2019 054 25 March

One-dimensional charged kaon femtoscopy in p–Pb collisions

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

The correlations of identical charged kaons were measured in p–Pb collisions
at $\sqrt{s_{\rm NN}}=5.02$ TeV by the ALICE experiment at the LHC. The
femtoscopic invariant radii and correlation strengths were extracted from one-
dimensional kaon correlation functions and were compared with those obtained
in pp and Pb–Pb collisions at $\sqrt{s}=7$ TeV and $\sqrt{s_{\rm NN}}=2.76$
TeV, respectively. The presented results also complement the identical-pion
femtoscopic data published by the ALICE collaboration. The extracted radii
increase with increasing charged-particle multiplicity and decrease with
increasing pair transverse momentum. At comparable multiplicities, the radii
measured in p–Pb collisions are found to be close to those observed in pp
collisions. The obtained femtoscopic parameters are reproduced by the EPOS 3
hadronic interaction model and disfavor models with large initial size or
strong collective expansion at low multiplicities.

##  1 Introduction

The Bose–Einstein enhancement of the production of two identical pions at low
relative momenta (or, in other words, quantum statistics correlations) was
first observed in the $\overline{\rm p}$p annihilation more than 50 years ago
[1]. These correlations encode information about the space–time structure of
the interaction region of particles created in collisions at kinetic freeze-
out (“particle-emitting source”) [2, 3, 4]. Since that time the correlation
method has been developed [5, 6] and it is now known as “correlation
femtoscopy”. Femtoscopy measures the apparent width of the distribution of the
relative separation of emission points, which is conventionally called the
“radius parameter”. The method was successfully applied to the measurement of
the space–time characteristics of particle production processes at high
energies in particle [7, 8] and heavy-ion collisions (see, e.g., [9, 4] and
references therein).

Identical boson correlations, especially of identical charged pions, have been
used extensively over the years to experimentally study properties of the
emitting source created in various collision systems [10]. Identical charged
kaon femtoscopy studies were also carried out, for example, in Au–Au
collisions at $\sqrt{s_{\rm NN}}=200$ GeV by the STAR [11] and PHENIX [12]
collaborations and in pp collisions at $\sqrt{s}=~{}7$ TeV and Pb–Pb
collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV by the ALICE collaboration [13,
14].

The study of femtoscopic correlations in asymmetric collision systems is
particularly interesting because it provides a bridge between small (pp) and
large (A–A) collision systems, and may lead to additional constraints on model
scenarios which were successfully used to describe pp and A–A collisions. The
A–A femtoscopy results are interpreted within the hydrodynamic framework as a
signature of collective radial flow [10, 15, 16, 17]. Attempts to describe the
pp data in the same framework have not been successful so far and it is
speculated that additional effects related to the uncertainty principle may
play a role in such small systems [18]. The results obtained in asymmetric
collisions are difficult to interpret unambiguously. For instance, the
femtoscopic study of the data obtained at RHIC for d–Au collisions [19, 20]
suggest that a hydrodynamic evolution may be present in such a system, while
at the LHC the ALICE three-pion [21] and three-dimensional two-pion [22]
analyses in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV demonstrate
the more important role of the initial state shape and size of the created
system.

The excellent particle identification capabilities of the ALICE detector [23]
and the data sample collected in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV in 2013 allow one to perform the K±K±
femtoscopic analysis. Kaons are a convenient tool to study Bose–Einstein
correlations because they are less influenced by resonance decays than pions
and therefore more effectively probe femtoscopic correlations of directly-
produced particles. The comparison of kaon and pion correlation radii [22, 21,
14] as a function of pair transverse momentum $k_{\rm T}=|{\bf
p}_{\mathrm{T,1}}+{\bf p}_{\mathrm{T,2}}|/2$ or transverse mass $m_{\rm
T}=\sqrt{k_{\mathrm{T}}^{2}+m^{2}}$, where ${\bf p}_{\mathrm{T,1}}$ (${\bf
p}_{\mathrm{T,2}}$) is the transverse momentum of the first (second) particle
and $m$ is the kaon or pion mass, allows one to understand the collective
dynamics (collective flow) of the source created in high-energy collisions. In
particular, in the system created by colliding heavy ions, the decrease of the
correlation radii with increasing $k_{\mathrm{T}}$ ($m_{\mathrm{T}}$) is
usually considered as a manifestation of the strong collective expansion of
the matter created in such collisions. If the dependence of the interferometry
radii on pair momentum in p–Pb collisions followed the trends seen in heavy-
ion collisions, it would be an indication of collectivity or the creation of a
hot and dense system expanding hydrodynamically [24, 47, 44]. In addition,
comparing kaon femtoscopic results in pp, p–A, and A–A collision systems can
provide experimental constraints on the validity of hydrodynamic [24, 44]
and/or color glass condensate [Dusling:2013qoz, 25] approaches proposed for
the interpretation of the p–Pb data. In this work, the kaon femtoscopic radii
in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV are shown as a
function of $k_{\mathrm{T}}$ and multiplicity, and are compared with those in
pp and Pb–Pb collisions at $\sqrt{s}=7$ TeV [13] and
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [14], respectively. The presented data are
also compared with the EPOS 3.111 model [44], an event generator based on a
(3+1)D viscous hydrodynamical evolution starting from flux tube initial
conditions, which are generated in the Gribov-Regge multiple scattering
framework. The approach contains a full viscous hydrodynamical simulation and
a more sophisticated treatment of nonlinear effects in the parton evolution by
considering individual (per Pomeron) saturation scales than in previous EPOS
versions [46, 47]. There are also changes in the core–corona procedure
[Aichelin:2008mi] crucial in proton–nucleus collisions, so that the initial
energy of the flux tubes is separated into a part which constitutes the
initial conditions for hydrodynamic expansion (core) and the particles which
leave the “matter” (corona). This model reasonably reproduces multiplicity
distributions, transverse momentum spectra, and flow results, and it gives the
best description of kaon spectra [45, 46, 47, Werner:2015vza,
Acharya:2018egz].

