Multiplicity and event-scale dependent flow and jet fragmentation in pp collisions at √s = 13 TeV and in p–Pb collisions at √sNN = 5.02 TeV

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Multiplicity and event-scale dependent flow and jet fragmentation in pp collisions at √s = 13 TeV and in p–Pb collisions at √sNN = 5.02 TeV © 2024 the Authors Published version ALICE Collaboration ALICE Collaboration. (2024). Multiplicity and event-scale dependent flow and jet fragmentation in pp collisions at √s = 13 TeV and in p–Pb collisions at √sNN = 5.02 TeV. Journal of High Energy Physics, 2024(3), Article 92. https://doi.org/10.1007/JHEP03(2024)092 2024 JHEP03(2024)092 Published for SISSA by Springer Received: September 28, 2023 Revised: January 29, 2024 Accepted: February 20, 2024 Published: March 15, 2024 Multiplicity and event-scale dependent flow and jet fragmentation in pp collisions at √s= 13 TeV and in p–Pb collisions at √sNN = 5.02 TeV The ALICE collaboration E-mail: [email protected] Abstract: Longand short-range correlations for pairs of charged particles are studied via two-particle angular correlations in pp collisions at √s = 13 TeV and p–Pb collisions at √sNN = 5 . 02 TeV. The correlation functions are measured as a function of relative azimuthal angle ∆ φ and pseudorapidity separation ∆ η for pairs of primary charged particles within the pseudorapidity interval |η|< 0 . 9and the transverse-momentum interval 1 < pT< 4GeV/ c . Flow coefficients are extracted for the long-range correlations (1 . 6 <| ∆ η|< 1 . 8) in various high-multiplicity event classes using the low-multiplicity template fit method. The method is used to subtract the enhanced yield of away-side jet fragments in high-multiplicity events. These results show decreasing flow signals toward lower multiplicity events. Furthermore, the flow coefficients for events with hard probes, such as jets or leading particles, do not exhibit any significant changes compared to those obtained from high-multiplicity events without any specific event selection criteria. The results are compared with hydrodynamic-model calculations, and it is found that a better understanding of the initial conditions is necessary to describe the results, particularly for low-multiplicity events. Keywords: Collective Flow, Hadron-Hadron Scattering, Jets ArXiv ePrint: 2308.16591 Open Access, Copyright CERN, for the benefit of the ALICE Collaboration. Article funded by SCOAP3. https://doi.org/10.1007/JHEP03(2024)092 JHEP03(2024)092 Contents 1 Introduction 1 2 Experimental setup and data samples 3 3 Analysis procedure 4 3.1 Two-particle angular correlations 4 3.2 Extraction of flow coefficients 5 4 Systematic uncertainties 10 5 Results 12 5.1 Transverse-momentum and multiplicity dependence of anisotropic flow 12 5.2 Event-scale dependence of the flow coefficients 13 5.3 Comparisons with models 14 6 Conclusions 16 The ALICE collaboration 27 1 Introduction High-energy nucleus-nucleus (AA) collisions exhibit strong collectivity, which has been observed through anisotropy in the momentum distribution of emitted final-state particles at RHIC [ 1 – 4 ] and the LHC [ 5 – 8 ]. This momentum anisotropy is developed by the pressuredriven expansion of the strongly interacting quark-gluon plasma (QGP), which emerges from the initial spatial anisotropy in such collisions. The collective nature of the momentum anisotropy is mostly deduced via particle correlations which span over a wide range of pseudorapidity. The collective motion of the emitted particles, which reflects the collectivity of the initial medium, is generally quantified using a Fourier expansion, characterizing the so-called “anisotropic flow” [ 9 ]. In recent years, long-range correlations have been also observed in smaller collision systems such as high-multiplicity proton-proton (pp) [ 10 – 16 ], proton-nucleus (pA) [ 17 – 20 ], and in collisions of light nuclei [ 21 , 22 ]. These observations raise the question to what extent do small-system collisions and heavy-ion collisions share the underlying mechanism, which is responsible for the observed long-range correlations. A crucial evidence of a strongly interacting medium in small-system collisions would be the presence of jet quenching [ 23 , 24 ]. However, this phenomenon has not yet been observed in either high-multiplicity pp or p–Pb collisions [ 25 – 29 ], possibly due to the current experimental uncertainties being too large to observe it in such small-system collisions. Current approaches to model heavy-ion collisions divide the evolution of the out-ofequilibrium, strongly-coupled, quantum-chromodynamic medium into multiple stages, and each stage is described by an effective theory. To this date, the combination of color-glass – 1 – JHEP03(2024)092 condensate effective field theory (CGC-EFT) [ 30 , 31 ], causal hydrodynamics [ 32 – 40 ], and a hadronic cascade model [ 41 – 43 ] leads to the most successful description of a wide range of observables in heavy-ion collisions, e.g., particle spectra, centrality dependence of average particle transverse momenta, and multi-particle correlations [ 44 – 51 ]. By employing global Bayesian analyses, parameters of the multi-stage model, including those quantifying the transport properties of the QGP, can be constrained using measured data [ 52 – 55 ]. Despite the studies describing both heavy AA and pA collisions in a single framework [ 56 ], the origin of the flow-like correlations is still under debate. It is unclear whether the flow-like