arethe most central events referred to as 0X% centrality. A similarclassification is made in the simulation and thus an empiricallydefined class of events is related to Npart. Typical systematicuncertainties on the determination of the Npart vary from 1 to 2%in the most central collisions to more than 10% in more peripheralevents.

A very interesting topic in HI physics is the study of asymmetriccollisions systems such as the pPb at the LHC and dAu at RHIC.Centrality determination in these systems is even more challen-ging than in symmetric system. Recent results from the ATLAScollaboration [12] show that the approach based on the Glauber

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/nima

Nuclear Instruments and Methods inPhysics Research A

http://dx.doi.org/10.1016/j.nima.2014.09.0600168-9002/& 2014 Elsevier B.V. All rights reserved.

n Corresponding author.E-mail address: [email protected] (A. Milov).

Nuclear Instruments and Methods in Physics Research A 768 (2014) 170178

www.sciencedirect.com/science/journal/01689002www.elsevier.com/locate/nimahttp://dx.doi.org/10.1016/j.nima.2014.09.060http://dx.doi.org/10.1016/j.nima.2014.09.060http://dx.doi.org/10.1016/j.nima.2014.09.060http://crossmark.crossref.org/dialog/?doi=10.1016/j.nima.2014.09.060&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.nima.2014.09.060&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.nima.2014.09.060&domain=pdfmailto:[email protected]://dx.doi.org/10.1016/j.nima.2014.09.060

model which is used in the field for more than a decade may needimprovement. Due to the very important role that centrality playsin the HI studies, improving the centrality determination shouldhave a large impact on the entire field of HI physics.

The main disadvantage of the presently used centrality deter-mination approach is its use of model-based assumptions to relatethe measured detector response to Npart. Another disadvantage ofthe current method is its reliance on using the particles producedin the collision. This often results in an intrinsic correlationbetween particles being measured as a function of centrality andthe definition of centrality itself.

In the collider based HI experiments there is a unique opportunityto measure Npart by measuring spectator fragments, ions, protonsand neutrons which continue to propagate in the same direction asthe colliding ions before the interaction. Spectator fragments areformed by the nucleons which suffer no strong interaction withnucleons of the counterpart ion. The exact process of formingspectator fragments is not thoroughly studied, however the relationbetween Npart and the number of nucleons remaining in thefragments does not depend on this process

Npart 2AiAif : 1

where A is the mass number of a colliding ion and Af is the massnumber of the spectator fragment. The sum is taken over allspectator fragments on both sides of the interaction point. Sincenucleons forming fragments did not suffer strong interaction theyretain full longitudinal momentum, pz , and their momentum vectorafter interaction is approximately collinear with the vector of theinitial ion. The trajectories of the particles in the collider depend ontheir mass-to-charge (m=q) ratio. Colliding ions with a particularm=qstay on an equilibrium orbit, but fragments deviate from it, depend-ing on their ratio Af =Zf pm=q. Since lighter nuclei have less neutronscompared to protons than heavier nuclei, lighter fragments formedafter the collision typically have smaller mass-to-charge ratio. Theyare thus separated from the equilibrium beam by the magneticstructure of the collider according to their Af =Zf . This presents aunique opportunity for a collider-based HI experiment to build acentrality detector which measures Npart by detecting spectatorfragments and measuring their Af . Such approach is free of the maindisadvantages present in the currently used centrality determination:it is not model dependent and it uses particles created by physicsprocess which is decoupled from the particle production mechanismin the HI collision. This paper describes basic parameters of acentrality detector using the magnetic structure of RHIC. Threedetector stations are considered on each side of the interaction point.The Zero Degree Calorimeters (ZDC) [13], which are existing inte-grated parts of operating RHIC experiments, are used to detect freespectator neutrons. The main physics processes affecting detectorperformance are discussed based on the spectator fragmentationmodeled using the DPMJet [14] and QGSM [15,16] event generators.

Measuring the parameters of collisions by detecting the pro-ducts remaining after the interaction was suggested in [17]. TheNA49 experiment at the SPS measured the distribution of differentfragments remaining after the interaction of a Pb ion with a fixedPb target [18]. At electron colliders, energy lost by the electron andpositron was measured via their deflections in the magneticstructure of the collider rings [19]. This paper proposes anapplication of a similar approach to the HI collider experiments.

The paper is organized in the following sections: Section 2calculates fragment trajectories in the magnetic structure of RHICand explains the factors affecting the choice of detector stationpositions. Physics processes affecting distribution of the fragmentson the surface of detector stations are discussed in Section 3.Detector performance parameters, such as efficiency and centralitydetermination accuracy are presented in Section 5.1.

2. Modeling the collider structure

Spectator fragments with different Af =Zf are traced using theMAD-X (Methodical Accelerator Design) code [20]. In a formalismcommonly used to design accelerators, the transport of particlesfrom the interaction point (IP) to a given location along the ringcan be described with a matrix:

x

x0

y

y0

z

pz=pz

a1;1 a1;2 a1;5 a1;6a2;1 a2;2 a2;6

a3;3 a3;4 a3;5 a3;6a4;3 a4;4 a4;6

1 a5;61

0BBBBBBBB@

1CCCCCCCCA

x

x0

y

y0

z

pz=pz

IP

: 2

where x; y are linear and x0; y0 are angular transverse particlecoordinates, z is the longitudinal coordinate, and pz=pz is theresidual particle momentum. All coordinates, including pz=pz ,are defined with respect to a particle in equilibrium orbit locatedat the center of the beam. Matrix elements which are consideredequal to zero are not printed in the equation.