The paper is organized as follows: Section 2 shortly describes the ALICE
experimental setup and charged kaon selection criteria used in the presented
work. In Section 3, the femtoscopic correlation function analysis is described
in detail and the sources of systematic uncertainties are discussed. The
extracted radii and correlation strengths are shown and compared with model
predictions in Section 4. The obtained results are summarized in Section 5.

##  2 Description of the experiment and data selection

###  2.1 Experiment

The ALICE detector and its performance in the LHC Run 1 (2009 – 2013) are
described in [23] and [26], respectively. About 55$\times$106 p–Pb collision
events collected in 2013 at a center-of-mass energy per nucleon–nucleon pair
of $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV were analyzed in this work. Given the
energies of the colliding p and Pb beams, the nucleon–nucleon center-of-mass
system is shifted with respect to the ALICE laboratory system by 0.465 units
of rapidity in the direction of the proton beam. Throughout this paper $\eta$
represents the pseudorapidity measured in the laboratory frame.

The analyzed events were classified according to their multiplicity [27, 28]
using the measured energy deposition in the V0 detectors [29], which consist
of two arrays of scintillators located along the beamline installed on each
side of the interaction point and covering $2.8<\eta<5.1$ (V0A, located on the
Pb-remnant side) and $-3.7<\eta<-1.7$ (V0C) [30]. Charged kaons were
reconstructed with the central barrel detectors placed inside a solenoidal
magnet providing a 0.5 T field parallel to the beam direction, namely the Time
Projection Chamber (TPC) [31] and the Inner Tracking System (ITS) [23]. The
primary vertex was obtained from the ITS. Its position along the beam
direction (the “$z$-position”) was required to be within $\pm$10 cm of the
center of the ALICE detector to ensure uniform tracking performance. The TPC
was used to reconstruct tracks and their momenta. The TPC is divided by the
central electrode into two halves, each of which is composed of 18 sectors
(covering the full azimuthal angle) with 159 pad rows 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 pad rows. The TPC covers an acceptance of
$|\eta|<0.8$ for tracks which reach the outer radius of the detector and
$|\eta|<1.5$ for shorter tracks. The parameters of the track were 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
required to have $\chi^{2}/{\rm NDF}$ less than 2. The transverse momentum of
each track was determined from its curvature in the uniform magnetic field.
The track selection criteria based on the quality of the track reconstruction
fit and the number of detected tracking points in the TPC [26, 32] were used
to ensure that only well-reconstructed tracks were considered in the analysis.

Particle identification (PID) for reconstructed tracks was carried out using
the TPC together with the Time-of-Flight (TOF) [32] detector. The TOF is a
cylindrical detector consisting of 18 azimuthal sectors divided into five
modules along the beam axis at a radius $r\simeq 380$ cm. The active elements
are multigap resistive plate chambers. For TPC PID, a parametrized Bethe-Bloch
formula was used to calculate the specific energy loss ${\rm d}E/{\rm d}x$ in
the detector expected for a particle with a given mass, charge, and momentum.
For PID based on TOF information, the particle mass was used to calculate the
expected time-of-flight as a function of track length and momentum. For each
PID method, the signal for each reconstructed particle is compared with the
one expected for a kaon taking into account the detector resolution. The
allowed deviations ($n_{\sigma}$) depend on the momentum of the particle [14,
26, 32].

###  2.2 Charged kaon selection

Track reconstruction for the charged kaon analysis was performed using the
signals in the TPC. To ensure a good momentum resolution, each track was
required to be composed of at least 70 out of the 159 TPC clusters. 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 plane and
less than 3.0 cm in the longitudinal direction. The kinematic range for kaons
selected in this analysis is $0.14<p_{\rm T}<1.5$ GeV/$c$ and $|\eta|<0.8$.
Charged tracks with momentum $p<0.5$ GeV/$c$ were identified as kaons if they
satisfied the requirement $n_{\sigma,{\rm TPC}}<2$ in the TPC. Tracks with
$p>0.5$ GeV/$c$ were required to match to a signal in the TOF, and satisfy
$n_{\sigma,{\rm TPC}}<3$ as well as the following momentum-dependent
$n_{\sigma}$ selection: $n_{\sigma,{\rm TOF}}<2$ for $0.5<p<0.8$ GeV/$c$,
$n_{\sigma,{\rm TOF}}<1.5$ for $0.8<p<1.0$ GeV/$c$ and $n_{\sigma,{\rm
TOF}}<1$ for $1.0<p<1.5$ GeV/$c$. All selection criteria are listed in Tab. 1.