behavior originates from the early stages of the collision in the realm of applicability of CGC-EFT [ 57 , 58 ] or whether it develops during the collective evolution, where causal hydrodynamics is applicable [ 59 , 60 ]. Both scenarios may be responsible for the observed correlations in the final state [ 59 ]. Although collective models are successful in describing available two-particle correlation data from small-system collisions, they predict the opposite sign for four-particle azimuthal cumulants compared to experiment [ 12 , 14 , 61 ]. On the other hand, a semi-analytical toy model based on the Gubser hydrodynamic solution [ 62 , 63 ] can explain the twoand four-particle correlations in pp collisions [ 64 ]. In particular, this model has explained the relationship between the sign of the four-particle cumulants and fluctuations in the initial state [ 64 ]. Besides the models based on the causal hydrodynamic framework, there are other attempts to explain the observed flow-like signals in small-system collisions using alternative descriptions. For instance, a study based on the A Multi-Phase Transport model (AMPT) [ 65 ] leads to satisfactory agreement with the experimental data [ 66 ]. The applicability of fluiddynamical simulations and partonic cascade models in small-system collisions was explored in ref. [ 67 ]. In a kinetic-theory framework with isotropization-time approximation, it is possible to explain the long-range correlations by fluid-like (hydrodynamic) excitation for Pb–Pb collisions and particle-like (or non-hydrodynamic) excitation for pp or p–Pb collisions [ 68 – 70 ]. Another potential description for the collectivity in small-system collisions is provided by PYTHIA 8, in which interacting strings repel one another in a transverse direction by a mechanism dubbed as “string shoving” [ 71 , 72 ]. The repulsion of the strings causes microscopic transverse pressure, giving rise to long-range correlations of particles. The string shoving approach in PYTHIA 8 successfully reproduces the near-side ridge yield observed in measurements by ALICE [ 73 ] and CMS [ 12 ]. A systematic mapping of correlation effects across collision systems of various sizes is currently underway on the theoretical side, for example, see ref. [ 74 ]. A quantitative description of the full set of experimental data has not been achieved yet. A summary of various explanations for the observed correlations in small-system collisions is given in refs. [ 75 – 77 ]. Measurements of anisotropic flow in small-system collisions are strongly affected by non-flow effects, predominantly originating from correlations among the constituents of jet fragmentation processes. In case of two-particle correlations, the non-flow contribution is usually suppressed by requiring a large ∆ η gap between the two particles. This separation in pseudorapidity is also widely used in cumulant methods [ 13 , 78 ]. However, this ∆ η -gap method removes the non-flow contribution only on the near side (∆ φ∼ 0) and not on the away side (∆ φ∼π ). Later, a low-multiplicity template fit method was proposed to remove – 2 – JHEP03(2024)092 non-flow contributions on the away-side [ 10 , 19 , 79 ]. This method takes into account that the yield of jet fragments increases with increasing particle multiplicity [ 80 – 82 ]. By using the template fit method, the yield of away-side jet fragments can be subtracted, provided that the distribution that quantifies the shape of jet fragments is independent of the multiplicity class and therefore can be described by the low-multiplicity template. As an extension of the studies of the near-side long-range ridge and jet-fragmentation yields in pp collisions at the center-of-mass energy √s = 13 TeV [ 73 ] and in p–Pb collisions at the center-of-mass energy per nucleon pair √sNN = 5 . 02 TeV [ 17 , 83 ], this article studies the interplay of jet production and collective effects, i.e., shortand long-range correlations simultaneously in these systems. The article also reports flow coefficients extracted for collisions tagged with different event-scale selections. The event-scale selection requires a minimum transverse momentum of the leading particle or the reconstructed jet at midrapidity, which is expected to bias the impact parameter of pp collisions to be smaller on average [ 84 – 86 ]. At the same time, the transverse momentum of the leading particle or the reconstructed jet provides a measure of the four-momentum transfer ( Q2 ) in the hard-parton scattering [ 87 – 89 ]. The transverse-momentum threshold implies a higher Q2 for the collision. Such events with a large Q2 may, on average, have a lower impact parameter than pp events without any requirement on Q2 [ 85 ]. This article is organized as follows. First, the experimental setup and analysis method are described in section 2and section 3, respectively. Section 4discusses the systematic uncertainties. The results and their comparison with model calculations are presented and discussed in section 5. Finally, the results are summarized in section 6. 2 Experimental setup and data samples The analysis is based on pp and p–Pb data collected during the LHC Run 2 period. The pp collisions had a center-of-mass energy √s = 13 TeV, and they were recorded from 2016 to 2018. The p–Pb collisions had a center-of-mass energy per nucleon-nucleon pair √sNN = 5 . 02 TeV, and they were collected in 2016. It is worth noting that in p–Pb collisions there is a shift in the center-of-mass rapidity of ∆ y = 0 . 