Underlying-event properties in pp and p$-$Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV

We report about the properties of the underlying event measured with ALICE at the LHC in pp and p$-$Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV. The event activity, quantified by charged-particle number and summed-$p_{\rm T}$ densities, is measured as a function of the leading-particle transverse momentum ($p_{\rm T}^{\rm trig}$). These quantities are studied in three azimuthal-angle regions relative to the leading particle in the event: toward, away, and transverse. Results are presented for three different $p_{\rm T}$ thresholds (0.15, 0.5, and 1 GeV/$c$) at mid-pseudorapidity ($|\eta|<0.8$). The event activity in the transverse region, which is the most sensitive to the underlying event, exhibits similar behaviour in both pp and p$-$Pb collisions, namely, a steep increase with $p_{\rm T}^{\rm trig}$ for low $p_{\rm T}^{\rm trig}$, followed by a saturation at $p_{\rm T}^{\rm trig} \approx 5$ GeV/$c$. The results from pp collisions are compared with existing measurements at other centre-of-mass energies. The quantities in the toward and away regions are also analyzed after the subtraction of the contribution measured in the transverse region. The remaining jet-like particle densities are consistent in pp and p$-$Pb collisions for $p_{\rm T}^{\rm trig}>10$ GeV/$c$, whereas for lower $p_{\rm T}^{\rm trig}$ values the event activity is slightly higher in p$-$Pb than in pp collisions. The measurements are compared with predictions from the PYTHIA 8 and EPOS LHC Monte Carlo event generators.

T ≈ 5 GeV/c. The results from pp collisions are compared with existing measurements at other centre-of-mass energies. The quantities in the toward and away regions are also analyzed after the subtraction of the contribution measured in the transverse region. The remaining jet-like particle densities are consistent in pp and p-Pb collisions for p trig T > 10 GeV/c, whereas for lower p trig T values the event activity is slightly higher in p-Pb than in pp collisions. The measurements are compared with predictions from the PYTHIA 8 and EPOS LHC Monte Carlo event generators.

Introduction
In non-diffractive proton-proton (pp) collisions at high energies, the underlying event (UE) consists of the set of particles that arise from the proton break-up (beam remnants), and from other semi-hard scatterings, in a scenario of multiparton interactions (MPI) [1]. The UE activity accompanies high transverse momentum (p T ) particles produced by the main partonic scattering (jets). Experimental studies aimed at probing the UE component are commonly performed in azimuthal-angle regions where the contribution from the hard scattering is expected to be minimal. The present study follows the strategy originally introduced by the CDF collaboration [2]. Firstly, the leading particle (or trigger particle) in the event is found, i.e., the charged particle with the highest transverse momentum in the collision (p trig T ). Secondly, the associated particles for three different thresholds of the transverse momentum, p T > 0.15, 0.5, and 1 GeV/c, are grouped in three classes depending on their relative azimuthal angle with respect to the leading particle, |∆ϕ| = |ϕ assoc − ϕ trig |: -toward: | ∆ϕ |< 60 • , -transverse: 60 • <| ∆ϕ |< 120 • , and -away: | ∆ϕ |> 120 • .
The three topological regions corresponding to the azimuthal-angle intervals defined above are illustrated in Fig. 1. The toward region contains the primary jet of the collision, while the away region contains the recoiled jet [3]. In contrast, the transverse region is mostly dominated by the UE dynamics, but it also includes contributions from initial-and final-state radiation (ISR and FSR) [4]. This strategy [2] has been used by several experiments at RHIC [5], the Tevatron [2,[6][7][8], and the LHC [9][10][11][12][13][14]. The studies include measurements in events with Drell-Yan [15] and Z-boson [16-18] production.
Experimental results have shown that the event activity, quantified by charged-particle number or summedp T densities, in the transverse region rises steeply with increasing p trig T at low p trig T (< 5 GeV/c), and then it roughly saturates (plateau) for larger p trig T [14]. This saturation is expected in models that include the concept of impact parameter such that the requirement of the presence of a high-p T particle in a pp collision biases the selection of collisions towards those with a small impact parameter [19]. Based on UE observables measured at LHC centre-of-mass energies, √ s = 0.9, 7, and 13 TeV, the event activity in the plateau region has been found to increase faster with increasing √ s than in minimum-bias pp collisions [11,14]. An analogous study for p-Pb collisions has never been performed, although an attempt to determine the correlation between the impact parameter of the collision and the charged-particle multiplicity has been reported [20].
