2023 229 10 October

Femtoscopic correlations of identical charged pions and kaons in pp collisions

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

Collective behavior has been observed in high-energy heavy-ion collisions for
several decades. Collectivity is driven by the high particle multiplicities
that are produced in these collisions. At the Large Hadron Collider (LHC),
features of collectivity have also been seen in high-multiplicity
proton–proton collisions that can attain particle multiplicities comparable to
peripheral Pb–Pb collisions. One of the possible signatures of collective
behavior is the decrease of femtoscopic radii extracted from pion and kaon
pairs emitted from high-multiplicity collisions with increasing pair
transverse momentum. This decrease can be described in terms of an approximate
transverse mass scaling. In the present work, femtoscopic analyses are carried
out by the ALICE collaboration on charged pion and kaon pairs produced in pp
collisions at $\sqrt{s}=13$ TeV from the LHC to study possible collectivity in
pp collisions. The event-shape analysis method based on transverse sphericity
is used to select for spherical versus jet-like events, and the effects of
this selection on the femtoscopic radii for both charged pion and kaon pairs
are studied. This is the first time this selection method has been applied to
charged kaon pairs. An approximate transverse-mass scaling of the radii is
found in all multiplicity ranges studied when the difference in the Lorentz
boost for pions and kaons is taken into account. This observation does not
support the hypothesis of collective expansion of hot and dense matter that
should only occur in high-multiplicity events. A possible alternate
explanation of the present results is based on a scenario of common emission
conditions for pions and kaons in pp collisions for the multiplicity ranges
studied.

##  1 Introduction

The manifestation of collective effects in pp and p–A collisions with
increasing multiplicity of charged particles is intensely discussed in the
literature [1, 2, 3]. Surprisingly, these small colliding systems exhibit
several signatures attributed to the formation of a strongly-interacting
quark–gluon plasma in heavy-ion collisions, such as long-range ridge-like
structures [4, 5, 6] and strangeness enhancement [7]. A full understanding of
the mechanisms leading to collective effects observed in pp collisions at
large multiplicity has not yet been achieved. For this reason, it is important
to experimentally investigate the properties of small systems with the aim to
discriminate between different theoretical models. Namely, the hydrodynamic
models present the “heavy-ion view” of pp collisions e.g. Ref. [8], while
string models are the “high-energy view” e.g. models including interactions
between strings [9, 10].

The femtoscopy technique, which studies the final-state hadron–hadron
interactions via their momentum correlations, is an effective tool for the
extraction of the space–time characteristics of particle production processes,
in particular the radii of the emitting source and the decoupling time. This
method has already been employed in the past to study high-energy
hadron–hadron [11, 12] and heavy-ion collisions [13, 14] using quantum
statistical (QS) correlations and/or final-state interactions (FSI) of
particles emitted with small relative momenta.

The characteristic feature of femtoscopy in heavy-ion collisions is the
decrease of the source sizes for pairs of particles (with masses $m$ and
transverse momenta ${\bf p}_{\mathrm{T,1}}$ and ${\bf p}_{\mathrm{T,2}}$) with
increasing pair transverse momentum ${\it k_{\mathrm{T}}}=|{\bf
p}_{\mathrm{T,1}}+{\bf p}_{\mathrm{T,2}}|/2$ or transverse mass
$\it{m_{\mathrm{T}}}=\sqrt{{\it k_{\mathrm{T}}}^{2}+m^{2}}$, see e.g. recent
RHIC [15, 16, 17] and LHC [18, 19] results for pions. It was explained in Ref.
[20] that femtoscopy measurements do not probe the whole volume in case of an
expanding emitting source, but instead the region from which the particles
with similar momenta are emitted, the so called “homogeneity volume”. This
region is smaller than the total volume occupied by the system and decreases
with $\it{k_{\mathrm{T}}}$ ($\it{m_{\mathrm{T}}}$). Several theoretical models
based on the hydrodynamic approach successfully describe pion femtoscopy
measurements e.g. Refs. [21, 22, 23, 24, 25]. It is expected that these models
should describe the femtoscopy measurements for kaons and for heavier
particles also, particularly the $\it{m_{\mathrm{T}}}$ and multiplicity
dependencies of radii. In Ref. [26], it was shown that for the particular case
of small transverse flow the hydrodynamics leads to the same
$\it{m_{\mathrm{T}}}$-behavior of the longitudinal radii ($R_{\rm long}$) for
pions and kaons. It means that the thermal freeze-out occurs simultaneously
and that these two particle species are subject to the same velocity boost
from collective flow. Modern calculations made within the 3+1D hydrodynamic
model THERMINATOR-2 [23] at LHC energies demonstrate the approximate
$\it{m_{\mathrm{T}}}$ scaling of the three-dimensional radii for pions, kaons
and protons [25] when the radii versus $\it{m_{\mathrm{T}}}$ fall with some
degree of accuracy on one curve. The authors of Ref. [25] also investigated
one-dimensional radii ($R_{\rm inv}$) in pair reference frame (PRF) for the
case of lack of available experimental data. They have verified that the
violation of this scaling in the case when the three-dimensional scaling is
presented in the model has a trivial kinematic origin. It is possible to take
it into account and restore the $m_{\rm T}$ scaling for $R_{\rm inv}$ for
pions, kaons, and protons. The calculations performed within the Hydro-Kinetic
Model, including not only a hydrodynamic phase but also the hadronic
rescattering stage, predicted violation of this scaling between pions and
kaons at LHC energies [27, 28], mainly due to the rescatterings in the
hadronic phase. ALICE results for Pb–Pb collisions at
$\sqrt{s_{\rm{NN}}}=2.76$ TeV [29] have shown that the $\it{m_{\mathrm{T}}}$
scaling expected by pure hydrodynamical scenarios is broken. The comparison of
these two different evolution scenario demonstrate the importance of the
$\it{m_{\mathrm{T}}}$ scaling study.

