2017 185 21 July

Kaon femtoscopy in Pb–Pb at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV

ALICE Collaboration††thanks: See Appendix A for the list of collaboration
members ALICE Collaboration

We present the results of three-dimensional femtoscopic analyses for charged
and neutral kaons recorded by ALICE in Pb–Pb collisions at
$\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to measure the space-time
characteristics of particle production from the effects of quantum statistics
and final-state interactions in two-particle correlations. Kaon femtoscopy is
an important supplement to that of pions because it allows one to distinguish
between different model scenarios working equally well for pions. In
particular, we compare the measured 3D kaon radii with a purely hydrodynamical
calculation and a model where the hydrodynamic phase is followed by a hadronic
rescattering stage. The former predicts an approximate transverse mass
($m_{\mathrm{T}}$) scaling of source radii obtained from pion and kaon
correlations. This $m_{\mathrm{T}}$ scaling appears to be broken in our data,
which indicates the importance of the hadronic rescattering phase at LHC
energies. A $k_{\mathrm{T}}$ scaling of pion and kaon source radii is observed
instead. The time of maximal emission of the system is estimated using the
three-dimensional femtoscopic analysis for kaons. The measured emission time
is larger than that of pions. Our observation is well supported by the
hydrokinetic model predictions.

##  1 Introduction

Extremely high energy densities achieved in heavy-ion collisions at the Large
Hadron Collider (LHC) are expected to lead to the formation of the quark-gluon
plasma (QGP), a state characterized by partonic degrees of freedom [1, 2]. The
systematic study of many observables (transverse momentum spectra, elliptic
flow, jets, femtoscopy correlations) measured at the Relativistic Heavy Ion
Collider (RHIC) and the LHC confirmed the presence of strong collective motion
and the hydrodynamic behavior of the system (see e.g. [3, 4, 5, 6] and [7, 8,
9, 10]). Whereas since quite a long time hydrodynamics describes momentum
based observables, it could not describe spatial distributions at decoupling.
Correlation femtoscopy (commonly referred to as _femtoscopy_ or _HBT, Hanbury
Brown and Twiss interferometry_), measures the space-time characteristics of
particle production using particle correlations due to the effects of quantum
statistics and strong and Coulomb final-state interactions [11, 12, 13, 14,
15]. The problem to describe the spatio-temporal scales derived from
femtoscopy in heavy-ion collisions at RHIC was solved only a few years ago,
strongly constraining the hydrodynamical models [16, 17, 18]. The following
factors were understood to be important: existence of prethermal transverse
flow, a crossover transition between quark-gluon and hadron matter, non-
hydrodynamic behavior of the hadron gas at the latest stage (hadronic cascade
phase), and correct matching between hydrodynamic and non-hydrodynamics phases
(see e.g. [16]).

New challenges for hydrodynamics appeared when data were obtained at the LHC:
the large statistics now allows one to investigate not only pion femtoscopy,
which is the most common femtoscopic analysis, but also femtoscopy of heavier
particles in differential analyses with high precision.

The main objective of ALICE [19] at the LHC is to study the QGP. ALICE has
excellent capabilities to study femtoscopy observables due to good track-by-
track particle identification (PID), particle acceptance down to low
transverse momenta $p_{\rm T}$, and good resolution of secondary vertices. We
already studied pion correlation radii in Pb–Pb collisions at 2.76 TeV [20,
21]. Pion femtoscopy showed genuine effects originating from collective flow
in heavy-ion collisions, manifesting as a decrease of the source radii with
increasing pair transverse mass $m_{\rm T}=\sqrt{k_{\rm T}^{2}+m^{2}}$ [15,
22], where $k_{\rm T}=|\mathbf{p}_{\mathrm{T,1}}+\mathbf{p}_{\mathrm{T,2}}|/2$
is the average transverse momentum of the corresponding pair and $m$ is the
particles mass.

The next most numerous particle species after pions are kaons. The kaon
analyses are expected to offer a cleaner signal compared to pions, as they are
less affected by resonance decays. Studying charged and neutral kaon
correlations together provides a convenient experimental consistency check,
since they require different detection techniques. The theoretical models
which describe pion femtoscopy well, should describe kaon results with equal
precision.

Of particular interest is the study of the $m_{\rm T}$-dependence of pion and
kaon source radii. It was shown that the hydrodynamic picture of nuclear
collisions for the particular case of small transverse flow leads to the same
$m_{\rm T}$ behavior of the longitudinal radii ($R_{\rm long}$) for pions and
kaons [23]. This common $m_{\rm T}$-scaling for $\pi$ and $\rm K$ is an
indication that the thermal freeze-out occurs simultaneously for $\pi$ and
$\rm K$ and that these two particle species are subject to the same velocity
boost from collective flow. Previous kaon femtoscopy studies carried out in
Pb–Pb collisions at the SPS by the NA44 and NA49 Collaborations [24, 25]
reported the decrease of $R_{\rm long}$ with $m_{\rm T}$ as $\sim m_{\rm
T}^{-0.5}$ as a consequence of the boost-invariant longitudinal flow.
Subsequent studies carried out in Au–Au collisions at RHIC [26, 27, 28, 29]
have shown the same power in the $m_{\rm T}$-dependencies for $\pi$ and $\rm
K$ radii, consistent with a common freeze-out hypersurface. Like in the SPS
data, no exact universal $m_{\rm T}$-scaling for the 3D radii was observed at
RHIC, but still these experiments observed an approximate $m_{\rm T}$-scaling
for pions and kaons. The recent study of the $m_{\rm T}$-dependence of kaon
three-dimensional radii performed by the PHENIX collaboration [30]
demonstrated breaking of this scaling especially for the “long” direction.
PHENIX reported that the Hydro-Kinetic Model (HKM) describes well the overall
trend of femtoscopic radii for pions and kaons [31, 32].

We have published previously the study of one-dimensional correlation radii of
different particle species: $\pi^{\pm}\pi^{\pm}$, $\rm K^{\pm}\rm K^{\pm}$,
$\rm K^{0}_{S}\rm K^{0}_{S}$, $\rm p\rm p$, and
$\rm\overline{p}\rm\overline{p}$ correlations in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV for several intervals of centrality and
transverse mass [33]. The decrease of the source radii with increasing
transverse mass was observed for all types of particles, manifesting a
fingerprint of collective flow in heavy-ion collisions. The one-dimensional
femtoscopic radii demonstrated the approximate $m_{\rm T}$-scaling as it was
expected by hydrodynamic model considerations [15].

Recent calculations made within a 3+1D hydrodynamical model coupled with a
statistical hadronization code taking into account the resonance contribution,
THERMINATOR-2, showed the approximate scaling of the three dimensional radii
with transverse mass for pions, kaons and protons [34]. An alternative
calculation, that is the Hydro-Kinetic Model, including a hydrodynamic phase
as well as a hadronic rescattering stage, predicts violation of such a scaling
between pions and kaons at LHC energies [35]. Both models observe approximate
scaling if there is no rescattering phase. It is suggested in [35] that
rescattering has significantly different influence on pions and kaons and is
responsible for the violation of $m_{T}$-scaling at the LHC energies.
Moreover, the analysis of the emission times of pions and kaons obtained
within HKM in [36] showed that kaons are emitted later than pions due to
rescattering through the rather long-lived ${\rm K}^{*}(892)$ resonance. This
effect can explain the $m_{\rm T}$-scaling violation predicted in [35].

In [35] it was found that immediately decaying the ${\rm K}^{*}(892)$ and
$\phi$(1020) resonances at the chemical freeze-out hypersurface has only a
negligible influence on the kaon radii. In this scenario, resonances were
allowed to be regenerated in the hadronic phase. Further analysis in [36]
showed that it is indeed the regeneration of the ${\rm K}^{*}(892)$ resonance
through hadronic reactions which is responsible for the $m_{\rm T}$-scaling
violation predicted in [35]. This mechanism clearly manifests itself in the
prolonged emission time of kaons caused by the rather long lifetime of the
${\rm K}^{*}(892)$ resonance [35].

The approximate scaling of pion and kaon radii was predicted by investigating
3+1D hydrodynamical model + THERMINATOR-2 in [34] to hold for each of the
three-dimensional radii separately. The scaling of one-dimensional pion and
kaon radii was also studied in [34]. It was shown that after averaging the
three-dimensional radii and taking into account a mass-dependent Lorentz-boost
factor, a deviation between one-dimensional pion and kaon radii appeared.
These circumstances made it impossible to discriminate between THERMINATOR-2
[34] and the HKM calculation [35] in the earlier published one-dimensional
analysis of pion and kaon radii by ALICE [33]. The three-dimensional study
presented here is not impeded by these effects and allows one to discriminate
between the hypothesis of approximate scaling of three-dimensional radii
predicted in [34] and strong scaling violation proposed in [35]. Thus the
study of the $m_{\rm T}$-dependence of three-dimensional pion and kaon radii
can unambiguously distinguish between the different freeze-out scenarios and
clarify the existence of a significant hadronic phase.

One more interesting feature of femtoscopy studies of heavy-ion collisions
concerns the ratio of radius components in the transverse plane. The strong
hydrodynamic flow produces significant positive space-time correlations during
the evolution of the freeze-out hypersurface. This influences the extracted
radius parameters of the system in the plane perpendicular to the beam axis.
The radius along the pair transverse momentum is reduced by the correlation
with respect to the perpendicular one in the transverse plane. This effect
appears to be stronger at LHC than at RHIC energies [37, 38]. It was studied
by the ALICE collaboration for pions in Pb–Pb collisions at 2.76 TeV [21] at
different centralities. This work extends this study to kaons and compares the
obtained transverse radii with those found in the analysis for pions and to
the model calculations discussed above. The paper is organized as follows.
Section 2 explains the data selection and describes the identification of
charged and neutral kaons. In Section 3 the details of the analysis of the
correlation functions are discussed together with the investigation of the
systematic uncertainties. Section 4 presents the measured source radii as well
as the extracted emission times and compares them to model predictions.
Finally, Section 5 summarizes the obtained results and discusses them within
the hydrokinetic approach.

##  2 Data selection

Large sets of data were recorded by the ALICE collaboration at $\sqrt{s_{\rm
NN}}=2.76$ TeV in Pb–Pb collisions. The about 8 million events from 2010 (used
only in the $\rm K^{0}_{S}\rm K^{0}_{S}$ analysis) and about 40 million events
from 2011 made it possible to perform the three-dimensional analyses of
neutral and charged kaon correlations differentially in centrality and pair
transverse momentum $k_{\rm T}$. Three trigger types were used: minimum bias,
semi-central (10-50% collision centrality), and central (0-10% collision
centrality) [39]. The analyses were performed in the centrality ranges:
(0–5%), (0–10%), (10–30%), and (30–50%). The centrality was determined using
the measured amplitudes in the V0 detector [39]. The following transverse
momentum $k_{\mathrm{T}}$ bins were considered: (0.2–0.4), (0.4–0.6), and
(0.6–0.8) GeV/$c$ for charged kaons and (0.2–0.6), (0.6–0.8), (0.8–1.0), and
(1.0–1.5) GeV/$c$ for neutral kaons.

