Transverse momentum spectra and nuclear modification factors of charged particles in pp, p-Pb and Pb-Pb collisions at the LHC

We report the measured transverse momentum ($p_{\rm T}$) spectra of primary charged particles from pp, p-Pb and Pb-Pb collisions at a center-of-mass energy $\sqrt{s_{\rm NN}} = 5.02$ TeV in the kinematic range of $0.15<p_{\rm T}<50$ GeV/$c$ and $|\eta|<0.8$. A significant improvement of systematic uncertainties motivated the reanalysis of data in pp and Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV, as well as in p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV, which is also presented. Spectra from Pb-Pb collisions are presented in nine centrality intervals and are compared to a reference spectrum from pp collisions scaled by the number of binary nucleon-nucleon collisions. For central collisions, the $p_{\rm T}$ spectra are suppressed by more than a factor of 7 around 6-7 GeV/$c$ with a significant reduction in suppression towards higher momenta up to 30 GeV/$c$. The nuclear modification factor $R_{\rm pPb}$, constructed from the pp and p-Pb spectra measured at the same collision energy, is consistent with unity above 8 GeV/$c$. While the spectra in both pp and Pb-Pb collisions are substantially harder at $\sqrt{s_{\rm NN}} = 5.02$ TeV compared to 2.76 TeV, the nuclear modification factors show no significant collision energy dependence. The obtained results should provide further constraints on the parton energy loss calculations to determine the transport properties of the hot and dense QCD matter.


Introduction
The properties of hot and dense deconfined QCD matter, the Quark-Gluon Plasma (QGP), which is formed in high-energy heavy-ion collisions, can be characterized by the measurement of high transverse momentum particles produced by hadronisation of hard scattered partons in the early stage of the collision. It is expected that these partons lose energy by interactions with the hot and dense QCD matter, which leads to jet quenching [1]. Manifested also as a suppression of high-p T particles, jet quenching enables the extraction of the properties of the deconfined medium, in particular its transport coefficientq [2].
The modification of high-p T particle production is quantified with the nuclear modification factor R AA , defined as the ratio of the charged-particle p T spectrum in A-A collisions to that in pp collisions scaled by the average number of binary nucleon-nucleon collisions N coll for a given centrality class of A-A collisions, dN AA /dp T N coll dN pp /dp T = dN AA /dp T T AA dσ pp /dp T , where N AA and N pp are the charged-particle yields in A-A and pp collisions and σ pp is the production cross section in pp collisions, respectively. The average nuclear overlap function, T AA = N coll /σ NN inel , which depends on the collision centrality, is determined from the Glauber model of the nuclear collision geometry [3], where σ NN inel is the total inelastic nucleon-nucleon cross section. Over the years, a number of results on R AA have been reported by experiments at the Relativistic Heavy-Ion Collider (RHIC) and at the Large Hadron Collider (LHC). At RHIC, the yields of charged hadrons [4,5] or neutral pions [6] measured in the central Au-Au collisions at √ s NN = 130 and 200 GeV were found to be suppressed by a factor of about 5 in the p T range of 5-25 GeV/c, indicating for the first time strong medium effects on hadron production. The first R AA measurements for charged particles at the LHC [7-10] have shown that in central Pb-Pb collisions at √ s NN = 2.76 TeV the yields are suppressed by a factor of up to 7 for p T = 6-7 GeV/c. For larger p T , the suppression decreases, but remains significant (a factor of about 2) in the range of 30-150 GeV/c.
The first Pb-Pb collisions at √ s NN = 5.02 TeV were delivered by the LHC in 2015. Data in pp collisions at the same energy were also collected by the LHC experiments, allowing for a direct comparison of particle production in pp, p-Pb and Pb-Pb collisions. The first results on charged-particle R AA at √ s NN = 5.02 TeV have recently become available from the CMS Collaboration [11], showing that in central Pb-Pb collisions charged-particle production is suppressed by a factor of 7-8 for p T = 6-9 GeV/c. The suppression continues up to the highest p T measured and approaches unity in the vicinity of p T = 200 GeV/c. Measurements of p-Pb collisions at the LHC were performed to establish whether the initial state of the colliding nuclei plays a role in the observed suppression of high-p T hadron production in Pb-Pb collisions. The R pPb was found to be consistent with unity for p T up to a few tens of GeV/c, indicating that in this domain initial state effects do not influence particle production [12][13][14][15].
