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ATLAS NOTEATLAS-CONF-2013-096

September 11, 2013

Measurement of the centrality dependence of the charged particlepseudorapidity distribution in proton-lead collisions

at √sNN = 5.02 TeV with the ATLAS detector

The ATLAS Collaboration

Abstract

The ATLAS experiment at the LHC has measured the centrality dependence of chargedparticle pseudorapidity distributions, dNch/dη, in p+Pb collisions at a nucleon-nucleoncentre-of-mass energy of

√sNN = 5.02 TeV. Charged particles were reconstructed over

|η| < 2.7 using the ATLAS pixel detector. The proton-lead collision centrality was character-ized by the total transverse energy measured over the pseudorapidity interval 3.2 < η < 4.9in the direction of the lead beam. The dNch/dη distributions are found to vary strongly withcentrality, with an increasing asymmetry between the proton-going and Pb-going directionsas the collisions become more central. Three different calculations of the number of partic-ipants, Npart, have been carried out using a standard Glauber model as well as two Glauber-Gribov extensions. Charged particle multiplicities per participant pair, dNch/dη/(〈Npart〉/2),are found to vary differently with Npart for these three models, pointing to the importanceof the fluctuating nature of nucleon-nucleon collisions in the modeling of the initial state ofp+Pb collisions.

c© Copyright 2013 CERN for the benefit of the ATLAS Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-3.0 license.

1 Introduction

Proton or deuteron-nucleus (p/d+A) collisions at the LHC and RHIC provide an opportunity to study thephysics of the initial state of ultra-relativistic heavy ion (A+A) collisions without the obscuring effectsof thermalization and collective evolution thought to play an important role [1] in A+A collisions. Inparticular, p/d+A measurements can shed insight on the effect of an extended nuclear target on thedynamics of soft and hard scattering processes and subsequent particle production. Charged particlemultiplicity and pseudorapidity distributions are among the most basic experimental probes of particleproduction. Historically, measurements of charged particle pseudorapidity distributions have providedimportant insight on soft particle production dynamics in p+A collisions both at fixed target [2, 3, 4, 5]and at collider [6, 7] energies and have provided essential tests of models for inclusive soft hadronproduction.

More detailed insight can be provided by measurements of the charged particle multiplicities as afunction of “centrality”, an experimental quantity that provides an indirect constraint on the p/d+A col-lision geometry. Previous measurements at fixed-target energies have relied on the number of “grey”or “knocked-out” protons [8]. Measurements in d+Au collisions at RHIC have relied on experimentalmeasures of particle multiplicity at large pseudorapidity, either symmetric around mid-rapidity [9] orin the gold fragmentation direction [10]. These measurements have shown that the rapidity-integratedparticle multiplicity in d+Au collisions scales with the number of inelastically interacting, or “partici-pating”, nucleons, Npart. This scaling behaviour has been interpreted as the result of coherent multiplesoft interactions of the projectile nucleon in the target nucleus, and is known as the wounded-nucleonmodel [11]. Previous measurements of the centrality dependence of charged hadron pseudorapidity dis-tributions (dNch/dη) in p/d+A collisions [12, 6] show little growth or even a reduction in yield of veryforward particles and a strong increase in the yield of backward particles with increasing Npart. Here“forward” (backward) refers to particles with pseudorapidities closer to the proton (nucleus) rapiditythan the nucleus (proton) rapidity. This centrality dependence has been explained using well-knownphenomenology of soft hadron production [13].

There exist alternative descriptions of the centrality dependence of d+Au results at RHIC [14, 15] andthe inclusive p+Pb measurement at the LHC ([15, 16] and references therein) based on parton saturationmodels. A measurement of the centrality dependence of dNch/dη distributions will provide an essentialtest of such models of soft hadron production at the LHC. Such tests have become more urgent given theobservation of two-particle [17, 18, 19, 20] and multi-particle [21, 20] correlations in the final state ofp+Pb collisions at the LHC. These correlations are currently interpreted as resulting from either initial-state saturation effects [22, 23, 15] or from collective dynamics of the final state [24, 25, 26, 27, 28]. Foreither interpretation, information on the centrality dependence of dNch/dη can provide important inputfor determining the mechanism responsible for these structures.

The LHC provided its first proton-nucleus collisions in a short p+Pb pilot run at√

sNN= 5.02 TeVin September 2012. Over the several-hour run ATLAS collected an event sample corresponding to anestimated integrated luminosity of approximately 1 µb−1. This note presents the measurement of thecentrality dependence of dNch/dη over −2.7 < η < 2.7 in p+Pb collisions at

√sNN = 5.02 TeV, obtained

from the data collected during the pilot run. Charged particles were detected in the ATLAS pixel detectorand were reconstructed using a two-point tracklet algorithm similar to that used for the Pb+Pb multiplic-ity measurement [29]. Results are presented for several intervals in collision centrality characterised bythe total transverse energy measured in the section of ATLAS forward calorimeter spanning the pseudo-rapidity interval 3.2 < η < 4.9. A standard Glauber model [30] and its Glauber-Gribov extension [31, 32]are used to estimate 〈Npart〉 for each centrality interval, allowing a measurement of the Npart dependenceof the charged particle multiplicity.

1

2 Experimental setup

During the pilot run the LHC was configured with a 4 TeV proton beam and a 1.57 TeV per-nucleonPb beam that together produced collisions with a nucleon–nucleon centre-of-mass energy of

√sNN =

5.02 TeV, with a longitudinal boost corresponding to a rapidity shift of −0.465 relative to the ATLASlaboratory frame 1. In this configuration, the proton had negative rapidity and the lead nucleus hadpositive rapidity. For the remainder of this note the terms Pb-going and proton-going will be used torefer to positive and negative pseudorapidities, respectively.

The analysis presented in this note was performed using the ATLAS inner detector (ID), calorime-ters, minimum-bias trigger scintillators (MBTS), and the trigger and data acquisition systems [33]. Forthe nominal collision vertex position, the ATLAS inner detector measures charged particles within thepseudorapidity range |η| < 2.5 using a combination of silicon pixel detectors, silicon microstrip detectors(SCT), and a straw-tube transition-radiation tracker (TRT), all immersed in a 2 T axial magnetic field. Inorder to measure charged particles down to pT ∼ 100 MeV with good efficiency, and thus permit a moreprecise extrapolation over the full pT range, the charged particle pseudorapidity density measurementwas performed using only the pixel detector [34]. The pixel detector is divided into “barrel” and “end-cap” sections. The barrel section consists of three layers of staves, inclined at an angle of 20◦, at radiiof 50.5, 88.5, and 122.5 mm from the nominal beam axis, and extending ±400.5 mm from the nominalcentre of the detector in the z direction. The endcap consists of three disks placed symmetrically on eachside of the interaction region at z locations of ±493, ±578 and ±648 mm from the nominal centre of thedetector region. The typical pixel size is 50 µm × 400 µm in the φ − z plane. For events with zvtx = 0, thebarrel section of pixel detector measures charged particles up to |η| < 2.2. The endcap sections extendthe detector coverage, spanning the pseudorapidity interval 1.6 < |η| < 2.7.

The ATLAS forward calorimeter (FCal) consists of two sections, labeled A and C, that cover 3.2 <|η| < 4.9. The FCal modules are composed of tungsten and copper absorbers with liquid argon as theactive medium, which together provide 10 interaction lengths of material. The MBTS is sensitive tocharged particles in the range 2.1 < |η| < 3.9 using two hodoscopes, each of which is subdivided into16 counters positioned at z = ±3.6 m. Minimum-bias p+Pb collisions were selected by a trigger thatrequired a signal in at least two MBTS counters.

3 Event selection

In the offline analysis, charged particle tracks and collision vertices were reconstructed from clusters inthe pixel detector and the SCT using an algorithm optimized for p+p minimum-bias measurements [35].Separately, “pixel tracks” were reconstructed using only pixel clusters. The p+Pb events selected for thisanalysis were required to have a collision vertex satisfying |zvtx| < 175 mm, at least one hit in each sideof the MBTS, and a difference between the times measured in the two MBTS hodoscopes of less than10 ns. Events containing multiple p+Pb collisions (pileup) were suppressed by rejecting events with tworeconstructed vertices that are separated in z by more than 15 mm. The residual pileup fraction has beenestimated to be 10−4 [21].

The p+Pb inelastic cross-section has significant contributions from diffractive and electromagneticprocesses. The lead nucleus can excite the proton via incoherent diffractive, coherent diffractive, andelectromagnetic processes, and the proton can quasi-diffractively excite nucleons in the nucleus. The

1 The ATLAS reference system is a Cartesian right-handed coordinate system, with the nominal collision point at the origin.The anti-clockwise beam direction defines the positive z-axis, while the positive x-axis is defined as pointing from the collisionpoint to the centre of the LHC ring and the positive y-axis points upwards. The azimuthal angle φ is measured around the beamaxis, and the polar angle θ is measured with respect to the z-axis. Pseudorapidity is defined as η = − ln (tan(θ/2)). All pseu-dorapidity values quoted in this latter are defined in laboratory coordinates. Rapidity is defined y = 0.5 ln

[(E + pz)/(E − pz)

],

where E is the energy and pz is the longitudinal momentum.

