# Measurement of (anti)alpha production in central Pb-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.

► To cite this version:

Shreyasi Acharya, Dagmar Adamova, Gianluca Aglieri Rinella, Michelangelo Agnello, Neelima Agrawal, et al. Measurement of (anti)alpha production in central Pb-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV. Phys.Lett.B, 2024, 858, pp.138943. 10.1016/j.physletb.2024.138943. hal-04297439

HAL Id: hal-04297439

https://hal.science/hal-04297439v1

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# Measurement of (anti)alpha production in central Pb-Pb collisions
at $\sqrt{s_{NN}} = 5.02$ TeV

ALICE Collaboration*

## Abstract

In this letter, measurements of (anti)alpha production in central (0–10%) Pb-Pb collisions at a center-of-mass energy per nucleon–nucleon pair of $\sqrt{s_{NN}} = 5.02$ TeV are presented, including the first measurement of an antialpha transverse-momentum spectrum. Owing to its large mass, (anti)alpha production yields and transverse-momentum spectra are of particular interest because they provide a stringent test of particle production models. The averaged antialpha and alpha spectrum is included into a common blast-wave fit with lighter particles, indicating that the (anti)alpha also participates in the collective expansion of the medium created in the collision. A blast-wave fit including only protons, (anti)alpha, and other light nuclei results in a similar flow velocity as the fit that includes all particles. A similar flow velocity, but a significantly larger kinetic freeze-out temperature is obtained when only protons and light nuclei are included in the fit. The coalescence parameter $B_4$ is well described by calculations from a statistical hadronization model but significantly underestimated by calculations assuming nucleus formation via coalescence of nucleons. Similarly, the (anti)alpha-to-proton ratio is well described by the statistical hadronization model. On the other hand, coalescence calculations including approaches with different implementations of the (anti)alpha substructure tend to underestimate the data.

© 2023 CERN for the benefit of the ALICE Collaboration.

Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.

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

During the past five decades the production of light nuclei in heavy-ion reactions has been measured over a broad range of collision energies [1–19]. At center-of-mass energies of up to a few GeV light nucleus production is commonly understood in terms of nuclear break-up where the incoming nuclei disintegrate into lighter nuclear fragments. In contrast to this, the study of the production of antinuclei in heavy-ion collisions is a nascent field that emerged with the availability of heavy-ion colliders [20–36]. In particular, the antialpha was first observed only 13 years ago by the STAR Collaboration in Au–Au collisions at the Relativistic Heavy-Ion Collider (RHIC) [37]. At the Large Hadron Collider (LHC), which provides the highest center-of-mass energies for heavy-ion collisions to date, measurements of the production of nuclei and antinuclei have so far mainly been performed by the ALICE Collaboration in different collision systems [38–55]. Understanding the production mechanism of nuclei and antinuclei in ultrarelativistic collisions could provide deeper insights into the hadronization process and the quantum properties of composite hadronic systems, but a conclusive explanation has yet to be found.

Two different approaches exist that describe the production of light (anti)nuclei in heavy-ion collisions. In statistical hadronization models (SHMs), often simply called thermal models, the production of hadrons and nuclei is described in the framework of a grand-canonical ensemble employing only three parameters: temperature $T$, volume $V$, and baryo-chemical potential $\mu_B$ [56–62]. Previous measurements of the production of light (anti)nuclei in central Pb–Pb collisions by the ALICE Collaboration agreed well with a common SHM fit to all available hadron and nucleus measurements with a temperature of $T = (156.5 \pm 1.5)$ MeV and a baryo-chemical potential of $\mu_B = (0.7 \pm 3.8)$ MeV [60]. The temperature is commonly understood in terms of a chemical freeze-out temperature $T_{ch}$ at which the abundances of hadrons and nuclei are fixed during the fireball evolution [51, 59]. It is compatible with the (pseudo)critical temperature $T_c$ predicted by the lattice QCD calculations for the transition between a hadronic system and a quark–gluon plasma (QGP) at vanishing $\mu_B$ [63, 64]. The interpretation in the context of the production of nuclei, however, is not straightforward because significant modifications of the abundances of nuclei are expected from density and cross-section arguments due to inelastic processes in the subsequent fireball evolution, often called hadronic phase, below $T_{ch}$.

In another class of models, nucleus formation is conjectured via the coalescence of nucleons in the final state of the system evolution [65–68]. The coalescence process is typically associated with the kinetic freeze-out temperature $T_{kin}$, which corresponds to the temperature where the inelastic collisions cease and the (transverse) momentum spectra of the particles are frozen [59]. The invariant yield $E_A \frac{d^3N_A}{dp_A^3}$ of nuclei with mass number A is connected to the final-state momentum distribution of protons $E_p \frac{d^3N_p}{dp_p^3}$ via the coalescence parameter [67]:

$$B_A = E_A \frac{d^3N_A}{dp_A^3} \left( E_p \frac{d^3N_p}{dp_p^3} \right)^{-A}, \quad (1)$$

assuming that protons and neutrons are produced in equal amounts at ultrarelativistic collision energies since both belong to the same isospin doublet. The coalescence prescription can thus be employed to deduce the formation of nuclei based on measured proton yields as well as on nucleon distributions from event generators such as PYTHIA [69, 70] and EPOS [71], or transport models like UrQMD [72–74] or SMASH [75–77].

In pertinent formulations of the coalescence model, the coalescence probability incorporates a dependence on the spatial distribution of the nucleons at kinetic freeze-out and its overlap with the internal wave function of the nuclear cluster, leading to a characteristic dependence of $B_A$ and consequently the production yield of nuclei on the size of the collision system [78–88]. This motivated detailed studies
of nuclear formation in pp, p–Pb, and non-central Pb–Pb collisions, where the yield ratio of nucleus A relative to protons is studied as a function of the average charged-particle multiplicity per unit of pseudorapidity, $\langle dN_{ch}/d\eta \rangle$. Indeed, the present data tend to confirm the system-size dependence predicted by coalescence models for the yield ratios deuteron to proton (d/p), triton to proton (t/p), and $^3$He to proton ($^3$He/p) in small collision systems [39, 41–44, 46–48]. On the other hand, the statistical description of particle production in small collision systems requires a canonical formulation of the statistical hadronization model, leading to the Canonical Statistical Model (CSM). This formulation entails an additional model parameter, the so-called correlation volume $V_C$, inside which electric charge $Q$, strangeness $S$, and baryon number $B$ are conserved exactly [61, 62, 89–92]. CSM calculations of nucleus-to-proton ratios result in a suppression of the production of nuclei in small systems that is qualitatively compatible with the patterns observed in data, but still tends to overestimate the yields of nuclei for realistic assumptions of $V_C$ [50, 61, 91].

In central and semi-central Pb–Pb collisions, recent results for d/p and $^3$He/p are compatible with both statistical hadronization and coalescence models, while t/p in Pb–Pb is significantly closer to the coalescence model [52]. It should be noted, however, that the yield of nuclei in Pb–Pb collisions may also be modified by absorption effects during the hadronic phase, as indicated by calculations from the UrQMD model [74].

The observed stiffening of transverse-momentum ($p_T$) spectra of hadrons produced in heavy-ion collisions can be interpreted in terms of a common radial flow field, arising from hydrodynamic expansion. The so-called blast-wave model [93] describes the radial boost of the light-flavor hadrons and nuclei arising from hydrodynamic expansion with a common set of parameters: the kinetic freeze-out temperature $T_{kin}$, the mean radial expansion velocity $\langle \beta \rangle$, and an exponent $n$ of the radial velocity profile. The measured $p_T$ spectra are fitted with the Boltzmann-Gibbs blast-wave function [93]:

$$E \frac{d^3 N}{dp^3} \propto \int_0^R m_T I_0 \left( \frac{p_T \sinh(\rho(r))}{T_{kin}} \right) K_1 \left( \frac{m_T \cosh(\rho(r))}{T_{kin}} \right) r dr \quad (2)$$

where $m_T$ is the transverse mass ($m_T = \sqrt{m^2 + p_T^2}$), $I_0$ and $K_1$ are the modified Bessel functions, and $\rho$ is the velocity profile given by:

$$\rho(r) = \tanh^{-1} \beta(r) = \tanh^{-1} \left[ \left( \frac{r}{R} \right)^n \beta_{\max} \right], \quad (3)$$

where $r$ is the radial distance in the transverse plane, $R$ is the radius of the fireball and $\beta_{max}$ is the transverse expansion velocity at the surface of the expanding fireball.

