# Skewness and kurtosis of mean transverse momentum fluctuations at the LHC energies

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. Skewness and kurtosis of mean transverse momentum fluctuations at the LHC energies. Phys.Lett.B, 2024, 850, pp.138541. 10.1016/j.physletb.2024.138541. hal-04199220

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https://hal.science/hal-04199220v1

Submitted on 16 Jan 2025

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# Skewness and kurtosis of mean transverse momentum fluctuations at the LHC energies

ALICE Collaboration*

## Abstract

The first measurements of skewness and kurtosis of mean transverse momentum ($\langle p_T \rangle$) fluctuations are reported in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV, Xe-Xe collisions at $\sqrt{s_{NN}}$ = 5.44 TeV and pp collisions at $\sqrt{s}$ = 5.02 TeV using the ALICE detector. The measurements are carried out as a function of system size $\langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5}$, using charged particles with transverse momentum ($p_T$) and pseudorapidity ($\eta$), in the range $0.2 < p_T < 3.0$ GeV/c and $|\eta| < 0.8$, respectively. In Pb-Pb and Xe-Xe collisions, positive skewness is observed in the fluctuations of $\langle p_T \rangle$ for all centralities, which is significantly larger than what would be expected in the scenario of independent particle emission. This positive skewness is considered a crucial consequence of the hydrodynamic evolution of the hot and dense nuclear matter created in heavy-ion collisions. Furthermore, similar observations of positive skewness for minimum bias pp collisions are also reported here. Kurtosis of $\langle p_T \rangle$ fluctuations is found to be in good agreement with the kurtosis of Gaussian distribution, for most central Pb-Pb collisions. Hydrodynamic model calculations with MUSIC using Monte Carlo Glauber initial conditions are able to explain the measurements of both skewness and kurtosis qualitatively from semicentral to central collisions in Pb-Pb system. Color reconnection mechanism in PYTHIA8 model seems to play a pivotal role in capturing the qualitative behavior of the same measurements in pp collisions.

<footnote>*See Appendix A for the list of collaboration members</footnote>
# 1 Introduction

The properties of the hot and dense nuclear matter created in heavy-ion collisions at relativistic energies can be studied using event-by-event fluctuations of different quantities like multiplicity, net-charge, mean transverse momentum ($\langle p_T \rangle$), etc. [1-4]. The analysis of event-by-event fluctuations of these variables offers valuable means to probe the dynamical fluctuations that originate from the production of a quark-gluon plasma (QGP) [5] phase during heavy-ion collisions. Fluctuations in the thermodynamic quantity of temperature, which are associated with the phase transition in the quantum chromodynamics (QCD) phase diagram, can manifest themselves in the fluctuations of the $\langle p_T \rangle$ of the final-state particles [6]. A non-monotonic behavior of $\langle p_T \rangle$ fluctuations as a function of centrality or incident energy was suggested as one of the possible signals of the QGP [3]. However, $\langle p_T \rangle$ fluctuations are also affected by non-thermodynamic variations in the initial geometry of the collision that include fluctuations in the initial size, shape and orientation of the colliding nuclei, and the fluctuating number of nucleons participating in the collision. The $\langle p_T \rangle$ fluctuations measured at RHIC did not show any beam energy dependence, and the non-monotonic behavior with centrality was also not observed [7]. The previous measurements of $\langle p_T \rangle$ fluctuations in Pb-Pb collisions at centre-of-mass energy per nucleon pair, $\sqrt{s_{NN}} = 2.76$ TeV in ALICE [8] suggested a connection of the observed fluctuations of the $\langle p_T \rangle$ to the fluctuations in the initial state of the collision. Qualitatively, the data obtained from model calculations using the string melting approach in A Multi-Phase Transport (AMPT) model [9], where partons rescatter and recombine through a hadronic coalescence scheme, exhibit agreement with the observed results [8]. The string melting version was introduced in the model [10] to address and account for the effects of flow originating from the entire partonic system in the overlap volume of heavy-ion collisions, as opposed to considering only the contributions from minijet partons in the default version. By incorporating the string melting approach, the model was able to simulate the collective behavior of the partonic system during the early stages of the collision, leading to a more accurate description of the experimental observations of elliptic flow. The $\langle p_T \rangle$ fluctuations were also calculated in the color glass condensate (CGC) [11, 12] formulation, where they have been related to initial spatial fluctuations of glasma flux tube via their coupling to a collective flow field. The comparison of these calculations with data showed a good agreement in the semicentral and central collisions [13].

The space-time evolution of the QGP phase produced in the relativistic heavy-ion collisions is well described by the relativistic viscous hydrodynamics [14-16]. In Ref. [17], it has been proposed that the skewness of $\langle p_T \rangle$ fluctuations can serve as an essential probe of the hydrodynamic behavior of the system created in heavy-ion collisions. The $\langle p_T \rangle$ of the particles emitted at freeze-out was found to be correlated to the initial energy of the system at the beginning of the hydrodynamic evolution, instead of the energy of the system at freeze-out [18]. The fluctuations of $\langle p_T \rangle$ are therefore found to be related to the fluctuations of initial energy density in an *effective* hydrodynamic description [19]. It was shown that the skewness of $\langle p_T \rangle$ fluctuations are driven by the skewness of the initial energy density fluctuations, which implies that the $\langle p_T \rangle$ fluctuations arise from the same collective dynamics in the QGP phase that give rise to anisotropic flow. Furthermore, employing initial conditions from the TRENTo model [20] and evolving them with the V-USPHYDRO viscous hydrodynamic [21] simulations predicted positive skewness of $\langle p_T \rangle$ fluctuations surpassing expectations in independent particle emission scenarios. Additional information regarding these simulations can be found in Ref. [17].

The fluctuations in $\langle p_T \rangle$ of charged particles can be influenced by various physical effects, such as collective behavior of the system formed in the collisions, fluctuations in the number of participating nucleons, or the presence of jets and resonance decays. Examining the higher-order terms of $\langle p_T \rangle$ fluctuations will enable us to delve deeper into the intricate mechanisms underlying the observed fluctuations and acquire valuable insights. In this article, the first experimental study of skewness and kurtosis of $\langle p_T \rangle$ fluctuations that represent the third- and fourth-order fluctuations of $\langle p_T \rangle$ are reported at the Large Hadron Collider (LHC) energies. The observables used in this analysis are introduced in Sec. 2. Here, the multiparticle
$p_T$ correlators used to study the $\langle p_T \rangle$ fluctuations are defined. A brief description of the subsystems of ALICE detector relevant to this analysis is given in Sec. 3. The analysis technique and the method of estimating statistical and systematic uncertainties for the measurements are explained in Sec. 4. The skewness and the kurtosis of $\langle p_T \rangle$ fluctuations as a function of system size and the interpretation of results using theoretical models are presented in Sec. 5. The major findings of the analysis are summarized in Sec. 6.