Table 1: Charged kaon selection criteria. $p_{\rm T}$ |  $0.14<p_{\rm T}<1.5$ 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/$c$) | $<1.0$
Number of track points in TPC |  $\geq$70

The estimation of purity for $p<0.5$ GeV/$c$ was performed by parametrizing
the TPC d$E$/d$x$ distribution of the experimental data in momentum slices and
computing the fraction of particle species that could mistakenly contribute to
the kaon signal [26]. The use of momentum-dependent values for $n_{\sigma,{\rm
TPC}}$ and $n_{\sigma,{\rm TOF}}$ was the result of studies to obtain the best
kaon purity, defined as the fraction of accepted kaon tracks that correspond
to true kaons, while retaining a decent efficiency of the PID. The dominant
contamination for charged kaons comes from e± in the momentum range
$0.4<p<0.5$ GeV/$c$. The parameters of the function which fits the TPC
distribution in momentum slices depend on the fit interval and can be a source
of the systematic uncertainty associated with the single purity. The purity
for $p>0.5$ GeV/$c$, where the TOF information was employed, was studied with
DPMJET [33] simulations using GEANT [34] to model particle transport through
the detector. Based on the results of this study, the $n_{\sigma,{\rm TOF}}$
values were chosen to provide a charged kaon purity greater than 99%. The
momentum dependence of the single kaon purity in the region of maximal
contamination is shown in Fig. 1. The pair purity is calculated as the product
of two single-particle purities for pairs with $q_{\rm inv}<0.25$ GeV/$c$,
where the momenta are taken from the experimentally determined distribution.
The obtained K± pair purity is shown in Fig. 1 as a function of $k_{\rm T}$.
It can be seen from the figure that, despite the lower purity for single kaons
in the range $0.45<p<0.5$ GeV/$c$, the pair purity remains high in the wide
$k_{\mathrm{T}}$ bins used in the analysis due to the effects of averaging
over low-purity $0.45<p<0.5$ GeV/$c$ and high-purity $p<0.45$ GeV/$c$ or
$p>0.5$ GeV/$c$ bins in the full single-kaon momentum range. The systematic
uncertainties of the single purity values lead, in turn, to systematic
uncertainties of the obtained pair purity.

Figure 1: (color online) Single (a) and pair (b) K± purities for different
event multiplicity classes. The systematic uncertainties associated with the
purity correction are shown as boxes. Statistical uncertainties are
negligible. The momentum $p$ ($k_{\rm T}$) values for lower multiplicity
classes (blue and green symbols) are slightly offset for clarity.

The analysis was performed in three event multiplicity classes [35, 27, 28]:
0–20%, 20–40% and 40–90% and two pair transverse momentum $k_{\mathrm{T}}$
bins: (0.2–0.5) and (0.5–1.0) GeV/$c$. The multiplicity was determined based
on the sum of the signal amplitudes of V0A and V0C detectors, commonly
referred to as V0M. Table 2 shows the corresponding mean charged-particle
multiplicity densities $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ averaged
over $|\eta|<0.5$ using the method presented in [27]. The $\langle{\rm
d}N_{\rm ch}/{\rm d}\eta\rangle$ values were not corrected for trigger and
vertex-reconstruction inefficiency, which is about 4% for non-single
diffractive events [36]. At least one particle in the event had to be
reconstructed and identified as a charged kaon. The correlation signal was
constructed from events having at least two identical charged kaons. Events
with a single kaon were included in the event mixing procedure to determine
the reference distribution.

Table 2: V0M event classes and their corresponding $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ [27]. The given uncertainties are systematic only since the statistical uncertainties are negligible. Event class |  $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$, $|\eta|<0.5$
---|---
0–20% | 47.3$\pm$0.7
20–40% | 24.3$\pm$0.7
40–90% | 17.3$\pm$1.5

The femtoscopic correlation functions (CF) of identical particles are
sensitive to two-track reconstruction effects because the considered particles
are close in momentum and have close trajectories. Two kinds of two-track
effects were investigated. Track “splitting” occurs when one track is
mistakenly reconstructed as two. Track “merging” is the effect when two
different tracks are reconstructed as one. To remove these effects, pairs with
relative pseudorapidity $|\Delta\eta|<0.02$ and relative azimuthal angle
$|\Delta\varphi^{*}|<0.045$ were rejected. The modified azimuthal angle
$\varphi^{*}$ takes into account the bending of the tracks inside the magnetic
field and was calculated at a radial distance of 1.2 m [37].

##  3 Analysis technique

The correlation function of two particles with momenta ${\bf p_{1}}$ and ${\bf
p_{2}}$ is defined as a ratio

$C({\bf p}_{1},{\bf p}_{2})=\frac{A({\bf p}_{1},{\bf p}_{2})}{B({\bf
p}_{1},{\bf p}_{2})}$ (1)

of the two-particle distribution in the given event $A({\bf p}_{1},{\bf
p}_{2})$ to the reference distribution $B({\bf p}_{1},{\bf p}_{2})$ [38]. The
reference distribution is formed by mixing events containing at least one
charged kaon, where each event is mixed with five other events which have
similar $z$ position of the primary vertex and similar multiplicity [10]. The
mixed particles come from events for which the vertex positions in the beam
direction agree within 2 cm and the multiplicities do not differ by more than
1/4 of the width of the given multiplicity class. The correlation function is
measured as a function of the invariant pair relative momentum
$q_{\mathrm{inv}}=\sqrt{|{\bf q}|^{2}-q_{0}^{2}}$, where $q_{0}=E_{1}-E_{2}$
and ${\bf q}={\bf p_{1}}-{\bf p_{2}}$ are determined by the energy components
$E_{1}$, $E_{2}$ and momenta ${\bf p_{1}}$, ${\bf p_{2}}$ of the particles,
respectively. The correlation function is normalized to unity such that
$C\rightarrow 1$ in the absence of a correlation signal.

The obtained correlation function $C_{\rm raw}$ was also corrected for purity
before the fit [14, 39] according to

$C_{\rm corrected}=(C_{\rm raw}-1+P)/P,$ (2)

where the pair purity $P$ is taken from Fig. 1.

