Pseudorapidity distributions of charged particles as a function of mid- and forward rapidity multiplicities in pp collisions at √s = 5.02, 7 and 13 TeV

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/ Pseudorapidity distributions of charged particles as a function of mid- and forward rapidity multiplicities in pp collisions at √s = 5.02, 7 and 13 TeV © CERN for the benefit of the ALICE collaboration 2021 Published version ALICE Collaboration ALICE Collaboration. (2021). Pseudorapidity distributions of charged particles as a function of mid- and forward rapidity multiplicities in pp collisions at √s = 5.02, 7 and 13 TeV. European Physical Journal C, 81(7), Article 630. https://doi.org/10.1140/epjc/s10052-021-09349-5 2021 Eur. Phys. J. C (2021) 81:630 https://doi.org/10.1140/epjc/s10052-021-09349-5 Regular Article - Experimental Physics Pseudorapidity distributions of charged particles as a function of mid- and forward rapidity multiplicities in pp collisions at √s= 5.02, 7 and 13 TeV ALICE Collaboration CERN, 1211 Geneva 23, Switzerland Received: 30 September 2020 / Accepted: 18 June 2021 © CERN for the benefit of the ALICE collaboration 2021 Abstract The multiplicity dependence of the pseudorapidity density of charged particles in proton–proton (pp) collisions at centre-of-mass energies √s=5.02, 7 and 13 TeV measured by ALICE is reported. The analysis relies on track segments measured in the midrapidity range (|η|<1.5). Results are presented for inelastic events having at least one charged particle produced in the pseudorapidity interval |η|<1. The multiplicity dependence of the pseudorapidity density of charged particles is measured with mid- and forward rapidity multiplicity estimators, the latter being less affected by autocorrelations. A detailed comparison with predictions from the PYTHIA 8 and EPOS LHC event generators is also presented. The results can be used to constrain models for particle production as a function of multiplicity in pp collisions. 1 Introduction The study of high-multiplicity events in proton–proton (pp) and proton–nucleus high-energy collisions reveals striking similarities with respect to the observations made for larger systems like a nucleus–nucleus collision, which are interpreted in terms of the creation of a strongly-interacting, fluid-like QCD medium: the quark–gluon plasma (QGP). The ridge structure arising from long-range azimuthal correlations observed in pp data [1–3] is also found in p–Pb collisions [4–7], where the presence of double-ridge structures is reported [4]. More recently, an ALICE measurement reported an enhancement in the relative production of (multi- ) strange particles with respect to primary charged particles asafunctionofmultiplicityinppcollisions[8].Thissuggests that some observables related to the QGP formation might be driven just by the multiplicity regardless of collision systems at LHC energies. e-mail: [email protected] In pp and p–Pb collisions, the selection of events with large hadronic final-state multiplicities biases the sample towards a large average number of Multiple Parton Interactions (MPIs) at the LHC [9,10]. In the description provided by the colour reconnection (CR) mechanism [11,12], CR in MPIs is expected to be particularly pronounced at high multiplicity. The effects of prominent CR at high multiplicity are supposed to account for basic observables like the correlations between the average momentum and the multiplicity of charged particles [13] as well as for the shape of their pseudorapidity distribution [14]. Indeed, the transverse momentum (pT) spectra of charged particles at high multiplicity [15,16] can be attributed, in pp collisions, to a CR mechanism, while until now no multiplicity dependence study of charged particle pseudorapidity density has been published. This document provides a large set of charged-particle multiplicitydensitymeasurementsasafunctionofeventmultiplicity in pp collisions at different centre-of-mass energies. This work could shed light on the phenomenon of MPIs that is a key ingredient of models attempting to describe large-multiplicity events. In any collision system, the eventaveraged pseudorapidity density of primary charged particles [17], dNch/dη, is a key observable characterising the global properties of the collision. Especially in pp interactions, the dNch/dηis described by the combination of the perturbative hard partonic processes and the underlying event [18,19]. The underlying event includes various phenomena like initial- and final-state radiation, colourconnected beam remnants, and infrared MPIs. In particular, its normalisation is directly connected to the MPI cross section determined by the low-xbehaviour of the gluon partondistribution function and by the consequent colour screening effects at the pTcut-off, while its multiplicity distribution is more influenced by correlations within MPI in the fragmentation stage. The methods adopted in this analysis are based on those used in the inclusive dNch/dη(dNincl. ch /dη) measurementsofALICE[20–24]. This study introduces exclusive 0123456789().: V,-vol 123 630 Page 2 of 18 Eur. Phys. J. C (2021) 81:630 event classes for two complementary multiplicity estimators defined in the midrapidity and in the forward regions and exploiting high-multiplicity triggers to record a large sample of events for the highest multiplicity classes. The results are provided for an event selection defined in a fully experimental way. Measurements are performed for inelastic collisions with at least one charged particle produced in |η|<1 (INEL>0), corresponding to about 75% of the total inelastic cross section [13,23,25,26]. 