## 2 Observables

In this analysis, the fluctuations in event-by-event $\langle p_T \rangle$ of charged particles are investigated using multiparticle $p_T$ correlators. The event-by-event $\langle p_T \rangle$ is defined as

$$ \langle p_T \rangle = \frac{\sum_{i=1}^{N_{\text{ch}}} p_{T,i}}{N_{\text{ch}}}, \qquad (1) $$

where $p_{T,i}$ is the transverse momentum of the $i$th particle and $N_{\text{ch}}$ is the total number of charged particles in the event. Alternatively, one can employ the standard moment method for event-by-event analysis of $\langle p_T \rangle$ fluctuations. The moment method calculates various order moments of the $\langle p_T \rangle$ distribution, providing a comprehensive evaluation of the total fluctuation accounting for both the statistical and dynamical (non-statistical) parts. The advantage of employing multiparticle $p_T$ correlators [22, 23] is that they yield zero values for events with randomly sampled particles, thereby effectively isolating the non-statistical fluctuations of interest. The expressions for the two-particle $p_T$ correlator ($\langle \Delta p_{T,i} \Delta p_{T,j} \rangle$) and three-particle $p_T$ correlator ($\langle \Delta p_{T,i} \Delta p_{T,j} \Delta p_{T,k} \rangle$) [17] are denoted by Eqs. 3 and 4, respectively, where $Q_n$ is defined as

$$ Q_n = \sum_{i=1}^{N_{\text{ch}}} p_{T,i}^n. \qquad (2) $$

Constraints on the indices in summations in the definition of correlators ensure that self-correlations are eliminated. The algebraic expressions of the correlators in terms of $Q_n$'s where $n = 1, 2, ...$ were derived to account for the practical limitations of calculating multiparticle $p_T$ correlators with nested loops, especially when dealing with events characterized by large multiplicities. Since, the values of $Q_n$ can be obtained with Eq. 2 employing a single loop, it becomes feasible to directly utilize the later expressions with $Q_n$'s in Eqs. 3 and 4 for the calculation of two- and three-particle $p_T$ correlators, respectively. On similar lines, the four-particle $p_T$ correlator ($\langle \Delta p_{T,i} \Delta p_{T,j} \Delta p_{T,k} \Delta p_{T,l} \rangle$) is derived as shown in Eq. 5. These two-, three-, and four-particle correlators are related to the variance, skewness, and kurtosis of the $\langle p_T \rangle$ distribution, respectively.

$$ \langle \Delta p_{T,i} \Delta p_{T,j} \rangle = \left\langle \frac{\sum_{i,j}^{N_{\text{ch}}} (p_{T,i} - \langle\langle p_T \rangle\rangle)(p_{T,j} - \langle\langle p_T \rangle\rangle)}{N_{\text{ch}}(N_{\text{ch}} - 1)} \right\rangle_{\text{ev}} = \left\langle \frac{Q_1^2 - Q_2}{N_{\text{ch}}(N_{\text{ch}} - 1)} \right\rangle_{\text{ev}} - \left\langle \frac{Q_1}{N_{\text{ch}}} \right\rangle_{\text{ev}}^2, \quad (3) $$

$$ \begin{aligned} \langle \Delta p_{T,i} \Delta p_{T,j} \Delta p_{T,k} \rangle &= \left\langle \frac{\sum_{i \neq j \neq k}^{N_{\text{ch}}} (p_{T,i} - \langle\langle p_T \rangle\rangle)(p_{T,j} - \langle\langle p_T \rangle\rangle)(p_{T,k} - \langle\langle p_T \rangle\rangle)}{N_{\text{ch}}(N_{\text{ch}} - 1)(N_{\text{ch}} - 2)} \right\rangle_{\text{ev}} \\ &= \left\langle \frac{Q_1^3 - 3Q_2Q_1 + 2Q_3}{N_{\text{ch}}(N_{\text{ch}} - 1)(N_{\text{ch}} - 2)} \right\rangle_{\text{ev}} - 3 \left\langle \frac{Q_1^2 - Q_2}{N_{\text{ch}}(N_{\text{ch}} - 1)} \right\rangle_{\text{ev}} \left\langle \frac{Q_1}{N_{\text{ch}}} \right\rangle_{\text{ev}} + 2 \left\langle \frac{Q_1}{N_{\text{ch}}} \right\rangle_{\text{ev}}^3, \quad (4) \end{aligned} $$
$$ \langle \Delta p_{T,i} \Delta p_{T,j} \Delta p_{T,k} \Delta p_{T,l} \rangle = \left\langle \frac{\sum_{\substack{i,j,k,l, \\ i \neq j \neq k \neq l}}^{N_{\text{ch}}} (p_{T,i} - \langle\langle p_T \rangle\rangle)(p_{T,j} - \langle\langle p_T \rangle\rangle)(p_{T,k} - \langle\langle p_T \rangle\rangle)(p_{T,l} - \langle\langle p_T \rangle\rangle)}{N_{\text{ch}}(N_{\text{ch}}-1)(N_{\text{ch}}-2)(N_{\text{ch}}-3)} \right\rangle_{\text{ev}} \\ = \left\langle \frac{Q_1^4 - 6Q_4 + 8Q_1Q_3 - 6Q_1^2Q_2 + 3Q_2^2}{N_{\text{ch}}(N_{\text{ch}}-1)(N_{\text{ch}}-2)(N_{\text{ch}}-3)} \right\rangle_{\text{ev}} \\ - 4 \left\langle \frac{Q_1^3 - 3Q_2Q_1 + 2Q_3}{N_{\text{ch}}(N_{\text{ch}}-1)(N_{\text{ch}}-2)} \right\rangle_{\text{ev}} \left\langle \frac{Q_1}{N_{\text{ch}}} \right\rangle_{\text{ev}} \\ + 6 \left\langle \frac{Q_1^2 - Q_2}{N_{\text{ch}}(N_{\text{ch}}-1)} \right\rangle_{\text{ev}} \left\langle \frac{Q_1}{N_{\text{ch}}} \right\rangle_{\text{ev}}^2 - 3 \left\langle \frac{Q_1}{N_{\text{ch}}} \right\rangle_{\text{ev}}^4. \qquad (5) $$

In the above equations, angular brackets $\langle \dots \rangle_{\text{ev}}$ denote an average over all events and $\langle\langle p_T \rangle\rangle = \langle Q_1 / N_{\text{ch}} \rangle_{\text{ev}}$ is the event-by-event $\langle p_T \rangle$ averaged over all events. The standardized skewness ($\gamma_{\langle p_T \rangle}$) and the intensive skewness ($\Gamma_{\langle p_T \rangle}$) are two measures of the skewness of the $\langle p_T \rangle$ distribution, constructed using the two-particle and three-particle $p_T$ correlators [17], given by

$$ \gamma_{\langle p_T \rangle} = \frac{\langle \Delta p_{T,i} \Delta p_{T,j} \Delta p_{T,k} \rangle}{\langle \Delta p_{T,i} \Delta p_{T,j} \rangle^{3/2}}, \qquad (6) $$

and

$$ \Gamma_{\langle p_T \rangle} = \frac{\langle \Delta p_{T,i} \Delta p_{T,j} \Delta p_{T,k} \rangle \langle \langle p_T \rangle \rangle}{\langle \Delta p_{T,i} \Delta p_{T,j} \rangle^2}. \qquad (7) $$

The kurtosis $\kappa_{\langle p_T \rangle}$ of $\langle p_T \rangle$ distribution is defined as

$$ \kappa_{\langle p_T \rangle} = \frac{\langle \Delta p_{T,i} \Delta p_{T,j} \Delta p_{T,k} \Delta p_{T,l} \rangle}{\langle \Delta p_{T,i} \Delta p_{T,j} \rangle^2}. \qquad (8) $$

The article focuses on analyzing higher order fluctuations of $\langle p_T \rangle$, particularly the third and fourth order. Three key observables, namely the standardized skewness, intensive skewness, and kurtosis of the $\langle p_T \rangle$ distribution (defined in Eqs. 6, 7, and 8, respectively), are investigated as a function of the system size in Pb–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV, Xe–Xe collisions at $\sqrt{s_{NN}} = 5.44$ TeV, and pp collisions at $\sqrt{s} = 5.02$ TeV.