The study of (anti)alpha production in central Pb–Pb collisions is particularly interesting because it is the heaviest nucleus measured at the LHC so far. In the SHM, there is a strong mass dependence of the statistical penalty factor for typical values of $T_{ch}$ and $\mu_B$, while predictions of coalescence models depend on nucleon densities and geometrical factors to the power of A. This makes the (anti)alpha a very sensitive probe for stringent tests of the production models of light nuclei. Previous measurements of the integrated yields of antialpha and alpha in central Pb–Pb collisions at a center-of-mass energy per nucleon–nucleon pair of $\sqrt{s_{NN}} = 2.76$ TeV agreed with a global fit of the SHM to the yields of all measured hadrons and nuclei [40]. No predictions for A = 4 from coalescence models existed at the time.

In this letter, we present results on (anti)alpha production in central Pb–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV, including the first ever measured transverse-momentum spectrum of the antialpha. The results are compared to predictions by coalescence and statistical hadronization models. Together with previous results for different hadron species and lighter nuclei, the $p_T$ spectra are analyzed employing the blast-wave
model. Throughout this letter, especially in the figures but also at some occasions in the text, $^4$He instead of alpha is stated, which are used as equivalent. Note that with $^4$He not the chemical element with electron shell but the $^4$He nucleus is meant.

In Sec. 2 the analysis is described, followed by the presentation of the systematic uncertainties in Sec. 3. The results are discussed in Sec. 4 and the conclusion is given in Sec. 5.

## 2 Data analysis

The presented results are based on a data set of Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV, collected in 2018, where $99.5 \times 10^6$ events in the 0–10% centrality interval [94] were analyzed.

The ALICE apparatus [95, 96] provides excellent particle identification and vertexing capabilities. The (anti)alpha was reconstructed and identified using the Inner Tracking System (ITS), the Time Projection Chamber (TPC), the Transition Radiation Detector (TRD), and the Time-Of-Flight detector (TOF). These detectors are all located inside a homogeneous magnetic field with a strength of 0.5 T and cover the full azimuth in the pseudorapidity range $|\eta| < 0.9$. Interactions located inside $|z| < 10$ cm are selected, where $z$ is the distance from the nominal interaction point along the beam direction.

The ITS [97] is a silicon detector consisting of six cylindrical layers. It is used for charged-particle tracking and for the reconstruction of primary and secondary vertices. It can also be used to separate primary nuclei from secondary, knocked-out nuclei from the detector material, via the distance of closest approach (DCA) of the track to the primary vertex.

The TPC [98] is the main tracking device of the ALICE apparatus. It is a gas-filled cylinder and provides charged-particle tracking and particle identification via the specific energy loss per path length (dE/dx) with a resolution of 6% in Pb–Pb collisions.

The TOF detector [99] provides identification of light (anti)nuclei by means of the velocity determination from the calculated path length of the track and the time-of-flight measurement. Its total time resolution for tracks in Pb–Pb collisions corresponds to about 65 ps which is determined by the intrinsic time resolution of the detector and the resolution of the event collision time measurement. By combining TPC and TOF information, (anti)alphas can be identified from $p_T$ = 2 GeV/c up to 6 GeV/c in Pb–Pb collisions.

The TRD [100] can be used to improve the momentum resolution and significantly reduces the probability of random matches between tracks and TOF hits.

The V0 detectors [101] measure the arrival time of particles with a resolution of 1 ns, by utilizing a pair of forward and backward scintillator arrays (covering the pseudorapidity ranges $2.8 < \eta < 5.1$ and $-3.7 < \eta < -1.7$). They are used for triggering purposes and for rejection of beam–gas interactions. In addition, they provide the centrality trigger in Pb–Pb collisions [94], and they are also used for offline centrality determination.

The Zero Degree Calorimeter (ZDC) consists of two sets of hadronic calorimeters, which are located 112.5 m away from the interaction point on both sides of it, and of one set of electromagnetic calorimeters, placed 7 m away from the interaction point [95] on one side of it. It is located at 0° relative to the beam direction.

### 2.1 Event and track selection

The data were collected using a minimum-bias trigger requiring at least one hit in both V0 detectors. Furthermore, a trigger on central collisions was used, also determined by the V0 detectors, selecting collisions in the 0–10% centrality interval. To reject the events triggered by the interactions of the beam with the residual gas in the LHC vacuum pipe, the timing information of the V0 scintillator arrays is
used. A further selection using the ZDC is applied in order to reject the electromagnetic beam-beam
interactions and beam-satellite bunch collisions [102]. This is done by selecting good events from the
correlation between the sum and the difference of arrival times measured in each of the ZDCs [96]. All
these rejection steps are done in the offline analysis.

The production yield of (anti)alphas is measured at midrapidity ($|y| < 0.5$). Only tracks in the full tracking acceptance of $|η| < 0.8$ are selected. In order to guarantee good track momentum and $dE/dx$ resolution in the relevant $p_T$ ranges, the selected tracks are required to have at least 70 out of 159 possible reconstructed points in the TPC and at least two points in the ITS out of which at least one is in the two innermost layers, the Silicon Pixel Detector (SPD). The requirement of at least one point in the SPD assures a resolution better than 300 µm on the distance of closest approach to the primary vertex for the selected tracks [96]. Furthermore, it is required that the $\chi^2$ per TPC reconstructed point is less than 2.5 and tracks with a kink, which originate from weak decays, where the decay products are one charged and at least one neutral particle, are rejected.

## 2.2 Particle identification

Particles with electric charge $z = 2$ are well separated in the TPC from the particles with $z = 1$, as they have a four times larger specific energy loss ($dE/dx$). However, to distinguish the alphas from the much more abundant $^3$He (by a factor of the order of $10^3$) the $dE/dx$ information is combined with the mass calculated from the time-of-flight measured with the TOF and the track momentum. The energy loss in the TPC can be described by the Bethe-Bloch formula for a given mass hypothesis. To select the (anti)alphas it is required that the energy loss of the track lies in a $3\ \sigma$ window around the expected values for alpha particles, where $\sigma$ is the $dE/dx$ resolution. In addition, it is required that the track is matched to a hit in the TOF detector. Figure 1 shows the $m^2/z^2$ distribution of the TOF detector for antialpha candidates (green) in the $p_T$ interval between 3 and 6 GeV/c. The $m^2/z^2$ for true (anti)alphas is 3.475 GeV$^2/c^4$. Note that in the $m^2/z^2$ distributions, $^4$He are clearly separated from $^3$He, for which $m^2/z^2$ is 2.0 GeV$^2/c^4$. The background (magenta) is coming from TOF mismatches, which is the case if a track in the TPC is associated with the wrong hit in the TOF detector, resulting in a wrong mass. To describe the background a data-driven approach with only one free parameter is used. The background is determined by selecting all tracks in the TPC outside a $3\ \sigma$ interval of the expected Bethe-Bloch curve for alpha particles and in addition outside a $3\ \sigma$ interval of the expected curve for the deuteron mass hypothesis, as alphas and deuterons have similar $m^2/z^2$. The background is then scaled to the height of the $^4$He histogram by normalizing to the sideband on the right of the $^4$He peak between 4.4 and 6 GeV$^2/c^4$ and subtracted. This is done in each $p_T$ interval separately except for the first $p_T$ interval of the $^4\overline{\text{He}}$ (2–3 GeV/c), where there is no background. The $^3$He contribution under the $^4$He peak is described by an exponential fit to the tail of the $^3$He peak (blue dashed line). This is done in one $p_T$ interval from 3 to 6 GeV/c and an (anti)$^3$He fraction (3% for $^3\overline{\text{He}}$ and 9% for $^3\text{He}$) is determined for particles and antiparticles separately, which is then subtracted in each $p_T$ interval individually. The (anti)alpha signal is counted in every $p_T$ interval between 3 and $4.2\ \text{GeV}^2/c^4$ due to the asymmetric shape of the signal in $m^2/z^2$.

The $^4\overline{\text{He}}$ raw yield is extracted in four $p_T$ intervals between 2 and 6 GeV/c. The $^4\text{He}$ raw yield is only extracted in three $p_T$ intervals between 3 and 6 GeV/c, due to the large contribution of knocked-out alphas from the detector material and the support structure at low $p_T$. For the statistical uncertainties of the data points the Poisson statistics is used.