Charged particle tracking is generally performed using the Time Projection
Chamber (TPC) [40] and the Inner Tracking System (ITS) [19]. The ITS also
provides high spatial resolution in determining the primary collision vertex.

Particle identification (PID) for reconstructed tracks was carried out using
both the TPC and the Time-of-Flight (TOF) detector [41]. For TPC PID, a
parametrization of the Bethe-Bloch formula was employed to calculate the
specific energy loss (d$E$/d$x$) in the detector expected for a particle with
a given mass and momentum. For PID with TOF, the particle mass hypothesis was
used to calculate the expected time-of-flight as a function of track length
and momentum. For each PID method, a value $N_{\sigma}$ was assigned to each
track denoting the number of standard deviations between the measured track
d$E$/d$x$ or time-of-flight and the calculated one as described above.
Different cut values of $N_{\sigma}$ were chosen based on detector performance
for various particle types and track momenta (see Table 1 for specific values
used in both analyses). More details on PID can be found in Secs. 7.2–7.5 of
[42].

The analysis details for charged and neutral kaons are discussed separately
below. All major selection criteria are also listed in Table 1.

###  2.1 Charged kaon selection

Track reconstruction for the charged kaon analysis was performed using the
tracks’ signal in the TPC. The TPC is divided by the central electrode into
two halves, each of them is composed of 18 sectors (covering the full
azimuthal angle) with 159 padrows placed radially in each sector. A track
signal in the TPC consists of space points (clusters), each of which is
reconstructed in one of the padrows. A track was required to be composed out
of at least 70 such clusters. The parameters of the track are determined by
performing a Kalman fit to a set of clusters with an additional constraint
that the track passes through the primary vertex. The quality of the fit is
requested to have $\chi^{2}/{\mathrm{NDF}}$ better than 2. The transverse
momentum of each track was determined from its curvature in the uniform
magnetic field. The momentum from this fit in the TPC was used in the
analysis. Tracks were selected based on their distance of closest approach
(DCA) to the primary vertex, which was required to be less than 2.4 cm in the
transverse and less than 3.0 cm in the longitudinal direction.

$\rm K^{\pm}$ identification was performed using the TPC (for all momenta) and
the TOF detector (for $p>0.5$ GeV/$c$). The use of different values for
$N_{\sigma,{\mathrm{TPC}}}$ and $N_{\sigma,{\mathrm{TOF}}}$ was the result of
studies to obtain the best kaon purity, defined as the fraction of accepted
kaon tracks that correspond to true kaon particles, while retaining a decent
efficiency. The estimation of purity for $p<0.5$ GeV/c was performed by
parametrizing the TPC d$E$/d$x$ distribution in momentum slices for the
contributing species [42]. The dominant contamination for charged kaons comes
from $\rm e^{\pm}$ in the momentum range $0.4<p<0.5$ GeV/$c$. The purity for
$p>0.5$ GeV/$c$, where the TOF information was employed, was studied with
HIJING [43] simulations using GEANT [44] to model particle transport through
the detector; the charged kaon purity was estimated to be greater than 99%.
The momentum dependence of the single kaon purity is shown in Fig. 1(a). The
pair purity is calculated as the product of two single-particle purities,
where the momenta are taken from the experimentally determined distribution.
The $\rm K^{\pm}$ pair purity as a function of $k_{\rm T}$ at three different
centralities is shown in Fig.1(b). Kaon pair transverse momentum is an
averaged $p_{\rm T}$ of single kaons taken from the whole $p_{\rm T}$ range,
which is the reason why the pair purities are larger than single particle
ones.

Figure 1: Single $\rm K^{\pm}$ purity (a) and pair purity for small relative
momenta (b) for different centralities. In (b) the $k_{\rm T}$ values for
different centrality intervals are slightly offset for clarity.

Two kinds of two-track effects have been investigated: splitting, where a
signal produced by one particle is incorrectly reconstructed as two tracks,
and merging, where two particles are reconstructed as only one track. These
detector inefficiencies can be suppressed by employing specific pair selection
criteria. We used the same procedure as in [21] which works here as well with
slightly modified cut values. Charged kaon pairs were required to have a
separation of $|\Delta\varphi^{*}|>0.04$ and $|\Delta\eta|>0.02$. Here,
$\varphi^{*}$ is the azimuthal position of the track in the TPC at $R$ = 1.2
m, taking into account track curvature in the magnetic field, and $\eta$ is
the pseudorapidity. Also, all track pairs sharing more than $5\%$ of TPC
clusters were rejected.

Charged kaon selection
---
$p_{\rm T}$ |  $0.15<p_{\rm T}<1.5$ GeV/$c$
$|\eta|$ | $<0.8$
$\rm DCA_{\rm transverse}$ to primary vertex |  $<2.4$ cm
$\rm DCA_{\rm longitudinal}$ to primary vertex |  $<3.0$ cm
$N_{\sigma,\rm TPC}$ (for $p<0.5$ GeV/$c$) | $<2$
$N_{\sigma,\rm TPC}$ (for $p>0.5$ GeV/$c$) | $<3$
$N_{\sigma,\rm TOF}$ (for $0.5<p<0.8$ GeV/$c$) | $<2$
$N_{\sigma,\rm TOF}$ (for $0.8<p<1.0$ GeV/$c$) | $<1.5$
$N_{\sigma,\rm TOF}$ (for $1.0<p<1.5$ GeV/$c$) | $<1.0$
Neutral kaon selection
$|\eta|$ | $<0.8$
Daughter-daughter $\rm DCA_{3D}$ |  $<0.3$ cm
$\rm DCA_{3D}$ to primary vertex |  $<0.3$ cm
Invariant mass |  $0.480<m_{\pi^{+}\pi^{-}}<0.515$ GeV/${c}^{2}$
Daughter $p_{\rm T}$ |  $>0.15$ GeV/$c$
Daughter $|\eta|$ | $<0.8$
Daughter $\rm DCA_{3D}$ to primary vertex |  $>0.4$ cm
Daughter $N_{\sigma,\rm TPC}$ | $<3$
Daughter $N_{\sigma,\rm TOF}$ (for $p>0.8$ GeV/$c$) | $<3$
Table 1: Single particle selection criteria.

###  2.2 Neutral kaon selection

The decay channel $\rm K^{0}_{S}\rightarrow\pi^{+}\pi^{-}$ was used for the
identification of neutral kaons. The secondary pion tracks were reconstructed
using TPC and ITS information. The single-particle cuts for parents ($\rm
K^{0}_{S}$) and daughters ($\pi^{\pm}$) used in the decay-vertex
reconstruction are shown in Table 1. The daughter-daughter DCA, that is the
distance of closest approach of the two daughter pions from a candidate $\rm
K^{0}_{S}$ decay, proved useful in rejecting background topologies. PID for
the pion daughters was performed using both TPC (for all momenta) and TOF (for
$p>0.8$ GeV/$c$). The very good detector performance is reflected in the FWHM
of the $\rm K^{0}_{S}$ peak of only 8 MeV/$c^{2}$. The selection criteria used
in this analysis were chosen as a compromise to maximize statistics while
keeping a high signal purity. The neutral kaon purity (defined as
Sig./[Sig.+Bkg.] for $0.480<m_{\pi^{+}\pi^{-}}<0.515$ GeV/$c^{2}$) was larger
than 0.95.

Two main two-particle cuts were used in the neutral kaon analysis. To resolve
two-track inefficiencies associated with the daughter tracks, such as the
splitting or merging of tracks discussed above, a separation cut was employed
in the following way. For each kaon pair, the spatial separation between the
same-sign pion daughters was calculated at several points throughout the TPC
(every 20 cm radially from 85 cm to 245 cm) and averaged. If the average
separation of either pair of tracks was below 5 cm, the kaon pair was not
used. Another cut was used to prevent two reconstructed kaons from using the
same daughter track. If two kaons shared a daughter track, one of them was
excluded using a procedure which compared the two $\rm K^{0}_{S}$ candidates
and kept the candidate whose reconstructed parameters best matched those
expected for a true $\rm K^{0}_{S}$ particle in two of three categories
(smaller $\rm K^{0}_{S}$ DCA to primary vertex, smaller daughter-daughter DCA,
and $\rm K^{0}_{S}$ mass closer to the PDG value [45]). This procedure was
shown, using HIJING+GEANT simulations, to have a success rate of about 95% in
selecting a true $\rm K^{0}_{S}$ particle over a fake one. More details about
the $\rm K^{0}_{S}\rm K^{0}_{S}$ analysis can be found in Refs. [46, 47]. $\rm
K^{0}_{S}$ candidate selection criteria developed in other works [33] were
used here as well; they are included in Table 1.

##  3 Correlation functions

The femtoscopic correlation function $C$ is constructed experimentally as the
ratio $C({\bf q})=A({\bf q})/B({\bf q})$, where $A({\bf q})$ is the measured
distribution of the difference ${\bf q}={\bf p}_{2}-{\bf p}_{1}$ between the
three-momenta of the two particles ${\bf p_{1}}$ and ${\bf p_{2}}$ taken from
the same event, $B({\bf q})$ is a reference distribution of pairs of particles
taken from different events (mixed). For a detailed description of the
formalism, see e.g. [14]. The pairs in the denominator distribution
$B(\textbf{q})$ are constructed by taking a particle from one event and
pairing it with a particle from another event with a similar centrality and
primary vertex position along the beam direction. Each event is mixed with
five (ten) others for the $\rm K^{0}_{S}$ ($\rm K^{\pm}$) analysis. The
numerator and denominator are normalized in the full $q=\sqrt{|{\bf
q}|^{2}-q_{0}^{2}}$ range used (0–0.3 GeV/$c$) such that $C(q)\rightarrow 1$
means no correlation. Pair cuts have been applied in exactly the same way for
the same-event (signal) and mixed-event (background) pairs.

The momentum difference is calculated in the longitudinally co-moving system
(LCMS), where the longitudinal pair momentum vanishes, and is decomposed into
($q_{\rm out}$, $q_{\rm side}$, $q_{\rm long}$), with the “long” axis going
along the beam, “out” along the pair transverse momentum, and “side”
perpendicular to the latter in the transverse plane (Bertsch-Pratt
convention).

The correlation functions have been corrected for momentum resolution effects,
by using the HIJING event generator and assigning a quantum-statistical weight
to each particle pair. Further, these modified events were propagated through
the full simulation of the ALICE detectors [19]. The ratios of the correlation
functions obtained before and after this full event simulation have been taken
as the correction factors. The correlation function from the data has been
divided by this $q$-dependent factor. The correction increases the obtained
radii by 3–5%.