2

different contributions to the excitation of the proton cannot be easily distinguished without large-acceptance forward detectors, including the zero degree calorimeters, which were not operational duringthe pilot run. To remove potentially significant contributions from electromagnetic processes, a rapiditygap analysis similar to that applied in a measurement of diffraction in 7 TeV proton-proton collisions [36]was applied to the p+Pb data. The full pseudorapidity coverage of the detector, −4.9 < η < 4.9, was di-vided into ∆η = 0.2 intervals, and each interval containing one or more reconstructed tracks or calorime-ter clusters with pT > 200 MeV was considered as occupied. Then the edge-gaps on each side of thedetector were calculated as the distance in pseudorapidity between the detector edge (-4.9 or 4.9) and thenearest occupied interval. Events with large edge-gaps on the Pb-going side of the detector, ∆ηPbgap & 2,typically result from electromagnetic or diffractive excitation of the proton. These two contributionscannot be easily distinguished, and both of them have no significant signal in Pb-going FCal, so theywere both excluded from this analysis. No requirement was imposed on gaps on the proton-going side.The gap requirement removed a fraction, fgap = 6%, of the events passing the vertex and MBTS cuts andyielded a total of 2131219 events for use in this analysis.

4 Monte Carlo data sets

The response of the ATLAS detector and the performance of reconstruction algorithms were evaluatedusing 1 million minimum-bias 5.02 TeV Monte Carlo p+Pb events produced by version 1.38b of theHIJING event generator [37] with diffractive processes disabled, and fully simulated using GEANT4 [38,39]. The momentum four-vector of each generated particle was longitudinally boosted by a rapidity of-0.465 to match the LHC p+Pb beam conditions. The simulated Monte Carlo events were then digitizedusing data conditions appropriate to the pilot p+Pb run and fully reconstructed using the same algorithmsthat were applied to the experimental data. Separate PYTHIA6 [40] and PYTHIA8 p+p samples weregenerated at

√s = 5.02 TeV with particle kinematics boosted to match the p+Pb beam conditions.

Separate samples of 5.02 TeV minimum-bias, single diffractive, and non-diffractive p+p collisions with1 million events each were produced using PYTHIA6 (version 6.425, AMBT2 tune [41], CTEQ6L1PDFs) and PYTHIA8 (version 8.150, 4C tune [42], MSTW2008LO PDFs) and fully simulated in thesame manner as the p+Pb events.

5 Centrality selection

For Pb+Pb collisions, ATLAS uses the total transverse energy, ∑ ET , measured in the two forwardcalorimeter sections to characterize the collision centrality [43]. However, the intrinsic asymmetry ofp+Pb collisions and the rapidity shift of the centre-of-mass causes a different response of the two sidesof the ATLAS calorimeter to soft particle production. For p+Pb collisions included in this analysis,Fig. 1 shows the correlation between the summed transverse energies measured in the proton-going(−4.9 < η < −3.2) and Pb-going (3.2 < η < 4.9) directions, ΣEpT and ΣE

PbT , respectively. The trans-

verse energies shown in the figure and used in this analysis were evaluated at the electromagnetic energyscale and have not been corrected for hadronic response. Figure 1 shows that ΣEpT rapidly saturates withincreasing ΣEPbT for ΣE

PbT & 30 GeV, indicating that ΣE

pT is less sensitive than ΣE

PbT to the increased par-

ticle production expected to be associated with multiple interactions of the proton in the target nucleus incentral collisions. Thus, ΣEPbT is used to characterize p+Pb collision centrality for the analysis presentedhere.

The distribution of ΣEPbT for events passing the applied p+Pb analysis selections is shown in Fig. 2.Following standard techniques [29], centrality intervals were defined in terms of percentiles of the ΣEPbTdistribution after accounting for an estimated inefficiency (see Appendix A) for inelastic p+Pb events to

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[GeV]PbTEΣ0 50 100 150 200

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Figure 1: Distribution of proton-going (ΣEpT) versus Pb-going (ΣEPbT ) forward calorimeter total trans-

verse energy (see text) for p+Pb collisions included in this analysis.

pass the applied event selections of 1 − εinel = 2 ± 2%. The following centrality intervals were used inthis analysis: 0–1%, 1–5%, 5–10%, 10–20%, 20–30%, 30–40%, 40–60%, 60–90%. The ΣEPbT rangescorresponding to these centrality intervals are indicated by the alternating filled and unfilled regions inFig. 2. The most peripheral 90–100% collisions were excluded from the analysis due to uncertainties

[GeV]PbTEΣ0 100 200

]-1

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eVP

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Figure 2: Distribution of ΣEPbT values for events satisfying all analysis cuts including the Pb-goingrapidity gap exclusion (see text). The alternating shaded and unshaded bands indicate centrality intervals,from right to left, 0–1%, 1–5%, 5–10%, 10–20%, 20–30%, 30–40%, 40–60%, 60–90% and 90–100%(not used in this analysis).

regarding their composition and their reconstruction efficiency.Following standard procedures, a Glauber analysis [30] was applied to estimate 〈Npart〉 for each of

the centrality intervals used in this analysis. A detailed description of that analysis, which uses theconvolution properties of gamma distributions to describe the measured ΣEPbT distribution, is provided inAppendix A. Only a summary of the method is given here.

A Glauber Monte Carlo program [44] was used to simulate the geometry of inelastic p+Pb collisions

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and calculate the probability distribution for Npart, P(Npart). The simulations used a Woods-Saxon nu-clear density distribution and an inelastic nucleon-nucleon cross-section of σNN = 70±5 mb. Separately,PYTHIA8 simulations of p+p events were used to obtain a detector-level nucleon-nucleon ΣEPbT distri-bution, to be used as input to the Glauber model. This was fit to a gamma distribution. Then, an extensionof the wounded-nucleon (WN) model that included non-linear dependence of ΣEPbT on Npart was used todefine Npart-dependent gamma distributions for ΣEPbT , with the constraint that the distributions reduceto the PYTHIA8 distribution for Npart = 2. The gamma distributions were summed over Npart with aP(Npart) weighting to produce a hypothetical ΣEPbT distribution. That distribution was fit to the measuredΣEPbT distribution shown in Fig. 2 with the parameters of the extended WN model allowed to vary freely.From the results of the fit, the distribution of Npart values and the corresponding 〈Npart〉, were calculatedfor each centrality interval.

In addition to the usual Glauber Monte Carlo simulation, an extension of the Glauber model was alsoused to calculate P(Npart). This takes into account event-to-event fluctuations in the nucleon-nucleoncross-section, σNN, [31, 32], and is referred to in the rest of this note as “Glauber-Gribov.” Two sets ofGlauber-Gribov Npart results were obtained for two different values of the parameter, Ω, that determinesthe width of the assumed Gaussian fluctuations in σNN. For the purposes of this analysis, both valuesΩ = 0.55 and Ω = 1.01 are considered plausible and results from both parameters are studied to evaluatethe potential physics implications of the Glauber-Gribov extension.

The 〈Npart〉 values calculated using the above-described procedure are shown in Fig. 3 for the threedifferent P(Npart) simulations. The error bars in the figure show asymmetric systematic uncertaintiesdetermined by varying different assumptions of the Glauber/Glauber-Gribov modeling including σNN,εinel, the form of the WN extension, and the properties of the nuclear density distribution. For centralcollisions, the 〈Npart〉 uncertainties are dominated by the uncertainty in the WN model extension andσNN. For more peripheral collisions the uncertainty on εinel also makes a significant contribution.

The differences in the 〈Npart〉 values between the Glauber and the two Glauber-Gribov models resultsfrom the different shapes of the p+Pb Npart distributions in these models. The narrower Npart distributionin the Glauber model requires larger fluctuations in ΣEPbT at fixed Npart to describe the tail of the ΣE

PbT

distribution. In contrast, the broader Npart distributions associated with the Glauber-Gribov models re-quire smaller intrinsic fluctuations in ΣEPbT at fixed Npart. As a result, the 〈Npart〉 corresponding to eventswith large ΣEPbT is systematically larger for the Glauber-Gribov models and is largest for Ω = 1.01.

6 Measurement of charged particle multiplicity

As described previously, the multiplicity measurement was performed using only the pixel detector tomaximize the efficiency for reconstructing charged particles with low transverse momenta. Two ap-proaches are used in this analysis. The first is the two-point tracklet method used widely in heavy ioncollision experiments [29, 45, 46]. Two variants of this method have been implemented in this analysis toproduce the dNch/dη result and to estimate the systematic uncertainties, as described below. The secondis the use of pixel tracks, described in Section 3. It has a smaller acceptance, but provides measurementsof the particle pT. The dNch/dη measured using pixel tracks is used as a cross-check to that measuredusing the two-point tracklets.

In the two-point tracklet algorithm, the event vertex and clusters on an inner pixel layer define asearch region for clusters in the outer layers. The algorithm uses all clusters, except for those which1) have low energy deposits inconsistent with minimum-ionizing particles originating from the primaryvertex, 2) are duplicate clusters resulting from the overlap of the pixel modules or 3) include a small setof pixels at the centre of the pixel modules that share readout channels [34]. Clusters in the same layerof the pixel detector were considered as one if they were separated by less than a certain distance. Suchclusters have a high probability to be correlated to the same particle.