## 2.3 Corrections to the spectra

The transverse-momentum spectra of the (anti)alphas are obtained by correcting the raw yields in the different $p_T$ intervals of the analysis for tracking efficiency and detector acceptance. This is done by using Monte Carlo events, simulated with the HIJING event generator [103]. As HIJING does not include
<figure><img src="image_2.png" /><figcaption>**Figure 1:** (Color online) $m^2/z^2$ distribution for $^4\overline{\text{He}}$ candidates (green). The background (magenta) is constructed by selecting all candidates outside the $^4\overline{\text{He}}$ TPC window of $3\sigma$ around the alpha mass hypothesis ($|n\sigma_{\text{TPC}}(^4\overline{\text{He}})| > 3$) and in addition outside the $3\sigma$ window around the deuteron mass hypothesis ($|n\sigma_{\text{TPC}}(\overline{\text{d}})| > 3$). The blue line is an exponential fit to the rise at lower masses originating from $^3\text{He}$ candidates.</figcaption></figure>

(anti)alphas, they are injected into the event with flat distributions in $p_T$ (between 0 and 10 GeV/c), azimuth (between 0 and $2\pi$), and rapidity ($|y| < 1$). The GEANT4 [104] transport code is used to propagate the generated particles through a full simulation of the ALICE detector setup. The combined acceptance×efficiency was determined for the (anti)alphas in the 0–10% centrality interval. As the nuclei are not produced with flat $p_T$ distribution, the acceptance×efficiency was weighted with a blast-wave shape applying an iterative method (see e.g. Ref. [52]), where the blast-wave parameters were taken from a fit to the (anti)alpha spectra.

### 3 Systematic uncertainties

To estimate the systematic uncertainties, different sources affecting the (anti)alpha measurement were studied, which are described in the following.

The first considered source of systematic uncertainty is related to possible imperfections in the description of the track reconstruction efficiency in the Monte Carlo simulations, which is usually estimated by varying the track selection criteria and by comparing the probability of attaching ITS hits to a TPC track (matching efficiency) in the data and in the simulation. Owing to the low number of counts of the (anti)alpha analysis the systematic variations of the track selection criteria were found to be not significant within the statistical uncertainties by applying the check proposed by Barlow [105]. Therefore, the method based on varying the selections could not be used and instead systematic uncertainties based on similar studies of identified charged particles were assigned, namely 5% for the TPC–ITS matching
efficiency for all $p_T$ intervals [106].

For the signal extraction an uncertainty of 6% was assumed, derived from the analyses of more abundantly produced nuclei, for which a similar method of yield extraction was used [39, 52]. In addition, the scaled background was shifted up and down by 30% and the $^3$He contribution was determined with different fit ranges of the exponential fit to the tail of the $^3$He in the $m^2/z^2$ distribution. This results in an uncertainty for the signal extraction between 6% and 22% for the $^{4}$He and between 9% and 14% for the $^4$He.

The limited knowledge of the interaction of (anti)nuclei with the detector material leads to another large contribution to the systematic uncertainties. The hadronic interaction cross section implemented in GEANT4 [104, 107–109] is used to determine the acceptance×efficiency. As there is no measurement of the $^{4}$He inelastic interaction cross section so far, an uncertainty of 7% is assumed, as done for the $^{4}$He measured in the Pb–Pb data sample at $\sqrt{s_{NN}}$ = 2.76 TeV [40]. For the alpha an uncertainty for the inelastic cross section of 4% is taken from a measurement of the AMS experiment [110].

The material budget of the ALICE apparatus employed in the MC simulation was varied by ± 4.5%, corresponding to the uncertainty of the ALICE material budget determination [96]. This results in an uncertainty on the (anti)alpha spectra of 2%.

The blast-wave weighting of the acceptance×efficiency only affects the first $p_T$ interval of the $^{4}$He spectrum and the uncertainty was determined to be 3%. This is half of the difference to the case when no blast-wave weighting is taken into account.

As there is a contribution of feed-down to the (anti)alphas from the decay of $^{4}_{\Lambda}H$ and $^{4}_{\Lambda}\overline{H}$, an additional uncertainty of 3% for particles and antiparticles in all $p_T$ intervals was taken into account, estimated from a Monte Carlo study where these hypernuclei have been injected.

In total, all these contributions result in a systematic uncertainty between 12% and 24% for $^{4}$He and between 12% and 16% for $^4$He.

Most of the systematic uncertainties are correlated between $^4$He and $^{4}$He. The uncorrelated contributions are the uncertainty coming from the inelastic interaction cross section as well as the uncertainties on the background subtraction and the (anti)$^3$He contribution, which are part of the signal extraction.

## 4 Results

The size of the data sample presented in this letter exceeds that of a previous measurement in Pb–Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV [40] by about a factor of five. This allows for the determination of the transverse-momentum spectra for alpha and antialpha, as shown in Fig. 2. In the case of the antialpha, this is the first ever measurement of the $p_T$ distribution. In the $p_T$ interval between 4 and 5 GeV/c there is a $2\sigma$ discrepancy between particle and antiparticle yields, relative to the combination of statistical and systematic uncertainties, while in the other $p_T$ intervals the alpha and antialpha yields are consistent within statistical uncertainties. The antialpha-to-alpha ratio is shown in the lower panel of Fig. 2, where the error bars represent the statistical uncertainties and the boxes represent the uncorrelated systematic uncertainties, as the correlated ones cancel. Both spectra were combined for further analysis by constructing the weighted average of the data points, where statistical and systematic uncertainties were considered.

The combined (anti)alpha $p_T$ spectrum was compared to those of other light-flavored hadrons [106] and nuclei [52], measured in central (0-10%) Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV, by performing a simultaneous blast-wave fit to all $p_T$ spectra (see Fig. 3, left). The fit range of $\pi$, K, p was restricted in the momentum range in order to minimize biases from resonance decays at low $p_T$ and from hard processes at high $p_T$. The fit is performed in the following $p_T$ intervals: 0.5–1 GeV/c for charged pions,
<figure><img src="image_3.png" /><figcaption>**Figure 2:** Measured transverse momentum distributions of $^4$He and $^{4\overline{He}}$ (upper panel). The vertical lines indicate the statistical uncertainties, while boxes represent the systematic ones. In the case that the statistical uncertainties would overlap the $^4$He points are a bit shifted on the x-axis. The lower panel shows the ratio between $^{4\overline{He}}$ and $^4$He with statistical and uncorrelated systematic uncertainties as the correlated systematic uncertainties cancel.</figcaption></figure>

0.2–1.5 GeV/c for charged kaons, and 0.3–3 GeV/c for (anti)protons. These regions are the same as in the previous publications that showed results for global blast-wave fits [39, 106, 111]. The spectra of antideuterons, antitritons, $^3$He, and alpha were fitted over the full measured $p_T$ range.

One should note, blast-wave fits are a simplified approach mimicking the hydrodynamics behind the radial expansion and have certain limitations, e.g. it is known that the temperature is particularly sensitive to the fit range and the used particle species. In particular, in blast-wave fits using the FastReso package [112, 113] the quality of the fits is rather good using a single temperature of about 150 MeV for chemical and kinetic freeze out and these fits do not show a dependence of the temperature on centrality [114]. This is possible in the FastReso approach because the feed-down from resonances is taken into account by the package. In addition, there are other approaches utilizing data from LHC that can describe the data in an extended blast-wave model approach with more parameters [115]. In any case, the standard (Boltzmann-Gibbs) blast-wave fit provides a simple and solid approach to compare the spectra of nuclei and lighter hadrons, which is the goal of the study presented here.