###  3.1 Charged kaon

The three-dimensional correlation functions were fitted by the Bowler-Sinyukov
formula [48, 49]:

$C({\bf q})=N\left(1-\lambda\right)+N\lambda K(q)\left[1+\exp\left(-R_{\rm
out}^{2}q_{\rm out}^{2}-R_{\rm side}^{2}q_{\rm side}^{2}-R_{\rm
long}^{2}q_{\rm long}^{2}\right)\right],$ (1)

where $R_{\rm out}$, $R_{\rm side}$, and $R_{\rm long}$ are the Gaussian
femtoscopic radii in the LCMS frame, $N$ is the normalization factor, and $q$
is the momentum difference in the pair rest frame (PRF) 111Average $q$ in PRF
for the given “out-side-long” bin is determined during the $C({\bf q})$
construction and used as an argument of the $K$-function. . The $\lambda$
parameter, which characterizes the correlation strength, can be affected by
long-lived resonances, coherent sources [50, 51, 52], and non-Gaussian
features of the particle-emission distribution. We account for Coulomb effects
through $K(q)$, calculated according to Ref. [49, 51] as

$K(q)=C({\rm QS+Coulomb})/C(\rm QS).$ (2)

Figure 2: A sample projected $\rm K^{\pm}\rm K^{\pm}$ correlation function
with fit. The error bars are statistical only. Systematic uncertainties on the
points are equal to or less than the statistical error bars shown.

Here, the theoretical correlation function $C(\rm QS)$ takes into account
quantum statistics only and $C(\rm QS+\rm Coulomb)$ considers quantum
statistics and the Coulomb final-state interaction (FSI) contribution to the
wave function [14].

The experimental correlation functions have been corrected for purity
according to:

$C_{\mathrm{corrected}}=(C_{\mathrm{raw}}-1+\zeta)/\zeta,$ (3)

where $\zeta$ is the pair purity taken from Fig. 1.

Figure 2 shows a sample projected $\rm K^{\pm}\rm K^{\pm}$ correlation
function with a fit performed according to Eq. (1). When the 3D correlation
function is projected on one axis, the momentum differences in the two other
directions are required to be within (-0.04,0.04) GeV/$c$.

###  3.2 Neutral kaon

$\rm K^{0}_{S}\rm K^{0}_{S}$ correlation functions were fitted using a
parametrization which includes Bose-Einstein statistics as well as strong
final-state interactions [53, 28]. Strong final-state interactions have an
important effect on $\rm K^{0}_{S}\rm K^{0}_{S}$ correlations. Particularly,
the $\rm K^{0}\rm\overline{K}{}^{0}$ channel is affected by the near-threshold
resonances $\mathrm{f}_{0}(980)$ and $\mathrm{a}_{0}(980)$. Using the equal
emission time approximation in the pair rest frame (PRF) [53], the elastic
$\rm K^{0}\rm\overline{K}{}^{0}$ transition is written as a stationary
solution $\Psi_{-\vec{k}\mkern 2.0mu\vphantom{k}^{*}}(\vec{r}\mkern
2.0mu\vphantom{r}^{*})$ of the scattering problem in the PRF, where
$\vec{k}\mkern 2.0mu\vphantom{k}^{*}$ and $\vec{r}\mkern
2.0mu\vphantom{r}^{*}$ represent the momentum of a particle and the emission
separation of the pair in the PRF (the $-\vec{k}\mkern 2.0mu\vphantom{k}^{*}$
subscript refers to a reversal of time from the emission process), which at
large distances has the asymptotic form of a superposition of a plane wave and
an outgoing spherical wave,

$\Psi_{-\vec{k}\mkern 2.0mu\vphantom{k}^{*}}(\vec{r}\mkern
2.0mu\vphantom{r}^{*})=e^{-i\vec{k}\mkern
2.0mu\vphantom{k}^{*}\cdot\vec{r}\mkern
2.0mu\vphantom{r}^{*}}+g(k^{*})\dfrac{e^{ik^{*}r^{*}}}{r^{*}}\;,$ (4)

where $g(k^{*})$ is the s-wave scattering amplitude for a given system. For
$\rm K^{0}\rm\overline{K}{}^{0}$, $g(k^{*})$ is dominated by the
$\mathrm{f}_{0}$ and $\mathrm{a}_{0}$ resonances and written in terms of the
resonance masses and decay couplings [28]:

$\displaystyle g(k^{*})$
$\displaystyle=\dfrac{1}{2}[g_{0}(k^{*})+g_{1}(k^{*})]\;,$ (5) $\displaystyle
g_{I}(k^{*})$
$\displaystyle=\dfrac{\gamma_{r}}{m_{r}^{2}-s-i\gamma_{r}k^{*}-i\gamma_{r}^{\prime}k_{r}^{\prime}}\;.$
(6)

Here, $s=4(m^{2}_{K}+k^{*2})$; $\gamma_{r}(\gamma_{r}^{\prime})$ refers to the
couplings of the resonances to the $\mathrm{f}_{0}\rightarrow\rm
K^{0}\rm\overline{K}{}^{0}(\mathrm{f}_{0}\rightarrow\pi\pi)$ and
$\mathrm{a}_{0}\rightarrow\rm
K^{0}\rm\overline{K}{}^{0}(\mathrm{a}_{0}\rightarrow\pi\eta)$ channels;
$m_{r}$ is the resonance mass; and $k_{r}^{\prime}$ refers to the momentum in
the PRF of the second decay channel ($\mathrm{f}_{0}\rightarrow\pi\pi$ or
$\mathrm{a}_{0}\rightarrow\pi\eta$) with the corresponding partial width
$\Gamma_{r}^{\prime}=\gamma_{r}^{\prime}k_{r}^{\prime}/m_{r}$ . The amplitudes
$g_{I}$ of isospin $I=0$ and $I=1$ refer to the $\mathrm{f}_{0}$ and
$\mathrm{a}_{0}$, respectively. The parameters associated with the resonances
and their decays are taken from several experiments [54, 55, 56, 57], and the
values are listed in Table 2.

Ref | $m_{\mathrm{f}_{0}}$ | $\gamma_{\mathrm{f}_{0}K\bar{K}}$ | $\gamma_{\mathrm{f}_{0}\pi\pi}$ | $m_{\mathrm{a}_{0}}$ | $\gamma_{\mathrm{a}_{0}K\bar{K}}$ | $\gamma_{\mathrm{a}_{0}\pi\eta}$
---|---|---|---|---|---|---
[54] | 0.973 | 2.763 | 0.5283 | 0.985 | 0.4038 | 0.3711
[55] | 0.996 | 1.305 | 0.2684 | 0.992 | 0.5555 | 0.4401
[56] | 0.996 | 1.305 | 0.2684 | 1.003 | 0.8365 | 0.4580
[57] | 0.978 | 0.792 | 0.1990 | 0.974 | 0.3330 | 0.2220
Table 2: The $\mathrm{f}_{0}$ and $\mathrm{a}_{0}$ masses and coupling
parameters, all in GeV.

The correlation function is then calculated by integrating
$\Psi_{-\vec{k}\mkern 2.0mu\vphantom{k}^{*}}(\vec{r}\mkern
2.0mu\vphantom{r}^{*})$ in the Koonin-Pratt equation [58, 59]

$C(\vec{k}\mkern 2.0mu\vphantom{k}^{*},\vec{K})=\int d^{3}\,\vec{r}\mkern
2.0mu\vphantom{r}^{*}\,S_{\vec{K}}(\vec{r}\mkern
2.0mu\vphantom{r}^{*})\lvert\Psi^{S}_{-\vec{k}\mkern
2.0mu\vphantom{k}^{*}}(\vec{r}\mkern 2.0mu\vphantom{r}^{*})\rvert^{2}\,,$ (7)

where $S_{\vec{K}}(\vec{r}\mkern 2.0mu\vphantom{r}^{*})$ is the Gaussian
source distribution in terms of $R_{\rm out}$, $R_{\rm side}$, and $R_{\rm
long}$, $\vec{K}$ is the average pair momentum, and $\Psi^{S}_{-\vec{k}\mkern
2.0mu\vphantom{k}^{*}}(\vec{r}\mkern 2.0mu\vphantom{r}^{*})$ is the
symmetrized version of $\Psi_{-\vec{k}\mkern
2.0mu\vphantom{k}^{*}}(\vec{r}\mkern 2.0mu\vphantom{r}^{*})$ for bosons.
Although Eq. (7) can be integrated analytically for $\rm K^{0}_{S}\rm
K^{0}_{S}$ correlations with FSI for the one-dimensional case [28], for the
three-dimensional case this integration cannot be performed analytically. In
order to form the 3D correlation function, we combine a Monte Carlo emission
simulation with a calculation of the two-particle wavefunction, thus
performing a numerical integration of Eq. (7). The Monte Carlo emission
simulation consists of generating the pair positions sampled from a three-
dimensional Gaussian in the PRF, with three input radii as the width
parameters, and generating the particle momenta sampled from a distribution
taken from data. Using the MC-sampled positions and momenta, we calculate
$\Psi^{S}_{-\vec{k}\mkern 2.0mu\vphantom{k}^{*}}(\vec{r}\mkern
2.0mu\vphantom{r}^{*})$. We then build a correlation function using the
wavefunction weights to form the signal distribution, and an unweighted
distribution acts as a background. This theoretical correlation function is
then used to fit the data. Finally, we make a Lorentz boost, $\gamma$, of
$R_{\rm out}$ from the PRF to the LCMS frame ($R_{\rm side}$ and $R_{\rm
long}$ are not affected by the boost). More details on the 3D fitting
procedure can be found in Ref. [46].

Figure 3 shows a sample projected $\rm K^{0}_{S}\rm K^{0}_{S}$ correlation
function with fit. Also shown is the contribution to the fit from the quantum
statistics part only. As seen, the FSI part produces a significant depletion
of the correlation function in the $q$ range 0–0.1 GeV/$c$ in each case.

Figure 3: A sample projected $\rm K^{0}_{S}\rm K^{0}_{S}$ correlation function
with fit. Also shown is the contribution to the fit from the quantum
statistics part only. The error bars are statistical only. Systematic
uncertainties on the points are equal to or less than the statistical error
bars shown.