2 Experimental setup The full description and performance of the ALICE detectors can be found elsewhere [27,28]. The detectors used in this analysis are briefly presented below. The V0 detector [29] is made of two arrays (V0A and V0C) of 32 scintillating counters each. The V0A is located at a distance of 329 cm away from the interaction point (IP) along the beam direction (z) and it covers the pseudorapidity range 2.8<η<5.1. The V0C is installed at z=−88 cm, covering the pseudorapidity range −3.7<η<−1.7. Both counters cover the full azimuth. The V0 detector provides the minimum-bias and beam-gas removal trigger to ALICE. It measures the signal amplitude created by charged particles and their arrival times with a time resolution better than 1 ns. The silicon pixel detector (SPD) [30,31] is the innermost detector of ALICE. It is located inside a large solenoid that produces a homogeneous magnetic field of 0.5 T. The SPD consists of two cylindrical layers coaxial to the beam line at radii 3.9 and 7.6 cm. It is made of 10 million pixels distributed on 240 sensors that cover the pseudorapidity range |η|<2 for the first layer and |η|<1.4 for the second layer for particles that originate from collisions at the nominal interaction point. An enlarged pseudorapidity coverage of |η|<2 is reached using events whose primary vertex is not at zero, but within ±10 cm from the nominal interaction point. The SPD provides a precise measurement of the position of the primary interaction vertex with a spatial resolutionofonaverage30 µm inthebeam direction[23,31].The multiplicity measurement of this analysis relies on the reconstruction of tracklets, which are track segments connecting hits on the two SPD layers and pointing to the primary vertex. Due to the bending in the magnetic field and multiple scattering, the reconstruction efficiency of tracklets is limited to pT>50 Mev/c. 3 Data sample and analysis The minimum-bias pp data samples at √s= 5.02, 7 and 13 TeV used in this analysis correspond to the integrated luminosities Lint =12.4±0.3, 3.78 ±0.13 and 0.946 ± 0.020 nb−1, respectively [28,32,33]. The data sample at √s= 13 TeV benefits from a high-multiplicity trigger that was implemented in ALICE at the beginning of the LHC Run 2. The minimum-bias trigger (MBAND) requires hits in both the V0A and V0C detectors in coincidence of a beam crossing. The contribution from diffractive interactions is minimised by requiring at least one SPD tracklet in |η|<1; the resulting data sample is called MBAND>0. The contamination from beam-induced background is removed by using the timing information of the V0 detectors and taking into account the correlation between tracklets and clusters in the SPD detector [28]. The events used for the analysis are required to have a primary vertex in the fiducial region |z|<10cm. The primary vertex is reconstructed by correlating hits in the two SPD layers. The contamination from in-bunch pile-up events is removed offline excluding events with multiple vertices reconstructed in the SPD [23]. The pile-up probability estimated considering the beam conditions ranges from 10−3to 10−2.After the offline rejection, the remaining pile-up has a negligible impact on the final results. This was verified by analysing data samples separately with high and low initial pile-up contamination. Multiplicity classes are defined by a probability (percentile) range that is interpreted as a fractional cross section σ/σMBAND>0, with the visible cross section in pp collisions, σMBAND>0, constituting 100%. Percentile values for higher multiplicity collisions are close to 0% and for lower ones close to 100%. Forward multiplicity classes are estimated by V0M, which is the sum of the energy deposition measured by the V0A and V0C scintillators. The distribution of the V0M amplitude scaled by its average value V0M (self-normalised V0M) is shown in Fig. 1aforMB AND>0pp collisions at √s=13 TeV. A dedicated high-multiplicity trigger is defined by the threshold V0M/V0M>∼4.9, corresponding to σ/σMBAND>0=0.1%. The SPD tracklets are used to define multiplicity classes in the midrapidity region |η|<2. The distribution of the self-normalised number of SPD tracklets for MBAND>0pp collisions in |η|<2is shown in Fig. 1b. For all the midrapidity multiplicity classes, only the minimum-bias trigger is used because the highmultiplicity trigger relying on V0M amplitudes would give an additional bias. The data analysis is performed by classifying MBAND>0data samples using the mid and forward multiplicity estimators. The multiplicity percentile intervals of the visible cross