In this paper, we report the measurement of transverse momentum spectra of charged particles in pp and Pb-Pb collisions at √ s NN = 5.02 TeV. The resulting p T spectra are used to determine the nuclear modification factors in Pb-Pb collisions at the highest energy currently accessible at the LHC. The p T spectrum measured in pp collisions at the same collision energy as p-Pb is also used as the reference to calculate R pPb . These measurements allow us to compare the particle production in pp, p-Pb and Pb-Pb collisions at the same √ s NN , for the first time with ALICE at the LHC. In addition, we report a reanalysis of data collected in pp and Pb-Pb collisions at √ s NN = 2.76 TeV, and in p-Pb collisions at √ s NN = 5.02 TeV. The reanalysis is warranted by significant improvements in track selection and efficiency corrections, which benefit from the experience accumulated in the past years as well as better knowledge of the particle production at the LHC energies. This leads to significantly-reduced systematic uncertainties by a factor of about 2 as compared to previously published results [8,13,16], which the current analysis supersedes. The increase in √ s NN from 2.76 TeV to 5.02 TeV for Pb-Pb collisions leads to ∼ 20% increase in the particle multiplicity [17] indicating that the larger medium density is reached at the higher collision energy. We characterize this medium by comparing the p T spectra and nuclear modification factors measured at the two energies.

Experiment and data analysis
The data in Pb-Pb and pp collisions at √ s NN = 2.76 TeV and in p-Pb collisions at √ s NN = 5.02 TeV were collected with the ALICE apparatus [18] in 2010, 2011 and 2013, respectively. Details on the ALICE experimental conditions and the detector performance are given in [19]. The data in Pb-Pb and pp collisions at √ s NN = 5.02 TeV were recorded in 2015.

Trigger and event selection
The analysis is based on tracking information from the Inner Tracking System (ITS) [20] and the Time Projection Chamber (TPC) [21], both are located in the central barrel of the experiment and embedded in a solenoidal magnetic field of 0.5 T parallel to its axis.
The minimum-bias (MB) interaction trigger was based on signals from the forward scintillator arrays (V0A and V0C) and the two innermost layers of the ITS, the Silicon Pixel Detector (SPD), in coincidence with two beam bunches crossing in the ALICE interaction region. The pp collisions at √ s = 2.76 TeV were selected requiring a signal in either one of the V0A or the V0C detectors or in the SPD. The Pb-Pb collisions at √ s NN = 2.76 TeV were selected based on different combinations of hits in the SPD and either V0A or V0C detector. The efficiency for hadronic interactions is approximately 100% in the 0-80% centrality range considered in this analysis, see details in [19]. For measurements of pp, p-Pb and Pb-Pb collisions at √ s NN = 5.02 TeV the trigger required a signal in both V0A and V0C detectors.
The offline event selection was optimized to reject beam-induced background in all collision systems. The background events were efficiently rejected by exploiting the timing signals in the two V0 detectors. In Pb-Pb collisions background was also rejected exploiting the correlation between the arrival times measured in each neutron Zero Degree Calorimeter (ZDC), positioned on both sides of the interaction point at 114.0 m for pp and Pb-Pb data at √ s NN = 2.76 TeV and at 112.5 m for the rest data sets. The contamination from electromagnetic interactions in Pb-Pb collisions was strongly suppressed using signals from the ZDCs (see [19] for details).
The primary event vertex is determined with tracks from the central barrel. For the analysis of pp collisions, if no vertex is found using tracks, the vertex reconstruction is performed using SPD tracklets; track segments reconstructed based on the information from the two innermost layers of the ITS. To ensure a uniform acceptance and reconstruction efficiency in the pseudorapidity region |η| < 0.8, only events with a reconstructed vertex within ±10 cm from the center of the detector along the beam direction are used. It corresponds to around 2 standard deviations from the mean of the interaction region distribution (Gaussian shape) determined for all collisions systems and energies.
In Pb-Pb collisions, the centrality quantifies the fraction of the geometrical cross-section of the colliding nuclei, and it is related to their geometrical overlap region. It is determined using the sum of the amplitudes of the V0A and V0C signals [22]. The analysis is limited to the 0-80% most central events, to ensure that effects of trigger inefficiency and contamination by electromagnetic processes [23], as well as possible biases in the selection of more peripheral events [24], are negligible. The average quantities characterizing a centrality class, such as the mean number of participants N part , the mean number of binary collisions N coll or the average nuclear overlap function T AA were obtained [22] by fitting the experimental distributions with a Glauber Monte Carlo model [3], coupled to the model of particle production with f · N part + (1 − f ) · N coll particle sources, each source producing particles according to a Neg-  ative Binomial Distribution (NBD). This approach is inspired by two-component models [25,26], which decompose nucleus-nucleus collisions into soft and hard interactions, where the soft interactions produce particles with an average multiplicity proportional to N part , and the probability for hard interactions to occur is proportional to N coll . The fit parameter f represents the contribution of soft processes to the particle production and amounts to about 0.8 for the two energies. In this calculations, we used an inelastic nucleon-nucleon cross-section σ NN = (67.6 ± 0.6) mb for √ s NN = 5.02 TeV and σ NN = (61.8 ± 0.9) mb for √ s NN = 2.76 TeV, obtained by interpolation [3] of the existing world data.