###  3.3 Systematic uncertainties

The effects of various sources of systematic uncertainty on the extracted fit
parameters were studied as functions of centrality and $k_{\rm T}$. For each
source, we take the maximal deviation and apply it symmetrically as the
uncertainty. Table 3 shows minimum and maximum uncertainty values for various
sources of systematic uncertainty for charged and neutral kaons. The
systematic errors are summed up quadratically. The values of the total
uncertainty are not necessarily equal to the sum of the individual
uncertainties, as the latter can come from different centrality or $k_{\rm T}$
bins. Both analyses studied the effects of changing the selection criteria
used for the events, particles, and pairs (variation of cut values up to
$\pm$25$\%$) and varying the range of $q$ values over which the fit is
performed (variation of $q$ limits up to $\pm$25$\%$). Uncertainties
associated with momentum resolution corrections are included into the $\rm
K^{\pm}$ analysis; for the $\rm K^{0}_{S}$ analysis, these uncertainties are
found to be small compared to other contributions. Both analyses were
performed separately for the two different polarities of the ALICE solenoid
magnetic field, the difference was found to be negligible.

For the $\rm K^{0}_{S}$ fitting procedure, the mean $\gamma$ value is
calculated for each centrality and $k_{\rm T}$ selection and used to scale
$R_{\rm out}$. However, each bin has a spread of $\gamma$ values associated
with it. The standard deviation of the mean $\gamma$ value for each $k_{\rm
T}$ bin was used as an additional source of systematic error for $R_{\rm
out}$. For $\rm K^{0}_{S}$, an uncertainty on the strong FSI comes from the
fact that several sets of $\rm\mathrm{f}_{0}(980)$ and
$\rm\mathrm{a}_{0}(980)$ parameters are available [57, 54, 55, 56]; each set
is used to fit the data, the results are averaged, and the maximal difference
was taken as a systematic error.

The $\rm K^{\pm}$ analysis has uncertainties associated with the choice of the
radius for the Coulomb function. For each correlation function it is set to
the value from the one-dimensional analysis [33]. Its variation by $\pm 1$ fm
is a source of systematic uncertainty. Another source of systematic
uncertainty is misidentification of particles and the associated purity
correction. A 10% variation of the parameters in the purity correction was
performed. We also incorporated sets with a reduced electron contamination by
I) tightening the PID criteria, in particular extending the momentum range
where the TOF signal was used and requiring the energy-loss measurement to be
consistent with the kaon hypothesis within one sigma, and II) completely
excluding the momentum range 0.4–0.5 GeV/$c$.

|  $R_{\rm out}$ [%] |  $R_{\rm side}$ [%] |  $R_{\rm long}$ [%] |  $\lambda$ [%]
---|---|---|---|---
Charged kaon |  |  |
Single particle selection | 0–2 | 0–2 | 0–2 | 0–2
PID and purity |  $<$0.1 |  $<$0.1 |  $<$0.1 | 1–10
Pair selection | 2–8 | 1–6 | 2–10 | 6–15
Fit range | 1–3 | 1–4 | 1–7 | 1–7
Coulomb function | 3–5 | 1–2 | 2–3 | 8–10
Momentum resolution | 1–2 | 1–2 | 1–3 | 2–6
Total (quad. sum) | 7–11 | 7–9 | 7–12 | 10–17
Neutral kaon |  |  |
Single particle and pair selection | 0–1 | 1–5 | 1–4 | 6–14
Pair selection | 2–8 | 1–6 | 2–10 | 6–15
FSI Model | 1–6 | 1–6 | 1–15 | 3–9
$\gamma$ | 5–10 |  $<$0.1 |  $<$0.1 |  $<$0.1
Fit range | 0–6 | 0–6 | 0–10 | 0–6
Momentum resolution |  $<$0.1 | 0–3 | 0–6 | 2–3
Total (quad. sum) | 6–11 | 3–7 | 2–15 | 7–16
Table 3: Minimum and maximum uncertainty values for various sources of
systematic uncertainty for charged and neutral kaons (in percent). Note that
each value is the maximum uncertainty from a specific source, but can pertain
to a different centrality or $k_{\rm T}$ bin. Thus, the maximum total
uncertainties are smaller than (or equal to) the quadratic sum of the maximum
individual uncertainties.

##  4 Results and discussion

Figure 4 shows the $m_{\mathrm{T}}$-dependence of the extracted femtoscopic
radii $R_{\rm out}$, $R_{\rm side}$, and $R_{\rm long}$ in three centrality
selections for pions [21] and charged and neutral kaons. The obtained radii
are smaller for more peripheral collisions than for central ones. The radii
decrease with increasing $m_{\mathrm{T}}$ and each particle species roughly
follows an $m_{\mathrm{T}}^{-1/2}$ dependence. The radii in “out” and “long”
directions exhibit larger values for kaons than for pions at the same
transverse mass demonstrating that the $m_{\mathrm{T}}$-scaling is broken.
This difference increases with centrality and is maximal for the most central
collisions. Also presented in Fig. 4 are the predictions of the (3+1)D
hydrodynamical model coupled with the statistical hadronization code
THERMINATOR-2 [34]. The model describes well the $m_{\mathrm{T}}$-dependence
of pion radii, but underestimates kaon radii. Consistent with the data, the
(3+1)D Hydro+THERMINATOR-2 model shows mild breaking in the “long” direction
for central collisions, but it underestimates the breaking in the “out”
direction. The significance of this breaking of the scaling is discussed
further in this section.

In addition to the aforementioned three-dimensional radii, here for the 0–5%
most central events, Fig. 5 also shows the $m_{\mathrm{T}}$ dependence of the
ratio $R_{\rm out}/R_{\rm side}$ for charged and neutral kaons in comparison
with HKM predictions [35] with and without the hadronic rescattering phase.
The HKM calculations without rescattering exhibit an approximate
$m_{\mathrm{T}}$-scaling but do not describe the data, while the data are well
reproduced by the full hydro-kinetic model calculations thereby showing the
importance of the rescattering phase at LHC energies. The $R_{\rm out}$ and
$R_{\rm side}$ radii are both influenced by flow and rescatterings, so their
ratio is rather robust against these effects. The fact that $R_{\rm
out}/R_{\rm side}$ ratio of pions and kaons coincide in the HKM simulations
(Fig. 5) is related to some underestimation of $R_{\rm side}$ radii for pions
while pion $R_{\rm out}$ radii are slightly overestimated in the model.

Figure 4:  The 3D LCMS radii vs. $m_{\mathrm{T}}$ for charged (light green
crosses) and neutral (dark green squares) kaons and pions [21] (blue circles)
in comparison with the theoretical predictions of the (3+1)D Hydro +
THERMINATOR-2 model [34] for pions (blue solid lines) and kaons (red solid
lines).  Figure 5:  The 3D LCMS radii vs. $m_{\mathrm{T}}$ for 0–5% most
central collisions in comparison with the theoretical predictions of HKM [35]
for pions (blue lines) and kaons (red lines).  Figure 6:  The 3D LCMS radii
vs. $k_{\mathrm{T}}$ for charged (light green crosses) and neutral (dark green
squares) kaons and pions [21] (blue circles).

It was predicted in [35] that the radii scale better with $k_{\mathrm{T}}$ at
LHC energies as a result of the interplay of different factors in the model,
including the particular initial conditions. Figure 6 illustrates the
$k_{\mathrm{T}}$-dependence of the femtoscopic radii $R_{\rm out}$, $R_{\rm
side}$, and $R_{\rm long}$. Unlike the $m_{\mathrm{T}}$-dependence, the radii
seem to scale better with $k_{\mathrm{T}}$ in accordance with this prediction.

The ratio $R_{\rm out}/R_{\rm side}$ appears to be sensitive to the space-time
correlations present at the freeze-out hypersurface [37, 38, 21]. As it was
observed in [21], the ratio for pions is consistent with unity, slowly
decreasing for more peripheral collisions and higher $k_{\mathrm{T}}$. In Fig.
7, the ratio $R_{\rm out}/R_{\rm side}$ is shown for pions and kaons at
different centralities. The systematic uncertainties partially cancel in the
ratio. Systematic uncertainties are correlated in $m_{\rm T}$ for each type of
particle pair; no correlation between the systematic uncertainties of the
charged and neutral species exists. The measured $R_{\rm out}/R_{\rm side}$
ratios are slightly larger for kaons than for pions. This is an indication of
different space-time correlations for pions and kaons, and a more prolonged
emission duration for kaons.

Figure 7:  $R_{\rm out}/R_{\rm side}$ vs. $m_{\mathrm{T}}$ for pions [21] and
kaons for different centrality intervals. Figure 8:  $R^{2}_{\rm long}$ vs.
$m_{\mathrm{T}}$ for kaons and pions. The solid lines show the fit using Eq.
(9) for pions and kaons to extract the emission times ($\tau$); the dashed and
dotted lines show the fit using Eq. (8) with $T_{\rm kin}$ = 0.144 GeV and
$T_{\rm kin}$ = 0.120 GeV, respectively. For pions at small $m_{\mathrm{T}}$,
the dashed and dotted line coincide.

In our previous pion femtoscopy analysis [20] the information about the
emission time (decoupling time) at kinetic freeze-out $\tau\sim 10$ fm/$c$ was
extracted by fitting the $m_{\mathrm{T}}$-dependence of $R_{\rm long}^{2}$
using the blast-wave expression [60]:

$R_{\rm long}^{2}=\tau^{2}\frac{T_{\rm
kin}}{m_{\mathrm{T}}}\frac{K_{2}(m_{\mathrm{T}})}{K_{1}(m_{\mathrm{T}})},$ (8)

where $T_{\rm kin}$ is the temperature at kinetic freeze-out, and $K_{n}$ are
the integer-order modified Bessel functions. We tried to use Eq. (8) to fit
the $R_{\rm long}^{2}$ $m_{\mathrm{T}}$-dependence (Fig. 8) for pions and
kaons taking the thermal freeze-out temperature $T_{\rm kin}$ = 0.120 GeV as
in [20] (dotted lines) and $T_{\rm kin}$ = 0.144 GeV (dashed lines). The
emission times extracted from the fit are presented in Table 4. However,
though this formula works well for pions, it fails to describe kaon
longitudinal radii. Large transverse flow may be partially responsible for
this failure [36]. The following analytical formula for the time of maximal
emission, $\tau_{max}$, is proposed in [36]:

$R_{\rm long}^{2}=\tau_{\rm max}^{2}\frac{T_{\rm
max}}{m_{\mathrm{T}}\cosh{y_{\mathrm{T}}}}(1+\frac{3T_{\rm
max}}{2m_{\mathrm{T}}\cosh{y_{\mathrm{T}}}}),$ (9)

where $\cosh{y_{\mathrm{T}}}=(1-v_{\mathrm{T}}^{2})^{-1/2}$,
$v_{\mathrm{T}}=\frac{\beta p_{\rm T}}{\beta m_{\mathrm{T}}+\alpha}$, $T_{\rm
max}$ is the temperature at the hypersurface of maximal emission,
$\beta=1/T_{\rm max}$, and $\alpha$ is a free parameter determining the
intensity of flow 222 The authors of [36] use full evolutionary model (HKM)
that has no sharp/sudden kinetic freeze-out. For such type of models a
continuous hadron emission takes place instead. Then for each particle
species, considered within certain transverse momentum bin, there is a 4D
layer, adjacent to the space-like hypersurface of maximal emission, where most
of selected particles are emitted from. This non-enclosed hypersurface is
characterized by the (average) proper time $\tau_{\rm max}$ – time of maximal
emission, and the effective temperature $T_{\rm max}$. The proposed
phenomenological expression for $R_{\rm long}$ is associated just with this
hypersurface and is based on the model that is different from the blast-wave
parameterization for sudden freeze-out. So the blast-wave temperature $T_{\rm
kin}$ can differ from the temperature parameter $T_{\rm max}$. . The advantage
of the formula given in Eq. (9) is that it is derived for a scenario with
transverse flow of any intensity, which is especially important for LHC
energies.

