Production of pions, kaons, and protons as a function of the relative transverse activity classifier in pp collisions at $\sqrt{s}=13$ TeV

The production of $\pi^\pm$, ${\rm K}^\pm$, and $(\overline{\rm p})$p is measured in pp collisions at $\sqrt{s}=13$ TeV in different topological regions. Particle transverse momentum ($p_{\rm T}$) spectra are measured in the ``toward'', ``transverse'', and ``away'' angular regions defined with respect to the direction of the leading particle in the event. While the toward and away regions contain the fragmentation products of the near-side and away-side jets, respectively, the transverse region is dominated by particles from the Underlying Event (UE). The relative transverse activity classifier, $R_{\rm T}=N_{\rm T}/\langle N_{\rm T}\rangle$, is used to group events according to their UE activity, where $N_{\rm T}$ is the measured charged-particle multiplicity per event in the transverse region and $\langle N_{\rm T}\rangle$ is the mean value over all the analysed events. The first measurements of identified particle $p_{\rm T}$ spectra as a function of $R_{\rm T}$ in the three topological regions are reported. The yield of high transverse momentum particles relative to the $R_{\rm T}$-integrated measurement decreases with increasing $R_{\rm T}$ in both the toward and away regions, indicating that the softer UE dominates particle production as $R_{\rm T}$ increases and validating that $R_{\rm T}$ can be used to control the magnitude of the UE. Conversely, the spectral shapes in the transverse region harden significantly with increasing $R_{\rm T}$. This hardening follows a mass ordering, being more significant for heavier particles. The $p_{\rm T}$-differential particle ratios $({\rm p+\overline{p}})/(\pi^+ +\pi^-)$ and $({\rm K^+ +K^-})/(\pi^+ +\pi^-)$ in the low UE limit $(R_{\rm T}\rightarrow 0)$ approach expectations from Monte Carlo generators such as PYTHIA 8 with Monash 2013 tune and EPOS LHC, where the jet-fragmentation models have been tuned to reproduce ${\rm e^+ e^-}$ results.


Introduction
In recent years, proton-proton (pp) and proton-lead (p-Pb) collisions, commonly denoted as small collision systems, have attracted the heavy-ion community's attention due to several measurements in high-multiplicity pp and p-Pb collisions, which show similar features as those observed in heavy-ion collisions. Observations of radial [1][2][3][4] and anisotropic [5,6] flows (collective phenomena), as well as strangeness enhancement [1,7,8] in heavy-ion collisions, are associated with the formation of the strongly interacting quark-gluon plasma (QGP). However, these signatures have also been observed in pp and p-Pb collisions [2,4,8,9]. In particular, the p T -differential baryon-to-meson ratios in small collision systems showcase radial-flow like effects when studied as a function of the charged particle multiplicity of the event [2,3]. In order to pin down the origins of the effects observed in small collision systems, it has been proposed to study particle production as a function of the Underlying Event (UE) activity [10]. The UE is defined as the particles that do not originate from the fragmentation products of the partons produced in the hardest scattering. It consists of the set of particles arising from initial-and final-state radiation, beam remnants and multiple parton interactions (MPIs) [11]. In the context of MPI models, the measurement of identified particle yields and ratios as a function of the UE activity allows one to measure event properties in an MPI-suppressed (-enhanced) environment. Moreover, as shown in [12], these measurements can also provide insights into possible effects that give similar signatures as radial flow but are produced by jet hardening with increasing multiplicity.
At the LHC energies, particles and anti-particles are produced in equal amounts [13]. In the remaining of this paper and unless stated otherwise, the notation π, K and p is adopted to refer to (π + + π − ), (K + + K − ), and (p + p), respectively. In this study, the production of π, K, and p is studied as a function of the UE activity in pp collisions at centre-of-mass energy, √ s = 13 TeV. The UE is examined using the event topology defined by the leading charged particle in the event, which is defined as the charged particle with the highest transverse momentum in the range 5 ≤ p leading T < 40 GeV/c, and reconstructed in the pseudorapidity interval |η| < 0.8. The lower p leading T threshold corresponds to the onset of the UE plateau in the transverse region (transverse to the direction of the leading particle) [14][15][16][17]. In the plateau region, quantities such as the average charged-particle density, ⟨N ch ⟩, and the average transverse momentum sum, ⟨∑ p T ⟩, have little dependence on the p T of the leading particle or jet. This study uses a lower threshold on the p leading T of 5 GeV/c to guarantee that the multiple soft scatterings that contribute to the UE are largely independent of the p leading T . In [18] a slow rise of the UE plateau is reported. This can be explained by additional contributions from wide-angle radiation associated with the hard scattering. Since wide-angle contamination becomes significant for jet p T > 50 GeV/c [18], an upper limit on p leading T of 40 GeV/c is used to reduce its effects.
To study the particle production associated with different underlying physics mechanisms, the conventional division of the azimuthal (ϕ) plane into regions relative to the direction of the leading particle [19] is used (see Fig. 1). The observables reported in this paper are measured in three different topological regions, the toward, transverse, and away regions. These are defined based on the absolute difference in azimuthal angle between the leading and associated particles, |∆ϕ| = |ϕ leading − ϕ|. The associated particles are measured in the kinematic range 0.15 ≤ p T < 5 GeV/c and |η| < 0.8. The toward, transverse, and away regions are defined by |∆ϕ| < 60 • , 60 • ≤ |∆ϕ| < 120 • , and |∆ϕ| ≥ 120 • , respectively. The particle production in the toward and away regions contains the constituents of the leading and away-side jets, respectively, the transverse region is mainly sensitive to multiple parton interactions and initial-and final-state radiations.