In p-Pb collisions, the average quantities N part , N coll and T pPb were determined [22] following the procedure described in [27], with the updated inelastic nucleon-nucleon cross-section σ NN = (67.6 ± 0.6) mb at √ s NN = 5.02 TeV and nuclear density function. In order to omit potential biases on the p T spectra related to p-Pb collision centrality determination [27], only p-Pb events in the 0-100% centrality interval were used in the presented analysis.
The number of events satisfying the trigger and offline selection criteria for various collision systems and energies are listed in Table 1.

Track selection
Primary charged particles are measured in the kinematic range |η| < 0.8 and 0.15 < p T < 50 GeV/c. A primary charged particle is defined [28] to be a charged particle with a mean proper lifetime τ larger than 1 cm/c which is either produced directly in the interaction, or from decays of particles with τ smaller than 1 cm/c, excluding particles produced in interactions with the detector material. The trackselection criteria were identical for all data sets and were optimized for best track quality and minimal contamination from secondary particles. Each track is required to have: -at least 2 hits in the ITS detector, of which at least one hit is in the two innermost (SPD) layers; -the length L (in cm) of its projection curve calculated in the TPC readout plane, excluding the information from the pads at the sector boundaries (∼ 3 cm from the sector edges), larger than A − B · p C T , with A = 130 cm, B = 1.0 cm · (GeV/c) −C , C = −1.5 and p T in units of GeV/c; -the number of crossed TPC pad rows larger than 0.85·L (the height of pad rows varies from 7.5 mm to 15 mm [21]); a TPC readout pad row is considered crossed if there is a cluster in this row and in any of its neighboring 2 rows; -the number of TPC clusters (one cluster per pad row) larger than 0.7 · L; -the ratio of crossed TPC pad rows to the number of findable TPC clusters (maximum number of clusters which can be assigned to a track in the TPC fiducial volume, excluding the information from the pads at the sector boundaries) larger than 0.8; -the fraction of TPC clusters shared with another track lower than 0.4; -the fit quality for the ITS and TPC track points satisfying χ 2 ITS /N hits < 36 and χ 2 TPC /N clusters < 4, respectively; χ 2 TPC−ITS < 36, where χ 2 TPC−ITS is calculated comparing the track parameters of the helix fit from the combined ITS+TPC track reconstruction to that derived only from the TPC and constrained by the interaction point, see details in [8]; -the distance of closest approach to the primary vertex in the transverse plane |DCA xy | < A + B · p C T , with A = 0.0182 cm, B = 0.035 cm · (GeV/c) −C , C = −1.0 and p T in units of GeV/c; and along the beam axis |DCA z | < 2 cm.

Corrections
The data are presented as differential cross sections for inelastic (INEL) pp collisions and transverse momentum spectra for non-single diffractive (NSD) p-Pb and centrality-selected INEL Pb-Pb collisions 1 N ev which are obtained by correcting the charged particle yields N rec reconstructed in the (∆η, ∆p T ) intervals for all detector effects that either influence the event reconstruction, and thus are relevant only for the overall normalization (event-level corrections), or influence the track reconstruction and are relevant for both the spectral shape and normalization (track-level corrections). The ε MB and ε VZ denote the MB trigger and event vertex reconstruction efficiencies, and C(∆η, ∆p T ) are track-level correction factors. One should note that the ε VZ is calculated for the triggered events. In general, both the ε MB and ε VZ are multiplicity dependent. Details of the correction procedure and variables are described in the following.

Event-level corrections
In Eq. 2 the minimum-bias cross section σ pp MB in triggered pp collisions is determined by the van-der-Meer scans and depends on the trigger settings, it was measured to be 55.4 ± 1.0 mb at √ s = 2.76 TeV [29] and 51.2 ± 1.2 mb at √ s = 5.02 TeV [30], with the MB trigger OR (V0A or V0C or SPD) and AND (V0A and V0C), respectively. The differential charged-particle yields d 2 N/dηdp T were calculated for the MB event class N MB ev by normalizing to the number of reconstructed events N rec ev , which have a reconstructed event vertex within ±10 cm from of the center of the detector and correcting for the event vertex reconstruction efficiency ε VZ .
For NSD p-Pb collisions, the efficiency of the trigger (ε MB ) and event vertex reconstruction (ε VZ ), as in Eq. 3, were estimated using GEANT3 detector simulation with a combination of event generators as described in [12]. The obtained values ε MB = 99.2% and ε VZ = 98.6% were used for corrections.
For Pb-Pb collisions, the trigger and event vertex reconstruction is fully efficient for the centrality intervals considered in this work, as estimated using Monte Carlo simulations with GEANT3 and HIJING [34] as event generator.

Track-level corrections
The differential charged-particle yields d 2 N/dηdp T (Eqs 2 and 3) are obtained from the reconstructed yields of tracks N rec (∆η, ∆p T ) corrected using correction factors C(∆η, ∆p T ), which are products of acceptance, efficiency, purity and p T resolution. The efficiency and purity of the primary charged particle reconstruction as well as acceptance correction for the pp, p-Pb and Pb-Pb data are calculated using Monte Carlo event generators with GEANT3 detector modeling combined with data-driven corrections, which are discussed in detail in the following sections.