The fit results are shown in the left panel of Fig. 3 and the fit parameters are reported in Table 1 (Fit A). The freeze-out parameters, in particular $\langle\beta\rangle$ and $T_{kin}$, are consistent with those obtained in Pb–Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV [39]. The data-to-model ratios, shown in the bottom panel of Fig. 3 left, indicate that the spectra of nuclei are reasonably well described by the common fit within their uncertainties. This suggests that also relatively heavy compound objects like (anti)alpha nuclei participate in a common flow field.
<figure><img src="image_4.png" /><figcaption>**Figure 3:** (Color online) Combined blast-wave fit of all available light flavored hadron $p_T$ spectra including nuclei [52, 106] (left) and only p, $\bar{d}$, $\bar{t}$, $^{3}\text{He}$ and $^{4}\text{He}$ $p_T$ spectra (right) in Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV for 0–10% central events (upper panels). The lower panels show the ratio between each data point and the blast-wave model fit for each species.</figcaption></figure>

<table><caption>**Table 1:** Parameters obtained from the combined blast-wave fits (Fig. 3) to the $p_T$ spectra of different combinations of light-flavor hadrons and nuclei measured in central (0–10%) Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV. The uncertainty from the fits corresponds to the statistical uncertainty. Systematics, that have been evaluated by changing the fit strategy slightly, are of similar size as the statistical uncertainties. The last column shows the $\chi^2$ value and the corresponding number of degrees of freedom (ndf) for each fit.</caption><thead><tr><th></th><th>Fitted particles</th><th>⟨β⟩</th><th>β<sub>max</sub></th><th>T<sub>kin</sub> (MeV)</th><th>n</th><th>χ<sup>2</sup>/ndf</th></tr></thead><tbody><tr><td>Fit A</td><td>π,K,p,d,t,<sup>3</sup>He,<sup>4</sup>He</td><td>0.664 ± 0.002</td><td>0.873 ± 0.004</td><td>108 ± 2</td><td>0.63 ± 0.02</td><td>381.1 / 92</td></tr><tr><td>Fit B</td><td>p,d,t,<sup>3</sup>He,<sup>4</sup>He</td><td>0.670 ± 0.002</td><td>0.853 ± 0.004</td><td>132 ± 4</td><td>0.55 ± 0.02</td><td>176.5 / 64</td></tr><tr><td>Fit C</td><td>d,t,<sup>3</sup>He,<sup>4</sup>He</td><td>0.684 ± 0.003</td><td>0.863 ± 0.005</td><td>108 ± 6</td><td>0.52 ± 0.02</td><td>44.5 / 37</td></tr><tr><td>Fit D</td><td>π,K,p</td><td>0.664 ± 0.002</td><td>0.909 ± 0.003</td><td>85 ± 4</td><td>0.74 ± 0.01</td><td>113.0 / 54</td></tr></tbody></table>

The coalescence picture assumes that nuclei are formed at a late stage of the collision, i.e. at or after kinetic freeze-out. In this case, one may expect that the $p_T$ spectra of protons and (anti)nuclei exhibit a common temperature and velocity field that characterizes the source at or after the stage of nuclear cluster formation. To elucidate this further a blast-wave fit was performed, where only protons and (anti)nuclei are included (Fit B). The data points are well described by the common fit, as shown in Fig. 3 (right). Actually, the protons are well described over a larger range in Fit B (right panel of Fig. 3) than in Fit A. The fit parameters indicate a similar velocity field as in the case when $\pi$ and K are included in the fit (Fit A), but a significantly larger kinetic freeze-out temperature of $T_{kin}$ = (132 ± 4) MeV. In the context of final-state coalescence, this finding is unexpected. However, it matches the conjecture of statistical hadronization including formation of (anti)nuclei close to the phase boundary, without significant rescattering at later stages of the system evolution. Possible explanations for such a scenario in terms of pre-hadronic multi-quark states have been proposed in Ref. [60].

The result is challenged by a fit to only the (anti)nuclei (Fit C) which yields $T_{kin}$ = (108 ± 6) MeV, which is consistent within the uncertainties with the result of Fit A. This seems to be more in agreement with the expectation of the coalescence model, namely that the protons freeze out earlier as suggested by Fit B, i.e. at a higher temperature, and the nuclei are formed later from these protons and neutrons available for the coalescence process. A fit to only $\pi$, K, p (Fit D) results in $T_{kin}$ = (85 ± 4) MeV, indicating that
very low apparent kinetic freeze-out temperatures are driven by the lightest particles. It should be noted that lighter particles are more prone to contributions from resonance decays and hard scatterings over a wider $p_T$ range than heavier particles.

From the quality of the fits, i.e. the $\chi^2/ndf$ values given in Table 1, it seems like the separation into nuclei (Fit C) and light-flavored hadrons (Fit D) is best. Nevertheless, the temperature of the latter is lower than Fit C, so the coalescence picture is again questioned from this inconsistency between blast-wave results. Indeed, the temperatures extracted from the fits would imply that the protons used in the coalescence process freeze out later than the nuclei formed from them.

Clearly, these findings can not be used for any strong conclusion, in particular since the blast-wave model is only a simplified hydrodynamical picture that has certain limits as discussed above.

The rapidity densities $dN/dy$ are obtained by integration over the blast-wave function. To this end, a blast-wave fit was performed to the $p_T$ spectra of all particles except (anti)alpha. The resulting fit parameters are used to constrain the shape for (anti)alpha while the normalization is obtained by a fit to the (anti)alpha distributions. This procedure was applied separately for the alpha and antialpha $p_T$ distributions as well as to the combined spectrum. The derived rapidity densities are summarized in Table 2. The statistical uncertainties are those of the normalization from the fit, while the systematic uncertainties reflect the variation of $dN/dy$ if the data points are shifted by their systematic uncertainties. The results for alpha and antialpha are consistent within their uncertainties. Also reported are the SHM results obtained from a fit of all available hadron yields using a grand-canonical ensemble [58, 61, 116].

<table><caption>**Table 2:** Rapidity densities of $^4$He and $^{4}\overline{\text{He}}$ and their average, together with the statistical hadronization model predictions [58, 61, 116]. The experimental values are given in addition also the statistical (second value) and systematic uncertainties (third value).</caption><thead><tr><th>dN/dy (10<sup>-6</sup>):</th><th><sup>4</sup>He</th><th><sup>4</sup>He</th><th>(<sup>4</sup>He+<sup>4</sup>He)/2</th></tr></thead><tbody><tr><td>Experiment</td><td>(1.30 ± 0.28 ± 0.18)</td><td>(0.83 ± 0.22 ± 0.12)</td><td>(1.00 ± 0.19 ± 0.10)</td></tr><tr><td>SHM (T<sub>ch</sub> = 156 MeV)</td><td>0.945</td><td>0.949</td><td>0.947</td></tr></tbody></table>

The presented (anti)alpha transverse-momentum spectra allow for the first time a determination of the coalescence parameter $B_4$ at LHC energies. To this end, Eq. 1 was employed where the proton $p_T$ distributions were taken from Ref. [106] after averaging the measurements in the 0–5% and 5–10% centrality intervals. The $B_4$ values shown in Fig. 4 exhibit an increasing trend with $p_T/A$, which is the transverse momentum per nucleon. This trend is similar to earlier measurements in heavy-ion collisions for lighter nuclei [39, 52]. The results in Fig. 4 are compared to predictions from coalescence [87] and from statistical hadronization models. For the latter, the (anti)alpha and proton yields ($dN/dy$) are calculated for a chemical freeze-out temperature of $T_{ch}$ = 156 MeV and the shapes of the transverse momentum distributions are taken from the blast-wave fit. While SHM, combined with the spectral shape derived from the blast-wave fit, slightly underpredicts the data, the coalescence prediction is about one order of magnitude below the data in all $p_T$ intervals.

The ratio of alpha to proton $dN/dy$ in central Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV is shown in Fig. 5 as a function of the pseudorapidity density of charged particles produced at midrapidity in the collision, $\langle dN_{ch}/d\eta \rangle_{|\eta_{lab}|<0.5}$. In addition, the ratio from the 10% most central Pb–Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV [40] and the upper limit in p–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV [117] are depicted. The new result agrees well with the measurement at lower energy [40]. Furthermore, predictions from the canonical statistical model (CSM) for $T_{ch}$ = 155 MeV and three different values of the correlation volume $V_C$ are displayed [61]. The curves differ at low $\langle dN_{ch}/d\eta \rangle$, corresponding to the multiplicity of charged particles produced in small collision systems, but coincide in central Pb–Pb collisions where they are consistent within uncertainties with the measurements. Also shown are different calculations from coalescence models. The “box coalescence” (using a maximal difference in coordinate space and momentum for the coalescing partners) implemented in the UrQMD [74] model, indicated by the magenta band (represent-
<figure><img src="image_5.png" /><figcaption>**Figure 4:** (Color online) The coalescence parameter $B_4$ as a function of $p_T/A$, calculated from the averaged $^4$He and $\overline{^4}$He spectra and the protons from [106]. Statistical uncertainties are indicated by the vertical lines and the boxes correspond to the systematic uncertainties. The blue dashed line and the full black line indicate the values for the SHM combined with blast-wave $p_T$ shapes and the coalescence predictions from Refs. [86, 87], respectively.</figcaption></figure>