The UE activity is quantified using the relative transverse activity classifier R T [10], which is defined as N T /⟨N T ⟩, where N T is the measured charged-particle multiplicity per event in the transverse region and ⟨N T ⟩ is the mean value over all the analysed events. By construction, R T cleanly separates events with "higher-than-average" UE from "lower-than-average" ones irrespective of the centre-of-mass energy. Of Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration Figure 1: Illustration of the toward, transverse, and away regions in the azimuthal angle plane with respect to the direction of the leading particle. The leading particle is represented with the longest upright arrow. The UE is represented with the small arrows transverse to the leading particle. The red cones represent the jet and away-side jet.
particular interest is whether events with very low UE activity, which are dominated by the jet activity, exhibit particle ratios and spectra consistent with fragmentation models tuned to e + e − data and whether events with high UE activity exhibit any clear signs of flow or other collective effects [10]. Finally, it is worth mentioning that this study is complementary to the measurements made using transverse spherocity, in which global event properties are studied for jet-like and isotropic topologies [20] [21].
The structure of the paper is as follows: In Sec. 2, the data analysis is described, Sec. 3 discusses the systematic uncertainties, and in Sec. 4, the results are presented. Finally, in Sec. 5, the conclusions are given.
2 Analysis procedure

Event and track selection
This study was carried out with the data collected in pp collisions at √ s = 13 TeV by the ALICE Collaboration during the LHC runs from 2016 and 2018. A detailed description of the ALICE apparatus and its performance can be found in [22,23]. The subdetectors used in this analysis are the V0 [24], the Inner Tracking System (ITS) [25], the Time Projection Chamber (TPC) [26], and the Time-Of-Flight (TOF) [27]. These subdetectors are located inside a B = 0.5 T solenoidal magnetic field. The V0 detector consists of two arrays of 32 scintillators each, covering the forward (V0A, 2.8 < η < 5.1) and backward (V0C, −3.7 < η < −1.7) pseudorapidity regions. The ITS is the innermost barrel detector. It consists of six cylindrical layers of high-resolution silicon tracking detectors: the two innermost layers of the Silicon Pixel Detector (SPD) provide a digital readout and are also used as a trigger detector. The Silicon Drift Detector (SDD) and the Silicon Strip Detector (SSD) compose the four outer layers of the ITS. Together, they provide the amplitude of the charge signal, which is used for particle identification through the measurement of the specific energy loss (dE/dx). The TPC is the primary detector for tracking and particle identification. It is a large cylindrical drift detector with a diameter and length of about 5 m, which covers the pseudorapidity range |η| < 0.8 with full-azimuth coverage. Particle identification is The distributions presented in this study correspond to primary charged particles, which are defined as particles with a mean proper lifetime τ larger than 1 cm/c, which are either produced directly in the interaction or from decays of particles with τ smaller than 1 cm/c, excluding particles produced in interactions with material [29]. Primary charged particles are reconstructed using the ITS and TPC detectors, which provide measurements of the track transverse momentum and azimuthal angle. 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 is in the SPD layers. 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 associated to the track, respectively. Finally, tracks are also required to have a transverse momentum larger than 0.15 GeV/c and to be reconstructed in |η| < 0.8. To limit the contamination from secondary particles, a selection on the distance of closest approach (DCA) to the reconstructed vertex in the direction parallel to the beam axis (z) of |DCA z | < 2 cm is applied. Also, a p T -dependent selection on the DCA in the transverse plane (DCA xy ) of the selected tracks to the primary vertex is applied. Moreover, tracks associated with the decay products of weakly decaying kaons ("kinks") are rejected. In ALICE, the set of tracks reconstructed with the above-mentioned selection criteria is commonly referred to as "global tracks".
The use of global tracks yields a significantly non-uniform efficiency as a function of the azimuthal angle and pseudorapidity. In order to obtain a high and uniform tracking efficiency together with good momentum resolution, "hybrid tracks" are used [30,31]. Hybrid tracks correspond to the union of two different sets of tracks selected with complementary criteria: (i) tracks containing at least one spacepoint reconstructed in one of the two innermost layers of the ITS (global tracks) and (ii) 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. Hybrid tracks are used to select the leading particle, as well as to measure N T and the p T spectra. Furthermore, in order to select high-quality high-p T tracks, a selection based on the geometrical track length (L) is applied [32]. This selection criterion excludes the information from the readout pads at the TPC sector boundaries (≈ 3 cm from the sector edges).

Particle identification
ALICE's tracking and particle identification (PID) capabilities allow measuring the transverse momentum spectra of π, K, and p over a wide range of transverse momentum. In this study the p T spectra are measured in the p T < p leading T interval, using the standard particle identification techniques which have been reported in previous ALICE publications [3,28,[33][34][35]. Table 1 shows the three techniques used Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration for the PID and the p T intervals each method covers. Analysis At low p T , the average energy loss, ⟨dE/dx⟩, is proportional to 1/(β γ) 2 and the relatively large π − K and p − K separation power makes it possible to perform particle identification in this region on a trackby-track basis [28]. Thus in the TPC analysis, the relative particle abundances, which are defined as the measured fractions of π, K, and p with respect to all the measured primary charged particles are obtained from fitting n σ distributions in narrow intervals of transverse momentum. For each track, the n σ is defined as the difference between the measured and expected dE/dx values normalised to the resolution, n σ = (dE/dx measured − ⟨dE/dx expected ⟩)/σ . While the signal of π and p can be fitted with a Gaussian parameterisation, the one for K uses the sum of two Gaussians as parameterisation to take into account the contamination by electrons.