The block-diagonal form of the matrix for indices i; jr4corresponds to the case when the particle translations along xand y coordinates are decoupled from each other. Such approx-imation is sufficient for relatively short distances z consideredfurther. Particle coordinates in longitudinal directions affect trans-lation in both x and y directions. At RHIC, the interaction regionhas a typical width of about 15 cm around the nominal IP, and theevent vertex position in z can be measured with high precision foreach collision. Measuring the vertex position eliminates theimpact of z coordinate in Eq. (2) and therefore all interactionsare modeled at the nominal IP.

Measuring spectators fragments relies on the fact that theparticles with non-equilibrium longitudinal momentumpz=pza0 have different trajectories in the collider. Coupling ofthe transverses coordinates to the longitudinal momentum isgiven by the last column of the matrix in Eq. (2). For values ofpz=pz{1 matrix elements ai;j can be considered as constantcoefficients. However, for light fragments pz=pz 1Af =Zf =AAu=ZAu is significantly different from zero, and therefore adifferent matrix was calculated for each value of Af =Zf .

Fig. 1 shows the spectator fragment trajectories calculated in xcoordinate. The equilibrium Au beam with A=Z 2:5 is shown asthe filled area. The size of the beam is

ffiffiffiffiffiffi

p, where is the

collider beta-function and is the beam emittance. AtffiffiffiffiffiffiffiffisNN

p 200 GeV 0:023 mradmm and the value of the function at the IP is 1:0 m. Hashed areas correspond to thelocations of collider magnetic elements, and the outer line showsthe dimension of the vacuum beam pipe. The trajectories offragments with Af =Zf o2:5 are shown in the overlaid lines.Neutron trajectories are not shown in the plot; they continuealong straight lines in the laboratory coordinate system andterminate in the ZDC, located at a distance of 18 m from the IP,between the first and second magnets. All particles are deflectedto the same side of the Au beam, except tritium which hasAf =Zf 3 and therefore appears on the other side of the equili-brium beam. With the exception of tritium, the magnitude ofdeflection increases with decreasing Af =Zf .

Protons and 32He, the lightest charged fragments, are deflectedout of the beam pipe between the first and second dipole magnets.Therefore, to measure these fragments the first detection stationmust be placed after the first magnet. Its location is chosen to be atz14 m. The next station is needed to detect fragments with2oAf =Zf o2:1. To conform to this deflection pattern, the secondstation is located at z20 m from the IP. The next station is tomeasure the largest Af =Zf fragments, and for this the detector

S. Tarafdar et al. / Nuclear Instruments and Methods in Physics Research A 768 (2014) 170178 171

should be placed as close as possible to the equilibrium beam.Placement of detector elements too close to the circulating beamcan cause beam loss, and so to reach higher Af =Zf the third stationis located further away from the IP where the size of theequilibrium beam becomes smaller and the deflection of thefragments displaces them significantly from the beam. The laststation is placed at z72 m. In this calculations the apertureconstrains in x direction are taken to be 8 of the beam in thedirection closer to the equilibrium beam. In the opposite directionthey are taken equal to the dimension of the beam pipe. Detectoracceptance in the vertical direction is taken to be 760 mm fromthe beam center. The aperture of the ZDC is taken to be 755 mm[13] at 18 m from the IP.

3. Generators of the spectator fragments

Fragmentation of Pb ions in a 158A GeV fixed target experimentwas measured by the NA49 Collaboration [18] for all fragments,protons, and neutrons. However, for performance studies of acentrality detector one needs more detailed information about

spectator nucleon fragmentation and aggregation. As discussed inthe previous section detecting spectator fragments with Af =Zfclose to 2.5 is problematic. Such fragments are produced inperipheral collisions (see Fig. 4) and the detector performanceshould have centrality dependence. To understand this depen-dence and other factors affecting the detector performance spec-tator fragments were generated by two Monte Carlo generators:DPMJet and QGSM. A comparison between them and to availableexperimental data is discussed in this section.

The DPMJet generator is based on the Dual Parton Model (DPM)[21] and is capable of simulating hadronhadron, nucleusnucleus, photonhadron and photonnucleus interactions from afew GeV up to the highest cosmic ray energies. The QGSMgenerator is based on the Quark-Gluon String Model [22] andhas the capability of simulating hadron-hadron, nucleus-nucleusand hadron-nucleus interaction. Both models take into accountFermi break up, multi-fragmentation, evaporation, and fissionprocesses.

Both DPMJet and QGSM generators identify the physics processfrom which fragments originate and provide the kinematic infor-mation for each produced fragment. Spectators have rapiditycomparable to the rapidity of the equilibrium beam ybeam 5:36.The rapidity distribution of all particles produced by DPMJet andQGSM generators around the beam rapidity is shown in Fig. 2. Theresults of DPMJet are shown with empty histograms and theresults of QGSM with filled histograms.