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centrality

60-90%40-60%

30-40%20-30%

10-20% 5-10%

1-5% 0-1%

0-90%

〉 pa

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Glauber = 0.55ΩGlauber-Gribov = 1.01ΩGlauber-Gribov

Figure 3: 〈Npart〉 values resulting from fits to the measured ΣEPbT distribution (see Fig. 2) using Glauberand Glauber-Gribov Npart distributions. The error bars indicate asymmetric systematic uncertainties (seeAppendix A).

The pseudorapidity and azimuthal angle of the cluster in the innermost layer (η, φ) and the differencebetween those parameters for the cluster in two layers (∆η,∆φ) are taken as the parameters of the re-constructed tracklet. The ∆η of a tracklet is largely determined by the multiple scattering of the incidentparticles in the material of the beam pipe and detector. This effect plays a less significant role in the ∆φof a tracklet, which is driven primarily by the bending of charged particles in the magnetic field, andhence one expects ∆φ to be larger. The tracklet selection cuts are:

|∆η| < 0.015, |∆φ| < 0.1,|∆η| < |∆φ|. (1)

Keeping tracklets with |∆φ| < 0.1 corresponds to accepting particles with pT & 100 MeV. The depen-dence of the multiple scattering on particle momentum suggests the requirement on the relation between∆η and ∆φ of the tracklet given in the second row of Eq. 1.

The Monte Carlo (MC) simulation for the dNch/dη analysis is based on the HIJING event generator,which is described in Section 4. Generator (truth) level particles are defined as primary particles if theyoriginate directly from the collision or result from decays of particles with cτ < 1 mm. All other particlesare defined as secondaries. Tracklets are classified as primary or secondary depending on whether the as-sociated truth particle is primary or secondary. Tracklets can also be formed from the random associationof hits produced by unrelated particles, or hits in the detector which are not associated to any generatedparticle. These tracklets are referred to as “fakes”.

The contribution of fake tracklets is relatively difficult to model in the simulation, because of the apriori unknown contributions of multiple sources, such as noise clusters or very low energy particles.To address this problem, the tracklet algorithm is used in two different implementations referred to as“Method 1” and “Method 2”. In Method 1, at most one tracklet is reconstructed for a given cluster on thefirst pixel layer. If multiple clusters on the second pixel layer fall within the search region, the resultingtracklets are merged into a single tracklet. This approach limits, but does not eliminate, the presence offake tracklets. Method 2 reconstructs tracklets for all combinations of clusters in only two pixel layers.To account for the fake tracklets arising from random combinations of clusters, the same analysis isperformed after inverting the x and y positions of all clusters on the second layer with respect to the

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primary vertex (x − xvtx, y − yvtx) → (−(x − xvtx),−(y − yvtx)). The tracklet yield from this “flipped”analysis is then subtracted from the original tracklet yield to obtain an estimated yield of true trackletsN2p,

N2p(η) = Nev2p(η) − Nfl2p(η), (2)

where Nev2p represents the yield of two-point tracklets using Method 2 and Nfl2p represents the yield ob-

tained by flipping the clusters in the second pixel layer.Distributions of ∆η and ∆φ of reconstructed tracklets for data and simulated events are shown in

Fig. 4 for the barrel (upper) and endcap (lower) parts of the pixel detector. The data is indicated by

η∆-0.01 0 0.01

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cmy

Figure 4: ∆η (left) and ∆φ (right) for the tracklets reconstructed with Method 1 measured in the data(circles) and MC (histograms) in p+Pb collisions at

√sNN = 5.02 TeV. The lowest (green) histogram

are the fake tracklets, the middle region (cyan) are secondary particles, and the upper (yellow) region isthe contribution of the primary particles.

black circles and simulated events are shown with filled histograms. The simulation results show thethree contributions from primary (yellow), secondary (cyan) and fake (green) tracklets. The selectioncriteria specified by Eq. 1 are shown in Fig. 4 with vertical lines and applied in ∆φ for ∆η plots and viceversa. Outside those lines, the contributions of secondary and fake tracklets are more difficult to control,especially in the endcap region.

The left panel of Fig. 5 shows the distributions of the number of tracklets reconstructed with Method 2and satisfying the criteria of Eq. 1 as a function of pseudorapidity in the 0-10% centrality interval for data(markers) and for the MC (lines). The results of flipped reconstruction are also shown in the plot. Dataand MC distributions are similar but not identical, reflecting the fact that HIJING does not reproduce

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flipped

Figure 5: η-distribution of number of tracklets reconstructed with Method 2. Left panel shows compar-ison of the data (markers) to MC (lines). The results of the flipped reconstruction are shown with openmarkers for data and dashed line for MC. Right panel shows the result of MC for three contributions: pri-mary (yellow) secondary (cyan) and fake (green). Square markers show the result of simulation obtainedwith flipped reconstruction events.

the data in detail. A breakdown of the MC distribution into primary, secondary and fake contributionsis shown in the right panel of Fig. 5. The distribution of Nfl2p(η) given in eq. 2 and plotted with openmarkers follows exactly the green histogram, which justifies the subtraction of the fake component inMethod 2. Of the three methods used in this analysis, Method 2 has the largest contribution of fakes. Inthe 0-10% centrality interval, the fake contribution amounts to 8% of the yield at mid-rapidity and up to16% at large pseudorapidity. In the same centrality interval, the contribution of fakes in Method 1 variesfrom 2% to 10% and from 0.2% to 1.5% in the pixel track method. Method 1 and the pixel track methodrely on the MC to correct for the contribution from fakes and all three methods rely on the MC to correctfor the contribution of secondary particles.

The data analysis and corresponding corrections were performed in 8 intervals of detector occupancy(O) parametrized using the number of reconstructed clusters in the first pixel layer, and in 7 intervals ofzvtx, each 50 mm wide. For each analysis method, a multiplicative correction factor was obtained fromthe MC simulations. It corrected for several effects: inactive areas in the detector and reconstructionefficiency; contributions of residual fakes and secondary particles; and losses due to track or trackletsselection cuts including particles with pT below 100 MeV. The correction factor is evaluated as a functionof occupancy O, event vertex zvtx, and pseudorapidity as:

C(O, zvtx, η) ≡Npr(O, zvtx, η)Nrec(O, zvtx, η)

, (3)

where Npr and Nrec represent the number particles at the generator level and the number of tracks ortracklets at the reconstruction level respectively. These factors are then applied to obtain the corrected,per-event charged particle pseudorapidity distributions according to

dNchdη

=1

Nevt

∑zvtx

∆Nraw(O, zvtx, η)C(O, zvtx, η)∆η

, (4)

where ∆Nraw indicates either the number of reconstructed pixel tracks or two-point tracklets and Nevt isthe total number of analysed events.

Figure 6 shows the effect of the applied correction for all three methods. The left panel shows the

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Method 1 rawMethod 2 rawpixel tracks method rawMethod 1 correctedMethod 2 correctedpixel tracks method corrected

Figure 6: Left: η-distribution from the MC for the generated primary charged particles (histogram),tracklets from Method 1 (circles), tracklets from Method 2 after flipped event subtraction (squares), andpixel tracks (diamonds). Right: Open markers represent the same distributions as in the left panel,reconstructed in the data. Filled markers of the same shape represent corrected distributions.

MC results based on HIJING. The distribution of generated primary charged particles is shown by asolid line and the distributions of reconstructed tracks and tracklets are indicated by markers. Amongthe three methods, the correction factors for Method 1 are the smallest, while the pixel track methodrequires the largest corrections. The variation of the reconstructed distribution for the pixel track methodaround η = ±2 is related to the transition between the barrel and endcap regions of the detector. Theopen markers in the right panel of Fig. 6 show the reconstructed distribution from the data and thefilled markers are the corresponding distribution for the three methods after applying corrections. Thecorrected results are in good agreement with each other, which demonstrates that the rejection of fakesand the rest of the correction procedure are well understood. In this analysis Method 1 is chosen as thedefault result for dNch/dη, Method 2 is used for systematic uncertainties and the pixel track method isused primarily as a consistency test, as discussed in detail below.

7 Systematic uncertainties

The systematic uncertainties on dNch/dη measurement arise from three main sources: 1) inaccuracies ofdetector description in simulations, 2) sensitivity to selection criteria used in the analysis, including theresidual contributions of fakes and secondaries and 3) differences between the generated particles usedin the simulation and the data. To extract uncertainties for each source, one of the parameters used inthe analysis, such as tracklets selection criteria, simulated particle composition, etc. was altered withinacceptable limits. The analysis was performed fully for each variation of the parameters and comparedto the standard results of Method 1.

The uncertainty on the detector description arises primarily from the details of the pixel detectoracceptance and efficiency. The locations of the inactive pixel modules were precisely matched betweenthe data and simulation. Areas smaller than a single module which were found to have intermittentinefficiencies were estimated to contribute less than 1.7% uncertainty to the final result. This uncertaintyhas no centrality dependence, and is approximately independent of pseudorapidity.

The uncertainties related to the description of the inactive detector material were evaluated using aMC sample with 10% extra material. The net effect on the final result is found to be 2%, independent ofcentrality.