In the TOF analysis, the particle abundances are also measured on a track-by-track basis by fitting the measured β 1 distributions in momentum intervals. In the interval 1 < p < 2 GeV/c, the π − K and p − K separation power of hadron identification is large enough [28] such that one can perform single fits to the signal of π, K, and p using a Gaussian parameterisation convoluted with an exponential tail. The parameters (µ, σ and ξ , where µ and σ represent the mean and standard deviation of the Gaussian paramerisation, and ξ represents the β value at which the exponential tail begins) of the single fits are extracted from data in 1 < p < 2 GeV/c and are used to extrapolate to higher momentum values. Finally, the extrapolated functional forms are used to fit the β distributions with the sum of three contributions to describe the signals of the three species simultaneously.
In the rTPC analysis, the method described in [33-35] is used. In the relativistic rise region of the TPC (3 ≲ β γ ≲ 1000), the ⟨dE/dx⟩ increases as log(β γ) and the π − K and p − K separation power for hadron identification is almost constant [28]. The knowledge of these two features makes it possible to perform a two-dimensional fit of the correlation between dE/dx and momentum. In order to accomplish this, the first step is to parameterise the Bethe-Bloch and resolution curves in the relativistic rise region. The Bethe-Bloch parameterisation provides the relation between the ⟨dE/dx⟩ and β γ, and the parameterised resolution gives the relation between σ dE/dx and ⟨dE/dx⟩. For the parameterisation, high-purity samples of identified hadrons are used, namely p(p) and π ± from Λ(Λ) and K 0 S decays, respectively, and e ± from γ-conversions [33-35]. Once the Bethe-Bloch and resolution curves are parameterised, they are used to perform the two-dimensional fit. The two-dimensional fit is only used to improve the Bethe-Bloch parameterisation in the transition to the plateau region. Then, the particle ratios are obtained from onedimensional fits to the dE/dx distributions in momentum intervals using the sum of four Gaussians as a fit function to describe simultaneously the signal of π, K, p, and e, where the µ and σ of each of the Gaussian distributions are fixed based on the ⟨dE/dx⟩(β γ) and σ dE/dx (⟨dE/dx⟩) obtained with the above procedure.

Corrections
The p T spectra of π, K, and p are corrected for acceptance and reconstruction inefficiency. The spectra measured with the TOF detector are also corrected for TPC-TOF matching inefficiency. The acceptance and efficiencies are obtained from simulations using the PYTHIA8 Monte Carlo event generator with the 1 β = L/c∆t, where L is the track length and ∆t is the measured time-of-flight. Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration Monash 2013 tune (indicated as PYTHIA8 Monash in the following) [36]. Subsequently, the propagation of simulated particles through the ALICE apparatus is carried out using GEANT3 [37]. The simulated events are reconstructed using the same algorithms as for the data. The obtained acceptance and reconstruction efficiencies are independent of the charged-particle multiplicity. Hence, the R T -integrated values are applied for all the R T classes. As GEANT3 does not fully describe the interaction of lowmomentum p and K − with the detector material, an additional correction factor to the efficiency for these two particles is estimated with GEANT4 [38] and FLUKA [39], respectively. These corrections are the same as the ones applied in [3].
The p T spectra of π and p contain a large contribution from secondary particles from interactions in the material and particle decays (π ± from K 0 S and p(p) from Λ and Σ + ). Since the strangeness production is underestimated in the Monte Carlo event generators, a data-driven approach is used to estimate the fraction of non-primary particles as a function of p T so that it can be subtracted from the measured spectra. The estimation of this correction is based on a multi-template fit method to describe the measured DCA xy distributions [40]. In practice, three Monte Carlo templates representing the expected shapes of DCA xy distributions of primary particles, secondaries from weak decays, and secondaries from interactions in the material are used to fit the data DCA xy distributions. The fits are performed in |DCA xy | ≤ 3 cm and in p T bins. Since the TOF analysis only uses tracks matched with the TOF detector, these corrections are estimated separately for the low-and intermediate-p T regions. At p T = 0.45 GeV/c the contribution from non-primary π + (p) was found to be about 4%(20%) while at p T = 2.0 GeV/c it decreases to about 1%(4%). Furthermore the correction decreases asymptotically at higher p T . Therefore, the correction for the TOF is extrapolated to higher p T and then applied.

Unfolding the charged-particle multiplicity distributions
The charged-particle multiplicity in the transverse region, N T , is used to characterise the event activity. However, the limited acceptance and finite resolution of the detector cause a smearing of the measured charged-particle multiplicity distribution Y (N T,m ). This section introduces the one-dimensional unfolding method to correct for these detector effects and efficiency losses. The adopted approach is based on the iterative Bayesian unfolding method by G. D'Agostini [41]. Bayesian unfolding requires the knowledge of the smearing matrix S mt , which comprises information about the limited acceptance and finite resolution. It represents the conditional probability P(N T,m |N T,t ) of an event with the true multiplicity N T,t to be measured as one with multiplicity N T,m . Figure 2 (left) shows the smearing matrix obtained with simulated events using PYTHIA8 Monash. The values along the diagonal of the smearing matrix represent the probability that a measured event is reconstructed with the true number of particles. At the same time, the off-diagonal elements give the probability that fewer or more particles are reconstructed due to detector inefficiencies and background, e.g., secondary particles misidentified as primary particles.