###  3.1 Correlation function parametrization

The CFs can be parametrized by various formulae depending on the origin of
correlations between the considered particles. The pairwise interactions
between K±K± that form the basis for femtoscopy are quantum statistics and the
Coulomb interaction. Strong final-state interactions between kaons are
negligible [40]. Assuming a Gaussian distribution of a particle source in the
pair rest frame, the fit of the kaon CF is performed using the Bowler–Sinyukov
formula [41, 42]

$C(q_{\mathrm{inv}})=N\left[1-\lambda+\lambda
K(r,q_{\mathrm{inv}})\left(1+\exp{\left(-R_{\mathrm{inv}}^{2}q^{2}_{\mathrm{inv}}\right)}\right)\right]\,D(q_{\mathrm{inv}}).$
(3)

The factor $K(r,q_{\mathrm{inv}})$ describes the Coulomb interaction with a
radius $r$, $D(q_{\mathrm{inv}})$ parametrizes the baseline including all non-
femtoscopic effects, for instance resonance decays, and $N$ is a normalization
coefficient. The Coulomb interaction is determined as

$\displaystyle K(r,q_{\mathrm{inv}})=\frac{C_{\rm QS+Coulomb}}{C_{\rm QS}},$
(4)

where $C_{\rm QS}$ is a theoretical CF calculated with pure quantum
statistical (QS) weights (wave function squared) and $C_{\rm QS+Coulomb}$
corresponds to quantum statistical plus Coulomb weights [41, 43]. The
parameters $R_{\mathrm{inv}}$ and $\lambda$ describe the size of the source
and the correlation strength, respectively.

###  3.2 Fitting procedure

The parameters $R_{\mathrm{inv}}$ and $\lambda$ can be extracted using Eq. (3)
with various assumptions to handle the non-femtoscopic baseline $D$ from
background effects outside the femtoscopic peak region. There are various
methods to deal with the baseline. The simplest way is to assume that it is
flat, $D(q_{\mathrm{inv}})=1$, which can be reasonable in cases where non-
femtoscopic effects are negligible. As can be seen in Fig. 2, the baseline of
the obtained experimental functions is not flat. Therefore, it would be more
reasonable to describe it, for instance, by a first-order polynomial function
$D(q_{\mathrm{inv}})=N(1+aq_{\mathrm{inv}})$ which reproduces this baseline
slope. It interpolates the baseline behavior at high $q_{\mathrm{inv}}$ taking
into account all non-femtoscopic effects which make it non-flat. Then being
extrapolated to low $q_{\mathrm{inv}}$, it is supposed to imitate the existing
non-femtoscopic effects. The most natural way to describe the baseline is to
use Monte Carlo (MC) models where events are generated from physical
considerations and contain all but QS and Coulomb effects. A suitable MC model
has to reasonably describe the baseline at high $q_{\mathrm{inv}}$, where non-
femtoscopic effects are significant, and also contain non-femtoscopic effects
at low $q_{\mathrm{inv}}$. The EPOS 3 [44] model without QS and Coulomb
interaction effects included was used to describe the baseline
$D(q_{\mathrm{inv}})$. As seen from Fig. 2, EPOS 3 describes the experimental
CF outside the correlation peak. The extracted parameter values depend on the
fit range, which should be chosen taking into account the characteristic width
of the femtoscopic effect observed. In this analysis, the EPOS 3 baseline was
fit with a first-order polynomial in $0<q_{\rm inv}<1.0$ GeV/$c$ (to flatten
statistical uncertainties) and then the experimental CF was fit with Eq. (3)
in the range $0<q_{\rm inv}<0.5$ GeV/$c$. The Coulomb interaction radius was
set to $r=1.5$ fm, which is on average close to the extracted radii values.

Figure 2:  (color online) K±K± experimental correlation functions corrected
for purity according to Eq. (2) (red points) and EPOS 3 model baselines [44]
(black points) versus pair relative invariant momentum $q_{\mathrm{inv}}$. The
CFs are presented in three event multiplicity classes: 0–20%, 20–40% and
40–90% and two pair transverse momentum $k_{\mathrm{T}}$ bins: (0.2–0.5) and
(0.5–1.0) GeV/$c$. The black line shows the fit of EPOS 3 by a first-order
polynomial for $0<q_{\mathrm{inv}}<1.0$ GeV/$c$. The red line shows the
subsequent fit of the CF up to $q_{\mathrm{inv}}<$0.5 GeV/$c$ by Eq. (3). The
CFs are normalized to unity in the range $0.5<q_{\mathrm{inv}}<1.0$ GeV/$c$.
Statistical (lines) and systematic uncertainties (boxes) are shown.

###  3.3 Systematic uncertainties

The effects of various sources of systematic uncertainty on the extracted
parameters were studied as functions of multiplicity and $k_{\rm T}$. The
systematic uncertainties were estimated by varying the selection criteria used
for the events, particles, and pairs (with variation limits up to
$\pm$20$\%$). The influence of the fit range was estimated by variation of the
$q_{\rm inv}$ upper limit by $\pm$40$\%$. Another source of systematic
uncertainty is the misidentification of particles and the associated purity
correction. A $\pm$10% variation of the parameters (Sec. 2.2) used for the
purity correction estimation was performed. To reduce the electron
contamination, the PID criteria were tightened, in particular by extending the
momentum range where the TOF signal was used and the energy-loss measurement
was required to be consistent with the kaon hypothesis within $n_{\sigma,{\rm
TPC}}<1$.

There is also an uncertainty associated with the choice of the radius of the
Coulomb interaction. It was set to 1.5 fm as a result of averaging of the
three radii values that were extracted from the respective multiplicity bins
and varied by $\pm 0.5$ fm. The relative difference was taken as a systematic
uncertainty. Uncertainties associated with momentum resolution were estimated
using a MC simulation with the DPMJET 3.05 [33] model. The effect is limited
to low pair relative momentum, where it smears the correlation function and is
especially pronounced for narrow femtoscopic peaks. In p–Pb collisions the
$q_{\rm inv}$ region of the femtoscopic effect is one order of magnitude wider
than the region affected by this inefficiency and, consequently, the
corresponding uncertainty is minor.

