Analysis of the apparent nuclear modification in peripheral Pb-Pb collisions at 5.02

Charged-particle spectra at midrapidity are measured in Pb–Pb collisions at the centre-of-mass energy per nucleon–nucleon pair √ s NN = 5 . 02 TeV and presented in centrality classes ranging from most central (0–5%) to most peripheral (95–100%) collisions. Possible medium effects are quantiﬁed using the nuclear modiﬁcation factor ( R AA ) by comparing the measured spectra with those from proton–proton collisions, scaled by the number of independent nucleon–nucleon collisions obtained from a Glauber model. At large transverse momenta (8 < p T < 20 GeV / c ), the average R AA is found to increase from about 0 . 15 in 0–5% central to a maximum value of about 0 . 8 in 75–85% peripheral collisions, beyond which it falls off strongly to below 0 . 2 for the most peripheral collisions. Furthermore, R AA initially exhibits a positive slope as a function of p T in the 8–20 GeV / c interval, while for collisions beyond the 80% class the slope is negative. To reduce uncertainties related to event selection and normalization, we also provide the ratio of R AA in adjacent centrality intervals. Our results in peripheral collisions are consistent with a PYTHIA-based model without nuclear modiﬁcation, demonstrating that biases caused by the event selection and collision geometry can lead to the apparent suppression in peripheral collisions. This explains the unintuitive observation that R AA is below unity in peripheral Pb–Pb, but equal to unity in minimum-bias p–Pb collisions despite similar charged-particle multiplicities. © 2019 Conseil Européen pour la Recherche Nucléaire. Published by Elsevier


Introduction
Transport properties of the Quark-Gluon Plasma (QGP) can be extracted from measurements of observables in high-energy nucleus-nucleus (AA) collisions, which involve large momentum transfers, such as jets originating from hard parton-parton scatterings in the early stage of the collision. While propagating through the expanding medium, these hard partons lose energy due to medium-induced gluon radiation and collisional energy loss, a process known as "jet quenching" [1,2]. Due to the energy loss, the rate of high-p T particles is expected to be suppressed relative to proton-proton collisions. The effect is typically quantified by the nuclear modification factor R AA = 1 N coll dN AA ch /dp T dN pp ch /dp T = 1 T AA dN AA ch /dp T dσ pp ch /dp T , (1) defined as the ratio of the per-event yields in AA and pp collisions normalized to an incoherent superposition of N coll binary pp collisions. The average number of collisions N coll is determined from E-mail address: alice -publications @cern .ch.
a Monte Carlo Glauber model [3][4][5] and related to the average nuclear overlap T AA = N coll /σ NN inel , where σ NN inel is the total inelastic nucleon-nucleon cross section. The yields measured in AA collisions, as well as N coll , depend on the collision centrality, and R AA is constructed to be unity in the absence of nuclear effects where particle production is dominated by hard processes. The collision centrality is expressed in percentiles of the total hadronic cross section, with the highest (lowest) centrality 0% (100%) referring to the most central (peripheral) collisions with zero (maximal) impact parameter. Experimentally, centrality is typically determined by ordering events according to multiplicity or energy deposition in a limited rapidity range and by fitting the corresponding distribution with a Glauber-based model of particle production [6].
