Charged-particle production as a function of the relative transverse activity classifier in pp, p–Pb, and Pb–Pb collisions at the LHC

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Charged-particle production as a function of the relative transverse activity classifier in pp, p–Pb, and Pb–Pb collisions at the LHC © CERN, for the beneft of the ALICE Collaboration. Article funded by SCOAP3 . Published version ALICE Collaboration ALICE Collaboration. (2024). Charged-particle production as a function of the relative transverse activity classifier in pp, p–Pb, and Pb–Pb collisions at the LHC. Journal of High Energy Physics, 2024(1), Article 56. https://doi.org/10.1007/JHEP01(2024)056 2024 JHEP01(2024)056 Published for SISSA by Springer Received: October 17, 2023 Accepted: December 20, 2023 Published: January 11, 2024 Charged-particle production as a function of the relative transverse activity classifier in pp, p–Pb, and Pb–Pb collisions at the LHC The ALICE collaboration E-mail: [email protected] Abstract: Measurements of charged-particle production in pp, p–Pb, and Pb–Pb collisions in the toward, away, and transverse regions with the ALICE detector are discussed. These regions are defined event-by-event relative to the azimuthal direction of the charged trigger particle, which is the reconstructed particle with the largest transverse momentum ( ptrig T ) in the range 8 < ptrig T< 15 GeV /c . The toward and away regions contain the primary and recoil jets, respectively; both regions are accompanied by the underlying event (UE). In contrast, the transverse region perpendicular to the direction of the trigger particle is dominated by the so-called UE dynamics, and includes also contributions from initial- and final-state radiation. The relative transverse activity classifier, RT = NT ch/⟨NT ch⟩ , is used to group events according to their UE activity, where NT ch is the charged-particle multiplicity per event in the transverse region and ⟨NT ch⟩ is the mean value over the whole analysed sample. The energy dependence of the RT distributions in pp collisions at √s = 2 . 76, 5.02, 7, and 13 TeV is reported, exploring the Koba-Nielsen-Olesen (KNO) scaling properties of the multiplicity distributions. The first measurements of charged-particle pT spectra as a function of RT in the three azimuthal regions in pp, p–Pb, and Pb–Pb collisions at √sNN = 5.02 TeV are also reported. Data are compared with predictions obtained from the event generators PYTHIA 8 and EPOS LHC. This set of measurements is expected to contribute to the understanding of the origin of collective-like effects in small collision systems (pp and p–Pb). Keywords: Hadron-Hadron Scattering , Hard Scattering, Multi-Parton Interactions ArXiv ePrint: 2310.07490 Open Access, Copyright CERN, for the benefit of the ALICE Collaboration. Article funded by SCOAP3. https://doi.org/10.1007/JHEP01(2024)056 JHEP01(2024)056 Contents 1 Introduction 1 2 Analysis procedure 4 2.1 Event and track selection 4 2.2 Corrections 6 2.3 Bayesian unfolding of the multiplicity distributions 6 2.4 Unfolding of the pTspectra as a function of RT8 2.5 Systematic uncertainties 8 3 Results and discussion 11 3.1 Energy dependence of the relative transverse activity classifier 11 3.2 Transverse momentum spectra as a function of the relative transverse activity classifier 12 3.3 Average transverse momentum and integrated yield as a function of the relative transverse activity classifier 15 4 Conclusion 17 The ALICE collaboration 23 1 Introduction In proton-proton (pp) collisions in which a partonic scattering with large momentum transfer occurs, along with the particles originating from the hadronisation of the parton showers initiated by the hard-scattered partons (jets), also lowpT particles from proton break-up (“proton remnants”) and multi-parton interactions (MPI), are produced [ 1 ]. This collection of lowpT particles is termed as underlying event (UE). Understanding and accurate modelling such components is important to ensure a proper description of particle production in nuclear collisions. To this end, the kinematic region containing the fragmentation products of the main partonic scattering needs to be separated from the remaining UE part [ 2 ]. Experimentally, it is impossible to uniquely separate the UE from the event-by-event hard scattering process. However, the UA1 experiment in proton-antiproton collisions at CERN perfomed the first study of this kind by measuring the transverse energy density outside the leading jet, which is also known as jet pedestal region [ 3 – 5 ]. Another approach based on the definition of three distinct topological regions was introduced by the CDF Collaboration [ 6 ]. The three topological regions are defined