As was explained in Sec. 3.2, the fitting procedure requires knowledge of the
non-femtoscopic background shape and magnitude. In this analysis, the EPOS 3
model was used for this purpose. The systematic uncertainty associated with
the baseline was estimated using an alternative MC model, DPMJET, as well as
the two methods based on the use of polynomials described in Sec. 3.2.

Table 3 presents the uncertainty range for all considered sources of
systematic uncertainty, where the minimum (maximum) was chosen from all
available values in all multiplicity and $k_{\rm T}$ bins. For each source and
each multiplicity and $k_{\rm T}$ bin, the maximum deviation from the
parameters obtained with the optimal data selection criteria and fitting
methods was taken and applied symmetrically as the uncertainty. The limited
data sample for p–Pb collisions leads to quite high statistical uncertainty
values and most of the systematic uncertainty contributions were found to be
much smaller than the quadratic difference of the statistical uncertainties.
Therefore, the systematic uncertainty values were added in quadrature,
considering only those whose statistical significance level exceeded 50%
[Barlow:2002yb]. As can be seen from Table 3, the main sources of systematic
uncertainty on the extracted parameters are the pair selection criteria, the
influence of the fit range, the radius of the Coulomb interaction and the
baseline description. All of them contribute to the uncertainty associated
with the radii. The extracted correlation strengths have higher statistical
uncertainties than the radii and, consequently, for them the pair selection
criteria is the only source of systematic uncertainty which exceeds the
statistical significance level chosen in this analysis.

Table 3: Minimum and maximum uncertainty values for various sources of systematic uncertainty (in percent), the punctuation ‘–’ means that the contribution from the given source is negligible. Note that each value is the minimum–maximum uncertainty from a specific source, but can pertain to different multiplicity or $k_{\rm T}$ bins. Thus, the maximum total uncertainties are smaller than (or equal to) the sum of the maximum individual uncertainties shown in this table. Systematic uncertainties whose statistical significance level exceeds 50% were included in the total systematic uncertainty value. |  $R_{\rm inv}$ (%) |  $\lambda$ (%)
---|---|---
Single particle selection | 0–1.5 | 0–3.2
PID and purity | – | 0–0.6
Pair selection | 0–3 | 0–6
Baseline | 1–4.8 | 0.2–4.1
Fit range | 0.6–7 | 0.5–5.7
Coulomb function | 0–2.3 | 1.8–3.8
Momentum resolution | 0–1 | 0–1

##  4 Results and discussion

The extracted $R_{\mathrm{inv}}$ and $\lambda$ parameters are depicted in
Figs. 3 and 3, respectively. Statistical and systematic uncertainties as
described in Sec. 3.3 are shown for all results. Figure 3 also shows
comparisons with the EPOS 3 model (with femtoscopic effects included [46, 48,
49]) for the same collision system and energy in the same multiplicity and
$k_{\rm T}$ bins as the experimental data. Two cases are considered, one with
and another one without the hadronic cascade (UrQMD) phase [50]. The EPOS 3
calculations for the radii without the cascade exhibit practically no
$k_{\mathrm{T}}$-dependence and do not describe the data, while the data are
well reproduced by the full EPOS 3 model calculations thereby showing the
importance of the hadronic cascade phase at LHC energies. This observation
agrees with the conclusion from the three-dimensional K± femtoscopic analysis
in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV [39] where the hydro-
kinetic model HKM [51] with the hadronic rescattering phase described the
charged kaon femtoscopic radii well. The extracted experimental $\lambda$
values are about 0.45, whereas the EPOS 3 ones are about 0.65, i.e. apparently
larger than the experimental $\lambda$ values. The value of the $\lambda$
parameter may be influenced by non-Gaussian features of the correlation
function [52], by a finite coherent component of kaon emission [43, 53] and
also the contribution of kaons from K∗ decays ($\Gamma\sim$50 MeV, where
$\Gamma$ is the decay width) and from other long-lived resonances [54]. The
reason for the difference between the experimental correlation strengths and
those obtained with EPOS 3 could be that the model does not accurately account
for all contributions of kaons from various resonance decays [55]. Another
explanation could be a partial coherence of the real emitting source [56, 57,
53, 42], which is not taken into account in the EPOS 3 model.

Figure 3: (color online) Experimental K±K± invariant radii $R_{\mathrm{inv}}$
(a) and correlation strengths $\lambda$ (b) shown versus pair transverse
momentum $k_{\mathrm{T}}$ for three multiplicity classes and compared with the
EPOS 3 model predictions with and without the hadronic cascade phase.
Statistical (lines) and systematic uncertainties (boxes) are shown. The points
for lower multiplicity classes (blue and green symbols) are slightly offset in
the $x$ direction for clarity.

In Fig. 4, the radii from pp collisions at $\sqrt{s}=7$ TeV [13] and p–Pb
collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV at similar multiplicity are
compared as a function of pair transverse momentum $k_{\rm T}$. The
corresponding radii in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV [14]
are not shown because they were obtained for multiplicities which are not
available in this study. The figure shows that at the same multiplicity, the
radii in p–Pb collisions are consistent with those in pp collisions within
uncertainties. The statistical significance of this observation (4–15%) does
not allow this result to be precisely compared with the results of the one-
dimensional three-pion cumulants [21] and three-dimensional two-pion [22]
analyses where the radii in pp collisions were obtained to be 5–15% and 10–20%
smaller than those in p–Pb collisions, respectively.

Figure 4: Comparison of femtoscopic radii, as a function of pair transverse
momentum $k_{\rm T}$, obtained in pp [13] and p–Pb collisions. Statistical
(lines) and systematic uncertainties (boxes) are shown.