The one-dimensional unfolded distribution Y (N T,t ) is given as the linear combination between the elements of the unfolding matrix M1 tm (see the right panel of Fig. 2) and the measured distribution, .
(1) P 0 (N T,m ) represents a prior probability distribution. It can be any arbitrary distribution at the start of the unfolding process. Here, the measured multiplicity distribution is used as the prior distribution. An updated prior distribution, is obtained from the second iteration and onwards. Thus, the unfolding matrix is improved as the prior Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration   distribution is updated. Finally, a new unfolded distribution closer to the true one can be obtained using Eq. 1 with the updated M1 tm . The smearing in Fig. 2 left shows very few events below the main correlation band between 7 < N T,t < 15 and 15 < N T,m < 30. This small population comes from statistical fluctuations of the response matrix. Since the unfolding matrix M1 tm is proportional to P(N T,m |N T,t ), these events show up in M1 tm in the intervals 22 < N T,t < 30 and 7 < N T,m < 17, as can be seen in Fig. 2 right. However, given their very small contribution, they are not affecting the unfolding process.
This iterative process makes the unfolded distribution to converge to the true one eventually. However, it also compounds the effects of statistical uncertainties in the smearing matrix. Therefore, a larger number of iterations does not guarantee a better result: eventually, the true distribution might be contaminated by statistical fluctuations [42]. In order to decide when to stop the iterations, the χ 2 /N df between the unfolded and the true distribution as a function of the number of iterations is computed for a Monte Carlo generated sample. The minimum value of the ratio χ 2 /N df indicates when to stop the iterative process. This study found that the optimal number of iterations is three.

Unfolding the p T spectra
Unfolding the transverse momentum spectra as a function of the multiplicity is treated differently depending on the topological region. The toward and away regions are straightforward cases as there is no overlap between the tracks used for the spectra and the tracks used for the multiplicity calculation as the latter is measured in the transverse region. Therefore, the one-dimensional unfolding matrix M1 tm is directly applied in these two regions. This also makes it trivial to see that the same unfolding matrix can be used for all identified particle spectra. Hence, the fully corrected p T spectra as a function of N T,t are obtained in a two-step procedure: 1. Correct the raw p T spectra at particle level for tracking inefficiency and secondary particle contamination. The efficiency correction is applied here as the one-dimensional unfolding only affects the classification of the events.
2. Apply the one-dimensional unfolding matrix. The spectra as a function of N T,t are given by: The transverse region requires a more elaborate method since both p T spectra and multiplicity are measured using the same tracks. In other words, one is no longer dealing with the problem of rearranging events but rather how tracks should be unshuffled to match the true transverse momentum distributions.
Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration This poses a multi-dimensional problem with two dimensions associated to the true and measured multiplicities and two additional dimensions (true and measured yields) for each p T bin. Instead of performing the full multi-dimensional unfolding, an approximate method is employed in which the multiplicity smearing matrix is assumed to be independent of the transverse momentum. This is a very good approximation as the efficiency is essentially flat in p T for the track selection and p T ranges used here.
In this approach, a new response matrix is obtained by multiplying every column of the original multiplicity response matrix with the respective number of measured particles as weights. After row-wise normalisation, the desired track smearing matrix is obtained.
The unfolding is done bin-by-bin in p T with this modified response matrix. For a particular transverse momentum bin, the measured multiplicity distribution is unfolded using the iterative unfolding procedure described in Sec. 2.4. This approach yields unfolding matrices that depend on the transverse momentum. Henceforth, these matrices will be called M2 tm (p T ). It should be stressed that this method works here because the tracking efficiency does not depend strongly on the transverse momentum for hybrid tracks and because the same tracks to measure N T are used to obtain the spectra.
Similar to the toward and away regions, the two-step procedure is followed to obtain the fully corrected transverse momentum spectra. The only difference is that in the transverse region the p T -dependent M2 tm (p T ) matrices are used The method described above unfolds the spectra of all charged particles and yields the unfolding matrices M1 tm and M2 tm (p T ). When unfolding the spectra of identified particles (for example, π in the transverse region), Eq. 3 is applied using the M2 tm (p T ) matrices from charged particles and then exchanging dY (N T,m , p T )/dp T for dY π (N T,m , p T )/dp T . The unfolding of π spectra in the toward and away regions is done with the same strategy but using M1 tm instead.

Systematic uncertainties
In this section, the estimation of the systematic uncertainties is described. The systematic uncertainties on the p T spectra are divided into two categories, R T -dependent and R T -independent uncertainties. The total systematic uncertainty on the p T spectra is given as the sum in quadrature of all the individual sources of uncertainty.
R T -dependent systematic uncertainties The unfolding method described in Sec. 2.4 shows deficiencies, mainly when unfolding the p T spectra for low multiplicities in the transverse region. To account for these deficiencies, the following contributions to the systematic uncertainty on the N T distribution are considered: -Monte Carlo (MC) non-closure: PYTHIA8 Monash is the default tune for the generation of the multiplicity response matrix and N T distributions with and without the detector's efficiency losses. The unfolded N T spectrum from the simulation is compared to the generated one. Thus, any statistically significant difference between the generated and unfolded distributions is referred to as MC non-closure and is added in quadrature to the total systematic uncertainty. During the unfolding procedure, the MC closure improves with the number of iterations, with an optimal number of three, which leads to a negligible MC non-closure.