Tracking efficiency The efficiency of the primary charged particle reconstruction is shown in Fig. 1 (left). While the low efficiency at low p T is related to the strong track curvature caused by the magnetic field and to the energy loss in the detector material, the characteristic shape around p T of 1 GeV/c is caused primarily by the track length requirement. Tracks in this momentum range are more likely to cross the TPC sector boundaries and are thus reconstructed with lower efficiencies. The asymptotic value reached at high p T reflects the acceptance limitations (detector boundaries and active channels) of the measurement.
The tracking efficiency depends on particle species, as can be seen in Fig. 1 (left), and was calculated using a detector simulation with the PYTHIA 8 (Monash 2013 tune) event generator and the GEANT3 transport code. The efficiency is particularly species-dependent at low p T (below 0.5 GeV/c) due to differences in ionization energy loss in the detector material, hadronic interaction cross-section or decay probability.
A particular case is that of charged hyperons, for which the reconstruction efficiency is very low and essentially negligible below 10 GeV/c, due to the fact that they decay before any significant interaction with the detector. For higher p T , they reach the detector and can be observed with increasing efficiency. One should note that the reconstruction efficiency is different for the Σ + and Σ − hyperons in the p T range considered, because of their different lifetimes. The tracking efficiency for other primary charged particle species, including electrons, muons and Ξ and Ω hyperons (denoted as "Rest") is also shown.
In order to reduce statistical fluctuations at high p T , we parameterized the efficiency above p T = 1 GeV/c for each particle species. Each parameterization is a combination of the universal (independent of particle species) function f (p T ) = a (1 − b · e −cp T ) and the survival probability P(p T ) = e −d·m/p T ·τ that a particle with the mass m and a mean proper lifetime τ survives a minimal distance d before decaying. The fitting parameters (a, b and c) are determined from the fit to the efficiency calculated as an average of efficiencies for stable particles. The calculations were performed for d = 200 cm, corresponding to the minimum track length in the ITS and the TPC required in the analysis.
The parametrized efficiencies shown in Fig. 1 (left) were used to determine data-driven correction factors in the efficiency rewieghting procedure, which is discussed below. Reweighting with measured particle composition The experimental knowledge of the primary particle composition has significantly improved recently at the LHC [35 -44], which allows for a precise determination of the tracking efficiency. For the first time, we determined the tracking efficiency by reweighting the primary particle composition based on data driven method.
In the right panel of Fig. 1 [38,39]. In particular, the Σ + (1385) and Σ − (1385) hyperons and their antiparticles are underestimated by a factor of 2-3 in the recent PYTHIA 8 tunes. The p T spectra of Σ ± hyperons have not been measured. Therefore, the p T spectra of Σ ± are approximated using the measured spectrum of Λ hyperons [37] scaled by the ratio of Σ ± to Λ hyperons from the Monte Carlo generator.
Relative particle abundances measured in pp collisions at √ s = 7 TeV are used to reweight the tracking efficiency determined for √ s = 2.76 and 5.02 TeV collision energies, based on the experimental knowledge that their energy dependence is weak [37]. The relative abundance of other particle species containing electrons, muons and Ξ and Ω hyperons (denoted "Rest" in Fig. 1) is taken from simulations without further modification and has only a small influence on the final result (< 1%). The measured p T spectra of kaons, protons and Λ are extrapolated down to p T = 0.15 GeV/c using a parameterization proposed by Bylinkin and Rostovtsev [45]. For high p T , beyond the reach of the identified particle measurement, the relative abundances are assumed to be independent of p T , as motivated by pQCD [46].
The reweighting of the efficiency has also been applied in the analysis of p-Pb and Pb-Pb data. The relative particle abundances obtained from Monte Carlo simulations with DPMJET (p-Pb) [47] and HIJING (Pb-Pb) event generators are reweighted using ALICE measurements of identified particle species (pions, kaons, protons and Λ hyperons) for p-Pb collisions at √ s NN = 5 TeV [36, 40] and Pb-Pb collisions at √ s NN = 2.76 TeV [41-44]. The relative particle abundances at low p T are determined by extrapolating the measured p T spectra of kaons, protons and Λ hyperons down to p T = 0.15 GeV/c using a blast-wave parameterization [48]. As in the pp case, for p T beyond the reach of these measurements, the relative abundances are assumed to be independent of p T .
In the left panel of Fig. 2 the combined tracking efficiency and acceptance obtained from MC simulations (open symbols) and after reweighting (full symbols) is shown as a function of p T for pp, p-Pb, and central (0-5%) and peripheral (70-80%) Pb-Pb collisions. The effect of the reweighting on the efficiency corrections is shown in the bottom panel. It amounts to a difference of about 7% at p T around 3 GeV/c for the most central Pb-Pb collisions, and is lower in peripheral Pb-Pb collisions, p-Pb and pp collisions. When comparing central to peripheral Pb-Pb collisions, the importance of an increasing radial flow that shifts the heavy Σ ± baryons to larger momenta becomes apparent.