from the angular difference between the trigger and associated particles, | ∆ φ| = φassoc −φtrig , where φtrig and φassoc refer to the value of the azimuthal angle for the trigger particle and for associated particles in the event, respectively [ 7 ]. The trigger particle is the one with the largest transverse momentum ( ptrig T ) in the event, and the rest are termed as associated particles. The criteria for the definition of the different topological regions are depicted in figure 1. The toward region ( | ∆ φ|< π/ 3) contains the – 1 – JHEP01(2024)056 main jet while the away region ( | ∆ φ|> 2 π/ 3) may involve the fragments of the recoil jet. In general, these two regions are less sensitive to the UE. In contrast, the transverse region ( π/ 3 <| ∆ φ|< 2 π/ 3) is less affected by contributions from the hard scattering. However, this region is expected to contain particles from initial- and final-state radiation (ISR and FSR) [ 6 ]. Moreover, the multiplicity density in the transverse region in events with jets is known to be about twice the multiplicity density in minimum bias collisions due to a centrality bias induced by the presence of a hard scattering, which restricts the impact parameter fluctuations [ 7 ]. Recently, data at high multiplicity from pp collisions at RHIC [ 8 ] and from pp and p–Pb collisions at the LHC [ 9 , 10 ] have shown striking similarities with heavy-ion data, such as collectivity and strangeness enhancement, which could be explained by the formation of a strongly-coupled quark-gluon plasma (sQGP) [ 11 , 12 ]. In order to understand the origin of these collective-like effects in pp collisions, it is important to use observables sensitive to them and compare the data with models such as PYTHIA 8 [ 13 ] and EPOS LHC [ 14 ]. In PYTHIA 8, mechanisms like colour reconnection [ 15 ], rope hadronisation [ 16 ], and string shoving [ 17 ] can produce effects resembling those from a collective behaviour, while the core-corona approach implemented in EPOS LHC, including a collective expansion for the core, can describe some aspects of the data in pp and p–Pb collisions. Despite the similarities between the results from small collision system (pp and p–Pb collisions) and heavy-ion collisions, one of the major difficulties in getting a clear picture is to understand the selection biases and autocorrelation effects in different collision systems. By selecting a high event activity (high particle multiplicity) in small collision system, the event sample is naturally biased towards hard processes [ 7 ]. To overcome such selection biases and get an insight on how these biases affect the charged-particle pT spectra, the transverse region can be used to build a new event classifier, RT , which is expected to have low sensitivity to the hard processes [ 18 ]. The relative transverse activity classifier, RT , is the ratio of the primary charged-particle multiplicity in the transverse region ( NT ch ) obtained event-by-event to the average value ( ⟨NT ch⟩ ) [ 7 , 18 ]. It is defined as RT=NT ch ⟨NT ch⟩.(1.1) Although the purpose of RT is to quantify the UE activity of the events, it can still be influenced by jet fragments, especially for events with high RT values in experiments with limited acceptance [ 19 , 20 ]. For small systems, RT can help to reveal whether the properties of events with lower UE contribution (“low-UE”) are compatible with equivalent measurements in e + e − collisions (jet universality), and whether the scaling behaviour of events with higher UE contribution (“high-UE”) exhibits properties of non-trivial soft-QCD dynamics, such as colour reconnection or other phenomena [ 18 , 21 , 22 ]. The event classifier RT has been recently used in the analysis of identified charged-particle production in pp collisions at √s = 13 TeV at the LHC [ 23 ]. In this paper, RT is used for the first time for p–Pb and Pb–Pb collisions as well as pp collisions at lower centre-of-mass energies. The application of RT to p–Pb and Pb–Pb data would provide a new set of multidimensional measurements, which can serve to improve the theoretical modelling of the complex interplay of hard and soft QCD processes across system sizes. This is particularly relevant for the new developments in PYTHIA 8 [ 24 ]. – 2 – JHEP01(2024)056 Figure 1. Schematic representation of the toward, transverse, and away regions in the azimuthal plane with respect to the leading particle, i.e.the particle with the highest pT in the event. Figure taken from ref. [2]. The energy dependence of the RT distributions in pp collisions at centre-of-mass energies √s = 2 . 