-Dependence on the choice of the MC model: EPOS LHC [43] is used to generate a different multiplicity response matrix. This response matrix is used to unfold the N T and p T spectra. The ratio Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration between the final unfolded distributions using PYTHIA8 Monash and EPOS LHC was quantified and added to the total systematic uncertainty. In the interval 0 < N T < 18, the relative systematic uncertainty is below 2 %, increasing to about 4 % at N T ≈ 18. Due to statistical limitations on the response matrix, a constant 4 % relative systematic uncertainty for N T ≥ 18 was assigned.
-Track selection: This uncertainty is quantified by changing the track selection criteria with respect to the nominal one. In particular, the minimum number of crossed rows in the TPC is set to 60 and 100 (the nominal is 70). The track fit quality in the ITS and TPC quantified by the χ 2 ITS /N hits and the χ 2 TPC /N clusters must not exceed 25 and 49 (the nominal is 36), and 3 and 5 (the nominal is 4), respectively. The maximum distance of closest approach to the vertex along the beam axis (DCA z ) is set to 1 and 5 cm (the nominal is 2 cm). Furthermore, the parameters of the geometrical length cut to select the leading particle are also varied. For a particular parameter variation, the maximum difference between the results obtained with the tighter and looser selections with respect to the nominal value is quantified. The total systematic uncertainty from track variations is given as the sum in quadrature of the different parameter variations. The relative systematic uncertainty is on average 1 % in the interval 0 < N T < 18 and increases for higher N T values. For N T ≥ 18, the statistical fluctuations become significant. Therefore, a constant 2 % relative systematic uncertainty was assigned.

R T -independent systematic uncertainties
The R T -independent systematic uncertainties are divided into two categories. The first category includes the uncertainties common to the different analyses, such as those due to the track quality criteria and the p T -dependent ITS-TPC matching efficiency. The ITS-TPC matching efficiency is derived from matching ITS pure tracks with the corresponding ITS+TPC tracks (in the same phase-space region) and by comparing the matching efficiency in data and Monte Carlo simulations. The second category groups the analysis specific uncertainties. It includes the uncertainties on the secondary particle contamination correction estimation, the signal extraction technique and the TPC-TOF matching efficiency.
As described in Sec. 2.3, the secondary particle contamination correction is based on multi-template fits to the DCA xy distributions in transverse momentum intervals. The estimation of the systematic uncertainty follows the procedure described in [28]. Namely, the fitting range is changed from the nominal values of ±3 cm to ±1.5 cm.
To estimate possible systematic effects attributed to the signal extraction technique in the TPC analysis, a similar procedure to the one described in [28] was applied. The signal extraction technique changed from fitting n σ distributions to bin counting in the range of ±3σ . The systematic uncertainty on the particle fractions is given as the difference between the nominal particle fractions and the ones obtained from bin counting.
As described in Sec 2.2, the measurement of the particle fractions in the TOF analysis is based on fits to β distributions in momentum intervals. Hence, the systematic uncertainty is mainly driven by the uncertainty in the parameterisation of the µ, σ , and ξ curves for π, K, and p. The relative difference between the fitted curves and the actual measured µ, σ , and ξ values was computed to evaluate the effect of the parameterisations. Thus, the systematic uncertainty in the extraction of the particle fractions is obtained by refitting the β distributions while randomly varying the constrained parameters µ, σ , and ξ within the uncertainty of the parameterisations assuming a Gaussian variation centred at the nominal value. The refitting was performed 1000 times, and the systematic uncertainty on the particle fractions as a function of the transverse momentum is given as the standard deviation of the associated distributions. This approach is motivated by work developed in [28,33,35].
The measurement of the systematic uncertainty on the extraction of the particle fractions in the rTPC analysis follows the method from [28,33,35]. In this analysis, the primary source of systematic un-Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration certainty comes from the imprecise description of the detector response, namely the Bethe-Bloch and resolution parameterisations. To estimate the systematic effect, the relative difference between the parameterisations and the actual ⟨dE/dx⟩ and σ dE/dx values are measured. The particle fractions are measured following a fitting procedure where the constrained parameters, ⟨dE/dx⟩ and σ dE/dx , are allowed to vary randomly within the uncertainty of the parameterisations. The fitting procedure was repeated 1000 times and the systematic uncertainty in the particle fractions is given as the standard deviation of the associated distributions.
When computing the p T -differential particle ratios, all the systematic uncertainties cancel out in the ratios except those attributed to the signal extraction and feed-down. In the high p T region (rTPC analysis) the procedure described in [33] is used to extract the signal extraction systematic uncertainty on the K/π and p/π ratios directly from fits to the dE/dx distributions. Table 2 lists a summary of the systematic uncertainties at different p T values for the spectra and particle ratios in the transverse region. The table is divided into common and analysis-specific uncertainties.