Underlying-event properties in pp and p-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration for each topological region in p-Pb collisions is compared with that in pp collisions at the same p trig T . In order to search for a possible system size dependence of the jet-like particle densities, the jet-like signal (in the toward and away regions) is further isolated by subtracting the UE contribution estimated from the transverse region. The results from pp collisions are compared to predictions from the EPOS tune LHC [33] and PYTHIA 8.244 (Monash 2013 tune [30]) Monte Carlo event generators, hereinafter referred to as EPOS LHC and PYTHIA 8/Monash, respectively. For p-Pb collisions, data are compared to EPOS LHC and PYTHIA 8/Angantyr [34].
For pp collisions, the modelling of UE in PYTHIA 8/Monash considers an impact-parameter dependent MPI activity. The partonic configuration is hadronised using string fragmentation as described by the Lund string model [35], followed by the decays of unstable particles. In collisions with several MPI, individual long strings connected to the remnants are replaced by shorter additional strings connecting partons from different semi-hard scatterings (colour reconnection). The Monash 2013 tune used minimum-bias, Drell-Yan, and UE data from the LHC to constrain the initial-state radiation and multiparton interactions, combined with data from the SPS and the Tevatron to constrain the scaling with the collision energy. The simulation of p-Pb collisions was performed with the recent model named Angantyr [34], which is based on an extrapolation of pp dynamics with a minimum number of free parameters. The model does not assume the formation of a hot thermalised medium, instead, the generalisation to collisions involving nuclei is inspired by the Fritiof model [36] and the notion of "wounded" or "participating" nucleons. The number of wounded nucleons is calculated from the Glauber model in impact parameter space. With these assumptions, the model is able to give a good description of general final-state properties such as multiplicity and transverse momentum distributions of particles produced in interactions involving heavy nuclei.
In EPOS LHC, the description of multiple partonic scatterings is based on a combination of Gribov-Regge theory and pQCD [37]. An elementary scattering corresponds to a parton ladder, containing a hard scattering which is calculated based on pQCD, including initial-and final-state radiation. Parton ladders that are formed in parallel to each other share the total collision energy leading to consistent treatment of energy conservation in hadronic collisions. String hadronisation in EPOS is based on the local density of the string segments per unit volume with respect to a critical-density parameter. Eventby-event, string segments in low-density regions hadronise normally and independently, creating the so-called corona, while string segments in high-density regions are used to create a core with collective expansion resulting in radial and longitudinal flow effects. The EPOS LHC tune considered here [33] This analysis is based on the data recorded by the ALICE apparatus during the pp run at √ s = 5.02 TeV in 2015, and the p-Pb run at √ s NN = 5.02 TeV in 2016. The data were collected using a minimumbias trigger, which required a signal in both V0A and V0C detectors. Only events with a reconstructed vertex within ±10 cm from the nominal interaction point along the beam direction are used. Runs with a low number of interactions per bunch crossing (µ) were selected resulting in average µ values of 0.020 and 0.005 for pp and p-Pb collisions, 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 interaction vertices reconstructed using the SPD information. The remaining undetected pileup is negligible for this analysis, while the fraction of wrongly-tagged events due to SPD vertex splitting from a single interaction is < 10 −4 for both collision systems. The offline event selection is optimised to reject beam-induced background by exploiting the timing signals in the two V0 sub-detectors. The event selection also requires at least one track with a minimum transverse momentum (p T = 0.15, 0.5, and 1.0 GeV/c) in the acceptance range |η| < 0.8. The results presented in this article were obtained from the analysis of about 180 and 332 million minimum-bias pp and p-Pb collisions, respectively.