465 in the direction of the proton beam due to the asymmetric collision system. A comprehensive description of the ALICE detector and its performance can be found in refs. [ 8 , 90 , 91 ]. The analysis utilizes the V0 detector [ 92 ], the Inner Tracking System (ITS) [ 93 , 94 ], and the Time Projection Chamber (TPC) [ 95 ]. The V0 detector consists of two stations on both sides of the interaction point, V0A and V0C, each comprising 32 plastic scintillator tiles, covering the full azimuthal angle within the pseudorapidity intervals 2 . 8 < η < 5 . 1and − 3 . 7 < η < − 1 . 7, respectively. The ITS is a silicon tracker with six layers of silicon sensors. The two innermost layers of the ITS are called the Silicon Pixel Detector (SPD) [ 96 ]. In addition to the two SPD layers, the middle two layers are the Silicon Drift Detector, and the outermost layers are the Silicon Strip Detector. The TPC is a gas-filled cylindrical tracking detector providing up to 159 reconstruction points for charged tracks traversing the full radial extent of the detector. The V0 provides a minimum bias (MB) trigger in both pp and p–Pb collisions and an additional high-multiplicity trigger in pp collisions. The MB trigger is obtained by a time – 3 – JHEP03(2024)092 coincidence of V0A and V0C signals. Amplitudes of V0A and V0C signals are proportional to charged-particle multiplicity, and their sum is denoted as V0M. The high-multiplicity trigger in pp collisions requires the V0M signal to exceed five times the mean value measured in MB collisions, selecting the 0.1% of MB events with the largest V0M multiplicity. The centrality in p–Pb collisions is determined using the V0A detector, which is located in the Pb-going direction [ 25 ]. The analyzed data samples of MB and high-multiplicity pp events at √s = 13 TeV correspond to integrated luminosities ( Lint ) of about 19 nb −1 and 11 pb −1 , respectively [ 97 ]. In p–Pb collisions at √sNN = 5 . 02 TeV, the corresponding integrated luminosity is Lint ∼ 0 . 3nb −1 . Positions of primary vertices are reconstructed from signals measured by the SPD. The reconstructed primary vertices are required to be within 8 cm of the nominal interaction point along the beam direction. Pileup events are identified as events with multiple reconstructed primary vertices. These events are rejected if the distance between any of the vertices to the main primary vertex is greater than 0.8cm. The probability of pileup events is estimated to range from 10 −3 to 10 −2 for MB and high-multiplicity events in pp collisions [ 98 ]. The pileup probability is estimated to be negligible in p–Pb collisions [ 29 ]. Charged-particle tracks are reconstructed using the combined information from the ITS and TPC. For charged particles emitted from a vertex located within |zvtx|< 8cm along the beam direction, the ITS and TPC provide a pseudorapidity coverage of |η|< 1 . 4and 0.9, respectively. Both detectors have full coverage in azimuth. They are placed in a uniform magnetic field of 0.5 T that is oriented along the beam direction. The charged-particle selection criteria are optimized to ensure a uniform efficiency over the midrapidity range |η|<0.9to mitigate the effects of small areas where some ITS layers are inactive in both collision systems. The selected sample of tracks consists of two classes. Tracks in the first class must have at least one hit in the SPD. Tracks of the second class do not have any hits in the SPD, but their origin is constrained to the primary vertex [ 17 ]. Charged-particle tracks are reconstructed down to a transverse momentum ( pT ) of 0.15 GeV/ c with an efficiency of approximately 65% [ 99 ]. The efficiency increases to 80% for particles with pT> 1GeV/ c . The pT resolution is approximately 1% for primary charged particles [ 100 ] with pT< 1GeV/ c , and it linearly increases to 6% at pT∼ 50GeV/ c in pp collisions and 10% in p–Pb collisions [ 101 ]. 3 Analysis procedure 3.1 Two-particle angular correlations Two-particle angular correlations are measured as a function of the relative azimuthal angle (∆ φ ) and the relative pseudorapidity (∆ η ) between a trigger and associated particles 1 Ntrig d2Npair d∆ηd∆φ=B(0,0) S(∆η, ∆φ) B(∆η, ∆φ)pT,trig, pT,assoc ,(3.1) where pT,trig and pT,assoc denote the transverse momentum of the trigger and associated particles, respectively. While the transverse momentum range for associated particles is fixed to 1 < pT,assoc < 4GeV/ c for trigger particles, several transverse momentum ranges are – 4 – JHEP03(2024)092 considered. The lower limit of pT,trig and pT,assoc ( > 1GeV/ c ) is chosen in order to avoid jet-like contributions from lower pT particles which extend into the larger ∆ η range because of the limited η acceptance [ 73 ]. The numbers of trigger particles and trigger-associated particle pairs are denoted as Ntrig and Npair , respectively. The average number of pairs in the same event, denoted by S (∆ η, ∆ φ ), is given by 1 Ntrig d2Nsame d∆ηd∆φ . The B (∆ η, ∆ φ )represents the number of pairs in mixed events and is normalized with its value at the point where ∆ η = 0 and ∆ φ = 0, denoted as B (0 , 0). To correct for acceptance effects, S (∆ η, ∆ φ )is divided by B (∆ η, ∆ φ ) /B (0 , 0). The particles are weighted by the inverse of the tracking efficiency, which is obtained in the same way as in ref. [ 73 ]. In that study, the tracking efficiency and the secondary contamination (fake rate) were calculated using a detector simulation with the PYTHIA 8 event generator