# Multiplicity and event-scale dependent flow and jet fragmentation in pp collisions at $\sqrt{s} = 13$ TeV and in p-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV

Shreyasi Acharya, Dagmar Adamova, Gianluca Aglieri Rinella, Michelangelo Agnello, Neelima Agrawal, Zubayer Ahammed, Shakeel Ahmad, Sang Un Ahn, Ishaan Ahuja, Alexander Akindinov, et al.

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## ► To cite this version:

Shreyasi Acharya, Dagmar Adamova, Gianluca Aglieri Rinella, Michelangelo Agnello, Neelima Agrawal, et al. Multiplicity and event-scale dependent flow and jet fragmentation in pp collisions at $\sqrt{s} = 13$ TeV and in p-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. Journal of High Energy Physics, 2024, 03, pp.092. 10.1007/JHEP03(2024)092. [hal-04199237](https://hal.science/hal-04199237v1)

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https://hal.science/hal-04199237v1

Submitted on 16 Jan 2025

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# Multiplicity and event-scale dependent flow and jet fragmentation in pp collisions at $\sqrt{s} = 13$ TeV and in p-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV

ALICE Collaboration*

## Abstract

Long- and short-range correlations for pairs of charged particles are studied via two-particle angular correlations in pp collisions at $\sqrt{s} = 13$ TeV and p-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. The correlation functions are measured as a function of relative azimuthal angle $\Delta\phi$ and pseudorapidity separation $\Delta\eta$ for pairs of primary charged particles within the pseudorapidity interval $|\eta| < 0.9$ and the transverse-momentum interval $1 < p_T < 4$ GeV/c. Flow coefficients are extracted for the long-range correlations ($1.6 < |\Delta\eta| < 1.8$) 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.

<footnote>*See Appendix A for the list of collaboration members</footnote>
# 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 pressure-driven 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-of-equilibrium, 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 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 two- and 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 fluid-dynamical 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 experi-
mental 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
$\Delta\eta$ gap between the two particles. This separation in pseudorapidity is also widely used in cumulant
methods [13, 78]. However, this $\Delta\eta$-gap method removes the non-flow contribution only on the near
side ($\Delta\phi \sim 0$) and not on the away side ($\Delta\phi \sim \pi$). Later, a low-multiplicity template fit method was
proposed to remove 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 colli-
sions at the center-of-mass energy $\sqrt{s} = 13$ TeV [73] and in p-Pb collisions at the center-of-mass energy
per nucleon pair $\sqrt{s_{NN}} = 5.02$ TeV [17, 83], this article studies the interplay of jet production and col-
lective effects, i.e., short- and 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 av-
erage [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 ($Q^2$) in the hard-parton scattering [87–89]. The
transverse-momentum threshold implies a higher $Q^2$ for the collision. Such events with a large $Q^2$ may,
on average, have a lower impact parameter than pp events without any requirement on $Q^2$ [85].

This article is organized as follows. First, the experimental setup and analysis method are described
in Sec. 2 and Sec. 3, respectively. Section 4 discusses the systematic uncertainties. The results and
their comparison with model calculations are presented and discussed in Sec. 5. Finally, the results are
summarized in Sec. 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 $\sqrt{s} = 13$ TeV, and they were recorded from 2016 to 2018. The p–Pb collisions had a center-of-mass energy per nucleon–nucleon pair $\sqrt{s_{NN}} = 5.02$ 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 $\Delta y = 0.465$ 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 com-
prising 32 plastic scintillator tiles, covering the full azimuthal angle within the pseudorapidity intervals
$2.8 < \eta < 5.1$ and $-3.7 < \eta < -1.7$, 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 addi-
tion 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 coincidence of V0A and VOC signals. Amplitudes of V0A and VOC 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 $\sqrt{s} = 13$ TeV correspond to integrated luminosities ($\mathcal{L}_{int}$) of about 19 nb$^{-1}$ and 11 pb$^{-1}$, respectively [97]. In p–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV, the corresponding integrated luminosity is $\mathcal{L}_{int} \sim 0.3$ nb$^{-1}$.

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 0.8 cm. 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 $|z_{VTX}| < 8$ cm along the beam direction, the ITS and TPC provide a pseudorapidity coverage of $|\eta| < 1.4$ and 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 $|\eta| < 0.9$ to 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 ($p_T$) of 0.15 GeV/c with an efficiency of approximately 65% [99]. The efficiency increases to 80% for particles with $p_T > 1$ GeV/c. The $p_T$ resolution is approximately 1% for primary charged particles [100] with $p_T < 1$ GeV/c, and it linearly increases to 6% at $p_T \sim 50$ GeV/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 ($\Delta\phi$) and the relative pseudorapidity ($\Delta\eta$) between a trigger and associated particles

$$ \frac{1}{N_{\text{trig}}} \frac{d^2 N_{\text{pair}}}{d\Delta\eta d\Delta\phi} = B(0,0) \left. \frac{S(\Delta\eta, \Delta\phi)}{B(\Delta\eta, \Delta\phi)} \right|_{p_{\text{T, trig}}, p_{\text{T, assoc}}} \quad (1) $$

where $p_{T, trig}$ and $p_{T, assoc}$ denote the transverse momentum of the trigger and associated particles, respectively. While the transverse momentum range for associated particles is fixed to $1 < p_{T, assoc} < 4$ GeV/c for trigger particles, several transverse momentum ranges are considered. The lower limit of $p_{T, trig}$ and $p_{T, assoc}$ ($> 1$ GeV/c) is chosen in order to avoid jet-like contributions from lower $p_T$ particles which extend into the larger $\Delta\eta$ range because of the limited $\eta$ acceptance [73]. The numbers of trigger particles and trigger-associated particle pairs are denoted as $N_{\text{trig}}$ and $N_{\text{pair}}$, respectively. The average number of pairs in the same event, denoted by $S(\Delta\eta, \Delta\phi)$, is given by $\frac{1}{N_{\text{trig}}} \frac{d^2 N_{\text{same}}}{d\Delta\eta d\Delta\phi}$. The $B(\Delta\eta, \Delta\phi)$ represents the number of pairs in mixed events and is normalized with its value at the point where $\Delta\eta = 0$ and $\Delta\phi = 0$, denoted as $B(0,0)$. To correct for acceptance effects, $S(\Delta\eta, \Delta\phi)$ is divided by $B(\Delta\eta, \Delta\phi)/B(0,0)$. 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 $z_{VTX}$ interval. The correlation functions are averaged over the vertex intervals, resulting in the final per-trigger yield [104, 105].

<figure><img src="image_3.png" /><figcaption>**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 $\sqrt{s} = 13$ TeV pp collisions in the top panels. The corresponding distributions for $\sqrt{s_{NN}} = 5.02$ TeV p–Pb collisions are shown in the bottom panels. All correlation functions are shown for $1 < p_{T,\text{trig}} < 2$ GeV/c and $1 < p_{T,\text{assoc}} < 4$ GeV/c, respectively.</figcaption></figure>

The fully corrected correlation functions from pp and p–Pb collisions are shown in Fig. 1. The z-axis is scaled in order to exhibit the ridge structures at large $\Delta\eta$ 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 $\Delta\eta$ ($1.6 < |\Delta\eta| < 1.8$) to remove non-flow contributions from near-side jet fragments. The per-trigger yield as a function of $\Delta\phi$ is expressed as
$$Y(\Delta\varphi) = \frac{1}{N_{\text{trig}}} \frac{dN_{\text{pair}}}{d\Delta\varphi} = \int_{1.6<|\Delta\eta|<1.8} \left[ \frac{1}{N_{\text{trig}}} \frac{d^2N_{\text{pair}}}{d\Delta\eta d\Delta\varphi} \right] \frac{1}{\delta_{\Delta\eta}} d\Delta\eta, \quad (2)$$

where the factor $\delta_{\Delta\eta} = 0.4$ normalizes the obtained per-trigger yield per unit of pseudorapidity. The per-trigger yields are extracted for the considered $p_{T,\text{trig}}$ and $p_{T,\text{assoc}}$ 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 $N_{\text{ch}}$ at midrapidity ($|\eta| < 0.5$) used in Sec. 5 is 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

$$Y_{\text{HM}}(\Delta\varphi) = G (1 + 2v_{2,2} \cos(2\Delta\varphi) + 2v_{3,3} \cos(3\Delta\varphi)) + F Y_{\text{LM}}(\Delta\varphi), \quad (3)$$

where $Y_{\text{LM}}(\Delta\varphi)$ 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 correlation, is denoted as $G$. The scale factor $F$ compensates for the increased yield of away-side-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 $v_{n,n}$ and is performed in various high-multiplicity classes as well as in different $p_{T,\text{trig}}$ intervals. This method assumes that $Y_{\text{LM}}$ 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 $\Delta\eta$. This modification of the jet shape is considered as one of the sources of systematic uncertainty and will be discussed in Sec. 4.