Numerous measurements of R AA reported by experiments at the Relativistic Heavy-Ion Collider (RHIC) [7][8][9][10][11][12][13][14][15][16] and at the Large Hadron Collider (LHC) [17][18][19][20][21][22] revealed that high-p T particle production is suppressed strongly in central collisions, and that the suppression reduces with decreasing centrality. Furthermore, control measurements of possible nuclear modification arising from the initial state in d-Au and p-Pb collisions [23-28] and with electromagnetic probes in AA collisions [29-33] (which should not be affected by partonic matter) demonstrated that the observed suppression is due to final state interactions, such as parton energy loss. Contrary to expectations, R AA was also found to be below . In a finalstate dominated scenario, such differences relative to unity imply a large jet quenching parameter for peripheral collisions, up to an order of magnitude larger than for cold nuclear matter [34], and consequently raise expectations of the relevance of parton energy loss even in small collision systems [35][36][37]. However, it has been pointed out recently [38] that event selection and geometry biases -just like those discussed for p-Pb collisions [39] -can cause an apparent suppression of R AA in peripheral collisions, even in the absence of nuclear effects, while self-normalized coincidence observables [40,41] are not affected. The impact parameter of individual NN collisions is correlated to the overall collision geometry leading to an NN impact parameter bias in the transverse plane [42], for peripheral collisions the NN impact parameter is biased towards larger values. Centrality classification based on multiplicity can bias the mean multiplicity of individual nucleon-nucleon (NN) collisions, and hence the yield of hard processes in AA collisions due to correlated soft and hard particle production, amplifying the inherent NN impact parameter bias. The presence of the multiplicity bias in peripheral Pb-Pb collisions was already demonstrated in Ref. [39] showing the averaged multiplicity of the Glauber-NBD fit is lower than the average number of ancestors times the mean multiplicity of NBD (left panel of figure 8 in Ref. [39]). In the present paper, we aim to study its relevance on charged-particle spectra in Pb-Pb collisions at √ s NN = 5.02 TeV, in 20 centrality classes ranging from 0-5% to 95-100% collisions. The spectra at midrapidity are measured in the range 0.15 < p T < 30 GeV/c except for the 95-100% class, where it is 0.15 < p T < 20 GeV/c. Using the charged-particle spectra from pp collisions at the same energy [22], we construct the nuclear-modification factor and study the centrality dependence of its average at high p T , as well as its slope at low and high p T . To reduce uncertainties related to event selection and normalization, which are particularly large for peripheral collisions, we also provide the ratio of R AA in adjacent centrality intervals, defined as where i + 1 denotes a 5% more central centrality class than i.
The definition of R +1 corresponds approximately to the change of log R AA with centrality, and its value would be constant for an exponential dependence. Similar to R AA , we quantify the centrality dependence of the average R +1 at high p T , as well as its slope at low and at high p T . Where possible, the results are compared to a PYTHIA-based model of independent pp collisions without nuclear modification [38]. The remainder of the paper is structured as follows: Section 2 describes the experimental setup. Section 3 describes the charged particle measurement with emphasis on corrections and uncertainties related to the most peripheral collisions. Section 4 describes the results. Section 5 provides a summary of our findings.

Experimental setup
The ALICE detector is described in detail in Ref. [43], and a summary of its performance can be found in Ref. [44]. Chargedparticle reconstruction at midrapidity is based on tracking information from the Inner Tracking System (ITS) and the Time Projection Chamber (TPC), both located inside a solenoidal magnetic field of 0.5 T parallel to the beam axis.
The ITS [45] consists of three sub-detectors, each composed of two layers to measure the trajectories of charged particles and to reconstruct primary vertices. The two innermost layers are the Silicon Pixel Detectors (SPD), the middle two layers are Silicon Drift Detectors (SDD), the outer two layers are Silicon Strip Detectors (SSD).
The TPC [46] is a large (90 m 3 ) cylindrical drift detector. It covers a pseudorapidity range of |η| < 0.9 over full azimuth, providing up to 159 reconstructed space points per track. Charged particles originating from the primary vertex can be reconstructed down to p T ≈ 100 MeV/c. The relative p T resolution depends on momentum, is approximately 4% at 0.15 GeV/c, 1% at 1 GeV/c and increases linearly approaching 4% at 50 GeV/c. The pp and Pb-Pb collision data at √ s NN = 5.02 TeV were recorded in 2015. In total, about 110 · 10 6 pp and 25 · 10 6 Pb-Pb events satisfying the minimum bias trigger and a number of offline event selection criteria were used in the analysis. The minimumbias trigger required a signal in both, the V0-A and V0-C, scintillator arrays, covering 2.8 < η < 5.1 and −3.7 < η < −1.7, respectively [47]. Beam background events were rejected efficiently by exploiting the timing signals in the V0 detectors, and in Pb-Pb collisions also by using the two Zero Degree Calorimeters (ZDCs). The latter are positioned close to beam rapidity on both sides of the interaction point.

Data analysis
The measurements of charged-particle spectra in pp and Pb-Pb collisions at √ s NN = 5.02 TeV are described in detail in Ref. [22].