9

Uncertainties due to tracklet selection cuts were evaluated by independently varying the cuts on |∆η|and |∆φ| up and down by 40%. The effect of these variations is less than 1%, except at high-η, and hasonly a weak centrality dependence.

The HIJING event generator used in the analysis is known to be inconsistent with the pT distributionsmeasured in data. This was addressed by re-weighting the HIJING distribution using the reconstructedspectrum measured with the pixel track method. Since a full spectral analysis was not performed in theframework of this dNch/dη measurement, the systematic uncertainty on this procedure was assigned tobe equal to the magnitude of the variation produced by the re-weighting procedure. This is less than 0.5%for |η| < 1.5 and grows to 3.0% towards the edges of the η acceptance. The uncertainty has a centralitydependence because the pT distributions in central and peripheral collisions are different.

Tracklets are reconstructed in Method 1 for particles with pT > 100 MeV. The unmeasured region ofthe spectrum contributes approximately 6% to the final dNch/dη. The systematic uncertainty on the ex-trapolation to pT=0 is partially included in the variation of the tracklet ∆φ selection criteria. In addition,this uncertainty was evaluated by varying the shape of the spectra below 100 MeV. This uncertainty wasconservatively estimated to reach up to 2.5% at high η and has a weak centrality dependence.

To test the sensitivity to the particle composition in HIJING, the fraction of pions, kaons and protonsin HIJING were varied within a range according to the differences between p+p and Pb+Pb measuredby the CMS and ALICE experiments [47, 48]. The resulting changes of dNch/dη are found to be lessthan 1% for all centrality intervals.

The three methods have quite different sensitivities to fake tracks and tracklets. While all three meth-ods agree with each other very well, Method 1 and Method 2 require corrections of a similar magnitudewhile the pixel track method requires significantly larger correction. The uncertainties due to the pres-ence of residual fakes are estimated by comparing the results between the two tracklet methods. Thedifference in the most central collisions is found to be less than 1.5% in the barrel region and increasesto about 2.5% at the far edges of the measured pseudorapidity range.

The uncertainty related to the event selection procedure described in Section 5 is evaluated by varyingthe ΣEPbT ranges used to define centrality intervals, according to an overall trigger and event selectionefficiency of 98 ± 2%. The variation is performed by generating new centrality intervals assuming thisefficiency is 96% and 100%. This resulting change of the dNch/dη is less than 0.5% in central collisionsand increase to 6% in peripheral collisions.

The systematic uncertainties are summarized in Table 1. All uncertainties are treated as independent,so the resulting total systematic uncertainty is a quadratic sum of the individual contributions.

Uncertainty 60-90% Uncertainty 0-1%Source barrel endcap barrel endcupMC detector description 1.7% 1.7%Extra material 1% 2% 1% 2%Tracklet selection 0.5% 1.5% 0.5% 1.5%pT re-weighting 0.5% 0.5% 0.5% 3.0%Extrapolation to pT=0 1% 2.5% 1% 2%Particle composition 1% 1%Analysis method 1.5% 2.0% 1.5% 2.5%Event selection 5.0% 6.0% 0.5% 0.5%

Table 1: Summary of the various sources of systematic uncertainties and their estimated impact on thedNch/dη measurement in central (0-1%) and peripheral (60-90%) p+Pb collisions.

10

8 Results

Figure 7 presents the charged particle pseudorapidity density for p+Pb collisions at√

sNN = 5.02 TeVin the pseudorapidity interval |η| < 2.7 for eight centrality intervals. In the most peripheral collisions

η-3 -2 -1 0 1 2 3

η/d

chdN

0

10

20

30

40

50

60

70ATLAS Preliminary

-1bµ= 1 int

p+Pb L = 5.02 TeVNNs

= -0.465cm

y

0-1%

1-5%

5-10%

10-20%

20-30%

30-40%

40-60%

60-90%

Figure 7: dNch/dηmeasured in different centrality intervals. Statistical uncertainties, shown with verticalbars are typically smaller than the marker size, colour band shows the systematic uncertainty of theresults.

(centrality interval 60-90%) dNch/dη has what appears to be a double-peak structure, similar to that seenin proton-proton collisions [35, 49]. In more central collisions, the shape of dNch/dη becomes progres-sively more asymmetric, with more particles produced in the Pb-going direction than in the proton-goingdirection.

To investigate further the centrality evolution, the distributions in the various centrality intervals aredivided by the distribution in the 60-90% centrality interval. The ratios are shown in Fig. 8. The doublepeak structure seen in the distributions in Fig. 7 disappears in the ratios. The ratios are observed to grownearly linearly with pseudorapidity, with a slope that increases from peripheral to central collisions. In the0-1% centrality interval, the ratio increases by almost a factor of two over the measured η-range. Theseratios are fit with a second-order polynomial function, and the fit results are summarized in Table 2.

Figure 9 shows the dNch/dη divided by the number of participant pairs (〈Npart〉/2) as a functionof 〈Npart〉 for three different implementations of the Glauber model; standard Glauber (top panel) andGlauber-Gribov model with Ω = 0.55 and 1.01 in the middle and lower panels respectively. Since thecharged particle yields have significant pseudorapidity dependence, the dNch/dη/(〈Npart〉/2) is presentedin five η intervals including the full pseudorapidity interval, −2.7 < η < 2.7.

The dNch/dη/(〈Npart〉/2) values from the standard Glauber model are approximately constant up to〈Npart〉 ≈ 10 and then increase for larger 〈Npart〉. This trend is absent in the Glauber-Gribov model withΩ = 0.55, which shows a relatively constant behaviour for the integrated yield divided by the number ofparticipant pairs. Finally, the dNch/dη/(〈Npart〉/2) values from the Glauber-Gribov model with Ω = 1.01

11

η-3 -2 -1 0 1 2 3

)60

-90%

|η/d

ch)

/ (dN

cent

.|η

/dch

(dN

0

1

2

3

4

5

6

7

8

9 ATLAS Preliminary-1bµ= 1

intp+Pb L

= 5.02 TeVNNs

= -0.465cm

y

0-1%

1-5%

5-10%

10-20%

20-30%

30-40%

40-60%

Figure 8: Ratios of dNch/dη distributions measured in different centrality intervals, dNch/dη|cent, to thatin the peripheral (60-90%) centrality interval. Lines show the results of second order polynomial fits tothe data points.

Centrality ratio c b a0 - 1% / 60 - 90% 6.78±0.28 0.77±0.05 -0.033±0.0061 - 5% / 60 - 90% 5.35±0.22 0.515±0.031 -0.030±0.005

5 - 10% / 60 - 90% 4.49±0.18 0.377±0.021 -0.0218±0.003510 - 20% / 60 - 90% 3.77±0.14 0.269±0.014 -0.0169±0.002520 - 30% / 60 - 90% 3.11±0.11 0.182±0.010 -0.0113±0.002030 - 40% / 60 - 90% 2.61±0.08 0.122±0.006 -0.0076±0.001640 - 60% / 60 - 90% 1.95±0.06 0.0595±0.0031 -0.0037±0.0011

Table 2: Parameters of second order polynomial fits (c+bη+aη2) to dNch/dη ratios shown in Fig. 8. Thestated uncertainties combined statistical and systematic contributions, with the latter making the largercontribution.

show a slight decrease with 〈Npart〉 in all η intervals.The presence or absence of 〈Npart〉 scaling does not in itself suggest a preference for one or another of

the implementations of the Glauber model. However, this study emphasizes that considering fluctuationsof the nucleon-nucleon cross section in the Glauber-Gribov model may lead to significant changes in theNpart scaling behaviour of the p+Pb dNch/dη data and, thus, their possible interpretations.

12

0 10 20 30

/2)

〉 pa

rtN〈

/ (

η/d

chdN

2

4

6

8 Preliminary ATLAS-1bµ = 1

intp+Pb L

= 5.02 TeVNNs = -0.465

cmy

< 2.7η-2.7 <

< 2.7η 2 < < 1η 0 < < 0η -1 < < -2η-2.7 < Glauber

0 10 20 30

2

4

6

8

=0.55ΩGlauber-Gribov

〉 part

N〈0 10 20 30

2

4

6

8

0

=1.01ΩGlauber-Gribov

Figure 9: dNch/dη/(〈Npart〉/2) as a function of 〈Npart〉 in several η-regions for the three implementationsof the Glauber model: the standard Glauber model (top panel), the Glauber-Gribov model with Ω=0.55(middle panel) and the Glauber-Gribov model with Ω=1.01 (bottom panel). The open boxes representthe systematic uncertainty of the dNch/dη measurement only, and the width of the box is chosen forbetter visibility (they are not shown for −1.0 < η < 0 and 0 < η < 1). The shaded boxes representthe total uncertainty, which is dominated by the uncertainty on the 〈Npart〉 given in Table 4 and Fig. 3.They are shown for −2.7 < η < 2.7. Note that this uncertainty is asymmetric in both directions, due tothe asymmetric nature of the uncertainties on 〈Npart〉. The statistical uncertainties are smaller than themarker size for all points.