Figure 2 shows the template fit results for the 0–0.1% multiplicity interval in pp collisions at $\sqrt{s} = 13$ 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.

In the following, the near and away-side jet fragmentation yields are calculated to verify the template fit method by comparing the jet fragmentation yields to the PYTHIA model. The away-side jet fragmentation yields in the PYTHIA model are obtained using the standard $\Delta\varphi$ analysis [106], while in the data, the away-side jet fragmentation yields are extracted using the template fit method because of the flow
<figure><img src="image_4.png" /><figcaption>**Figure 2:** Per-trigger yield in $1.6 < |\Delta\eta| < 1.8$ extracted from 0–0.1% and 60–100% multiplicity percentile events in $\sqrt{s} = 13$ TeV pp collisions. The data are fitted with the template fit method described by Eq. 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 $v_{2,2}$ and $v_{3,3}$ signals, respectively. To improve visibility, the baselines of flow signals are shifted by $FY_{LM,\text{min}}$, which represents the minimum yield of $FY_{LM}(\Delta\phi)$. The signal-to-fit ratio is shown in the bottom panel. The $\chi^2$ divided by the number of degrees of freedom is 0.894.</figcaption></figure>

modulations in the data. The comparison between the data and the PYTHIA model provides a validation of the template fit method.

Equivalently to Eq. (2), measured data are used to obtain the near-side $\Delta\eta$ correlations with

$$Y(\Delta\eta) = \frac{1}{N_{\text{trig}}} \frac{dN_{\text{pair}}}{d\Delta\eta} = \int_{|\Delta\phi|<1.3} \left[ \frac{1}{N_{\text{trig}}} \frac{d^2 N_{\text{pair}}}{d\Delta\eta d\Delta\phi} \right] \frac{1}{\delta_{\Delta\phi}} d\Delta\phi - D_{\text{ZYAM}}, \quad (4)$$

where $\delta_{\Delta\phi} = 2.6$ and $D_{ZYAM}$ defines the baseline of the ZYAM background subtraction [107]. The baseline is obtained by finding the minimum of the distribution defined by the integral in Eq. (4). As flow has a weak $\eta$ dependence [7, 108, 109], the jet-fragmentation yield can be calculated after the ZYAM background subtraction [107]. The near-side jet-like yields were extracted by integrating the $Y(\Delta\eta)$

$$Y_{\text{frag}}^{\text{near}} = \int_{|\Delta\eta|<1.3} \left( \frac{1}{N_{\text{trig}}} \frac{dN_{\text{pair}}}{d\Delta\eta} \right) d\Delta\eta. \quad (5)$$

The away-side jet-like yield in data is calculated by integrating the low-multiplicity template over $\pi/2 < \Delta\phi < 3/2\pi$ and scaling it by the parameter $F$ from Eq. (3), $Y_{\text{frag}}^{\text{away, HM}} = Y_{\text{frag}}^{\text{away, LM}} \times F$. The $Y_{\text{frag}}^{\text{away, LM}}$

<table><caption>**Table 1:** The scale factor $F$ for various multiplicity intervals in pp collisions (top) and p–Pb collisions (bottom), with $1 < p_{T,\text{trig}} < 2$ GeV/c and $1 < p_{T,\text{assoc}} < 4$ GeV/c. The table reports statistical uncertainties only. Average systematic uncertainty of $F$ is about 3.8% for both collision systems and multiplicity intervals.</caption><thead><tr><th></th><th>0–0.1%</th><th>1–5%</th><th>5–20%</th><th>20–60%</th><th></th><th></th></tr></thead><tbody><tr><th>V0M (pp)</th><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th><i>F</i></th><td>1.504±0.017</td><td>1.414±0.030</td><td>1.360±0.019</td><td>1.208±0.015</td><td></td><td></td></tr><tr><th>V0A (p–Pb)</th><td>0–5%</td><td>5–10%</td><td>10–20%</td><td>0–20%</td><td>20–40%</td><td>40–60%</td></tr><tr><th><i>F</i></th><td>1.135±0.026</td><td>1.140±0.026</td><td>1.152±0.021</td><td>1.145±0.017</td><td>1.092±0.015</td><td>1.083±0.015</td></tr></tbody></table>
is directly obtained by integrating the away-side low-multiplicity $\Delta\phi$ correlation function in the low-multiplicity sample over $\pi/2 < \Delta\phi < 3\pi/2$. As PYTHIA does not include any flow contributions in its model, $Y^{\text{away}}$ can be directly measured from the $\Delta\phi$ correlation functions.

<figure><img src="image_5.png" /><figcaption>**Figure 3:** The $Y_{\text{frag}}$ for the near- and away-side as a function of multiplicity percentiles with both ALICE and PYTHIA data. Systematic uncertainties are represented by the boxes. The bottom panel presents ratios of the yields. Here the reported uncertainty is obtained by adding statistical error and systematic uncertainty in quadrature. For PYTHIA, the statistical uncertainty is smaller than the thickness of the lines.</figcaption></figure>

Figure 3 presents the $Y_{\text{frag}}^{\text{near}}$ and $Y_{\text{frag}}^{\text{away}}$, for both ALICE data and PYTHIA 8 Tune 4C [110], as a function of the V0M multiplicity intervals in pp collisions at $\sqrt{s} = 13$ TeV. The transverse momentum range for trigger particles is $1 < p_{\text{T, trig}} < 2$ GeV/c and for associated particles $1 < p_{\text{T, assoc}} < 4$ GeV/c. The near-to away-side ratio for ALICE and PYTHIA data is shown in the bottom panel. While PYTHIA overestimates both near-side and away-side yields measured by ALICE, the corresponding ratio is consistent with the ALICE data in the all considered V0M multiplicity intervals. The value of this ratio can be explained by the pair acceptance effect caused by the limited ALICE $\eta$ acceptance [106]. The observed agreement implies that the enhanced jet fragmentation yields in the away-side in high-multiplicity events with respect to low-multiplicity events [81, 82] are taken into account by the low-multiplicity template method. In summary, the difference between the near-side and away-side jet fragmentation yields in PYTHIA is solely caused by the jet acceptance effects which affect the two-particle correlation functions. The corresponding ratio in data, where the away-side jet fragmentation yields are measured with the low-multiplicity template, agrees well with PYTHIA as well as with the expectation in Ref. [106].