The collision point or primary event vertex was determined from reconstructed tracks. If no vertex was found using tracks, the vertex reconstruction was performed using track segments constructed from the two innermost layers of the ITS. Events with a reconstructed vertex within ±10 cm from the centre of the detector along the beam direction are used to ensure a uniform acceptance and reconstruction efficiency at midrapidity. Primary charged particles [48] were measured in the kinematic range of |η| < 0.8 and 0.15 < p T < 30 GeV/c. The detector simulations were performed using the PYTHIA [49] and HIJING [50] Monte Carlo event generators with GEANT3 [51] for modelling the detector response. Track-level corrections include acceptance, efficiency, purity and p T resolution, which were obtained using an improved method tuned on data to reduce the systematic uncertainties related to particle species dependence (see Ref. [22] for details). Events are classified in percentiles of the hadronic crosssection using the sum of the amplitudes of the V0-A and V0-C signals (V0M estimator) [6]. The absolute scale of the centrality is defined by the range of 0-90% centrality in which a Glauber-based multiplicity model is fitted to the V0M distribution. The lower centrality limit of 90% of this range with its corresponding V0M signal is denoted the anchor point (AP). The multiplicity for each particle source is modelled with a negative binomial distribution, where the effective number of independent particle production sources is described by a linear combination of the number of participants (N part ) and collisions (N coll ). The AP was shifted by ±0.5%, leading to a systematic uncertainty in the normalization of the spectra of up to 6.7% for the 85-90% centrality class. Unlike previous measurements in Pb-Pb collisions, the analysis was not limited to 0-90% most central events, where effects of trigger inefficiency and contamination by electromagnetic processes are negligible, but also included the 90-100% most peripheral collisions. The V0M value corresponding to 95% of the hadronic cross section was determined by selecting either 95% of the events given by the Glauber-NBD parametrization, or the number of events in the 0-90% centrality class multiplied by the factor 95/90, where the latter is used as a variation to assess the systematic uncertainty of the approach. The difference on the measured yields between the two ways was assigned as additional systematic uncertainty. For the centrality class 90-95% (95-100%) the combined uncertainty amounts to a fully correlated part of 10.8% (11.7%) on the normalization of the spectra and a 2.9% (4.6%) residual effect on the shape. The trigger and event-vertex reconstruction efficiency and the related systematic uncertainties for peripheral Pb-Pb collisions were estimated from simulations using HIJING and PYTHIA including single-and double-diffractive processes, but ignoring possible differences from nuclear effects. The V0M distribution in the simulations was reweighted with the measured V0M distribution. The combined efficiency was found to be 0.985 ± 0.015 for the 90-95% and 0.802 ± 0.057 for the 95-100% centrality classes, respectively, while fully efficient for more central collisions. In addition, in the most peripheral bin a p T -dependent signal loss of up to 14.7% at low p T is corrected for. To account for diffractive processes in this correction and its systematic uncertainty, two limiting scenarios have been considered: a) the signal loss is assumed to be as in pp collisions in the V0M range of the 95-100% bin; b) only the fraction of events with a single nucleon-nucleon collision are corrected for assuming the signal loss from minimum-bias pp collisions.
Contamination of the peripheral bins by electromagnetic interactions was studied in the data by removing all events with small energy deposits in the neutron ZDCs. The resulting change of the spectrum with the requirements of at least a five-neutron equivalent energy in both neutron ZDCs amounts to 5% for the 95-100% centrality class, 3% for the 90-95% class and 2% for the 80-85% and 85-90% classes and is assigned as systematic uncertainty. To account for contamination of the trigger from events without reconstructed vertex, those events are removed from the analysis and the resulting change is assigned as systematic uncertainty on the normalization (6.8% in the 95-100% class and 0.5% in the 90-95% class).
Systematic uncertainties related to vertex selection, track selection, secondary-particle contamination, primary-particle composition, p T resolution, material budget and tracking efficiency were estimated as described in Ref. [22] and are assigned as bin-by-bin uncertainties. The systematic uncertainties related to the centrality selection were estimated by a comparison of the p T spectra when the limits of the centrality classes are shifted due to an uncertainty of ±0.5% in the fraction of the hadronic cross section used in the analysis. They are split into two parts: one part that is fully correlated between the p T bins assigned as a normalization uncertainty plus an additional part taking into account residual differences in the spectral shape assigned as a bin-by-bin uncertainty. The overall normalization uncertainty of R AA contains the uncertainty related to the centrality selection, the uncertainty of N coll , the uncertainty of the trigger efficiency, the uncertainty of the trigger contamination and the normalization uncertainty of the pp reference spectrum added in quadrature. Note that most uncertainties are correlated to a large extent between adjacent centrality bins leading to reduced uncertainties in R +1 .