Analysis details 3.1 Track reconstruction and selection
The event properties are studied from the number and the momenta of the primary charged particles in the pseudorapidity interval |η| < 0.8. Primary particles are defined as 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 a mean proper lifetime smaller than 1 cm/c [40]. Charged particles are reconstructed with the ITS and TPC detectors, providing a measurement of the track transverse momentum p T and azimuthal angle ϕ, which are used in the analysis. Tracks are required to have at least two hits in the ITS detector, of which at least Underlying-event properties in pp and p-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration one in either of the two innermost layers. The ratio of crossed TPC pad rows to the number of findable TPC clusters is required to be larger than 0.8, and the fraction of TPC clusters shared with another track should be less than 0.4. In addition, tracks are required to have a number of crossed TPC pad rows larger than 0.85 × L, where L (in cm) is the geometrical track length calculated in the TPC readout plane, excluding the information from the pads at the sector boundaries (≈ 3 cm from the sector edges). The number of TPC clusters associated to the track is required to be larger than 0.7 × L. The fit quality for the ITS and TPC track points must satisfy χ 2 ITS /N hits < 36 and χ 2 TPC /N clusters < 4, respectively, where N hits and N clusters are the number of hits in the ITS and the number of clusters in the TPC, respectively. To select primary particles, tracks having a large distance of closest approach (DCA) to the reconstructed vertex in the longitudinal (d z > 2 cm) and radial (d xy > 0.018 cm +0.035 cm×(GeV/c)×p −1 T ) directions are rejected. To further reduce the contamination from secondary particles, only tracks with χ 2 TPC−ITS < 36 are included in the analysis, where χ 2 TPC−ITS is calculated by comparing the track parameters from the combined ITS and TPC track reconstruction to those derived only from the TPC and constrained by the interaction point [41]. For this track selection [42], the momentum resolution is approximately 3-4% at p T = 0.15 GeV/c, it 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, and collision system. The measurements presented in this work are not corrected for momentum resolution but the effects are included by the systematic uncertainties.

Underlying-event observables
The transverse momentum spectra (p T ) as a function of p trig T are corrected for all p trig T intervals and are extracted for each topological region. Then, both the primary charged-particle number and the summed transverse-momentum densities are calculated from the p T spectra. The event activity in each topological region is measured as a function of p trig T . It is quantified with the primary charged-particle number density: and the summed transverse-momentum density: where N ev (p trig T ) is the total number of events with the leading particle in a given p trig T interval; N ch (p trig T ) and ∑ p T (p trig T ) stand for multiplicity and sum of the p T of all reconstructed tracks within a given topological region, respectively. Finally, ∆η is the pseudorapidity interval used in the analysis. This paper also reports the charged-particle number and the summed-p T densities in the toward and away regions after the subtraction of the event activity in the transverse region. All these quantities are measured as a function of p trig T . The charged-particle number density in the jet-like signal is derived from the difference between the number density in the toward (or away) region and that in the transverse region: In the same way, the summed-p T density in the jet-like signal is obtained as follows: Underlying-event properties in pp and p-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration The ratio between these two quantities gives the average transverse momentum in the jet-like signal: .

Corrections
The correction of p T spectra of charged particles follows the standard procedure of the ALICE collaboration [42,43]. The raw yields are corrected for efficiency and contamination from secondary particles. The efficiency correction is calculated from Monte Carlo simulations including the propagation of particles through the detector using GEANT 3 [44]. For pp and p-Pb collisions the PYTHIA 8 and EPOS LHC Monte Carlo event generators are used for this purpose, respectively. As the relative abundances of different charged particle species are different in the data and in the simulations, the efficiency obtained from the simulations is re-weighted considering the primary charged particle composition measured by ALICE [45], as described in Ref. [42]. At p T = 0.15 GeV/c the efficiency correction amounts to ≈ 35%, which is related to the strong track curvature caused by the magnetic field and to the energy loss in the detector material. It is followed by a maximum value of 78% at p T ≈ 0.4 GeV/c, and a minimum (≈ 53%) at around p T of 1 GeV/c which is caused primarily by the track length requirement. At higher p T the efficiency correction reaches an asymptotic value of 70% which reflects the acceptance limitations (detector boundaries and active channels) of the measurement [42]. The residual contamination from secondary particles in the sample of selected tracks is estimated via a fit to the measured d xy distributions by a combination of the d xy distributions (templates) of primary and secondary particles obtained from the simulations [42].