The values in the toward and away regions are the same as those of the transverse region. The only topological-region-dependent uncertainty is the one attributed to the MC non-closure. Table 2: Summary of systematic uncertainties on the π, K, and p p T spectra. The uncertainties are shown for different representative p T values. The last two rows show the total systematic uncertainty on the p T spectra and the p T -differential particle ratios. These values correspond to the spectra in the transverse region in the 0 ≤ R T < 0.5 class. Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration

Results
This section presents the results of the production of π, K, and p as a function of the relative transverse activity classifier, R T . The data are compared with predictions from PYTHIA8 Monash [36], PYTHIA8 with ropes hadronisation model (indicated as PYTHIA8 ropes) [44], HERWIG7 [45,46], and EPOS LHC [43]. PYTHIA8 with Monash tune is one of the most popular event generators at LHC energies for most observables but lacks the QGP-like effects observed in small collision systems such as strangeness enhancement, while the other three models are known to describe the strangeness enhancement in small collision systems better [8,44,47]. Hence, these models allow for testing a broad range of possible dynamic effects. In PYTHIA8 Monash, the soft-inclusive particle production is based on multiple perturbative parton-parton interactions (MPI) [11]. This model also includes a colour reconnection (CR) mechanism [48], allowing each MPI system's partons to be colour connected with a higher-p T MPI system. In particular, PYTHIA8 Monash describes the enhanced p T -differential proton-to-pion ratio at intermediate p T [3] by introducing the colour reconnection mechanism and does not need to assume the formation of a medium [49]. PYTHIA8 ropes model allows strings to fuse in an environment with a high density of strings and form "colour ropes". Consequently, colour ropes are expected to produce more strange hadrons and baryons, the latter via probabilistic collapses of ropes to string junctions. EPOS LHC is a core-corona model, which assumes the formation of a QGP medium in the high-density core regions in pp collisions. The hadronisation of the corona is based on string fragmentation, while the particles associated with the core are thermally produced (grand-canonical thermal description). In EPOS LHC, particle production in low-multiplicity events is mainly dominated by string fragmentation. In contrast, high-multiplicity events are core dominated, and a large production of strange hadrons and baryons is expected. Particle production in the HERWIG7 is based on cluster hadronisation and it has its own colour reconnection mechanism where baryonic clusters are allowed to be produced in a geometric manner. This model also includes a non-perturbative gluon splitting mechanism to create more ss pairs to account for the strangeness enhancement [50].
The p T spectra as a function of R T are normalised to the total number of events in each R T class. The relation between R T intervals and N T classes is given in Table 3. The R T distribution is constructed using the unfolded N T distribution for which the ⟨N T ⟩ is equal to 7.366 ± 0.002 (stat.). For each R T bin the intervals under the N T column are inclusive meaning that for 0 ≤ R T < 0.5, N T is equal to 0, 1, 2 or 3.   Figure 3 shows the unfolded N T and R T probability distributions in the transverse region integrated over all the events with the leading particle along with different model predictions. For each model, the ⟨N T ⟩ corresponds to the mean value of the corresponding N T spectrum. It is observed that PYTHIA8 Monash and PYTHIA8 ropes give the best qualitative description of the N T distribution, while EPOS LHC (HERWIG7) overestimates (underestimates) the data for N T > 10. However, when R T is computed, all the models underestimate the data for R T ≳ 2. This is because the models poorly describe the low-N T region, so they predict larger ⟨N T ⟩ values than the measured ones. Finally, the R T probability distribution is compared with the previous ALICE result [14], which used a limited data sample and applied the unfolding at the level of the R T distribution while in the current analysis the R T spectrum is derived from the N T distribution. The new result is in agreement with the previous ALICE measurement within 1.5%.  results in the toward, away, and transverse regions are shown on the left, middle, and right panels, respectively. The lower panels show the ratios between the R T -dependent p T spectra and the R T -integrated p T spectrum. The R T -independent systematic uncertainties cancel out in the ratios. The R T -dependent systematic uncertainties are correlated and cancel out only partly. From the ratios to the R T -integrated spectrum, it is observed that the toward and away regions share a similar feature at low transverse momentum: a depletion of low-p T particles with increasing R T . Furthermore, this effect follows a mass ordering, being larger for heavier particles. This behaviour is reminiscent of radial flow effects, in which the depletion of low-p T particles is compensated by an increasing number of particles at intermediate p T . The particle production in the toward and away regions is dominated by the leading and awayside jet fragmentation into high-p T particles. This can be observed in the ratio between the spectra in 0 ≤ R T < 0.5 and the R T -integrated ones (bottom panels of Figures 4 to 6), which increases with p T (in the interval p T ≳ 2 GeV/c), and the effect is more evident for pions. The opposite is observed for the spectral shapes at high R T ; they soften with increasing R T for p T ≳ 2 GeV/c. This can be interpreted as a "dilution" of the jet with increasing UE activity. When R T → ∞ the particle multiplicity from the UE is higher than the particle multiplicity from the jet in the toward region. Thus, average quantities like ⟨p T ⟩ of pions and kaons in the toward region decreases at high R T (see Fig. 10). The ⟨p T ⟩ of protons increases instead with increasing R T because there other