Fig. 2 shows the rapidity distribution of final state particles inthe forward region near the beam rapidity. Final state particleswith non-zero baryonic number and jyj45, generated in a physicsprocess that involves only one of the colliding ions are selected asspectators. Spectator fragments with Af 41 have a distinct peak atthe rapidity of the beam due to heavier particles sharing a verysimilar trajectory with the equilibrium beam. Spectators withAf 1 (protons and neutrons) have a wider distribution. Chargedparticles produced in HI interactions, i.e. non-spectator particles,including baryons, are also shown in the plot.

After accounting for all the spectators produced in eachmodeled event, Npart is defined according to Eq. (1). Fig. 3 showsthe Npart probability distribution generated by the DPMJet and theQGSM models as well the Glauber model. The DPMJet and Glaubermodels show good agreement whereas the QGSM model shows asignificant deficit at high Npart and excess at lower Npart.

Spectator fragmentation into final state particles within a givenNpart window is also found to be different between the DPMJet andQGSM generators. The difference is seen at all centralities in Fig. 4

|y|4.5 5 5.5 6

)dN

/dy

evt

(1/N

-110

1

10

210

QGSM DPMJET > 1 fA

= 1 fA

From HI collision

Fig. 2. The rapidity distribution of the fragments produced per event 1=NevtdN=dyby the QGSM generator (filled histograms) and by the DPMJet generator (emptyhistograms) as a function of rapidity jyj. Charged particles produced in HIinteraction by the DPMJet generator are shown with hashed histogram.

partN0 100 200 300

Pro

babi

lity

-510

-410

-310

-210QGSMDPMJetGlauber

Fig. 3. The Npart distribution produced by the DPMJet and the QGSM generators andby the MC Glauber model.

z [m]

0 10 20 30 40 50 60 70

x [m

m]

-80

-60

-40

-20

0

20

40

60

80

Fig. 1. Spectator fragment trajectories in the RHIC magnetic structure. Hashedboxes correspond to the locations of collider magnetic elements, the beam pipe isshown with the solid outer line, vertical lines indicate the locations of detectorstations. The filled area is the size () of the equilibrium beam. Lines are thetrajectories of fragments with different Af =Zf .

S. Tarafdar et al. / Nuclear Instruments and Methods in Physics Research A 768 (2014) 170178172

which shows the Af distribution of spectator fragments producedby the generators for different Npart intervals. The distributionsshow that QGSM tends to produce lighter fragments than DPMJetin central and mid-central events, and in peripheral events thetrend is opposite.

Although the full fragmentation spectrum has not been measuredat RHIC, the performance of the two models may be gauged bycomparing their production of free spectator neutrons, Nf :n:, (i.e. afragment composed of a single neutron) to data measurements. Thiscan be done using the response of the ZDC calorimeters installed inthe RHIC experiments, which measure the energy carried mainly byfree spectator neutrons. Fig. 5 shows the Nf :n: as a function of Npart forthe generators used in the analysis. Panel (a) shows the result forDPMJet and panel (b) for QGSM. The filled symbols superimposed onthe scatterplot are the mean values of Nf :n: at each value of Npart.

These values are compared to the values derived from the datapublished by the PHENIX experiment [23]. The distribution of energymeasured in the acceptance of PHENIX ZDC versus charge measuredby the BeamBeam Counters (BBC) is shown in Fig. 1 of Ref. [23]. Thevalues on the axes of the plot are given in arbitrary units. The chargemeasured in the BBC is proportional to the number of producedparticles which is proportional to Npart. This relation is used by thePHENIX experiment to determine centrality. One can further approx-imate that the maximum value of the BBC, equal to 1:5 in arbitraryunits of Fig. 1 in Ref. [23] corresponds to the maximum number ofparticipants Npart 353 in Table XIII of the same reference. Thedominant part of the energy measured by the ZDC is carried by thefree neutrons, each delivering on average the same energy 100 GeV.Therefore, the ZDC response is proportional to Nf :n:. The maximumaveraged Nf :n: in the data is assumed to be the same as generated byDPMJet and QGSM within the aperture of the ZDC.

Panel (c) of Fig. 5 shows the comparison between the Nf :n:extracted from the data and that produced by the generators. TheDPMJet generator better describes the centrality dependence ofNf :n: compared to QGSM. In the interval Npart above 150, the curve

produced by the DPMJet generator shows the same trend as thedata estimate. The absolute values are different, which can be anartefact of the procedure used to derive the data estimate. At lowNpart both generators show significant deviations from the esti-mate, producing lesser Nf :n:. The implication of this discrepancy isdiscussed in Section 6.

4. Detector performance

The detector performance depends on how completely andaccurately spectator fragments can be reconstructed based ontheir kinematic reconstruction in the detectors. Several factorslisted below have an impact on the measurement of spectators.

4.1. Collider effects

Ions in the beam have spatial and angular dispersions definedby the function of the collider and the emittance of the beam.Most of the modern collider based detectors are equipped with avertex detector which can determine the position of an eventvertex in transverse plane with an accuracy better than thecoordinate dispersion of the particles in the beam. However inthese studies, precision vertex information is not used and thetransverse dispersions present in the equilibrium beam smear thecalculation of spectator kinematics, see Eq. (2). The magnitude ofthis effect is visible in panel (b) of Fig. 6.