9 Conclusions

This note presents ATLAS measurements of the centrality dependence of the charged particle pseu-dorapidity distribution, dNch/dη, in p+Pb collisions at a nucleon-nucleon centre-of-mass energy of√

sNN = 5.02 TeV. The results are shown as a function of pseudorapidity over the range −2.7 < η < 2.7and for the 90% most central p+Pb collisions. The analysis was performed primarily with the ATLASpixel detector, and the collision centrality was defined using a forward calorimeter covering 3.2 < η < 4.9in the Pb-going direction. The average number of participants in each centrality interval, 〈Npart〉, was es-timated using a Monte Carlo Glauber model. The Glauber modeling was performed both in the standardway, with a fixed nucleon-nucleon cross section, as well as in a Glauber-Gribov approach, which allows

13

the nucleon-nucleon cross section to fluctuate event-by-event.The shape of dNch/dη evolves gradually with centrality from an approximately symmetric shape in

the most peripheral collisions to a highly asymmetric distribution in the most central collisions. Theratios of dNch/dη distributions in different centrality intervals to the dNch/dη in the most peripheralinterval are approximately linear in η with a slope that is strongly dependent on centrality.

The Npart dependence of dNch/dη/(〈Npart〉/2) was found to be sensitive to the Glauber modeling,especially in the most central collisions: while the standard Glauber modeling leads to a strong increasein the multiplicity per participant pair for the 30% most central collisions, the Glauber-Gribov approachleads to a much milder centrality dependence. These results point to the importance of understandingnot just the initial state of the nuclear wave function, but also the fluctuating nature of nucleon-nucleoncollisions themselves. A deeper understanding of this physics is needed before more precise connectionscan be made between particle production and the geometry of the initial state.

References

[1] L. P. Csernai, J. Kapusta, and L. D. McLerran, Phys. Rev. Lett. 97 (2006) 152303,arXiv:nucl-th/0604032 [nucl-th].

[2] W. Busza and R. Ledoux, Ann. Rev. Nucl. Part. Sci. 38 (1988) 119–159.

[3] J. Elias, W. Busza, C. Halliwell, D. Luckey, P. Swartz, et al., Phys. Rev. D 22 (1980) 13.

[4] Bari-Cracow-Liverpool-Munich-Nijmegen Collaboration Collaboration, C. De Marzo et al.,Phys. Rev. D 26 (1982) 1019.

[5] D. Brick, M. Widgoff, P. Beilliere, P. Lutz, J. Narjoux, et al., Phys. Rev. D 39 (1989) 2484–2493.

[6] PHOBOS Collaboration, B. Back et al., Phys. Rev. Lett. 93 (2004) 082301,arXiv:nucl-ex/0311009 [nucl-ex].

[7] ALICE Collaboration, Phys. Rev. Lett. 110 082302 (2013), arXiv:1210.4520 [nucl-ex].

[8] C. De Marzo, M. De Palma, A. Distante, C. Favuzzi, P. Lavopa, et al., Phys. Rev. D 29 (1984)2476–2482.

[9] PHOBOS Collaboration, B. Back et al., Phys. Rev. C72 (2005) 031901,arXiv:nucl-ex/0409021 [nucl-ex].

[10] PHENIX Collaboration, S. Adler et al., Phys. Rev. C77 (2008) 014905, arXiv:0708.2416[nucl-ex].

[11] A. Bialas, M. Bleszynski, and W. Czyz, Nucl. Phys. B111 (1976) 461.

[12] D. H. Brick et al., Phys. Rev. D 41 (1990) 765–773.

[13] A. Adil and M. Gyulassy, Phys.Rev. C72 (2005) 034907, arXiv:nucl-th/0505004[nucl-th].

[14] P. Tribedy and R. Venugopalan, Phys. Lett. B710 (2012) 125–133, arXiv:1112.2445[hep-ph].

[15] J. L. Albacete, A. Dumitru, and C. Marquet, Int. J. Mod. Phys. A28 (2013) 1340010,arXiv:1302.6433 [hep-ph].

14

http://dx.doi.org/10.1103/PhysRevLett.97.152303http://arxiv.org/abs/nucl-th/0604032http://dx.doi.org/10.1146/annurev.ns.38.120188.001003http://dx.doi.org/10.1103/PhysRevD.22.13http://dx.doi.org/10.1103/PhysRevD.26.1019http://dx.doi.org/10.1103/PhysRevD.39.2484http://dx.doi.org/10.1103/PhysRevLett.93.082301http://arxiv.org/abs/nucl-ex/0311009http://dx.doi.org/10.1103/PhysRevLett.110.082302http://arxiv.org/abs/1210.4520http://dx.doi.org/10.1103/PhysRevD.29.2476http://dx.doi.org/10.1103/PhysRevD.29.2476http://dx.doi.org/10.1103/PhysRevC.72.031901http://arxiv.org/abs/nucl-ex/0409021http://dx.doi.org/10.1103/PhysRevC.77.014905http://arxiv.org/abs/0708.2416http://arxiv.org/abs/0708.2416http://dx.doi.org/10.1016/0550-3213(76)90329-1http://dx.doi.org/10.1103/PhysRevD.41.765http://dx.doi.org/10.1103/PhysRevC.72.034907http://arxiv.org/abs/nucl-th/0505004http://arxiv.org/abs/nucl-th/0505004http://dx.doi.org/10.1016/j.physletb.2012.02.047, 10.1016/j.physletb.2012.12.004http://arxiv.org/abs/1112.2445http://arxiv.org/abs/1112.2445http://dx.doi.org/10.1142/S0217751X13400101http://arxiv.org/abs/1302.6433

[16] ALICE Collaboration, Phys. Rev. Lett. 110 (2013) 032301, arXiv:1210.3615 [nucl-ex].

[17] CMS Collaboration, Phys. Lett. B718 (2013) 795–814, arXiv:1210.5482 [nucl-ex].

[18] ALICE Collaboration, Phys. Lett. B719 (2013) 29–41, arXiv:1212.2001.

[19] ATLAS Collaboration, Phys. Rev. Lett. 110 (2013) 182302, arXiv:1212.5198 [hep-ex].

[20] CMS Collaboration, Phys. Lett. B724 (2013) 213–240, arXiv:1305.0609 [nucl-ex].

[21] ATLAS Collaboration, Phys. Lett. B725 (2013) 60–78, arXiv:1303.2084 [hep-ex].

[22] K. Dusling and R. Venugopalan, Phys. Rev. D87 (2013) 054014, arXiv:1211.3701 [hep-ph].

[23] K. Dusling and R. Venugopalan, Phys. Rev. D87 (2013) 094034, arXiv:1302.7018 [hep-ph].

[24] P. Bozek and W. Broniowski, Phys. Rev. C88 (2013) 014903, arXiv:1304.3044 [nucl-th].

[25] E. Shuryak and I. Zahed, arXiv:1301.4470 [hep-ph].

[26] A. Bzdak, B. Schenke, P. Tribedy, and R. Venugopalan, arXiv:1304.3403 [nucl-th].

[27] G.-Y. Qin and B. Mller, arXiv:1306.3439 [nucl-th].

[28] W. Broniowski and P. Bozek, arXiv:1308.2370 [nucl-th].

[29] ATLAS Collaboration, Phys. Lett. B710 (2012) 363–382, arXiv:1108.6027 [hep-ex].

[30] M. L. Miller, K. Reygers, S. J. Sanders, and P. Steinberg, Ann. Rev. Nucl. Part. Sci. 57 (2007)205–243.

[31] V. Guzey and M. Strikman, Phys. Lett. B633 (2006) 245–252, arXiv:hep-ph/0505088[hep-ph].

[32] M. Alvioli and M. Strikman, Phys. Lett. B722 (2013) 347–354, arXiv:1301.0728 [hep-ph].

[33] ATLAS Collaboration, Eur. Phys. J. C72 (2012) 1849.

[34] G. Aad, M. Ackers, F. Alberti, M. Aleppo, G. Alimonti, et al., JINST 3 (2008) P07007.

[35] ATLAS Collaboration, New J. Phys. 13 (2011) 053033, arXiv:1012.5104 [hep-ex].

[36] ATLAS Collaboration, Eur. Phys. J. C72 (2012) 1926, arXiv:1201.2808 [hep-ex].

[37] X.-N. Wang and M. Gyulassy, Phys. Rev. D44 (1991) 3501–3516.

[38] GEANT4 Collaboration, S. Agostinelli et al., Nucl. Instrum. Meth. A506 (2003) 250–303.

[39] ATLAS Collaboration, Eur. Phys. J. C70 (2010) 823–874, arXiv:1005.4568[physics.ins-det].

[40] T. Sjostrand, S. Mrenna, and P. Z. Skands, JHEP 05 (2006) 026.

[41] ATLAS Collaboration,, “Summary of ATLAS Pythia 8 tunes.”https://cds.cern.ch/record/1363300. ATL-PHYS-PUB-2011-009.

[42] ATLAS Collaboration,, “ATLAS tunes of PYTHIA 6 and Pythia 8 for MC11.”https://cds.cern.ch/record/1474107. ATL-PHYS-PUB-2012-003.