### 3 Experimental setup

The measurements reported in the article are obtained using the data recorded by the ALICE detector at the LHC. A detailed description of the ALICE detector and its performance can be found in Refs. [24, 25]. The primary sub-detectors relevant to this analysis are the Time Projection Chamber (TPC) [26], the Inner Tracking System (ITS) [25], and the V0 detector [27]. The TPC and ITS are used for tracking and reconstructing the primary vertex, while the V0 detector is used for triggering and the default centrality estimation. The V0 detector consists of two scintillator arrays, V0A and V0C, located on both sides of the interaction point, covering the pseudorapidity ($\eta$) intervals $2.8 < \eta < 5.1$ and $-3.7 < \eta < -1.7$, respectively [27]. The data analyzed here are obtained from Pb–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV, Xe–Xe collisions at $\sqrt{s_{NN}} = 5.44$ TeV, and pp collisions at $\sqrt{s} = 5.02$ TeV. These datasets were recorded in 2015 (pp and Pb–Pb) and 2017 (Xe–Xe) during LHC Run 2. A minimum bias (MB) trigger condition is applied to select collision events that requires at least one hit in both the V0A and the V0C detectors. Events that pass the MB trigger criteria and have a reconstructed primary vertex position within 10 cm along the beam axis to the nominal interaction point are selected in the analysis. Using information from multiple detectors as described in Ref. [25], events with more than one reconstructed primary interaction
<figure><img src="image_3.png" /><figcaption>**Figure 1:** Efficiency uncorrected mean transverse momentum distributions for different centrality classes in Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV.</figcaption></figure>

vertex (pile-up events) are rejected. In total, 84 million Pb–Pb collisions, 1.2 million Xe–Xe collisions, and 95 million pp collisions pass the above mentioned criteria and are used for the analysis.

The charged-particle tracks reconstructed using the ITS and the TPC in the ALICE central barrel are selected in the kinematic range $0.2 < p_T < 3.0 \text{ GeV/c}$ and $|\eta| < 0.8$, where $p_T$ is the track momentum in the plane transverse to the beam axis. The accepted tracks exhibit approximately uniform azimuthal acceptance in this region. The tracks that have at least 70 out of a maximum possible 159 reconstructed space points in the TPC, and at least one hit in the two innermost layers of the ITS (ITS has in total six layers) are selected. This selection assures a resolution better than 300 $\mu$m [25] on the distance-of-closest-approach (DCA) to the primary vertex in the plane perpendicular (DCA$_{xy}$) and parallel (DCA$_z$) to the beam axis for the selected tracks. In order to suppress the contamination from secondary particles, the DCA of the tracks to the primary vertex must be within 1 cm in the longitudinal direction and 0.1 cm in the transverse plane. Moreover, the $\chi^2$ per degree of freedom of the track fit to the space points in the TPC and the ITS are required to be less than 4 (2.5 for Pb–Pb) and 36, respectively.

# 4 Data analysis

The mean transverse momentum $\langle p_T \rangle$ distributions obtained for three different centrality classes in Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV are shown in Fig. 1. The distributions are not corrected for detector inefficiencies. The centrality classes are formed by splitting the events based on the measured amplitude distribution in the V0A and V0C detectors as described in Refs. [28, 29]. The mean of the $\langle p_T \rangle$ distributions are found to increase whereas the width of the distribution decreases from peripheral to central collisions. The larger width of the distribution for peripheral (lower multiplicity) collisions indicates larger fluctuations compared to the central (higher multiplicity) collisions. Similar behavior is observed in Xe–Xe collisions at $\sqrt{s_{NN}}$ = 5.44 TeV and pp collisions at $\sqrt{s}$ = 5.02 TeV.

Before starting the analysis with the $\langle p_T \rangle$ correlators presented in Sec. 2, it is important to demonstrate that these fluctuations are not a trivial consequence of fluctuating $N_{ch}$ in a given centrality class. The definition of $\langle p_T \rangle$ in Eq. 1 clearly shows that the varying multiplicity in different events of the same centrality class can affect the $\langle p_T \rangle$ distributions and consequently its fluctuations. To examine whether
<figure><img src="image_4.png" /><figcaption>**Figure 2:** Comparison of event-by-event mean transverse momentum $\langle p_T \rangle$ distribution from actual analysis and modified analysis in which $N_{ch}$ in each event is fixed to $N_{ch}^{\min}$ ($N_{ch}^{\min}$ is the minimum number of charged particles in a given centrality class) and $N_{ch}^{\min}$ number of particles are selected in each event randomly for the 0–5% (left), 30–40% (middle), and 50–60% (right) centrality classes.</figcaption></figure>

these fluctuations persist after removing the stochastic effects of the multiplicity, a check is performed. For each centrality class, the minimum number of tracks per event in the kinematic acceptance of the analysis, $N_{ch}^{\min}$ is determined. In each event of the centrality class, the $N_{ch}^{\min}$ number of tracks are then selected randomly to calculate the genuine $\langle p_T \rangle$ distribution free from biases of multiplicity fluctuations. The left panel of Fig. 2 shows the $\langle p_T \rangle$ distribution for the 0–5% central events in Pb–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. The distribution in red markers shows the original event-by-event $\langle p_T \rangle$ distribution in which $N_{ch}$ fluctuates whereas the distribution shown with black markers is the $\langle p_T \rangle$ distribution in which $N_{ch}$ is fixed to $N_{ch}^{\min}$ in each event of the centrality class. A Gaussian function is used to fit the two distributions and the ratio of data to fit is shown in the bottom panel of Fig. 2. The ratio shows that the data points are above the fit in the right-side of the distribution, and below the fit in the left-side, indicating that the $\langle p_T \rangle$ distributions are positively skewed. The $\langle p_T \rangle$ distributions exhibit substantial deviations from a Gaussian distribution even under the condition of a fixed $N_{ch}$, thereby reflecting the analogous traits observed in the original distribution with fluctuating $N_{ch}$. The middle and right panels of Fig. 2 visually exemplify the consistent manifestation of these characteristics within the distributions of $\langle p_T \rangle$ for both semicentral and peripheral collisions. It is concluded that the positive skewness in the event-by-event $\langle p_T \rangle$ distributions is not a trivial consequence of event-by-event statistical fluctuations of $N_{ch}$, and therefore new and non-trivial information can be extracted from higher-order moments of $\langle p_T \rangle$ fluctuations.

The $\langle p_T \rangle$ correlators described in Eqs. 3, 4, and 5 are calculated using charged-particle tracks in different centrality (multiplicity) classes. For Pb–Pb collisions, the observables are analyzed in 18 equal-width centrality classes ranging between zero to ninety percent, i.e., 0–5%, 5–10%, ..., 85–90%. For Xe–Xe collisions, the total number of events are divided into four centrality classes, 0–20%, 20–40%, 40–60%, and 60–80%. The centrality classes are taken wider for Xe–Xe collisions because of the limited data sample. In pp collisions, the events are classified into ten multiplicity classes, 0–1%, 1–5%, 5–10%, 10–15%, 15–20%, 20–30%, 30–40%, 40–50%, 50–70%, and 70–100%. The method of defining these multiplicity classes can be found in Ref. [30].