Figure 5 compares femtoscopic radii as a function of the measured charged-
particle multiplicity density $\langle N_{\rm ch}\rangle^{1/3}$, at low (Fig.
5) and high (Fig. 5) $k_{\rm T}$ in pp [13], p–Pb and Pb–Pb [14] collisions.
The obtained radii increase with $N_{\rm ch}$ and follow the multiplicity
trend observed in pp collisions. The radii are equal in p–Pb and pp collisions
at similar multiplicity within uncertainties. This result could indicate that
the dynamics of the source in p–Pb collisions at low multiplicities is similar
to that in pp collisions. In particular, if there is a collective expansion of
the sources created in pp and p–Pb collisions, these results indicate that the
expansion is not significantly stronger in p–Pb than in pp collisions [24]. As
seen from the figure, the radii in p–Pb and Pb–Pb collisions were obtained in
very different ranges of multiplicity and cannot be compared at the same
$N_{\rm ch}$. In order to make a stronger conclusion between different
collision systems, as was done in the pion correlation analyses [22, 21], a
larger experimental data set should be considered.

Figure 5: Comparison of femtoscopic radii, as a function of the measured
charged-particle multiplicity density $\langle N_{\rm ch}\rangle^{1/3}$, at
low (a) and high (b) $k_{\rm T}$ obtained in pp [13], p–Pb and Pb–Pb [14]
collisions. Statistical (lines) and systematic uncertainties (boxes) are
shown.

Figures 6 and 6 show the correlation strengths $\lambda$ in pp [13], p–Pb and
Pb–Pb [14] collisions at low and high $k_{\rm T}$, respectively. All $\lambda$
values are less than unity probably due to the influence of long-lived
resonances and a non-Gaussian shape of the kaon CF peak. It can be noticed
from the figure that the correlation strength parameters in Pb–Pb collisions
tend to be higher than those in pp and p–Pb collisions. That could point to a
more Gaussian source created in Pb–Pb collisions.

Figure 6: Comparison of correlation strengths $\lambda$, as a function of the
measured charged-particle multiplicity density $\langle N_{\rm
ch}\rangle^{1/3}$, at low (a) and high (b) $k_{\rm T}$ obtained in pp [13],
p–Pb and Pb–Pb [14] collisions. Statistical (lines) and systematic
uncertainties (boxes) are shown.

Figure 7 compares correlation strengths $\lambda$ in pp [13], p–Pb and Pb–Pb
collisions as a function of $k_{\rm T}$ for all available multiplicity bins.
As seen from the figure, the correlation strengths in all multiplicity and all
$k_{\rm T}$ bins do not show any noticeable $k_{\rm T}$ or multiplicity
dependence. The systematic uncertainty values obtained for the compared
collision systems are visibly different since even the same source of
uncertainty gives a rather different contribution to the total uncertainty
value in every collision system.

Figure 7: (color online) The K±K± correlation strengths $\lambda$ in pp [13],
p–Pb and Pb–Pb [14] collisions versus pair transverse momentum $k_{\rm T}$ in
all multiplicity and $k_{\rm T}$ bins. Statistical (lines) and systematic
uncertainties (boxes) are shown. The data points for lower multiplicity
classes (blue and green symbols) are slightly offset in $k_{\rm T}$ with
respect to the highest multiplicity classes (red symbols) for better
visibility.

##  5 Summary

In this work, one-dimensional identical charged kaon correlations were
obtained and analyzed for the first time in proton–nucleus collisions, that is
in p–Pb at $\sqrt{s_{\rm NN}}=5.02$ TeV. The source size $R_{\rm inv}$ and
correlation strength $\lambda$ were extracted from a correlation function
parametrized in terms of the invariant pair relative momentum
$q_{\mathrm{inv}}$. The obtained radii $R_{\rm inv}$ decrease with increasing
pair transverse momentum $k_{\rm T}$ and with decreasing event multiplicity.
This is similar to the behavior of pion radii in the three-dimensional two-
pion correlation analysis in p–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV
and one-dimensional three-pion cumulant results in pp collisions at
$\sqrt{s}=7$ TeV, p–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and Pb–Pb
collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV.

The obtained radii $R_{\rm inv}$ are reproduced well by the EPOS 3 model
(including femtoscopic effects) calculations with the hadronic rescattering
phase, whose importance was also demonstrated in the three-dimensional
femtoscopic analysis of K± pair correlations in Pb–Pb collisions. The values
of the correlation strength parameters $\lambda$ in EPOS 3 are apparently
larger than the experimental $\lambda$ values, which could be due to coherent
sources not incorporated in EPOS 3 and long-lived resonances not taken into
account accurately enough in this model.