At the LHC, the femtoscopic sizes range for various colliding systems from 2–7
fm for Pb–Pb to 1–2 fm for pp and p–Pb collisions, which opens a possible
access to different energy densities of the system created during such
collisions and probably helps understand the conditions required for the QGP
formation. The multiplicity and $\it{m_{\mathrm{T}}}$ dependencies were
studied for pions and kaons by ALICE for Pb–Pb collisions e.g. Refs. [19, 29]
and for pp and p–Pb collisions e.g. Refs. [30, 30, 31, 32, 33, 34, 35]. In pp
collisions, it was observed for both types of pairs that for higher charged-
particle multiplicity ranges the measured size of the source decreased with
increasing $\it{m_{\mathrm{T}}}$, similarly to the trend seen in heavy-ion
collisions. Instead, at low charged-particle multiplicities, the measured
source radii increased with increasing $\it{m_{\mathrm{T}}}$ [30, 30, 32, 33].
Unfortunately, there are almost no theoretical models for pp collisions which
include the space–time coordinates and can be used to describe femtoscopic
observables. Attempts to describe the behavior of femtoscopic radii in pp
collisions at the LHC from the hydrodynamic point of view were performed in
e.g. Refs. [36, 37], from the view of the uncertainty principle in Ref. [38],
from the view of the string models in Ref. [39] using LUND hadronization
scheme which automatically introduces the space–momentum correlations similar
to the correlations in hydrodynamic models, where they arise due to transverse
collective flow.

The study of femtoscopic correlations in pp collisions is more challenging
than in A–A collisions due to the strong non-femtoscopic contributions, i.e.
correlations due to multi-body resonance decays, mini-jets, and energy-
momentum conservation. Typically, a baseline distribution function is
constructed to remove these non-femtoscopic effects, after which the
hadron–hadron correlations due to pure QS and FSI can be studied. There are
various methods to exclude them: (1) the so called “double ratio” technique,
dividing the experimental correlation function by the baseline extracted from
Monte Carlo simulations [30]; (2) the “cluster subtraction” technique, using
the opposite-sign pair (e.g. $\pi^{+}\pi^{-}$) distributions as a baseline
[40]; (3) a “hybrid method” between (1) and (2), as described in Ref. [41,
40]) and (4) the three-particle cumulant method [42], which significantly
suppresses the mini-jet related contributions and can be used as an
alternative to the study of two-particle correlations.

A method to suppress, in particular, mini-jet contributions in two-particle
correlation functions was suggested in Ref. [43] and it is based on applying
event-shape selections. It was shown that it is possible to differentiate
between jet-like and spherical event topologies using a global characteristic
of the event such the transverse sphericity [44, 45] and the transverse
spherocity [46, 47]. It was observed for the first time in Ref. [43] that the
pion radii for jet-like events are smaller than the source radii for spherical
events. In jet-like events, the radii dependence on multiplicity is such that
they increase with increasing $k_{\rm T}$ in the lowest multiplicity interval
and decrease with $k_{\rm T}$ for the highest multiplicities. There are no
multiplicity dependence for these events. The radii for spherical events show
an increase in system size with increasing multiplicity. They do not show any
visible trend with ${\it k_{\mathrm{T}}}$, which differs from the results of
sphericity-integrated (minimum-bias) pion and kaon analyses in Refs. [30, 33],
where the obtained radii decrease with increasing ${\it k_{\mathrm{T}}}$. This
different behavior suggests [43] that the lower part of the transverse
sphericity spectrum contributes to the observed slope in minimum bias (MB) pp
collisions.

In this work, the femtoscopic correlations of identical charged pions and
kaons are investigated in pp collisions at $\sqrt{s}=13$ TeV. The purpose of
this analysis is to study the transverse-momentum and multiplicity dependence
of pion and kaon femtoscopic radii separately for jet-like and spherical
events. The influence of the sphericity selections on the kaon femtoscopic
radii is studied for the first time.