The flow coefficients, $v_n$, of the trigger particles, can be extracted from the template fit with the use of the observed factorization of $v_{n,n}$ coefficients to single harmonics [10, 19] by using

$$v_n(p_{\text{T, trig}}) = v_{n,n}(p_{\text{T, trig}}, p_{\text{T, assoc}}) / \sqrt{v_{n,n}(p_{\text{T, assoc}}, p_{\text{T, assoc}})}, \quad (6)$$

where $v_{n,n}(p_{\text{T, assoc}}, p_{\text{T, assoc}})$ denote $v_{n,n}$ coefficients extracted using trigger and associated particles with $p_{\text{T}}$ in the range 1–4 GeV/c. In the following sections, unless explicitly stated otherwise, $v_n$ will refer to $v_n(p_{\text{T, trig}})$. Different event scale selections were investigated by selecting events that include a hard jet or a high-$p_{\text{T}}$ leading particle at midrapidity (i.e., the particle with the highest reconstructed $p_{\text{T}}$ inside the
acceptance region in an event). This event scale was set by requiring a minimum $p_T$ of the leading track ($p_{T,LP}$) or the reconstructed jet ($p_{T,jet}^{ch}$) at midrapidity [73]. The leading particle track was required to be within $|\eta| < 0.9$ and $0 < \phi < 2\pi$, and the jets were reconstructed with the anti-$k_T$ algorithm [111, 112], with $R = 0.4$ using charged particles only. Jet constituents were combined using the boost-invariant $p_T$ recombination scheme. The jets are selected in the full azimuth ($0 < \phi < 2\pi$) and their pseudorapidity is constrained to $|\eta_{jet}| < 0.4$. The $p_T$ of jets $p_{T,jet}^{ch}$ is corrected for the underlying event density that is measured using the $k_T$ algorithm with $R = 0.2$ following the procedure described in Ref. [113].

## 4 Systematic uncertainties

<table><caption>**Table 2:** The relative systematic uncertainties of $Y^{\text{near}}$, $Y^{\text{away,LM}}$, $F$, $v_2$, and $v_3$. The quantities $Y^{\text{near}}$, $Y^{\text{away,LM}}$, $F$ are only measured in pp collisions, whereas $v_2$ and $v_3$ are measured in both pp and p–Pb collisions. The quoted ranges correspond to minimum and maximum uncertainties. Those uncertainties that are considered to be negligible are marked “negl.”. The systematic variations which are not relevant for the measurement are denoted as “N.A.”.</caption><thead><tr><th rowspan="3">Sources</th><th colspan="6">Systematic uncertainty (%)</th></tr><tr><th colspan="2">Y<sup>near</sup></th><th>F</th><th colspan="2">v<sub>2</sub></th><th colspan="2">v<sub>3</sub></th></tr><tr><th>pp</th><th>pp</th><th>pp</th><th>pp</th><th>p-Pb</th><th>pp</th><th>p-Pb</th></tr></thead><tbody><tr><td>Primary vertex</td><td>±0.2–0.5</td><td>±0.1</td><td>±1.0–2.5</td><td>±0.2–1.8</td><td>±0.8</td><td>±1.4</td><td>±3.9</td></tr><tr><td>Pileup rejection</td><td>±0.1–0.5</td><td>±0.2</td><td>±0.4–1.5</td><td>negl.</td><td>±0.6</td><td>negl.</td><td>±1.4</td></tr><tr><td>Tracking</td><td>±1.0–3.0</td><td>±2.0</td><td>±0.6–2.4</td><td>±0.2–3.0</td><td>negl.</td><td>±5.0–6.9</td><td>negl.</td></tr><tr><td>Event mixing</td><td>±0.2–0.7</td><td>±0.2–0.5</td><td>±0.0–3.3</td><td>±0.3–4.6</td><td>±0.8</td><td>±2.8–3.1</td><td>±0.8</td></tr><tr><td>Low-mult. definition</td><td>N.A.</td><td>±0.5–3.5</td><td>±0.7–6.0</td><td>negl.</td><td>±1.9</td><td>negl.</td><td>±9.2</td></tr><tr><td>ITS–TPC matching</td><td>±2.0–3.0</td><td>±2.0–3.0</td><td>N.A.</td><td>N.A.</td><td>N.A.</td><td>N.A.</td><td>N.A</td></tr><tr><td>Efficiency correction</td><td>±1.0–4.4</td><td>±1.0–4.4</td><td>N.A.</td><td>N.A.</td><td>N.A.</td><td>N.A.</td><td>N.A</td></tr><tr><td>Δη gap range</td><td>N.A.</td><td>N.A.</td><td>±0.1–3.2</td><td>±1.0–5.0</td><td>±0.4</td><td>negl.</td><td>negl.</td></tr><tr><td>Jet shape modification</td><td>N.A.</td><td>N.A.</td><td>N.A</td><td>±1.0</td><td>±1.0</td><td>±3.0</td><td>±8.0</td></tr><tr><td>Total (in quadrature)</td><td>±2.5–6.1</td><td>±5.0–5.5</td><td>±1.8–7.1</td><td>±1.3–5.8</td><td>±2.5</td><td>±6.8–8.0</td><td>±12.8</td></tr></tbody></table>

Systematic uncertainties are estimated by varying the analysis selection criteria and corrections. Independent systematic checks are performed and the differences between results obtained from each variation and the default selection are considered as the systematic uncertainty for each source [114]. The total systematic uncertainty is obtained by adding the contributions from different sources in quadrature. A summary of all systematic uncertainties is provided in Table 2.

The uncertainty attributed to the chosen primary vertex range is estimated by varying the selected range from $|z_{vtx}| < 8$ cm to $|z_{vtx}| < 6$ cm. The variation of the range allows testing detector acceptance effects on the measurement.

Another source of systematic uncertainty is related to pileup rejection. The rejection of pileup events is adjusted by modifying the number of track contributors required for the reconstruction of pileup event vertices, changing it from the default value of 3 to 5.

The systematic uncertainty due to the choice of track-selection criteria is estimated by employing alternative track-selection criteria, which single out so-called “global track”, which are described in Ref. [115]. A global track is required to have two hits in the ITS (at least one in the SPD) and at least 70 clusters in the TPC. Due to inefficiencies in certain parts of the SPD, the azimuthal distribution of global tracks is not uniform. This can be corrected by using corresponding mixed events and accounting for the corresponding tracking efficiency.

An additional systematic uncertainty from the event-mixing is estimated by varying the interval of the primary vertex range, where events are mixed. The default size of the primary vertex bins of mixed
events is decreased from 2 cm to 1 cm.

The systematic uncertainty associated with the low-multiplicity definition is estimated by changing the
range of the low-V0M-multiplicity interval. There is no universal definition for the low-multiplicity
interval. The default range for the low-multiplicity interval in the present article is 60–100%, and it is
changed to 70–100% to estimate the related systematic uncertainty. Note that for the measurement of
$Y^{\text{near}}$, the low-multiplicity-interval definition is irrelevant.

The systematic uncertainty resulting from matching a track reconstructed by the TPC and the correspond-
ing signal in the ITS is estimated by evaluating the fraction of mismatches in real data using simulations.
Primary tracks have a higher matching efficiency than secondary tracks produced far from the interaction
point or in interactions with detector material. To address the effect of different fractions of primary and
secondary tracks in data and simulations on the matching efficiency, particle abundances in the simula-
tion are reweighted to reflect real data. This resulted in modified matching efficiency.

The systematic uncertainty arising from the efficiency correction is estimated by performing a closure
test, where two correlation functions are compared. The first correlation function is constructed using
true information from the Monte Carlo samples described in Sec. 2. This provides a baseline for the
expected correlation function. The second correlation function is constructed using reconstructed tracks
corrected for tracking efficiency. By comparing the two correlation functions, it is possible to estimate
the magnitude of the uncertainty introduced by the correction.

Due to the limited $\eta$ acceptance of the TPC, non-flow contributions, mainly originating from fragmen-
tation of jets, affect the flow measurement. As the shape of short-range correlations, mostly attributed
to jets, is getting broader with decreasing $p_T$, the systematic uncertainty from $\eta$ acceptance significantly
depends on $p_T$. To estimate the related uncertainty, the long range $\Delta\phi$ correlations are measured for an
extended $\Delta\eta$ gap, the default size of $\Delta\eta$ gap 1.6 is increased to 1.7.