76, 5.02, 7, and 13 TeV is studied in this paper, exploring the KNO [ 25 ] scaling of the multiplicity distributions in the transverse region [ 21 ]. The KNO scaling is the hypothesis that at high √s the probability distributions P ( n )of producing n particles in a certain collision process should exhibit the scaling relation P(n) = 1 ⟨n⟩Ψn ⟨n⟩,(1.2) with ⟨n⟩ being the average multiplicity. This means that after scaling with ⟨n⟩ , measured P ( n )at different energies collapse onto a universal function Ψ[ 26 ]. The KNO scaling is expected in models which assume that a single pp collision is merely a superposition of a given number of elementary partonic collisions emitting particles independently [ 27 ]. Therefore, multi-parton interactions are expected to produce such an effect [ 21 ]. Also, a study on pT -spectra of primary charged particles as a function of RT in pp, p–Pb , and Pb–Pb collisions at a centre-of-mass energy per nucleon pair of √sNN = 5 . 02 TeV on the RT distributions is presented. The pT spectra are studied in the toward, away, and transverse regions. The results from pp collisions are compared with predictions from PYTHIA 8 with Monash tune [ 28 ] (from now on referred to as PYTHIA 8) and EPOS LHC. For p–Pb and Pb–Pb collisions, data are compared with EPOS LHC and PYTHIA 8/Angantyr [ 24 ]. In pp collisions, the implementation of hard processes in PYTHIA 8 starts with the choice of the parton distribution functions (PDFs) of the protons. The next step is to simulate the hard scattering process, where partons from the colliding protons interact at high energies. This process is described using perturbative quantum chromodynamics (pQCD) calculations [ 13 ]. The event generation begins with a fixed order matrix element calculation – 3 – JHEP01(2024)056 either in leading-order (LO), next-to-leading order (NLO) or beyond (NNLO) [ 29 ]. During the hard scattering process, partons may emit ISR and FSR which are simulated using parton shower algorithms [ 13 ]. PYTHIA 8 with Monash tune has a default parameterisation of the model based on MPI and colour reconnection. After the hard scattering and parton showering, coloured strings are formed between the final-state partons [ 30 ]. The hadronisation mechanism in PYTHIA 8 is based on the Lund string fragmentation model [ 13 ], followed by particle decays. The hadronisation process leads to the production of jets and the UE. The Angantyr model in PYTHIA 8 is an extrapolation of the pp dynamics to collisions with nuclei with a minimal set of tunable parameters that tries to describe the general features of the final state in p-A and A-A collisions, such as multiplicity and transverse momentum distributions, without including a hydrodynamic evolution. It is based on the Fritiof model and the number of participating nucleons is calculated using the Glauber formalism [ 1 , 24 ]. On the other hand, the event generation process in EPOS LHC arises from the parton-based Gribov-Regge theory [ 31 ], pQCD, and the Lund string model. An elementary scattering corresponds to a scattering of primary partons, which contains a hard scattering (pQCD), accompanied by ISR and FSR. String hadronisation relies on the local density of string segments per volume unit with respect to a critical density parameter. Each string is classified according to a core-corona approach where a low-density corona region accompanies a high-density core region [ 31 ]. In the core, the string energy density is sufficient to invoke a QGP description that is subject to hydrodynamic evolution [ 32 ]. This article is structured as follows: section 2is devoted to the discussion of the main aspects of the analysis, such as event and track selection, corrections, systematic uncertainties as well as the unfolding method for the RT distributions and pT spectra. The results are discussed in section 3, and finally section 4summarises the main results. 2 Analysis procedure 2.1 Event and track selection The present study is performed using the LHC Run 1 and Run 2 data collected with the ALICE detector. The Inner Tracking System (ITS [ 33 ]), Time Projection Chamber (TPC [ 34 ]), and V0 [ 35 ] are the main detectors used in the current analysis. The ITS is composed of six cylindrical layers of high-resolution silicon tracking detectors. The two innermost layers, closest to the interaction point (IP), consist of hybrid Silicon Pixel Detectors (SPD) at radial distances of 3.9 and 7.6 cm from the beam axis with a pseudorapidity coverage of |η|< 2and |η|< 1 . 4, respectively. The TPC is a cylindrical drift detector that covers a radial distance of 85–247 cm from the beam axis and its longitudinal dimension extends from about − 250 cm to +250 cm around the nominal IP. The V0 detector consists of two arrays of scintillating counters (V0A and V0C) placed on each side of the IP covering the full azimuthal acceptance and the pseudorapidity ranges of 2 . 