Due to the finite acceptance and the efficiency of the detection apparatus, the leading particle may not be detected, and a track with lower p T could be considered as the trigger particle. If the misidentified leading particle has a different p T but roughly the same direction as the true leading particle, this leads to a small effect on the UE observables [11]. On the other hand, if the misidentified leading particle has a significantly different direction than the true one, this will cause a rotation of the event topology and a bias on the UE observables. Therefore, the particle densities are corrected for these effects using a data-driven procedure described in detail in Ref. [11]. A minor correction due to the finite vertex reconstruction efficiency is also applied to the UE observables. The statistical uncertainty from the MC simulations was properly propagated to the final statistical uncertainties on data, but the analysis was performed in such a way that the correction factors are not strongly affected by the MC statistical uncertainties.

Systematic uncertainties
The relative systematic uncertainties on the quantities presented in Eqs. 1, 2, 3, 4, and 5 are summarised in Table 1 for pp and p-Pb collisions. The details about the different conditions varied in the analysis to estimate the systematic uncertainties are described below.
-Secondary contamination: the fits to the d xy distributions with the templates from the simulations were repeated using different fit intervals, namely −1 < d xy < 1 cm and −2 < d xy < 2 cm, instead of the default interval −3 < d xy < 3 cm. The maximum deviation with respect to the result obtained with the default fit range was assigned as systematic uncertainty.
-Correction method: a possible bias introduced by imperfections in the correction procedure was estimated by performing the analysis on a Monte Carlo sample of pp collisions simulated with a given event generator. The generated particles were propagated through the detector and the reconstructed quantities were corrected with the same procedure applied to the real data utilising the Underlying-event properties in pp and p-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration correction factors extracted from simulations performed with the same event generator. The reconstructed quantities considers all tracks which satisfies the selection criteria, they include tracks from primary and secondary particles, as well as fake tracks. Momentum resolution effects are also considered in the reconstructed quantities. With this approach, one expects to reproduce the generated yields, i.e. the yields obtained from the event generator without any detector effect, within statistical uncertainty. This consideration holds only if each correction is evaluated with respect to all the variables to which the given correction is sensitive. Any statistically significant difference between input and corrected distributions is added in quadrature to the total systematic uncertainty. This uncertainty is the only one which is different for each topological region.
-Track selection: the systematic uncertainty related to the track selection criteria was determined by varying the track quality cuts [42,43]. In particular, 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 ) were varied in the ranges of 25-49 and 3-5, respectively. The minimum ratio of crossed TPC pad rows to the number of findable TPC clusters was varied within (0.7-0.9). The maximum fraction of shared TPC clusters was varied between 0.2 and 1, and the maximum d z was varied within 1-5 cm. The impact on the results due to the hit requirement in the SPD was also evaluated by removing that requirement from the track selection. The maximum deviation of the results obtained varying the selections (only a single track cut at a time) with respect to the result obtained using the default track selection criteria was assigned as systematic uncertainty on each individual track-quality variable. The total uncertainty is then calculated as the sum in quadrature of each contribution. Table 1: Main sources and values of the relative systematic uncertainties of the charged-particle number and summed-p T densities in pp and p-Pb collisions at √ s NN = 5.02 TeV. The average values of the uncertainties for the p trig T intervals 0.5-2 GeV/c and 5-40 GeV/c are displayed in the left and right columns, respectively. These uncertainties correspond to the transverse momentum threshold p T > 0.5 GeV/c. When more than one number is quoted, the values refer to the uncertainty in toward, transverse, and away regions, respectively; they are independent of the azimuthal region in all other cases.

Number density
Summed-p T density p   -ITS-TPC track matching efficiency: a systematic uncertainty on the track reconstruction efficiency originates from possible differences in the probability to match the TPC tracks to the ITS hits in data and in simulations. It was estimated by comparing the matching efficiency in data and simulations and propagating their difference to the underlying-event observables used in the analysis.
-Leading-particle misidentification bias: the uncertainty on the leading-track misidentification correction is estimated from the discrepancy between the data-driven correction used in the analysis and the correction obtained from simulated data where the true leading particle is known.