Finally, it is worth considering the possible impact of the multiplicity dependence of the jet-shape modi-
fications discussed in Sec. 3. This is studied by examining the shape modification of the jet-peak distri-
bution in the near-side region as a function of $\Delta\eta$ and multiplicity. The observed change in the width is
used to estimate the possible effect on the long-range, per-trigger-yield distribution as a function of $\Delta\phi$.
The effect on $v_2$ is found to be less than 1% in pp and p-Pb collisions for the kinematic ranges analyzed.
The effect on $v_3$ is found to be less than 8% in p-Pb collisions. These values are included in the total sys-
tematic uncertainty. However, it is important to note that other analyses with different kinematic ranges
should also perform a similar check to assess the systematic uncertainty associated with this effect. It is
possible that this effect may not always be as small as in our analysis.

# 5 Results

## 5.1 Transverse-momentum and multiplicity dependence of anisotropic flow

Figure 4 illustrates the extracted values of $v_2$ and $v_3$ as a function of $p_{T,\text{trig}}$ as obtained from Eq. (3). The results correspond to the high-multiplicity pp collisions at $\sqrt{s} = 13$ TeV and p-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. Both sets of results demonstrate an increasing trend in the magnitudes of $v_n$ with rising $p_{T,\text{trig}}$. The $v_2$ data points reach a maximum between 2.5 and 3.0 GeV/c, similarly to what has been observed in Pb-Pb collisions [5, 116]. The magnitudes of $v_2$ in p-Pb collisions are higher than those in pp collisions, which might be related to the larger p-Pb system size together with a likely longer lifetime of the hypothetically created medium. However, the magnitudes of $v_3$ are similar in both systems, indicating that $v_3$ is less sensitive to the size of the systems. These results are comparable to those obtained by ATLAS in different multiplicity classes, where the same method was used to extract the flow coefficients [19]. Even though the $\Delta\eta$ and $p_{T,\text{assoc}}$ ranges used by ATLAS are wider, $2.0 < |\Delta\eta| < 5.0$ and $0.5 < p_{T,\text{assoc}} < 5$ GeV/c, respectively, the results are consistent within uncertainties.
Figure 5 presents the magnitudes of $v_2$ and $v_3$, as a function of charged-particle multiplicity at midrapidity for both pp collisions at $\sqrt{s} = 13$ TeV and p–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. As in Fig. 4, the $\Delta\eta$ gap is $1.6 < |\Delta\eta| < 1.8$ and $v_2$ is measured in $1 < p_T < 4$ GeV/c for both collision systems. Additionally, the corresponding results for pp collisions at $\sqrt{s} = 13$ TeV with $1 < p_T < 2$ GeV/c are presented. First, it is observed that the magnitude of $v_n$ increases with increasing multiplicity for both collision systems and $p_T$-ranges. Second, $v_2$ in p–Pb is higher than in pp collisions in the measured multiplicity range. These two observations are compatible with previous results from Refs. [10, 11, 19]. There is no significant difference between the two collision systems when considering the $v_3$ dependence on multiplicity as shown on the right-hand-side panel of Fig. 5. The $v_3$ measurements exhibit a comparable subtle dependence on multiplicity, with higher values observed in collisions with greater particle multiplicities. For the two different $p_T$ intervals presented for the pp collisions, the $v_2$ in $1.0 < p_T < 4.0$ GeV/c shows a hint of larger magnitude than the $v_2$ in $1.0 < p_T < 2.0$ GeV/c. The difference in magnitude is significant only in the highest multiplicity point. This agrees with what is observed in Fig. 4, where the $v_2$ magnitude has its largest value in $2.5 < p_T < 3.0$ GeV/c. It is found that for the considered $p_T$ selections, the observed multiplicity dependencies differ only marginally. It is worth noting that the results presented from pp and p–Pb collisions were obtained from two different beam energies. In Ref. [19], it was found that the magnitudes of $v_2$ and $v_3$ in pp collisions between 13 and 5.02 TeV show no significant variation with center-of-mass energy.

## 5.2 Event-scale dependence of the flow coefficients

Figure 6 presents the extracted magnitude of $v_2$ and $v_3$ as a function of the minimum $p_T$ of the leading particle $p_{T,min}^{\text{LP}}$ and that of the jet ($p_{T,min}^{\text{jet}}$) as introduced in Sec. 1. The results are presented for the 0–0.1% multiplicity class of pp collisions at $\sqrt{s} = 13$ TeV and for the two different $p_T$-ranges. To reduce the impact of the detector edge effects on the jet measurements, the jet axes are required to have a pseudorapidity $|\eta_{jet}| < 0.4$, following a similar selection as in Refs. [117–119]. The $v_2$ and $v_3$ values for both $p_T$ ranges do not show any dependence on event-scale selection within the uncertainties. This finding is consistent with the results of the ridge yields [73] and $v_2$ measurements with a tagged Z boson from the ATLAS collaboration [120]. These results suggest that the presence of a hard-scattering process does not significantly change the long-range correlation involving soft particles. However, the presented measurements are only limited to the low $p_T^{\text{jet}}$. Future measurements with multi-jet events at midrapidity

<figure><img src="image_6.png" /><figcaption>**Figure 4:** The magnitude of $v_2$ (left) and $v_3$ (right) as a function of $p_T$ for the 0–0.1% multiplicity interval in pp collisions at $\sqrt{s} = 13$ TeV and 0–20% in p–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. The boxes around the data points represent the estimated systematic uncertainty and the error bars correspond to statistical errors.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Figure 5:** The magnitudes of $v_2$ (left panel) and $v_3$ (right panel) for two different collision systems, pp and p-Pb as a function of charged-particle multiplicity at midrapidity. For pp collisions, two different $p_T$ intervals are shown, $1.0 < p_T < 2.0$ GeV/c and $1.0 < p_T < 4.0$ GeV/c. The boxes around the data points represent the estimated systematic uncertainties and the error bars correspond to statistical errors.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 6:** The magnitudes of $v_2$ (top) and $v_3$ (bottom) as a function of $p_{T,\min}^{\text{LP}}$ (left) and $p_{T,\min}^{\text{jet}}$ (right) for the high-multiplicity in pp collisions at $\sqrt{s} = 13$ TeV. The measured $p_T$ intervals are $1 < p_T < 2$ GeV/c (in red) and $1 < p_T < 4$ GeV/c (in black). The statistical errors and systematic uncertainties are shown as vertical bars and boxes, respectively.</figcaption></figure>

with higher $Q^2$ reach can shed more light on the expected impact parameter dependence [84–86].
<figure><img src="image_9.png" /><figcaption>**Figure 7:** The measured and calculated evolution of $v_2$ (left) and $v_3$ (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.</figcaption></figure>

## 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, TRENTo+iEBE-VISHNU, consists of the TRENTo 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 $\sqrt{s_{NN}} = 5.02$ TeV. Two different MAP values are used for the calculations. They are based on Ref. [55] and Ref. [52] and in Fig. 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 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 TRENTo+iEBE-VISHNU does not contain any non-flow.

Figure 7 shows that TRENTo+iEBE-VISHNU overestimates both $v_2$ and $v_3$ data increase with multiplicity. However, TRENTo+iEBE-VISHNU 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 $\eta/s = 0.12$ and a temperature dependent $\zeta/s(T)$ [123]. This model describes well the multiplicity dependence
of $v_2$ 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 $N_{ch} > 25$ as well as the trend of the multiplicity dependence. The model shows that $v_2$ decreases with increasing multiplicity, while the experimental result shows the opposite. For $v_3$, the model accurately describes the magnitudes and multiplicity dependence across the measured multiplicity ranges. The magnitudes of $v_3$ 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].