and the GEANT3 transport code [ 102 ]. To account for differences in particle composition between real data and PYTHIA, the tracking efficiency is determined from the above mentioned PYTHIA-based simulation with reweighted primary particle-species composition. The weights reflect realistic abundances of different particle species, which were extracted by a data-driven method [ 101 , 103 ]. Events to be mixed are required to have primary vertices within the same 2 cm wide zvtx interval. The correlation functions are averaged over the vertex intervals, resulting in the final per-trigger yield [ 104 , 105 ]. The fully corrected correlation functions from pp and p–Pb collisions are shown in figure 1. The z -axis is scaled in order to exhibit the ridge structures at large ∆ η regions. As a result, the jet peaks are sheared off in all figures. The flow modulation structure is clearly observed to emerge in the high-multiplicity collisions for both systems, while it is not seen in the low-multiplicity collisions. The away-side regions are populated mostly by back-to-back jet correlations. The per-trigger yield is determined by integrating the correlation function at large ∆ η (1 . 6 <| ∆ η|< 1 . 8) to remove non-flow contributions from near-side jet fragments. The per-trigger yield as a function of ∆ φ is expressed as Y(∆φ) = 1 Ntrig dNpair d∆φ=Z1.6<|∆η|<1.8"1 Ntrig d2Npair d∆ηd∆φ#1 δ∆η d∆η, (3.2) where the factor δ∆η = 0 . 4normalizes the obtained per-trigger yield per unit of pseudorapidity. The per-trigger yields are extracted for the considered pT,trig and pT,assoc intervals in several multiplicity classes: 0–0.1%, 1–5%, 5–20%, 20–60%, and 60–100% in pp collisions, and 0–5%, 5–10%, 10–20%, 20–40%, 40–60%, and 60–100% in p–Pb collisions. The conversion of the measured forward event multiplicities to the charge-particle multiplicities Nch at midrapidity ( |η|< 0 . 5) used in section 5is based on ref. [ 98 ]. 3.2 Extraction of flow coefficients As discussed in refs. [ 10 , 19 ], the correlation function in a given multiplicity interval is fitted with YHM(∆φ) = G(1 + 2v2,2cos(2∆φ)+2v3,3cos(3∆φ)) + F YLM(∆φ),(3.3) where YLM (∆ φ )is the measured per-trigger yield from low-multiplicity events. The normalization factor for the first three Fourier terms, which parameterize the long-range, flow-like – 5 – JHEP03(2024)092 1−01 η ∆ 1− 0 1 2 3 4 ϕ ∆ 1.2 1.25 1.3 ) ϕ ∆ d η ∆ / d pair N 2 )(d trig N(1/ 0.1%, V0M−0 c < 2 GeV/ T,trig p1 < c < 4 GeV/ T,assoc p1 < = 13 TeVs pp ALICE 1−01 η ∆ 1− 0 1 2 3 4 ϕ ∆ 0.08 0.1 0.12 0.14 ) ϕ ∆ d η ∆ / d pair N 2 )(d trig N(1/ 100%, V0M−60 c < 2 GeV/ T,trig p1 < c < 4 GeV/ T,assoc p1 < = 13 TeVs pp ALICE 1−01 η ∆ 1− 0 1 2 3 4 ϕ ∆ 1.6 1.7 1.8 ) ϕ ∆ d η ∆ / d pair N 2 )(d trig N(1/ 5%, V0A−0 c < 2 GeV/ T,trig p1 < c < 4 GeV/ T,assoc p1 < = 5.02 TeV NN s Pb −p ALICE 1−01 η ∆ 1− 0 1 2 3 4 ϕ ∆ 0.26 0.28 0.3 0.32 0.34 ) ϕ ∆ d η ∆ / d pair N 2 )(d trig N(1/ 100%, V0A−60 c < 2 GeV/ T,trig p1 < c < 4 GeV/ T,assoc p1 < = 5.02 TeV NN s Pb −p ALICE Figure 1. Two-dimensional correlation functions are presented for high-multiplicity (0–0.1% or 0–5%, on the left) and low-multiplicity (60–100%, on the right) events in √s = 13 TeV pp collisions in the top panels. The corresponding distributions for √sNN = 5 . 02 TeV p–Pb collisions are shown in the bottom panels. All correlation functions are shown for 1 < p T,trig < 2GeV/ c and 1 < p T,assoc < 4GeV/ c , respectively. correlation, is denoted as G . The scale factor F compensates for the increased yield of awayside-jet hadrons in the analyzed multiplicity class relative to the low-multiplicity template that corresponds to the 60–100% class [ 81 , 82 ]. The fit determines the scale factor F , pedestal G , and vn,n and is performed in various high-multiplicity classes as well as in different pT,trig intervals. This method assumes that YLM does not contain a near-side-peak structure that would originate from jet fragmentation or a near-side ridge. Furthermore it is assumed that the shape of the away-side-peak structure remains the same when changing the multiplicity class. The first assumption is ensured using the selected low-multiplicity template which does not have a strong near-side-peak structure compared to the studied higher-multiplicity classes. The second assumption, which involves the modification of jet shapes, was tested by projecting the near-side jet peaks onto ∆η. This modification of the jet shape is considered as one of the sources of systematic uncertainty and will be discussed in section 4. – 6 – JHEP03(2024)092 1.150 1.175 1.200 1.225 1.250 1.275 1.300 1 N trig d N pair d Signal (0–0.1% V0M) Fit FYLM +G G(1 + 2v2,2cos(2∆ϕ)) +FYLM,min G(1 + 2v3,3cos(3∆ϕ)) +FYLM,min 0.99 1.00 Data/Fit 1 0 1 2 3 4 (rad) ALICE pp √s= 13 TeV 1< pT,trig <2 GeV/c 1< pT,assoc <4 GeV/c 1.6<|∆η|<1.8 Figure 2. Per-trigger yield in 1 . 6 <| ∆ η|< 1 . 