The kaon $R_{\rm inv}$ values in p–Pb and pp collisions show the same trend
with multiplicity. However, it is difficult to say whether the same is true
for the Pb–Pb points because of a large gap in multiplicities available in
p–Pb and Pb–Pb collisions. The results disfavor models which incorporate
substantially stronger collective expansion in p–Pb collisions compared to pp
collisions at similar multiplicity. The correlation strength $\lambda$ does
not show any trends with multiplicity or $k_{\rm T}$. The fact that the
correlation strength in Pb–Pb collisions tends to be higher than in pp and
p–Pb collisions could be an indication of a more Gaussian source created in
Pb–Pb collisions. However, a stronger conclusion is prevented due to large
statistical and systematic uncertainties, especially for the Pb–Pb data.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians
for their invaluable contributions to the construction of the experiment and
the CERN accelerator teams for the outstanding performance of the LHC complex.
The ALICE Collaboration gratefully acknowledges the resources and support
provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG)
collaboration. The ALICE Collaboration acknowledges the following funding
agencies for their support in building and running the ALICE detector: A. I.
Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation
(ANSL), State Committee of Science and World Federation of Scientists (WFS),
Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M
2467-N36] and 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; Croatian Science Foundation and Ministry
of Science and Education, 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 Carlsberg Foundation and Danish
National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics
(HIP), Finland; Commissariat à l’Energie Atomique (CEA), Institut National de
Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National
de la Recherche Scientifique (CNRS) and Rlégion des Pays de la Loire, 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), 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; 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 Ministry of Research and
Innovation and Institute of Atomic Physics, 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; 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. Acharyaorg141&D. Adamováorg93&S.P. Adhyaorg141&A. Adlerorg74&J.
Adolfssonorg80&M.M. Aggarwalorg98&G. Aglieri Rinellaorg34&M. Agnelloorg31&N.
Agrawalorg10&Z. Ahammedorg141&S. Ahmadorg17&S.U. Ahnorg76&S. Aiolaorg146&A.
Akindinovorg64&M. Al-Turanyorg105&S.N. Alamorg141&D.S.D. Albuquerqueorg122&D.
Aleksandrovorg87&B. Alessandroorg58&H.M. Alfandaorg6&R. Alfaro Molinaorg72&B.
Aliorg17&Y. Aliorg15&A. Aliciorg10,org53,org27&A. Alkinorg2&J. Almeorg22&T.
Altorg69&L. Altenkamperorg22&I. Altsybeevorg112&M.N. Anaamorg6&C.
Andreiorg47&D. Andreouorg34&H.A. Andrewsorg109&A. Andronicorg144&M.
Angelettiorg34&V. Anguelovorg102&C. Ansonorg16&T. Antičićorg106&F.
Antinoriorg56&P. Antonioliorg53&R. Anwarorg126&N. Apadulaorg79&L.
Aphecetcheorg114&H. Appelshäuserorg69&S. Arcelliorg27&R. Arnaldiorg58&M.
Arratiaorg79&I.C. Arseneorg21&M. Arslandokorg102&A. Augustinusorg34&R.
Averbeckorg105&S. Azizorg61&M.D. Azmiorg17&A. Badalàorg55&Y.W. Baekorg40&S.
Bagnascoorg58&R. Bailhacheorg69&R. Balaorg99&A. Baldisseriorg137&M.
Ballorg42&R.C. Baralorg85&R. Barberaorg28&L. Barioglioorg26&G.G.
Barnaföldiorg145&L.S. Barnbyorg92&V. Barretorg134&P. Bartaliniorg6&K.
Barthorg34&E. Bartschorg69&N. Bastidorg134&S. Basuorg143&G. Batigneorg114&B.
Batyunyaorg75&P.C. Batzingorg21&D. Bauriorg48&J.L. Bazo Albaorg110&I.G.
Beardenorg88&C. Beddaorg63&N.K. Beheraorg60&I. Belikovorg136&F.
Belliniorg34&R. Bellwiedorg126&L.G.E. Beltranorg120&V. Belyaevorg91&G.
Bencediorg145&S. Beoleorg26&A. Bercuciorg47&Y. Berdnikovorg96&D.
Berenyiorg145&R.A. Bertensorg130&D. Berzanoorg58&L. Betevorg34&A.
Bhasinorg99&I.R. Bhatorg99&H. Bhattorg48&B. Bhattacharjeeorg41&A.
Bianchiorg26&L. Bianchiorg126,org26&N. Bianchiorg51&J. Bielčíkorg37&J.
Bielčíkováorg93&A. Bilandzicorg103,org117&G. Biroorg145&R. Biswasorg3&S.
Biswasorg3&J.T. Blairorg119&D. Blauorg87&C. Blumeorg69&G. Bocaorg139&F.
Bockorg34,org94&A. Bogdanovorg91&L. Boldizsárorg145&A. Bolozdynyaorg91&M.
Bombaraorg38&G. Bonomiorg140&M. Bonoraorg34&H. Borelorg137&A.
Borissovorg91,org144&M. Borriorg128&H. Bossiorg146&E. Bottaorg26&C.
Bourjauorg88&L. Bratrudorg69&P. Braun-Munzingerorg105&M. Bregantorg121&T.A.
Brokerorg69&M. Brozorg37&E.J. Bruckenorg43&E. Brunaorg58&G.E.
Brunoorg33,org104&M.D. Bucklandorg128&D. Budnikovorg107&H. Bueschingorg69&S.
Bufalinoorg31&O. Bugnonorg114&P. Buhlerorg113&P. Buncicorg34&O.
Buschorg133org*&Z. Butheleziorg73&J.B. Buttorg15&J.T. Buxtonorg95&D.
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Herrmannorg144&K.F. Hetlandorg36&T.E. Hildenorg43&H. Hillemannsorg34&C.
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Kalweitorg34&J.H. Kangorg147&V. Kaplinorg91&S. Karorg6&A. Karasu Uysalorg77&O.
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Khanzadeevorg96&Y. Kharlovorg90&A. Khatunorg17&A. Khuntiaorg118,org49&B.
Kilengorg36&B. Kimorg60&B. Kimorg133&D. Kimorg147&D.J. Kimorg127&E.J.
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Kirschorg39&I. Kiselorg39&S. Kiselevorg64&A. Kisielorg142&J.L. Klayorg5&C.
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Klewinorg102&A. Klugeorg34&M.L. Knichelorg34&A.G. Knospeorg126&C.
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Krzewickiorg39&A.M. Kuberaorg95&V. Kučeraorg60&C. Kuhnorg136&P.G.
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Kurepinorg62&A.B. Kurepinorg62&S. Kushpilorg93&J. Kvapilorg109&M.J.
Kweonorg60&Y. Kwonorg147&S.L. La Pointeorg39&P. La Roccaorg28&Y.S. Laiorg79&R.
Langoyorg124&K. Lapidusorg34,org146&A. Lardeuxorg21&P. Larionovorg51&E.
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Leeorg147&F. Lehasorg89&S. Lehnerorg113&J. Lehrbachorg39&R.C. Lemmonorg92&I.
León Monzónorg120&E.D. Lesserorg20&M. Lettrichorg34&P. Lévaiorg145&X.
Liorg12&X.L. Liorg6&J. Lienorg124&R. Lietavaorg109&B. Limorg18&S.
Lindalorg21&V. Lindenstruthorg39&S.W. Lindsayorg128&C. Lippmannorg105&M.A.
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Masoniorg54&L. Massacrierorg61&E. Massonorg114&A. Mastroserioorg138,org52&A.M.
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Mohantyorg85&M. Mohisin Khanorg17orgIII&M. Mondalorg141&M.M. Mondalorg66&C.
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Oginoorg81&A. Ohlsonorg102&J. Oleniaczorg142&A.C. Oliveira Da Silvaorg121&M.H.
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Pestovorg4&V. Petráčekorg37&M. Petroviciorg47&R.P. Pezziorg71&S. Pianoorg59&M.
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## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