8 < η < 5 . 1and − 3 . 7 < η < − 1 . 7, respectively [ 36 ]. The V0 detector and the SPD are used for triggering and background rejection. The data were collected using a minimum-bias (MB) trigger, which required a signal in both V0A and V0C detectors. The offline event selection is optimised to reject beam-induced background in all collision systems by utilising the timing signals in the two V0 detectors. In Pb–Pb collisions, – 4 – JHEP01(2024)056 in order to suppress the beam induced background and the electromagnetic interactions, the V0-timing selection is complemented by correlating the timing signals of the neutron zero degree calorimeters (ZDC [ 37 ]), which are positioned on both sides of the IP at 112.5 m distance along the beam axis [ 38 ]. Runs with a low number of interactions per bunch crossing ( µ ) were selected resulting in average µ values of 0.020, 0.005, and 0.001 for pp, p–Pb , and Pb–Pb collisions at √sNN = 5 . 02 TeV, respectively. Therefore, events with multiple collisions (pile-up) constitute a small fraction of the triggered events. They are identified and rejected based on the presence of multiple offline reconstruction primary vertices in the SPD [ 7 , 36 , 39 ]. To ensure that a hard scattering took place in a collision, events are required to have a trigger particle with transverse momentum above a given threshold. For the energy dependence of the RT distributions in pp collisions, the trigger particle is chosen in the same pT interval (5–40 GeV /c ) as used in previous publications for pp collisions at √s = 13 TeV [ 7 , 23 ]. However, for the system size dependence of pT spectra as a function of RT in pp, p–Pb, and Pb–Pb collisions with a trigger particle within 8 < ptrig T< 15 GeV /c are considered. This choice is motivated from previous ALICE results where the particle production in the toward and away regions are studied as a function of the collision centrality using heavy-ion data [ 2 , 40 ]. For p–Pb and Pb–Pb collisions, in this particular ptrig T interval the jet-like correlations dominate over the collective effects, and therefore, the separation in three topological regions is appropriate [ 40 ]. This work is based on the analysis of ALICE data including p–Pb and Pb–Pb collisions at √sNN = 5 . 02 TeV and pp collisions at √s = 2 . 76, 5.02, 7, and 13 TeV. The measurements of the transverse momentum spectra focus on primary charged particles [ 41 ], i.e. particles with a mean proper lifetime larger than 1 cm /c , which are either produced directly in the interaction or from decays of particles with mean proper lifetime smaller than 1 cm /c . Primary charged particles are measured in the pseudorapidity range of |η|< 0 . 8and with pT> 0 . 5GeV /c . They are reconstructed using the ITS and TPC detectors, which provide measurements of the transverse momentum of the track and its azimuthal angle. For the measurement of the pT spectra as a function of RT , the track selection criteria are similar to those used in the RT studies for identified charged particles reported in ref. [ 23 ]. In particular, tracks are required to cross at least 70 TPC pad rows. They are also required to have at least two hits in the ITS, out of which at least one has to be from track segments in the SPD layers. The fit quality for the ITS and TPC track points must satisfy χ2 ITS/Nhits < 36 and χ2 TPC/Nclusters < 4, respectively, where Nhits and Nclusters are the number of hits in the ITS and the number of clusters in the TPC associated with the track, respectively. To limit the contamination from secondary particles, a selection on the distance of closest approach (DCA) to the reconstructed primary vertex in the direction parallel to the beam axis ( z ) of |DCAz|< 2cm is applied. Also, a pT -dependent selection on the DCA in the transverse plane ( DCAxy ) of the selected tracks to the primary vertex is applied ( |DCAxy|< 0 . 0105 cm + 0 . 0350 cm × ( GeV/c ) −C×pC T with pT in GeV/c and C = − 1 . 1) [ 2 ]. Moreover, tracks associated with the decay products of weakly decaying kaons (“kinks”) are rejected. These track selection criteria yield a significantly non-uniform efficiency as a function of the azimuthal angle and the pseudorapidity. This is mostly due to the requirement of SPD hits. In order to obtain a high and uniform tracking efficiency together with good momentum resolution, they are – 5 – JHEP01(2024)056 complemented by tracks without an associated hit in the SPD for which the position of the reconstructed primary vertex is used in the fit of the tracks [ 42 , 43 ]. Both sets of tracks are used to select the trigger particle as well as to measure RT and the pT spectra. On the other hand, for the measurement of the RT distributions in pp collisions similar track selection criteria as described in ref. [ 7 ] were considered. However, in order to guarantee a uniform response in the azimuth, the DCA cut was loosen ( |DCAxy|< 2 . 