The $\langle p_T \rangle$ correlators are calculated in the unit multiplicity bins of a given centrality class, and then merged using centrality bin width correction formula [31]. In this way, both the effects of multiplicity fluctuations, and the necessity of using non-trivial multiplicity weight to determine all-event averages
<table><caption>**Table 1:** Contributions to the total systematic uncertainty on standardized skewness $\gamma_{\langle p_T \rangle}$, intensive skewness $\Gamma_{\langle p_T \rangle}$, and kurtosis $\kappa_{\langle p_T \rangle}$ in Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV, Xe-Xe collisions at $\sqrt{s_{NN}} = 5.44$ TeV, and pp collisions at $\sqrt{s} = 5.02$ TeV. Ranges are given where the uncertainties depend on centrality or multiplicity.</caption><thead><tr><th>Observables</th><th>Sources of systematic uncertainty</th><th>Pb-Pb</th><th>Xe-Xe</th><th>pp</th></tr></thead><tbody><tr><td rowspan="10">γ<sub>⟨p<sub>T</sub>⟩</sub></td><td>Vertex z-position</td><td>0.7-2.7%</td><td>1.5-9.1%</td><td>0.3-0.8%</td></tr><tr><td>Pileup</td><td>0.5-6.4%</td><td>-</td><td>-</td></tr><tr><td>χ<sup>2</sup><sub>TPC</sub>/n<sub>TPCclusters</sub></td><td>0.5-2.6%</td><td>3.4-6.5%</td><td>0.1-0.4%</td></tr><tr><td>χ<sup>2</sup><sub>ITS</sub>/n<sub>ITSclusters</sub></td><td>0.5-2.2%</td><td>3.6-11.3%</td><td>&lt; 0.1%</td></tr><tr><td>n<sub>TPCcrossedrows</sub></td><td>0.6-3.8%</td><td>2.6-6.8%</td><td>0.9-1.9%</td></tr><tr><td>DCA<sub>xy</sub></td><td>0.6-4.5%</td><td>2.5-7.3%</td><td>0.5-1.1%</td></tr><tr><td>DCA<sub>z</sub></td><td>0.4-1.8%</td><td>2.8-5.9%</td><td>&lt; 0.1%</td></tr><tr><td>MC closure</td><td>2.3%</td><td>2.6%</td><td>2.7%</td></tr><tr><td>Total</td><td>2.9-8.7%</td><td>9.1-17.2%</td><td>2.9-3.6%</td></tr><tr><td rowspan="10">Γ<sub>⟨p<sub>T</sub>⟩</sub></td><td>Vertex z-position</td><td>0.6-2.7%</td><td>1.7-9.1%</td><td>0.3-0.8%</td></tr><tr><td>Pileup</td><td>0.5-6.3%</td><td>-</td><td>-</td></tr><tr><td>χ<sup>2</sup><sub>TPC</sub>/n<sub>TPCclusters</sub></td><td>0.4-2.7%</td><td>3.6-6.9%</td><td>0.1-0.3%</td></tr><tr><td>χ<sup>2</sup><sub>ITS</sub>/n<sub>ITSclusters</sub></td><td>0.4-2.2%</td><td>3.7-11.4%</td><td>&lt; 0.1%</td></tr><tr><td>n<sub>TPCcrossedrows</sub></td><td>0.8-3.8%</td><td>3.0-7.0%</td><td>0.3-1.7%</td></tr><tr><td>DCA<sub>xy</sub></td><td>0.7-4.7%</td><td>0.4-4.2%</td><td>0.3-1%</td></tr><tr><td>DCA<sub>z</sub></td><td>0.4-1.9%</td><td>2.7-6.0%</td><td>&lt; 0.1%</td></tr><tr><td>MC closure</td><td>3.6%</td><td>2.3%</td><td>0.4%</td></tr><tr><td>Total</td><td>4-9%</td><td>9.5-17.6%</td><td>0.8-2.1%</td></tr><tr><td rowspan="10">κ<sub>⟨p<sub>T</sub>⟩</sub></td><td>Vertex z-position</td><td>0.1-3.6%</td><td>0.9-4.5%</td><td>0.1-1.4%</td></tr><tr><td>Pileup</td><td>0.2-4.5%</td><td>-</td><td>-</td></tr><tr><td>χ<sup>2</sup><sub>TPC</sub>/n<sub>TPCclusters</sub></td><td>0.1-1.8%</td><td>0.9-4.6%</td><td>0.1-1.1%</td></tr><tr><td>χ<sup>2</sup><sub>ITS</sub>/n<sub>ITSclusters</sub></td><td>0.1-0.9%</td><td>1.2-3.9%</td><td>&lt; 0.1%</td></tr><tr><td>n<sub>TPCcrossedrows</sub></td><td>0.1-1.3%</td><td>3.0-7.0%</td><td>0.3-1.7%</td></tr><tr><td>DCA<sub>xy</sub></td><td>0.1-2.3%</td><td>0.3-0.9%</td><td>0.5-3.3%</td></tr><tr><td>DCA<sub>z</sub></td><td>0.1-2.9%</td><td>0.7-1.9%</td><td>&lt; 0.1%</td></tr><tr><td>MC closure</td><td>0.3%</td><td>1.3%</td><td>0.9%</td></tr><tr><td>Total</td><td>0.5-7.3%</td><td>2.7-11.7%</td><td>1.8-4.7%</td></tr></tbody></table>
from single-event averages, are eliminated. The statistical uncertainties are evaluated using the boot-
strap method. By repeatedly resampling the dataset and analyzing each resample, the bootstrap method
provides a robust and computationally feasible approach for estimating the uncertainties associated with
the observed results. It allows for a comprehensive assessment of the variability in the data, taking into
account the inherent fluctuations and dependencies present in the measurements. The systematic uncer-
tainties on the observables are estimated separately for each collision system by varying event and track
selection criteria. The uncertainties related to the event selection include the variation of the accepted
vertex position along the beam direction and pileup cut where applicable. The uncertainties due to track
selection include the variation of the selection criteria on DCA<sub>xy</sub>, DCA<sub>z</sub>, the number of reconstructed
space points in the TPC, and the quality of the track fit from their nominal values. Systematic uncer-
tainties obtained from the contribution of each of these sources are considered as uncorrelated and the
total systematic uncertainty on the observables is obtained by adding them in quadrature. Table 1 shows
the summary of the contributions to the total systematic uncertainty on standardized skewness, intensive
skewness, and kurtosis in Pb-Pb, Xe-Xe, and pp collisions.

The standardized skewness, intensive skewness, and kurtosis reported in this draft are considered robust
and independent of detection efficiencies [17]. The detector inefficiencies cancel to leading order within
these ratios, despite their potential presence in individual p<sub>T</sub> correlators. Consequently, efficiency cor-
rection is not carried out for these ratios. The robustness of the measured ratios is further affirmed by
performing a Monte Carlo (MC) closure test. The MC closure test uses simulations based on different
event generators for producing particles that corresponds to generated (true) results and GEANT3 [32]
for the transport of particles through the geometry of ALICE detectors. For Pb-Pb and Xe-Xe collisions,
the MC events are generated using HIJING (Heavy-Ion Jet Interaction Generator) [33] whereas for pp
collisions, the events are produced by PYTHIA8 [34, 35] event generator with Monash2013 tune. The
experimental conditions prevailing during the data taking are accounted for in the generated events using
GEANT3 by reproducing the actual configuration of different detectors during the runs. Results obtained
from the generated events are compared with their corresponding reconstructed ones (without applying
efficiency corrections), and they show a good agreement within uncertainties. The ratio of the recon-
structed to the generated results for the observables are fitted with zeroth-order polynomial functions to
quantify the amount of closure obtained. The percentages of agreement for standardized skewness, inten-
sive skewness, and kurtosis are 97.3%, 99.6% and 99.1%, respectively, in pp collisions at $\sqrt{s} = 5.02$ TeV.
Similar study is also performed for the other two collision systems, Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$
and Xe-Xe collisions at $\sqrt{s_{NN}} = 5.44$ TeV. The percentages of closure for the observables (standardized
skewness, intensive skewness, kurtosis) in Pb-Pb (Xe-Xe) collisions are found to be 97.7% (97.4%),
96.4% (97.7%), and 99.7% (98.7%). These differences are added to the systematic uncertainties and
reported in Table 1.