section P(MBAND>0)=σ/σMBAND>0can be converted to fractional intervals with respect to the INEL>0cross section P(INEL>0)=σ/σINEL>0in pp collisions by following the conversion rule 123 Eur. Phys. J. C (2021) 81:630 Page 3 of 18 630 0246810 〉V0M〈V0M/ 5− 10 4− 10 3− 10 2− 10 1− 10 1 10 2 10 3 10 Normalised counts Min. Bias data (%) 1 − 05− 1 10− 515− 10 20− 15 30− 20 40− 30 50− 40 70− 50 100− 70 High-Mult data (%) 0.01− 00.1− 0.01 ALICE = 13 TeVspp, Forward Multiplicity Classes (a) 0246810 〉 SPD Tracklet N 〈 / SPD Tracklet N 5− 10 4− 10 3− 10 2− 10 1− 10 1 10 2 10 3 10 Normalised counts Min. Bias data (%) 1− 05− 1 10− 5 15 − 10 20− 15 30− 20 40− 30 50− 40 70− 50 100− 70 ALICE = 13 TeVspp, Central Multiplicity Classes (b) Fig. 1 The distribution of the V0M amplitude (total energy deposition in the region −3.7<η<−1.7and2.8<η<5.1) scaled by its average value V0Mthat is used to determine the forward multiplicity classes (a) and the distribution of the total number of SPD tracklets in an event (NSPD Tracklet,−2<η<2) scaled by its average value NSPD Trackletthat is used to determine the midrapidity multiplicity classes (b) in pp collisions at √s=13 TeV. Note that the percentile values of themultiplicityclassesare fractions of thevisiblecrosssection σ/σMBAND>0(see text for details) Table 1 Correspondence of the multiplicity classes between P(MBAND>0)and P(INEL>0). The trigger efficiency is estimated using PYTHIA 8 Monash 2013 [34–36] and GEANT 3 [37] P(MBAND>0)(%) Forward multiplicity estimator Midrapidity multiplicity estimator √s(TeV) √s(TeV) 5.02 7 13 5.02 7 13 P(INEL>0)(%) P(INEL>0)(%) 0–0.01 0–0.0091 0–0.0090 0–0.0091 0.01–0.1 0.0091–0.0915 0.0090–0.0897 0.0091–0.0915 0.1–0.5 0.0915–0.4576 0.0897–0.4478 0.0915–0.4573 0.5–1 0.4576–0.9152 0.4478–0.8955 0.4573–0.9146 0–1 0–0.9152 0–0.8955 0–0.9146 0–0.9095 0–0.8887 0–0.9288 1–5 0.9152–4.577 0.8955–4.478 0.9146–4.574 0.9095–4.548 0.8887–4.444 0.9288–4.644 0–5 0–4.577 0–4.478 0–4.574 0–4.548 0–4.444 0–4.644 5–10 4.577–9.156 4.478–8.956 4.574–9.149 4.548–9.096 4.444–8.888 4.644–9.288 10–15 9.156–13.74 8.956–13.44 9.149–13.73 9.096–13.65 8.888–13.33 9.288–13.93 15–20 13.74–18.32 13.44–17.92 13.73–18.31 13.65–18.20 13.33–17.78 13.93–18.58 20–30 18.32–27.51 17.92–26.90 18.31–27.50 18.20–27.32 17.78–26.67 18.58–27.88 30–40 27.51–36.76 26.90–35.92 27.50–36.75 27.32–36.49 26.67–35.59 27.88–37.20 40–50 36.76–46.11 35.92–45.02 36.75–46.12 36.49–45.77 35.59–44.53 37.20–46.58 50–70 46.11–65.45 45.02–63.66 46.12–65.53 45.77–64.91 44.53–62.88 46.58–65.82 70–100 65.45–100 63.66–100 65.53–100 64.91–100 62.88–100 65.82–100 Pi(INEL>0)=Pi(MBAND>0)/i jPj(MBAND>0)/j,(1) where iindicates a specific multiplicity class, jruns over all multiplicity classes for a given collision energy and multiplicity estimator, and i(j)istheMB AND>0trigger efficiency for the INEL>0event sample NMBAND>0/NINEL>0for the ith (jth) multiplicity class. The correspondence between P(INEL>0)and P(MBAND>0)is reported in Table 1.Inthis document, multiplicity classes for the results of ALICE are represented with P(MBAND>0), which is a quantity defined using detector-level variables. In order to perform precise comparisons of particle-level simulations with the ALICE data, the P(INEL>0)intervals corresponding to a given P(MBAND>0)interval for each centre-of-mass energy and multiplicity class reported in Table 1need to be used in the particle-level simulations. Alternatively, the values of dNch/dηwith ALICE data for the multiplicity classes of P(MBAND>0)in Table 1can be corrected such that they correspond to the multiplicityclassesofP(INEL>0)given in the leftmost column of Table 2. For example, the correction factor of 0.9995 for 123 630 Page 4 of 18 Eur. Phys. J. C (2021) 81:630 Table 2 The correction factors of dNch/dηfrom the multiplicity classes P(INEL>0) in Table 1to those of P(INEL>0)in the leftmost column of this table. The correction factors are estimated for the generated values of dNch/dηusing PYTHIA 8 Monash 2013 [34–36] P(INEL>0)(%)Forward multiplicity estimator Mid-rapidity multiplicity estimator √s(TeV) √s(TeV) 5.02 7 13 5.02 7 13 Correction factor Correction factor 0–0.01 0.9995 0.9959 0.9842 0.01–0.1 0.9938 0.9921 0.9939 0.1–0.5 0.9934 0.9907 0.9933 0.5–1 0.9916 0.9901 0.9915 0–1 0.9927 0.9906 0.9924 0.9892 0.9853 0.9924 1–5 0.9864 0.9827 0.9855 0.9809 0.9768 0.9842 5–10 0.9768 0.9722 0.9763 0.9709 0.9634 0.9778 10–15 0.9694 0.9588 0.9667 0.9607 0.9522 0.9684 15–20 0.9565 0.9473 0.9545 0.9516 0.9392 0.9580 20–30 0.9455 0.9289 0.9382 0.9369 0.9210 0.9472 30–40 0.9249 0.9072 0.9187 0.9205 0.8968 0.9290 40–50 0.9052 0.8752 0.9003 0.9010 0.8730 0.9147 50–70 0.9242 0.8867 0.8998 0.8962 0.8534 0.9003 70–100 0.9716 0.9573 0.9662 0.9215 0.8897 0.9284 the P(INEL>0)=0–0.01% interval of the forward multiplicity estimator at √s=5.02 TeV is the ratio of the generated values of dNch/dηbetween P(INEL>0)=0–0.01% and 0–0.0091% with PYTHIA 8 Monash 2013 [34–36]. The data measurement of dNch/dηfor P(MBAND>0)=0–0.01% wouldthereforeneedtobemultipliedbythisfactorinorderto compare directly with a generated interval of P(INEL>0)= 0–0.01%. The value of dNch/dηis obtained by correcting the number of SPD tracklets for detector acceptance as well as reconstruction and selection efficiency following the procedure developed earlier [23,24,38–40]. The corrections are estimated with Monte Carlo simulations based on PYTHIA 8 Monash 2013 [34–36] for particle generation and GEANT 3[37] for the transport of particles through the geometry of ALICE. PYTHIA 8 has a strangeness content that underestimates the data by a pT-dependent factor, which approaches 2 around pT=10 GeV/c[41]. The discrepancy is resolved by normalising the strangeness content in PYTHIA 8 to match the one in the data. This corrects dNch/dηdownward by about 1%. 