The analytical formula Eq. (9) was used to fit the $m_{\mathrm{T}}$-dependence
of $R_{\rm long}^{2}$ (Fig. 8). The fit was performed using the following
parameters determined in [36] by fitting light flavor particle spectra [61]:
$T_{\rm max}$ = 0.144 GeV, and $\alpha_{\pi}$ = 5.0 and $\alpha_{K}$ = 2.2.

The extracted times of maximal emission are presented in Table 4.

method |  $T$ (GeV) | $\alpha_{\pi}$ | $\alpha_{K}$ |  $\tau_{\pi}$ (fm/$c$) |  $\tau_{K}$ (fm/$c$)
---|---|---|---|---|---
fit with BW Eq. (8) | 0.120 | - | - | 9.6 $\pm$ 0.2 | 10.6 $\pm$ 0.1
fit with BW Eq. (8) | 0.144 | - | - | 8.8 $\pm$ 0.2 | 9.5 $\pm$ 0.1
fit with Eq. (9) | 0.144 | 5.0 | 2.2 | 9.3 $\pm$ 0.2 | 11.0 $\pm$ 0.1
fit with Eq. (9) | 0.144 | 4.3 $\pm$ 2.3 | 1.6 $\pm$ 0.7 | 9.5 $\pm$ 0.2 | 11.6 $\pm$ 0.1
Table 4: Emission times for pions and kaons extracted using the Blast-wave
formula Eq. (8) and the analytical formula Eq. (9).

In order to estimate the systematic errors of the extracted times of maximal
emission we also have performed fitting with $T_{\rm max}$, $\alpha_{\pi}$ and
$\alpha_{K}$ varied within the range of their uncertainty [36]: $\pm$0.03 GeV,
$\pm$3.5 and $\pm$0.7, respectively. The maximum deviations from the central
values appeared to be (+1.8, -0.5) fm/$c$ for pions and (+0.5, -0.1) fm/$c$
for kaons. These systematic errors are fully correlated. Regardless of the
specific parameter choice, we consistently observe the time of maximal
emission for kaons to be larger than the one for pions. The extracted times of
maximal emission are rather close to those obtained within the HKM model [36]:
$\tau_{\pi}=9.44\pm 0.02$ fm/$c$, $\tau_{K}=12.40\pm 0.04$ fm/$c$ 333These
results were obtained in [36] using the small interval $q$=0-0.04 GeV/$c$ in
order to minimize influence of the non-Gaussian tails. It is found in [36]
that if even strong non-Gaussian behavior is observed for the kaon correlation
function in wide $q$-interval, one can nevertheless utilize the same formula
Eq. (9), but making free the parameter $\alpha$ for kaons. Then one gets
practically the same effective time for kaon emission, as it is obtained from
the fit of the correlation function in the small interval $q$=0-0.04 GeV/$c$;
for pions there is no such problem.. There is evidence that the time of
maximal emission for pions is smaller than the one for kaons. This observation
can explain the observed breaking of $m_{\mathrm{T}}$-scaling between pions
and kaons. It is interesting to note that in [36] this difference in the
emission times is explained by the different influence of resonances on pions
and kaons during the rescattering phase due to kaon rescattering through the
$\rm{K}^{*}$(892) resonance (with lifetime of 4–5 fm/$c$). It was shown in
[36] that a significant regeneration of the $\rm{K}^{*}(892)$ takes place in
full HKM simulations with rescatterings (UrQMD cascade), whereas this process
is not present in a scenario where only resonance decays are taken into
account.

Similar findings were reported in [62], where the production yield of
$\rm{K}^{*}$(892) in heavy-ion collisions at the LHC was studied. Also there,
the inclusion of a hadronic phase in the theoretical modeling of the
production process proved to be essential in order to reproduce the
experimentally found suppression pattern of $\rm{K}^{*}(892)$ production when
compared to pp collisions [63].

##  5 Summary

We presented the first results of three-dimensional femtoscopic analyses for
charged and neutral kaons in Pb–Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76
TeV.

A decrease of source radii with increasing transverse mass and decreasing
event multiplicity was observed. The $m_{\mathrm{T}}$ scaling expected by pure
hydro-dynamical models appears to be broken in our data. A scaling of pion and
kaon radii with $k_{\rm T}$ was observed instead. The measured ratio of
transverse radii $R_{\rm out}/R_{\rm side}$ is larger for kaons than for
pions, indicating different space-time correlations. A new approach [36] for
extracting the emission times for pions and especially for kaons was applied.
It was shown that the measured time of maximal emission for kaons is larger
than that of pions.