-Event-selection bias: the systematic uncertainty due to event selection is obtained by varying from 5 to 15 cm the cut on the absolute value of the z component of the vertex position. The maximum deviation of the results obtained varying the vertex position with respect to the result obtained using the default cut (10 cm) is assigned as systematic uncertainty. This contribution is found to be negligible.

Results and discussion
4.1 Underlying-event observables: pp compared to p-Pb collisions Figure 2 compares the charged-particle number density as a function of p trig T in the transverse region for the three p T thresholds: 0.15 GeV/c, 0.5 GeV/c, and 1 GeV/c. Figure 2 also shows the predictions of the event generators. For all the figures presented in this paper the statistical uncertainties in Monte Carlo predictions are not shown to facilitate the visualization of the data. In general the statistical error in MC is up to 2% and 7% for p trig T values of 10 and 20 GeV/c, respectively. The results from pp and p-Pb collisions exhibit similar behaviour: the number density steeply rises for low p trig T , and it flattens at p trig T ≈ 5 GeV/c (plateau region). In the plateau region, the event activity in p-Pb collisions is ≈ 2 times larger than the one measured in pp collisions. This increase is smaller than that (about a factor of 3) observed for the charged-particle multiplicity densities dN ch /dη in non-single-diffractive p-Pb collisions compared to pp collisions at the same nucleon-nucleon centre-of-mass energy [46]. It should also be Underlying-event properties in pp and p-Pb collisions at √ s NN = 5.  noted that for both collision systems increasing the p T threshold from 0.15 GeV/c to 1.0 GeV/c reduces the charged-particle number density by about a factor of 4. For pp collisions, the charged-particle number density shows a slightly increasing trend with increasing p trig T in the plateau region (p trig T > 5 GeV/c). This increase is more pronounced for larger values of the p T threshold for associated tracks, indicating an increased contribution of correlated hard processes (initial-and final-state radiation) to the transverse region. For example, for the p T threshold p T > 1 GeV/c, the charged-particle number density increases from 0.3 to 0.45 (i.e., by about 50%) when p trig T is increased from 5 to 40 GeV/c. Whereas for the p T threshold p T > 0.15 GeV/c, the increase is less than 10%. In contrast, for p-Pb collisions the chargedparticle number density in the plateau region is flat for all the p T thresholds. This behaviour also suggests that the contamination from the main partonic scattering in the transverse region is smaller in p-Pb than in pp collisions. Figure 2 also shows the predictions of the event generators. EPOS LHC better describes the p trig T dependence of the charged-particle multiplicity density for pp collisions relative to p-Pb collisions. For p-Pb collisions, EPOS LHC significantly underestimates the charged-particle number density, and it does not reproduce the trend with p trig T and the value at the plateau observed in data. In contrast, PYTHIA 8/Angantyr qualitatively reproduces the measured trends with p trig T in p-Pb collisions, providing a good quantitative description of the data for the lowest p T threshold (p T > 0.15 GeV/c), while it underestimates the measured densities in the plateau region for higher p T thresholds. In the following, measurements with the p T threshold requirement of 0.5 GeV/c for associated particles are reported and discussed. Results for other p T thresholds (p T > 0.15 GeV/c and > 1.0 GeV/c) are presented in Appendix A. 5 GeV/c the charged-particle number density becomes almost independent of p trig T (plateau) in the transverse region, as already pointed out above, while in the toward and away regions it continues to rise with increasing p trig T . The continuous rise observed for the toward and away regions can be attributed to the fact that produced particles in these regions do not originate only from the UE, but have also a contribution due to fragments from hard scatterings, which are mostly collimated in azimuth. The contribution from fragments increases with                  Results for data and comparison with models PYTHIA 8 (green) and EPOS LHC (red) predictions for the away (upper) and toward (bottom) regions, after the subtraction of the charged-particle number (left) and summed-p T (right) densities in the transverse region, are shown. Bottom panels: charged-particle number and summed-p T densities measured in pp collisions divided by those in p-Pb collisions are displayed for both data and models.