Background hits in the detector stations produced by theparticles outgoing from the equilibrium beam, or by their second-aries, are not considered in this work. These may be coming fromthe beamgas interactions, from the interactions of spectatorfragments hitting the walls of the beam pipe or collider structureelements. They can produce significant number of hits in thestations and affect the detector performance. However, under-standing of these processes requires more realistic simulation of

Fig. 4. The Af distribution produced by the DPMJet (line) and by the QGSM (filledhistogram) generators for the events with different Npart . The distributions arenormalized by the number of MC events and by the average number of spectatornucleons. Values in the bins Af o8 are staggered from the center of the bin.

20

40

60

80 DPMJET

20

40

60

80 QGSM

partN0 100 200 300

0

20

40

60

80Derived from dataDPMJETQGSM

f.n.

NFig. 5. The number of free spectator neutrons within ZDC acceptance versus Npart.Panel (a) shows the results of the DPMJet generator and panel (b) of the QGSMgenerator. The markers in the plot are the averaged values. In panel (c) the twocurves from panel (a) and (b) are compared with the same quantity derived fromthe data [23] as described in the text.


the collider structure elements and of the detector hardwareinside the stations, which lies outside the scope of this paper.The pile-up, caused by multiple HI interactions inside the samecrossing of the ion beams or coming from two subsequent beamcrossings is also not considered.

4.2. Collision effects

Particles created in HI collisions with sufficiently high rapidityform a background to the spectators in the detector. These aresimulated by DPMJet and are traced though the collider structurein the same way as spectator fragments. In the QGSM generatorproduced particles are not simulated.

The detector performance is directly related to the ability withwhich Af =Zf and ultimately Af can be reconstructed. The dominantfactor that weakens the correlation between the particle's positionin the detector and its Af =Zf value is the Fermi motion of thenucleons inside the colliding ions. In the process of fragmentcreation it results in an angle of the spectator fragments withrespect to the initial direction of the ion and changes its long-itudinal momentum. In these studies the effects of the Fermimotion in the longitudinal and transverse directions are taken asmodeled by the generators, but they are shown separately.

Let pF be the Fermi momentum of a nucleon in the ion restframe, then in the laboratory frame the average angle of afragment with respect to the ion direction and the longitudinalmomentum dispersion relative to pz are given by the followingequations:

y0 x0 1ffiffiffiffiffiffiffiffi3Af

p pF

pz

pz=pz1ffiffiffiffiffiffiffiffi3Af

p pF

mN3

where mN is nucleon mass. Both dispersions decrease p1=ffiffiffiffiffiAf

p,

however the angular dispersion of fragments also diminishes withbeam energy (pz

ffiffiffiffiffiffiffiffisNN

p=2), whereas the longitudinal momentum

dispersion does not depend on the beam energy.

4.3. Spectator deflection in the detector stations

The positions of charged spectator fragments in the x directionat the location of the first detector station (z14 m), calculatedusing Eq. (2), are shown in Fig. 6. In the case that a single fragmententers the aperture of more than one station it is considered to bemeasured in the station closest to the IP and is ignored in thesubsequent stations.

Panel (a) corresponds to the ideal case, in which the chargedfragment distributions are calculated without any distortions.Peaks from left to right correspond to protons, 32He, particles withAf =Zf 2, 2oAf =Zf o2:5, and tritium (which appears in thepositive region of the axis). Integrals of the peaks correspond tothe production rates of spectator fragments produced in allcentralities. In this ideal case, all spectator fragments with thesame Af =Zf arrive at the same point in the detector resulting insharp peaks. The equilibrium beam, with A=Z 2:5, arrives at x0and is not shown in the figure. Results of calculations taking intoaccount angular and spatial dispersions of the ion beam are shownin panel (b). This is done by assigning to each spectator fragmentposition and angle of the corresponding ion at the IP. Including thelongitudinal Fermi motion component makes the peaks signifi-cantly wider and they start to overlap as shown in panel (c).Adding to these effects also the transverse components of theFermi motion is shown in panel (d) of the figure.

The beam dispersions and the dispersions due to the transverseFermi motion depend on the parameters of the collider. At LHCenergies transverse Fermi motion plays a less significant role thanat RHIC, while at the NICA collider [24] their contributions aremore significant. The longitudinal component remains the same atall energies.

Fig. 7 shows the x position distributions of charged spectatorfragments in each of the three detector stations. The calculationsare performed using the DPMJet generator, including all relevanteffects discussed above. Panel (a) shows the deflection in the firststation at z14 m, panel (b) the second station at z20 m, andpanel (c) the third station at z72 m. The x positions of theparticles in the third stations are inverted x-x because it islocated on the other side of the equilibrium beam than the othertwo stations as shown in Fig. 1.

The primary goal of the first station is to detect protons and32He spectators. The distributions shown in panel (a) are the samedistributions as the proton, 32He, and inclusive distributions shownin panel (d) of Fig. 6. Spectators entering into the detectoraperture, shown with vertical bars, are considered detected. Thesecond station is intended to detect fragments with 2rAf =Zf2:1.The distribution of such particles at the location of the secondstation is shown with hashed histogram in panel (b). Spectatorsresiding within the station aperture are detected in the secondstation. Spectators detected in station 1 are shown by the dashedhistogram. The third station is designed to measure spectatorswith Af =Zf2:1. Their distribution at the location of the thirdstation is shown in panel (c) with hashed histogram. Spectatorsdetected in the other two stations are shown by the dashedhistogram.