8extracted from 0–0.1% and 60–100% multiplicity percentile events in √s = 13 TeV pp collisions. The data are fitted with the template fit method described by eq. 3.3. The black markers show the signal for the 0–0.1% multiplicity percentile. The red squares correspond to the low-multiplicity signal. The red and gray curves correspond to the extracted v2,2 and v3,3 signals, respectively. To improve visibility, the baselines of flow signals are shifted by FYLM,min , which represents the minimum yield of FYLM (∆ φ ). The signal-to-fit ratio is shown in the bottom panel. The χ2divided by the number of degrees of freedom is 0.894. Figure 2shows the template fit results for the 0–0.1% multiplicity interval in pp collisions at √s = 13 TeV. Values of the extracted scale factor F in different multiplicity intervals and systems are summarized in table 1. In pp collisions, the value of F is observed to increase slightly as the event multiplicity increases. The F value, which is measured for the highest-multiplicity bin, is approximately 25% larger than the value found for the 20–60% bin. A similar dependence on multiplicity is observed for p–Pb collisions, although the dependence on the multiplicity interval is weaker. In the first three columns of table 1, representing collisions with higher multiplicities, there is an increase in the F value, while as shown by the subsequent columns, there is a decrease for lower multiplicity collisions. When comparing the F values from pp and p–Pb collisions, which have similar centrality, the value of F in p–Pb collisions is found to be smaller and closer to unity. This suggests that the jet fragmentation yield on the away-side increases with multiplicity, and that this feature is more pronounced in pp collisions. The difference between the two systems is likely to be explained by the true-geometry-driven centrality in p–Pb collisions, as opposed to the jet-dominated bias in pp collisions. The previous analyses published by ALICE in refs. [ 17 , 83 ] assumed that the jet contribution remains constant as a function of multiplicity (i.e. F was assumed to be 1). However, this assumption may lead to an underestimation of non-flow contamination in the measurements of anisotropic flow. – 7 – JHEP03(2024)092 0.04 0.06 0.08 0.10 0.12 0.14 v 2 Leading Particle |ηLP|<0.9 anti-kTcharged-particle jet R= 0.4 |ηjet|<0.4 0.00 0.02 0.04 0.06 0.08 0.10 0.12 v 3 All p T 3 5 7 9 13 20 p LP T,min (GeV/ c ) 1< pT<4 GeV/c 1< pT<2 GeV/c All p T 10 20 30 40 p jet T,min (GeV/ c ) pp √s= 13 TeV 0–0.1% 1.6<|∆η|<1.8 LP Jet LP Jet ALICE Figure 6. The magnitudes of v2 (top) and v3 (bottom) as a function of p LP T,min (left) and p jet T,min (right) for the high-multiplicity in pp collisions at √s = 13 TeV. The measured pT intervals are 1 < pT< 2 GeV/c (in red) and 1 < pT< 4 GeV/c (in black). The statistical errors and systematic uncertainties are shown as vertical bars and boxes, respectively. with multi-jet events at midrapidity with higher Q2 reach can shed more light on the expected impact parameter dependence [ 84 – 86 ]. 5.3 Comparisons with models In this section, the results are compared to various model calculations. The results from p–Pb collisions are compared with hydrodynamic calculations using the parameterization from an improved global Bayesian analysis. The analysis involves new sophisticated collective flow observables as obtained from two different beam energies in Pb–Pb collisions [ 55 ], constraining the initial conditions and transport properties of the QGP. This hydrodynamic model, T R ENTo+iEBE-VISHNU, consists of the T R ENTo model [ 121 ] to simulate the initial condition, which is connected with a free streaming to a 2+1 dimensional causal hydrodynamic model VISH2+1 [ 122 ]. The evolution is continued after hadronization with a hadronic cascade model (UrQMD) [ 41 , 42 ]. A model calculation is performed using the best-fit parameterization for transport coefficients selected based on maximum a posteriori (MAP) for Pb–Pb collisions at √sNN = 5 . 02 TeV. Two different MAP values are used for the calculations. They are based on ref. [ 55 ] and ref. [ 52 ] and in figure 7 they are labeled MAP(2021) and MAP(QM2018), respectively. The parameterization for the initial conditions, which include a sub-nucleon structure with six constituent partons per nucleon ( m = 6), is taken from a model calibration with additional p–Pb data [ 56 ]. All kinematic selections, such as the transverse momentum – 14 – JHEP03(2024)092 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 v 2 0 10 20 30 40 50 60 N ch(| |< 0.5) pp √s= 13 TeV p–Pb √sNN = 5.02 TeV GubsHyd, param0, pp 13 TeV GubsHyd, param1, pp 13 TeV GubsHyd, param2, p–Pb 5.02 TeV 0 10 20 30 40 50 60 N ch(| |< 0.5) 0.00 0.02 0.04 0.06 0.08 0.10 v 3 TRENTo, MAP(QM2018), m= 6, p–Pb 5.02 TeV TRENTo, MAP(2021), m= 6, p–Pb 5.02 TeV IP-Glasma η/s = 0.12, ζ/s(T), p–Pb 5.02 TeV IP-Glasma η/s = 0.12, ζ/s(T), pp 13 TeV ALICE 1.6<|∆η|<1.8 1< pT<4 GeV/c Figure 7. The measured and calculated evolution of v2 (left) and v3 (right) in pp and p–Pb collisions as a function of charged-particle multiplicity at midrapidity. The blue and red markers represent the measured p–Pb and pp data, respectively. The calculations provided by hydrodynamical models [ 52 , 55 , 64 , 74 ] are presented with colored lines. The corresponding bands mark their statistical uncertainty. For GubsHyd calculations, the statistical uncertainty is smaller than the line thickness. and pseudorapidity intervals, are matched to the data reported in this article. The flow coefficients in the hydrodynamic calculation are extracted with the two-particle cumulant method, as the T R ENTo+iEBE-VISHNU does not contain any non-flow. Figure 7shows that T R ENTo+iEBE-VISHNU overestimates both v2 and v3 . In the studied range, the v2 and v3 data increase with multiplicity. However, T R ENTo+iEBEVISHNU predicts the opposite trend, which is similar to what is found in large collision systems [ 47 ]. The large discrepancies in the prediction might be alleviated by inclusion of the newly measured p–Pb constraints in a future Bayesian parameter estimation as well as by improvements of the initial condition model for small-system collisions. The results are also compared with IP-Glasma+MUSIC+UrQMD hydrodynamic calculations [ 74 ]. This model uses IP-Glasma initial conditions [ 30 ] including sub-nucleonic fluctuations with three hot spots per nucleon. The hydrodynamic evolution is performed by MUSIC [ 36 ] and coupled with UrQMD [ 41 , 42 ], which performs hadronic cascade. The model calculations are performed assuming constant η/s = 0 . 