The comparison of measured three-dimensional radii with a model, wherein the
hydrodynamic phase is followed by the hadronic rescattering phase [35], and
pure hydrodynamical calculations [34, 35] has shown that pion femtoscopic
radii are well reproduced by both approaches while the behavior of the three-
dimensional kaon radii can be described only if the hadronic rescattering
phase is present in the model.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians
for their invaluable contributions to the construction of the experiment and
the CERN accelerator teams for the outstanding performance of the LHC complex.
The ALICE Collaboration gratefully acknowledges the resources and support
provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG)
collaboration. The ALICE Collaboration acknowledges the following funding
agencies for their support in building and running the ALICE detector: A. I.
Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation
(ANSL), State Committee of Science and World Federation of Scientists (WFS),
Armenia; Austrian Academy of Sciences 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), Universidade Federal do
Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil;
Ministry of Science & Technology of China (MSTC), National Natural Science
Foundation of China (NSFC) and Ministry of Education of China (MOEC) , China;
Ministry of Science, Education and Sport and Croatian Science Foundation,
Croatia; Ministry of Education, Youth and Sports of the Czech Republic, Czech
Republic; The Danish Council for Independent Research — Natural Sciences, the
Carlsberg Foundation 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, Wissenschaft, Forschung und Technologie
(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) and
Council of Scientific and Industrial Research (CSIR), New Delhi, India;
Indonesian Institute of Science, Indonesia; Centro Fermi - Museo Storico della
Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica
Nucleare (INFN), Italy; Institute for Innovative Science and Technology ,
Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion
of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports,
Science and Technology (MEXT), 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 Science and Higher
Education and National Science Centre, 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 and Romanian National Agency for Science, Technology and
Innovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of
Education and Science of the Russian Federation and National Research Centre
Kurchatov Institute, Russia; Ministry of Education, Science, Research and
Sport of the Slovak Republic, Slovakia; National Research Foundation of South
Africa, South Africa; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear
(CEADEN), Cubaenergía, Cuba, Ministerio de Ciencia e Innovacion and Centro de
Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Spain;
Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW),
Sweden; European Organization for Nuclear Research, Switzerland; National
Science and Technology Development Agency (NSDTA), Suranaree University of
Technology (SUT) and Office of the Higher Education Commission under NRU
project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), 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. Acharyaorg139&J. Adamorg99&D. Adamováorg96&J. Adolfssonorg34&M.M.
Aggarwalorg101&G. Aglieri Rinellaorg35&M. Agnelloorg31&N. Agrawalorg48&Z.
Ahammedorg139&N. Ahmadorg17&S.U. Ahnorg80&S. Aiolaorg143&A.
Akindinovorg65&S.N. Alamorg139&J.L.B. Albaorg114&D.S.D. Albuquerqueorg125&D.
Aleksandrovorg92&B. Alessandroorg59&R. Alfaro Molinaorg75&A.
Aliciorg54,org27,org12&A. Alkinorg3&J. Almeorg22&T. Altorg71&L.
Altenkamperorg22&I. Altsybeevorg138&C. Alves Garcia Pradoorg124&C.
Andreiorg89&D. Andreouorg35&H.A. Andrewsorg113&A. Andronicorg109&V.
Anguelovorg106&C. Ansonorg99&T. Antičićorg110&F. Antinoriorg57&P.
Antonioliorg54&R. Anwarorg127&L. Aphecetcheorg117&H. Appelshäuserorg71&S.
Arcelliorg27&R. Arnaldiorg59&O.W. Arnoldorg107,org36&I.C. Arseneorg21&M.
Arslandokorg106&B. Audurierorg117&A. Augustinusorg35&R. Averbeckorg109&M.D.
Azmiorg17&A. Badalàorg56&Y.W. Baekorg61,org79&S. Bagnascoorg59&R.
Bailhacheorg71&R. Balaorg103&A. Baldisseriorg76&M. Ballorg45&R.C.
Baralorg68&A.M. Barbanoorg26&R. Barberaorg28&F. Barileorg33,org53&L.
Barioglioorg26&G.G. Barnaföldiorg142&L.S. Barnbyorg95&V. Barretorg82&P.
Bartaliniorg7&K. Barthorg35&E. Bartschorg71&M. Basileorg27&N. Bastidorg82&S.
Basuorg141&G. Batigneorg117&B. Batyunyaorg78&P.C. Batzingorg21&I.G.
Beardenorg93&H. Beckorg106&C. Beddaorg64&N.K. Beheraorg61&I. Belikovorg135&F.
Belliniorg27,org35&H. Bello Martinezorg2&R. Bellwiedorg127&L.G.E.
Beltranorg123&V. Belyaevorg85&G. Bencediorg142&S. Beoleorg26&A.
Bercuciorg89&Y. Berdnikovorg98&D. Berenyiorg142&R.A. Bertensorg130&D.
Berzanoorg35&L. Betevorg35&A. Bhasinorg103&I.R. Bhatorg103&A.K. Bhatiorg101&B.
Bhattacharjeeorg44&J. Bhomorg121&L. Bianchiorg127&N. Bianchiorg51&C.
Bianchinorg141&J. Bielčíkorg39&J. Bielčíkováorg96&A. Bilandzicorg107,org36&G.
Biroorg142&R. Biswasorg4&S. Biswasorg4&J.T. Blairorg122&D. Blauorg92&C.
Blumeorg71&G. Bocaorg136&F. Bockorg84,org35,org106&A. Bogdanovorg85&L.
Boldizsárorg142&M. Bombaraorg40&G. Bonomiorg137&M. Bonoraorg35&J. Bookorg71&H.
Borelorg76&A. Borissovorg19&M. Borriorg129&E. Bottaorg26&C. Bourjauorg93&L.
Bratrudorg71&P. Braun-Munzingerorg109&M. Bregantorg124&T.A. Brokerorg71&M.
Brozorg39&E.J. Bruckenorg46&E. Brunaorg59&G.E. Brunoorg33&D. Budnikovorg111&H.
Bueschingorg71&S. Bufalinoorg31&P. Buhlerorg116&P. Buncicorg35&O.
Buschorg133&Z. Butheleziorg77&J.B. Buttorg15&J.T. Buxtonorg18&J.
Cabalaorg119&D. Caffarriorg35,org94&H. Cainesorg143&A. Calivaorg64&E. Calvo
Villarorg114&P. Cameriniorg25&A.A. Caponorg116&F. Carenaorg35&W.
Carenaorg35&F. Carnesecchiorg27,org12&J. Castillo Castellanosorg76&A.J.
Castroorg130&E.A.R. Casulaorg55&C. Ceballos Sanchezorg9&P. Cerelloorg59&S.
Chandraorg139&B. Changorg128&S. Chapelandorg35&M. Chartierorg129&S.
Chattopadhyayorg139&S. Chattopadhyayorg112&A. Chauvinorg36,org107&M.
Cherneyorg99&C. Cheshkovorg134&B. Cheynisorg134&V. Chibante Barrosoorg35&D.D.
Chinellatoorg125&S. Choorg61&P. Chochulaorg35&M. Chojnackiorg93&S.
Choudhuryorg139&T. Chowdhuryorg82&P. Christakoglouorg94&C.H.
Christensenorg93&P. Christiansenorg34&T. Chujoorg133&S.U. Chungorg19&C.
Cicaloorg55&L. Cifarelliorg12,org27&F. Cindoloorg54&J. Cleymansorg102&F.
Colamariaorg33&D. Colellaorg35,org66&A. Colluorg84&M. Colocciorg27&M.
Concasorg59orgI&G. Conesa Balbastreorg83&Z. Conesa del Valleorg62&M.E.
Connorsorg143orgII&J.G. Contrerasorg39&T.M. Cormierorg97&Y. Corrales
Moralesorg59&I. Cortés Maldonadoorg2&P. Corteseorg32&M.R. Cosentinoorg126&F.
Costaorg35&S. Costanzaorg136&J. Crkovskáorg62&P. Crochetorg82&E.
Cuautleorg73&L. Cunqueiroorg72&T. Dahmsorg36,org107&A. Daineseorg57&M.C.
Danischorg106&A. Danuorg69&D. Dasorg112&I. Dasorg112&S. Dasorg4&A.
Dashorg90&S. Dashorg48&S. Deorg124,org49&A. De Caroorg30&G. de Cataldoorg53&C.
de Contiorg124&J. de Cuvelandorg42&A. De Falcoorg24&D. De
Gruttolaorg30,org12&N. De Marcoorg59&S. De Pasqualeorg30&R.D. De
Souzaorg125&H.F. Degenhardtorg124&A. Deistingorg109,org106&A. Delofforg88&C.
Deplanoorg94&P. Dhankherorg48&D. Di Bariorg33&A. Di Mauroorg35&P. Di
Nezzaorg51&B. Di Ruzzaorg57&M.A. Diaz Corcheroorg10&T. Dietelorg102&P.
Dillensegerorg71&R. Diviàorg35&Ø. Djuvslandorg22&A. Dobrinorg35&D. Domenicis
Gimenezorg124&B. Dönigusorg71&O. Dordicorg21&L.V.V. Doremalenorg64&A.K.
Dubeyorg139&A. Dublaorg109&L. Ducrouxorg134&A.K. Duggalorg101&P.
Dupieuxorg82&R.J. Ehlersorg143&D. Eliaorg53&E. Endressorg114&H. Engelorg70&E.
Eppleorg143&B. Erazmusorg117&F. Erhardtorg100&B. Espagnonorg62&S.
Esumiorg133&G. Eulisseorg35&J. Eumorg19&D. Evansorg113&S. Evdokimovorg115&L.
Fabbiettiorg107,org36&J. Faivreorg83&A. Fantoniorg51&M. Faselorg97,org84&L.
Feldkamporg72&A. Felicielloorg59&G. Feofilovorg138&J. Ferenceiorg96&A.
Fernández Téllezorg2&E.G. Ferreiroorg16&A. Ferrettiorg26&A.
Festantiorg29,org35&V.J.G. Feuillardorg76,org82&J. Figielorg121&M.A.S.
Figueredoorg124&S. Filchaginorg111&D. Finogeevorg63&F.M.
Fiondaorg22,org24&E.M. Fioreorg33&M. Florisorg35&S. Foertschorg77&P.
Fokaorg109&S. Fokinorg92&E. Fragiacomoorg60&A. Francesconorg35&A.
Franciscoorg117&U. Frankenfeldorg109&G.G. Fronzeorg26&U. Fuchsorg35&C.
Furgetorg83&A. Fursorg63&M. Fusco Girardorg30&J.J. Gaardhøjeorg93&M.
Gagliardiorg26&A.M. Gagoorg114&K. Gajdosovaorg93&M. Gallioorg26&C.D.
Galvanorg123&P. Ganotiorg87&C. Garabatosorg109&E. Garcia-Solisorg13&K.
Gargorg28&C. Gargiuloorg35&P. Gasikorg36,org107&E.F. Gaugerorg122&M.B. Gay
Ducatiorg74&M. Germainorg117&J. Ghoshorg112&P. Ghoshorg139&S.K. Ghoshorg4&P.
Gianottiorg51&P. Giubellinoorg109,org59,org35&P. Giubilatoorg29&E. Gladysz-
Dziadusorg121&P. Glässelorg106&D.M. Goméz Coralorg75&A. Gomez
Ramirezorg70&A.S. Gonzalezorg35&V. Gonzalezorg10&P. González-Zamoraorg10&S.
Gorbunovorg42&L. Görlichorg121&S. Gotovacorg120&V. Grabskiorg75&L.K.
Graczykowskiorg140&K.L. Grahamorg113&L. Greinerorg84&A. Grelliorg64&C.
Grigorasorg35&V. Grigorievorg85&A. Grigoryanorg1&S. Grigoryanorg78&N.
Grionorg60&J.M. Gronefeldorg109&F. Grosaorg31&J.F. Grosse-Oetringhausorg35&R.
Grossoorg109&L. Gruberorg116&F. Guberorg63&R. Guernaneorg83&B.
Guerzoniorg27&K. Gulbrandsenorg93&T. Gunjiorg132&A. Guptaorg103&R.
Guptaorg103&I.B. Guzmanorg2&R. Haakeorg35&C. Hadjidakisorg62&H.
Hamagakiorg86&G. Hamarorg142&J.C. Hamonorg135&M.R. Haqueorg64&J.W.
Harrisorg143&A. Hartonorg13&H. Hassanorg83&D. Hatzifotiadouorg12,org54&S.
Hayashiorg132&S.T. Heckelorg71&E. Hellbärorg71&H. Helstruporg37&A.
Herghelegiuorg89&G. Herrera Corralorg11&F. Herrmannorg72&B.A. Hessorg105&K.F.
Hetlandorg37&H. Hillemannsorg35&C. Hillsorg129&B. Hippolyteorg135&J.
Hladkyorg67&B. Hohlwegerorg107&D. Horakorg39&S. Hornungorg109&R.
Hosokawaorg133,org83&P. Hristovorg35&C. Hughesorg130&T.J. Humanicorg18&N.
Hussainorg44&T. Hussainorg17&D. Hutterorg42&D.S. Hwangorg20&S.A. Iga
Buitronorg73&R. Ilkaevorg111&M. Inabaorg133&M. Ippolitovorg85,org92&M.
Irfanorg17&M.S. Islamorg112&M. Ivanovorg109&V. Ivanovorg98&V.
Izucheevorg115&B. Jacakorg84&N. Jacazioorg27&P.M. Jacobsorg84&M.B.
Jadhavorg48&J. Jadlovskyorg119&S. Jaelaniorg64&C. Jahnkeorg36&M.J.
Jakubowskaorg140&M.A. Janikorg140&P.H.S.Y. Jayarathnaorg127&C. Jenaorg90&S.
Jenaorg127&M. Jercicorg100&R.T. Jimenez Bustamanteorg109&P.G. Jonesorg113&A.
Juskoorg113&P. Kalinakorg66&A. Kalweitorg35&J.H. Kangorg144&V. Kaplinorg85&S.
Karorg139&A. Karasu Uysalorg81&O. Karavichevorg63&T. Karavichevaorg63&L.
Karayanorg109,org106&P. Karczmarczykorg35&E. Karpechevorg63&U.