Purity The contribution from secondary particles, i.e. products of weak decays of kaons, Λ hyperons and muons, and particles arising from interactions in the detector material, was estimated using the transverse impact parameter d xy distributions of particles in data and Monte Carlo simulations. Exploiting the differences, especially in the tails, of the d xy distributions between primary and secondary particles, the measured distributions were fitted by a linear combination of d xy distributions (templates) for primary and secondary particles obtained from the Monte Carlo simulations in different p T bins (as described in more detail in [41]). The effect of this data-driven correction, shown in the bottom panel of Fig. 2 (right), depends on p T and is different for pp, p-Pb and Pb-Pb collisions. The resulting contamination with secondary particles, i.e. the fraction of secondary particles in the sample of selected particles, ranges from 8.5% in pp to 20% in central Pb-Pb collisions at p T = 0.15 GeV/c and decreases to around 1.0% for p T > 5 GeV/c, as shown in the upper panel of Fig. 2 (right).
Transverse momentum resolution The transverse momentum of charged particles is reconstructed from the track curvature measured in the ITS and the TPC (see [19] for details). The modification of the spectra arising from the finite momentum resolution is estimated from the error obtained from the corresponding covariance matrix element of the Kalman fit. The relative p T resolution, σ (p T )/p T , depends on momentum and is approximately 3-4% at p T = 0.15 GeV/c, has a minimum of 1.0% at p T = 1.0 GeV/c, and increases linearly for larger p T , approaching 3-10% at 50 GeV/c, depending on collision energy, system or Pb-Pb centrality interval. The p T resolution has been verified by studying the  widths of the invariant mass distributions of K 0 s reconstructed from their decays to two charged pions. To account for the finite p T resolution, correction factors to the spectra were determined based on the Bayesian unfolding approach [49] implemented in the RooUnfold package [50]. This unfolding is based on the response matrix, R det m,t , which relates the measured spectrum M m and the true spectrum T t , M m = R det m,t · T t , where m and t are indices indicating the bin number. The response matrix was generated for each data set and Pb-Pb collision centrality using GEANT3 detector simulations with different Monte-Carlo generators. For p T > 10 GeV/c, another unfolding procedure similar to what was done in previous work [16] was also used.
The correction factors depend on the collision energy and system as well as on the collision centrality, due the change of the spectral shape. For momenta below 10 GeV/c, the corrections are significant only in the first momentum bin p T = 0.15-0.2 GeV/c, and reach 3%(2.5%) for pp(Pb-Pb) at √ s NN = 2.76 TeV, 3% for p-Pb at √ s NN = 5.02 TeV and around 1% for pp(Pb-Pb) at √ s NN = 5.02 TeV. At low p T , these corrections are independent of Pb-Pb collision centrality. For p T > 10 GeV/c, both unfolding methods yield almost identical correction factors. For √ s NN = 5.02 TeV, the correction factors reach 5%, 1.5% and 3% (4%) at p T = 50 GeV/c for pp, p-Pb and 0-5%(70-80%) central Pb-Pb collisions, respectively. For √ s NN = 2.76 TeV, they amount to 4% for pp and 4% (8%) for 0-5%(70-80%) central Pb-Pb collisions at the highest p T . The resulting p T -dependent correction factors are applied (bin-by-bin) to the measured p T spectra.
Trigger and vertex selection The event selection (trigger and vertex) introduces a small p T -dependence in the correction on the p T spectra in pp collisions. This is due to the fact that the low-multiplicity pp events, which are also characterized by a softer spectrum, are mostly rejected by the trigger and vertex selection criteria. The effect on the p T spectra was calculated from simulations with the PYTHIA 8 (Monash 2013 tune) and the PYTHIA 6 (Perugia2011 tune) event generators and was estimated to be around 0.4-0.6% (2.2-2.6%) for p T < 1 GeV/c at √ s = 2.76 (5.02) TeV. The spectra are corrected by the average bias of these two generators, resulting in 0.5% (2.4%) corrections to the spectra.
Acceptance correction for the p-Pb data The two-in-one magnet design of the LHC imposes the same magnetic rigidity of the beams in the two rings. The configuration for p-Pb collisions with pro-tons at 4 TeV energy colliding with 208 82 Pb ions at 82×4 TeV results in a shift in the rapidity of the nucleon-nucleon center-of-mass system by ∆y NN = 0.465 in the direction of the proton beam (negative z-direction). Therefore the detector coverage |η lab | < 0.8 corresponds to roughly −0.3 < η cms < 1.3. For massless or high p T particles, η cms = η lab + y NN but the differential yield of non-massless particles at low p T suffers from a distortion, which is estimated and corrected for based on the HIJING event generator weighted by the measured relative particle abundances [36,40]. For p T = 0.5 GeV/c the correction is 2% for −0.3 < η cms < 1.3.