15

http://dx.doi.org/10.1103/PhysRevLett.110.032301http://arxiv.org/abs/1210.3615http://dx.doi.org/10.1016/j.physletb.2012.11.025http://arxiv.org/abs/1210.5482http://dx.doi.org/10.1016/j.physletb.2013.01.012http://arxiv.org/abs/1212.2001http://dx.doi.org/10.1103/PhysRevLett.110.182302http://arxiv.org/abs/1212.5198http://dx.doi.org/10.1016/j.physletb.2013.06.028http://arxiv.org/abs/1305.0609http://dx.doi.org/10.1016/j.physletb.2013.06.057http://arxiv.org/abs/1303.2084http://dx.doi.org/10.1103/PhysRevD.87.054014http://arxiv.org/abs/1211.3701http://dx.doi.org/10.1103/PhysRevD.87.094034http://arxiv.org/abs/1302.7018http://dx.doi.org/10.1103/PhysRevC.88.014903http://arxiv.org/abs/1304.3044http://arxiv.org/abs/1301.4470http://arxiv.org/abs/1304.3403http://arxiv.org/abs/1306.3439http://arxiv.org/abs/1308.2370http://dx.doi.org/10.1016/j.physletb.2012.02.045http://arxiv.org/abs/1108.6027http://dx.doi.org/10.1146/annurev.nucl.57.090506.123020http://dx.doi.org/10.1146/annurev.nucl.57.090506.123020http://dx.doi.org/10.1016/j.physletb.2005.11.065, 10.1016/j.physletb.2008.04.010http://arxiv.org/abs/hep-ph/0505088http://arxiv.org/abs/hep-ph/0505088http://dx.doi.org/10.1016/j.physletb.2013.04.042http://arxiv.org/abs/1301.0728http://dx.doi.org/10.1140/epjc/s10052-011-1849-1http://dx.doi.org/10.1088/1748-0221/3/07/P07007http://dx.doi.org/10.1088/1367-2630/13/5/053033http://arxiv.org/abs/1012.5104http://dx.doi.org/10.1140/epjc/s10052-012-1926-0http://arxiv.org/abs/1201.2808http://dx.doi.org/10.1016/S0168-9002(03)01368-8http://dx.doi.org/10.1140/epjc/s10052-010-1429-9http://arxiv.org/abs/1005.4568http://arxiv.org/abs/1005.4568http://dx.doi.org/10.1088/1126-6708/2006/05/026https://cds.cern.ch/record/1363300https://cds.cern.ch/record/1474107

[43] ATLAS Collaboration, Phys. Lett. B707 (2012) 330–348, 1108.6018.

[44] B. Alver, M. Baker, C. Loizides, and P. Steinberg, arXiv:0805.4411.

[45] PHENIX Collaboration, K. Adcox et al., Phys. Rev. Lett. 86 (2001) 3500–3505,nucl-ex/0012008.

[46] PHOBOS Collaboration, B. Alver et al., Phys. Rev. C83 (2011) 024913, arXiv:1011.1940[nucl-ex].

[47] CMS Collaboration, arXiv:1307.3442 [hep-ex].

[48] ALICE Collaboration, L. Barnby, AIP Conf.Proc. 1422 (2012) 85–91, arXiv:1110.4240[nucl-ex].

[49] ATLAS Collaboration, Phys. Lett. B688 (2010) 21–42, arXiv:1003.3124 [hep-ex].

[50] V. Gribov, Sov. Phys. JETP 29 (1969) 483–487.

[51] H. Heiselberg, G. Baym, B. Blaettel, L. Frankfurt, and M. Strikman, Phys. Rev. Lett. 67 (1991)2946–2949.

[52] A. Donnachie and P. Landshoff, Phys. Lett. B296 (1992) 227–232, arXiv:hep-ph/9209205[hep-ph].

[53] TOTEM Collaboration, G. Antchev et al., Phys. Rev. Lett. 111 (2013) 012001.

[54] H. De Vries, C. De Jager, and C. De Vries, Atom. Data Nucl. Data Tabl. 36 (1987) 495–536.

[55] M. Tannenbaum, Prog. Part. Nucl. Phys. 53 (2004) 239–252.

[56] P. Steinberg, arXiv:nucl-ex/0703002 [NUCL-EX].

[57] ATLAS Collaboration, JHEP 1211 (2012) 033, arXiv:1208.6256 [hep-ex].

16

http://dx.doi.org/10.1016/j.physletb.2011.12.056http://arxiv.org/abs/1108.6018http://arxiv.org/abs/0805.4411http://arxiv.org/abs/nucl-ex/0012008http://dx.doi.org/10.1103/PhysRevC.83.024913http://arxiv.org/abs/1011.1940http://arxiv.org/abs/1011.1940http://arxiv.org/abs/1307.3442http://dx.doi.org/10.1063/1.3692201http://arxiv.org/abs/1110.4240http://arxiv.org/abs/1110.4240http://dx.doi.org/10.1016/j.physletb.2010.03.064http://arxiv.org/abs/1003.3124http://dx.doi.org/10.1103/PhysRevLett.67.2946http://dx.doi.org/10.1103/PhysRevLett.67.2946http://dx.doi.org/10.1016/0370-2693(92)90832-Ohttp://arxiv.org/abs/hep-ph/9209205http://arxiv.org/abs/hep-ph/9209205http://dx.doi.org/10.1103/PhysRevLett.111.012001http://dx.doi.org/10.1016/j.ppnp.2004.02.021http://arxiv.org/abs/nucl-ex/0703002http://dx.doi.org/10.1007/JHEP11(2012)033http://arxiv.org/abs/1208.6256

Appendix A: Glauber and Glauber-Gribov analysis

The geometry of nucleus-nucleus (A+A) and proton/deuteron-nucleus (p/d+A) collisions is often stud-ied using Glauber Monte Carlo models [30, 44] that simulate the interactions of the incident nucleonsusing a semi-classical eikonal approximation. However, it has been argued that in high energy p+Acollisions, the Glauber model must be corrected to account for the fact that the incoming proton is offshell between successive interactions in the target nucleus[50]. In addition, event-to-event fluctuationsin the configuration of the incoming proton can change its effective scattering cross-section [51, 31, 32].At high energies, the configuration of the proton is taken to be frozen over the time scale of the p+Acollision. To evaluate the impact of these frozen fluctuations of the projectile proton, a modified ver-sion of the PHOBOS Glauber Monte Carlo [44], referred to as “Glauber-Gribov” in the rest of this note,was developed that implemented event-to-event variations in the Glauber Monte Carlo nucleon-nucleoncross-section. Following Refs. [31] and [32], the probability distribution of σtot values was taken to be 2

Ph(σtot) = ρσtot

σtot + σ0exp

{− (σtot/σ0 − 1)

2

Ω2

}. (5)

Here, ρ is a normalization constant, Ω controls the width of the Ph(σtot) distribution, and σ0 determines〈σtot〉. The inelastic fraction of the total cross-section is taken to be constant [32], σNN = λσtot, so theprobability distribution for σNN is given by

PH(σNN) =1λ

P(σNN/λ) (6)

Estimates of Ω were provided in Ref. [31] for centre-of-mass energies 1.8, 9, and 14 TeV. An interpola-tion of those values to

√sNN = 5.02 TeV for use in this analysis yielded Ω = 0.55, a value that is only

marginally larger than the value at 9 TeV, Ω = 0.52. The corresponding value of σ0 = 78.6 mb was de-termined by requiring a total cross-section, σtot = 86 mb, consistent with the Donnachie and Landshoff[52] parameterization used in [31]. An alternative choice of σtot consistent with more recent measure-ments [53] has only a small effect on the final distribution. Recently, updated estimates, Ω = 1.01 andσ0 = 72.5 mb corresponding to σtot = 94.8 mb were obtained [32] using results of diffraction measure-ments at the LHC. For the purposes of this note, the Glauber-Gribov analysis was performed using bothΩ = 0.55 and 1.01 in order to evaluate the sensitivity of the physics conclusions to the choice of Ω. Foreach of the Ω values, λ was chosen to produce a σNN value of 70 mb with the results λ = 0.82 and 0.74,respectively, for Ω = 0.55 and 1.01.

The Glauber-Gribov PH(σNN) distributions are shown in the left panel of Fig. 10 for both values of Ωand corresponding σ0 and λ values. The distribution of the number of participants, Npart, obtained fromthe two Glauber-Gribov formulations are shown in the right panel of Fig. 10 together with a standardGlauber MC Npart distribution obtained using a fixed inelastic cross-section, σNN = 70 mb. For all threecalculations, the lead nucleon density distribution was taken to be Woods-Saxon with radius and skindepth parameters, R = 6.62 fm and a = 0.546 fm [54]. The Glauber-Gribov Npart distributions are muchbroader than the Glauber distribution due to the σNN cross-section fluctuations in the Glauber-Gribovformulations.

To connect an experimental measurement of collision centrality such as ΣEPbT to the results of theGlauber or Glauber-Gribov Monte Carlo, a model for the Npart dependence of the ΣEPbT distribution isrequired. The usual basis for such models, previously applied to A+A and p/d+A collisions, is the WNmodel [11]. When applied to this analysis, this model predicts that ΣEPbT would increase proportionallyto Npart with the proportionality constant equal to one half the corresponding average FCal

∑ET in p+p

2The first arXiv version of [32] contained a subsequently fixed typographical error that made the distribution exponentialinstead of Gaussian.