Ordering events according to multiplicity introduces a bias relative to using the impact parameter in Glauber-based particle production models. It is expected that part of the bias introduced by the ordering can be cancelled in R AA , when N coll is also obtained in the same way as in the data. The difference relative to averaging over impact parameter is quantified in Fig. 1, which shows the ratio of N coll by slicing either in multiplicity (estimated using the V0M amplitude) N mult coll or impact parameter N geo coll , as carried out so far at the LHC. The difference is below 5% up to 80%  centrality, and then increases strongly up to 40% for more peripheral classes. The average quantities for a centrality class, such as the number of participants N part , the number of binary collisions N coll and the nuclear overlap function T AA , were obtained by averaging over the V0M multiplicity intervals, and are summarized in Table 1. For the calculation of R AA and R +1 we use only those multiplicity averaged quantities. As before [5,6], the uncertainties on the mean were obtained by changing the various ingredients of the Glauber MC model by one standard deviation. The resulting relative uncertainties on the mean are below 6%, however in particular for peripheral collisions the widths of the respective distributions are significantly larger.
The charged particle multiplicity dN ch /dη and the average transverse momentum p T for all centrality intervals are listed in Table 2, values given for dN ch /dη and p T >0 are extrapolated to p T = 0 using a modified Hagedorn function fitted to the data, as described in Ref. [52].

Table 2
Summary of the average dN ch /dη and p T in |η| < 0.8 for all centrality classes. While p T >0.15 is averaged over the measured range 0.15 < p T < 10 GeV/c, p T >0 is extrapolated to p T = 0. All uncertainties listed are systematic uncertainties.  From central to peripheral collisions R AA increases, which in particular above about 10 GeV/c can be understood as the progressive reduction of medium-induced parton energy loss. Furthermore, the shape is similar from the most central up to the 80-85% centrality class, namely an increase at low p T , a maximum around 2-3 GeV/c, related to radial flow, then a decrease with a local minimum at about 7 GeV/c, followed by a mild increase. Above 80-85% centrality, the evolution is different as already at low p T the slope is negative and R AA decreases monotonously with increasing p T . The change in behaviour seems to occur in the 75-85% interval, since the 80-85% R AA values appear to be the same or even lower than those of the 75-80% interval. For the most peripheral classes, the reduction of the nuclear modification factor with increasing p T is qualitatively similar to the one observed for low multiplicity p-Pb [39] collisions, indicating that the underlying bias towards more peripheral collisions with a reduced rate of hard scatterings per nucleon-nucleon collisions is the same. If instead of using N mult coll , we had used N geo coll in the normalization of R AA , the results for peripheral collisions above 80% would be even lower, namely by the ratio quantified in Fig. 1.

Results
To quantify these observations we provide in Fig. 3 the average R AA at high p T (within 8 < p T < 20 GeV/c), which increases smoothly from most central up to 70-75% centrality and drops strongly beyond the 80-85% centrality class. The data are compared to the high p T limit of a PYTHIA-based model (HG-PYTHIA) [38], which for every binary nucleon-nucleon collision superimposes a number of PYTHIA events incoherently without nuclear modification. The essential feature of the model is that particle production per nucleon-nucleon collision originates from a fluctuating number of multiple partonic interactions depending on the nucleon-nucleon impact parameter. Despite the fact that HG-PYTHIA is a rather simple approach, for 75-80% and more peripheral collisions, it describes the average R AA relatively well suggesting that the apparent suppression for peripheral collisions is not caused by parton energy loss, but rather by the event selection criteria imposed to determine the centrality of the collisions. The data are significantly lower than the model calculation for the most peripheral centrality classes, possibly due to a significant contribution of diffraction, which is not modelled in HG-PYTHIA.
The slope of a linear fit to R AA performed for 8 < p T < 20 GeV/c, the region where the R AA in central collisions rises after its minimum, is shown in Fig. 4 as a function of centrality. This high-p T slope is positive and initially increasing mildly before decreas- ing with decreasing centrality up to about 80% centrality, beyond which it is close to zero, and then even is negative in the highest centrality class. At low to intermediate p T (within 0.4-1.2 GeV/c), the regime which is strongly influenced by the hydrodynamic expansion, the R AA exhibits another rise. The slope extracted in the p T range 0.4-1.2 GeV/c is also shown in Fig. 4. The R AA at low and high p T is consistent with being linearly dependent on p T in the chosen fit ranges, resulting χ 2 /NDF are below unity. While the absolute values of the slopes are very different (note the normalisation), the shape of the centrality dependence of the slope at low p T is remarkably similar to that extracted at high p T . This hints at a close correlation between these two regimes, possibly induced by the geometry or density dependence of parton energy loss on the one hand and collective expansion on the other hand. In peripheral collisions, in particular above 90% centrality, the low p T slope is negative, indicating that the very peripheral events are increasingly softer.