increasing p trig T causing the rise of event activity. A qualitatively similar behaviour in pp and p-Pb collisions is observed. However, the event activity in the toward and away regions in pp collisions increases faster with p trig T than in p-Pb collisions, namely, the increase of the particle density from p trig T = 5 GeV/c up to p trig T = 40 GeV/c amounts to a factor of ≈ 2 and ≈ 1.4 in pp and p-Pb collisions, respectively. Moreover, at p trig T = 35 GeV/c the relative level of the event activity in the transverse region with respect to that in the toward (away) region is ≈ 0.4 and ≈ 0.60 (≈ 0.5 and ≈ 0.65) for pp and p-Pb collisions, respectively. This indicates that the UE contribution to the toward and away regions is larger in p-Pb than in pp collisions, which is expected because of multiple nucleon-nucleon collisions in a single p-Pb collision that give a large additional UE, with respect to MPI in the same pp collision. Figure 4 shows comparisons between the data from pp collisions and the predictions of event generators for both the primary charged-particle number, and the summed-p T densities in the three considered azimuthal regions (toward, away, and transverse). Although the modelling of the UE activity in PYTHIA 8/Monash is completely different with respect to that implemented in EPOS LHC, both models qualitatively describe the measured charged-particle densities in the three azimuthal regions. In the away Underlying-event properties in pp and p-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration region, within uncertainties, PYTHIA 8/Monash describes the data better than EPOS LHC in the full p trig T range of the measurement. The maximum deviation of EPOS LHC with respect to data is around 10% and 20% for the number density and summed-p T density, respectively, in the p trig T interval 5-15 GeV/c. Regarding the toward region, PYTHIA 8/Monash predictions overestimate the event activity by 10% for p trig T < 5 GeV/c, whereas for higher p trig T PYTHIA 8/Monash describes the data quite well. The situation is the opposite for EPOS LHC: at low p trig T EPOS LHC describes well the event activity, but it significantly underestimates the particle densities for higher p trig T (> 8 GeV/c) by ≈ 30%. Figure 5 shows data-to-model comparisons for the case of p-Pb collisions. For the transverse region, as already pointed out above, PYTHIA 8/Angantyr provides a better qualitative description of the measured trend of the charged-particle number densities as compared to EPOS LHC. However, both PYTHIA 8/Angantyr and EPOS LHC underestimate the charged-particle summed-p T (number) density for p trig T > 5 GeV/c by more than 20% (10%). While for PYTHIA 8/Angantyr this discrepancy stays roughly constant up to p T ≈ 3 GeV/c, for EPOS LHC the discrepancy increases up to 50% at p T ≈ 3 GeV/c. For the toward and away regions, as visible from the ratio plots in the bottom panels of  Figure 6 shows the jet-like contribution to the charged-particle number and summed-p T densities in the toward and away regions as a function of p trig T for pp and p-Pb collisions at √ s NN = 5.02 TeV. As discussed earlier, the event activity for the jet-like signals is obtained from the event activity in the toward and away regions after subtracting the event activity in the transverse region (see Eq. 3 and Eq. 4). In contrast to the behaviour observed for the toward and away regions, where at p trig T ≈ 5 GeV/c the event activity tends to flatten out, the densities in the jet-like signals rise with increasing p trig T in the entire range of the measurement.