Kebschullorg70&R. Keidelorg145&D.L.D. Keijdenerorg64&M. Keilorg35&B.
Ketzerorg45&Z. Khabanovaorg94&P. Khanorg112&S.A. Khanorg139&A.
Khanzadeevorg98&Y. Kharlovorg115&A. Khatunorg17&A. Khuntiaorg49&M.M.
Kielbowiczorg121&B. Kilengorg37&B. Kimorg133&D. Kimorg144&D.J. Kimorg128&H.
Kimorg144&J.S. Kimorg43&J. Kimorg106&M. Kimorg61&M. Kimorg144&S. Kimorg20&T.
Kimorg144&S. Kirschorg42&I. Kiselorg42&S. Kiselevorg65&A. Kisielorg140&G.
Kissorg142&J.L. Klayorg6&C. Kleinorg71&J. Kleinorg35&C. Klein-Bösingorg72&S.
Klewinorg106&A. Klugeorg35&M.L. Knichelorg35,org106&A.G. Knospeorg127&C.
Kobdajorg118&M. Kofaragoorg142&T. Kolleggerorg109&V. Kondratievorg138&N.
Kondratyevaorg85&E. Kondratyukorg115&A. Konevskikhorg63&M.
Konyushikhinorg141&M. Kopcikorg119&M. Kourorg103&C. Kouzinopoulosorg35&O.
Kovalenkoorg88&V. Kovalenkoorg138&M. Kowalskiorg121&G. Koyithatta
Meethaleveeduorg48&I. Králikorg66&A. Kravčákováorg40&M. Krivdaorg66,org113&F.
Krizekorg96&E. Kryshenorg98&M. Krzewickiorg42&A.M. Kuberaorg18&V.
Kučeraorg96&C. Kuhnorg135&P.G. Kuijerorg94&A. Kumarorg103&J. Kumarorg48&L.
Kumarorg101&S. Kumarorg48&S. Kunduorg90&P. Kurashviliorg88&A.
Kurepinorg63&A.B. Kurepinorg63&A. Kuryakinorg111&S. Kushpilorg96&M.J.
Kweonorg61&Y. Kwonorg144&S.L. La Pointeorg42&P. La Roccaorg28&C. Lagana
Fernandesorg124&Y.S. Laiorg84&I. Lakomovorg35&R. Langoyorg41&K.
Lapidusorg143&C. Laraorg70&A. Lardeuxorg21,org76&A. Lattucaorg26&E.
Laudiorg35&R. Lavickaorg39&R. Leaorg25&L. Leardiniorg106&S. Leeorg144&F.
Lehasorg94&S. Lehnerorg116&J. Lehrbachorg42&R.C. Lemmonorg95&V. Lentiorg53&E.
Leograndeorg64&I. León Monzónorg123&P. Lévaiorg142&X. Liorg14&J. Lienorg41&R.
Lietavaorg113&B. Limorg19&S. Lindalorg21&V. Lindenstruthorg42&S.W.
Lindsayorg129&C. Lippmannorg109&M.A. Lisaorg18&V. Litichevskyiorg46&W.J.
Llopeorg141&D.F. Lodatoorg64&P.I. Loenneorg22&V. Loginovorg85&C.
Loizidesorg84&P. Loncarorg120&X. Lopezorg82&E. López Torresorg9&A.
Loweorg142&P. Luettigorg71&J.R. Luhderorg72&M. Lunardonorg29&G.
Luparelloorg60,org25&M. Lupiorg35&T.H. Lutzorg143&A. Maevskayaorg63&M.
Magerorg35&S. Mahajanorg103&S.M. Mahmoodorg21&A. Maireorg135&R.D.
Majkaorg143&M. Malaevorg98&L. Malininaorg78orgIII&D. Mal’Kevichorg65&P.
Malzacherorg109&A. Mamonovorg111&V. Mankoorg92&F. Mansoorg82&V.
Manzariorg53&Y. Maoorg7&M. Marchisoneorg77,org131&J. Marešorg67&G.V.
Margagliottiorg25&A. Margottiorg54&J. Marguttiorg64&A. Marínorg109&C.
Markertorg122&M. Marquardorg71&N.A. Martinorg109&P. Martinengoorg35&J.A.L.
Martinezorg70&M.I. Martínezorg2&G. Martínez Garcíaorg117&M. Martinez
Pedreiraorg35&A. Masorg124&S. Masciocchiorg109&M. Maseraorg26&A.
Masoniorg55&E. Massonorg117&A. Mastroserioorg53&A.M. Mathisorg107,org36&A.
Matyjaorg121,org130&C. Mayerorg121&J. Mazerorg130&M. Mazzilliorg33&M.A.
Mazzoniorg58&F. Meddiorg23&Y. Melikyanorg85&A. Menchaca-Rochaorg75&E.
Meninnoorg30&J. Mercado Pérezorg106&M. Meresorg38&S. Mhlangaorg102&Y.
Miakeorg133&M.M. Mieskolainenorg46&D.L. Mihaylovorg107&K.
Mikhaylovorg65,org78&J. Milosevicorg21&A. Mischkeorg64&A.N. Mishraorg49&D.
Miśkowiecorg109&J. Mitraorg139&C.M. Mituorg69&N. Mohammadiorg64&B.
Mohantyorg90&M. Mohisin Khanorg17orgIV&E. Montesorg10&D.A. Moreira De
Godoyorg72&L.A.P. Morenoorg2&S. Morettoorg29&A. Morrealeorg117&A.
Morschorg35&V. Mucciforaorg51&E. Mudnicorg120&D. Mühlheimorg72&S.
Muhuriorg139&M. Mukherjeeorg4&J.D. Mulliganorg143&M.G. Munhozorg124&K.
Münningorg45&R.H. Munzerorg71&H. Murakamiorg132&S. Murrayorg77&L. Musaorg35&J.
Musinskyorg66&C.J. Myersorg127&J.W. Myrchaorg140&D. Nagorg4&B. Naikorg48&R.
Nairorg88&B.K. Nandiorg48&R. Naniaorg12,org54&E. Nappiorg53&A.
Narayanorg48&M.U. Naruorg15&H. Natal da Luzorg124&C. Nattrassorg130&S.R.
Navarroorg2&K. Nayakorg90&R. Nayakorg48&T.K. Nayakorg139&S. Nazarenkoorg111&A.
Nedosekinorg65&R.A. Negrao De Oliveiraorg35&L. Nellenorg73&S.V. Nesboorg37&F.
Ngorg127&M. Nicassioorg109&M. Niculescuorg69&J. Niedzielaorg35,org140&B.S.
Nielsenorg93&S. Nikolaevorg92&S. Nikulinorg92&V. Nikulinorg98&F.
Noferiniorg54,org12&P. Nomokonovorg78&G. Noorenorg64&J.C.C. Norisorg2&J.
Normanorg129&A. Nyaninorg92&J. Nystrandorg22&H. Oeschlerorg106org*&S.
Ohorg143&A. Ohlsonorg35,org106&T. Okuboorg47&L. Olahorg142&J.
Oleniaczorg140&A.C. Oliveira Da Silvaorg124&M.H. Oliverorg143&J.
Onderwaaterorg109&C. Oppedisanoorg59&R. Oravaorg46&M. Oravecorg119&A. Ortiz
Velasquezorg73&A. Oskarssonorg34&J. Otwinowskiorg121&K. Oyamaorg86&Y.
Pachmayerorg106&V. Pacikorg93&D. Paganoorg137&P. Paganoorg30&G. Paićorg73&P.
Palniorg7&J. Panorg141&A.K. Pandeyorg48&S. Panebiancoorg76&V.
Papikyanorg1&G.S. Pappalardoorg56&P. Pareekorg49&J. Parkorg61&S.
Parmarorg101&A. Passfeldorg72&S.P. Pathakorg127&V. Paticchioorg53&R.N.
Patraorg139&B. Paulorg59&H. Peiorg7&T. Peitzmannorg64&X. Pengorg7&L.G.
Pereiraorg74&H. Pereira Da Costaorg76&D. Peresunkoorg92,org85&E. Perez
Lezamaorg71&V. Peskovorg71&Y. Pestovorg5&V. Petráčekorg39&V. Petrovorg115&M.
Petroviciorg89&C. Pettaorg28&R.P. Pezziorg74&S. Pianoorg60&M. Piknaorg38&P.
Pillotorg117&L.O.D.L. Pimentelorg93&O. Pinazzaorg35,org54&L. Pinskyorg127&D.B.
Piyarathnaorg127&M. Płoskońorg84&M. Planinicorg100&F. Pliquettorg71&J.
Plutaorg140&S. Pochybovaorg142&P.L.M. Podesta-Lermaorg123&M.G.
Poghosyanorg97&B. Polichtchoukorg115&N. Poljakorg100&W. Poonsawatorg118&A.
Poporg89&H. Poppenborgorg72&S. Porteboeuf-Houssaisorg82&V.
Pozdniakovorg78&S.K. Prasadorg4&R. Preghenellaorg54&F. Prinoorg59&C.A.
Pruneauorg141&I. Pshenichnovorg63&M. Puccioorg26&G. Pudduorg24&P.
Pujahariorg141&V. Puninorg111&J. Putschkeorg141&A. Rachevskiorg60&S.
Rahaorg4&S. Rajputorg103&J. Rakorg128&A. Rakotozafindrabeorg76&L.
Ramelloorg32&F. Ramiorg135&D.B. Ranaorg127&R. Raniwalaorg104&S.
Raniwalaorg104&S.S. Räsänenorg46&B.T. Rascanuorg71&D. Ratheeorg101&V.
Ratzaorg45&I. Ravasengaorg31&K.F. Readorg97,org130&K. Redlichorg88orgV&A.
Rehmanorg22&P. Reicheltorg71&F. Reidtorg35&X. Renorg7&R. Renfordtorg71&A.R.
Reolonorg51&A. Reshetinorg63&K. Reygersorg106&V. Riabovorg98&R.A.
Ricciorg52&T. Richertorg64&M. Richterorg21&P. Riedlerorg35&W. Rieglerorg35&F.
Riggiorg28&C. Risteaorg69&M. Rodríguez Cahuantziorg2&K. Røedorg21&E.
Rogochayaorg78&D. Rohrorg42,org35&D. Röhrichorg22&P.S. Rokitaorg140&F.
Ronchettiorg51&E.D. Rosasorg73&P. Rosnetorg82&A. Rossiorg29,org57&A.
Rotondiorg136&F. Roukoutakisorg87&A. Royorg49&C. Royorg135&P. Royorg112&A.J.
Rubio Monteroorg10&O.V. Ruedaorg73&R. Ruiorg25&B. Rumyantsevorg78&A.
Rustamovorg91&E. Ryabinkinorg92&Y. Ryabovorg98&A. Rybickiorg121&S.
Saarinenorg46&S. Sadhuorg139&S. Sadovskyorg115&K. Šafaříkorg35&S.K.
Sahaorg139&B. Sahlmullerorg71&B. Sahooorg48&P. Sahooorg49&R. Sahooorg49&S.
Sahooorg68&P.K. Sahuorg68&J. Sainiorg139&S. Sakaiorg133&M.A. Salehorg141&J.
Salzwedelorg18&S. Sambyalorg103&V. Samsonovorg85,org98&A. Sandovalorg75&D.
Sarkarorg139&N. Sarkarorg139&P. Sarmaorg44&M.H.P. Sasorg64&E.
Scapparoneorg54&F. Scarlassaraorg29&R.P. Scharenbergorg108&H.S. Scheidorg71&C.
Schiauaorg89&R. Schickerorg106&C. Schmidtorg109&H.R. Schmidtorg105&M.O.
Schmidtorg106&M. Schmidtorg105&N.V. Schmidtorg71,org97&S. Schuchmannorg106&J.
Schukraftorg35&Y. Schutzorg135,org117,org35&K. Schwarzorg109&K.
Schwedaorg109&G. Scioliorg27&E. Scomparinorg59&R. Scottorg130&M.
Šefčíkorg40&J.E. Segerorg99&Y. Sekiguchiorg132&D. Sekihataorg47&I.
Selyuzhenkovorg85,org109&K. Senosiorg77&S. Senyukovorg35,org3,org135&E.
Serradillaorg10,org75&P. Settorg48&A. Sevcencoorg69&A. Shabanovorg63&A.
Shabetaiorg117&R. Shahoyanorg35&W. Shaikhorg112&A. Shangaraevorg115&A.
Sharmaorg101&A. Sharmaorg103&M. Sharmaorg103&M. Sharmaorg103&N.
Sharmaorg101,org130&A.I. Sheikhorg139&K. Shigakiorg47&Q. Shouorg7&K.
Shtejerorg9,org26&Y. Sibiriakorg92&S. Siddhantaorg55&K.M. Sielewiczorg35&T.
Siemiarczukorg88&D. Silvermyrorg34&C. Silvestreorg83&G. Simatovicorg100&G.
Simonettiorg35&R. Singarajuorg139&R. Singhorg90&V. Singhalorg139&T.
Sinhaorg112&B. Sitarorg38&M. Sittaorg32&T.B. Skaaliorg21&M. Slupeckiorg128&N.
Smirnovorg143&R.J.M. Snellingsorg64&T.W. Snellmanorg128&J. Songorg19&M.
Songorg144&F. Soramelorg29&S. Sorensenorg130&F. Sozziorg109&E. Spiritiorg51&I.
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Strmenorg38&A.A.P. Suaideorg124&T. Sugitateorg47&C. Suireorg62&M.
Suleymanovorg15&M. Suljicorg25&R. Sultanovorg65&M. Šumberaorg96&S.
Sumowidagdoorg50&K. Suzukiorg116&S. Swainorg68&A. Szaboorg38&I. Szarkaorg38&U.
Tabassamorg15&J. Takahashiorg125&G.J. Tambaveorg22&N. Tanakaorg133&M.
Tarhiniorg62&M. Tariqorg17&M.G. Tarzilaorg89&A. Tauroorg35&G. Tejeda
Muñozorg2&A. Telescaorg35&K. Terasakiorg132&C. Terrevoliorg29&B.
Teyssierorg134&D. Thakurorg49&S. Thakurorg139&D. Thomasorg122&F.
Thoresenorg93&R. Tieulentorg134&A. Tikhonovorg63&A.R. Timminsorg127&A.
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Trombettaorg33&L. Tropporg40&V. Trubnikovorg3&W.H. Trzaskaorg128&B.A.
Trzeciakorg64&T. Tsujiorg132&A. Tumkinorg111&R. Turrisiorg57&T.S.
Tveterorg21&K. Ullalandorg22&E.N. Umakaorg127&A. Urasorg134&G.L. Usaiorg24&A.
Utrobicicorg100&M. Valaorg119,org66&J. Van Der Maarelorg64&J.W. Van
Hoorneorg35&M. van Leeuwenorg64&T. Vanatorg96&P. Vande Vyvreorg35&D.
Vargaorg142&A. Vargasorg2&M. Vargyasorg128&R. Varmaorg48&M. Vasileiouorg87&A.
Vasilievorg92&A. Vauthierorg83&O. Vázquez Doceorg107,org36&V.
Vecherninorg138&A.M. Veenorg64&A. Velureorg22&E. Vercellinorg26&S. Vergara
Limónorg2&R. Vernetorg8&R. Vértesiorg142&L. Vickovicorg120&S. Vigoloorg64&J.
Viinikainenorg128&Z. Vilakaziorg131&O. Villalobos Baillieorg113&A. Villatoro
Telloorg2&A. Vinogradovorg92&L. Vinogradovorg138&T. Virgiliorg30&V.
Vislaviciusorg34&A. Vodopyanovorg78&M.A. Völklorg106,org105&K.
Voloshinorg65&S.A. Voloshinorg141&G. Volpeorg33&B. von Hallerorg35&I.
Vorobyevorg107,org36&D. Voscekorg119&D. Vranicorg35,org109&J. Vrlákováorg40&B.
Wagnerorg22&H. Wangorg64&M. Wangorg7&D. Watanabeorg133&Y.
Watanabeorg132,org133&M. Weberorg116&S.G. Weberorg109&D.F. Weiserorg106&S.C.
Wenzelorg35&J.P. Wesselsorg72&U. Westerhofforg72&A.M. Whiteheadorg102&J.
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Wittorg130&S. Yalcinorg81&K. Yamakawaorg47&P. Yangorg7&S. Yanoorg47&Z.
Yinorg7&H. Yokoyamaorg133,org83&I.-K. Yooorg35,org19&J.H. Yoonorg61&V.
Yurchenkoorg3&V. Zaccoloorg59,org93&A. Zamanorg15&C. Zampolliorg35&H.J.C.
Zanoliorg124&N. Zardoshtiorg113&A. Zarochentsevorg138&P. Závadaorg67&N.
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Zhangorg7&Y. Zhangorg7&C. Zhangorg64&Z. Zhangorg82,org7&C. Zhaoorg21&N.
Zhigarevaorg65&D. Zhouorg7&Y. Zhouorg93&Z. Zhouorg22&H. Zhuorg22&J. Zhuorg7&A.
Zichichiorg12,org27&A. Zimmermannorg106&M.B. Zimmermannorg35&G.
Zinovjevorg3&J. Zmeskalorg116&S. Zouorg7&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