The article is organized as follows. Section 2 briefly describes the ALICE
experimental setup. Section 3 presents the event selection criteria. Section 4
introduces the definition of sphericity, discusses the analysis methods to
extract the femtoscopic correlation function for pion and kaon pairs and the
estimation of the systematic uncertainties. The extracted femtoscopic
parameters are shown and discussed in Section 5. The results are summarized in
Section 6.

##  2  Experimental setup

A detailed description of the ALICE detector and its performance can be found
in Refs. [48, 49]. In the present analysis, the information from the Inner
Tracking System (ITS) [50], the Time Projection Chamber (TPC) [51], the Time-
Of-Flight (TOF) [52], and the V0 [53] detectors are used.

The V0 detector is used for triggering on collision events. It is composed of
two small-angle scintillator arrays, located at 340 cm and 90 cm from the
nominal interaction point along the beam line and covering $2.8<\eta<5.1$
(V0A) and $-3.7<\eta<-1.7$ (V0C), respectively. The events are selected with
the MB trigger, which requires simultaneous signals in both parts of the V0
detector in coincidence with two beam bunches crossing in the ALICE
interaction region. The rejection of pile-up events is performed by using the
vertexing capabilities of the Silicon Pixel Detector (SPD) [49], which forms
the two innermost layers of the ITS. Events with multiple vertices identified
with the SPD (in-bunch pile-up) are removed from the analysis. Pile-up events
from different bunch crossings are rejected by requiring the tracks to have
hits in the SPD. The remaining leftover pile-up is negligible in the present
analysis.

Charged particles are reconstructed with the central barrel ITS and TPC
detectors placed inside a solenoidal magnet providing a uniform 0.5 T field
parallel to the beam direction. The primary vertex is reconstructed using the
ITS. This detector is a silicon tracker with six layers of silicon sensors
covering the pseudorapidity range $|\eta|<0.9$ [50]. The TPC is the main
tracking detector in ALICE, which measures the ionization energy loss of
particles. The chamber is divided into two halves by a central electrode. The
end caps on either side are composed of 18 sectors (covering the full
azimuthal angle) with 159 pad rows placed radially in each sector. The TPC
covers an acceptance of $|\eta|<0.9$ for tracks which reach the outer radius
of the detector.

Particle identification (PID) for reconstructed tracks is carried out using
the TPC together with the TOF [52] detectors. The TOF is a cylindrical
detector consisting of 18 azimuthal sectors divided into five modules along
the beam axis with active element multi-gap resistive plate chambers. Pions
and kaons were identified using the TPC and TOF detectors. The deviation of
the specific energy loss (d$E$/d$x$) measured in the TPC from the one
calculated using the Bethe–Bloch parametrization was required to be within a
certain number of standard deviations ($n_{\sigma_{\mathrm{TPC}}}$). A similar
$n_{\sigma_{\mathrm{TOF}}}$ method was applied for the particle identification
in the TOF. The deviation is computed between the measured time of flight and
the one calculated for a given particle path length, momentum, and mass.

##  3  Data selection

The data samples used in this work were recorded by ALICE in 2016–2018 during
the LHC Run 2 period at $\sqrt{s}=13$ TeV. After application of all selection
criteria, about 109 minimum bias events were analyzed.

Events were accepted if they had the collision vertex position measured along
the beam line within $\pm 10$ cm from the nominal interaction point. The
charged particle tracks were required to be reconstructed with the ITS and TPC
detectors with a $\chi^{2}$ per number of degrees of freedom ($\chi^{2}/{\rm
NDF})$ smaller than 4.0 and each track segment was reconstructed from at least
70 out of the 159 possible space points. The distance of closest approach
(DCA) to the primary vertex was required to be smaller than 0.3 cm in both the
transverse plane and the longitudinal direction.

Femtoscopic correlation functions of identical particles are sensitive to two-
track reconstruction effects because the particles of interest have close
momenta and close trajectories. Two kinds of two-track effects, splitting and
merging, were studied. The splitting of the tracks means that one track is
reconstructed as two. The track merging means that two different tracks are
reconstructed as one. To remove these effects, the distance between the tracks
of two particles was calculated at up to nine points throughout the TPC volume
(every 20 cm from 85 cm to 245 cm in radial direction) and then averaged. It
was required that the particles for each pair had an average TPC separation of
at least 3 cm.

Pions and kaons were selected in the pseudorapidity $|\eta|<0.8$ range. For
pions, the transverse momentum $0.15<p_{\rm T}<4.0$ GeV$/c$ range was used.
The pion selection criteria are presented in Table 1. The pion purity is about
99% for track momenta $p<2.0$ GeV$/c$, while, for the $2<p_{\rm T}<4$ GeV$/c$
interval, it decreases to 80% due to an increasing contamination from kaons.