ing the statistical uncertainty of the prediction), shows a non-monotonic behavior that can be explained by absorption processes in the hadronic phase of Pb–Pb collisions [118]. In central Pb–Pb collisions, the UrQMD hybrid model underestimates the data by about a factor of three. Finally, calculations of an analytical coalescence approach are presented, in which the internal structure of the alpha nucleus is taken into account [119]. The assumption of a structureless alpha particle (p-p-n-n) and calculations considering a d-p-n, d-d, $^3$H-p or $^3$He-n substructures are compared. All analytical coalescence curves coincide for large system sizes where they underestimate the data by about a factor of three. This might be connected to the fact that the binding energy of the alpha is not taken into account in the model. Neglecting the binding energy might be working well for the $A=2$ and $A=3$ nuclei, but not for the alpha, since it is much tighter bound compared to lighter nuclei ($E_B = 2.2$ MeV for the deuteron, whereas the alpha is bound by 28.3 MeV). Interestingly, the presented data even allows for the sum of contributions from coalescence and statistical hadronization predictions. Since these processes are not mutually exclusive one could actually imagine it as interplay of these two production mechanisms.

# 5 Conclusion

New results on (anti)alpha production in central Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV were presented, including the first differential measurement of the antialpha transverse-momentum distribution. Predictions from statistical hadronization models are compatible with the measured coalescence parameters $B_4$ and the (anti)alpha-to-proton yield ratio. In contrast, different implementations of the coalescence model underestimate the data significantly. These findings for the production of (anti)alpha are different from
<figure><img src="image_6.png" /><figcaption>**Figure 5:** (Color online) $^4$He/p ratios for the measured data points as a function of charged-particle multiplicity $\langle dN_{ch}/d\eta \rangle_{|\eta_{lab}|<0.5}$ compared to model predictions. For comparison the result from the 10% most central Pb–Pb collisions at $\sqrt{s_{NN}} = 2.76$ TeV [40] and the upper limit at 90% CL from p–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV [117] is also shown. The thermal model curves are from the CSM [61]. For the coalescence model two different approaches are displayed: analytical and UrQMD hybrid coalescence [118, 119]. The analytical coalescence is shown for five different substructures.</figcaption></figure>

the results for A = 3 nuclei [52], where both classes of models differ only by about 30% and the data tend to lie in between.

A blast-wave analysis of the $p_T$ distributions together with other hadrons and light nuclei from central Pb–Pb collisions suggests that also relatively heavy compound objects like (anti)alpha nuclei participate in a common flow field. On the other hand, it is remarkable that a blast-wave fit including only protons and light nuclei up to $^4$He results in a kinetic freeze-out temperature that is rather close to the chemical freeze-out temperature obtained from statistical hadronization models. Note that one should be careful with any strong conclusion from the blast-wave fit, since it has certain limitations. Nevertheless, this result does not agree with naïve expectations based on the coalescence picture, but is in line with a scenario where the yields of light nuclei in central Pb–Pb collisions are dominated by thermal production close to the QCD phase boundary. It should be noted that thermal production and coalescence are not mutually exclusive processes and that the data presented here are even compatible with the sum of contributions from coalescence and statistical hadronization, suggesting a possible interplay of these two production mechanisms.

The recent upgrades of the ALICE detector will enable the collection of substantially larger data samples
during LHC Runs 3 and 4. This will allow for more differential measurements of (anti)alpha production, enabling in particular a systematic study of its dependence on multiplicity and collision system size. The large sensitivity of the (anti)alpha yield to the different production scenarios may help to shed light on the interplay between coalescence and thermal production and a possible transition between them at intermediate system sizes.

## Acknowledgements

We thank J. Steinheimer and K.-J. Sun for useful discussions and for providing their predictions.

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrasstructures 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 Founda-
tion (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; 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 127, D. Adamová 86, G. Aglieri Rinella 33, M. Agnello 30, N. Agrawal 52, Z. Ahammed 135,
S. Ahmad 16, S.U. Ahn 72, I. Ahuja 38, A. Akindinov 141, M. Al-Turany 97, D. Aleksandrov 141,
B. Alessandro 57, H.M. Alfanda 6, R. Alfaro Molina 68, B. Ali 16, A. Alici 26,
N. Alizadehvandchali 116, A. Alkin 33, J. Alme 21, G. Alocco 53, T. Alt 65, A.R. Altamura 51,
I. Altsybeev 95, J.R. Alvarado 45, M.N. Anaam 6, C. Andrei 46, N. Andreou 115, A. Andronic 126,
E. Andronov 141, V. Anguelov 94, F. Antinori 55, P. Antonioli 52, N. Apadula 74, L. Aphecetche 103,
H. Appelshäuser 65, C. Arata 73, S. Arcelli 26, M. Aresti 23, R. Arnaldi 57, J.G.M.C.A. Arneiro 110,
I.C. Arsene 20, M. Arslandok 138, A. Augustinus 33, R. Averbeck 97, M.D. Azmi 16, H. Baba 124,
A. Badalà 54, J. Bae 104, Y.W. Baek 41, X. Bai 120, R. Bailhache 65, Y. Bailung 49, R. Bala 91,
A. Balbino 30, A. Baldisseri 130, B. Balis 2, D. Banerjee 4, Z. Banoo 91, F. Barile 32, L. Barioglio 95,
M. Barlou 78, B. Barman 42, G.G. Barnaföldi 47, L.S. Barnby 85, E. Barreau 103, V. Barret 127, L. Barreto 110,
C. Bartels 119, K. Barth 33, E. Bartsch 65, N. Bastid 127, S. Basu 75, G. Batigne 103, D. Battistini 95,
B. Batyunya 142, D. Bauri 48, J.L. Bazo Alba 101, I.G. Bearden 83, C. Beattie 138, P. Becht 97,
D. Behera 49, I. Belikov 129, A.D.C. Bell Hechavarria 126, F. Bellini 26, R. Bellwied 116,
S. Belokurova 141, L.G.E. Beltran 109, Y.A.V. Beltran 45, G. Bencedi 47, S. Beole 25, Y. Berdnikov 141,
A. Berdnikova 94, L. Bergmann 94, M.G. Besoiu 64, L. Betev 33, P.P. Bhaduri 135, A. Bhasin 91,
M.A. Bhat 4, B. Bhattacharjee 42, L. Bianchi 25, N. Bianchi 50, J. Bielčík 36, J. Bielčíková 86,
A.P. Bigot 129, A. Bilandzic 95, G. Biro 47, S. Biswas 4, N. Bize 103, J.T. Blair 108, D. Blau 141,
M.B. Blidaru 97, N. Bluhme 39, C. Blume 65, G. Boca 22,56, F. Bock 87, T. Bodova 21, S. Boi 23,
J. Bok 17, L. Boldizsár 47, M. Bombara 38, P.M. Bond 33, G. Bonomi 134,56, H. Borel 130,
A. Borissov 141, A.G. Borquez Carcamo 94, H. Bossi 138, E. Botta 25, Y.E.M. Bouziani 65,
L. Bratrud 65, P. Braun-Munzinger 97, M. Bregant 110, M. Broz 36, G.E. Bruno 96,32, M.D. Buckland 24,
D. Budnikov 141, H. Buesching 65, S. Bufalino 30, P. Buhler 102, N. Burmasov 141, Z. Buthelezi 69,123,
A. Bylinkin 21, S.A. Bysiak 107, J.C. Cabanillas Noris 109, M. Cai 6, H. Caines 138, A. Caliva 29, E. Calvo
Villar 101, J.M.M. Camacho 109, P. Camerini 24, F.D.M. Canedo 110, S.L. Cantway 138, M. Carabas 113,
A.A. Carballo 33, F. Carnesecchi 33, R. Caron 128, L.A.D. Carvalho 110, J. Castillo Castellanos 130,
F. Catalano 33,25, C. Ceballos Sanchez 142, I. Chakaberia 74, P. Chakraborty 48, S. Chandra 135,
S. Chapeland 33, M. Chartier 119, S. Chattopadhyay 135, S. Chattopadhyay 99, T. Cheng 97,6,
C. Cheshkov 128, B. Cheynis 128, V. Chibante Barroso 33, D.D. Chinellato 111, E.S. Chizzali 11,95,
J. Cho 59, S. Cho 59, P. Chochula 33, D. Choudhury 42, P. Christakoglou 84, C.H. Christensen 83,
P. Christiansen 75, T. Chujo 125, M. Ciacco 30, C. Cicalo 53, M.R. Ciupek 97, G. Clai III,52, F. Colamaria 51,
J.S. Colburn 100, D. Colella 96,32, M. Colocci 26, M. Concas 14V,33, G. Conesa Balbastre 73, Z. Conesa del
Valle 131, G. Contin 24, J.G. Contreras 36, M.L. Coquet 130, P. Cortese 133,57, M.R. Cosentino 112,
F. Costa 33, S. Costanza 22,56, C. Cot 131, J. Crkovská 94, P. Crochet 127, R. Cruz-Torres 74, P. Cui 6,
A. Dainese 55, M.C. Danisch 94, A. Danu 64, P. Das 80, P. Das 4, S. Das 4, A.R. Dash 126,
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 134, R. Del Grande 95, L. Dello Stritto 33,29,
W. Deng 6, P. Dhankher 19, D. Di Bari 32, A. Di Mauro 33, B. Diab 130, R.A. Diaz 142,7, T. Dietel 114,
Y. Ding 6, J. Ditzel 65, R. Divià 33, D.U. Dixit 19, Ø. Djuvsland 21, U. Dmitrieva 141, A. Dobrin 64,
B. Dönigus 65, J.M. Dubinski 136, A. Dubla 97, S. Dudi 90, P. Dupieux 127, M. Durkac 106,
N. Dzalaiova 13, T.M. Eder 126, R.J. Ehlers 74, F. Eisenhut 65, R. Ejima 92, D. Elia 51, B. Erazmus 103,
F. Ercolessi 26, B. Espagnon 131, G. Eulisse 33, D. Evans 100, S. Evdokimov 141, L. Fabbietti 95,
M. Faggin 28, J. Faivre 73, F. Fan 6, W. Fan 74, A. Fantoni 50, M. Fasel 87, A. Feliciello 57,
G. Feofilov 141, A. Fernández Téllez 45, L. Ferrandi 110, M.B. Ferrer 33, A. Ferrero 130, C. Ferrero 57,
A. Ferretti 25, V.J.G. Feuillard 94, V. Filova 36, D. Finogeev 141, F.M. Fionda 53, E. Flatland 33,
F. Flor 116, A.N. Flores 108, S. Foertsch 69, I. Fokin 94, S. Fokin 141, E. Fragiacomo 58, E. Frajna 47,
U. Fuchs 33, N. Funicello 29, C. Furget 73, A. Furs 141, T. Fusayasu 98, J.J. Gaardhøje 83,
M. Gagliardi 25, A.M. Gago 101, T. Gahlaut 48, C.D. Galvan 109, D.R. Gangadharan 116, P. Ganoti 78,
C. Garabatos 97, A.T. Garcia 131, T. García Chávez 45, E. Garcia-Solis 9, C. Gargiulo 33, P. Gasik 97,
A. Gautam 118, M.B. Gay Ducati 67, M. Germain 103, A. Ghimouz 125, C. Ghosh 135, M. Giacalone 52,
G. Gioachin 30, P. Giubellino 97,57, P. Giubilato 28, A.M.C. Glaenzer 130, P. Glässel 94, E. Glimos 122,
D.J.Q. Goh 76, V. Gonzalez 137, P. Gordeev 141, M. Gorgon 2, K. Goswami 49, S. Gotovac 34,
V. Grabski 68, L.K. Graczykowski 136, E. Grecka 86, A. Grelli 60, C. Grigoras 33, V. Grigoriev 141,
S. Grigoryan 142,1, F. Grosa 33, J.F. Grosse-Oetringhaus 33, R. Grosso 97, D. Grund 36, N.A. Grunwald 94,
G.G. Guardiano 111, R. Guernane 73, M. Guilbaud 103, K. Gulbrandsen 83, T. Gündem 65, T. Gunji 124,
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Koryciak,² A. Kotliarov,⁸⁶ N. Kovacic,⁸⁹ V. Kovalenko,¹⁴¹ M. Kowalski,¹⁰⁷ V. Kozhuharov,³⁷ I. Králik,⁶¹ A. Kravčáková,³⁸ L. Krcal,³³,³⁹ M. Krivda,¹⁰⁰,⁶¹ F. Krizek,⁸⁶ K. Krizkova Gajdosova,³³ M. Kroesen,⁹⁴ M. Krüger,⁶⁵ D.M. Krupova,³⁶ E. Kryshen,¹⁴¹ V. Kučera,⁵⁹ C. Kuhn,¹²⁹ P.G. Kuijer,⁸⁴ T. Kumaoka,¹²⁵ D. Kumar,¹³⁵ L. Kumar,⁹⁰ N. Kumar,⁹⁰ S. Kumar,³² S. Kundu,³³ P. Kurashvili,⁷⁹ A. Kurepin,¹⁴¹ A.B. Kurepin,¹⁴¹ A. Kuryakin,¹⁴¹ S. Kushpil,⁸⁶ V. Kuskov,¹⁴¹ M. Kutyla,¹³⁶ M.J. Kweon,⁵⁹ Y. Kwon,¹³⁹ S.L. La Pointe,³⁹ P. La Rocca,²⁷ A. Lakrathok,¹⁰⁵ M. Lamanna,³³ A.R. Landou,⁷³ R. Langoy,¹²¹ P. Larionov,³³ E. Laudi,³³ L. Lautner,³³,⁹⁵ R. Lavicka,¹⁰² R. Lea,¹³⁴,⁵⁶ H. Lee,¹⁰⁴ I. Legrand,⁴⁶ G. Legras,¹²⁶ J. Lehrbach,³⁹ T.M. Lelek,² R.C. Lemmon,⁸⁵ I. León Monzón,¹⁰⁹ M.M. Lesch,⁹⁵ E.D. Lesser,¹⁹ P. Lévai,⁴⁷ X. Li,¹⁰ B.E. Liang-gilman,¹⁹ J. Lien,¹²¹ R. Lietava,¹⁰⁰ I. Likmeta,¹¹⁶ B. Lim,²⁵ S.H. Lim,¹⁷ V. Lindenstruth,³⁹ A. Lindner,⁴⁶ C. Lippmann,⁹⁷ D.H. Liu,⁶ J. Liu,¹¹⁹ G.S.S. Liveraro,¹¹¹ I.M. Lofnes,²¹ C. Loizides,⁸⁷ S. Lokos,¹⁰⁷ J. Lomker,⁶⁰ P. Loncar,³⁴ X. Lopez,¹²⁷ E. López Torres,⁷ P. Lu,⁹⁷,¹²⁰ F.V. Lugo,⁶⁸ J.R. Luhder,¹²⁶ M. Lunardon,²⁸ G. Luparello,⁵⁸ Y.G. Ma,⁴⁰ M. Mager,³³ A. Maire,¹²⁹ E.M. Majerz,² M.V. Makariev,³⁷ M. Malaev,¹⁴¹ G. Malfattore,²⁶ N.M. Malik,⁹¹ Q.W. Malik,²⁰ S.K. Malik,⁹¹ L. Malinina,¹, VII, ¹⁴² D. Mallick,¹³¹,⁸⁰ N. Mallick,⁴⁹ G. Mandaglio,³¹,⁵⁴ S.K. Mandal,⁷⁹ V. Manko,¹⁴¹ F. Manso,¹²⁷ V. Manzari,⁵¹ Y. Mao,⁶ R.W. Marcjan,² G.V. Margagliotti,²⁴ A. Margotti,⁵² A. Marín,⁹⁷ C. Markert,¹⁰⁸ P. Martinengo,³³ M.I. Martínez,⁴⁵ G. Martínez García,¹⁰³ M.P.P. Martins,¹¹⁰ S. Masciocchi,⁹⁷ M. Masera,²⁵ A. Masoni,⁵³ L. Massacrier,¹³¹ O. Massen,⁶⁰ A. Mastroserio,¹³²,⁵¹ O. Matonoha,⁷⁵ S. Mattiazzo,²⁸ A. Matyja,¹⁰⁷ C. Mayer,¹⁰⁷ A.L. Mazuecos,³³ F. Mazzaschi,²⁵ M. Mazzilli,³³ J.E. Mdhluli,¹²³ Y. Melikyan,⁴⁴ A. Menchaca-Rocha,⁶⁸ J.E.M. Mendez,⁶⁶ E. Meninno,¹⁰² A.S. Menon,¹¹⁶ M. Meres,¹³ Y. Miałe,¹²⁵ L. Micheletti,³³ D.L. Mihaylov,⁹⁵ K. Mikhaylov,¹⁴²,¹⁴¹ D. Miśkowiec,⁹⁷ A. Modak,⁴ B. Mohanty,⁸⁰ M. Mohisin Khan,⁴ V, ¹⁶ M.A. Molander,⁴⁴ S. Monira,¹³⁶ C. Mordasini,¹¹⁷ D.A. Moreira De Godoy,¹²⁶ I. Morozov,¹⁴¹ A. Morsch,³³ T. Mrnjavac,³³ V. Muccifora,⁵⁰ S. Muhuri,¹³⁵ J.D. Mulligan,⁷⁴ A. Mulliri,²³ M.G. Munhoz,¹¹⁰ R.H. Munzer,⁶⁵ H. Murakami,¹²⁴ S. Murray,¹¹⁴ L. Musa,³³ J. Musinsky,⁶¹ J.W. Myrcha,¹³⁶ B. Naik,¹²³ A.I. Nambrath,¹⁹ B.K. Nandi,⁴⁸ R. Nania,⁵² E. Nappi,⁵¹ A.F. Nassirpour,¹⁸ A. Nath,⁹⁴ C. Nattrass,¹²² M.N. Naydenov,³⁷ A. Neagu,²⁰ A. Negru,¹¹³ E. Nekrasova,¹⁴¹ L. Nellen,⁶⁶ R. Nepeivoda,⁷⁵ S. Nese,²⁰ G. Neskovic,³⁹ N. Nicassio,⁵¹ B.S. Nielsen,⁸³ E.G. Nielsen,⁸³ S. Nikolaev,¹⁴¹ S. Nikulin,¹⁴¹ V. Nikulin,¹⁴¹ F. Noferini,⁵² S. Noh,¹² P. Nomokonov,¹⁴² J. Norman,¹¹⁹ N. Novitzky,⁸⁷ P. Nowakowski,¹³⁶ A. Nyanin,¹⁴¹ J. Nystrand,²¹ S. Oh,¹⁸ A. Ohlson,⁷⁵ V.A. Okorokov,¹⁴¹ J. Oleniacz,¹³⁶ A. Onnerstad,¹¹⁷ C. Oppedisano,⁵⁷ A. Ortiz Velasquez,⁶⁶ J. Otwinowski,¹⁰⁷ M. Oya,⁹² K. Oyama,⁷⁶ Y. Pachmayer,⁹⁴ S. Padhan,⁴⁸ D. Pagano,¹³⁴,⁵⁶ G. Paić,⁶⁶ S. Paisano-Guzmán,⁴⁵ A. Palasciano,⁵¹ S. Panebianco,¹³⁰ H. Park,¹²⁵ H. Park,¹⁰⁴ J. Park,⁵⁹ J.E. Parkkila,³³ Y. Patley,⁴⁸ B. Paul,²³ M.M.D.M. Paulino,¹¹⁰
H. Pei 6, T. Peitzmann 60, X. Peng 11, M. Pennisi 25, S. Perciballi 25, D. Peresunko 141, G.M. Perez 7,
Y. Pestov 141, V. Petrov 141, M. Petrovici 46, R.P. Pezzi 103,67, S. Piano 58, M. Pikna 13, P. Pillot 103,
O. Pinazza 52,33, L. Pinsky116, C. Pinto 95, S. Pisano 50, M. Płoskoń 74, M. Planinic89, F. Pliquett65,
M.G. Poghosyan 87, B. Polichtchouk 141, S. Politano 30, N. Poljak 89, A. Pop 46,
S. Porteboeuf-Houssais 127, V. Pozdniakov 142, I.Y. Pozos 45, K.K. Pradhan 49, S.K. Prasad 4,
S. Prasad 49, R. Preghenella 52, F. Prino 57, C.A. Pruneau 137, I. Pshenichnov 141, M. Puccio 33,
S. Pucillo 25, Z. Pugelova106, S. Qiu 84, L. Quaglia 25, S. Ragoni 15, A. Rai 138,
A. Rakotozafindrabe 130, L. Ramello 133,57, F. Rami 129, T.A. Rancien73, M. Rasa 27, S.S. Räsänen 44,
R. Rath 52, M.P. Rauch 21, I. Ravasenga 33, K.F. Read 87,122, C. Reckziegel 112, A.R. Redelbach 39,
K. Redlich 16,79, C.A. Reetz 97, H.D. Regules-Medel45, A. Rehman21, F. Reidt 33, H.A. Reme-Ness 35,
Z. Rescakova38, K. Reygers 94, A. Riabov 141, V. Riabov 141, R. Ricci 29, M. Richter 20,
A.A. Riedel 95, W. Riegler 33, A.G. Riffero 25, C. Ristea 64, M.V. Rodriguez 33, M. Rodríguez
Cahuantzi 45, S.A. Rodríguez Ramírez45, K. Røed 20, R. Rogalev 141, E. Rogochaya 142,
T.S. Rogoschinski 65, D. Rohr 33, D. Röhrich 21, P.F. Rojas45, S. Rojas Torres 36, P.S. Rokita 136,
G. Romanenko 26, F. Ronchetti 50, A. Rosano 31,54, E.D. Rosas66, K. Roslon 136, A. Rossi 55,
A. Roy 49, S. Roy 48, N. Rubini 26, D. Ruggiano 136, R. Rui 24, P.G. Russek 2, R. Russo 84,
A. Rustamov 81, E. Ryabinkin 141, Y. Ryabov 141, A. Rybicki 107, H. Rytkonen 117, J. Ryu 17,
W. Rzesa 136, O.A.M. Saarimaki 44, S. Sadhu 32, S. Sadovsky 141, J. Saetre 21, K. Šafařík 36, P. Saha42,
S.K. Saha 4, S. Saha 80, B. Sahoo 48, B. Sahoo 49, R. Sahoo 49, S. Sahoo62, D. Sahu 49, P.K. Sahu 62,
J. Saini 135, K. Sajdakova38, S. Sakai 125, M.P. Salvan 97, S. Sambyal 91, D. Samitz 102, I. Sanna 33,95,
T.B. Saramela110, D. Sarkar 83, P. Sarma 42, V. Sarritzu 23, V.M. Sarti 95, M.H.P. Sas 33, S. Sawan80,
E. Scapparone 52, J. Schambach 87, H.S. Scheid 65, C. Schiaua 46, R. Schicker 94, F. Schlepper 94,
A. Schmah97, C. Schmidt 97, H.R. Schmidt93, M.O. Schmidt 33, M. Schmidt93, N.V. Schmidt 87,
A.R. Schmier 122, R. Schotter 129, A. Schröter 39, J. Schukraft 33, K. Schweda 97, G. Scioli 26,
E. Scomparin 57, J.E. Seger 15, Y. Sekiguchi124, D. Sekihata 124, M. Selina 84, I. Selyuzhenkov 97,
S. Senyukov 129, J.J. Seo 94, D. Serebryakov 141, L. Serkin 66, L. Šerkšnytė 95, A. Sevcenco 64,
T.J. Shaba 69, A. Shabetai 103, R. Shahoyan33, A. Shangaraev 141, B. Sharma 91, D. Sharma 48,
H. Sharma 55, M. Sharma 91, S. Sharma 76, S. Sharma 91, U. Sharma 91, A. Shatat 131, O. Sheibani116,
K. Shigaki 92, M. Shimomura77, J. Shin12, S. Shirinkin 141, Q. Shou 40, Y. Sibiriak 141, S. Siddhanta 53,
T. Siemiarczuk 79, T.F. Silva 110, D. Silvermyr 75, T. Simantathammakul105, R. Simeonov 37, B. Singh91,
B. Singh 95, K. Singh 49, R. Singh 80, R. Singh 91, R. Singh 49, S. Singh 16, V.K. Singh 135,
V. Singhal 135, T. Sinha 99, B. Sitar 13, M. Sitta 133,57, T.B. Skaali20, G. Skorodumovs 94,
M. Slupecki 44, N. Smirnov 138, R.J.M. Snellings 60, E.H. Solheim 20, J. Song 17, C. Sonnabend 33,97,
J.M. Sonneveld 84, F. Soramel 28, A.B. Soto-hernandez 88, R. Spijkers 84, I. Sputowska 107, J. Staa 75,
J. Stachel 94, I. Stan 64, P.J. Steffanic 122, S.F. Stiefelmaier 94, D. Stocco 103, I. Storehaug 20,
P. Stratmann 126, S. Strazzi 26, A. Sturniolo 31,54, C.P. Stylianidis84, A.A.P. Suaide 110, C. Suire 131,
M. Sukhanov 141, M. Suljic 33, R. Sultanov 141, V. Sumberia 91, S. Sumowidagdo 82, I. Szarka 13,
M. Szymkowski 136, S.F. Taghavi 95, G. Taillepied 97, J. Takahashi 111, G.J. Tambave 80, S. Tang 6,
Z. Tang 120, J.D. Tapia Takaki 118, N. Tapus113, L.A. Tarasovicova 126, M.G. Tarzila 46, G.F. Tassielli 32,
A. Tauro 33, G. Tejeda Muñoz 45, A. Telesca 33, L. Terlizzi 25, C. Terrevoli 116, S. Thakur 4,
D. Thomas 108, A. Tikhonov 141, N. Tiltmann 126, A.R. Timmins 116, M. Tkacik106, T. Tkacik 106,
A. Toia 65, R. Tokumoto92, K. Tomohiro92, N. Topilskaya 141, M. Toppi 50, T. Tork 131, P.V. Torres66,
V.V. Torres 103, A.G. Torres Ramos 32, A. Trifiró 31,54, A.S. Triolo 33,31,54, S. Tripathy 52,
T. Tripathy 48, S. Trogolo 33, V. Trubnikov 3, W.H. Trzaska 117, T.P. Trzcinski 136, A. Tumkin 141,
R. Turrisi 55, T.S. Tveter 20, K. Ullaland 21, B. Ulukutlu 95, A. Uras 128, M. Urioni 134, G.L. Usai 23,
M. Vala38, N. Valle 22, L.V.R. van Doremalen60, M. van Leeuwen 84, C.A. van Veen 94, R.J.G. van
Weelden 84, P. Vande Vyvre 33, D. Varga 47, Z. Varga 47, M. Vasileiou 78, A. Vasiliev 141, O. Vázquez
Doce 50, O. Vazquez Rueda 116, V. Vechernin 141, E. Vercellin 25, S. Vergara Limón45, R. Verma48,
L. Vermunt 97, R. Vértesi 47, M. Verweij 60, L. Vickovic34, Z. Vilakazi123, O. Villalobos Baillie 100,
A. Villani 24, A. Vinogradov 141, T. Virgili 29, M.M.O. Virta 117, V. Vislavicius75, A. Vodopyanov 142,
B. Volkel 33, M.A. Völkl 94, S.A. Voloshin 137, G. Volpe 32, B. von Haller 33, I. Vorobyev 33,
N. Vozniuk 141, J. Vrláková 38, J. Wan40, C. Wang 40, D. Wang40, Y. Wang 40, Y. Wang 6,
A. Wegrzynek 33, F.T. Weiglhofer39, S.C. Wenzel 33, J.P. Wessels 126, J. Wiechula 65, J. Wikne 20,
G. Wilk 79, J. Wilkinson 97, G.A. Willems 126, B. Windelband 94, M. Winn 130, J.R. Wright 108,
W. Wu40, Y. Wu 120, R. Xu 6, A. Yadav 43, A.K. Yadav 135, Y. Yamaguchi 92, S. Yang21, S. Yano 92,
E.R. Yeats19, Z. Yin 6, I.-K. Yoo 17, J.H. Yoon 59, H. Yu12, S. Yuan21, A. Yuncu 94, V. Zaccolo 24,
C. Zampolli e$^{33}$, F. Zanone e$^{94}$, N. Zardoshti e$^{33}$, A. Zarochentsev e$^{141}$, P. Závada e$^{63}$, N. Zaviyalov$^{141}$, M. Zhalov e$^{141}$, B. Zhang e$^{6}$, C. Zhang e$^{130}$, L. Zhang e$^{40}$, S. Zhang e$^{40}$, X. Zhang e$^{6}$, Y. Zhang$^{120}$, Z. Zhang e$^{6}$, M. Zhao e$^{10}$, V. Zherebchevskii e$^{141}$, Y. Zhi$^{10}$, C. Zhong$^{40}$, D. Zhou e$^{6}$, Y. Zhou e$^{83}$, J. Zhu e$^{55,6}$, Y. Zhu$^{6}$, S.C. Zugravel e$^{57}$, N. Zurlo e$^{134,56}$

## Affiliation Notes

¹ Deceased

II Also at: Max-Planck-Institut fur Physik, Munich, Germany

III Also at: Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy

IV Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy

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 Krakow, 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 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

74 Lawrence Berkeley National Laboratory, Berkeley, California, United States

75 Lund University Department of Physics, Division of Particle Physics, Lund, Sweden

76 Nagasaki Institute of Applied Science, Nagasaki, Japan

77 Nara Women's University (NWU), Nara, Japan

78 National and Kapodistrian University of Athens, School of Science, Department of Physics, Athens, Greece

79 National Centre for Nuclear Research, Warsaw, Poland

80 National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India

81 National Nuclear Research Center, Baku, Azerbaijan

82 National Research and Innovation Agency - BRIN, Jakarta, Indonesia

83 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

84 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

85 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom

86 Nuclear Physics Institute of the Czech Academy of Sciences, Husinec-Řež, Czech Republic

87 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
88 Ohio State University, Columbus, Ohio, United States

89 Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia

90 Physics Department, Panjab University, Chandigarh, India

91 Physics Department, University of Jammu, Jammu, India

92 Physics Program and International Institute for Sustainability with Knotted Chiral Meta Matter (SKCM2),
Hiroshima University, Hiroshima, Japan

93 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany

94 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

95 Physik Department, Technische Universität München, Munich, Germany

96 Politecnico di Bari and Sezione INFN, Bari, Italy

97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung
GmbH, Darmstadt, Germany

98 Saga University, Saga, Japan

99 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India

100 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom

101 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru

102 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

103 SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France

104 Sungkyunkwan University, Suwon City, Republic of Korea

105 Suranaree University of Technology, Nakhon Ratchasima, Thailand

106 Technical University of Košice, Košice, Slovak Republic

107 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland

108 The University of Texas at Austin, Austin, Texas, United States

109 Universidad Autónoma de Sinaloa, Culiacán, Mexico

110 Universidade de São Paulo (USP), São Paulo, Brazil

111 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

112 Universidade Federal do ABC, Santo Andre, Brazil

113 Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, Bucharest, Romania

114 University of Cape Town, Cape Town, South Africa

115 University of Derby, Derby, United Kingdom

116 University of Houston, Houston, Texas, United States

117 University of Jyväskylä, Jyväskylä, Finland

118 University of Kansas, Lawrence, Kansas, United States

119 University of Liverpool, Liverpool, United Kingdom

120 University of Science and Technology of China, Hefei, China

121 University of South-Eastern Norway, Kongsberg, Norway

122 University of Tennessee, Knoxville, Tennessee, United States

123 University of the Witwatersrand, Johannesburg, South Africa

124 University of Tokyo, Tokyo, Japan

125 University of Tsukuba, Tsukuba, Japan

126 Universität Münster, Institut für Kernphysik, Münster, Germany

127 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

128 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, Lyon, France

129 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France

130 Université Paris-Saclay, Centre d'Etudes de Saclay (CEA), IRFU, Département de Physique Nucléaire (DPhN),
Saclay, France

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

132 Università degli Studi di Foggia, Foggia, Italy

133 Università del Piemonte Orientale, Vercelli, Italy

134 Università di Brescia, Brescia, Italy

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

136 Warsaw University of Technology, Warsaw, Poland

137 Wayne State University, Detroit, Michigan, United States

138 Yale University, New Haven, Connecticut, United States

139 Yonsei University, Seoul, Republic of Korea

140 Zentrum für Technologie und Transfer (ZTT), Worms, Germany
<footnote n="141">141 Affiliated with an institute covered by a cooperation agreement with CERN</footnote>

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