To quantify the performance of an ideal detector, the assump-tion is made that all detected spectator fragments are recon-structed with their true Af . Then using Eq. (1) a reconstructednumber of participants, Nrecpart, is calculated, which can be comparedto the event's true number of participants, Ntruepart. The calculationof Nrecpart includes the contribution of background particles

-210

-110

1

10

-210

-110

1

10

-210

-110

-120 -100 -80 -60 -40 -20 0 20

-210

-110

parti

cles

per

eve

nt p

er m

m

x [mm]

Fig. 6. Position of different types of charged particles at the location of the firstdetector station (z14 m). Relative amplitudes of different particles correspond tothe sample of all centralities, generated with DPMJet. Panel (a) shows the idealcase. Panel (b) includes into consideration the dispersions in the ion beam. Panel(c) includes the ion beam dispersions and the longitudinal Fermi motion and paneld) includes the beam dispersions and the full Fermi motion.


produced in the HI collision that enter the detector. Fig. 8 showsthe two-dimensional Ntruepart versus N

recpart distribution calculated

using DPMJet.There are three distinct regions in the plot. The region at

(Nrecpart320, Ntruepart40) corresponds to events in which two heavy

fragments with Af =Zf close to 2.5 are produced in a peripheral

collision and neither is reconstructed by the detector. In suchevents the centrality cannot be determined, however such eventsshould have a significant mismatch between the large Nrecpartmeasured by the centrality detector and low number of producedparticle measured by any other detector subsystem. Such anidentification procedure is equivalent to removing events belowthe solid line shown in the figure.

The region at (Nrecpart 200, Ntruepart60) corresponds to peripheralevents in which one heavy fragment escapes detection. Theseevents can be identified by comparing the response of thecentrality detectors on both sides of the IP. The asymmetry inthe number of participants, NNpartNSpart=NNpartNSpart where Nand S are the opposite sides of the IP, is shown in the insert.Rejecting events with high asymmetry as indicated by the dashedline in the insert would result in rejecting events located belowthe dashed line in the main area of the figure. The centrality in thisclass of events can still be measured on one side and extrapolatedto a total Npart by multiplying by a factor of 2. In the presentedanalysis the extrapolation is not done and these events are notfurther considered.

The bulk of events are close to the diagonal Ntruepart Nrecpart. Theseare the events with properly reconstructed Npart. Fig. 8 shows thateven in this region, Nrecpart somewhat underestimates N

truepart due to

fragments which miss the detectors. This necessitates a correctionfor the finite acceptance of the detector stations. The optimalcorrection can be derived from analysis of the real detector'sperformance by reconstructing the nuclear fragmentation andcalculating a correction for each A/Z on a statistical basis.

5. Results

5.1. Efficiency and resolution of centrality determination

The fraction of all events in which centrality can be determined,the centrality determination efficiency, is shown in Fig. 9 as afunction of Npart. The two curves correspond to the results of theDPMJet and QGSM generators and both approach unity at highNpart. In peripheral events, the efficiency rapidly falls to zero withdecreasing Npart. The low efficiency notwithstanding, low Npartevents which are detected have a robust centrality determinationeven in Nrecparto20. In peripheral events the DPMJet generator basedcalculations show higher efficiency for the same Nrecpart compared toQGSM. This is related to the differences in the Af distributionsdiscussed in Section 3.

The resolution of the Npart determination is defined as the R.M.S.of the Ntruepart distribution for a given N

recpart divided by its mean value

-210

-110

1 H11

He23

Produced particlesAll

-210

-110

AllPreviously detected

2.1 f / Z f A 2

-120 -100 -80 -60 -40 -20 0 20

-210

-110

AllPreviously detected

2.1 f / Z f A

parti

cles

per

eve

nt p

er m

m

x [mm]

Fig. 7. Position of different types of charged particles at the locations of the firststation (a), the second station (b) and the third station (c). Stations are optimized tomeasure particles shown with hashed histograms. Distributions of spectatorsdetected the stations closer to the IP are shown with dashed histograms. Thestation acceptance is shown with vertical lines. The distributions in the thirdstations are inverted: x-x.

recpartN

0 100 200 300 400

true

part

N

0

100

200

300

400

cut1 cut2 C

ount

s

024681012recpartN0 200

Ass

ymet

ry

-1

0

1

Fig. 8. The true number of participants, Ntruepart versus the number of reconstructedparticipants, Nrecpart. The insert shows the asymmetry in the number of participantsreconstructed on both sides of the IP. Lines indicate event selection criteriaexplained in the text.

partN0 100 200 300

Effi

cien

cy

0

0.5

1

DPMJETQGSM

Fig. 9. Fraction of all events in which the Npart determination is possible, thecentrality determination efficiency.


Ntruepart. Resolution of Npart is shown in Fig. 10. The width of the Npartdistribution has two contributions. The first depends on the widthof the centrality interval, i.e. the width of the percentile (or Nrecpart)over which the averaging is done. The second is the intrinsicresolution of the method and the detectors that are used formeasuring Npart. Fig. 10 has two sets of curves: filled markerscorrespond to the resolution in predefined centrality intervals, openmarkers correspond to the intrinsic detector resolution.