Table 1: Charged pion selection criteria. Selection criterium | Value
---|---
$p_{\rm T}$ |  $0.15<p_{\rm T}<4.0$ GeV$/c$
$|\eta|$ | $<0.8$
$\rm DCA_{\rm transverse}$ |  $<0.3$ cm
$\rm DCA_{\rm longitudinal}$ |  $<0.3$ cm
$n_{\sigma_{\rm TPC}}$ |  $<3$ (for $p<0.5$ GeV$/c$)
$\sqrt{n_{\sigma_{\mathrm{TPC}}^{2}}+n_{\sigma_{\mathrm{TOF}}}^{2}}^{{\phantom{1}}^{\phantom{1}}}$ |  $<3$ (for $0.5<p<4.0$ GeV$/c$)
Number of track points in TPC |  $\geq$ 70

The selection criteria for the kaons are reported in Table 2. In order to
avoid strong contamination from pions, narrower momentum ranges were used for
kaons, namely $0.15<p_{\rm T}<1.5$ GeV$/c$. The dominant contamination for
charged kaons is from ${\rm e}^{\pm}$ in the particle momentum range
$0.4<p<0.5$ GeV$/c$ resulting in a kaon purity of approximately 90%. Outside
this range, the kaon purity is about 99%.

Table 2: Charged kaon selection criteria. Selection criterium | Value
---|---
$p_{\rm T}$ |  $0.15<p_{\rm T}<1.5$ GeV$/c$
$|\eta|$ | $<0.8$
$\rm DCA_{\rm transverse}$ |  $<0.3$ cm
$\rm DCA_{\rm longitudinal}$ |  $<0.3$ cm
|  $<2$ (for $0.15<p<0.4$ GeV$/c$)
$n_{\sigma_{\rm TPC}}$ |  $<1$ (for $0.4<p<0.45$ GeV$/c$)
|  $<2$ (for $0.45<p<1.5$ GeV$/c$)
|  $<2$ (for $0.5<p<0.8$ GeV$/c$)
$n_{\sigma_{\rm TOF}}$ |  $<1.5$ (for $0.8<p<1.0$ GeV$/c$)
|  $<1.0$ (for $1.0<p<1.5$ GeV$/c$)
Number of track points in TPC |  $\geq$ 70

##  4 Analysis technique

Pions and kaons were selected in the same raw charged-particle multiplicity
intervals $N_{\rm trk}$ of (1–18), (19–30), and ($>30$) in order to compare
the obtained results in the same multiplicity conditions. The sphericity
calculations (see Section 4.1) require at least three tracks with $p_{\rm
T}>0.5$ GeV$/c$. Therefore, the lowest multiplicity interval is (1–18) if the
sphericity calculation is not performed, while it is (3–18) when the
sphericity is calculated. From now on, the lowest multiplicity interval will
be denoted as (1–18) for both cases. The multiplicity for primary charged
tracks [54] was estimated using the combined reference multiplicity estimator
(SPD tracklets and tracks reconstructed in the ITS and the TPC) in the
$|\eta|<0.8$ range. The SPD tracklets are track segments built by associating
pairs of hits in the two SPD layers. For each raw multiplicity interval, the
average charged-particle pseudorapidity density $\langle{\rm d}N_{\rm ch}/{\rm
d}\eta\rangle$ was obtained by converting the measured event multiplicities
using Monte Carlo simulations with the PYTHIA 8.2 event generator [55] (with
the Monash tune [56]) and the GEANT3 package [57] for the transport of the
generated particles through the ALICE detector. The intervals and their
corresponding $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$, for both cases
with and without sphericity event selections ($S_{\rm T}$, defined in next
section), are shown in Table 3. The systematic uncertainties for these
densities were evaluated as the difference between their magnitudes when
taking into account or not the detector efficiency correction using the Monte
Carlo simulation mentioned above. The estimated value for these uncertainties
is about 5 $\%$.

Table 3: Raw charged-particle multiplicity ($N_{\rm trk}$) intervals and corresponding average $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ calculated from corrected multiplicity distributions in the $|\eta|<0.8$ range. The values are quoted with their systematic uncertainties, the statistical uncertainties are negligible. $N_{\rm trk}$ | $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle_{S_{\rm T}>0.7}$ | $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle_{S_{\rm T}<0.3}$ | $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$
---|---|---|---
3(1)–18 | 7.8 $\pm$ 0.4 | 6.2 $\pm$ 0.3 | 5.1 $\pm$ 0.2
19–30 | 15.0 $\pm$ 0.7 | 13.5 $\pm$ 0.6 | 14.3 $\pm$ 0.7
$>30$ | 25.4 $\pm$ 1.0 | 21.8 $\pm$ 0.9 | 24.7 $\pm$ 0.1

###  4.1 Transverse sphericity

In collider experiments, the study of the shape of the emitting source is
often performed in the transverse $x$–$y$ plane in order to avoid distortions
related to the Lorentz boost in the beam direction along the $z$ axis [45].
Following this principle, the transverse sphericity ($S_{\rm T}$) was used to
study event characteristics in pp collisions at the LHC by the ALICE
Collaboration [58]. The transverse sphericity is defined as

$S_{\rm T}=\frac{2\min(\lambda_{1},\lambda_{2})}{\lambda_{1}+\lambda_{2}},$
(1)

where $\lambda_{1}$ and $\lambda_{2}$ are the eigenvalues of the matrix of
transverse particle momenta