orgIIGeorgia State University, Atlanta, Georgia, United States

orgIIIM.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of
Nuclear, Physics, Moscow, Russia

orgIVDepartment of Applied Physics, Aligarh Muslim University, Aligarh, India

orgVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

org1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia

org2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

org3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

org4Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org5Budker Institute for Nuclear Physics, Novosibirsk, Russia

org6California Polytechnic State University, San Luis Obispo, California,
United States

org7Central China Normal University, Wuhan, China

org8Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France

org9Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

org10Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain

org11Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org12Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi’, Rome, Italy

org13Chicago State University, Chicago, Illinois, United States

org14China Institute of Atomic Energy, Beijing, China

org15COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

org16Departamento de Física de Partículas and IGFAE, Universidad de Santiago
de Compostela, Santiago de Compostela, Spain

org17Department of Physics, Aligarh Muslim University, Aligarh, India

org18Department of Physics, Ohio State University, Columbus, Ohio, United
States

org19Department of Physics, Pusan National University, Pusan, Republic of
Korea

org20Department of Physics, Sejong University, Seoul, Republic of Korea

org21Department of Physics, University of Oslo, Oslo, Norway

org22Department of Physics and Technology, University of Bergen, Bergen,
Norway

org23Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

org24Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

org25Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

org26Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

org27Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

org28Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

org29Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

org30Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org32Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org33Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org34Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden

org35European Organization for Nuclear Research (CERN), Geneva, Switzerland

org36Excellence Cluster Universe, Technische Universität München, Munich,
Germany

org37Faculty of Engineering, Bergen University College, Bergen, Norway

org38Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia

org39Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org40Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org41Faculty of Technology, Buskerud and Vestfold University College,
Tonsberg, Norway

org42Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org43Gangneung-Wonju National University, Gangneung, Republic of Korea

org44Gauhati University, Department of Physics, Guwahati, India

org45Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

org46Helsinki Institute of Physics (HIP), Helsinki, Finland

org47Hiroshima University, Hiroshima, Japan

org48Indian Institute of Technology Bombay (IIT), Mumbai, India

org49Indian Institute of Technology Indore, Indore, India

org50Indonesian Institute of Sciences, Jakarta, Indonesia

org51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org52INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy

org53INFN, Sezione di Bari, Bari, Italy

org54INFN, Sezione di Bologna, Bologna, Italy

org55INFN, Sezione di Cagliari, Cagliari, Italy

org56INFN, Sezione di Catania, Catania, Italy

org57INFN, Sezione di Padova, Padova, Italy

org58INFN, Sezione di Roma, Rome, Italy

org59INFN, Sezione di Torino, Turin, Italy

org60INFN, Sezione di Trieste, Trieste, Italy

org61Inha University, Incheon, Republic of Korea

org62Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud,
CNRS-IN2P3, Orsay, France

org63Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org64Institute for Subatomic Physics of Utrecht University, Utrecht,
Netherlands

org65Institute for Theoretical and Experimental Physics, Moscow, Russia

org66Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org67Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic

org68Institute of Physics, Bhubaneswar, India

org69Institute of Space Science (ISS), Bucharest, Romania

org70Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org71Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org72Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany

org73Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org74Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org75Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org76IRFU, CEA, Université Paris-Saclay, Saclay, France

org77iThemba LABS, National Research Foundation, Somerset West, South Africa

org78Joint Institute for Nuclear Research (JINR), Dubna, Russia

org79Konkuk University, Seoul, Republic of Korea

org80Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org81KTO Karatay University, Konya, Turkey

org82Laboratoire de Physique Corpusculaire (LPC), Clermont Université,
Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

org83Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org84Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org85Moscow Engineering Physics Institute, Moscow, Russia

org86Nagasaki Institute of Applied Science, Nagasaki, Japan

org87National and Kapodistrian University of Athens, Physics Department,
Athens, Greece

org88National Centre for Nuclear Studies, Warsaw, Poland

org89National Institute for Physics and Nuclear Engineering, Bucharest,
Romania

org90National Institute of Science Education and Research, HBNI, Jatni, India

org91National Nuclear Research Center, Baku, Azerbaijan

org92National Research Centre Kurchatov Institute, Moscow, Russia

org93Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org94Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam,
Netherlands

org95Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org96Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež
u Prahy, Czech Republic

org97Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org98Petersburg Nuclear Physics Institute, Gatchina, Russia

org99Physics Department, Creighton University, Omaha, Nebraska, United States

org100Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

org101Physics Department, Panjab University, Chandigarh, India

org102Physics Department, University of Cape Town, Cape Town, South Africa

org103Physics Department, University of Jammu, Jammu, India

org104Physics Department, University of Rajasthan, Jaipur, India

org105Physikalisches Institut, Eberhard Karls Universität Tübingen, Tübingen,
Germany

org106Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org107Physik Department, Technische Universität München, Munich, Germany

org108Purdue University, West Lafayette, Indiana, United States

org109Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org110Rudjer Bošković Institute, Zagreb, Croatia

org111Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org112Saha Institute of Nuclear Physics, Kolkata, India

org113School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org114Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org115SSC IHEP of NRC Kurchatov institute, Protvino, Russia

org116Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org117SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org118Suranaree University of Technology, Nakhon Ratchasima, Thailand

org119Technical University of Košice, Košice, Slovakia

org120Technical University of Split FESB, Split, Croatia

org121The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org122The University of Texas at Austin, Physics Department, Austin, Texas,
United States

org123Universidad Autónoma de Sinaloa, Culiacán, Mexico

org124Universidade de São Paulo (USP), São Paulo, Brazil

org125Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org126Universidade Federal do ABC, Santo Andre, Brazil

org127University of Houston, Houston, Texas, United States

org128University of Jyväskylä, Jyväskylä, Finland

org129University of Liverpool, Liverpool, United Kingdom

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

org134Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, Lyon, France

org135Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg,
France, Strasbourg, France

org136Università degli Studi di Pavia, Pavia, Italy

org137Università di Brescia, Brescia, Italy

org138V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia

org139Variable Energy Cyclotron Centre, Kolkata, India

org140Warsaw University of Technology, Warsaw, Poland

org141Wayne State University, Detroit, Michigan, United States

org142Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org143Yale University, New Haven, Connecticut, United States

org144Yonsei University, Seoul, Republic of Korea

org145Zentrum für Technologietransfer und Telekommunikation (ZTT),
Fachhochschule Worms, Worms, Germany