The results of calculations are compared to an estimate basedon the data published by the PHENIX experiment which is shownwith filled circles. The estimate is based on the widths of the Npartdistributions in 5% centrality intervals shown in the left panel ofFig. 18 in Ref. [25]. The values in the plot are divided by Npart inthe same centrality intervals given in Ref. [23] and are plottedversus Npart. The error bars correspond to the systematic uncer-tainties which are given in the same publication. The results of thecalculations for DPMJet and QGSM models are shown in the samecentrality intervals as the data estimate, calculated using Nrecpart.These estimates include the width of the centrality intervals andthe intrinsic resolution of the method, but not the resolution of thedetector, which is discussed below. As one can see the resolutiondepends on the choice of generator and is comparable to currentlyused techniques.

To address the question of intrinsic resolution of the methodand the contribution which is coming from possible choice ofdetector technology to be used in the detector stations, theresolution was calculated with the DPMJet generator in narrowNrecpart intervals. The resulting curves are shown in Fig. 10 with openmarkers. Open squares correspond to the case when each Af ismeasured perfectly, i.e. the true Af is accepted for each detectedparticle. The open circles (charge and position) correspond to thecase in which the Zf of the fragment is measured perfectly, but themass is taken at an average value of all spectators with measuredZf at the x-position in the detector. The open diamond (chargeonly) markers correspond to the case when the coordinate is notreconstructed at all, but the mass is taken as an average mass of allfragments for a given Zf .

The curves are all similar, because the dominant factor whichdetermines the resolution is the loss of spectator fragmentscoming from increased deflection due to Fermi motion (seeFig. 6). The curves are not flat at Npart 250 due to the asymmetrycut shown in the insert of Fig. 8. The cut results in a smallinefficiency for measuring the centrality even in the mid-central

region, however these events are identifiable as such and may beexcluded from analysis.

5.2. Possible choices of the detector technology

The key requirement for each detector station is the ability toreconstruct Zf . A suitable choice to achieve this using existingtechnology is a Cherenkov radiation detector. The resolutionneeded to distinguish two fragments with charges Zf 1 and Zfis estimated by the following equation:

dqqZ2f Zf 12ffiffiffiffiffiffi

12p

Z2f Zf ffiffiffi

3p

Z2f 1ffiffiffi

3p

Zf ; 4

neglecting the difference between Z2f and Zf 2.

Different stations are designed to register particles with differ-ent Af =Zf and therefore different Zf , as explained in Section 4.3.Station 1 mainly detects fragments with Zf 1 and 2. The meancharge of fragments in station 2 is Zf 20 and is Zf 40 instation 3. From Eq. (4), the required resolution for measuring Zf ineach station is 30%, 3% and 1.5% respectively. A Cherenkov detectorwith a 5 cm radiator, an index of refraction in the range of opticalglass, 20% light collection efficiency, and 10% photosensor quan-tum efficiency yields approximately 20 photoelectrons per frag-ment in station 1, 4103 in station 2, and 1:5 104 in station3. This would provide enough photoelectrons to meet the desiredresolution. The Cherenkov detector must have sufficient granular-ity to measure multiple fragments simultaneously. The averagenumbers of fragments in each stations does not exceed 10,suggesting that the detector has to have from tens to a hundredindividual channels.

Fig. 10 shows that measuring fragment positions has only smalleffect on the final Npart resolution. However, measurement of thefragment position is important for detector alignment and forrejecting background, it can be useful to trace particles from onestation to another. A possible choice of detector technology fordetermining fragment position is a silicon pixel based tracker withseveral layers along the fragment trajectory. A similar choice ofdetector technologies is suggested for the forward physics upgradeof the ATLAS detector at the LHC [26].

5.3. Measurement of the event plane orientation

Azimuthal anisotropy of particle emission in heavy-ion colli-sion is an important observable to understand the medium createdin HI collision. The harmonics of the azimuthal anisotropy ofparticle emission are studied by all HI experiments [2731]. Themeasurement of the nth harmonic relies on the determination ofparticle emission angles with respect to the event plane n of thecorresponding harmonic. The event planes are measured in theforward region using particles produced in the collision, except for1, which cannot be determined with produced particles and ismeasured using the ZDC.

The proposed detector offers an opportunity to measure 1.Determination of the 1 event plane can be made by measuringspectator fragment positions in all three stations. The resolutiond1 can be then estimated as

d 1

f j 5

where is the average emission angle of all spectators, and isthe relative angle between the direction of spectator fragmentsand the ion ( is assumed to be the same for all fragments in anevent). The factor f , accounts for resolution differences in the xand y directions. In the case x y, the modulus of this functionaveraged over all angles is 1. This condition is true in all threedetector stations. The average emission angle can be estimated

partN0 100 200 300

reso

lutio

npa

rtN

0

0.1

0.2

Centrality bins 5%Estimate from dataQGSM idealDPMJET ideal

Narrow binsDPMJET idealDPMJET charge and positionDPMJET charge only

Fig. 10. Resolution of Npart determination for calculations using the DPMJet and theQGSM generators in different centrality bins (filled markers) and for differentchoices of detector technologies (open markers). Calculated resolution is comparedto the estimation based on the data, which is derived from publications [23,25].


by measuring deflection of the particles in the detector stations.

di

xi xia1;2d

Aif

diAif

6

The index i refers to spectators in a given detector station and d tothe three detector stations. It can also be done in each stationindividually. The (xi xi) is relative deflection of the fragment in astation with respect to an average position of all fragments withthe same Af =Zf . Coefficient a1;2d is the matrix element for dthstation in Eq. (2). Each spectator fragment is summed with aweight equal to the Af , to account for the fact that heavierfragments have lesser distortion due to Fermi motion, and there-fore their contributions to the 1 measurement are more accurate.