$S_{\rm T}=\frac{1}{\sum_{i}p_{\rm T}^{i}}\sum_{i}\frac{1}{p_{\rm
T}^{i}}\left(\begin{array}[]{cc}(p_{\rm x}^{i})^{2}&p_{\rm x}^{i}\,p_{\rm
y}^{i}\\\ p_{\rm x}^{i}\,p_{\rm y}^{i}&(p_{\rm y}^{i})^{2}\end{array}\right),$
(2)

with $p_{\rm x}^{i}$ and $p_{\rm y}^{i}$ being the components of the
transverse momentum for $i$-th particle $\vec{p}_{\rm T}^{i}$. The transverse
sphericity takes values in the (0–1) range. By definition of sphericity, in
case of $S_{\rm T}\rightarrow 0$, the emitting source is a strongly elongated
ellipse, while $S_{\rm T}\rightarrow 1$ corresponds to a nearly isotropic
source in momentum or coordinate space. To ensure good resolution of the
transverse sphericity calculation, only events with more than two primary
tracks in $|\eta|<0.8$ and $p_{\rm T}>0.5$ GeV$/c$ were selected [44].
Following Ref. [43], $S_{\rm T}>0.7$ was used in this analysis to select
spherical events. It is expected that for these events, the multiple soft
particle production processes dominates. For jet-like events with $S_{\rm
T}<0.3$, hard processes such as jets and mini-jets become dominant.

Figure 1 shows the experimental probability of having events with different
transverse sphericity for the given raw multiplicity intervals: (1–18),
(19–30), and ($>30$). Sphericity is correlated with multiplicity, so the
number of events with small $S_{\rm T}$ values is higher in the lowest
multiplicity interval, while the larger multiplicity intervals contain more
events with large sphericity values.

Figure 1: The experimental probability $P$ of having events of different
transverse sphericity $S_{\rm T}$ in the given raw multiplicity $N_{\rm trk}$
intervals: (1–18), (19–30), and ($>30$). There are no corrections applied for
the efficiency of the sphericity selection. Only statistical uncertainties are
shown and are smaller than the marker size.

The difference between spherical events, jet-like events, and events without
sphericity selection can be clearly seen in Fig. 2, which presents the
experimental and Monte Carlo distributions of the azimuthal angle difference
$\Delta\varphi$ between the trigger and the associated particles, where the
trigger particle is the particle with the largest $p_{\rm T}$ in the event,
$p_{\rm T}^{\rm trig}>0.5$ GeV$/c$, $p_{\rm T}^{\rm assoc}<p_{\rm T}^{\rm
trig}$. All distributions are normalized by the number of associated
particles: $N_{\rm{assoc}}(S_{\rm T}(0,1))=N_{\rm{assoc}}(S_{\rm
T}<0.3)+N_{\rm{assoc}}(S_{\rm T}>0.7)+N_{\rm{assoc}}(S_{\rm T}(0.3,0.7))$.

The Monte Carlo simulations with PYTHIA 8 as event generator and GEANT 3 for
the simulation of the detector and the propagation of particles through the
detector material, describe the $\Delta\varphi$ distributions reasonably well
for all sphericity selections. The jet-like events demonstrate a strong
anisotropic structure. The peak at $\Delta\varphi\sim 0$ corresponds to
correlations within the jet determined by the trigger particle. The peak at
$\Delta\varphi\to\pi$ corresponds to the correlation of the particle
associated with the jet moving in the opposite direction. Both peaks are
absent for the sphericity selection $S_{\rm T}>0.7$. The $\Delta\varphi$
distribution shows some specific features with respect to the distribution
without sphericity selection, which are reasonably well described by PYTHIA 8.
The spherical events are much more isotropic than the jet-like ones, and the
jet structures are suppressed.

Figure 2:  The pion raw experimental distribution of the azimuthal angle
difference $\Delta\varphi$ between the trigger and the associated particles
for $S_{\rm T}>0.7$ (red circles), $S_{\rm T}<0.3$ (blue squares) and $S_{\rm
T}$ (0,1) (green stars) compared with MC PYTHIA 8 calculations shown with the
corresponding open markers. The calculations include particle transport
through the ALICE detector using the GEANT 3 transport package. The
statistical uncertainties are smaller than the marker size.

###  4.2 Correlation functions

The particle source created in hadronic or nuclear collisions is usually
investigated using momentum correlations of two or more emitted particles.
This analysis studies two-particle correlations. The observable of interest is
the correlation function (CF) defined as

$C({\bf p}_{1},{\bf p}_{2})=A({\bf p}_{1},{\bf p}_{2})/B({\bf p}_{1},{\bf
p}_{2}),$ (3)

where $A({\bf p}_{1},{\bf p}_{2})$ is the two-particle momentum distribution
in the given event, and $B({\bf p}_{1},{\bf p}_{2})$ is a reference
distribution [59]. The former includes information on the source as well as on
the FSI of the emitted hadrons and/or QS effects. The latter is constructed by
mixing particles emitted in two different collisions to avoid any influence of
pair correlation. In the present work, the reference distribution is
constructed by mixing ten events with similar multiplicity and of close
sphericities. It is also required that events in a mixed event pool have their
vertex positions within 2 cm from each other along the beam direction.