Finally, the results are compared with the GubsHyd model, a semi-analytical model based on the ana-
lytical 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 men-
tioned 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_RENTo or IP-Glasma, the initial state fluctuation is modeled
directly. It assumes that proton ellipticity $\epsilon_2$ and RMS radius $r_{rms}$ fluctuate independently. These fluctua-
tions are described by Gaussian probability distributions, which have widths $\sigma_\epsilon$ and $\sigma_r$, respectively. The
multiplicity dependence of the $v_2\{2\}$ of two-particle correlation functions depends on $\sigma_r$ and $\chi\sigma_\epsilon$, where
the coefficient $\chi$ encapsulates a correction for idealizations used in GubsHyd, including the absence of
dissipation effects. The values of $\sigma_r$ and $\chi\sigma_\epsilon$ were obtained by comparing the model with data. Since no
non-flow effect is considered in the calculation, $v_2\{2\}$ is comparable with the flow measurements in the
present study. The calculations for two sets of parameters are compared to data in Fig. 7. The “param0”
parameterization is based on the prediction proposed in Ref. [64] that $\chi\sigma_\epsilon = 0.097$ and $\sigma_r = 0.4$ fm.
The other parameterizations “param1” and “param2” employ different $\chi\sigma_\epsilon$ and $\sigma_r$ values. The model
captures the multiplicity dependence of $v_2$ well.

In summary, the measured $v_2$ 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 $v_2$, 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 $v_2$, 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 $v_2$ at low multiplicities is still challenging to test with the current experimental uncertainties. For $v_3$, 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 $v_3$ 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 $\sqrt{s} = 13$ TeV and p–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. Flow coefficients are extracted from long-range correlations ($1.6 < |\Delta\eta| < 1.8$) 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 $v_2$ and $v_3$ measurements, which reflect the possible differences in the away-side jet peak shapes in
high- and low-multiplicity 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 $p_T$ dependence of $v_2$ and $v_3$ is consistent with the measurements by ATLAS and shows that both $v_2$ and $v_3$ increase with $p_T$ and reach their maximum at $2.5 < p_T < 3.0$ GeV/c. The measurement of $v_2$ as a function of charged-particle multiplicity in $|\eta| < 0.5$ shows a weak multiplicity dependence both for pp and p–Pb collisions and tends to decrease toward lower multiplicities. The pp data suggests that the $v_2$ signal may disappear when the measurement is pursued further below $N_{ch} = 10$.

The comparisons to viscous hydrodynamic models show that the magnitudes of $v_2$ 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 high-$p_T$ leading particles do not show any changes both in $v_2$ and $v_3$ 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].

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: 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 National-stiftung 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 Infras-structures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC), Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für 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. In addition, individual groups or members have received support from: European Research Council, Strong 2020 - Horizon 2020 (grant nos. 950692, 824093), European Union; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland.