To study how the skewness and kurtosis of $\langle p_T \rangle$ distributions vary with the size of the collision system and to have a comparison between heavy-ion collisions (Pb-Pb and Xe-Xe) and small systems like pp collisions, expressing the centrality (multiplicity for pp collisions) classes as average charged particle multiplicity density ($\langle dN_{ch}/d\eta \rangle|_{\eta}|_{<0.5}$) is more suitable. The conversion of centrality to $\langle dN_{ch}/d\eta \rangle|_{\eta}|_{<0.5}$ is performed using the measured values of $\langle dN_{ch}/d\eta \rangle|_{\eta}|_{<0.5}$ for certain centrality classes from Ref. [36] for Pb-Pb collisions. It should be noted that the centrality classes used in this analysis are narrower and different from that in the reference. A linear relation is observed between average number of charged particles ($\langle N_{acc} \rangle$) in the kinematic range ($|\eta| < 0.8$ and $0.2 < p_T < 0.3$ GeV/c) of this analysis and $\langle dN_{ch}/d\eta \rangle|_{\eta}|_{<0.5}$ over the full centrality range. The extracted fit parameters from the linear relation between $\langle N_{acc} \rangle$ and $\langle dN_{ch}/d\eta \rangle|_{\eta}|_{<0.5}$ were used to assign a value of $\langle dN_{ch}/d\eta \rangle|_{\eta}|_{<0.5}$ for any value of $\langle N_{acc} \rangle$. Hence, by calculating the $\langle N_{acc} \rangle$ for the centrality classes of this analysis, the corresponding value of $\langle dN_{ch}/d\eta \rangle|_{\eta}|_{<0.5}$ is obtained. This method was previously used in the study of second-order fluctuations of $\langle p_T \rangle$ in Ref. [8]. Similar approach is followed for Xe-Xe collisions using $\langle dN_{ch}/d\eta \rangle|_{\eta}|_{<0.5}$ values of centrality classes from Ref. [37]. For pp collisions, the measured values of $\langle dN_{ch}/d\eta \rangle|_{\eta}|_{<0.5}$
are taken from Ref. [30] since the multiplicity classes are the same.

# 5 Results

## 5.1 Standardized skewness

The standardized skewness of charged particles produced in Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV and Xe-Xe collisions at $\sqrt{s_{NN}} = 5.44$ TeV as a function of system size denoted by the cubic root of average charged particle multiplicity density, $\langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5}$ is shown in Fig. 3. The femtoscopic radii associated with the radius of the fireball at freeze-out, scale linearly with $\langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5}$ and therefore it is used as a proxy for the system size [38]. The uncertainties on $\langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5}$ are obtained by propagating the uncertainty on $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}$. It is observed that $\gamma_{\langle p_T \rangle}$ decreases with increasing $\langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5}$ for both Pb-Pb and Xe-Xe collisions. This is generally expected from fluctuations in a dilution scenario caused by superposition of partially independent particle-emitting sources [7, 8]. If the fluctuations in $\langle p_T \rangle$ have been purely statistical and generated by finite multiplicity ($N$), then $\gamma_{\langle p_T \rangle}$ would have a dependence of $1/\sqrt{N}$. A slight enhancement of $\gamma_{\langle p_T \rangle}$ in the most central ($\langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5} > 11$) Pb-Pb collisions is also observed within uncertainty. One of the probable reasons could be the reduction of two-particle correlations $\langle \Delta p_i \Delta p_j \rangle$ towards the central collisions reported previously in Ref. [8]. Hydrodynamic model calculations from Ref. [17] that uses $T_{RENTO}$ initial conditions evolved by hydrodynamic code V-USPHYDRO referred as V-USPHYDRO model in the figures are compared with the data for both Pb-Pb and Xe-Xe collisions. A small specific shear viscosity, $\eta/s = 0.047$ is used in the V-USPHYDRO model. As shown in Fig. 3, the V-USPHYDRO model calculations capture the general system size dependence of the measurement, but fail to describe it quantitatively. In the model, $\gamma_{\langle p_T \rangle}$ is larger in Pb-Pb collisions compared to Xe-Xe collisions for almost all multiplicities, however data do not show such system dependence. Model calculations using HIJING [33], which incorporates various phenomena like multiple minijet production with initial and final state radiation or nuclear effects such as parton shadowing and jet quenching, are shown in the figure. HIJING considers nucleus-nucleus collisions as superposition of independent binary collisions of wounded nucleons. The latest version of the model, HIJING/$\overline{B}\overline{B}$ v2.0 with shadowing and jet quenching effects [39] is used. The $\gamma_{\langle p_T \rangle}$ in HIJING model exhibits a strong dependence with $\langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5}$ and reproduces the measurement in the semiperipheral to semicentral region. Calculations performed using the MC-Glauber+MUSIC model, which adopts the Glauber Monte Carlo [40] approach to generate initial conditions for the collisions, followed by the MUSIC hydrodynamic model [41] with $\eta/s = 0.1$ are presented. Notably, both the HIJING and MC-Glauber+MUSIC model utilize the Monte Carlo Glauber initial conditions, with the primary difference lying in the subsequent evolution. While HIJING lacks the implementation of collective phenomena, MUSIC incorporates such effects. Interestingly, the results obtained for the $\gamma_{\langle p_T \rangle}$ in Pb-Pb collisions remain same for both models from semiperipheral to semicentral collisions. This prompts the question of whether the $\gamma_{\langle p_T \rangle}$ is primarily sensitive to the details of the initial conditions.

The results in Pb-Pb and Xe-Xe are also compared with the measurements carried out in pp collisions at $\sqrt{s} = 5.02$ TeV. The $\gamma_{\langle p_T \rangle}$ in pp collisions shows a steeper decrease with increasing $\langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5}$ compared to heavy-ion collisions. The observed $\gamma_{\langle p_T \rangle}$ is also found smaller in pp collisions than in Pb-Pb collisions in the overlapping $\langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5}$ region. The measurements in pp collisions are compared with PYTHIA8 [35] model, which is a pQCD based MC event generator. The PYTHIA8 model is found to describe numerous experimental results in pp collisions at LHC energies quite successfully [42–44]. This model can involve color reconnection (CR) mechanism [45] in pp collisions, which could contribute to explaining certain collective effects that have been observed in these collisions. Comparison of the measurements in pp collisions with PYTHIA8 model for both cases, with and without enabling CR mechanism (referred as PYTHIA8 CR ON and PYTHIA8 CR OFF), are presented. PYTHIA8 CR OFF
<figure><img src="image_5.png" /><figcaption>Figure 3: Standardized skewness $\gamma_{\langle p_T \rangle}$ shown as a function of $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$ in Pb–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV, Xe–Xe collisions at $\sqrt{s_{NN}} = 5.44$ TeV, and pp collisions at $\sqrt{s} = 5.02$ TeV. The predictions from different event generators and hydrodynamic model calculations from V-USPHYDRO [17] and MC-Glauber+MUSIC [40, 41] are denoted by colored bands. The statistical (systematic) uncertainties are represented by vertical bars (boxes).</figcaption></figure>

model calculations utterly fail to describe the measurements both qualitatively and quantitatively. On the other hand, PYTHIA CR ON calculations reproduce the dependence of $\gamma_{\langle p_T \rangle}$ with $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$ although with a larger slope.