17

[mb]NNσ0 50 100 150 200 250

)N

Nσ(

HP

0

0.005

0.01

0.015

0.02

=0.55ΩGlauber-Gribov

=1.01ΩGlauber-Gribov

ATLAS Simulation Preliminary = 5.02 TeVNNsp+Pb

partN0 10 20 30 40 50 60

)pa

rtN(

P

-510

-410

-310

-210

-110

standard Glauber=0.55ΩGlauber-Gribov =1.01ΩGlauber-Gribov

ATLAS Simulation Preliminary = 5.02 TeVNNsp+Pb

Figure 10: Left: Glauber-Gribov PH(σNN) distributions (see text) for Ω = 0.55 and 1.01. Right: Glauberand Glauber-Gribov Monte Carlo Npart distributions for 5.02 TeV p+Pb collisions obtained from 1 millionsimulated events each.

collisions. For fixed Npart, the ΣEPbT distribution from the WN model can be obtained as an n-fold con-volution, where n is equal to Npart, of the corresponding p+p A-side FCal

∑ET (ΣEAT ) distribution. This

convolution is straightforward to implement because transverse energy distributions in p+p collisionsare typically well described by gamma distributions [55]

gamma(x; k, θ) =1

Γ(k)1θ

( xθ

)k−1e−x/θ. (7)

The gamma distribution has the property that an N-fold convolution of a distribution with parameters kand θ yields another gamma distribution with the same θ parameter and a modified k parameter, k′ = Nk.For a set of inelastic collisions having a distribution of Npart values, the corresponding WN dNevt/dETdistribution would be obtained by summing the gamma distributions over different Npart values weightedby P(Npart) (as in the right panel of Figure 10).

Attempts to fit the measured ΣEPbT distribution in p+Pb collisions, using the WN-convolved gammadistributions with k0 and θ0 as free parameters, yield unsatisfactory results. The Glauber Npart distributionhas the wrong shape to allow even an approximate description of the distribution shown in Fig. 2. Asa result, for this analysis, a generalization of the WN model was implemented taking advantage of theconvolution properties of the gamma distribution. The generalization parameterizes the Npart dependenceof the k and θ parameters of the gamma distribution as

k(Npart

)= k0 + k1

(Npart − 2

),

θ(Npart

)= θ0 + θ1 log

(Npart − 1

). (8)

For k1 = k0/2 and θ1 = 0, this model reduces to the WN model. The log(Npart − 1) term allows for apossible variation in the effective acceptance of the FCal due to an Npart-dependent backward shift in thep+Pb centre-of-mass system [56]. This model provides a reasonable description of the measured ΣEPbTdistribution for both the Glauber and two Glauber-Gribov Npart distributions. Two alternative parame-terizations for k

(Npart

)and θ

(Npart

)were used to evaluate systematic uncertainties. One of these kept

θ constant, θ(Npart

)= θ0 while allowing for a quadratic dependence of k on Npart. The other included

both a quadratic term in k(Npart

)and the logarithmic term in θ

(Npart

)but fixed k1 = k0/2 to reduce the

number of free parameters.To limit the number of free parameters when fitting the ΣEPbT distribution, k0 and θ0 were obtained by

fitting the PYTHIA8 and PYTHIA6 detector-level ΣEAT distributions to a gamma distribution convoluted

18

with a Gaussian noise distribution. The parameters of the noise were determined using “empty” eventswith no beam bunches crossing at the ATLAS interaction point. The distributions, the correspondingfits, and the resulting fit parameters, k0 and θ0 are shown in Fig. 11. The distributions in Fig. 11 were

[GeV]TFCal A E

-10 0 10 20 30 40 50

cou

nts

1

10

210

310

fit to gamma function

= 3.4140θ = 1.402, 0k

ATLAS Simulation PreliminaryPYTHIA 8, 5.02 TeV

[GeV]TFCal A E

-10 0 10 20 30 40 50

cou

nts

1

10

210

310

fit to gamma function

= 2.6770θ = 1.231, 0k

ATLAS Simulation PreliminaryPYTHIA 6, 5.02 TeV

Figure 11: PYTHIA8 and PYTHIA6 Monte Carlo simulated detector-level ΣEAT distributions for5.02 TeV p+p collisions with p+Pb kinematics. The solid curves show the results of gamma functionfits (see text). The resulting parameters are indicated on the figures.

evaluated for all Monte Carlo events, i.e. without application of the vertex, MBTS timing, and gap cutsapplied to the p+Pb analysis, in order to obtain the unbiased ΣEAT distribution for the convolution. ThePYTHIA8 results were used as the primary p+p reference in the analysis and the PYTHIA6 results wereused to evaluate systematic uncertainties. Measurements of the transverse energy distributions in 7 TeVp+p collisions [57] and comparisons of the results to various MC models show that both PYTHIA6 andPYTHIA8 approximately reproduce the shape of the ∑ ET distribution in the range |η| > 3.2, though theyunder-predict the average transverse energy by of order 10%.

When trying to model the measured ΣEPbT distributions, the potential loss of inelastic p+Pb collisionsdue to event selection cuts must be accounted for. Because the recorded p+Pb event sample contains aΣEPbT -dependent mixture of diffractive, non-diffractive, and residual photo-nuclear and electromagneticevents that have different efficiencies, a purely data-driven determination of the inefficiency is not pos-sible. Therefore, a conservative assumption that the p+Pb inefficiency for a given ΣEPbT is equal to thatin p+p collisions was made and the inefficiency was determined from the simulated PYTHIA samplesusing the same event cuts as those applied in the p+Pb analysis. That inefficiency is dominated by theremoval of diffractive events by the MBTS and gap requirements. PYTHIA8 (PYTHIA6) predicts a78% (72%) event selection efficiency for inelastic 5.02 TeV p+p collisions with the p+Pb kinematics.The corresponding efficiencies for non-diffractive events are 99% (98%). In higher multiplicity p+Pbcollisions, non-diffractive events have negligible inefficiency.

To fit the measured ΣEPbT distribution, a hypothetical distribution was produced by summing the Npart-dependent gamma distributions according to the specific model assumptions, e.g. Eq. 8, and weightingby P(Npart), as shown in the right panel of Fig. 10. The resulting distribution was corrected for eventselection efficiency and then convolved with a Gaussian noise distribution measured in empty events.This distribution was then fit to the measured ΣEPbT distribution. Results of the fit procedure for the modeldefined in Eq. 8 are shown in Fig. 12 for the Glauber and the two Glauber-Gribov Npart distributions.The resulting fit parameters, k1 and θ1, are presented in Table 3. The top panel of the figure shows acomparison of the re-binned ΣEPbT distribution to the best fit hypothetical dNevt/dET distributions. Theratios of the fit distributions to the measured distribution are shown in the three lower panels. The fitprovides a good description of the ΣEPbT distribution for ΣE

PbT < 100 GeV for all three geometric models.

At higher ΣEPbT the fit does a better job describing the data for the Glauber Npart distribution.

19

]-1

[GeV

Pb

TEΣ

/dN

dev

tN

1/

-610

-510

-410

-310

-210

Glauber = 0.55ΩGlauber-Gribov, = 1.01ΩGlauber-Gribov,

PreliminaryATLAS-1bµ = 1 intLp+Pb,

= 5.02 TeVNNs

0

1

2Glauber

0

1

2 = 0.55ΩGlauber-Gribov,

[GeV]PbTEΣ0 50 100 150

0

1

2 = 1.01ΩGlauber-Gribov,

fit /

data

Figure 12: Top panel: Measured ΣEPbT distribution compared to Glauber (solid), Glauber-Gribov withΩ = 1.01 (long dashed), and Glauber-Gribov with Ω = 0.55 (short dashed) fits. Lower panels: ratios ofGlauber and Glauber-Gribov fit distributions to the data distribution.

The results of the fitting described above provide an estimate of the total p+Pb event selection effi-ciency. For the default PYTHIA8-based results, the measured ΣEPbT distribution accounts for 98% of thesimulated distributions for all three geometric models. However, a detailed analysis of the residual differ-ences between the best fit and measured distributions indicates an excess of low ΣEPbT events in the datathat varies from ∼ 0% for the Glauber fit to 1.8% for the Glauber-Gribov fit with Ω = 1.01. Thus, for thisGlauber-Gribov case, the 98% total efficiency could result from a 96.2% inelastic p+Pb efficiency plus acontamination at low ΣEPbT from events not described by the simulation of 1.8%. This contamination rateis compatible with independent estimates of the rate for collisions involving diffractive excitation of theproton to pass the applied event selection. The alternative models for k

(Npart

)and θ

(Npart

)also yield a

total efficiency of 98% and contamination rate that varies from 0-2%. For PYTHIA6, the ΣEPbT fits using

Glauber model k1 θ1standard Glauber 0.425(2) +1.32(1)Glauber-Gribov Ω = 1.01 1.139(3) -0.209(2)Glauber-Gribov Ω = 0.55 0.901(3) +0.074(4)

Table 3: Optimal fit parameters and uncertainties obtained from fits to the measured ΣEPbT distribution(see text).

20

the default model yield a total efficiency of 97% and up to 1% contamination of events not describedby the simulation. The total efficiency was then taken to be 98% and the uncertainty was conservativelyestimated to be twice the PYTHIA8-PYTHIA6 difference, 2%.