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A The ALICE Collaboration

S. Acharya 128, D. Adamová 87, G. Aglieri Rinella 33, M. Agnello 30, N. Agrawal 52, Z. Ahammed 136,
S. Ahmad 16, S.U. Ahn 72, I. Ahuja 38, A. Akindinov 142, M. Al-Turany 98, D. Aleksandrov 142,
B. Alessandro 57, H.M. Alfanda 6, R. Alfaro Molina 68, B. Ali 16, A. Alici 26,
N. Alizadehvandchali 117, A. Alkin 33, J. Alme 21, G. Alocco 53, T. Alt 65, A.R. Altamura 51,
I. Altsybeev 96, J.R. Alvarado 45, M.N. Anaam 6, C. Andrei 46, N. Andreou 116, A. Andronic 127,
V. Anguelov 95, F. Antinori 55, P. Antonioli 52, N. Apadula 75, L. Aphecetche 104, H. Appelshäuser 65,
C. Arata 74, S. Arcelli 26, M. Aresti 23, R. Arnaldi 57, J.G.M.C.A. Arneiro 111, I.C. Arsene 20,
M. Arslandok 139, A. Augustinus 33, R. Averbeck 98, M.D. Azmi 16, H. Baba 125, A. Badalà 54,
J. Bae 105, Y.W. Baek 41, X. Bai 121, R. Bailhache 65, Y. Bailung 49, A. Balbino 30, A. Baldisseri 131,
B. Balis 2, D. Banerjee 4, Z. Banoo 92, R. Barbera 27, F. Barile 32, L. Barioglio 96, M. Barlou 79,
B. Barman 42, G.G. Barnaföldi 47, L.S. Barnby 86, V. Barret 128, L. Barreto 111, C. Bartels 120,
K. Barth 33, E. Bartsch 65, N. Bastid 128, S. Basu 76, G. Batigne 104, D. Battistini 96, B. Batyunya 143,
D. Bauri 48, J.L. Bazo Alba 102, I.G. Bearden 84, C. Beattie 139, P. Becht 98, D. Behera 49,
I. Belikov 130, A.D.C. Bell Hechavarria 127, F. Bellini 26, R. Bellwied 117, S. Belokurova 142,
Y.A.V. Beltran 45, G. Bencedi 47, S. Beole 25, Y. Berdnikov 142, A. Berdnikova 95, L. Bergmann 95,
M.G. Besoiu 64, L. Betev 33, P.P. Bhaduri 136, A. Bhasin 92, M.A. Bhat 4, B. Bhattacharjee 42,
L. Bianchi 25, N. Bianchi 50, J. Bielčík 36, J. Bielčíková 87, J. Biernat 108, A.P. Bigot 130,
A. Bilandzic 96, G. Biro 47, S. Biswas 4, N. Bize 104, J.T. Blair 109, D. Blau 142, M.B. Blidaru 98,
N. Bluhme 39, C. Blume 65, G. Boca 22,56, F. Bock 88, T. Bodova 21, A. Bogdanov 142, S. Boi 23,
J. Bok 59, L. Boldizsár 47, M. Bombara 38, P.M. Bond 33, G. Bonomi 135,56, H. Borel 131,
A. Borissov 142, A.G. Borquez Carcamo 95, H. Bossi 139, E. Botta 25, Y.E.M. Bouziani 65,
L. Bratrud 65, P. Braun-Munzinger 98, M. Bregant 111, M. Broz 36, G.E. Bruno 97,32,
M.D. Buckland 24, D. Budnikov 142, H. Buesching 65, S. Bufalino 30, P. Buhler 103, N. Burmasov 142,
Z. Buthelezi 69,124, A. Bylinkin 21, S.A. Bysiak 108, M. Cai 6, H. Caines 139, A. Caliva 29, E. Calvo
Villar 102, J.M.M. Camacho 110, P. Camerini 24, F.D.M. Canedo 111, S.L. Cantway 139, M. Carabas 114,
A.A. Carballo 33, F. Carnesecchi 33, R. Caron 129, L.A.D. Carvalho 111, J. Castillo Castellanos 131,
F. Catalano 33,25, C. Ceballos Sanchez 143, I. Chakaberia 75, P. Chakraborty 48, S. Chandra 136,
S. Chapeland 33, M. Chartier 120, S. Chattopadhyay 136, S. Chattopadhyay 100, T. Cheng 98,6,
C. Cheshkov 129, B. Cheynis 129, V. Chibante Barroso 33, D.D. Chinellato 112, E.S. Chizzali 11,96,
J. Cho 59, S. Cho 59, P. Chochula 33, D. Choudhury 42, P. Christakoglou 85, C.H. Christensen 84,
P. Christiansen 76, T. Chuj 126, M. Ciacco 30, C. Cicalo 53, F. Cindolo 52, M.R. Ciupek 98, G. Clai III,52,
F. Colamaria 51, J.S. Colburn 101, D. Colella 97,32, M. Colocci 26, M. Concas 14V,33, G. Conesa
Balbastre 74, Z. Conesa del Valle 132, G. Contin 24, J.G. Contreras 36, M.L. Coquet 131,
P. Cortese 134,57, M.R. Cosentino 113, F. Costa 33, S. Costanza 22,56, C. Cot 132, J. Crkovská 95,
P. Crochet 128, R. Cruz-Torres 75, P. Cui 6, A. Dainese 55, M.C. Danisch 95, A. Danu 64, P. Das 81,
P. Das 4, S. Das 4, A.R. Dash 127, S. Dash 48, A. De Caro 29, G. de Cataldo 51, J. de Cuveland 39, A. De
Falco 23, D. De Gruttola 29, N. De Marco 57, C. De Martin 24, S. De Pasquale 29, R. Deb 135, R. Del
Grande 96, L. Dello Stritto 29, W. Deng 6, P. Dhankher 19, D. Di Bari 32, A. Di Mauro 33, B. Diab 131,
R.A. Diaz 143,7, T. Dietel 115, Y. Ding 6, J. Ditzel 65, R. Divià 33, D.U. Dixit 19, Ø. Djuvsland 21,
U. Dmitrieva 142, A. Dobrin 64, B. Dönigus 65, J.M. Dubinski 137, A. Dubla 98, S. Dudi 91,
P. Dupieux 128, M. Durkac 107, N. Dzalaiova 13, T.M. Eder 127, R.J. Ehlers 75, F. Eisenhut 65, R. Ejima 93,
D. Elia 51, B. Erazmus 104, F. Ercolessi 26, B. Espagnon 132, G. Eulisse 33, D. Evans 101,
S. Evdokimov 142, L. Fabbietti 96, M. Faggin 28, J. Faivre 74, F. Fan 6, W. Fan 75, A. Fantoni 50,
M. Fasel 88, A. Feliciello 57, G. Feofilov 142, A. Fernández Téllez 45, L. Ferrandi 111, M.B. Ferrer 33,
A. Ferrero 131, C. Ferrero 57, A. Ferretti 25, V.J.G. Feuillard 95, V. Filova 36, D. Finogeev 142,
F.M. Fionda 53, E. Flatland 33, F. Flor 117, A.N. Flores 109, S. Foertsch 69, I. Fokin 95, S. Fokin 142,
E. Fragiacomo 58, E. Frajna 47, U. Fuchs 33, N. Funicello 29, C. Furget 74, A. Furs 142,
T. Fusayasu 99, J.J. Gaardhøje 84, M. Gagliardi 25, A.M. Gago 102, T. Gahlaut 48, C.D. Galvan 110,
D.R. Gangadharan 117, P. Ganoti 79, C. Garabatos 98, T. García Chávez 45, E. Garcia-Solis 9,
C. Gargiulo 33, P. Gasik 98, A. Gautam 119, M.B. Gay Ducati 67, M. Germain 104, A. Ghimouz 126,
C. Ghosh 136, M. Giacalone 52, G. Gioachin 30, P. Giubellino 98,57, P. Giubilato 28, A.M.C. Glaenzer 131,
P. Glässel 95, E. Glimos 123, D.J.Q. Goh 77, V. Gonzalez 138, P. Gordeev 142, M. Gorgon 2,
K. Goswami 49, S. Gotovac 34, V. Grabski 68, L.K. Graczykowski 137, E. Grecka 87, A. Grelli 60,
C. Grigoras 33, V. Grigoriev 142, S. Grigoryan 143,1, F. Grosa 33, J.F. Grosse-Oetringhaus 33,
R. Grosso 98, D. Grund 36, N.A. Grunwald 95, G.G. Guardiano 112, R. Guernane 74, M. Guilbaud 104,
K. Gulbrandsen 84, T. Gündem 65, T. Gunji 125, W. Guo 6, A. Gupta 92, R. Gupta 92, R. Gupta 49,
K. Gwizdziel 137, L. Gyulai 47, C. Hadjidakis 132, F.U. Haider 92, S. Haidlova 36, H. Hamagaki 77,
A. Hamdi 75, Y. Han 140, B.G. Hanley 138, R. Hannigan 109, J. Hansen 76, M.R. Haque 137,
J.W. Harris 139, A. Harton 9, H. Hassan 118, D. Hatzifotiadou 52, P. Hauer 43, L.B. Havener 139,
S.T. Heckel 96, E. Hellbär 98, H. Helstrup 35, M. Hemmer 65, T. Herman 36, G. Herrera Corral 8,
F. Herrmann 127, S. Herrmann 129, K.F. Hetland 35, B. Heybeck 65, H. Hillemanns 33, B. Hippolyte 130,
F.W. Hoffmann 71, B. Hofman 60, G.H. Hong 140, M. Horst 96, A. Horzyk 2, Y. Hou 6, P. Hristov 33,
C. Hughes 123, P. Huhn 65, L.M. Huhta 118, T.J. Humanic 89, A. Hutson 117, D. Hutter 39, R. Ilkaev 142,
H. Ilyas 14, M. Inaba 126, G.M. Innocenti 33, M. Ippolitov 142, A. Isakov 85, 87, T. Isidori 119,
M.S. Islam 100, M. Ivanov 13, M. Ivanov 98, V. Ivanov 142, K.E. Iversen 76, M. Jablonski 2, B. Jacak 75,
N. Jacazio 26, P.M. Jacobs 75, S. Jadlovska 107, J. Jadlovsky 107, S. Jaelani 83, C. Jahnke 111,
M.J. Jakubowska 137, M.A. Janik 137, T. Janson 71, S. Ji 17, S. Jia 10, A.A.P. Jimenez 66, F. Jonas 88, 127,
D.M. Jones 120, J.M. Jowett 33, 98, J. Jung 65, M. Jung 65, A. Junique 33, A. Jusko 101, J. Kaewjai 106,
P. Kalinak 61, A.S. Kalteyer 98, A. Kalweit 33, V. Kaplin 142, A. Karasu Uysal 73, D. Karatovic 90,
O. Karavichev 142, T. Karavicheva 142, P. Karczmarczyk 137, E. Karpechev 142, M.J. Karwowska 33, 137,
U. Kebschull 71, R. Keidel 141, D.L.D. Keijdener 60, M. Keil 33, B. Ketzer 43, S.S. Khade 49,
A.M. Khan 121, S. Khan 16, A. Khanzadeev 142, Y. Kharlov 142, A. Khatun 119, A. Khuntia 36,
B. Kileng 35, B. Kim 105, C. Kim 17, D.J. Kim 118, E.J. Kim 70, J. Kim 140, J.S. Kim 41, J. Kim 59,
J. Kim 70, M. Kim 19, S. Kim 18, T. Kim 140, K. Kimura 93, S. Kirsch 65, I. Kisel 39, S. Kiselev 142,
A. Kisiel 137, J.P. Kitowski 2, J.L. Klay 5, J. Klein 33, S. Klein 75, C. Klein-Bösing 127, M. Kleiner 65,
T. Klemenz 96, A. Kluge 33, A.G. Knospe 117, C. Kobdaj 106, T. Kollegger 98, A. Kondratyev 143,
N. Kondratyeva 142, E. Kondratyuk 142, J. Konig 65, S.A. Konigstorfer 96, P.J. Konopka 33,
G. Kornakov 137, M. Korwieser 96, S.D. Koryciak 2, A. Kotliarov 87, V. Kovalenko 142,
M. Kowalski 108, V. Kozhuharov 37, I. Králik 61, A. Kravčáková 38, L. Krcal 33, 39, M. Krivda 101, 61,
F. Krizek 87, K. Krizkova Gajdosova 33, M. Kroesen 95, M. Krüger 65, D.M. Krupova 36,
E. Kryshen 142, V. Kučera 59, C. Kuhn 130, P.G. Kuijer 85, T. Kumaoka 126, D. Kumar 136, L. Kumar 91,
N. Kumar 91, S. Kumar 32, S. Kundu 33, P. Kurashvili 80, A. Kurepin 142, A.B. Kurepin 142,