Due to the experimental limitation in the number of pairs, the CF is commonly
defined in terms of a single kinematic variable instead of using the particle
momentum vectors (see Eq. (3)). In the following, the Lorentz-invariant
$q_{\rm inv}=\sqrt{{\bf q}^{2}-q_{0}^{2}}$ is used, where ${\bf q}={\bf
p}_{\mathrm{1}}-{\bf p}_{\mathrm{2}}$ is the pair momentum difference and
$q_{0}=E_{1}-E_{2}$ is the energy component difference.

The measured correlation functions are corrected using the so called double-
ratio technique for the MC simulated ones $C_{\rm MC}(q_{\mathrm{inv}})$. This
procedure assumes that the signal and the background are factorized. The
corrected correlation function can be written as

$C_{\rm corr}(q_{\mathrm{inv}})=\frac{C_{\rm data}(q_{\mathrm{inv}})}{C_{\rm
MC}(q_{\mathrm{inv}})}.$ (4)

Generally, the CF includes several effects, such as femtoscopic effects
(QS+Coulomb in the case of $\pi^{\pm}\pi^{\pm}$ and K±K± correlations), mini-
jet contributions at low $q_{\rm inv}$, and long-range correlations due to
energy–momentum conservation at high $q_{\rm inv}$. The latter are present in
the same-event pair relative-momentum distribution and absent in the mixed-
event distribution determining the CFs. If spherical events are selected with
$S_{\rm T}>0.7$, contributions of mini-jets are strongly suppressed. However,
there is still influence of long-range correlations due to the conservation
laws. Therefore, to correct the experimental CFs for these long-range effects
in spherical events, a MC model which correctly describes the shape of the
experimental CFs at large $q_{\rm inv}$ are used. The experimental CFs can be
divided by the MC ones (Eq. (4)), and the resulting CFs are considered to
contain only femtoscopic effects, which can be fitted with a function
including QS and Coulomb interaction. For pp collisions at $\sqrt{s}=13$ TeV,
the PYTHIA 8 [55] MC model gives the best description of the experimental
function outside the low $q_{\rm inv}$ region. For jet-like ($S_{\rm T}<0.3$)
events, there is a large contribution of mini-jets at low $q_{\rm inv}$ in
addition to the long-range correlations at high pair relative momentum. They
can also be corrected using PYTHIA 8 calculations in order to consider
femtoscopic correlations only.

The analysis was performed separately for positively and negatively charged
pions and kaons at two magnetic field polarities, after which the two-particle
correlations were combined using their statistical uncertainties as weights.

The analysis for pions and kaons was performed in the same three multiplicity
intervals. For pions, five pair transverse momentum $k_{\mathrm{T}}$ intervals
were used: (0.15–0.3), (0.3–0.5), (0.5–0.7), (0.7–0.9), and (0.9–1.2) GeV$/c$.
The analysis for kaons was performed in two $k_{\mathrm{T}}$ intervals:
(0.15–0.5), (0.5–1.2) GeV$/c$.

####  4.2.1 Pion correlation functions

Figure 3 shows the pion experimental CF (green solid circles) for events with
$S_{\rm T}>0.7$ in pp collisions at $\sqrt{s}=13$ TeV. The PYTHIA 8 (Monash)
model calculations including the ALICE detector response were used to describe
non-femtoscopic effects and are also shown in the figure (blue crosses). All
distributions are normalized to unity in the $0.7<q_{\rm inv}<0.8$ GeV$/c$
range, which is well outside the QS and Coulomb FSI region ($q_{\rm
inv}\lesssim 0.4$ GeV$/c$) and before the noticeable large $q_{\rm inv}$ slope
associated with energy and momentum conservation. The CFs shown in Fig. 3 are
flat for the low multiplicity intervals in the region $0.5<q_{\rm inv}<1.0$
GeV$/c$. For the two highest $k_{\rm T}$ intervals, some slope of baseline
appears. At $q_{\rm inv}>1.0$ GeV$/c$, the aforementioned kinematic effects
are present especially for the lowest multiplicity intervals.

The CFs decrease at $q_{\rm inv}\to 0$ for the PYTHIA 8 calculations for the
lowest multiplicity interval ($N_{\rm trk}\leq$18) in the (0.5–0.7) GeV$/c$,
(0.7–0.9) GeV$/c$ and (0.9–1.2) GeV$/c$ $k_{\rm T}$ intervals. The occurrence
of such minima is related to the three tracks requirement, necessary for the
transverse sphericity calculation [44]. Indeed, the number of available events
with three tracks with $p_{\rm T}>0.5$ GeV$/c$ decreases at small $q_{\rm
inv}$.