12 and a temperature dependent ζ/s ( T )[ 123 ]. This model describes well the multiplicity dependence of v2 in p–Pb collisions and the magnitude at the highest multiplicity within the statistical uncertainties of the model but overestimates the data for the lower multiplicity classes. As for pp collisions, the calculations clearly miss both the observed magnitude except for Nch > 25 as well as the trend of the multiplicity dependence. The model shows that v2 decreases with increasing multiplicity, while the experimental result shows the opposite. For v3 , the model accurately describes the magnitudes and multiplicity dependence across the measured multiplicity ranges. The magnitudes of v3 are slightly smaller in pp collisions than in p–Pb collisions according to the calculations, which agrees with the data within the uncertainties. The level of agreement between data and the IP Glasma model calculations is found to be similar to the results reported in ref. [ 13 ]. – 15 – JHEP03(2024)092 Finally, the results are compared with the GubsHyd model, a semi-analytical model based on the analytical Gubser solution to hydrodynamic equations [ 62 , 63 ], known as Gubser flow. In Gubser flow, the initial state of conformal matter is linearly perturbed by an initial elliptic shape. The model is employed to shed light on the possible sources of the observed discrepancy between more realistic models mentioned above and the measurements in pp collisions [ 64 ]. Instead of modeling the initial entropy density in this model, as it is typically done in T R ENTo or IP-Glasma, the initial state fluctuation is modeled directly. It assumes that proton ellipticity ϵ2 and RMS radius rrms fluctuate independently. These fluctuations are described by Gaussian probability distributions, which have widths σϵ and σr , respectively. The multiplicity dependence of the v2{ 2 } of two-particle correlation functions depends on σr and χσϵ , where the coefficient χ encapsulates a correction for idealizations used in GubsHyd, including the absence of dissipation effects. The values of σr and χσϵ were obtained by comparing the model with data. Since no non-flow effect is considered in the calculation, v2{ 2 } is comparable with the flow measurements in the present study. The calculations for two sets of parameters are compared to data in figure 7. The “param0” parameterization is based on the prediction proposed in ref. [ 64 ] that χσϵ = 0 . 097 and σr = 0 . 4fm. The other parameterizations “param1” and “param2” employ different χσϵ and σr values. The model captures the multiplicity dependence of v2 well. In summary, the measured v2 value decrease with decreasing multiplicity in both pp and p– Pb collisions. This trend is also predicted by GubsHyd model calculations (refs. [ 64 ] and [ 124 ]). Interestingly, the opposite trend is observed for the IP-GLASMA+MUSIC+UrQMD hydrodynamic calculations of v2 , where the value decreases with increasing charged-particle multiplicity [ 74 ]. Approaching a lower bound for the size of a hydrodynamized system as predicted in ref. [ 64 ], the decreasing trend of v2 , obtained by lowering the charged-particle multiplicity, changes and turns out to raise again after the observed minimum. However, this change in multiplicity dependence of v2 at low multiplicities is still challenging to test with the current experimental uncertainties. For v3 , the IP-Glasma+MUSIC+UrQMD hydrodynamic calculations [ 74 ] are the only ones that accurately describe its magnitude and multiplicity dependence across the measured ranges. The calculations predict that the magnitudes of v3 are slightly smaller in pp collisions than in p–Pb collisions, within the measured multiplicity ranges. The discrepancies between the predictions and the data can be further studied by including these measurements in a future Bayesian parameter estimation, as well as by improving the initial-condition model for the small-system collisions. 6 Conclusions Long-range angular correlations for pairs of charged particles are studied in pp collisions at √s = 13 TeV and p–Pb collisions at √sNN = 5 . 02 TeV. Flow coefficients are extracted from long-range correlations (1 . 6 <| ∆ η|< 1 . 8) for a broad range of charged-particle-multiplicity classes using the template method, which allows one to subtract the enhanced away-side jet fragmentation yields in high-multiplicity events with respect to low-multiplicity events. The method that was used to measure the flow coefficients within the considered kinematic ranges has been verified to be stable. The systematic uncertainties on v2 and v3 measurements, which reflect the possible differences in the away-side jet peak shapes in highand low-multiplicity – 16 – JHEP03(2024)092 events, were found to be 1% and 3–8%, respectively.However, it is important that these systematic uncertainties are reevaluated, when analyzing different kinematic ranges, as the effect may not always be negligible. The measured pT dependence of v2 and v3 is consistent with the measurements by ATLAS and shows that both v2 and v3 increase with pT and reach their maximum at 2 . 