effects like radial flow are more relevant. This can also be seen in the ratios to R T -integrated spectrum, where they decrease with increasing p T for events with high UE activity. The spectral shapes of all the species in the transverse region share a common feature: they harden with increasing UE activity. This effect can be attributed to jet hardening with increasing multiplicity. Figure 7 shows model-to-data ratios for the p T spectra. The ratios are shown for two types of events: low UE activity (0 ≤ R T < 0.5) and high UE activity (2.5 ≤ R T < 5). It is observed that the models can describe the pion and kaon spectra for p T > 2 GeV/c in the toward and away regions qualitatively for events with low UE activity. This is expected since for small R T values, one mainly observes the jet fragmentation products, and the models are tuned to e + e − data, which are jet-like. For this same R T interval, the models predict different yields in the transverse region. However, for p T ≳ 1 GeV/c all of the models underestimate the data. Moreover, increasing the UE activity makes the agreement between data and models worse. Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration     Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration Figure 8 shows the p T -differential kaon-to-pion (K/π) and proton-to-pion (p/π) ratios for the four different R T intervals in the three topological regions. The R T -dependent ratios are contrasted with the inclusive ratios in minimum bias collisions at the same centre-of-mass energy [3]. Minimum bias means integrated over R T and the azimuthal angle, and without the leading particle requirement. The K/π ratios in the toward and away regions show similar features: they increase with increasing UE activity. However, this is true only for 1 ≲ p T < 2 GeV/c. Conversely, the K/π ratio in the transverse region decreases with increasing R T . One also observes that the minimum-bias result is very similar to those measured in the transverse region. This suggests that the inclusive K/π ratio is dominated by bulk particle production. The p/π ratio in the toward and away regions measured in the lowest R T intervals is always below the inclusive one. Similar observations have been made for the Λ/K 0 S ratio in jets [51]. As the UE increases, the toward and away regions become more UE dominated (jet dilution) and the p/π ratio also increases. However, this is true only for p T ≳ 1 GeV/c. The growth of the p/π ratio might be attributed to a gradual increase of the collective radial flow with R T . Furthermore, the baryon-to-meson ratio for p T > 1 GeV/c in these two regions tends to increase with increasing R T and to approach the minimum bias ratio, which is similar to the one measured in the transverse region. The p/π ratio in the transverse region shows a mild dependence on R T . It is observed that the result in the highest UE activity interval is below the one in the lowest UE activity interval for p T ≲ 2 GeV/c, indicating a suppression of low-p T protons possibly due to collective radial flow. Furthermore, the observed maximum in the highest R T interval (centred at p T ≈ 3.5 GeV/c) is shifted to the right with respect to the one of the lowest R T interval (centred at p T ≈ 2.5 GeV/c). This might be attributed to the jet hardening effect with increasing multiplicity as discussed in [12].  Figure 8: p T -differential particle ratios as a function of R T . The top (bottom) row shows the K/π (p/π) ratio. The results in the toward, away, and transverse regions are shown from left to right. Statistical and systematic uncertainties are represented with error bars and boxes, respectively. The inclusive minimum-bias particle ratios in pp collisions at the same centre-of-mass energy [3] are overlaid. Figure 9 shows the p T -differential K/π and p/π ratios along with model predictions in two R T inter-Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration vals: 0 ≤ R T < 0.5 (low-UE activity) and 2.5 < R T < 5 (high-UE activity). The K/π and p/π ratios in the toward and away regions in events at low R T can be described qualitatively by PYTHIA8 Monash. However, this model predicts almost no evolution with R T . On the other hand, the PYTHIA8 ropes hadronisation model, which allows for the formation of colour ropes, predicts p/π ratios that evolve with R T , but overestimates the data, particularly for high-R T events. EPOS LHC also describes both ratios qualitatively in the limit of low UE activity and predicts an evolution with R T . It describes the K/π ratio but overestimates the p/π ratio in events with high R T . This was clear from the p T -integrated particle ratios: the transition from string fragmentation to statistical hadronisation needs improvement. Finally, HERWIG7 also predicts an evolution with R T and can describe rather well the K/π ratio, while it misses the p T trend of the p/π ratio. The fact that all models do a better job at describing both ratios at low than at high R T is expected since they are tuned to e + e − data. The model predictions in the away region are similar to those of the toward.

Ratio to
In the transverse region, PYTHIA8 Monash and PYTHIA8 ropes describe the splitting and ordering of the K/π ratio between the two R T classes qualitatively but underestimate the data. They can also describe the p/π ratio qualitatively. Moreover, those models predict the lower p/π ratio for p T ≲ 2 GeV/c in events with high R T compared to the low UE activity ratios. This effect, which can be attributed to the radial flow effects, is likely induced by the CR and ropes in PYTHIA8. EPOS LHC predicts the same K/π ratio for both R T classes, while the p/π ratio at low R T agrees with the data. Still, as previously mentioned, the transition from core-corona hadronisation is not well modeled. Finally, HERWIG7 gives a good qualitative description of the evolution of the p/π ratio with R T in the transverse region.
The p T -integrated yield (dN/dy) and the average transverse momentum (⟨p T ⟩) of pions, kaons, and protons are extracted from the p T -differential spectra in the different R T intervals and topological regions.