Event activity in the jet-like signals
At high p trig T (p trig T > 10 GeV/c), the event activity in the jet-like signals exhibits a remarkable similarity between measurements in pp and p-Pb collisions for both charged-particle multiplicity and summed-p T densities. Within 10%, both PYTHIA 8/Angantyr and EPOS LHC reproduce this feature. At low p trig T (p trig T < 10 GeV/c), the models overestimate the event activity in the jet-like signals measured in p-Pb collisions. The disagreement is more remarkable for EPOS LHC than for PYTHIA 8/Angantyr. For pp collisions, PYTHIA 8 slightly overestimates the event activity, while EPOS LHC underestimates the particle densities. For p trig T < 10 GeV/c, the event activity in pp collisions scaled to that in p-Pb collisions is smaller than unity, reaching a minimum of ≈ 0.8 at p trig T ≈ 3 GeV/c. This behaviour is not reproduced by PYTHIA 8/Angantyr, which gives a ratio above unity for p trig T > 1 GeV/c. In contrast, EPOS LHC exhibits a similar pattern, but the size of the effect is much larger than in data. The main difference between PYTHIA 8/Angantyr and EPOS LHC is that EPOS LHC incorporates collective flow, which is expected to be significant in the p     not reproduce this behaviour. They predict that in the away region the average p T for the jet-like signal in pp collisions is about 20% (10%) larger than in p-Pb collisions for p trig T < 2 GeV/c (p trig T > 5 GeV/c). For the toward region, the situation is similar at high p trig T ; however, for p trig T < 2 GeV/c, the p T in p-Pb collisions is predicted to be about 20% larger than in pp collisions. Although the main source of this discrepancy is the underestimation of the measured p T in p-Pb collisions by PYTHIA 8/Angantyr, the prediction for pp collisions is lower than the measured p T in the away region. The agreement of PYTHIA 8/Monash with pp data is better for the toward region. On the other hand, EPOS LHC reproduces the average p T for the two collision systems better than PYTHIA 8/Angantyr. Although, for p trig T < 10 GeV/c, EPOS LHC predicts the p T in the toward region to be larger in pp as compared to p-Pb collisions, leading to a bump-like structure in the ratio of pp over p-Pb results, which is not observed in the data.

Energy dependence of the underlying event in pp collisions
This subsection discusses the collision-energy dependence of the charged-particle number density in the transverse region. Given that data from experiments at RHIC, the Tevatron and the LHC, are available for the p T threshold, p T > 0.5 GeV/c, our results for this p T threshold are compared with existing measurements at other centre-of-mass energies.  Fig. 8). The fitting range was restricted to that common range in order to be consistent with the procedure used for the measurements at other centre-of-mass energies. Larger fitting ranges were also considered, and consistent results were obtained. The shapes of the particle densities as a function of p trig T are then compared after dividing the densities by the level of the plateau, as estimated from the fit to a constant value. The results are shown in Fig. 8 (right). For the two higher energies, the p trig T coverage extends beyond the fitting range, i.e. to p trig T > 10 GeV/c. In this range, the densities agree within the statistical and systematic uncertainties. In the rise region ( p trig T < 5 GeV/c), one observes a clear ordering among the four collision energies, the lowest energy having the highest density relative to the plateau. Moreover, at lower √ s, the plateau values seem to be reached at a slightly lower p trig T . This feature is also observed in pp collisions simulated with the PYTHIA 8 event generator [52]. Figure 9 shows the √ s dependence of the charged-particle number density measured in the transverse azimuthal interval and in the high p trig T interval of the plateau region. Results from various experiments at RHIC [3], the Tevatron [2,56], and the LHC [11, 51, 53-55, 57] are displayed. The ATLAS, CDF, CMS, and STAR data points are taken from the compilation reported by the STAR collaboration [3]. The event activity shows a modest increase from √ s = 0.2 up to 0.9 TeV, while for higher energies it exhibits a steeper rise. This behaviour is described by a function of the form ∝ s 0.27 + 0.14 log(s), in which the power-law term describes the UE contribution, whereas the logarithmic term describes the contribution from ISR and FSR. The parametrisation was taken from Ref. [58]. A comparison to the charged particle multiplicity at mid-pseudorapidity in minimum-bias pp data, where dN ch /dη can be parameterised as dN ch /dη ∝ s 0.114 [59], suggests that the UE contribution increases faster with centre-of-mass energy than the charged particle multiplicity in minimum-bias pp collisions.
Underlying-event properties in pp and p-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration

Conclusions
In this paper, the measurements of underlying-event observables performed in pp and p-Pb collisions at a centre-of-mass energy per nucleon-nucleon collisions of 5.02 TeV were reported. The analysis was carried out following the strategy introduced by the CDF collaboration consisting of the definition of three azimuthal regions relative to the highest transverse momentum particle in the collision (p trig T ). The charged-particle production is measured within the pseudorapidity interval |η| < 0.8; and it is quantified with the number and summed-p T densities considering particles above a given p T threshold. Three p T thresholds are considered: 0.15, 0.5, and 1 GeV/c. These quantities are reported as a function of p trig T , and for the toward, away, and transverse azimuthal regions. The transverse region is the most sensitive to the underlying event; while the toward and away regions include both the underlying-event and jet fragments from the main partonic scattering. For the isolation of the jet-like signal, the event activity in the transverse region is subtracted from those measured in the toward and away regions. Results for pp collisions are compared with data at other centre-of-mass energies and with MC predictions. In addition, the event activities measured in pp and p-Pb collisions are compared with each other at the same p trig T value. The main conclusions of the present work are listed below.