Systematic uncertainty
The relative systematic uncertainties on the p T spectra are summarized in Table 2.
-The effect of the selection of events based on the vertex position is studied by comparing the fully corrected p T spectra obtained with alternative vertex selections corresponding to ±5 and ±20 cm.
-The systematic uncertainties related to the track selection criteria (listed above) were studied by varying the track quality cuts. In particular, we varied the upper limits of the track fit quality parameters in the ITS (χ 2 ITS /N hits ) and the TPC (χ 2 TPC /N clusters ) in the ranges of 25-49 and 3-5, respectively. The systematic uncertainties related to high-p T fake tracks [8] were estimated by modifying the upper limits of the track matching criteria given by the χ 2 TPC−ITS in the range of 25-49. The resulting uncertainty dominates at high p T for all collision systems.
-The systematic uncertainty on the secondary-particle contamination (Fig. 2, right) includes contributions from the template fits to the measured impact parameter distributions. We have varied the fit model using templates with two (primaries, secondaries) or three (primaries, secondaries from material, secondaries from weak decays of K 0 s and Λ) components, as well as the fit ranges. The maximum difference between the data and the 2 component-template fit is summed in quadrature with the difference between results obtained from the 2 and the 3 component-template fits and result is assigned as the systematic uncertainty on the contamination. This contribution dominates for the lowest p T independently of the collision system.
-The systematic uncertainty on the primary particle composition consists of several contributions, including the extrapolation of the spectra to low p T , the approximation of the relative particle abundances at high p T , the efficiency parameterization at high p T , the uncertainties of the measured particle spectra and the MC assumptions on the Σ ± /Λ spectra ratios. For the extrapolation to low p T , we have studied different parameterizations (Bylinkin and Rostovtsev, modified Hagedorn [51], Blast-Wave) and fit ranges. We have varied the p T thresholds for the approximation of the relative particle abundances as well as the efficiency parameterization at high p T . The measured particle spectra were varied within systematic uncertainties (one particle species at a time), and the resulting differences to the nominal spectra were added in quadrature to the systematic uncertainties. We have also assigned an additional uncertainty related to the different spectral shape of Σ ± and Λ from the MC generators.
-To account for the imperfect description of the experimental setup in simulations, we compared the track matching between the TPC and the ITS information in data and Monte Carlo after scaling of the fraction of secondary particles obtained from the fits to the d xy distributions. After rescaling the fraction of secondary particles, the agreement between data and Monte Carlo is within 4%. This value is assigned as an additional systematic uncertainty.
-The systematic uncertainty on the p T resolution at low p T (only first p T bin) was estimated by changing Monte-Carlo generators in the unfolding procedure. The pp collisions were simulated with PYTHIA and PHOJET, p-Pb collisions with HIJING and DPMJET, and Pb-Pb collisions with HIJING and AMPT [52]. The average correction factor of two generators was assigned as systematic uncertainty. At low p T , we observe a weak dependence of correction factors on the considered Monte-Carlo generators. The resulting uncertainties amount to 3%(2.5%) for pp(Pb-Pb) collisions at √ s NN = 2.76 TeV, to 3% for p-Pb collisions at √ s NN = 5.02 TeV, and to 1% for pp and Pb-Pb collisions at √ s NN = 5.02 TeV. The systematic uncertainty on the p T resolution at high p T (> 10 GeV/c) was estimated using the azimuthal angle dependence of the 1/p T spectra for positively and negatively charged particles. The relative shift of the spectra for oppositely charged particles along 1/p T determines the size of uncertainty for a given angle. We used the RMS of the 1/p T shift distribution for the full azimuth as additional smearing of the p T resolution. We checked that these shifts are due to detector effects (such as E × B effect) and are not related to the physics of hadronic interaction in GEANT3. To take into account the decrease in the p T resolution with increasing interaction rate, we have studied the systematic uncertainty for the pp and Pb-Pb data sets at √ s NN = 5.02 TeV, obtained from the difference of the spectra at high and low interaction rate. The uncertainty is negligible for pp collisions, and is about 1% for Pb-Pb collisions.
-For the correction due to the trigger and vertex selection, calculated as the average bias of two generators, half of the value is assigned as systematic uncertainty.
-The systematic uncertainty for the acceptance correction on the p-Pb data was estimated by varying the relative particle abundances within their measured uncertainties and by changing the fit function for the low-p T extrapolation. The uncertainty is sizable only at low p T where it reaches 0.2%.
-The material budget in the simulation was varied by ±4.5% [19], resulting in the systematic uncertainty in the range of 0.1-0.9%.
-The normalization uncertainty on the spectra in pp collisions was propagated from the cross section measurements.
-The systematic uncertainties related to 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 and by a comparison of results obtained using the SPD detector to estimate centrality as opposed to the V0A and V0C.