Since the spectra are measured for p T > 0.3 GeV/c (π, K) and p T > 0.45 (p) GeV/c, they are first extrapolated to p T = 0. The extrapolation procedure is carried out by fitting the spectra with Lévy-Tsallis parameterisations [52,53]. The parameterisation is only used in the p T intervals with no data. For example, for the 0 ≤ R T < 0.5 interval in the transverse region the fractions of extrapolated yields amount to 38%, 19%, and 22% for π, K, and p, respectively. To estimate the systematic uncertainty associated with the extrapolation procedure, several other parameterisations such as the Fermi-Dirac, Bose-Einstein, Blast-Wave, and m T -exponential are used to estimate the extrapolated yield. The maximum difference between the nominal and extrapolated yields is associated as the systematic uncertainty of the extrapolation procedure. For example, the systematic uncertainties on the dN/dy (⟨p T ⟩) amount to 2%(1.7%), 2.7%(2.3%), and 2%(1.5%) for π, K, and p, respectively, for the 0 ≤ R T < 0.5 interval in the transverse region. Figure 10 shows the average transverse momentum as a function of R T in the different topological regions. The ⟨p T ⟩ of π and K in the toward region is the largest in the 0 ≤ R T < 0.5 (low UE activity) interval. This feature reflects the presence of the jet fragmenting mainly into low-mass hadrons (π and K) with large transverse momentum. As the UE activity increases, the ⟨p T ⟩ of π and K slowly decreases and tends to flatten for R T > 1.5 due to the jet dilution effect: the toward and away regions become dominated by the UE. Conversely, the ⟨p T ⟩ of protons increases with R T , which can be attributed to the additional radial flow effect. Moreover, the ⟨p T ⟩ of all the species at high-R T tend to approach the values measured at high R T in the transverse region. All models can describe the ⟨p T ⟩ qualitatively in the toward region, but EPOS LHC is the only one that predicts an increasing trend of the proton ⟨p T ⟩. Particle production in the away region is similar to that in the toward. It is primarily dominated by the away-side jet. It is observed that the ⟨p T ⟩ of all the species increases with R T . Furthermore, the ⟨p T ⟩ tends to approach the values of the transverse region at large R T where the UE dominates. PYTHIA8 Monash and ropes give a fair qualitative description of the evolution of ⟨p T ⟩ of pions with R T in the away region while the ⟨p T ⟩ of protons in the same region is only described by EPOS LHC.
The ⟨p T ⟩ in the transverse region increases with R T for all the species; however, the rate of increase Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration  Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration exhibits a mass ordering, being more significant for heavier particles. Similar observations have been made in multiplicity-dependent studies [2,3]. The rise of the ⟨p T ⟩ with increasing R T is likely attributed to autocorrelation effects. Since R T and the p T spectra are measured in the same ∆ϕ region, the high multiplicity requirement in the transverse region increases the probability to have a jet in the same region. Finally, it is observed that all the models predict the increase of the ⟨p T ⟩ with R T .  Figure 11 shows the R T -dependence of the p T -integrated particle ratios calculated from the extrapolated dN/dy. As the UE activity increases, the yield of kaons and protons relative to that of pions increases in the transverse region and in turn, the particle ratios grow until they saturate at R T ≈ 1.5. In contrast, in the toward and away regions the K/π ratio is constant as a function of R T , while the p/π ratio decreases with increasing UE activity. Furthermore, both ratios in the toward and away regions approach the values of the transverse region at large R T . All models predict the increasing trend of the particle ratios with R T in the transverse region. PYTHIA8 Monash and HERWIG7 predict similar p/π ratios to the data. PYTHIA8 ropes overestimates the p/π by a large amount (almost a factor of 2) while EPOS LHC, although overpredicting, is closer to the data. One can notice that while EPOS LHC precisely describes the proton ⟨p T ⟩ as a function of R T in all the topological regions, the p/π ratio is only described in the low-UE limit (0 ≤ R T < 0.5), where string fragmentation dominates, indicating that the core overestimates the production of protons. PYTHIA8 Monash overpredicts the p/π ratio by about 10 % over the entire R T range and underestimates the K/π ratio. In the toward and away regions none of the models reproduce the trend of both ratios: HERWIG7 and PYTHIA8 Monash predict a strongly decreasing trend for K/π that is not supported by the data. PYTHIA8 ropes and EPOS LHC predict an increasing trend for p/π that is in contradiction with the data. Finally, it is noted that while all the models capture most of the measured trends for ⟨p T ⟩ in Fig. 10, none of the models describes the particle ratio Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration  Figure 11: Transverse momentum-integrated particle ratios as a function of R T . The particle ratios in the toward, away, and transverse regions are shown from left to right. The top (bottom) row plots the K/π (p/π). The statistical and systematic uncertainties are represented with error bars and boxes, respectively. The shaded bands around the model lines represent the statistical uncertainties. trends of Fig. 11 for both p/π and K/π.

Conclusions
The production of π, K, and p was measured at mid-pseudorapidity in different topological regions as a function of the relative transverse activity classifier, R T in pp collisions at √ s = 13 TeV containing a high p T (5 ≤ p leading T < 40 GeV/c) leading particle. R T has been utilised to investigate differentially in different topological regions where the particle production is expected to be dominantly driven by pQCDlike processes (toward and away regions and low R T ) and regions where soft non-perturbative QCD processes dominate (transverse region or high R T ). In particular, since conventional UE (Underlying Event) studies average over the event activity, this analysis allows us to get further insight into collective effects and the interplay between hard and soft production in pp collisions. Furthermore, the models can describe the new results in the toward and away regions when the UE is suppressed (0 ≤ R T < 0.5), which was expected since they are tuned to reproduce jet-like e + e − measurements. However, when the UE increases, all models fail to reproduce the data at both qualitative and quantitative level. This demonstrates that by measuring the production of identified particles as a function of R T , one can reveal novel features of the UE. The new measurements presented here thus allow for substantial progress on the model side to nail down the properties of the UE.
Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration  [21] ALICE Collaboration, S. Acharya et al., "Charged-particle production as a function of multiplicity and transverse spherocity in pp collisions at √ s = 5.02 and 13 TeV", Eur. Phys. J. C 79 (2019) 857, arXiv:1905.07208 [nucl-ex].
Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration   Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration

A The ALICE Collaboration
Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration Production of π, K and p as a function of R T in pp collisions at √ s = 13 TeV ALICE Collaboration Production of π, K and p as a function of R T in pp collisions at √ s =