A. Kuryakin 142, S. Kushpil 87, V. Kuskov 142, M.J. Kweon 59, Y. Kwon 140, S.L. La Pointe 39, P. La
Rocca 27, A. Lakrathok 106, M. Lamanna 33, A.R. Landou 74, 116, R. Langoy 122, P. Larionov 33,
E. Laudi 33, L. Lautner 33, 96, R. Lavicka 103, R. Lea 135, 56, H. Lee 105, I. Legrand 46, G. Legras 127,
J. Lehrbach 39, T.M. Lelek 2, R.C. Lemmon 86, I. León Monzón 110, M.M. Lesch 96, E.D. Lesser 19,
P. Lévai 47, X. Li 10, J. Lien 122, R. Lietava 101, I. Likmeta 117, B. Lim 25, S.H. Lim 17,
V. Lindenstruth 39, A. Lindner 46, C. Lippmann 98, D.H. Liu 6, J. Liu 120, G.S.S. Liveraro 112,
I.M. Lofnes 21, C. Loizides 88, S. Lokos 108, J. Lömker 60, P. Loncar 34, X. Lopez 128, E. López
Torres 7, P. Lu 98, 121, F.V. Lugo 68, J.R. Luhder 127, M. Lunardon 28, G. Luparello 58, Y.G. Ma 40,
M. Mager 33, A. Maire 130, E.M. Majerz 2, M.V. Makariev 37, M. Malaev 142, G. Malfattore 26,
N.M. Malik 92, Q.W. Malik 20, S.K. Malik 92, L. Malinina 1, VII, 143, D. Mallick 132, 81, N. Mallick 49,
G. Mandaglio 31, 54, S.K. Mandal 80, V. Manko 142, F. Manso 128, V. Manzari 51, Y. Mao 6,
R.W. Marcjan 2, G.V. Margagliotti 24, A. Margotti 52, A. Marín 98, C. Markert 109, P. Martinengo 33,
M.I. Martínez 45, G. Martínez García 104, M.P.P. Martins 111, S. Masciocchi 98, M. Masera 25,
A. Masoni 53, L. Massacrier 132, O. Massen 60, A. Mastroserio 133, 51, O. Matonoha 76, S. Mattiazzo 28,
A. Matyja 108, C. Mayer 108, A.L. Mazuecos 33, F. Mazzaschi 25, M. Mazzilli 33, J.E. Mdhluli 124,
Y. Melikyan 44, A. Menchaca-Rocha 68, J.E.M. Mendez 66, E. Meninno 103, A.S. Menon 117,
M. Meres 13, S. Mhlanga 115, 69, Y. MIAKE 126, L. Micheletti 33, D.L. Mihaylov 96, K. Mikhaylov 143, 142,
A.N. Mishra 47, D. Miśkowiec 98, A. Modak 4, B. Mohanty 81, M. Mohisin Khan V, 16,
M.A. Molander 44, S. Monira 137, C. Mordasini 118, D.A. Moreira De Godoy 127, I. Morozov 142,
A. Morsch 33, T. Mrnjavac 33, V. Muccifora 50, S. Muhuri 136, J.D. Mulligan 75, A. Mulliri 23,
M.G. Munhoz 111, R.H. Munzer 65, H. Murakami 125, S. Murray 115, L. Musa 33, J. Musinsky 61,
J.W. Myrcha 137, B. Naik 124, A.I. Nambrath 19, B.K. Nandi 48, R. Nania 52, E. Nappi 51,
A.F. Nassirpour 18, A. Nath 95, C. Nattrass 123, M.N. Naydenov 37, A. Neagu 20, A. Negru 114,
E. Nekrasova 142, L. Nellen 66, R. Nepeivoda 76, S. Nese 20, G. Neskovic 39, N. Nicassio 51,
B.S. Nielsen 84, E.G. Nielsen 84, S. Nikolaev 142, S. Nikulin 142, V. Nikulin 142, F. Noferini 52,
S. Noh 12, P. Nomokonov 143, J. Norman 120, N. Novitzky 88, P. Nowakowski 137, A. Nyanin 142,
J. Nystrand 21, M. Ogino 77, S. Oh 18, A. Ohlson 76, V.A. Okorokov 142, J. Oleniacz 137, A.C. Oliveira
Da Silva 123, A. Onnerstad 118, C. Oppedisano 57, A. Ortiz Velasquez 66, J. Otwinowski 108, M. Oya 93,
K. Oyama 77, Y. Pachmayer 95, S. Padhan 48, D. Pagano 135, 56, G. Paić 66, S. Paisano-Guzmán 45,
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Schukraft<sup>33</sup>, K. Schweda<sup>98</sup>, G. Scioli<sup>26</sup>, E. Scomparin<sup>57</sup>, J.E. Seger<sup>15</sup>, Y. Sekiguchi<sup>125</sup>, D. Sekihata<sup>125</sup>, M. Selina<sup>85</sup>, I. Selyuzhenkov<sup>98</sup>, S. Senyukov<sup>130</sup>, J.J. Seo<sup>95,59</sup>, D. Serebryakov<sup>142</sup>, L. Šerkšnytė<sup>96</sup>, A. Sevcenco<sup>64</sup>, T.J. Shaba<sup>69</sup>, A. Shabetai<sup>104</sup>, R. Shahoyan<sup>33</sup>, A. Shangaraev<sup>142</sup>, A. Sharma<sup>91</sup>, B. Sharma<sup>92</sup>, D. Sharma<sup>48</sup>, H. Sharma<sup>55</sup>, M. Sharma<sup>92</sup>, S. Sharma<sup>77</sup>, S. Sharma<sup>92</sup>, U. Sharma<sup>92</sup>, A. Shatat<sup>132</sup>, O. Sheibani<sup>117</sup>, K. Shigaki<sup>93</sup>, M. Shimomura<sup>78</sup>, J. Shin<sup>12</sup>, S. Shirkin<sup>142</sup>, Q. Shou<sup>40</sup>, Y. Sibiriak<sup>142</sup>, S. Siddhanta<sup>53</sup>, T. Siemiarczuk<sup>80</sup>, T.F. Silva<sup>111</sup>, D. Silvermyr<sup>76</sup>, T. Simantathammakul<sup>106</sup>, R. Simeonov<sup>37</sup>, B. Singh<sup>92</sup>, B. Singh<sup>96</sup>, K. Singh<sup>49</sup>, R. Singh<sup>81</sup>, R. Singh<sup>92</sup>, R. Singh<sup>49</sup>, S. Singh<sup>16</sup>, V.K. Singh<sup>136</sup>, V. Singhal<sup>136</sup>, T. Sinha<sup>100</sup>, B. Sitar<sup>13</sup>, M. Sitta<sup>134,57</sup>, T.B. Skaali<sup>20</sup>, G. Skorodumovs<sup>95</sup>, M. Slupecki<sup>44</sup>, N. Smirnov<sup>139</sup>, R.J.M. Snellings<sup>60</sup>, E.H. Solheim<sup>20</sup>, J. Song<sup>17</sup>, C. Sonnabend<sup>33,98</sup>, F. Soramel<sup>28</sup>, A.B. Soto-hernandez<sup>89</sup>, R. Spijkers<sup>85</sup>, I. Sputowska<sup>108</sup>, J. Staa<sup>76</sup>, J. Stachel<sup>95</sup>, I. Stan<sup>64</sup>, P.J. Steffanic<sup>123</sup>, S.F. Stiefelmaier<sup>95</sup>, D. Stocco<sup>104</sup>, I. Storehaug<sup>20</sup>, P. Stratmann<sup>127</sup>, S. Strazzi<sup>26</sup>, A. Sturniolo<sup>31,54</sup>, C.P. Stylianidis<sup>85</sup>, A.A.P. Suaide<sup>111</sup>, C. Suire<sup>132</sup>, M. Sukhanov<sup>142</sup>, M. Suljic<sup>33</sup>, R. Sultanov<sup>142</sup>, V. Sumberia<sup>92</sup>, S. Sumowidagdo<sup>83</sup>, S. Swain<sup>62</sup>, I. Szarka<sup>13</sup>, M. Szymkowski<sup>137</sup>, S.F. Taghavi<sup>96</sup>, G. Taillepied<sup>98</sup>, J. Takahashi<sup>112</sup>, G.J. Tambave<sup>81</sup>, S. Tang<sup>6</sup>, Z. Tang<sup>121</sup>, J.D. Tapia Takaki<sup>119</sup>, N. Tapus<sup>114</sup>, L.A. Tarasovicova<sup>127</sup>, M.G. Tarzila<sup>46</sup>, G.F. Tassielli<sup>32</sup>, A. Tauro<sup>33</sup>, A. Tavira García<sup>132</sup>, G. Tejeda Muñoz<sup>45</sup>, A. Telesca<sup>33</sup>, L. Terlizzi<sup>25</sup>, C. Terrevoli<sup>117</sup>, S. Thakur<sup>4</sup>, D. Thomas<sup>109</sup>, A. Tikhonov<sup>142</sup>, N. Tiltmann<sup>127</sup>, A.R. Timmins<sup>117</sup>, M. Tkacik<sup>107</sup>, T. Tkacik<sup>107</sup>, A. Toia<sup>65</sup>, R. Tokumoto<sup>93</sup>, K. Tomohiro<sup>93</sup>, N. Topilskaya<sup>142</sup>, M. Toppi<sup>50</sup>, T. Tork<sup>132</sup>, V.V. Torres<sup>104</sup>, A.G. Torres Ramos<sup>32</sup>, A. Trifíró<sup>31,54</sup>, A.S. Triolo<sup>33,31,54</sup>, S. Tripathy<sup>52</sup>, T. Tripathy<sup>48</sup>, S. Trogolo<sup>33</sup>, V. Trubnikov<sup>3</sup>, W.H. Trzaska<sup>118</sup>, T.P. Trzcinski<sup>137</sup>, A. Tumkin<sup>142</sup>, R. Turrisi<sup>55</sup>, T.S. Tveter<sup>20</sup>, K. Ullaland<sup>21</sup>, B. Ulukutlu<sup>96</sup>, A. Uras<sup>129</sup>, G.L. Usai<sup>23</sup>, M. Vala<sup>38</sup>, N. Valle<sup>22</sup>, L.V.R. van Doremalen<sup>60</sup>, M. van Leeuwen<sup>85</sup>, C.A. van Veen<sup>95</sup>, R.J.G. van Weelden<sup>85</sup>, P. Vande Vyvre<sup>33</sup>, D. Varga<sup>47</sup>, Z. Varga<sup>47</sup>, P. Vargas Torres<sup>66</sup>, M. Vasileiou<sup>79</sup>, A. Vasiliev<sup>142</sup>, O. Vázquez Doce<sup>50</sup>, O. Vazquez Rueda<sup>117</sup>, V. Vechernin<sup>142</sup>, E. Vercellin<sup>25</sup>, S. Vergara Limón<sup>45</sup>, R. Verma<sup>48</sup>, L. Vermunt<sup>98</sup>, R. Vértesi<sup>47</sup>, M. Verweij<sup>60</sup>, L. Vickovic<sup>34</sup>, Z. Vilakazi<sup>124</sup>, O. Villalobos Baillie<sup>101</sup>, A. Villani<sup>24</sup>, A. Vinogradov<sup>142</sup>, T. Virgili<sup>29</sup>, M.M.O. Virta<sup>118</sup>, V. Vislavicius<sup>76</sup>, A. Vodopyanov<sup>143</sup>, B. Volkel<sup>33</sup>, M.A. Völkl<sup>95</sup>, K. Voloshin<sup>142</sup>, S.A. Voloshin<sup>138</sup>, G. Volpe<sup>32</sup>, B. von Haller<sup>33</sup>, I. Vorobyev<sup>96</sup>, N. Vozniuk<sup>142</sup>, J. Vrláková<sup>38</sup>, J. Wan<sup>40</sup>, C. Wang<sup>40</sup>, D. Wang<sup>40</sup>, Y. Wang<sup>40</sup>, Y. Wang<sup>6</sup>, A. Wegrzynek<sup>33</sup>, F.T. Weiglhofer<sup>39</sup>, S.C. Wenzel<sup>33</sup>, J.P. Wessels<sup>127</sup>, J. Wiechula<sup>65</sup>, J. Wikne<sup>20</sup>, G. Wilk<sup>80</sup>, J. Wilkinson<sup>98</sup>, G.A. Willems<sup>127</sup>, B. Windelband<sup>95</sup>, M. Winn<sup>131</sup>, J.R. Wright<sup>109</sup>, W. Wu<sup>40</sup>, Y. Wu<sup>121</sup>, R. Xu<sup>6</sup>, A. Yadav<sup>43</sup>, A.K. Yadav<sup>136</sup>,
S. Yalcin ◦ 73, Y. Yamaguchi ◦ 93, S. Yang 21, S. Yano ◦ 93, Z. Yin ◦ 6, I.-K. Yoo ◦ 17, J.H. Yoon ◦ 59, H. Yu 12,
S. Yuan 21, A. Yuncu ◦ 95, V. Zaccolo ◦ 24, C. Zampolli ◦ 33, F. Zanone ◦ 95, N. Zardoshti ◦ 33,