## 5.2 Intensive skewness

Figure 4 shows the intensive skewness studied with respect to $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$ in Pb–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV and Xe–Xe collisions at $\sqrt{s_{NN}} = 5.44$ TeV. The colored dashed lines indicate the independent baselines $\Gamma_{\text{independent}}$ evaluated for each system separately. The formula [17] used to calculate the independent baseline for intensive skewness is

$$ \Gamma_{\text{independent}} = \frac{\langle (p_T - \langle p_T \rangle)^3 \rangle \langle p_T \rangle}{\langle (p_T - \langle p_T \rangle)^2 \rangle^2}, \qquad (9) $$

where $\langle p_T \rangle$ is the average transverse momentum in given centrality class. The $p_T$ spectra for different centrality classes are the input distributions for the calculation of $\Gamma_{\text{independent}}$ as a function of centrality. The second and third central moments of the $p_T$ distributions, $\langle (p_T - \langle p_T \rangle)^2 \rangle$ and $\langle (p_T - \langle p_T \rangle)^3 \rangle$ are evaluated using the $p_T$ spectrum for each centrality class and the ratio of these moments gives the $\Gamma_{\text{independent}}$ for that centrality class. For Pb–Pb and Xe–Xe collisions, the $p_T$ spectra are taken from Refs. [46] and [47], respectively. Consecutively, the centralities are converted into $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}$ and $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$. A positive intensive skewness, larger than the independent baseline, is observed in both Pb–Pb and Xe–Xe collisions as a function of system size. This observation is in accordance with the predictions from the V-USPHYDRO hydrodynamic model calculations. The V-USPHYDRO model results describe the data qualitatively but do not show quantitative agreement. The HIJING model calculations though seem to capture the decreasing trend of the measurements in the semiperipheral to semicentral region ($3.8 \le \langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3} \le 8.9$) but are unable to explain the rise of $\Gamma_{\langle p_T \rangle}$ in the measurements
<figure><img src="image_6.png" /><figcaption>**Figure 4:** Intensive skewness $\Gamma_{\langle p_T \rangle}$ shown as a function of $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$ in Pb–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV, Xe–Xe collisions at $\sqrt{s_{NN}} = 5.44$ TeV, and pp collisions at $\sqrt{s} = 5.02$ TeV. The colored dashed lines represent the independent baseline for each system. The predictions from different event generators and hydrodynamic model calculations from V-USPHYDRO [17] and MC-Glauber+MUSIC [40, 41] are denoted by colored bands. The statistical (systematic) uncertainties are represented by vertical bars (boxes).</figcaption></figure>

from the semicentral to central region ($9.0 \le \langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3} \le 12.4$). The observed increase in both $\gamma_{\langle p_T \rangle}$ and $\Gamma_{\langle p_T \rangle}$ for $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3} > 11$ in Pb–Pb collisions might be indicative of the onset of thermalization [48, 49]. This phenomenon is distinct from hydrodynamization, which could occur in smaller systems and at shorter timescales. As a direct consequence of thermalization, a significant increase of the skewness of $\langle p_T \rangle$ fluctuations is predicted for most central collisions. If the system thermalizes, $\langle p_T \rangle$ increases with density which is a characteristic phenomenon in relativistic fluid dynamics. At fixed multiplicity, larger density corresponds to smaller volume and correspondingly larger impact parameter which suggests that the rise of skewness results from a reduction in impact parameter fluctuations within the most central collisions. The MC-Glauber+MUSIC model calculations exhibit similar behavior observed in the measurements of $\Gamma_{\langle p_T \rangle}$ in Pb–Pb collisions and provide better agreement quantitatively than the V-USPHYDRO model results. The increase of $\Gamma_{\langle p_T \rangle}$ for central collisions in the measurements, seems to be depicted by both of the hydrodynamic model calculations with different initial conditions and therefore demands theoretical inputs to understand this rise.

The measurement performed in pp collisions at $\sqrt{s} = 5.02$ TeV is also shown along with its independent baseline. For pp collisions, the baseline is calculated using the $p_T$ spectra from Ref. [50]. The hydrodynamic prediction of positive intensive skewness above its baseline is pronounced in the measurements in pp collisions as well. The distinct non-monotonic behavior observed in Pb–Pb collisions as a function of $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$ is noticeably attenuated in pp collisions. The $\Gamma_{\langle p_T \rangle}$ exhibits a subtle, monotonic decrease as $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$ increases in pp collisions. In the PYTHIA8 CR ON model, the results for $\Gamma_{\langle p_T \rangle}$ exhibit an increase as $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$ increases, which is in direct contrast to the observations from the PYTHIA8 CR ON model. While the PYTHIA8 CR ON model appears to be in closer agreement with the experimental measurements compared to CR OFF, neither model adequately captures the qualitative behavior observed in the measurements.
<figure><img src="image_7.png" /><figcaption>**Figure 5:** Kurtosis $\kappa_{\langle p_T \rangle}$ shown as a function of $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$ in Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV, Xe-Xe collisions at $\sqrt{s_{NN}} = 5.44$ TeV and pp collisions at $\sqrt{s} = 5.02$ TeV. The predictions from different event generators and hydrodynamic calculations from MC-Glauber+MUSIC model [40, 41] are represented by colored bands. The dashed line indicates the Gaussian baseline. The statistical (systematic) uncertainties are represented by vertical bars (boxes).</figcaption></figure>

## 5.3 Kurtosis

The kurtosis evaluated using Eq. 5 as a function of $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$ in Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV and Xe-Xe collisions at $\sqrt{s_{NN}} = 5.44$ TeV is shown in Fig. 5. The $\kappa_{\langle p_T \rangle}$ for a Gaussian distribution, which serves as a baseline for independent particle production, is shown with dotted line. The $\kappa_{\langle p_T \rangle}$ is found to decrease with increasing system size in Pb-Pb and Xe-Xe collisions and approaches the Gaussian baseline towards the most central Pb-Pb collisions. The measurements are compared with HIJING model calculations for both Pb-Pb and Xe-Xe collisions. While the HIJING model successfully capture the decreasing trend observed in the measurements with respect to $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$, it exhibits a pronounced and rapid decrease in $\kappa_{\langle p_T \rangle}$ compared to the data points. This is related to trivial system size dependence of $\kappa_{\langle p_T \rangle}$ in HIJING that should follow $1/N$ dependence. Throughout the entire range of $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$, the HIJING model overestimates the measurements. The MC-Glauber+MUSIC calculations reproduce the measurements in the central to midperipheral region ($5.4 \le \langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3} \le 12.4$). The measurements in pp collisions at $\sqrt{s} = 5.02$ TeV are also shown in the Fig. 5. In pp collisions, the $\kappa_{\langle p_T \rangle}$ decreases with $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$ and remains consistently above the Gaussian baseline even for the highest value of $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$. Calculations of $\kappa_{\langle p_T \rangle}$ in PYTHIA8 show similar behavior with $\langle dN_{ch}/d\eta \rangle_{|\eta|<0.5}^{1/3}$ as in data when CR mechanism is turned ON. PYTHIA8 CR OFF model completely fails to describe the measured $\kappa_{\langle p_T \rangle}$.

## 6 Summary

In summary, first results on higher order fluctuations of mean transverse momentum ($\langle p_T \rangle$) of charged particles, skewness, and kurtosis in Pb-Pb, Xe-Xe, and pp collisions at LHC energies are presented.
Two measures of skewness, standardized skewness and intensive skewness, are studied using three- and two-particle $p_T$ correlators as a function of system size ($\langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5}$). The standardized skewness is found to decrease with increasing system size in all three collision systems. Positive intensive skewness, larger than the baseline and consistent with the predictions from the hydrodynamics studies in Ref. [17], is observed in both Pb-Pb and Xe-Xe collisions. The anticipated positive intensive skewness for A-A collisions is likewise confirmed in pp collisions at similar collision energy. HIJING model calculations, which do not incorporate hydrodynamic evolution, are able to exhibit the qualitative behavior of intensive skewness in the region of $3.8 \le \langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5} \le 8.9$. The striking rise of intensive skewness in the most central region is unexplained by HIJING. This effect is, however captured in the hydrodynamic calculations of both V-USPHYDRO and MC-Glauber+MUSIC models. The MC-Glauber+MUSIC model shows good agreement with the measurements of the standardized skewness and intensive skewness in the region of $4.8 \le \langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5} \le 12.4$. In contrast, the V-USPHYDRO model, which utilizes $T_R$ to initial conditions, overestimates both measures of skewness. The discrepancy between the results obtained from the two hydrodynamic models suggests that these measurements can provide valuable insights into the initial stages of the collision. Also, the standardized skewness in HIJING and MC-Glauber+MUSIC models exhibits similar behavior, suggesting that its sensitivity may primarily be attributed to the details of the initial conditions rather than the subsequent evolution. In pp collisions, the PYTHIA8 model with the color reconnection mechanism enabled is able to qualitatively reproduce the measurements. The kurtosis measured using the two- and four-particle $p_T$ correlators shows a decrease with the system size. This decreasing behavior is reproduced by the HIJING model calculations in Pb-Pb and Xe-Xe collisions, which, however, do not show a quantitative agreement with the measurements. Hydrodynamic calculations from MC-Glauber+MUSIC model explain the measurement well in the region of $4.8 \le \langle dN_{ch}/d\eta \rangle^{1/3}_{|\eta|<0.5} \le 12.4$. The value of kurtosis from the MC-Glauber+MUSIC model has a similar value to that from a Gaussian distribution. The measurements of kurtosis in Pb-Pb collisions also agreeing with the Gaussian baseline for highest values of the system size, hint about the production of a locally thermalized system in most central Pb-Pb collisions.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: 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 Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, 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. Chujó 126, M. Ciacco 30, C. Cicalo 53, F. Cindolo 52, M.R. Ciupek 98, G. Clai 111, 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 $^{101}$,
M.J. Kabus $^{33,137}$, 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 $^{142}$, 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. Miškowiec $^{98}$, 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 $^{123}$, T.K. Nayak $^{81,117}$, 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 $^{45}$,
A. Palasciano$^{51}$, S. Panebianco$^{131}$, H. Park$^{126}$, H. Park$^{105}$, J. Park$^{59}$, J.E. Parkkila$^{33}$, Y. Patley$^{48}$, R.N. Patra$^{92}$, B. Paul$^{23}$, H. Pei$^{6}$, T. Peitzmann$^{60}$, X. Peng$^{11}$, M. Pennisi$^{25}$, S. Perciballi$^{25}$, D. Peresunko$^{142}$, G.M. Perez$^{7}$, Y. Pestov$^{142}$, V. Petrov$^{142}$, M. Petrovici$^{46}$, R.P. Pezzi$^{104,67}$, S. Piano$^{58}$, M. Pikna$^{13}$, P. Pillot$^{104}$, O. Pinazza$^{52,33}$, L. Pinsky$^{117}$, C. Pinto$^{96}$, S. Pisano$^{50}$, M. Płoskoń$^{75}$, M. Planinic$^{90}$, F. Pliquett$^{65}$, M.G. Poghosyan$^{88}$, B. Polichtchouk$^{142}$, S. Politano$^{30}$, N. Poljak$^{90}$, A. Pop$^{46}$, S. Porteboeuf-Houssais$^{128}$, V. Pozdniakov$^{143}$, I.Y. Pozos$^{45}$, K.K. Pradhan$^{49}$, S.K. Prasad$^{4}$, S. Prasad$^{49}$, R. Preghenella$^{52}$, F. Prino$^{57}$, C.A. Pruneau$^{138}$, I. Pshenichnov$^{142}$, M. Puccio$^{33}$, S. Pucillo$^{25}$, Z. Pugelova$^{107}$, S. Qiu$^{85}$, L. Quaglia$^{25}$, S. Ragoni$^{15}$, A. Rai$^{139}$, A. Rakotozafindrabe$^{131}$, L. Ramello$^{134,57}$, F. Rami$^{130}$, T.A. Rancien$^{74}$, M. Rasa$^{27}$, S.S. Räsänen$^{44}$, R. Rath$^{52}$, M.P. Rauch$^{21}$, I. Ravasenga$^{85}$, K.F. Read$^{88,123}$, C. Reckziegel$^{113}$, A.R. Redelbach$^{39}$, K. Redlich$^{VI,80}$, C.A. Reetz$^{98}$, H.D. Regules-Medel$^{45}$, A. Rehman$^{21}$, F. Reidt$^{33}$, H.A. Reme-Ness$^{35}$, Z. Rescakova$^{38}$, K. Reygers$^{95}$, A. Riabov$^{142}$, V. Riabov$^{142}$, R. Ricci$^{29}$, M. Richter$^{20}$, A.A. Riedel$^{96}$, W. Riegler$^{33}$, A.G. Riffero$^{25}$, C. Ristea$^{64}$, M.V. Rodriguez$^{33}$, M. Rodríguez Cahuantzi$^{45}$, S.A. Rodríguez Ramírez$^{45}$, K. Røed$^{20}$, R. Rogalev$^{142}$, E. Rogochaya$^{143}$, T.S. Rogoschinski$^{65}$, D. Rohr$^{33}$, D. Röhrich$^{21}$, P.F. Rojas$^{45}$, S. Rojas