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

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

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

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

org2Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine

org3Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

org5California Polytechnic State University, San Luis Obispo, California,
United States

org6Central China Normal University, Wuhan, China

org7Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France

org8Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

org9Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org10Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi’, Rome, Italy

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Chonbuk National University, Jeonju, Republic of Korea

org14Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

org15COMSATS University Islamabad, Islamabad, Pakistan

org16Creighton University, Omaha, Nebraska, United States

org17Department of Physics, Aligarh Muslim University, Aligarh, India

org18Department of Physics, Pusan National University, Pusan, Republic of
Korea

org19Department of Physics, Sejong University, Seoul, Republic of Korea

org20Department of Physics, University of California, Berkeley, California,
United States

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

org34European Organization for Nuclear Research (CERN), Geneva, Switzerland

org35Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia

org36Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway

org37Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org38Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org39Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org40Gangneung-Wonju National University, Gangneung, Republic of Korea

org41Gauhati University, Department of Physics, Guwahati, India

org42Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

org43Helsinki Institute of Physics (HIP), Helsinki, Finland

org44High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

org45Hiroshima University, Hiroshima, Japan

org46Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany

org47Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania

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, Sezione di Bari, Bari, Italy

org53INFN, Sezione di Bologna, Bologna, Italy

org54INFN, Sezione di Cagliari, Cagliari, Italy

org55INFN, Sezione di Catania, Catania, Italy

org56INFN, Sezione di Padova, Padova, Italy

org57INFN, Sezione di Roma, Rome, Italy

org58INFN, Sezione di Torino, Turin, Italy

org59INFN, Sezione di Trieste, Trieste, Italy

org60Inha University, Incheon, Republic of Korea

org61Institut de Physique Nucléaire d’Orsay (IPNO), Institut National de
Physique Nucléaire et de Physique des Particules (IN2P3/CNRS), Université de
Paris-Sud, Université Paris-Saclay, Orsay, France

org62Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org63Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht,
Netherlands

org64Institute for Theoretical and Experimental Physics, Moscow, Russia

org65Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org66Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

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

org68Institute of Space Science (ISS), Bucharest, Romania

org69Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org70Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org71Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org72Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org73iThemba LABS, National Research Foundation, Somerset West, South Africa

org74Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org75Joint Institute for Nuclear Research (JINR), Dubna, Russia

org76Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org77KTO Karatay University, Konya, Turkey

org78Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org79Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org80Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org81Nagasaki Institute of Applied Science, Nagasaki, Japan

org82Nara Women’s University (NWU), Nara, Japan

org83National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

org84National Centre for Nuclear Research, Warsaw, Poland

org85National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org86National Nuclear Research Center, Baku, Azerbaijan

org87National Research Centre Kurchatov Institute, Moscow, Russia

org88Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org89Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org90NRC Kurchatov Institute IHEP, Protvino, Russia

org91NRNU Moscow Engineering Physics Institute, Moscow, Russia

org92Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org93Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

org94Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org95Ohio State University, Columbus, Ohio, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

org97Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Jammu, Jammu, India

org100Physics Department, University of Rajasthan, Jaipur, India

org101Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany

org102Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org103Physik Department, Technische Universität München, Munich, Germany

org104Politecnico di Bari, Bari, Italy

org105Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org106Rudjer Bošković Institute, Zagreb, Croatia

org107Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org108Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

org109School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org110Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org111Shanghai Institute of Applied Physics, Shanghai, China

org112St. Petersburg State University, St. Petersburg, Russia

org113Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org114SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org115Suranaree University of Technology, Nakhon Ratchasima, Thailand

org116Technical University of Košice, Košice, Slovakia

org117Technische Universität München, Excellence Cluster ’Universe’, Munich,
Germany

org118The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org119The University of Texas at Austin, Austin, Texas, United States

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

org121Universidade de São Paulo (USP), São Paulo, Brazil

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University College of Southeast Norway, Tonsberg, Norway

org125University of Cape Town, Cape Town, South Africa

org126University of Houston, Houston, Texas, United States

org127University of Jyväskylä, Jyväskylä, Finland

org128University of Liverpool, Liverpool, United Kingdom

org129University of Science and Techonology of China, Hefei, China

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

org135Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, Lyon, France

org136Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg,
France, Strasbourg, France

org137Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU,
Départment de Physique Nucléaire (DPhN), Saclay, France

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

org141Variable Energy Cyclotron Centre, Homi Bhabha National Institute,
Kolkata, India

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

org144Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany

org145Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea