2021 232 5 November

Correlations of $[p_{\rm T}]$ and $v_{\rm n}$ in Pb–Pb and Xe–Xe collisions
ALICE Collaboration††thanks: See Appendix A for the list of collaboration
members ALICE Collaboration

Correlations between mean transverse momentum $[p_{\rm T}]$ and anisotropic
flow coefficients $v_{\rm 2}$ or $v_{\rm 3}$ are measured as a function of
centrality in Pb–Pb and Xe–Xe collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and
5.44 TeV, respectively, with ALICE. In addition, the recently proposed higher-
order correlation between $[p_{\rm T}]$, $v_{\rm 2}$, and $v_{\rm 3}$ is
measured for the first time, which shows an anticorrelation for the presented
centrality ranges. These measurements are compared with hydrodynamic
calculations using IP-Glasma and $\rm T_{R}ENTo$ initial-state shapes, the
former based on the Color Glass Condensate effective theory with gluon
saturation, and the latter a parameterized model with nucleons as the relevant
degrees of freedom. The data are better described by the IP-Glasma rather than
the $\rm T_{R}ENTo$ based calculations. In particular, Trajectum and JETSCAPE
predictions, both based on the $\rm T_{R}ENTo$ initial state model but with
different parameter settings, fail to describe the measurements. As the
correlations between $[p_{\rm T}]$ and $v_{\rm n}$ are mainly driven by the
correlations of the size and the shape of the system in the initial state,
these new studies pave a novel way to characterize the initial state and help
pin down the uncertainty of the extracted properties of the quark–gluon plasma
recreated in relativistic heavy-ion collisions.

The primary goal of ultrarelativistic heavy-ion collisions is to study the
quark–gluon plasma (QGP) [1], a deconfined state of quarks and gluons,
predicted by quantum chromodynamics (QCD) to emerge at extreme densities and
temperatures. High-energy heavy-ion collisions at Relativistic Heavy Ion
Collider (RHIC) [2, 3, 4, 5] and the Large Hadron Collider (LHC) at CERN [6,
7] have yielded strong evidence that the QGP is observed in such collisions,
enabling the study of its properties in the laboratory. A key phenomenon that
provides valuable information on the transport properties of the created QGP
matter is the anisotropic expansion of the produced particles [8]. The final
anisotropy can be quantified by a Fourier decomposition of the single particle
azimuthal distribution [9],

$P(\varphi)=\frac{1}{2\pi}\left[1+2\,\sum_{\rm n=1}^{\infty}{v_{\rm n}\,\cos
n(\varphi-\Psi_{\rm n})}\right].$ (1)

Here, $\varphi$ is the azimuthal angle of the emitted particle, and $v_{\rm
n}$ and $\Psi_{\rm n}$ are the $n$-th order flow coefficient and flow
symmetry-plane angle, respectively. Systematic measurements on fluctuations
and correlations of $v_{\rm n}$ coefficients and $\Psi_{\rm n}$ have been
previously reported in Refs. [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24, 25]. Comprehensive comparisons with hydrodynamic model
calculations provide critical information on the event average initial-state
shape and the initial energy density distribution in the nuclear overlap
region, as well as their event-by-event fluctuations. Additionally, they
constrain the shear and bulk viscosity over entropy density ratios of the QGP,
$\eta/s$ and $\zeta/s$, respectively [26, 27, 28, 29]. Even at fixed final-
state particle multiplicity, not only the shape but also the average size of
the nuclear overlap region will, in general, fluctuate from event to event.
These size fluctuations (at constant charged-particle density) lead to
fluctuations of the pressure gradient and therefore affect the radial flow,
thus influencing the transverse momentum ($p_{\rm T}$) spectra of the produced
particles. Arguably, the event-by-event fluctuations of the mean transverse
momentum $[p_{\rm T}]$ (the average transverse momentum of all particles in a
single event) are more sensitive to the equation-of-state and $\zeta$/s than
the measurements of the anisotropic flow [30, 31]. Despite their early success
in describing $v_{\rm n}$ measurements, hydrodynamic models have been able to
reproduce the observed $[p_{\rm T}]$ fluctuations only recently [32, 33, 34].
Notably the measurements of $v_{\rm n}$ and $[p_{\rm T}]$ are used as
independent experimental inputs for the Bayesian analyses [33, 34, 35, 36],
which extract state-of-the-art information on the initial conditions and the
final state properties, including the temperature dependence of $\eta/s$ and
$\zeta/s$.

Apart from the individual studies of $v_{\rm n}$ and $[p_{\rm T}]$, the
interplay between radial and anisotropic flow was qualitatively investigated
via anisotropic flow of identified hadrons [37, 38] and with event-shape
engineering (ESE) [39]. It was proposed that correlations between radial and
anisotropic flow could be quantified via correlations between $[p_{\rm T}]$
and $v_{\rm n}$ using a modified Pearson correlation coefficient [40],

$\rho(v_{\rm n}^{2},[p_{\rm T}])=\frac{{\rm Cov}(v_{\rm n}^{2},[p_{\rm
T}])}{\sqrt{{\rm Var}(v_{\rm n}^{2})}\,\sqrt{c_{\rm k}}},$ (2)

where ${\rm Cov}(v_{\rm n}^{2},[p_{\rm T}])$ is the covariance between $v_{\rm
n}^{2}$ and $[p_{\rm T}]$, it can be calculated using a three-particle
correlation following Eq. (1) in Ref. [40]. The variance of $v_{n}^{2}$
fluctuations is given by ${\rm Var}(v_{\rm n}^{2})$ and can be measured by
two- and four-particle cumulants, ${\rm Var}(v_{\rm n}^{2})=v_{\rm
n}\\{2\\}^{4}-v_{\rm n}\\{4\\}^{4}$. Dynamical transverse momentum
correlations are given by $c_{\rm k}$ [41, 42, 40, 43]. As $\rho(v_{\rm
n}^{2},[p_{\rm T}])$ (for n = 2, 3) can be qualitatively or even
quantitatively reproduced by the initial state correlations [31, 44, 45], its
measurements will provide valuable information on the overlap region’s shape
and size, and their correlations in the initial conditions. In particular,
$\rho(v_{\rm 2}^{2},[p_{\rm T}])$ is found to be sensitive to the nuclear
quadrupole deformation [46], adding a new tool to study the nuclear structure,
which has been addressed systematically only at low energies so far [47]. This
$\rho(v_{\rm n}^{2},[p_{\rm T}])$ (for n = 2, 3, 4) observable has been
measured previously [48], which reported a clear dependence on charged-
particle multiplicity, when selecting particles with $p_{\rm T}>0.5$ GeV/$c$.

Recently, a new observable that probes the correlations between $[p_{\rm T}]$
and two different $v_{\rm m}^{2}$ and $v_{\rm n}^{2}$ coefficients has been
introduced [49]. This observable $\rho(v_{\rm m}^{2},v_{\rm n}^{2},[p_{\rm
T}])$ can be achieved by replacing three observables A, B, and C with $v_{\rm
m}^{2}$, $v_{\rm n}^{2}$, and $[p_{\rm T}]$ in Eq. (24) from Ref. [49],

$\small{\rho(v_{\rm m}^{2},v_{\rm n}^{2},[p_{\rm T}])=\frac{Cor(v_{\rm
m}^{2},v_{\rm n}^{2},[p_{\rm T}])}{\sqrt{{\rm Var}(v_{\rm m}^{2})}\sqrt{{\rm
Var}(v_{\rm n}^{2})}\sqrt{c_{k}}}-\frac{\langle v_{\rm
m}^{2}\rangle}{\sqrt{{\rm Var}(v_{\rm m}^{2})}}\cdot\rho_{\rm n}-\frac{\langle
v_{\rm n}^{2}\rangle}{\sqrt{{\rm Var}(v_{\rm n}^{2})}}\cdot\rho_{\rm
m}-\frac{\langle[p_{\rm T}]\rangle}{\sqrt{c_{\rm k}}}\cdot\frac{SC({\rm
m,n})}{\sqrt{{\rm Var}(v_{\rm m}^{2})}\sqrt{{\rm Var}(v_{\rm n}^{2})}},}$ (3)

where $\rho_{i}=\rho(v_{i}^{2},[p_{\rm T}])$, $Cor(v_{\rm m}^{2},v_{\rm
n}^{2},[p_{\rm T}])$ is the correlation among $v_{\rm m}^{2}$, $v_{\rm
n}^{2}$, and $[p_{\rm T}]$ defined in Ref. [49], and $SC({\rm m,n})$ is the
symmetric cumulant between $v_{\rm m}^{2}$ and $v_{\rm n}^{2}$ [50, 16, 51].
The $\rho(v_{\rm m}^{2},v_{\rm n}^{2},[p_{\rm T}])$ is constructed based on
multiparticle cumulants [49, 52], where lower-order few particle correlations
have been removed, thus, it only reflects the genuine correlations between
$[p_{\rm T}]$, $v_{\rm n}$, and $v_{\rm m}$. It is potentially more sensitive
than $\rho(v_{\rm n}^{2},[p_{\rm T}])$ to the initial conditions and is
expected to be used to probe the initial momentum anisotropy [44], an
asymmetry in the transverse pressure of the system at the interface between a
pre-equilibrium description and a hydrodynamic description. The presence of an
initial momentum anisotropy was predicted from first-principle considerations
in the color glass condensate (CGC) effective theory of high-energy QCD [53,
54]. However, conclusive evidence for the CGC remains elusive.

In this Letter, the measurements of the centrality dependence of correlations
between flow coefficients and $[p_{\rm T}]$ in Pb–Pb and Xe–Xe collisions at
5.02 TeV and 5.44 TeV, respectively, are presented. The collision centrality
is determined using energy deposition in the two scintillator arrays of the V0
detector, V0A and V0C, which cover the pseudorapidity ranges of $2.8<\eta<5.1$
and $-3.7<\eta<-1.7$, respectively [55, 56]. Events that pass central, semi-
central, or minimum-bias trigger criteria with a reconstructed primary vertex
(PV) within $\pm 10$ cm of the nominal interaction point along the beam
direction are used. Background events are removed using information from
multiple detectors as described in Ref. [57]. A total of 245 million Pb–Pb
collisions and 1.2 million Xe–Xe collisions pass these criteria. The charged-
particle tracks are reconstructed using the Inner Tracking System (ITS) [58]
and the Time Projection Chamber (TPC) [59]. To select only high-quality
reconstructed tracks for the analysis, they are required to be in the
kinematic range $0.2<p_{\rm T}<3.0$ GeV/$c$ and $|\eta|<0.8$, to have more
than 70 TPC space points (out of a maximum of 159), and a $\chi^{2}$ per
degree of freedom of the track fit to the TPC space points to be lower than 2.
In order to reduce the contamination from secondary particles, the distance-
of-closest-approach (DCA) of the tracks to the PV must be within 2 cm in the
longitudinal direction and a $p_{\rm T}$-dependent distance selection in the
transverse plane, ranging from 0.2 cm at $p_{\rm T}=0.2$ GeV/$c$ to 0.02 cm at
$p_{\rm T}=3.0$ GeV/$c$, is applied. To suppress the non-flow contaminations,
which are the azimuthal angle correlations not associated to $\Psi_{\rm n}$,
multiparticle correlations with the subevent method [52, 60] are applied. For
this, the pseudorapidity acceptance of the central barrel is divided into
three regions (subevents), A, B, and C, corresponding to $-0.8<\eta_{\rm
A}<-0.4$, $|\eta_{\rm B}|<0.4$, and $0.4<\eta_{\rm C}<0.8$, respectively. Here
subevents A and C are used in the $v_{\rm n}$ measurements, while subevent B
is used for $[p_{\rm T}]$ measurements. The $v_{\rm n}$, $[p_{\rm T}]$, and
their correlations are measured in each event and corrected for detector
acceptance and track-reconstruction efficiency using the latest developments
based on generic framework with 3-subevent method [50, 60] including $[p_{\rm
T}]$ calculations.

Systematic uncertainties are estimated by varying event and track selection
criteria. Uncertainties related to the selection of the event include the
variation of the accepted vertex position along the beam line (9, 7 and 5 cm),
and consideration of different magnetic field directions, which are analyzed
separately. The resulting systematic uncertainty was found to be within 2%.
The systematic uncertainties related to track selection criteria are estimated
by considering different track reconstruction algorithms and reconstruction
qualities. The variations of the maximum allowed DCA to the primary vertex
along the beam line and in the transverse plane result in differences less
than 1%. The quality of reconstructed tracks is varied by increasing the
minimum number of space points in the TPC associated with the reconstructed
track to 80 and 90, which leads to a negligible effect on the measured
correlations. It is also found that the tracking efficiency exhibits a slight
centrality dependence, varying by about 4% with multiplicity. To account for
this, the tracking efficiency is varied by $\pm 4\%$ in a $p_{\rm
T}$-dependent way, so that the efficiency is at its nominal value at $p_{\rm
T}$ = 0.2 ${\rm GeV}/c$ and 4% larger or smaller at $p_{\rm T}$ = 3.0 ${\rm
GeV}/c$. This yields a systematic uncertainty below 1%. The residual non-flow
contaminations are studied with the 3-subevent method [60, 61] and the effects
are found to be negligible, which agrees with the findings from model studies
[61]. Only the sources of systematic uncertainty found to be statistically
significant by more than 1$\sigma$ following the procedure introduced in Ref.
[62] are added in quadrature to obtain the total systematic uncertainty.

The measurements of $\rho(v_{2}^{2},[p_{\rm T}])$ and $\rho(v_{3}^{2},[p_{\rm
T}])$ as a function of collision centrality in Pb–Pb collisions at
$\sqrt{s_{\rm NN}}=5.02$ TeV and Xe–Xe collisions at $\sqrt{s_{\rm NN}}=5.44$
TeV are presented in Fig. 1. In Pb–Pb and Xe–Xe collisions, $\rho(v_{\rm
2}^{2},[p_{\rm T}])$ has a weak centrality dependence and is positive in the
considered centrality range. This implies that $v_{2}$ and $[p_{\rm T}]$ are
positively correlated and confirms the previous studies using the ESE approach
[39]. The presented ALICE results also qualitatively agree with the previous
ATLAS measurements [48]. The stronger centrality dependence reported by the
ATLAS Collaboration might be attributed to the different kinematic selection
criteria and the choice of centrality determination. Hydrodynamic model
calculations from the v-USPhydro model [30], the Trajectum Bayesian analysis
[35], the JETSCAPE Bayesian analysis [36], and the IP-Glasma+MUSIC+UrQMD model
[31], whenever available, are compared to data. The width of the bands
illustrated in Fig. 1 denotes the statistical uncertainty of the model
calculations using maximum a posteriori (MAP) parametrization, while any
potential systematic uncertainty arising from different parametrizations of
the models has not been evaluated. The v-USPhydro model uses $\rm T_{R}ENTo$
initial conditions tuned in Ref. [63] and evolved by the v-USPhydro
hydrodynamic code [45]. The Trajectum [35] and JETSCAPE [36] predictions are
also based on $\rm T_{R}ENTo$ initial conditions but tuned as described in
Refs. [35] and [36], respectively. The IP-Glasma+MUSIC+UrQMD model uses IP-
Glasma initial conditions [64, 65] followed by the MUSIC hydrodynamic model
[66], coupled to a hadronic cascade model (UrQMD) [67, 68]. In general, these
models can quantitatively describe the previous measurements of particle
$p_{\rm T}$ distributions and anisotropic flow [69, 70]. As shown in Fig. 1,
the IP-Glasma+MUSIC+UrQMD calculations capture the general trend of the
measured $\rho(v_{\rm 2}^{2},[p_{\rm T}])$ with a weak centrality dependence,
qualitatively describe the measurements in Pb–Pb and Xe–Xe collisions, but
slightly overestimates the data. The v-USPhydro and Trajectum calculations
exhibit a strong centrality dependence, underestimate the data by more than
50% for centrality above 30%, and have an opposite sign with respect to data
for centralities above 40%. The discrepancies between the measurements and
$\rm T_{R}ENTo$-based calculations become more pronounced with the JETSCAPE
predictions [36], which become negative for semicentral collisions.

Figure 1: Centrality dependence of $\rho\left(v_{\rm 2}^{2},[p_{\rm
T}]\right)$ (top) and $\rho\left(v_{\rm 3}^{2},[p_{\rm T}]\right)$ (bottom) in
Pb–Pb collisions at $\sqrt{s_{{}_{\rm NN}}}=5.02$ TeV (a,c) and Xe–Xe
collisions at $\sqrt{s_{{}_{\rm NN}}}=5.44$ TeV (b, d). The statistical
(systematic) uncertainties are shown as vertical bars (filled boxes). The
initial-state estimations (ISE) are represented by lines, while IP-
Glasma+MUSIC+UrQMD [31], v-USPhydro [45], Trajectum [35], and JETSCAPE [36]
hydrodynamic model calculations are shown with hatched bands.

A recent study [71] showed that $\rho(v_{\rm 2}^{2},[p_{\rm T}])$ is more
sensitive to the initial conditions of the collisions rather than to the
transport properties of the QGP. This is also supported by the good agreement
between the various hydrodynamic calculations and the correlation coefficients
calculated directly from the corresponding initial-state model, which are
presented by solid or dashed lines in the top panel of Fig. 1. These initial-
state estimations (ISE) are calculated using the correlations of the energy of
the fluid per unit rapidity at the initial time $\tau_{\rm 0}$ and initial
anisotropy coefficient $\varepsilon_{\rm n}$ [45]. Thus, differences between
the calculations of $\rho(v_{\rm 2}^{2},[p_{\rm T}])$ shown in Fig.1 are not
primarily due to different hydrodynamic codes or treatments of hadronic
interactions in these models. The different model predictions are rather
caused by the difference in the initial energy density profile (geometric
effect) and, potentially, a contribution from an initial momentum anisotropy,
which is included in the IP-Glasma framework based on the CGC effective
theory. The effect of initial momentum anisotropy is studied by comparing the
hydrodynamic calculations using IP-Glasma initial conditions with and without
initial momentum anisotropy (with only the final state effect labelled “FSE”
shown by the light blue shadows). The IP-Glasma based calculations shown in
Fig. 1 (a) are consistent with each other in the 0–60% Pb–Pb collisions. Thus,
the different descriptions of ALICE data from IP-Glasma and $\rm T_{R}ENTo$
based calculations are mainly driven by the initial geometric effects, which
possibly originated from different values of $\omega$ parameter that
determines the width of the colliding nucleon in the initial conditions [72].
The variable $\rho(v_{\rm 2}^{2},[p_{\rm T}])$ is the first observable for
which such a significant difference is seen between $\rm T_{R}ENTo$ and IP-
Glasma models. Moreover, it is found that $\rho(v_{\rm 2}^{2},[p_{\rm T}])$ is
sensitive to the quadrupole deformation parameter $\beta_{2}$ of deformed
nuclei, such as 238U or 129Xe [73, 46]. Previous flow measurements in Xe–Xe
collisions [22] provided the estimation of $\beta_{2}\approx 0.16$ for Xe
using the data in the 0–5% central collisions. The $\rho(v_{\rm 2}^{2},[p_{\rm
T}])$ calculation with $\beta_{2}=0$ and 0.162, based on IP-Glasma initial
conditions in Fig. 1 (b), show a difference of 10–40% in the most central
collisions. Comparisons of presented ALICE measurements to IP-
Glasma+MUSIC+UrQMD calculations with the two different $\beta_{2}$ values
suggest that the data agrees better with the IP-Glasma+MUSIC+UrQMD model
calculations using $\beta_{2}=0.162$. Last but not least, the magnitude of
$\rho(v_{\rm 2}^{2},[p_{\rm T}])$ measured in Pb–Pb collisions is larger than
that in Xe–Xe collisions. Such a difference is predicted by both v-USPhydro
and IP-Glasma+MUSIC+UrQMD calculations and is believed to be useful to
discover a potential triaxial structure of 129Xe at the LHC energies [74, 75].
Comparisons with calculations that include different deformation scenarios
could provide strong constraints on the 129Xe nuclear structure. This is
highly non-trivial because it is not entirely clear at the moment if the
nuclear structure at the LHC energies, where the partonic degree of freedom is
relevant, should be quantified by the same set of parameters as the low energy
nuclear structure studies.

Figure 1 (bottom) shows the centrality dependence of $\rho(v_{\rm
3}^{2},[p_{\rm T}])$ in the two colliding systems. The results are consistent
within uncertainties for the considered centrality range. Both results show a
positive value and rather a weak centrality dependence and a modest increase
for centrality above 40% in Pb–Pb collisions. The IP-Glasma+MUSIC+UrQMD
calculations describe the presented ALICE measurements up to 50% centrality
for Pb–Pb collisions, at which point they diverge from data with opposite
trends for the full IP-Glasma+MUSIC+UrQMD calculation and the one with FSE
only. It is unclear yet whether this difference between IP-Glasma+MUSIC+UrQMD
calculation and the one with FSE can be attributed solely to the initial
momentum anisotropy originating from the contributions of CGC in the IP-Glasma
model, as only statistical uncertainties are considered in these calculations.
In addition, both calculations describe the ALICE measurements from Xe–Xe
collisions. The v-USPhydro calculations are roughly compatible with data in
Pb–Pb collisions and are consistent with ALICE measurements up to 40% Xe–Xe
collisions, then show a decreasing trend and become negative, which is not
observed in the data. Like v-USPhydro, the Trajectum calculation is based on
the $\rm T_{R}ENTo$ initial state model but with a different tuning; it is
negative for centrality above 10% and cannot describe the ALICE data in Pb–Pb
collisions. It is also seen in Fig. 1 (bottom) that the $\rho(v_{\rm
3}^{2},[p_{\rm T}])$ calculations follow the trend of the initial-state
estimations, which also show a significant difference and an opposite sign
compared to the measurements. Such differences are further enhanced in the
initial-state estimations from the JETSCAPE model, which does not consider the
subnucleon structure. It is argued in a recent paper [76] that the positive
$\rho(v_{\rm n}^{2},[p_{\rm T}])$ for centrality up to 60% shown in Fig. 1
suggests a nucleon size of order 0.4–0.5 fm. This is much smaller than the
values obtained from the recent Bayesian analyses [35, 36]. Using $\rho(v_{\rm
n}^{2},[p_{\rm T}])$ measurements to constrain the width of nucleon is
particularly interesting. It enables a new possibility to crosscheck different
determinations of the nucleon and subnucleon scales relevant to inelastic
processes at high energy in different experiments, e.g., in electron–ion
collisions at the future Electron-Ion Collider.

Figure 2: Centrality dependence of $\rho\left(v_{\rm 2}^{2},v_{\rm
3}^{2},[p_{\rm T}]\right)$ in Pb–Pb collisions, shown by the solid circles.
The statistical (systematic) uncertainties are shown as vertical bars (boxes).
The initial-state estimations (ISE) as well as IP-Glasma+MUSIC+UrQMD [31] and
v-USPhydro [45] hydrodynamic model calculations are compared with data.

In addition to $\rho(v_{\rm n}^{2},[p_{\rm T}])$, a newly proposed higher-
order correlation involving two flow coefficients, $\rho(v_{\rm n}^{2},v_{\rm
m}^{2},[p_{\rm T}])$ as defined in Eq. (3), is expected to bring further
constraints on the initial-state shape [49]. Figure 2 reports the first
measurement of $\rho(v_{\rm 2}^{2},v_{\rm 3}^{2},[p_{\rm T}])$ as a function
of centrality up to 50% in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV
while the measurement in Xe–Xe collision is very challenging due to limited
data sample. First of all, negative results are observed with more than
5$\sigma$ significance from zero for the 0–50% centrality interval, showing a
non-trivial anticorrelation between $[p_{\rm T}]$, $v_{2}$, and $v_{3}$. It
suggests an anticorrelation between entropy density, $\varepsilon_{2}$, and
$\varepsilon_{3}$ in the initial stage. The full IP-Glasma+MUSIC+UrQMD and
v-USPhydro calculations presented in Fig. 2 show a flat trend with centrality
as the ALICE data for the 0–40% centrality range within uncertainties. As
$\rho(v_{\rm 2}^{2},v_{\rm 3}^{2},[p_{\rm T}])$ follows the trend of initial-
state estimations and is mainly determined by the early stage [49], the
differences among theoretical model calculations should again mainly originate
from the initial conditions. Due to the large uncertainties of the model
calculations, one cannot clearly establish a preference from comparisons with
the ALICE data. Furthermore, the calculation of IP-Glasma with only the final
state effect (FSE) shows a strong centrality dependence. It is positive in
central collisions and gradually becomes negative in peripheral collisions.
This trend is different from that of full IP-Glasma+MUSIC+UrQMD calculations
and the experimental data.

In summary, the centrality dependence of correlations between anisotropic flow
coefficients and mean transverse momentum in Pb–Pb and Xe–Xe collisions has
been presented. These first ALICE measurements of $\rho(v_{\rm 2}^{2},[p_{\rm
T}])$ and $\rho(v_{\rm 3}^{2},[p_{\rm T}])$ are found to be positive in both
collision systems for the presented centrality ranges, confirming the positive
correlations between $v_{2}$ (or $v_{\rm 3}$) and $[p_{\rm T}]$. In addition,
the higher-order correlation coefficient $\rho(v_{\rm 2}^{2},v_{\rm
3}^{2},[p_{\rm T}])$ has been measured and found to be negative in Pb–Pb
collisions, suggesting an anticorrelation between entropy density, initial
anisotropy coefficients $\varepsilon_{2}$ and $\varepsilon_{3}$ in the initial
stage. The experimental data reported in this Letter can be described by
hydrodynamic models using IP-Glasma initial conditions, while they are not
well reproduced by calculations using different tunings of the $\rm T_{R}ENTo$
initial conditions. Such discrepancies cannot be attributed to the effect of
the initial momentum anisotropy predicted by the CGC framework, as its impact
is insignificant in the presented centrality ranges. Instead, the
discrepancies are expected to arise from different geometric effects in the
initial state. It should also be emphasized that the state-of-the-art
extraction of the QGP’s transport coefficients relies on Bayesian analyses,
which are all based on the $\rm T_{R}ENTo$ model so far. The presented
discrepancy between ALICE data and $\rm T_{R}ENTo$ model-based calculations
requires in-depth investigations, and the impact on the extraction of the
properties of QGP should be explored further. The presented ALICE measurements
are crucial on this matter, and including the presented data in the Bayesian
global fitting could be a valuable step toward a better constraint on the
initial state in nuclear collisions. Last but not least, the presented
measurements in Xe–Xe collisions open a new window to study the nuclear
structure using ultrarelativistic heavy-ion collisions at the LHC.

## Acknowledgments

The ALICE Collaboration would like to thank Giuliano Giacalone (v-USPhydro),
Chun Shen, Bjoern Schenke (IP-Glasma), Wilke van der Schee (Trajectum), Julia
Velkovska, Andi Mankolli (JETSCAPE), Piotr Bozek (Glauber+MUSIC) for providing
the latest predictions from the state-of-the-art models.

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; 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; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan Society for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT)of Applied Science (IIST), Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; 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 (NSDTA) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.

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##  Appendix A The ALICE Collaboration

S. Acharya143, D. Adamová97, A. Adler75, J. Adolfsson82, G. Aglieri Rinella34,
M. Agnello30, N. Agrawal54, Z. Ahammed143, S. Ahmad16, S.U. Ahn77, I. Ahuja38,
Z. Akbar51, A. Akindinov94, M. Al-Turany109, S.N. Alam16, D. Aleksandrov90, B.
Alessandro60, H.M. Alfanda7, R. Alfaro Molina72, B. Ali16, Y. Ali14, A.
Alici25, N. Alizadehvandchali126, A. Alkin34, J. Alme21, G. Alocco55, T.
Alt69, I. Altsybeev114, M.N. Anaam7, C. Andrei48, D. Andreou92, A.
Andronic146, M. Angeletti34, V. Anguelov106, F. Antinori57, P. Antonioli54, C.
Anuj16, N. Apadula81, L. Aphecetche116, H. Appelshäuser69, S. Arcelli25, R.
Arnaldi60, I.C. Arsene20, M. Arslandok148, A. Augustinus34, R. Averbeck109, S.
Aziz79, M.D. Azmi16, A. Badalà56, Y.W. Baek41, X. Bai130,109, R. Bailhache69,
Y. Bailung50, R. Bala103, A. Balbino30, A. Baldisseri140, B. Balis2, D.
Banerjee4, Z. Banoo103, R. Barbera26, L. Barioglio107, M. Barlou86, G.G.
Barnaföldi147, L.S. Barnby96, V. Barret137, C. Bartels129, K. Barth34, E.
Bartsch69, F. Baruffaldi27, N. Bastid137, S. Basu82, G. Batigne116, B.
Batyunya76, D. Bauri49, J.L. Bazo Alba113, I.G. Bearden91, C. Beattie148, P.
Becht109, I. Belikov139, A.D.C. Bell Hechavarria146, F. Bellini25, R.
Bellwied126, S. Belokurova114, V. Belyaev95, G. Bencedi147,70, S. Beole24, A.
Bercuci48, Y. Berdnikov100, A. Berdnikova106, L. Bergmann106, M.G. Besoiu68,
L. Betev34, P.P. Bhaduri143, A. Bhasin103, I.R. Bhat103, M.A. Bhat4, B.
Bhattacharjee42, P. Bhattacharya22, L. Bianchi24, N. Bianchi52, J. Bielčík37,
J. Bielčíková97, J. Biernat119, A. Bilandzic107, G. Biro147, S. Biswas4, J.T.
Blair120, D. Blau90,83, M.B. Blidaru109, C. Blume69, G. Boca28,58, F. Bock98,
A. Bogdanov95, S. Boi22, J. Bok62, L. Boldizsár147, A. Bolozdynya95, M.
Bombara38, P.M. Bond34, G. Bonomi142,58, H. Borel140, A. Borissov83, H.
Bossi148, E. Botta24, L. Bratrud69, P. Braun-Munzinger109, M. Bregant122, M.
Broz37, G.E. Bruno108,33, M.D. Buckland23,129, D. Budnikov110, H. Buesching69,
S. Bufalino30, O. Bugnon116, P. Buhler115, Z. Buthelezi73,133, J.B. Butt14, A.
Bylinkin128, S.A. Bysiak119, M. Cai27,7, H. Caines148, A. Caliva109, E. Calvo
Villar113, J.M.M. Camacho121, R.S. Camacho45, P. Camerini23, F.D.M. Canedo122,
F. Carnesecchi34,25, R. Caron140, J. Castillo Castellanos140, E.A.R. Casula22,
F. Catalano30, C. Ceballos Sanchez76, P. Chakraborty49, S. Chandra143, S.
Chapeland34, M. Chartier129, S. Chattopadhyay143, S. Chattopadhyay111, T.G.
Chavez45, T. Cheng7, C. Cheshkov138, B. Cheynis138, V. Chibante Barroso34,
D.D. Chinellato123, S. Cho62, P. Chochula34, P. Christakoglou92, C.H.
Christensen91, P. Christiansen82, T. Chujo135, C. Cicalo55, L. Cifarelli25, F.
Cindolo54, M.R. Ciupek109, G. ClaiII,54, J. CleymansI,125, F. Colamaria53,
J.S. Colburn112, D. Colella53,108,33, A. Collu81, M. Colocci34, M.
ConcasIII,60, G. Conesa Balbastre80, Z. Conesa del Valle79, G. Contin23, J.G.
Contreras37, M.L. Coquet140, T.M. Cormier98, P. Cortese31, M.R. Cosentino124,
F. Costa34, S. Costanza28,58, P. Crochet137, R. Cruz-Torres81, E. Cuautle70,
P. Cui7, L. Cunqueiro98, A. Dainese57, M.C. Danisch106, A. Danu68, P. Das88,
P. Das4, S. Das4, S. Dash49, A. De Caro29, G. de Cataldo53, L. De Cilladi24,
J. de Cuveland39, A. De Falco22, D. De Gruttola29, N. De Marco60, C. De
Martin23, S. De Pasquale29, S. Deb50, H.F. Degenhardt122, K.R. Deja144, R. Del
Grande107, L. Dello Stritto29, W. Deng7, P. Dhankher19, D. Di Bari33, A. Di
Mauro34, R.A. Diaz8, T. Dietel125, Y. Ding138,7, R. Divià34, D.U. Dixit19, Ø.
Djuvsland21, U. Dmitrieva64, J. Do62, A. Dobrin68, B. Dönigus69, A.K.
Dubey143, A. Dubla109,92, S. Dudi102, P. Dupieux137, N. Dzalaiova13, T.M.
Eder146, R.J. Ehlers98, V.N. Eikeland21, F. Eisenhut69, D. Elia53, B.
Erazmus116, F. Ercolessi25, F. Erhardt101, A. Erokhin114, M.R. Ersdal21, B.
Espagnon79, G. Eulisse34, D. Evans112, S. Evdokimov93, L. Fabbietti107, M.
Faggin27, J. Faivre80, F. Fan7, A. Fantoni52, M. Fasel98, P. Fecchio30, A.
Feliciello60, G. Feofilov114, A. Fernández Téllez45, A. Ferrero140, A.
Ferretti24, V.J.G. Feuillard106, J. Figiel119, V. Filova37, D. Finogeev64,
F.M. Fionda55, G. Fiorenza34,108, F. Flor126, A.N. Flores120, S. Foertsch73,
S. Fokin90, E. Fragiacomo61, E. Frajna147, A. Francisco137, U. Fuchs34, N.
Funicello29, C. Furget80, A. Furs64, J.J. Gaardhøje91, M. Gagliardi24, A.M.
Gago113, A. Gal139, C.D. Galvan121, D.R. Gangadharan126, P. Ganoti86, C.
Garabatos109, J.R.A. Garcia45, E. Garcia-Solis10, K. Garg116, C. Gargiulo34,
A. Garibli89, K. Garner146, P. Gasik109, E.F. Gauger120, A. Gautam128, M.B.
Gay Ducati71, M. Germain116, P. Ghosh143, S.K. Ghosh4, M. Giacalone25, P.
Gianotti52, P. Giubellino109,60, P. Giubilato27, A.M.C. Glaenzer140, P.
Glässel106, E. Glimos132, D.J.Q. Goh84, V. Gonzalez145, L.H. González-
Trueba72, S. Gorbunov39, M. Gorgon2, L. Görlich119, S. Gotovac35, V.
Grabski72, L.K. Graczykowski144, L. Greiner81, A. Grelli63, C. Grigoras34, V.
Grigoriev95, S. Grigoryan76,1, F. Grosa34,60, J.F. Grosse-Oetringhaus34, R.
Grosso109, D. Grund37, G.G. Guardiano123, R. Guernane80, M. Guilbaud116, K.
Gulbrandsen91, T. Gunji134, W. Guo7, A. Gupta103, R. Gupta103, S.P. Guzman45,
L. Gyulai147, M.K. Habib109, C. Hadjidakis79, H. Hamagaki84, M. Hamid7, R.
Hannigan120, M.R. Haque144, A. Harlenderova109, J.W. Harris148, A. Harton10,
J.A. Hasenbichler34, H. Hassan98, D. Hatzifotiadou54, P. Hauer43, L.B.
Havener148, S.T. Heckel107, E. Hellbär109, H. Helstrup36, T. Herman37, E.G.
Hernandez45, G. Herrera Corral9, F. Herrmann146, K.F. Hetland36, H.
Hillemanns34, C. Hills129, B. Hippolyte139, B. Hofman63, B. Hohlweger92, J.
Honermann146, G.H. Hong149, D. Horak37, S. Hornung109, A. Horzyk2, R.
Hosokawa15, Y. Hou7, P. Hristov34, C. Hughes132, P. Huhn69, L.M. Huhta127,
C.V. Hulse79, T.J. Humanic99, H. Hushnud111, L.A. Husova146, A. Hutson126,
J.P. Iddon34,129, R. Ilkaev110, H. Ilyas14, M. Inaba135, G.M. Innocenti34, M.
Ippolitov90, A. Isakov97, T. Isidori128, M.S. Islam111, M. Ivanov109, V.
Ivanov100, V. Izucheev93, M. Jablonski2, B. Jacak81, N. Jacazio34, P.M.
Jacobs81, S. Jadlovska118, J. Jadlovsky118, S. Jaelani63, C. Jahnke123,122,
M.J. Jakubowska144, A. Jalotra103, M.A. Janik144, T. Janson75, M. Jercic101,
O. Jevons112, A.A.P. Jimenez70, F. Jonas98,146, P.G. Jones112, J.M. Jowett
34,109, J. Jung69, M. Jung69, A. Junique34, A. Jusko112, M.J. Kabus144, J.
Kaewjai117, P. Kalinak65, A.S. Kalteyer109, A. Kalweit34, V. Kaplin95, A.
Karasu Uysal78, D. Karatovic101, O. Karavichev64, T. Karavicheva64, P.
Karczmarczyk144, E. Karpechev64, V. Kashyap88, A. Kazantsev90, U. Kebschull75,
R. Keidel47, D.L.D. Keijdener63, M. Keil34, B. Ketzer43, Z. Khabanova92, A.M.
Khan7, S. Khan16, A. Khanzadeev100, Y. Kharlov93,83, A. Khatun16, A.
Khuntia119, B. Kileng36, B. Kim17,62, C. Kim17, D.J. Kim127, E.J. Kim74, J.
Kim149, J.S. Kim41, J. Kim106, J. Kim74, M. Kim106, S. Kim18, T. Kim149, S.
Kirsch69, I. Kisel39, S. Kiselev94, A. Kisiel144, J.P. Kitowski2, J.L. Klay6,
J. Klein34, S. Klein81, C. Klein-Bösing146, M. Kleiner69, T. Klemenz107, A.
Kluge34, A.G. Knospe126, C. Kobdaj117, T. Kollegger109, A. Kondratyev76, N.
Kondratyeva95, E. Kondratyuk93, J. Konig69, S.A. Konigstorfer107, P.J.
Konopka34, G. Kornakov144, S.D. Koryciak2, A. Kotliarov97, O. Kovalenko87, V.
Kovalenko114, M. Kowalski119, I. Králik65, A. Kravčáková38, L. Kreis109, M.
Krivda112,65, F. Krizek97, K. Krizkova Gajdosova37, M. Kroesen106, M.
Krüger69, D.M. Krupova37, E. Kryshen100, M. Krzewicki39, V. Kučera34, C.
Kuhn139, P.G. Kuijer92, T. Kumaoka135, D. Kumar143, L. Kumar102, N. Kumar102,
S. Kundu34, P. Kurashvili87, A. Kurepin64, A.B. Kurepin64, A. Kuryakin110, S.
Kushpil97, J. Kvapil112, M.J. Kweon62, J.Y. Kwon62, Y. Kwon149, S.L. La
Pointe39, P. La Rocca26, Y.S. Lai81, A. Lakrathok117, M. Lamanna34, R.
Langoy131, K. Lapidus34, P. Larionov34,52, E. Laudi34, L. Lautner34,107, R.
Lavicka115,37, T. Lazareva114, R. Lea142,23,58, J. Lehrbach39, R.C. Lemmon96,
I. León Monzón121, E.D. Lesser19, M. Lettrich34,107, P. Lévai147, X. Li11,
X.L. Li7, J. Lien131, R. Lietava112, B. Lim17, S.H. Lim17, V. Lindenstruth39,
A. Lindner48, C. Lippmann109, A. Liu19, D.H. Liu7, J. Liu129, I.M. Lofnes21,
V. Loginov95, C. Loizides98, P. Loncar35, J.A. Lopez106, X. Lopez137, E. López
Torres8, J.R. Luhder146, M. Lunardon27, G. Luparello61, Y.G. Ma40, A.
Maevskaya64, M. Mager34, T. Mahmoud43, A. Maire139, M. Malaev100, N.M.
Malik103, Q.W. Malik20, S.K. Malik103, L. MalininaIV,76, D. Mal’Kevich94, D.
Mallick88, N. Mallick50, G. Mandaglio32,56, V. Manko90, F. Manso137, V.
Manzari53, Y. Mao7, G.V. Margagliotti23, A. Margotti54, A. Marín109, C.
Markert120, M. Marquard69, N.A. Martin106, P. Martinengo34, J.L. Martinez126,
M.I. Martínez45, G. Martínez García116, S. Masciocchi109, M. Masera24, A.
Masoni55, L. Massacrier79, A. Mastroserio141,53, A.M. Mathis107, O.
Matonoha82, P.F.T. Matuoka122, A. Matyja119, C. Mayer119, A.L. Mazuecos34, F.
Mazzaschi24, M. Mazzilli34, M.A. MazzoniI,59, J.E. Mdhluli133, A.F. Mechler69,
Y. Melikyan64, A. Menchaca-Rocha72, E. Meninno115,29, A.S. Menon126, M.
Meres13, S. Mhlanga125,73, Y. Miake135, L. Micheletti60, L.C. Migliorin138,
D.L. Mihaylov107, K. Mikhaylov76,94, A.N. Mishra147, D. Miśkowiec109, A.
Modak4, A.P. Mohanty63, B. Mohanty88, M. Mohisin KhanV,16, M.A. Molander44, Z.
Moravcova91, C. Mordasini107, D.A. Moreira De Godoy146, I. Morozov64, A.
Morsch34, T. Mrnjavac34, V. Muccifora52, E. Mudnic35, D. Mühlheim146, S.
Muhuri143, J.D. Mulligan81, A. Mulliri22, M.G. Munhoz122, R.H. Munzer69, H.
Murakami134, S. Murray125, L. Musa34, J. Musinsky65, J.W. Myrcha144, B.
Naik133, R. Nair87, B.K. Nandi49, R. Nania54, E. Nappi53, A.F. Nassirpour82,
A. Nath106, C. Nattrass132, A. Neagu20, A. Negru136, L. Nellen70, S.V.
Nesbo36, G. Neskovic39, D. Nesterov114, B.S. Nielsen91, E.G. Nielsen91, S.
Nikolaev90, S. Nikulin90, V. Nikulin100, F. Noferini54, S. Noh12, P.
Nomokonov76, J. Norman129, N. Novitzky135, P. Nowakowski144, A. Nyanin90, J.
Nystrand21, M. Ogino84, A. Ohlson82, V.A. Okorokov95, J. Oleniacz144, A.C.
Oliveira Da Silva132, M.H. Oliver148, A. Onnerstad127, C. Oppedisano60, A.
Ortiz Velasquez70, T. Osako46, A. Oskarsson82, J. Otwinowski119, M. Oya46, K.
Oyama84, Y. Pachmayer106, S. Padhan49, D. Pagano142,58, G. Paić70, A.
Palasciano53, J. Pan145, S. Panebianco140, J. Park62, J.E. Parkkila127, S.P.
Pathak126, R.N. Patra103,34, B. Paul22, H. Pei7, T. Peitzmann63, X. Peng7,
L.G. Pereira71, H. Pereira Da Costa140, D. Peresunko90,83, G.M. Perez8, S.
Perrin140, Y. Pestov5, V. Petráček37, M. Petrovici48, R.P. Pezzi116,71, S.
Piano61, M. Pikna13, P. Pillot116, O. Pinazza54,34, L. Pinsky126, C. Pinto26,
S. Pisano52, M. Płoskoń81, M. Planinic101, F. Pliquett69, M.G. Poghosyan98, B.
Polichtchouk93, S. Politano30, N. Poljak101, A. Pop48, S. Porteboeuf-
Houssais137, J. Porter81, V. Pozdniakov76, S.K. Prasad4, R. Preghenella54, F.
Prino60, C.A. Pruneau145, I. Pshenichnov64, M. Puccio34, S. Qiu92, L.
Quaglia24, R.E. Quishpe126, S. Ragoni112, A. Rakotozafindrabe140, L.
Ramello31, F. Rami139, S.A.R. Ramirez45, A.G.T. Ramos33, T.A. Rancien80, R.
Raniwala104, S. Raniwala104, S.S. Räsänen44, R. Rath50, I. Ravasenga92, K.F.
Read98,132, A.R. Redelbach39, K. RedlichVI,87, A. Rehman21, P. Reichelt69, F.
Reidt34, H.A. Reme-ness36, Z. Rescakova38, K. Reygers106, A. Riabov100, V.
Riabov100, T. Richert82, M. Richter20, W. Riegler34, F. Riggi26, C. Ristea68,
M. Rodríguez Cahuantzi45, K. Røed20, R. Rogalev93, E. Rogochaya76, T.S.
Rogoschinski69, D. Rohr34, D. Röhrich21, P.F. Rojas45, S. Rojas Torres37, P.S.
Rokita144, F. Ronchetti52, A. Rosano32,56, E.D. Rosas70, A. Rossi57, A. Roy50,
P. Roy111, S. Roy49, N. Rubini25, O.V. Rueda82, D. Ruggiano144, R. Rui23, B.
Rumyantsev76, P.G. Russek2, R. Russo92, A. Rustamov89, E. Ryabinkin90, Y.
Ryabov100, A. Rybicki119, H. Rytkonen127, W. Rzesa144, O.A.M. Saarimaki44, R.
Sadek116, S. Sadovsky93, J. Saetre21, K. Šafařík37, S.K. Saha143, S. Saha88,
B. Sahoo49, P. Sahoo49, R. Sahoo50, S. Sahoo66, D. Sahu50, P.K. Sahu66, J.
Saini143, S. Sakai135, M.P. Salvan109, S. Sambyal103, V. SamsonovI,100,95,
T.B. Saramela122, D. Sarkar145, N. Sarkar143, P. Sarma42, V.M. Sarti107,
M.H.P. Sas148, J. Schambach98, H.S. Scheid69, C. Schiaua48, R. Schicker106, A.
Schmah106, C. Schmidt109, H.R. Schmidt105, M.O. Schmidt34,106, M. Schmidt105,
N.V. Schmidt98,69, A.R. Schmier132, R. Schotter139, J. Schukraft34, K.
Schwarz109, K. Schweda109, G. Scioli25, E. Scomparin60, J.E. Seger15, Y.
Sekiguchi134, D. Sekihata134, I. Selyuzhenkov109,95, S. Senyukov139, J.J.
Seo62, D. Serebryakov64, L. Šerkšnytė107, A. Sevcenco68, T.J. Shaba73, A.
Shabanov64, A. Shabetai116, R. Shahoyan34, W. Shaikh111, A. Shangaraev93, A.
Sharma102, H. Sharma119, M. Sharma103, N. Sharma102, S. Sharma103, U.
Sharma103, A. Shatat79, O. Sheibani126, K. Shigaki46, M. Shimomura85, S.
Shirinkin94, Q. Shou40, Y. Sibiriak90, S. Siddhanta55, T. Siemiarczuk87, T.F.
Silva122, D. Silvermyr82, T. Simantathammakul117, G. Simonetti34, B. Singh107,
R. Singh88, R. Singh103, R. Singh50, V.K. Singh143, V. Singhal143, T.
Sinha111, B. Sitar13, M. Sitta31, T.B. Skaali20, G. Skorodumovs106, M.
Slupecki44, N. Smirnov148, R.J.M. Snellings63, C. Soncco113, J. Song126, A.
Songmoolnak117, F. Soramel27, S. Sorensen132, I. Sputowska119, J. Stachel106,
I. Stan68, P.J. Steffanic132, S.F. Stiefelmaier106, D. Stocco116, I.
Storehaug20, M.M. Storetvedt36, P. Stratmann146, C.P. Stylianidis92, A.A.P.
Suaide122, C. Suire79, M. Sukhanov64, M. Suljic34, R. Sultanov94, V.
Sumberia103, S. Sumowidagdo51, S. Swain66, A. Szabo13, I. Szarka13, U.
Tabassam14, S.F. Taghavi107, G. Taillepied137, J. Takahashi123, G.J.
Tambave21, S. Tang137,7, Z. Tang130, J.D. Tapia TakakiVII,128, M. Tarhini116,
M.G. Tarzila48, A. Tauro34, G. Tejeda Muñoz45, A. Telesca34, L. Terlizzi24, C.
Terrevoli126, G. Tersimonov3, S. Thakur143, D. Thomas120, R. Tieulent138, A.
Tikhonov64, A.R. Timmins126, M. Tkacik118, A. Toia69, N. Topilskaya64, M.
Toppi52, F. Torales-Acosta19, T. Tork79, A. Trifiró32,56, S. Tripathy54,70, T.
Tripathy49, S. Trogolo34,27, V. Trubnikov3, W.H. Trzaska127, T.P.
Trzcinski144, A. Tumkin110, R. Turrisi57, T.S. Tveter20, K. Ullaland21, A.
Uras138, M. Urioni58,142, G.L. Usai22, M. Vala38, N. Valle28, S. Vallero60,
L.V.R. van Doremalen63, M. van Leeuwen92, R.J.G. van Weelden92, P. Vande
Vyvre34, D. Varga147, Z. Varga147, M. Varga-Kofarago147, M. Vasileiou86, A.
Vasiliev90, O. Vázquez Doce52,107, V. Vechernin114, A. Velure21, E.
Vercellin24, S. Vergara Limón45, L. Vermunt63, R. Vértesi147, M. Verweij63, L.
Vickovic35, Z. Vilakazi133, O. Villalobos Baillie112, G. Vino53, A.
Vinogradov90, T. Virgili29, V. Vislavicius91, A. Vodopyanov76, B.
Volkel34,106, M.A. Völkl106, K. Voloshin94, S.A. Voloshin145, G. Volpe33, B.
von Haller34, I. Vorobyev107, N. Vozniuk64, J. Vrláková38, B. Wagner21, C.
Wang40, D. Wang40, M. Weber115, A. Wegrzynek34, S.C. Wenzel34, J.P.
Wessels146, J. Wiechula69, J. Wikne20, G. Wilk87, J. Wilkinson109, G.A.
Willems146, B. Windelband106, M. Winn140, W.E. Witt132, J.R. Wright120, W.
Wu40, Y. Wu130, R. Xu7, A.K. Yadav143, S. Yalcin78, Y. Yamaguchi46, K.
Yamakawa46, S. Yang21, S. Yano46, Z. Yin7, I.-K. Yoo17, J.H. Yoon62, S.
Yuan21, A. Yuncu106, V. Zaccolo23, C. Zampolli34, H.J.C. Zanoli63, N.
Zardoshti34, A. Zarochentsev114, P. Závada67, N. Zaviyalov110, M. Zhalov100,
B. Zhang7, S. Zhang40, X. Zhang7, Y. Zhang130, V. Zherebchevskii114, Y. Zhi11,
N. Zhigareva94, D. Zhou7, Y. Zhou91, J. Zhu109,7, Y. Zhu7, G. ZinovjevI,3, N.
Zurlo142,58