Using the results of the fits to the measured ΣEPbT distribution, the average number of participants〈Npart〉 can be evaluated for each of the centrality intervals included in the analysis. For the Glauber-Gribov simulations, which indicated a possible non-negligible contamination at low ΣEPbT , the boundariesof the centrality intervals were shifted to account for the true efficiency before the 〈Npart〉 values weredetermined. However, the resulting shift in the ΣEPbT intervals had negligible impact on the 〈Npart〉 valuesfor the centrality intervals included in this analysis. The 〈Npart〉 values obtained for the Glauber and thetwo Glauber-Gribov geometries are shown in Figure 3 and listed in Table 4.

The analysis described in this section and the 〈Npart〉 values are subject to systematic uncertaintiesdue to the event selection efficiency, the choice of Monte Carlo event generator, the choice of model todescribe the Npart dependence of the ΣEPbT distribution, inaccuracies in the PYTHIA description of thebase p+p gamma distribution, and uncertainties in the Glauber/Glauber-Gribov Monte Carlo due to σNNand the properties of the nuclear density distribution. To evaluate the impact of the total event selectionuncertainty, new centrality intervals were chosen assuming a total efficiency of 100% and 96% and thecomplete analysis was repeated. To account for possible inaccuracies in the PYTHIA dET/dη in the re-gion of the FCal acceptance, the analysis was repeated separately under ±10% re-scalings of PYTHIA8ΣEPbT values. Other variations for which the complete analysis was repeated are: the PYTHIA6 eventgenerator, alternative models for k

(Npart

)and θ

(Npart

), ±5 mb changes in σNN, and variations in nu-

clear density distribution parameters. To obtain systematic errors on Npart in each centrality interval,the maximum positive and negative fractional variation in 〈Npart〉 away from the default results was de-termined for different classes of variations: event selection efficiency, PYTHIA8 ΣEPbT energy scale, fitresults using alternative k

(Npart

)and θ

(Npart

)parameterizations for both PYTHIA8 and PYTHIA6, and

Glauber/Glauber-Gribov parameters including σNN and nuclear densities. The resulting maximal varia-tions were then summed in quadrature over the different classes separately for the positive and negativevariations. The resulting asymmetric uncertainties are indicated by the error bars on the points in Fig. 3and quoted in Table 4.

Centrality Glauber Glauber-Gribov Ω = 0.55 Glauber-Gribov Ω = 1.0160-90% 3.96+0.20−0.31

(+5%−8%

)3.56+0.19−0.17

(+5%−5%

)3.41+0.26−0.16

(+8%−5%

)40-60% 7.4+0.4−0.6

(+6%−8%

)6.6+0.4−0.4

(+6%−6%

)6.31+0.5−0.34

(+8%−5%

)30-40% 9.8+0.6−0.6

(+6%−6%

)9.2+0.5−0.5

(+6%−6%

)8.9+0.6−0.5

(+7%−5%

)20-30% 11.4+0.6−0.6

(+6%−6%

)11.2+0.6−0.7

(+6%−6%

)11.1+0.7−0.6

(+6%−6%

)10-20% 13.0+0.8−0.7

(+6%−6%

)13.7+0.8−0.8

(+6%−7%

)14.1+0.9−0.8

(+6%−6%

)5-10% 14.6+1.2−0.8

(+8%−6%

)16.5+1.0−1.0

(+6%−6%

)17.4+1.1−1.1

(+7%−6%

)1-5% 16.1+1.7−0.9

(+11%−6%

)19.5+1.3−1.3

(+7%−7%

)21.4+1.4−2.0

(+7%−9%

)0-1% 18.2+2.7−1.0

(+15%−5%

)24.1+1.6−2.0

(+7%−8%

)27.4+1.6−4

(+6%−16%

)0-90% 8.4+0.5−0.4

(+6%−5%

)8.5+0.5−0.5

(+6%−5%

)8.6+0.5−0.4

(+6%−5%

)Table 4: 〈Npart〉 values for centrality intervals used in this analysis together with asymmetric systematicuncertainties shown as both absolute and relative uncertainties.

21

Appendix B: Additional plots

Figure 13 shows the comparison between fully corrected dNch/dη distributions, including extrapolation

η-3 -2 -1 0 1 2 3

η/d

chdN

0

10

20

30

40

50

60

70ATLAS Preliminary

-1bµ= 1 int

p+Pb L = 5.02 TeVNNs

= -0.465cm

y

> 100 MeV T

p > 0 MeV

T p

Figure 13: Comparison between fully corrected dNch/dη distributions and the dNch/dη measured abovepT = 100 MeV for eight centrality intervals. The centrality intervals are ordered from top to bottom:0–1%, 1–5%, 5–10%, 10–20%, 20–30%, 30–40%, 40–60%, 60–90%. The shaded bands indicate thetotal systematic uncertainty including 〈Npart〉 uncertainties. Statistical uncertainties, shown with verticalbars are typically smaller than the marker size,

to pT = 0 MeV, and the dNch/dη measured above pT = 100 MeV in eight centrality intervals. Particleswith momentum above 100 MeV produce tracklets that satisfy the selection requirement of |∆φ| < 0.1,used in the analysis. The fraction of charged particles in the ”visible” part of the spectrum has weakcentrality dependence. At |η| = 0 it is approximately 95% of dNch/dη, consistent with the previous mea-surements published in [35]; it diminishes to 90% at the edges of the measured pseudorapidity interval.

Figure 14 shows ATLAS dNch/dη measured in the 0–90% centrality interval, scaled for comparisonto the minimum-bias events measured by the ALICE experiment [16]. The scaling factor used for theATLAS points was calculated as the ratio of the number of participants for minimum-bias events equalto 7.9±7.6% published by ALICE, and the 〈Npart〉 for the Glauber calculation in the 0–90% centralityinterval found by ATLAS, see Table 4. The uncertainties on Npart from both measurements are notincluded in the systematic uncertainty band plotted in the figure. These uncertainties are based on similaranalytical approaches but the correlation between them in two different experiments is hard to estimate.

The comparison of the ALICE minimum-bias results to the scaled ATLAS distribution shows con-sistency in shape and reasonable agreement in amplitudes. The ATLAS points exceed the ALICE mea-surement by less than 2 standard deviations computed using the combined systematic uncertainties fromthe the two experiments. The residual deviation may come from the different approaches in the eventselection, and from the estimates of the Npart.

Figure 15 shows dNch/dη per participant pair for the most central and most peripheral intervals of

22

η-3 -2 -1 0 1 2 3

η/d

chdN

0

5

10

15

20

25

ATLAS 0-90% scaled by 7.9/8.44ALICE [Phys. Rev. Lett. 110, 032301 (2013)]

ATLAS Preliminary-1bµ= 1

intp+Pb L

= 5.02 TeVNNs= -0.465

cmy

Figure 14: Comparison between the ATLAS 0–90% and ALICE [16] minimum-bias dNch/dη distribu-tions. For this comparison the ATLAS distribution has been multiplied by the minimum-bias Npart valuefrom the ALICE measurement and divided by the 0–90% 〈Npart〉 from ATLAS. The resulting scalingfactor is equal to 7.9/8.44.

centrality measured in the analysis as a function of η for three Glauber models. The results for the mostperipheral (60–90%) centrality interval shown with circles, reside approximately at the same magnitudein all three panels. This is due to relatively small difference between the calculations of 〈Npart〉 given inTable 4 for Glauber and Glauber-Gribov models in this centrality interval. In the region −1 < η < 0this magnitude is consistent with the (∝ s0.10) approximation of dNch/dη in inelastic p+p collisions,shown in Fig. 1 in Ref. [16]. The shape of the distribution indicates stronger particle production in theproton-going direction compare to the Pb-going. This can be explained by the higher energy of theproton, compared to the nucleon energy in lead in the laboratory system. In the 0-1% central collisions,shown with diamond markers in all three panels, this trend is reversed. The magnitude of dNch/dηper participant pair strongly depends on the model assumption, used to calculate 〈Npart〉. The point atwhich the central and peripheral scaled distributions cross each other also depends on the model choice.However, the location of this point at the left edge; in the middle; and on the right edge of the measuredη interval in the three panels of Fig. 15 is rather accidental.

23

-3 -2 -1 0 1 2 3

/2 )

〉 pa

rtN〈

/ (

η/d

chdN

4

6

8 Preliminary ATLAS-1bµ = 1

intp+Pb L

= 5.02 TeVNNs = -0.465

cmy

Glauber

-3 -2 -1 0 1 2 3

4

6

8 0 - 1% 60 - 90%

=0.55ΩGlauber-Gribov

η-3 -2 -1 0 1 2 3

4

6

8

=1.01ΩGlauber-Gribov

Figure 15: dNch/dη per pair of participants as a function of η for 0–1% and 60–90% centrality intervalsfor 3 different models used to calculate Npart. The standard Glauber calculation is shown in the toppanel, the Glauber-Gribov model with Ω = 0.55 in the middle and Ω = 1.01 is in the lowest panel.The bands shown with thin lines represent the systematic uncertainty of the dNch/dη measurement, theshaded bands indicates the total systematic uncertainty including the uncertainty on 〈Npart〉. Statisticaluncertainties, shown with vertical bars are typically smaller than the marker size.

24