For the evaluation of the total systematic uncertainty all contributions are considered to be uncorrelated and they are summed in quadrature. The improved reconstruction and track selection in the reanalysis of pp and Pb-Pb data at √ s NN = 2.76 TeV and p-Pb data at √ s NN = 5.02 TeV lead to significantly reduced systematic uncertainties by a factor of about 2 as compared to previously published results [8, 13, 16].

Spectra
The fully corrected p T spectra of primary charged particles measured in INEL pp and Pb-Pb collisions at √ s NN = 2.76 TeV and 5.02 TeV and in NSD p-Pb collisions at √ s NN = 5.02 are shown in Fig. 3. The Pb-Pb spectra are presented in nine centrality classes. For pp collisions, the p T -differential cross sections are divided by the corresponding inelastic nucleon-nucleon cross section at √ s = 2.76 (61.8 mb) and 5.02 TeV (67.6 mb) [3], respectively. The relative systematic uncertainties for the various datasets are shown in the bottom panels. Substantial improvements in track selection and efficiency corrections have been achieved. However the uncertainty on the pp data at √ s NN = 2.76 TeV is still larger than for the data at √ s NN = 5.02 TeV due to larger number of inactive channels in the SPD [19], which affects the track reconstruction and the determination of the secondary particle contribution. In Pb-Pb collisions the shape of the p T spectrum varies strongly with collision centrality. For peripheral collisions, the spectral shape is similar to that measured in pp collisions as well as to the spectrum in p-Pb collisions. With increasing collision centrality, a marked depletion of the Pb-Pb spectra develops for p T > 5 GeV/c. These measurements supersede our previous results [8, 13, 16], which allows for a better discrimination between jet quenching scenarios. Figure 4 compares the measured p T spectra in pp collisions with results from PYTHIA 8 (Monash-2013 tune), including colour reconnection, and EPOS LHC [53], which incorporates collective (flow-like) effects. These event generators show a similar description of the p T spectra at both energies. They reproduce the spectral shape within 20%. Figure 5 shows the ratios of p T spectra measured at √ s NN = 5.02 and √ s NN = 2.76 TeV in Pb-Pb and pp collisions. The ratios for Pb-Pb collisions are determined in nine centrality classes ranging from 0-5% (top-left) to the 70-80% (bottom-right). As indicated by the ratios, the p T spectra measured at higher collision energy are significantly harder for both Pb-Pb and pp collision systems. One can see that there is a similar energy dependence of the ratio for peripheral (70-80%) Pb-Pb and in pp collisions, while towards central Pb-Pb collisions a gradual reduction of the ratio is apparent.

Nuclear modification factors
In order to quantify in-medium modification of charged-particle transverse momentum spectrum, the nuclear modification factors are determined. Figure 6 shows the R AA for Pb-Pb collisions measured at

√
s NN = 2.76 and 5.02 TeV. The nuclear modification factor has a strong centrality dependence, and is very similar in magnitude for the two collision energies.
Given that the p T spectra are harder at the higher √ s NN (see Fig. 5) and that the medium density increases with √ s NN by ∼ 20% [17], this similarity of the R AA may indicate a larger parton energy loss in the hotter/denser and longer-lived deconfined medium produced at the higher center-of-mass energy. Assuming that the initial parton p T spectrum, parton distribution and fragmentation functions are not significantly modified by the energy increase, and that the parton energy loss in expanding medium is sublinear to the medium density increase, we would expect larger energy loss at √ s NN = 5.02 TeV than at √ s NN = 2.76 TeV, but no more than 20%.
In 0-5% central collisions the yield is suppressed by a factor of about 8 (R AA ≈ 0.13) at p T = 6-7 GeV/c. Above p T = 7 GeV/c, there is a significant rise of the nuclear modification factor, which reaches a value of about 0.4 for our highest p T bin, 30-50 GeV/c. In peripheral collisions (70-80%), the suppression is 30% for intermediate momenta and approaches unity for the highest p T bin. The normalization uncertainties for R AA originate from the pp measurement and centrality determination and were added in quadrature.
Figure 7 (left) shows the R pPb factor compared to R AA measured in the 0-5% and 70-80% centrality classes for Pb-Pb collisions at √ s NN = 5.02. The R pPb factor exhibits a maximum for the intermediate p T range, 2 < p T < 6 GeV/c, a feature generically called the Cronin effect [54]. A study on its dependence on the particle species [40] suggested that protons are responsible for the observed maximum. The maximum occurs at values of p T (3-5 GeV/c) larger than the maximum of R AA seen in the p T range  1.5-3 GeV/c. The R pPb factor is consistent with unity for p T 8 GeV/c, demonstrating that the strong suppression observed in central Pb-Pb collisions is not related to initial state effects but rather to the formation of hot and dense QCD matter. The ALICE results for R AA and R pPb measured at √ s NN = 5.02 TeV are compared to measurements by CMS [14] in Fig. 7 (right). Agreement within 1.5σ is observed for both R AA and R pPb taking into account the current uncertainties.