Figure 3: The $\pi^{\pm}\pi^{\pm}$ experimental correlation functions (green
solid circles) as function of the invariant pair relative momentum
$q_{\mathrm{inv}}$ in pp collisions at $\sqrt{s}=13$ TeV for the raw
multiplicity $N_{\rm trk}$ intervals of (1–18), (19–30), and ($>30$) in the
(0.15–0.3) GeV/$c$, (0.3–0.5) GeV/$c$, (0.5–0.7) GeV$/c$, (0.7–0.9) GeV$/c$
and (0.9–1.2) GeV$/c$ $k_{\rm T}$ intervals. A sphericity selection of $S_{\rm
T}>0.7$ is applied. The data are compared with PYTHIA 8 calculations, shown by
blue crosses. The error bars represent the statistical uncertainties, while
the systematic uncertainties are negligible.

Figure 4 illustrates the pion experimental correlation function in pp
collisions at $\sqrt{s}=13$ TeV compared with PYTHIA 8 model calculations for
events with $S_{\rm T}<0.3$. The CFs for jet-like events shown in this figure
exhibit a pronounced slope over the full $q_{\mathrm{inv}}$ range indicating
the presence of non-femtoscopic effects. These effects are especially
pronounced for $k_{\rm T}>0.5$ GeV$/c$. As can be seen from the figure, the
PYTHIA 8 model calculations describe reasonably well the pion experimental
data for jet-like events at large $q_{\mathrm{inv}}$ values.

Figure 4: The $\pi^{\pm}\pi^{\pm}$ experimental correlation functions (green
solid circles) as function of the invariant pair relative momentum
$q_{\mathrm{inv}}$ in pp collisions at $\sqrt{s}=13$ TeV for the raw
multiplicity $N_{\rm trk}$ intervals of (1–18), (19–30), and ($>30$) in the
(0.15–0.3) GeV/$c$, (0.3–0.5) GeV/$c$, (0.5–0.7) GeV$/c$, (0.7–0.9) GeV$/c$
and (0.9–1.2) GeV$/c$ $k_{\rm T}$ intervals. A sphericity selection of $S_{\rm
T}<0.3$ is applied. The data are compared with PYTHIA 8 calculations shown by
blue crosses. The error bars represent the statistical uncertainties, while
the systematic uncertainties are negligible.

####  4.2.2 Kaon correlation functions

Figure 5 shows the kaon experimental CF (green solid circles) for events with
$S_{\rm T}>0.7$ and the corresponding PYTHIA 8 calculations (blue crosses) in
pp collisions at $\sqrt{s}=13$ TeV.

The strength of the charged kaon correlations, represented by the magnitude of
$C(q_{\rm inv})$ for $q_{\rm inv}\to 0$, is smaller than observed for the
pions and decrease with $k_{\rm T}$. The CFs for spherical events are flat at
$q_{\rm inv}>0.5$ GeV$/c$ both for the data and the MC calculations. The non-
femtoscopic background contributions obtained using PYTHIA 8 were fitted with
a second-order polynomial, which then was used for the correction of the
experimental CFs for non-femtoscopic effects. The fit allows reducing the
impact of statistical fluctuations on the extracted femtoscopic parameters.

Figure 5: The K±K± experimental correlation functions (green solid circles) as
function of the invariant pair relative momentum $q_{\mathrm{\rm inv}}$ in pp
collisions at $\sqrt{s}=13$ TeV for the raw multiplicity $N_{\rm trk}$
intervals of (1–18), (19–30), and ($>30$) in the (0.15–0.5) GeV$/c$ and
(0.5–1.2) GeV$/c$ $k_{\rm T}$ intervals. A sphericity selection of $S_{\rm
T}>0.7$ is applied. The data are compared with PYTHIA 8 calculations shown by
blue crosses. The PYTHIA 8 calculations are approximated with a second-order
polynomial (red curves). The error bars represent the statistical
uncertainties, while the systematic uncertainties are negligible.

Figure 6 presents the kaon experimental correlation function for events with
$S_{\rm T}<0.3$ in pp collisions at $\sqrt{s}=13$ TeV, for the raw
multiplicity intervals $N_{\rm trk}$ of (1–18), (19–30), and ($>30$) in the
(0.15–0.5) GeV$/c$ and (0.5–1.2) GeV$/c$ $k_{\rm T}$ intervals. Similarly to
the pion CFs for jet-like events (see Fig. 4), the kaon jet-like CFs shown in
Fig. 6 exhibit a pronounced slope at low $q_{\mathrm{\rm inv}}$ indicating the
presence of non-femtoscopic effects. Such background is especially pronounced
for $k_{\rm T}>0.5$ GeV$/c$. As can be seen in the figure, the estimate of the
femtoscopic signal with respect to the background effects in the highest
$N_{\rm trk}>30$ multiplicity interval is not possible since the correlation
functions coincide with PYTHIA 8 within statistical uncertainties.