Fig. 11 shows as a function of Npart. Lines correspond to theresults of measuring with individual stations on both sides ofthe IP. Markers correspond to the combination of all three stations.The combined result does not include an additional measurementwhich can be provided by the ZDC. As measured by the ALICEcollaboration the average deflection of neutrons in the ALICE ZDCfor 3040% centrality is 0.92 mm at 110 m [32]. Assuming that theangle is inversely proportional to

ffiffiffiffiffiffiffiffisNN

p, Eq. (5) and Fig. 11, it

follows that d 1 1:1 rad.

6. Conclusions

This paper presents a detector concept for the direct measure-ment of the number of participants in heavy ion collisions bydetecting spectator fragments. The performance of the detector isevaluated based on the example of AuAu interactions atffiffiffiffiffiffiffiffisNN

p 200 GeV in RHIC. The location of 3 detector stations,integrated into the RHIC structure, are optimized for the bestdetector performance. The main performance parameters, such asthe efficiency of centrality determination and resolution in mea-suring the number of participants is presented as a function ofcollision centrality based on the fragmentation modeled by theDPMJet and QGSM generators.

The detector performance is compared to present techniquesfor measuring centrality and is found to be comparable to them.The results are significantly different for the DPMJet and QGSMgenerators which have different distributions of produced frag-ments for the same Npart. Comparison of generators to the existingdata is limited, and shows that both generators have significant

deviations from the measured quantities and that the DPMJetbetter reproduces available data.

Modern detector technologies are shown to be adequate toperform the measurements. The proposed concept offers anopportunity to make a precise measurement of the orientationof the first order event reaction plane. The main advantage of thecentrality detector is in measuring the number participants in amodel independent way, with no correlation to producedparticles.

Acknowledgements

The authors are thankful to our colleagues, Prof. Itzhak Tserruyaand Dr. Ilia Ravinovich at the Weizmann Institute of Science fornumerous useful discussion and help in preparing the document.Authors express their gratitude to Prof. Nestor Armesto fromUniversity of Santiago de Compostela, Dr. Oleg Rogachevsky fromthe Joint Institute of Nuclear research at Dubna for ideas and helpin using particle generators. Authors are thankful to Dr. VadimPtitsyn from the Brookhaven National Laboratory for his help withthe MAD-X code and information about RHIC structure. Work ofDr. S. Tarafdar is supported by VATAT Program for Fellowships forOutstanding Post-doctoral Researchers from China and India.

References

[1] E. Shuryak, Nuclear Physics A 750 (1) (2005) 64 http://www.sciencedirect.com/science/article/pii/S0375947404011340.

[2] B.V. Jacak, B. Muller, Science 337 (2012) 310 http://www.sciencemag.org/content/337/6092/310.full.html.

[3] B. Alver, et al., Physical Review C 83 (2011) 024913 http://journals.aps.org/prc/abstract/10.1103/PhysRevC.83.024913.

[4] A. Bialas, et al., Nuclear Physics B 111 (1976) 461 http://www.sciencedirect.com/science/article/pii/0550321376903291.

[5] F. Antinori, et al., Journal of Physics: Conference Series 5 (2005) 64 arXiv:hep-ex/0406004.

[6] S.V. Afanasiev, et al., Physical Review C 66 (2002) 054902 http://link.aps.org/doi/10.1103/PhysRevC.66.054902.

[7] S. Eremin, S. Voloshin, Physical Review C 67 (2003) 064905 http://link.aps.org/doi/10.1103/PhysRevC.67.064905.

[8] R. Nouicer, The European Physical Journal C 49 (1) (2007) 281 http://dx.doi.org/10.1140/epjc/s10052-006-0128-z.

[9] B. De, S. Bhattacharyya, Physical Review C 71 (2005) 024903 http://link.aps.org/doi/10.1103/PhysRevC.71.024903.

[10] S. Adler, et al., Physical Review C 89 (2014) 044905 http://link.aps.org/doi/10.1103/PhysRevC.89.044905.

[11] B. Alver, et al., Technical Report. arXiv:0805.4411 (May 2008).[12] Technical Report ATLAS-CONF-2013-096, CERN, Geneva (September 2013).[13] C. Adler, et al., Nuclear Instruments and Methods in Physics Research

Section A 470 (3) (2001) 488 http://www.sciencedirect.com/science/article/pii/S0168900201006271.

[14] S. Roesler, et al., arXiv:hep-ph/0012252.[15] N. Amelin, et al., Soviet Journal of Nuclear Physics 51 (1990) 1093.[16] N. Amelin, et al., Soviet Journal of Nuclear Physics 52 (1990) 172.[17] J. Chwastowski, M. Krasny, What can we gain by detecting nuclear fragments

in electron nucleus collisions at HERA? http://inspirehep.net/record/409130(1995).

[18] H. Appelshauser, et al., The European Physical Journal A Hadrons and Nuclei2 (4), http://dx.doi.org/10.1007/s100500050135.

[19] V. Aulchenko, et al., Nuclear Instruments and Methods in Physics ResearchSection A 379 (3) (1996) 360 http://www.sciencedirect.com/science/article/pii/0168900296006122.