-The underlying-event observables in pp collisions follow the same behaviour as observed at lower centre-of-mass energies. In the transverse region the charged-particle densities measured in the three azimuthal regions exhibit a fast rise for p trig T < 5 GeV/c followed by a flattening at higher p trig T (plateau). Data for the three azimuthal regions relative to the leading particle are reproduced by the PYTHIA 8 event generator with the Monash tune. EPOS LHC predicts a slightly different behaviour in particular at p trig T around 3 GeV/c where a bump structure is present in the three azimuthal regions which is not observed in the data.
-The underlying-event observables in p-Pb collisions qualitatively behave like in pp interactions.
The particle densities in the transverse region exhibit a saturation at p trig T ≈ 5 GeV/c. PYTHIA 8/Angantyr qualitatively reproduces this saturation but underestimates the particle densities. The EPOS LHC model does not describe the saturation and underestimates the event activity within the measured p trig T interval. For the toward and away regions, above the onset of the plateau, data exhibit Underlying-event properties in pp and p-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration a slower increase of the particle densities with increasing p trig T than that observed in pp collisions. EPOS LHC and PYTHIA 8/Angantyr underestimate the particle densities at high p trig T (> 8 GeV/c). At lower p trig T , EPOS LHC predicts a bump structure at p trig T ≈ 4 GeV/c which is not seen in data. For p trig T < 3 GeV/c, EPOS LHC describes the particle densities, whereas PYTHIA 8/Angantyr overestimates those in data by up to 30%.
-The particle densities in the toward and away regions after subtraction of the UE contribution as a function of p trig T in pp collisions are consistent with those measured in p-Pb collisions for p trig T > 10 GeV/c, i.e., no modification of the jet-like yield in p-Pb collisions relative to pp collisions is found. At lower p trig T , the charged-particle densities are larger in p-Pb collisions relative to pp collisions. This behaviour is expected given the larger collective flow effects in p-Pb collisions relative to pp collisions. This feature is qualitatively captured by the EPOS LHC generator, which incorporates collective flow effects in the modelling of the system created in the collision. However, the size of the effect is significantly larger in EPOS LHC than in data. An opposite trend is instead predicted by simulations with PYTHIA 8/Angantyr, which do not include collective effects. The average p T as a function of p trig T was also measured. The average p T values measured in pp and p-Pb collision are found to be consistent between each other in the entire p trig T interval of the measurement. Simulations with EPOS LHC predict instead a slightly lower average p T for jetlike signal in p-Pb collisions as compared to pp collisions for p trig T < 10 GeV/c, while PYTHIA 8 with the Monash and Angantyr tunes do not provide a good description for this observable.
The measurements reported in this article represent important input for the tuning of some of the parameters of the event generators in order to improve the modelling of soft particle production in pp and p-Pb collisions. Moreover, they can contribute to the understanding of the origin of signals resembling a collective behaviour in pp and p-Pb collisions.

Acknowledgements
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:        [40] ALICE Collaboration, "The ALICE definition of primary particles",. https://cds.cern.ch/record/2270008.        Underlying-event properties in pp and p-Pb collisions at √ s NN = 5.02 TeV ALICE Collaboration

A Appendix
A.1 Charged-particle densities as a function of p trig T for others p T thresholds The charged-particle number and summed-p T densities as a function of p trig T measured in pp collisions at √ s = 5.02 TeV, in the transverse, away, and toward regions for the transverse momentum thresholds p T > 0.15 GeV/c and p T > 1 GeV/c are shown in figures A.1 and A.2, respectively. The charged-particle number and summed-p T densities as a function of p