4) and no restriction on the number of reconstructed points in ITS was considered. The obtained results are consistent with those using the combination of tracks selected with the two sets of criteria described above. 2.2 Corrections For the measurements of the pT spectra of charged particles, the standard procedure of the ALICE Collaboration considers efficiency and secondary particle contamination to correct the raw yields [ 44 ]. The efficiency correction is calculated from Monte Carlo (MC) simulations, including particle propagation through the detector making use of the GEANT 3 transport code [ 45 ]. The event generators used in the analyses are PYTHIA 8 for pp collisions, EPOS LHC [ 14 ] for p–Pb collisions, and HIJING [ 46 ] for Pb–Pb collisions. Efficiency corrections purely based on MC are inaccurate since the event generators do not reproduce the relative abundances of the different particle species and, in particular, they tend to significantly underestimate the production of strange hadrons. To account for this effect, a procedure based on identified hadron production measurements is followed, where the efficiency obtained from MC simulations is reweighted taking into account the primary charged particle composition measured by ALICE [ 44 ]. This is done with data for pp, p–Pb , and Pb–Pb collisions at √sNN = 5 . 02 TeV [ 10 , 47 ]. The residual contamination from secondary particles, i.e. particles originating from weak decays or produced in interactions with the detector material, in the selected track sample is estimated by fitting the measured DCAxy distributions with a multi-component template model using as templates the DCA distributions for primary and secondary particles obtained from MC simulations [ 44 ]. 2.3 Bayesian unfolding of the multiplicity distributions The charged-particle multiplicity in the transverse region, NT ch , largely characterises the underlying-event activity. However, the measured charged-particle multiplicity distribution Y ( NT raw )is smeared out due to the limited acceptance and finite resolution of the detector. Hence, a one-dimensional unfolding technique based on Bayes’ theorem [ 48 ], correcting for these detector effects and efficiency losses, is introduced to recover the true multiplicity distribution. The Bayesian unfolding technique starts with the response matrix (smearing matrix) S1 , reflecting the detector effects on the measurements, which can be obtained from MC simulations including the transport of particles through the detector. The response matrix encodes the conditional probability S1≡P ( NT acc|NT ch )that an event with true multiplicity NT ch is measured as one with multiplicity NT acc . In the left panel of figure 2, the values along the diagonal of S1 represent the probability that a measured event is reconstructed with the correct charged-particle multiplicity. The off-diagonal elements give the probability that fewer (more) particles are reconstructed due to detector inefficiencies (contamination of secondaries – 6 – JHEP01(2024)056 0 5 10 15 20 25 30 35 T acc N 0 5 10 15 20 25 30 35 T ch N 3− 10 2− 10 1− 10 1 ) ch N| acc N(P = 13 TeVspp ALICE simulation Transverse PYTHIA 8 Monash tune c < 40 GeV/ trig T p5 < |<0.8 η , |c > 0.5 GeV/ T p 0 5 10 15 20 25 30 35 T acc N 0 5 10 15 20 25 30 35 T ch N 3− 10 2− 10 1− 10 1 ) acc N| ch N(P = 13 TeVspp ALICE simulation Transverse PYTHIA 8 Monash tune c < 40 GeV/ trig T p5 < |<0.8 η , |c > 0.5 GeV/ T p Figure 2. Response matrix S1 (left) and M1 matrix (right) of charged-particle multiplicity distributions in the transverse region in pp collisions at √s= 13 TeV (see text for details). and background particles). The one-dimensional unfolded distribution Y ( NT ch )is given as the linear combination between the elements of the matrix M1 and the measured distribution, Y(NT ch) = X NT raw M1Y(NT raw),where M1=S1P0(NT ch) PNT ch S1P0(NT ch).