Comparison with theoretical models
In Fig. 8 the measured R AA for 0-5% central collisions at √ s NN = 5.02 TeV is compared to model predictions. All presented models are based on the pQCD factorization, where the entire effect of energy loss is encoded in the medium-modified parton fragmentation function. All models include radiative energy loss based on different approaches. The model by Djordjevic et al. [57,58] and CUJET 3.0 [60,61] include in addition collisional energy loss. The energy loss is calculated in dynamically expanding medium in all models except that of Vitev et al. [55,56], in which the medium is composed of static scattering centers. In the following, the models are discussed in more detail.
The calculations by Vitev et al. are based on the SCET G model [55,56], which uses an extended softcollinear effective theory to describe inclusive particle production and suppression in the heavy-ion environment. This theoretical framework provides an analytic connection between generalized DGLAP evolution equations for the fragmentation functions in dense strongly-interacting matter and parton energy loss for hard processes. The calculations employ the pQCD-based hard cross section and QGP medium evolved parton-to-hadron fragmentation functions, combined with initial-state cold nuclear mat- ter (CNM) effects, which include dynamical nuclear shadowing, the Cronin effect and initial-state parton energy loss (see [56] and references therein for details). The two upper and lower curves represent calculations for the nuclear modification factor with variations of the coupling strength g = 1.9 ± 0.1 between the jet and the medium, which is a free parameter in the calculations. Djordjevic et al. [57,58] use a dynamical energy loss formalism based on pQCD calculations in a finite size dynamical QCD medium. While the initial p T spectrum is the same as that used in the SCET G model, the dynamical description of the medium provides a consistent treatment of both radiative and collisional energy loss, including a finite magnetic screening mass, which modifies the gluon self energy and therefore changes the energy loss, as well as a running coupling constant for the strongly-interacting medium. The two curves correspond to different electric-to-magnetic screening mass ratios in the range 0.4 < µ M /µ E < 0.6. The model of Bianchi et al. [59] uses the pQCD factorization scheme with a pQCD-based radiative energy loss in a hydrodynamically expanding medium. In this framework, high p T hadrons arise from fragmentation of hard partons, which lose energy prior to hadronization via interactions with the medium. The amount of energy loss is regulated by the medium transport coefficientq, which varies with the temperature-dependent entropy density of the medium as well as with the energy scale of jets propagating in the medium. The CUJET 3.0 model [60,61] is an extension of the perturbative-QCD-based Pb-Pb collisions at the LHC. The calculations by Andrés et al. [62] use the jet quenching formalism of quenching weights. This approach consists of fitting a K factor, defined as K ≡q/2ε 3/4 , that quantifies departure of this parameter from the perturbative estimate,q ideal ∼ 2ε 3/4 [63], where the local energy density ε is taken from a hydrodynamical model of the medium. The K factor is the only free parameter in the fit of nuclear modification factors. Without including new data at √ s NN = 5.02 TeV in the fit procedure, they predict a ∼ 15% larger suppression at √ s NN = 5.02 TeV as compared to √ s NN = 2.76 TeV, assuming the same value of K as the one obtained from the fit to the data at the lower energy.
All models presented here describe the main features of the data. The models by Vitev et al., Djordjevic et al. and CUJET 3.0 give quantitatively good description of the data. The model by Bianchi et al. is consistent with data within 1.5σ while that by Andrés et al. underestimates the data at high p T . However, one should note that this comparison is made between unbinned theory calculations and binned data in relatively large p T bins, which might introduce additional uncertainty.

Summary
In summary, we measured the primary charged particle p T spectra in pp and Pb-Pb collisions at √ s NN = 5.02 TeV. We also reanalyzed the data collected in pp and Pb-Pb collisions at √ s NN = 2.76 TeV as well as in p-Pb collisions at √ s NN = 5.02 TeV with the revised techniques. Thanks to an improved reconstruction, track selection and data-driven efficiency correction procedure we were able to reduce the systematic uncertainties by a factor of ∼ 2 as compared to previously published ALICE results. The measured spectra were used to determine the nuclear modification factors R pPb and R AA . The nuclear modification factor in p-Pb collisions is consistent with unity at high p T , showing that the strong suppression observed in Pb-Pb is not due to CNM effects but rather due to final state partonic energy loss in the hot and dense QGP created in Pb-Pb collisions. This suppression is weak in peripheral collisions and increases with centrality reaching a value of R AA = 0.13 at p T = 6-7 GeV, indicating an increasing parton energy loss with centrality. This suppression is found to be similar at √ s NN = 2.76 and 5.02 TeV, despite the much harder p T spectrum at the top energy, which may indicate a stronger parton energy loss         [15] ATLAS Collaboration, G. Aad et al., "Transverse momentum, rapidity, and centrality dependence of inclusive charged-particle production in √ s NN = 5.02 TeV p+Pb collisions measured by the ATLAS experiment," Phys. Lett. B763 (2016) 313-336, arXiv:1605.06436 [hep-ex].