5 < pT< 3 . 0 GeV/c . The measurement of v2 as a function of charged-particle multiplicity in |η|< 0 . 5shows a weak multiplicity dependence both for pp and p–Pb collisions and tends to decrease toward lower multiplicities. The pp data suggests that the v2 signal may disappear when the measurement is pursued further below Nch = 10. The comparisons to viscous hydrodynamic models show that the magnitudes of v2 and their multiplicity dependence are not described by state-of-the-art hydrodynamic calculations, which simulated initial conditions with two initial state models, especially for low-multiplicity p–Pb and pp collisions. As initial state effects tend to be more important at low multiplicity [ 56 , 59 ], these results may help to constrain the modeling of the initial state. Furthermore, the events including hard probes such as jets or highpT leading particles do not show any changes both in v2 and v3 within the uncertainties, which implies that the long-range correlation of soft particles is not significantly modified by the presence of the hard-scattering process. Even though it would be interesting to compare these results to the EPOS LHC [ 125 ] and PYTHIA8 String Shoving models [ 71 , 72 ] as done in ref. [ 17 ] for the ridge yields, it is not possible to reliably extract the flow coefficients because these models exhibit a near-side ridge structure in low-multiplicity events, thus making the use of the low-multiplicity template ill defined [ 126 ]. Acknowledgments The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), – 17 – JHEP03(2024)092 Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. 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Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia 2AGH University of Krakow, Cracow, Poland 3Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine 4 Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India 5California Polytechnic State University, San Luis Obispo, California, United States 6Central China Normal University, Wuhan, China 7Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba 8Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico 9Chicago State University, Chicago, Illinois, United States 10 China Institute of Atomic Energy, Beijing, China 11 China University of Geosciences, Wuhan, China 12 Chungbuk National University, Cheongju, Republic of Korea 13 Comenius University Bratislava, Faculty of Mathematics, Physics and Informatics, Bratislava, Slovak Republic 14 COMSATS University Islamabad, Islamabad, Pakistan 15 Creighton University, Omaha, Nebraska, United States – 31 – JHEP03(2024)092 16 Department of Physics, Aligarh Muslim University, Aligarh, India 17 Department of Physics, Pusan National University, Pusan, Republic of Korea 18 Department of Physics, Sejong University, Seoul, Republic of Korea 19 Department of Physics, University of California, Berkeley, California, United States 20 Department of Physics, University of Oslo, Oslo, Norway 21 Department of Physics and Technology, University of Bergen, Bergen, Norway 22 Dipartimento di Fisica, Università di Pavia, Pavia, Italy 23 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy 24 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy 25 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy 26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy 27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy 28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy 29 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy 30 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy 31 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy 32 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy 33 European Organization for Nuclear Research (CERN), Geneva, Switzerland 34 Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia 35 Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway 36 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic 37 Faculty of Physics, Sofia University, Sofia, Bulgaria 38 Faculty of Science, P.J. Šafárik University, Košice, Slovak Republic 39 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 40 Fudan University, Shanghai, China 41 Gangneung-Wonju National University, Gangneung, Republic of Korea 42 Gauhati University, Department of Physics, Guwahati, India 43 Helmholtz-Institut für Strahlenund Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany 44 Helsinki Institute of Physics (HIP), Helsinki, Finland 45 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico 46 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania 47 HUN-REN Wigner Research Centre for Physics, Budapest, Hungary 48 Indian Institute of Technology Bombay (IIT), Mumbai, India 49 Indian Institute of Technology Indore, Indore, India 50 INFN, Laboratori Nazionali di Frascati, Frascati, Italy 51 INFN, Sezione di Bari, Bari, Italy 52 INFN, Sezione di Bologna, Bologna, Italy 53 INFN, Sezione di Cagliari, Cagliari, Italy 54 INFN, Sezione di Catania, Catania, Italy 55 INFN, Sezione di Padova, Padova, Italy 56 INFN, Sezione di Pavia, Pavia, Italy 57 INFN, Sezione di Torino, Turin, Italy 58 INFN, Sezione di Trieste, Trieste, Italy 59 Inha University, Incheon, Republic of Korea 60 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, Netherlands 61 Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovak Republic 62 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India 63 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic – 32 – JHEP03(2024)092 64 Institute of Space Science (ISS), Bucharest, Romania 65 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 66 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico 67 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil 68 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico 69 iThemba LABS, National Research Foundation, Somerset West, South Africa 70 Jeonbuk National University, Jeonju, Republic of Korea 71 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik und Mathematik, Frankfurt, Germany 72 Korea Institute of Science and Technology Information, Daejeon, Republic of Korea 73 KTO Karatay University, Konya, Turkey 74 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France 75 Lawrence Berkeley National Laboratory, Berkeley, California, United States 76 Lund University Department of Physics, Division of Particle Physics, Lund, Sweden 77 Nagasaki Institute of Applied Science, Nagasaki, Japan 78 Nara Women’s University (NWU), Nara, Japan 79 National and Kapodistrian University of Athens, School of Science, Department of Physics , Athens, Greece 80 National Centre for Nuclear Research, Warsaw, Poland 81 National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India 82 National Nuclear Research Center, Baku, Azerbaijan 83 National Research and Innovation Agency - BRIN, Jakarta, Indonesia 84 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 85 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands 86 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom 87 Nuclear Physics Institute of the Czech Academy of Sciences, Husinec-Řež, Czech Republic 88 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States 89 Ohio State University, Columbus, Ohio, United States 90 Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia 91 Physics Department, Panjab University, Chandigarh, India 92 Physics Department, University of Jammu, Jammu, India 93 Physics Program and International Institute for Sustainability with Knotted Chiral Meta Matter (SKCM2), Hiroshima University, Hiroshima, Japan 94 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany 95 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 96 Physik Department, Technische Universität München, Munich, Germany 97 Politecnico di Bari and Sezione INFN, Bari, Italy 98 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 99 Saga University, Saga, Japan 100 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India 101 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 102 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru 103 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria 104 SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France 105 Sungkyunkwan University, Suwon City, Republic of Korea 106 Suranaree University of Technology, Nakhon Ratchasima, Thailand 107 Technical University of Košice, Košice, Slovak Republic 108 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 109 The University of Texas at Austin, Austin, Texas, United States 110 Universidad Autónoma de Sinaloa, Culiacán, Mexico 111 Universidade de São Paulo (USP), São Paulo, Brazil – 33 – JHEP03(2024)092 112 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 113 Universidade Federal do ABC, Santo Andre, Brazil 114 Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, Bucharest, Romania 115 University of Cape Town, Cape Town, South Africa 116 University of Derby, Derby, United Kingdom 117 University of Houston, Houston, Texas, United States 118 University of Jyväskylä, Jyväskylä, Finland 119 University of Kansas, Lawrence, Kansas, United States 120 University of Liverpool, Liverpool, United Kingdom 121 University of Science and Technology of China, Hefei, China 122 University of South-Eastern Norway, Kongsberg, Norway 123 University of Tennessee, Knoxville, Tennessee, United States 124 University of the Witwatersrand, Johannesburg, South Africa 125 University of Tokyo, Tokyo, Japan 126 University of Tsukuba, Tsukuba, Japan 127 Universität Münster, Institut für Kernphysik, Münster, Germany 128 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 129 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, Lyon, France 130 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France 131 Université Paris-Saclay, Centre d’Etudes de Saclay (CEA), IRFU, Départment de Physique Nucléaire (DPhN), Saclay, France 132 Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France 133 Università degli Studi di Foggia, Foggia, Italy 134 Università del Piemonte Orientale, Vercelli, Italy 135 Università di Brescia, Brescia, Italy 136Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India 137Warsaw University of Technology, Warsaw, Poland 138Wayne State University, Detroit, Michigan, United States 139Yale University, New Haven, Connecticut, United States 140Yonsei University, Seoul, Republic of Korea 141 Zentrum für Technologie und Transfer (ZTT), Worms, Germany 142 Affiliated with an institute covered by a cooperation agreement with CERN 143 Affiliated with an international laboratory covered by a cooperation agreement with CERN. IDeceased II Also at: Max-Planck-Institut fur Physik, Munich, Germany III Also at: Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy IV Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy VAlso at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India V I Also at: Institute of Theoretical Physics, University of Wroclaw, Poland V II Also at: An institution covered by a cooperation agreement with CERN – 34 –