[20] http://madx.web.cern.ch/madx/.[21] A. Capella, et al., Physical Report 236.[22] A. Kaidalov, Physics of Atomic Nuclei 66 (2003) 1994.[23] S. Adler, et al., Physical Review C 71 (2005) 034908 http://link.aps.org/doi/10.

1103/PhysRevC.71.034908.[24] D. Blaschke, et al., NICAWhite paper, http://theor.jinr.ru/twiki-cgi/view/NICA/

NICAWhitePaper.[25] M.L. Miller, et al., Annual Review of Nuclear and Particle Science 57 (2007) 205

arXiv:nucl-ex/0701025.[26] C. Royon, arXiv:1302.0623.[27] S. Adler, et al., Physical Review Letters 96 (2006) 032302 http://link.aps.org/

doi/10.1103/PhysRevLett.96.032302.

partN0 100 200 300

[mra

d]

0

0.2

0.4

0.6

0.8

1

Station 1Station 2Station 3Combined stations

Fig. 11. Spectator emission angle determination accuracy as a function of Npartfor each station and for the combination of all three stations.


http://www.sciencedirect.com/science/article/pii/S0375947404011340http://www.sciencedirect.com/science/article/pii/S0375947404011340http://www.sciencemag.org/content/337/6092/310.full.htmlhttp://www.sciencemag.org/content/337/6092/310.full.htmlhttp://journals.aps.org/prc/abstract/10.1103/PhysRevC.83.024913http://journals.aps.org/prc/abstract/10.1103/PhysRevC.83.024913http://www.sciencedirect.com/science/article/pii/0550321376903291http://www.sciencedirect.com/science/article/pii/0550321376903291http://arXiv:hep-ex/0406004http://arXiv:hep-ex/0406004http://link.aps.org/doi/10.1103/PhysRevC.66.054902http://link.aps.org/doi/10.1103/PhysRevC.66.054902http://link.aps.org/doi/10.1103/PhysRevC.67.064905http://link.aps.org/doi/10.1103/PhysRevC.67.064905http://dx.doi.org/10.1140/epjc/s10052-006-0128-zhttp://dx.doi.org/10.1140/epjc/s10052-006-0128-zhttp://link.aps.org/doi/10.1103/PhysRevC.71.024903http://link.aps.org/doi/10.1103/PhysRevC.71.024903http://link.aps.org/doi/10.1103/PhysRevC.89.044905http://link.aps.org/doi/10.1103/PhysRevC.89.044905http://arXiv:0805.4411http://www.sciencedirect.com/science/article/pii/S0168900201006271http://www.sciencedirect.com/science/article/pii/S0168900201006271http://arXiv:hep-ph/0012252http://refhub.elsevier.com/S0168-9002(14)01091-2/sbref15http://refhub.elsevier.com/S0168-9002(14)01091-2/sbref16http://inspirehep.net/record/409130http://dx.doi.org/10.1007/s100500050135http://www.sciencedirect.com/science/article/pii/0168900296006122http://www.sciencedirect.com/science/article/pii/0168900296006122http://madx.web.cern.ch/madx/http://refhub.elsevier.com/S0168-9002(14)01091-2/sbref22http://link.aps.org/doi/10.1103/PhysRevC.71.034908http://link.aps.org/doi/10.1103/PhysRevC.71.034908http://theor.jinr.ru/twiki-cgi/view/NICA/NICAWhitePaperhttp://theor.jinr.ru/twiki-cgi/view/NICA/NICAWhitePaperhttp://arXiv:nucl-ex/0701025http://arXiv:1302.0623http://link.aps.org/doi/10.1103/PhysRevLett.96.032302http://link.aps.org/doi/10.1103/PhysRevLett.96.032302

[28] A. Adare, et al., Physical Review C 85 (2012) 064914 http://link.aps.org/doi/10.1103/PhysRevC.85.064914.

[29] G. Aad, et al., Physics Letters B 707 (34) (2012) 330.[30] K. Aamodt, et al., Physical Review Letters 105 (2010) 252302 http://journals.

aps.org/prl/abstract/10.1103/PhysRevLett.105.252302.

[31] S. Chatrchyan, et al., Physical Review C 89 (2013) 044906 http://journals.aps.org/prc/abstract/10.1103/PhysRevC.89.044906.

[32] B. Abelev, et al., Physical Review Letters 111 (2013) 232302, http://link.aps.org/doi/10.1103/PhysRevLett.111.232302.


http://link.aps.org/doi/10.1103/PhysRevC.85.064914http://link.aps.org/doi/10.1103/PhysRevC.85.064914http://refhub.elsevier.com/S0168-9002(14)01091-2/sbref29http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.105.252302http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.105.252302http://journals.aps.org/prc/abstract/10.1103/PhysRevC.89.044906http://journals.aps.org/prc/abstract/10.1103/PhysRevC.89.044906http://link.aps.org/doi/10.1103/PhysRevLett.111.232302http://link.aps.org/doi/10.1103/PhysRevLett.111.232302

A centrality detector conceptIntroductionModeling the collider structureGenerators of the spectator fragmentsDetector performanceCollider effectsCollision effectsSpectator deflection in the detector stations

ResultsEfficiency and resolution of centrality determinationPossible choices of the detector technologyMeasurement of the event plane orientation

ConclusionsAcknowledgementsReferences

Documents

A centrality detector concept