(2.1) P0 ( NT ch )is a prior probability distribution, and the M1 matrix represents the conditional probability M1≡P ( NT ch|NT acc )that an event with reconstructed multiplicity NT acc has a true multiplicity NT ch . By definition, the elements of the response matrix and the M1 matrix (shown in the right panel of figure 2) fulfill the following normalisation conditions: PNT acc P ( NT acc|NT ch ) = 1, PNT ch P ( NT ch|NT acc ) = 1. The unfolding technique follows an iterative process. The measured multiplicity distribution is used as the prior distribution in the first iteration. An updated prior distribution, ˆ P(NT ch) = Y(NT ch) PNT ch Y(NT ch),(2.2) is obtained from the second iteration onwards. Hence, the unfolding matrix is optimised as the prior distribution is updated. Finally, a new unfolded distribution can be obtained using eq. (2.1) with the updated M1 . After each iteration, the iterative process makes the unfolded distribution closer to the true one. Meanwhile, the statistical uncertainties in the response matrix are also propagated to the unfolded distributions through M1 . Thus, the uncertainties of the response matrix enter a the new unfolded distribution as M1 is updated. Hence, a larger number of iterations does not guarantee a better unfolded distribution as it might be eventually contaminated by statistical fluctuations [ 49 ]. In order to decide when to stop the iterations, the χ2/ndf between the unfolded distributions in two consecutive iterations is computed. The criterion χ2/ndf ≲ 1is used to stop the iterative process. – 7 – JHEP01(2024)056 )c (GeV/ T p -1 )c (GeV/ T p/d ch N<5 d T R Ratio to model Ratio to 0< 1 2 3 4 5 6 7 4− 10 2− 10 1 2 10 3 10 Toward 〉 T ch N〈 17.97± ALICE: 276.52 PYTHIA: 280.61 EPOS: 195.30 = 5.02 TeV NN s Pb −Pb 1 2 3 4 5 6 7 c < 15 GeV/ trig T p8 < | < 0.8 η , |c > 0.5 GeV/ T p Away 1 2 3 4 5 6 7 Transverse ALICE 1 2 3 4 5 6 7 1− 10 1 10 < 0.5 T R0.0 < < 1.5 T R0.5 < < 2.5 T R1.5 < 1 2 3 4 5 6 7 Solid line: PYTHIA 8.244 (Angantyr) Dashed line: EPOS LHC 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Figure 6. Top panel: charged-particle transverse momentum spectra as a function of RT for different topological regions in p–Pb collisions at √sNN = 5 . 02 TeV. Data are compared with PYTHIA 8 Angantyr and EPOS LHC predictions. Middle panel: the ratio of the pT spectra in different RT intervals to the RT -integrated ones. The boxes and bars represent the systematic and statistical uncertainties, respectively. Bottom panel: the ratio of the pT spectra for each RT interval to the corresponding PYTHIA8 Angantyr and EPOS-LHC predictions. The shaded area represents the sum in quadrature of the systematic and statistical uncertainties. ref. [ 23 ]. For p–Pb collisions the data show compatible features with those of pp collisions in all the three topological regions. The behaviour of the charged-particle pT spectra as a function of RT in the toward and away regions in Pb–Pb collisions, where the jet bias is nearly absent in the transverse region, is qualitatively similar to that of pp and p–Pb collisions. This is understood with the fact that in all three collision systems, the production of particles in the toward and away regions is dominated by the fragmentation of the two outgoing hard partons and hence dominated by particles with high pT . However, the pT spectra in RT intervals converge to the RT -integrated result at higher pT values ( pT> 6GeV /c ) as compared to pp and p–Pb collisions. The behaviour in the transverse region the pT spectra in Pb–Pb collisions is found to be similar to that in toward and away regions. – 14 – JHEP01(2024)056 In figures 4,5, and 6, the measured spectra are also compared to PYTHIA 8 and EPOS LHC predictions and the bottom panels show data to model ratios. For pp collisions, PYTHIA 8 describes the RT dependence of the transverse momentum spectra in the full pT interval for the toward and away regions. A similar level of agreement is observed when comparing EPOS LHC with data except for RT< 0 . 5in the away region. For the transverse region, PYTHIA 8 captures the spectral shapes within two sigmas while EPOS LHC deviates from data, in particular at high pT . For p–Pb collisions, PYTHIA 8 Angantyr describes the high pT yield ( pT> 4GeV /c ) for the toward and away regions better than EPOS LHC. The models are able to describe the yield for RT< 1 . 5, but they underestimate the data, especially at low pT , in the highest RT interval. For the transverse region, none of the used models is able to capture the RT dependence of the pT spectra. For Pb–Pb collisions, PYTHIA 8 Angantyr overestimates the high pT yield ( pT> 3GeV /c ) for all three topological regions, but it fairly describes the data in the lower pT region. In contrast, EPOS LHC underestimates the yields in the three topological regions and the deviations from data increase with increasing pT . For the ratios of the pT spectra in different RT intervals to the inclusive spectra, the two models agree with each other in pp and p–Pb collisions, and also they agree with the experimental data. For Pb–Pb collisions, EPOS LHC gives a better qualitative description of the pT -dependent trend observed in data compared with PYTHIA 8 Angantyr for pT> 4 GeV /c . PYTHIA 8 Angantyr tends to give a good description only for pT< 4GeV /c . Note that the measured value of ⟨NT ch⟩ in pp collisions is found to be consistent with the PYTHIA 8 prediction while EPOS LHC deviates from the measured value by 6%. For p–Pb collisions, the values of ⟨NT ch⟩ deviate from data by 13% and 24% for PYTHIA 8 Angantyr and EPOS LHC, respectively. Similarly for Pb–Pb collisions, the values of ⟨NT ch⟩ deviate from data by 1.5% and 29% for PYTHIA 8 Angantyr and EPOS LHC, respectively. 3.3 Average transverse momentum and integrated yield as a function of the relative transverse activity classifier Figure 7shows the RT dependence of the mean transverse momentum, ⟨pT⟩ , derived from the pT spectra of charged particles in the measured pT range. The systematic uncertainties assigned to the pT spectra were propagated to ⟨pT⟩ [ 55 ]. Results are shown for the three topological regions as a function of RT for pp, p–Pb , and Pb–Pb collisions at √sNN = 5 . 02 TeV. The increasing trend of ⟨pT⟩ in the transverse region with increasing RT for the three collision system is similar to the results reported in ref. [ 55 ]. For the toward and away regions, the ⟨pT⟩ seems to be nearly flat as a function of RT , except for RT< 1, where the ⟨pT⟩ increases with decreasing RT . For RT> 1, the ⟨pT⟩ values in the toward and away regions are higher in pp than in p–Pb (and p–Pb is higher than Pb–Pb ) due to the larger contribution from the UE particles (which are softer than those of the leading jets) for larger collision systems. At RT≈ 0, the ⟨pT⟩ is observed to be similar in the three collision systems. Such behaviour is expected since the contribution of jets dominates at low- RT and hence all collision systems are expected to approach the pp collisions limit. At high values of RT , where the UE contribution is dominant, the ⟨pT⟩ values are similar in all three topological – 15 – JHEP01(2024)056 )c (GeV/〉 T p〈 0 1 2 3 4 1 1.2 1.4 1.6 1.8 Toward 0 1 2 3 4 1 1.2 1.4 1.6 1.8 Away c<15 GeV/ trig T p8< |<0.8η, |c<8 GeV/ T p0.5< 0 1 2 3 4 1 1.2 1.4 1.6 1.8 Transverse ALICE = 5.02 TeVs pp = 5.02 TeV NN sp-Pb = 5.02 TeV NN sPb-Pb T R Figure 7. ⟨pT⟩ of charged particles in toward (left), away (middle), and transverse (right) regions as a function of RTfor pp, p–Pb, and Pb–Pb collisions at √sNN = 5.02 TeV. )c (GeV/〉 T p〈Model/Data 0 1 2 3 4 1 1.2 1.4 1.6 1.8 = 5.02 TeVspp 0 1 2 3 4 = 5.02 TeV NN sp-Pb c<15 GeV/ trig T p8< |<0.8η, |c<8 GeV/ T p0.5< 0 0.5 1 1.5 2 = 5.02 TeV NN sPb-Pb ALICE Toward Away Transverse 0 1 2 3 4 0.9 1 1.1 Solid line: PYTHIA 8.244 Dashed line: EPOS LHC 0 1 2 3 4 PYTHIA 8.244 (Angantyr) 0 0.5 1 1.5 2 PYTHIA 8.244 (Angantyr) T R Figure 8. Top: ⟨pT⟩ of charged particles in pp (left), p–Pb (middle), and Pb–Pb (right) collisions at √sNN = 5 . 02 TeV as a function of RT for different topological regions compared with predictions from EPOS LHC and PYTHIA 8. Bottom: ratio of MC to data. The band around unity in the ratio depicts the experimental uncertainties. regions for a given collision system. The ⟨pT⟩ is compared with the predictions from EPOS LHC and PYTHIA 8 in figure 8. The models deviate by 10–20% from the experimental data, however, they show a trend with RT that is qualitatively similar to the measured one. Finally, the particle yields in the toward and away regions relative to those in the transverse region are studied as a function of RT . In pp collisions, due to the limited ALICE acceptance the particle multiplicities in the toward and away regions are expected to be proportional to that in the transverse region only for RT< 2. For example, it has been shown that the MPI activity (UE) is proportional to RT only up to RT = 2 [ 19 ]. At – 16 – JHEP01(2024)056 〉 T ch N〈Model/Data Yield / 0 1 2 3 4 0 1 2 3 4 = 5.02 TeVspp 0 1 2 3 4 = 5.02 TeV NN sp-Pb c<15 GeV/ trig T p8< |<0.8η, |c<8 GeV/ T p0.5< 0 0.5 1 1.5 2 = 5.02 TeV NN sPb-Pb ALICE Toward Away 0 1 2 3 4 0.8 1 1.2 1.4 Solid line: PYTHIA 8.244 Dashed line: EPOS LHC 0 1 2 3 4 PYTHIA 8.244 (Angantyr) 0 0.5 1 1.5 2 PYTHIA 8.244 (Angantyr) T R Figure 9. Top: integrated yield of charged particles in pp (left), p–Pb (middle), and Pb–Pb (right) collisions at √sNN = 5 . 02 TeV as a function of RT for toward and away regions compared with predictions from EPOS LHC and PYTHIA 8. Bottom: ratio of model predictions to data. The band around unity in the ratio depicts the experimental uncertainties. higher RT , the sample is biased towards multi-jet final states producing a hardening of the pT spectra in the transverse region. In order to further investigate this bias, figure 9 shows the pT -integrated yield normalised to ⟨NT ch⟩ of charged particles in pp (left), p–Pb (middle), and Pb–Pb (right) collisions as a function of RT for the toward and away regions at √sNN = 5 . 02 TeV. The NT ch -normalised integrated yield is also compared with the predictions from EPOS LHC and PYTHIA 8. The lower panels show the ratio of the model predictions to the data. For pp and p–Pb collisions, the normalised integrated yields for both toward and away regions show a linear increase for RT< 2and then they tend to saturate at high RT . PYTHIA 8 describes qualitatively the trend of the data while EPOS LHC shows no hint of saturation and thus overestimates the data at high RT in pp collisions, while in p–Pb collisions it predicts a completely different trend compared to the measured one. For Pb–Pb collisions, the behaviour of the normalised yield in both models seems to follow a linear trend. Both models show a different trend at low- RT , however, the prediction from PYTHIA 8 is found to be quantitatively consistent with the data within uncertainties. The EPOS LHC prediction shows about 40% higher yield with respect to the data at low- RT and approaches the measured values at high RT . 4 Conclusion The RT distributions have been measured in pp collisions at √s = 2 . 76, 5.02, 7, and 13TeV. They exhibit a Koba-Nielsen-Olesen (KNO)-like scaling for events with low- RT , while for UE-dominated events characterised by high RT , an indication of violation of the scaling is – 17 – JHEP01(2024)056 seen which might be attributed to high-multiplicity jets. In order to investigate the UE properties, the pT spectra as a function of RT have been studied at √sNN = 5 . 02 TeV in different collision systems. In general, the charged-particle spectra in RT intervals show a similar behaviour in pp and p–Pb collisions for all the three topological regions (toward, away, and transverse). The transverse region exhibits autocorrelation effects that give rise to a hardening of the spectra with increasing pT , in contrast to the toward and away regions, where particle production at lowpT increases (decreases) with increasing (decreasing) RT . At higher pT the spectral shapes become almost independent of RT . In these collision systems, a softening of the spectra occurs with increasing RT . In contrast to the small systems, Pb–Pb collisions do not show an autocorrelation effect in the transverse region. In this case, the behaviour of the three topological regions seems to be dominated by soft interactions. Subsequently, the study of the ⟨pT⟩ of charged particles in the three topological regions as a function of RT for the three collision systems shows that at RT∼ 0, the ⟨pT⟩ is, within the current uncertainties, independent of collision system size and such a limit is well described by models. Overall, PYTHIA 8 gives a better description of the data presented in this paper than EPOS LHC. The experimental results presented in this article will provide important contributions towards the development and tuning of MC event generators. Acknowledgments The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für – 18 – JHEP01(2024)056 Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. 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Dietel 115, – 23 – JHEP01(2024)056 123 University of Tennessee, Knoxville, Tennessee, United States 124 University of the Witwatersrand, Johannesburg, South Africa 125 University of Tokyo, Tokyo, Japan 126 University of Tsukuba, Tsukuba, Japan 127 Universität Münster, Institut für Kernphysik, Münster, Germany 128 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 129 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, Lyon, France 130 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France 131 Université Paris-Saclay, Centre d’Etudes de Saclay (CEA), IRFU, Départment de Physique Nucléaire (DPhN), Saclay, France 132 Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France 133 Università degli Studi di Foggia, Foggia, Italy 134 Università del Piemonte Orientale, Vercelli, Italy 135 Università di Brescia, Brescia, Italy 136 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India 137 Warsaw University of Technology, Warsaw, Poland 138 Wayne State University, Detroit, Michigan, United States 139 Yale University, New Haven, Connecticut, United States 140 Yonsei University, Seoul, Republic of Korea 141 Zentrum für Technologie und Transfer (ZTT), Worms, Germany 142 Affiliated with an institute covered by a cooperation agreement with CERN 143 Affiliated with an international laboratory covered by a cooperation agreement with CERN. IDeceased II Also at: Max-Planck-Institut fur Physik, Munich, Germany II I Also at: Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy IV Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy VAlso at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India V I Also at: Institute of Theoretical Physics, University of Wroclaw, Poland V II Also at: An institution covered by a cooperation agreement with CERN – 30 –