Affiliation Notes

I Deceased

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

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

IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute
of Nuclear, Physics, Moscow, Russia

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: University of Kansas, Lawrence, Kansas, United States

Collaboration Institutes

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

2 AGH University of Science and Technology, 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 Budker Institute for Nuclear Physics, Novosibirsk, Russia

6 California Polytechnic State University, San Luis Obispo, California, United
States

7 Central China Normal University, Wuhan, China

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

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

10 Chicago State University, Chicago, Illinois, United States

11 China Institute of Atomic Energy, Beijing, China

12 Chungbuk National University, Cheongju, Republic of Korea

13 Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

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 dell’Università and Sezione INFN, Cagliari, Italy

23 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

24 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

25 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

28 Dipartimento di Fisica e Nucleare e Teorica, Università di Pavia, Pavia,
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 e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

32 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy

33 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

34 European Organization for Nuclear Research (CERN), Geneva, Switzerland

35 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia

36 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway

37 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

38 Faculty of Science, P.J. Šafárik University, Košice, Slovakia

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 Hiroshima University, Hiroshima, Japan

47 Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany

48 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania

49 Indian Institute of Technology Bombay (IIT), Mumbai, India

50 Indian Institute of Technology Indore, Indore, India

51 Indonesian Institute of Sciences, Jakarta, Indonesia

52 INFN, Laboratori Nazionali di Frascati, Frascati, Italy

53 INFN, Sezione di Bari, Bari, Italy

54 INFN, Sezione di Bologna, Bologna, Italy

55 INFN, Sezione di Cagliari, Cagliari, Italy

56 INFN, Sezione di Catania, Catania, Italy

57 INFN, Sezione di Padova, Padova, Italy

58 INFN, Sezione di Pavia, Pavia, Italy

59 INFN, Sezione di Roma, Rome, Italy

60 INFN, Sezione di Torino, Turin, Italy

61 INFN, Sezione di Trieste, Trieste, Italy

62 Inha University, Incheon, Republic of Korea

63 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands

64 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

65 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

66 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

67 Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

68 Institute of Space Science (ISS), Bucharest, Romania

69 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

70 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

71 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

72 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico

73 iThemba LABS, National Research Foundation, Somerset West, South Africa

74 Jeonbuk National University, Jeonju, Republic of Korea

75 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

76 Joint Institute for Nuclear Research (JINR), Dubna, Russia

77 Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea

78 KTO Karatay University, Konya, Turkey

79 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France

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

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

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

83 Moscow Institute for Physics and Technology, Moscow, Russia

84 Nagasaki Institute of Applied Science, Nagasaki, Japan

85 Nara Women’s University (NWU), Nara, Japan

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

87 National Centre for Nuclear Research, Warsaw, Poland

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

89 National Nuclear Research Center, Baku, Azerbaijan

90 National Research Centre Kurchatov Institute, Moscow, Russia

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

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

93 NRC Kurchatov Institute IHEP, Protvino, Russia

94 NRC «Kurchatov»Institute - ITEP, Moscow, Russia

95 NRNU Moscow Engineering Physics Institute, Moscow, Russia

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

97 Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

98 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

99 Ohio State University, Columbus, Ohio, United States

100 Petersburg Nuclear Physics Institute, Gatchina, Russia

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

102 Physics Department, Panjab University, Chandigarh, India

103 Physics Department, University of Jammu, Jammu, India

104 Physics Department, University of Rajasthan, Jaipur, India

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

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

107 Physik Department, Technische Universität München, Munich, Germany

108 Politecnico di Bari and Sezione INFN, Bari, Italy

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

110 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

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

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

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

114 St. Petersburg State University, St. Petersburg, Russia

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

116 SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France

117 Suranaree University of Technology, Nakhon Ratchasima, Thailand

118 Technical University of Košice, Košice, Slovakia

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

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

121 Universidad Autónoma de Sinaloa, Culiacán, Mexico

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

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

124 Universidade Federal do ABC, Santo Andre, Brazil

125 University of Cape Town, Cape Town, South Africa

126 University of Houston, Houston, Texas, United States

127 University of Jyväskylä, Jyväskylä, Finland

128 University of Kansas, Lawrence, Kansas, United States

129 University of Liverpool, Liverpool, United Kingdom

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

131 University of South-Eastern Norway, Tonsberg, Norway

132 University of Tennessee, Knoxville, Tennessee, United States

133 University of the Witwatersrand, Johannesburg, South Africa

134 University of Tokyo, Tokyo, Japan

135 University of Tsukuba, Tsukuba, Japan

136 University Politehnica of Bucharest, Bucharest, Romania

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

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

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

140 Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment
de Physique Nucléaire (DPhN), Saclay, France

141 Università degli Studi di Foggia, Foggia, Italy

142 Università di Brescia, Brescia, Italy

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

144 Warsaw University of Technology, Warsaw, Poland

145 Wayne State University, Detroit, Michigan, United States

146 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany

147 Wigner Research Centre for Physics, Budapest, Hungary

148 Yale University, New Haven, Connecticut, United States

149 Yonsei University, Seoul, Republic of Korea