In order to study the shape evolution of R AA in more detail, we compute the ratio of adjacent centrality intervals, as given by Eq. (2). In this way a large part of the global uncertainties as well as of the systematic uncertainties cancel. Fig. 5 presents R +1 versus p T for charged particles at midrapidity in Pb-Pb collisions at √ s NN = 5.02 TeV for 5%-wide centrality classes. As for R AA the peripheral collisions are displayed in colour, with their corresponding global uncertainties, which are significantly smaller than for R AA except for the most peripheral class, denoted around 0.1 on the   abscissa. The ratio is found to be nearly identical for 0-5% central to 70-75% peripheral collisions (14 curves) within 10%. In addition, in this centrality range, the ratio is only slightly p T -dependent, although explained typically by distinct mechanism (radial flow at low p T and energy loss at high p T ). For more peripheral collisions, however, the R +1 changes significantly and reduces to about 0.4 for most peripheral collisions. While the quenching power of the medium apparently only gradually changes for about 75% of the Pb-Pb cross-section, the sudden drop for more than 75% peripheral collisions can hardly be explained by an increase in quenching. The evolution of the R +1 at high p T with centrality is characterized by taking the average R +1 for 8 < p T < 20 GeV/c, shown in Fig. 6. The average is about 1.14, slightly decreasing with decreasing centrality and beyond 75% centrality falls strongly, similar to predictions from HG-PYTHIA. An approximate constant value for R +1 up to about 60% centrality implies an exponential dependence on centrality. Fig. 7 shows the slope of a linear fit to the low momentum region (0.4-1.2 GeV/c) and the high-momentum region (8 < p T < 20 GeV/c) of R +1 . In the chosen fit ranges, the R +1 can be fitted by a linear function with χ 2 /NDF < 1. At low momentum, the slope of R +1 exhibits a mild centrality dependence, related to the reduced strength of radial flow, dropping strongly for peripheral collisions above 80%, as expected from ordering events according to multiplicity. At high momentum, the slope is non-zero, −0.0031 ± 0.0006, and within the uncertainties not dependent on centrality.

Summary
Charged-particle spectra at midrapidity were measured in Pb-Pb collisions at a centre-of-mass energy per nucleon pair of √ s NN = 5.02 TeV and presented in centrality classes ranging from the most central (0-5%) to the most peripheral (95-100%) collisions. Measurements beyond the 90% peripheral collisions at the LHC are presented for the first time. For a consistent treatment of the most peripheral collisions the number of binary collisions was calculated from a Glauber model in intervals of multiplicity rather than in impact parameter (Fig. 1). Possible medium effects were quantified by comparing the measured spectra with those from proton-proton collisions normalized by the number of independent nucleon-nucleon collisions obtained from a Glauber model (Fig. 2). At large transverse momenta (8 < p T < 20 GeV/c), the average R AA increases from about 0.15 in the 0-5% most central collisions to a maximum value of about 0.8 in the 75-85% peripheral collisions, beyond which it strongly falls off to below 0.2 for the most peripheral collisions (Fig. 3). Furthermore, R AA initially exhibits a positive slope as a function of p T in the 8-20 GeV/c interval, while for collisions beyond the 80% class the slope is negative (Fig. 4). The shape of the slope extracted at low p T , within 0.4-1.2 GeV/c, is remarkably similar, indicating that there may be a close correlation between these two regimes.
To reduce uncertainties related to event selection and normalization, the ratio of R AA in adjacent centrality intervals was measured (Fig. 5). Up to about 60% peripheral collisions, this ratio is fairly constant, even as a function of p T . It then starts to decrease and finally, for centralities beyond 75%, it falls off strongly ( Fig. 6) with its slopes at low and high momentum varying only mildly or not at all except for the most peripheral centrality intervals (Fig. 7). The trends observed in peripheral collisions are consistent with a simple PYTHIA-based model without nuclear modification, demonstrating that biases caused by the event selection and collision geometry can lead to an apparent suppression in peripheral collisions. This explains the contradictory and hard to reconcile observation that R AA is below unity in peripheral Pb-Pb, but equal to unity in minimum-bias p-Pb collisions despite similar chargedparticle multiplicities. With a correct treatment of the biases a smooth transition between Pb-Pb and minimum-bias p-Pb collisions is expected without the need to involve parton energy loss in peripheral collisions. Without such treatment, the measurement and interpretation of R AA in peripheral collisions, in particular above 80% centrality, have complications similar to p-Pb collisions, where the observable was named Q pPb [39] to distinguish it from the unbiased nuclear modification factor.