Torres$^{36}$, P.S. Rokita$^{137}$, G. Romanenko$^{26}$, F. Ronchetti$^{50}$, A. Rosano$^{31,54}$, E.D. Rosas$^{66}$, K. Roslon$^{137}$, A. Rossi$^{55}$, A. Roy$^{49}$, S. Roy$^{48}$, N. Rubini$^{26}$, D. Ruggiano$^{137}$, R. Rui$^{24}$, P.G. Russek$^{2}$, R. Russo$^{85}$, A. Rustamov$^{82}$, E. Ryabinkin$^{142}$, Y. Ryabov$^{142}$, A. Rybicki$^{108}$, H. Rytkonen$^{118}$, J. Ryu$^{17}$, W. Rzesa$^{137}$, O.A.M. Saarimaki$^{44}$, S. Sadhu$^{32}$, S. Sadovsky$^{142}$, J. Saetre$^{21}$, K. Šafařík$^{36}$, P. Saha$^{42}$, S.K. Saha$^{4}$, S. Saha$^{81}$, B. Sahoo$^{48}$, B. Sahoo$^{49}$, R. Sahoo$^{49}$, S. Sahoo$^{62}$, D. Sahu$^{49}$, P.K. Sahu$^{62}$, J. Saini$^{136}$, K. Sajdakova$^{38}$, S. Sakai$^{126}$, M.P. Salvan$^{98}$, S. Sambyal$^{92}$, D. Samitz$^{103}$, I. Sanna$^{33,96}$, T.B. Saramela$^{111}$, P. Sarma$^{42}$, V. Sarritzu$^{23}$, V.M. Sarti$^{96}$, M.H.P. Sas$^{33}$, S. Sawan$^{81}$, J. Schambach$^{88}$, H.S. Scheid$^{65}$, C. Schiaua$^{46}$, R. Schicker$^{95}$, F. Schlepper$^{95}$, A. Schmah$^{98}$, C. Schmidt$^{98}$, H.R. Schmidt$^{94}$, M.O. Schmidt$^{33}$, M. Schmidt$^{94}$, N.V. Schmidt$^{88}$, A.R. Schmier$^{123}$, R. Schotter$^{130}$, A. Schröter$^{39}$, J. Schukraft$^{33}$, K. Schweda$^{98}$, G. Scioli$^{26}$, E. Scomparin$^{57}$, J.E. Seger$^{15}$, Y. Sekiguchi$^{125}$, D. Sekihata$^{125}$, M. Selina$^{85}$, I. Selyuzhenkov$^{98}$, S. Senyukov$^{130}$, J.J. Seo$^{95,59}$, D. Serebryakov$^{142}$, L. Šerkšnytė$^{96}$, A. Sevcenco$^{64}$, T.J. Shaba$^{69}$, A. Shabetai$^{104}$, R. Shahoyan$^{33}$, A. Shangaraev$^{142}$, A. Sharma$^{91}$, B. Sharma$^{92}$, D. Sharma$^{48}$, H. Sharma$^{55}$, M. Sharma$^{92}$, S. Sharma$^{77}$, S. Sharma$^{92}$, U. Sharma$^{92}$, A. Shatat$^{132}$, O. Sheibani$^{117}$, K. Shigaki$^{93}$, M. Shimomura$^{78}$, J. Shin$^{12}$, S. Shirkin$^{142}$, Q. Shou$^{40}$, Y. Sibiriak$^{142}$, S. Siddhanta$^{53}$, T. Siemiarczuk$^{80}$, T.F. Silva$^{111}$, D. Silvermyr$^{76}$, T. Simantathammakul$^{106}$, R. Simeonov$^{37}$, B. Singh$^{92}$, B. Singh$^{96}$, K. Singh$^{49}$, R. Singh$^{81}$, R. Singh$^{92}$, R. Singh$^{49}$, S. Singh$^{16}$, V.K. Singh$^{136}$, V. Singhal$^{136}$, T. Sinha$^{100}$, B. Sitar$^{13}$, M. Sitta$^{134,57}$, T.B. Skaali$^{20}$, G. Skorodumovs$^{95}$, M. Slupecki$^{44}$, N. Smirnov$^{139}$, R.J.M. Snellings$^{60}$, E.H. Solheim$^{20}$, J. Song$^{17}$, C. Sonnabend$^{33,98}$, F. Soramel$^{28}$, A.B. Soto-hernandez$^{89}$, R. Spijkers$^{85}$, I. Sputowska$^{108}$, J. Staa$^{76}$, J. Stachel$^{95}$, I. Stan$^{64}$, P.J. Steffanic$^{123}$, S.F. Stiefelmaier$^{95}$, D. Stocco$^{104}$, I. Storehaug$^{20}$, P. Stratmann$^{127}$, S. Strazzi$^{26}$, A. Sturniolo$^{31,54}$, C.P. Stylianidis$^{85}$, A.A.P. Suaide$^{111}$, C. Suire$^{132}$, M. Sukhanov$^{142}$, M. Suljic$^{33}$, R. Sultanov$^{142}$, V. Sumberia$^{92}$, S. Sumowidagdo$^{83}$, S. Swain$^{62}$, I. Szarka$^{13}$, M. Szymkowski$^{137}$, S.F. Taghavi$^{96}$, G. Taillepied$^{98}$, J. Takahashi$^{112}$, G.J. Tambave$^{81}$, S. Tang$^{6}$, Z. Tang$^{121}$, J.D. Tapia Takaki$^{119}$, N. Tapus$^{114}$, L.A. Tarasovicova$^{127}$, M.G. Tarzila$^{46}$, G.F. Tassielli$^{32}$, A. Tauro$^{33}$, A. Tavira García$^{132}$, G. Tejeda Muñoz$^{45}$, A. Telesca$^{33}$, L. Terlizzi$^{25}$, C. Terrevoli$^{117}$, S. Thakur$^{4}$, D. Thomas$^{109}$, A. Tikhonov$^{142}$, N. Tiltmann$^{127}$, A.R. Timmins$^{117}$, M. Tkacik$^{107}$, T. Tkacik$^{107}$, A. Toia$^{65}$, R. Tokumoto$^{93}$, K. Tomohiro$^{93}$, N. Topilskaya$^{142}$, M. Toppi$^{50}$, T. Tork$^{132}$, V.V. Torres$^{104}$, A.G. Torres Ramos$^{32}$, A. Trifíró$^{31,54}$, A.S. Triolo$^{33,31,54}$, S. Tripathy$^{52}$, T. Tripathy$^{48}$, S. Trogolo$^{33}$, V. Trubnikov$^{3}$, W.H. Trzaska$^{118}$, T.P. Trzcinski$^{137}$, A. Tumkin$^{142}$, R. Turrisi$^{55}$, T.S. Tveter$^{20}$, K. Ullaland$^{21}$, B. Ulukutlu$^{96}$, A. Uras$^{129}$, G.L. Usai$^{23}$, M. Vala$^{38}$, N. Valle$^{22}$, L.V.R. van Doremalen$^{60}$, M. van Leeuwen$^{85}$, C.A. van Veen$^{95}$, R.J.G. van Weelden$^{85}$, P. Vande Vyvre$^{33}$, D. Varga$^{47}$, Z. Varga$^{47}$, P. Vargas Torres$^{66}$, M. Vasileiou$^{79}$, A. Vasiliev$^{142}$, O. Vázquez Doce$^{50}$, O. Vazquez Rueda$^{117}$, V. Vechernin$^{142}$, E. Vercellin$^{25}$, S. Vergara Limón$^{45}$, R. Verma$^{48}$, L. Vermunt$^{98}$, R. Vértesi$^{47}$, M. Verweij$^{60}$, L. Vickovic$^{34}$, Z. Vilakazi$^{124}$, O. Villalobos Baillie$^{101}$, A. Villani$^{24}$, A. Vinogradov$^{142}$, T. Virgili$^{29}$, M.M.O. Virta$^{118}$, V. Vislavicius$^{76}$, A. Vodopyanov$^{143}$, B. Volkel$^{33}$, M.A. Völkl$^{95}$, K. Voloshin$^{142}$, S.A. Voloshin$^{138}$, G. Volpe$^{32}$, B. von Haller$^{33}$, I. Vorobyev$^{96}$, N. Vozniuk$^{142}$, J. Vrláková$^{38}$, J. Wan$^{40}$, C. Wang$^{40}$, D. Wang$^{40}$, Y. Wang$^{40}$, Y. Wang$^{6}$, A. Wegrzynek$^{33}$, F.T. Weiglhofer$^{39}$, S.C. Wenzel$^{33}$, J.P. Wessels$^{127}$, J. Wiechula$^{65}$, J. Wikne$^{20}$, G. Wilk$^{80}$, J. Wilkinson$^{98}$, G.A. Willems$^{127}$, B. Windelband$^{95}$, M. Winn$^{131}$, J.R. Wright$^{109}$, W. Wu$^{40}$, Y. Wu$^{121}$, R. Xu$^{6}$, A. Yadav$^{43}$, A.K. Yadav$^{136}$,
S. Yalcin ◦ 73, Y. Yamaguchi ◦ 93, S. Yang21, S. Yano ◦ 93, Z. Yin ◦ 6, I.-K. Yoo ◦ 17, J.H. Yoon ◦ 59, H. Yu12,
S. Yuan21, A. Yuncu ◦ 95, V. Zaccolo ◦ 24, C. Zampolli ◦ 33, F. Zanone ◦ 95, N. Zardoshti ◦ 33,

A. Zarochentsev ◦ 142, P. Závada ◦ 63, N. Zaviyalov142, M. Zhalov ◦ 142, B. Zhang ◦ 6, C. Zhang ◦ 131,

L. Zhang ◦ 40, S. Zhang ◦ 40, X. Zhang ◦ 6, Y. Zhang121, Z. Zhang ◦ 6, M. Zhao ◦ 10, V. Zherebchevskii ◦ 142,

Y. Zhi10, D. Zhou ◦ 6, Y. Zhou ◦ 84, J. Zhu ◦ 55.6, Y. Zhu6, 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>