4 Systematic uncertainties Several sources of systematic uncertainties are investigated for this study and the estimated uncertainties are listed in Table 3. For each multiplicity class, the systematic uncertainties related to the model used in the correction procedure (“Model dependence”) are quoted as the difference of the results using corrections obtained with two different generators before the trigger efficiency correction: PYTHIA 8 Monash 2013 [34–36] and EPOS LHC [42,43]. The uncertainties attributed to the description of the trigger (“Trigger efficiency”) are also quoted as the difference of the simulated trigger efficiency (NMBAND>0/NINEL>0) between the two event generators. The effects of the difference in particle composition between data and Monte Carlo mostly originate from the underestimated yield related to the weak decays of light-flavour hadrons in the simulation and are obtained with reweighting techniques (“Strangeness correction”): strangeness yields in the simulation are reweighted during the correction step by a factor of 2 to be compatible with the data; the factor is varied by ±30% based on data [41] that covers the whole pTregion, resulting in variations of the obtained dNch/dηranging from ±0.5% at low multiplicities to±0.7%atthehighestmultiplicities.Additionally,theeffect of particle-species composition (“Particle composition”) is estimated by varying, in the simulation, the relative fraction of charged kaons, protons and other particles with respect to the fixed number of charged pions by ±30%, which covers the uncertainties in the measured particle-species composition at the LHC [44]. Relative variations of the final result are below ±0.5% in all multiplicity classes. Below 50 MeV/c, the tracklet reconstruction efficiency sharply drops because of the bending in the magnetic field and to less extent due to the scattering and absorption in the detector material. To estimate the uncertainty due to the extrapolation to zero pT (“Zero-pTextrapolation”), the number of particles below 50 MeV/cisvariedsufficientlyintheeventgeneratorby+100% and −50%, adopted from the previous study [23]. The corre- 123 Eur. Phys. J. C (2021) 81:630 Page 5 of 18 630 Table 3 Systematic uncertainties from the highest to the lowest multiplicity class for both the mid- and forward rapidity multiplicity estimators in pp collisions at √s=13 TeV. The last column reports the effects on the inclusive dNch/dη source Uncertainty (%) at √s=13TeV Forward σ/σMBAND>0Midrapidity σ/σMBAND>0σ/σINEL>0 0–0.01% 40–50% 70–100% 0–1% 40–50% 70–100% 0–100% Uncorrelated Trigger efficiency neg. 0.2 0.2 neg. 0.2 0.2 0.2 Strangeness correction 0.7 0.6 0.5 0.7 0.6 0.5 0.5 Zero-pTextrapolation 0.7 0.8 1.0 0.7 0.9 1.0 1.0 Correlated Model dependence neg 0.1 0.1 0.1 0.1 0.1 0.1 Detector acceptance and efficiency 0.8 0.7 0.6 1.8 2.0 2.8 0.7 Particle composition 0.5 0.5 0.5 0.5 0.5 0.5 0.5 Material budget 0.2 0.2 0.2 0.2 0.2 0.2 0.2 ALICE pp collisions = 5.02 TeV s = 7 TeVs Multiplicity estimation < 5.1 η < -1.7 and 2.8 < η -3.7 < = 13 TeVs σ /σ 10 20 30 40 50 η /d ch Nd 1 −01 0 1 2 3 4 5 Incl. ) η /d ch N)/(d η /d ch N(d 1−01 η 1−01 (%) AND>0 MB 0.01− 0 0.1− 0.01 0.5− 0.1 1− 0.5 5 − 1 10− 5 15− 10 20− 15 30− 20 40− 30 50− 40 70 − 50 100− 70 Fig. 2 Charged-particle pseudorapidity density (upper panels) and the same scaled by 1/(dNch/dη)incl.(lower panels) for the 0–0.01 to 70– 100% multiplicity classes measured with the forward multiplicity estimator (−3.7<η<−1.7and2.8<η<5.1) in pp collisions at √s= 5.02, 7 and 13 TeV. Correlated and uncorrelated systematic uncertainties are summed in quadrature in the upper panels and shown as boxes. Correlated systematic uncertainties are cancelled out in the lower panels sponding uncertainty is around ±1% and slightly dependent on the multiplicity class. The effect of the limited tracking acceptance and efficiency (“Detector acceptance and efficiency”) is estimated by varying the range of primary vertex selection along the beam direction (zvtx) from |zvtx|<10 cm to the narrower |zvtx|<7 cm and broader |zvtx|<15 cm; the effect on dNch/dηis below ±2% in all the multiplicity classes. The uncertainty due to the non-uniformity in azimuthal acceptance is studied by measuring dNch/dηindependently in three different azimuthal regions of the SPD, which are then compared with the corresponding full azimuth measurement: it varies from ±0.8% to ±2% with respect to the SPD configuration. The corresponding uncertainty is summed in quadrature for that in “Detector acceptance and efficiency”. The material budget in the ALICE central barrel is known to a precision of about 5% [28]. The corresponding systematic uncertainty on dNch/dη(“Material budget”), obtained by varying the material budget in the simulation, is estimated to be about ±0.2%. Variations for the particle-species composition, material budget, tracking acceptance, and efficiency correction produce a change in the measurement that behaves the same across energies and multiplicity classes. The corresponding systematic uncertainties are considered then as correlated. Conversely, variations on the correction for the contribution 123 630 Page 6 of 18 Eur. Phys. J. C (2021) 81:630 ALICE pp collisions = 5.02 TeVs = 7 TeVs Multiplicity estimation < 2 η -2 < = 13 TeV s 10 20 30 40 50 η /d ch Nd 1−01 0 1 2 3 4 5 Incl. ) η /d ch N)/(d η /d ch N(d 1−01 η 1 −01 (%) AND>0 MB σ / σ 1− 0 5− 1 10 − 5 15− 10 20− 15 30− 20 40− 30 50 − 40 70 − 50 100− 70 Fig. 3 Charged-particle pseudorapidity density (upper panels) and the same scaled by 1/(dNch/dη)incl.(lower panels) for the 0–1 to70–100% multiplicity classes measured with the midrapidity multiplicity estimator(−2<η<2)inppcollisionsat√s=5.02, 7 and 13 TeV.Correlated and uncorrelated systematic uncertainties are summed in quadrature in the upper panels and shown as boxes. Correlated systematic uncertainties are cancelled out in the lower panels of strangeness particles, the trigger efficiency, and the extrapolation to zero-pTaffect each energy and multiplicity class differently, so these contributions are considered as uncorrelated. 5 Results The dNch/dηmeasurements at √s= 5.02, 7 and 13 TeV for different classes of the forward multiplicity estimators are reported in Fig. 2; in the upper panels in absolute scale and in the lower panels, normalised to the inclusive dNch/dη (dNincl. ch /dη,dNch/dηfor 0–100%). As shown in the lower panels of Fig. 2, the pseudorapidity densities for the highest multiplicity classes (0–0.01%) are around 5 times larger than those of the inclusive ones for the three different collision energies. The asymmetry of the dNch/dηdistributions for the forward multiplicity classes is due to the asymmetric pseudorapidity acceptance of the V0 detector. This effect is more pronounced for the highest multiplicity classes. The upper panels in Fig. 3show the dNch/dηmeasurements at √s= 5.02, 7 and 13 TeV for different multiplicity classes defined by the midrapidity multiplicity estimator. The shapes of the pseudorapidity distributions of primary charged particles are different when compared with those obtained with the forward multiplicity estimator. The midrapidity multiplicity estimator is defined in a symmetric pseudorapidity region (−2<η<2) and clearly gives rise to autocorrelations as it includes the region where the pseudorapidity distributions are measured (−1.5<η<1.5). As shown in the lower panels of Fig. 3, for the three different collision energies, the pseudorapidity densities for the highest multiplicity classes (0–1%) are around 4–5 times larger than those of the inclusive ones, with the highest enhancement observed at midrapidity (η=0). The measurements are compared with the predictions from PYTHIA 8 Monash 2013 [34–36] with and without CR and the ones from EPOS LHC [42,43]. The effect of CR can be explored with PYTHIA 8 Monash 2013 by switching the effect on and off. EPOS LHC describes the collectivity effect in high multiplicity pp collisions differently with a hydrodynamic evolution of the core with a high-energy density that is formed by many colour string fields. The multiplicity classes of the models are estimated for generated charged particles in the same geometrical acceptances of the forward rapidity (−3.7<η<−1.7 and 2.8<η<5.1) and midrapidity (|η|<2) multiplicity estimators and the percentile value of the multiplicity class is calibrated for generated INEL>0 events. Figure 4reports the comparison of the data with these models for the 0–1% and 70–100% classes by the forward multiplicity estimator. PYTHIA 8 Monash 2013, implementing CR in the string fragmentation process, describes the data within 5% for all the centre-of-mass energies for the 0–1% multiplicity class. For the 70–100% class, PYTHIA 8 underestimates the data by up to 10%. When switching off CR, while keeping all the other model parameters stable, PYTHIA 8 overestimates (underestimates) the data by about30% for the 0–1%(70–100%)multiplicity class. EPOS LHC, which incorporates a collective flow-like description of the core, describes the data within 20% for both forward multiplicityclasses.EPOSLHCalsooverestimates(underestimates) the data for the 0–1% (70–100%) multiplicity class 123 Eur. Phys. J. C (2021) 81:630 Page 7 of 18 630 1−01 η ALICE pp collisions = 5.02 TeVs 1−01 = 7 TeVs 1%− : 0 AND>0 MB σ/σForward data PYTHIA8 Monash PYTHIA8 Monash no CR EPOS LHC 100%− : 70 AND>0 MB σ /σForward = 13 TeVs 4 5 6 Incl. ) η /d ch N)/(d η /d ch N(d 1 1.2 1.4 Model/Data 0.3 0.4 0.5 Incl. ) η /d ch N)/(d η /d ch N(d 1−01 0.6 0.8 1 Model/Data 1−01 η 1−01 Fig. 4 The panels in the first and third row show the normalised pseudorapidity density distributions of charged particles in pp collisions at √s= 5.02, 7 and 13 TeV compared with different models for the 0–1% and 70–100% multiplicity classes by the forward rapidity multiplicity estimator, respectively. The panels in the second and fourth row report the corresponding model/data ratio. Note that the multiplicity classes of the models correspond to σ/σINEL>0, which is slightly different from the σ/σMBAND>0of the ALICE data like PYTHIA 8 Monash 2013. For the two classes, PYTHIA 8 describes the data better than EPOS LHC. Figure 5shows the comparison according to the data with these models for the 0–1% and 70–100% classes by the midrapidity multiplicity estimator. EPOS LHC describes the data within 5% for all the centre-of-mass energies for the 0–1% multiplicity class. For the 70–100% class, EPOS LHC underestimates the data by up to 20%. PYTHIA 8 reproduces the data within 5% for all centre-of-mass energies for the 0– 1% multiplicity class, but it is not as good as EPOS LHC in the0–1%multiplicityclass.Forthe70–100%class,PYTHIA 8 describes the data within 10% and it is better than those of EPOS LHC. When switching off CR, PYTHIA 8 overestimates (underestimates) the data by about 15% (30%) for the 0–1% (70–100%) multiplicity class. The value of dNch/dηis determined by integrating dNch/dηin |η|<0.5. Table 4shows the values of dNch/dη for different mid- and forward rapidity multiplicity classes in pp collisions at √s= 5.02, 7 and 13 TeV. The autocorrelation effect for the midrapidity estimator results in larger values of dNch/dηin the highest multiplicity classes and in smaller ones for the lowest multiplicity classes compared with those with the forward multiplicity estimator. The energy dependence of dNch/dηfor the multiplicity classesdefinedbytheforwardmultiplicityestimatorisshown in the upper panel of Fig. 6. The LHC measurements for the dNch/dηcan be directly compared with the ones from the NAL Bubble Chamber (pp) [45], ISR (pp) [46], UA1 (pp) [47], UA5 (pp) [48], CDF (pp) [49], STAR (pp) [50] and PHOBOS (pp) [51]. A phenomenological power-law fit sαdescribes the centre-of-mass energy (√s) evolution of these measurements for non-single diffractive (NSD), INEL and INEL>0events up to LHC energies [23]. Such a fit is performed practically for the values of Table 4in different multiplicity classes to describe the dependence of dNch/dηon the centre-of-mass energy. Corresponding exponents are shown in the legend of Fig. 6. The average pseudorapidity density at midrapidity as a function of centre-of-mass energy increases rapidly for higher multiplicity classes. The lower panel of Fig. 6 shows dNch/dηnormalised to its inclusive value denoted as dNch/dη/dNch/dηincl.for the forward multiplicity classes. The steeper increasing trend of dNch/dη/ dNch/dηincl.observed for higher multiplicity classes may arise from the increase of the MPI cross sections with the centre-of-mass energy [23]. The exponent values αof the power-law fit (sα)ofALICE data in Fig. 6are compared with those of PYTHIA 8 and EPOS LHC in Table 5for the forward multiplicity classes. The multiplicity classes represent P(MBAND>0)for ALICE 123 630 Page 8 of 18 Eur. Phys. J. C (2021) 81:630 1−01 η ALICE pp collisions = 5.02 TeVs 1−01 1−01 η = 7 TeVs 1%− : 0 AND>0 MB σ /σCentral data PYTHIA8 Monash PYTHIA8 Monash no CR EPOS LHC 100%− : 70 AND>0 MB σ/σCentral = 13 TeVs 4 5 6 7 Incl. ) η /d ch N)/(d η /d ch N(d 0.9 1 1.1 1.2 Model/Data 0.2 0.25 0.3 0.35 Incl . ) η /d ch N)/(d η /d ch N(d 1−01 0.6 0.8 1 Model/Data 1−01 η 1−01 Fig. 5 The panels in the first and third row show the normalised pseudorapidity density distributions of charged particles in pp collisions at √s= 5.02, 7 and 13 TeV compared with different models for the 0–1% and 70–100% multiplicity classes by the midrapidity multiplicity estimator, respectively. The panels in the second and fourth row report the corresponding model/data ratio. The multiplicity classes of the models correspond to σ/σINEL>0, which is slightly different from the σ/σMBAND>0of the ALICE data data, while P(INEL>0)for the models. Overall, the energy dependence of dNch/dηof the data for different multiplicity classes is not described well by the models. Also, the exponent values of the fit for the models fail to describe the steeper behaviour of the energy dependence of dNch/dη that is measured in data with increasing multiplicities for the highest multiplicity classes. This suggests more tuning is needed to constrain models for the energy dependence of charged particle production with respect to different multiplicity classes. 6 Conclusions The energy and multiplicity dependence of the chargedparticle pseudorapidity density dNch/dηand the average charged-particle pseudorapidity density dNch/dηin proton–proton (pp) collisions at √s= 5.02, 7 and 13 TeV are measured. The yields of charged particles in the 0–1% and 0– 0.01% multiplicity classes for the mid- and forward rapidity multiplicity estimators, respectively, are up to about a factor of 5 higher with respect to the inclusive measurements for all investigated centre-of-mass energies. The results from the multiplicity-dependent analysis presented for both the mid- and forward rapidity multiplicity estimators in ALICE can be used as an input for improving our understanding of multiple parton interactions (MPIs) implemented in Monte Carlo models. Most of the results are described well by PYTHIA 8 with the Monash tune and by EPOS LHC. The effects of the colour reconnection (CR) is found to be important to constrain MPIs and describe the scale of the pseudorapidity density as a function of multiplicity for both the mid and forward multiplicity estimators as seen by the expected values for PYTHIA 8 with and without CR. The results can be used 123 Eur. Phys. J. C (2021) 81:630 Page 15 of 18 630 J. 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Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia 2Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine 3Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India 4Budker Institute for Nuclear Physics, Novosibirsk, Russia 5California Polytechnic State University, San Luis Obispo, CA, USA 6Central China Normal University, Wuhan, China 7Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France 8Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba 9Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico 10 Centro Fermi-Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi’, Rome, Italy 11 Chicago State University, Chicago, IL, USA 12 China Institute of Atomic Energy, Beijing, China 13 Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava, Bratislava, Slovakia 14 COMSATS University Islamabad, Islamabad, Pakistan 15 Creighton University, Omaha, NE, USA 16 Department of Physics, Aligarh Muslim University, Aligarh, India 17 Department of Physics, Pusan National University, Pusan, Republic of Korea 18 Department of Physics, Sejong University, Seoul, Republic of Korea 19 Department of Physics, University of California, Berkeley, CA, USA 20 Department of Physics, University of Oslo, Oslo, Norway 21 Department of Physics and Technology, University of Bergen, Bergen, Norway 22 Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN, Rome, Italy 23 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy 123 630 Page 16 of 18 Eur. Phys. J. C (2021) 81:630 24 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy 25 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy 26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy 27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy 28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padua, Italy 29 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy 30 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy 31 Dipartimento di Scienze e Innovazione Tecnologica dell’Università del Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy 32 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy 33 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy 34 European Organization for Nuclear Research (CERN), Geneva, Switzerland 35 Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia 36 Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway 37 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic 38 Faculty of Science, P.J. Šafárik University, Kosice, Slovakia 39 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 40 Fudan University, Shanghai, China 41 Gangneung-Wonju National University, Gangneung, Republic of Korea 42 Department of Physics, Gauhati University, Guwahati, India 43 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany 44 Helsinki Institute of Physics (HIP), Helsinki, Finland 45 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico 46 Hiroshima University, Hiroshima, Japan 47 Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation (ZTT), Worms, Germany 48 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania 49 Indian Institute of Technology Bombay (IIT), Mumbai, India 50 Indian Institute of Technology Indore, Indore, India 51 Indonesian Institute of Sciences, Jakarta, Indonesia 52 INFN, Laboratori Nazionali di Frascati, Frascati, Italy 53 INFN, Sezione di Bari, Bari, Italy 54 INFN, Sezione di Bologna, Bologna, Italy 55 INFN, Sezione di Cagliari, Cagliari, Italy 56 INFN, Sezione di Catania, Catania, Italy 57 INFN, Sezione di Padova, Padua, Italy 58 INFN, Sezione di Roma, Rome, Italy 59 INFN, Sezione di Torino, Turin, Italy 60 INFN, Sezione di Trieste, Trieste, Italy 61 Inha University, Incheon, Republic of Korea 62 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, The Netherlands 63 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia 64 Institute of Experimental Physics, Slovak Academy of Sciences, Kosice, Slovakia 65 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India 66 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 67 Institute of Space Science (ISS), Bucharest, Romania 68 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 69 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico 70 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil 71 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico 72 iThemba LABS, National Research Foundation, Somerset West, South Africa 73 Jeonbuk National University, Jeonju, Republic of Korea 74 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik und Mathematik, Frankfurt, Germany 123 Eur. Phys. J. C (2021) 81:630 Page 17 of 18 630 75 Joint Institute for Nuclear Research (JINR), Dubna, Russia 76 Korea Institute of Science and Technology Information, Daejeon, Republic of Korea 77 KTO Karatay University, Konya, Turkey 78 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France 79 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France 80 Lawrence Berkeley National Laboratory, Berkeley, CA, USA 81 Lund University Department of Physics, Division of Particle Physics, Lund, Sweden 82 Moscow Institute for Physics and Technology, Moscow, Russia 83 Nagasaki Institute of Applied Science, Nagasaki, Japan 84 Nara Women’s University (NWU), Nara, Japan 85 Department of Physics, School of Science, National and Kapodistrian University of Athens, Athens, Greece 86 National Centre for Nuclear Research, Warsaw, Poland 87 National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India 88 National Nuclear Research Center, Baku, Azerbaijan 89 National Research Centre Kurchatov Institute, Moscow, Russia 90 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 91 Nikhef, National institute for subatomic physics, Amsterdam, The Netherlands 92 NRC Kurchatov Institute IHEP, Protvino, Russia 93 NRC “Kurchatov” Institute-ITEP, Moscow, Russia 94 NRNU Moscow Engineering Physics Institute, Moscow, Russia 95 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, UK 96 Nuclear Physics Institute of the Czech Academy of Sciences, ˇ Režu Prahy, Czech Republic 97 Oak Ridge National Laboratory, Oak Ridge, TN, USA 98 Ohio State University, Columbus, OH, USA 99 Petersburg Nuclear Physics Institute, Gatchina, Russia 100 Physics Department, Faculty of science, University of Zagreb, Zagreb, Croatia 101 Physics Department, Panjab University, Chandigarh, India 102 Physics Department, University of Jammu, Jammu, India 103 Physics Department, University of Rajasthan, Jaipur, India 104 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany 105 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 106 Physik Department, Technische Universität München, Munich, Germany 107 Politecnico di Bari and Sezione INFN, Bari, Italy 108 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 109 Rudjer Boškovi´c Institute, Zagreb, Croatia 110 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia 111 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India 112 School of Physics and Astronomy, University of Birmingham, Birmingham, UK 113 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru 114 St. Petersburg State University, St. Petersburg, Russia 115 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria 116 SUBATECH, IMT Atlantique, CNRS-IN2P3, Université de Nantes, Nantes, France 117 Suranaree University of Technology, Nakhon Ratchasima, Thailand 118 Technical University of Košice, Kosice, Slovakia 119 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 120 The University of Texas at Austin, Austin, TX, USA 121 Universidad Autónoma de Sinaloa, Culiacán, Mexico 122 Universidade de São Paulo (USP), São Paulo, Brazil 123 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 124 Universidade Federal do ABC, Santo Andre, Brazil 125 University of Cape Town, Cape Town, South Africa 126 University of Houston, Houston, TX, USA 123 630 Page 18 of 18 Eur. Phys. J. C (2021) 81:630 127 University of Jyväskylä, Jyvaskyla, Finland 128 University of Liverpool, Liverpool, UK 129 University of Science and Technology of China, Hefei, China 130 University of South-Eastern Norway, Tonsberg, Norway 131 University of Tennessee, Knoxville, TN, USA 132 University of the Witwatersrand, Johannesburg, South Africa 133 University of Tokyo, Tokyo, Japan 134 University of Tsukuba, Tsukuba, Japan 135 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 136 CNRS/IN2P3, IPN-Lyon, Université de Lyon, Université Lyon 1, Villeurbanne, Lyon, France 137 CNRS, IPHC UMR 7178, Université de Strasbourg, 67000 Strasbourg, France 138 Départment de Physique Nucléaire (DPhN), IRFU, Université Paris-Saclay Centre d’Etudes de Saclay (CEA), Saclay, France 139 Università degli Studi di Foggia, Foggia, Italy 140 Università degli Studi di Pavia and Sezione INFN, Pavia, Italy 141 Università di Brescia and Sezione INFN, Brescia, Italy 142 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India 143 Warsaw University of Technology, Warsaw, Poland 144 Wayne State University, Detroit, MI, USA 145 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik, Münster, Germany 146 Wigner Research Centre for Physics, Budapest, Hungary 147 Yale University, New Haven, CT, USA 148 Yonsei University, Seoul, Republic of Korea aAlso at: Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy bAlso at: Dipartimento DET del Politecnico di Torino, Turin, Italy cAlso at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia dAlso at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India eAlso at: Institute of Theoretical Physics, University of Wroclaw, Wrocław, Poland fDeceased 123