A. Zarochentsev ◦ 142, P. Závada ◦ 63, N. Zaviyalov 142, M. Zhalov ◦ 142, B. Zhang ◦ 6, C. Zhang ◦ 131,

L. Zhang ◦ 40, S. Zhang ◦ 40, X. Zhang ◦ 6, Y. Zhang 121, Z. Zhang ◦ 6, M. Zhao ◦ 10, V. Zherebchevskii ◦ 142,

Y. Zhi 10, D. Zhou ◦ 6, Y. Zhou ◦ 84, J. Zhu ◦ 55.6, Y. Zhu 6, S.C. Zugravel ◦ 57, N. Zurlo ◦ 135.56

## Affiliation Notes

1. Deceased

II. Also at: Max-Planck-Institut für 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

V. Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India

VI. Also at: Institute of Theoretical Physics, University of Wroclaw, Poland

VII. Also at: An institution covered by a cooperation agreement with CERN

## Collaboration Institutes

1. A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia

2. AGH University of Kraków, Cracow, Poland

3. Bogolyubov 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

5. California Polytechnic State University, San Luis Obispo, California, United States

6. Central China Normal University, Wuhan, China

7. Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba

8. Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico

9. Chicago 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

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 Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany

44 Helsinki Institute of Physics (HIP), Helsinki, Finland

45 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

46 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

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

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, Département de Physique Nucléaire (DPhN),
Saclay, France

132 Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France

133 Università degli Studi di Foggia, Foggia, Italy

134 Università del Piemonte Orientale, Vercelli, Italy

135 Università di Brescia, Brescia, Italy

136 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India

137 Warsaw University of Technology, Warsaw, Poland

138 Wayne State University, Detroit, Michigan, United States

139 Yale University, New Haven, Connecticut, United States

140 Yonsei University, Seoul, Republic of Korea
<footnote n="141">141 Zentrum für Technologie und Transfer (ZTT), Worms, Germany</footnote>

<footnote n="142">142 Affiliated with an institute covered by a cooperation agreement with CERN</footnote>

<footnote n="143">143 Affiliated with an international laboratory covered by a cooperation agreement with CERN.</footnote>