Figure 6:  The K±K± experimental correlation functions (green solid circles)
as function of the invariant pair relative momentum $q_{\mathrm{\rm inv}}$ in
pp collisions at $\sqrt{s}=13$ TeV for the raw multiplicity $N_{\rm trk}$
intervals of (1–18), (19–30), and ($>30$) in the (0.15–0.5) GeV$/c$ and
(0.5–1.2) GeV$/c$ $k_{\rm T}$ intervals. A sphericity selection of $S_{\rm
T}<0.3$ is applied. The data are compared with PYTHIA 8 calculations, shown by
blue crosses and approximated with a second-order polynomial (red curves). The
error bars represent the statistical uncertainties, while the systematic
uncertainties are negligible.

###  4.3 Correlation function parametrization

In the previous analyses performed by the ALICE Collaboration in pp
collisions, the Gaussian distribution of a particle source in the pair
reference frame (PRF) was assumed for pions [30] and kaons [33]. In those
cases, the fit was performed using the Bowler–Sinyukov formula [60, 61]

$C(q_{\mathrm{\rm inv}})=N\left(1-\lambda+\lambda K(r,q_{\mathrm{\rm
inv}})\left(1+\exp{\left(-R_{\mathrm{\rm inv}}^{2}q_{\mathrm{\rm
inv}}^{2}\right)}\right)\right),$ (5)

where $N$ is a normalization coefficient and $K(r,q_{\mathrm{\rm inv}})$ is
the Coulomb function with a radius $r$ defined as

$\displaystyle K(r,q_{\mathrm{\rm inv}})=\frac{C({\rm QS+Coulomb})}{C({\rm
QS})}.$ (6)

The parameters $R_{\mathrm{\rm inv}}$ and $\lambda$ describe the size of the
source and the correlation strength, respectively (see Eq. (5)). The term
$C({\rm QS})$ in Eq. (6) is a theoretical CF calculated with pure QS weights
(wave function squared) and $C({\rm QS+Coulomb})$ corresponds to ${\rm
QS+Coulomb}$ weights. However, since the pion CFs are strongly non-Gaussian
due to the large resonance contribution, an exponential Bowler–Sinyukov
function was used to fit the pion CF like in Ref. [43]:

$C(q_{\mathrm{\rm inv}})=N\left(1-\lambda+\lambda K(r,q_{\mathrm{\rm
inv}})\left(1+\exp{\left(-R_{\mathrm{\rm inv}}q_{\mathrm{\rm
inv}}\right)}\right)\right)D(q_{\rm inv}),$ (7)

where $D(q_{\rm inv})=bq_{\rm inv}+1$ accounts for the slope of the baseline
which remains after the division by PYTHIA 8.

The measured pion CFs shown in Figs. 3–4 were divided by the PYTHIA 8 baseline
and fit with the exponential Bowler–Sinyukov formula of Eq. (7). Figure 7
presents some examples of the pion CF fit with the Gaussian function of Eq.
(5) (dotted line) and the exponential of Eq. (7) (solid line) Bowler–Sinyukov
formulae. The exponential fit function describes the pion CF well both for
spherical and jet-like events, although the description is not ideal for
$q_{\rm inv}<0.05$ GeV$/c$.

The kaon CFs for spherical and jet-like events were corrected using a second-
order polynomial to describe the non-femtoscopic background as explained above
and fitted with the Gaussian Bowler–Sinyukov formula (Eq. (5)). An example of
such a fit is shown in Fig. 8 both for spherical and jet-like events. For the
largest multiplicity bin for $S_{\rm T}<0.3$ selection, kaon CFs do not
exhibit any femtoscopic peak after the correction for the baseline and,
therefore, the fit was not performed.

Figure 7: Examples of the pion CFs fitted with the Gaussian Eq. (5) (dotted
line) and the exponential (solid line) Bowler–Sinyukov Eq. (7) formulae for
spherical (left panel) and jet-like (right panel) events. Only statistical
uncertainties are shown. Systematic uncertainties are negligible.

Figure 8: Examples of the kaon CFs fitted with the Gaussian Eq. (5) (dotted
line) Bowler–Sinyukov formula for spherical (left panel) and jet-like (right
panel) events. Only statistical uncertainties are shown. Systematic
uncertainties are negligible.

###  4.4 Systematic uncertainties

In this section, the systematic uncertainties estimated for the extracted
source parameters $R_{\rm inv}$ and $\lambda$ for $\pi^{\pm}\pi^{\pm}$ and
K±K± correlations at different sphericities are discussed.

The systematic uncertainty contributions related to particle selection and fit
criteria $\Delta_{\rm sys}=|y_{0}-y_{\rm var}|$ were considered, taking into
account their statistical significance level determined by the Barlow factor
[62]

$B=\frac{|y_{0}-y_{\rm var}|}{\sqrt{\sigma_{0}^{2}+\sigma_{\rm
var}^{2}-2\rho\sigma_{0}\sigma_{\rm var}}},$ (8)

where $y_{0}$ is the default value, $y_{\rm var}$ is a value obtained with
some variation of either the selection criteria or fit conditions,
$\sigma_{0}$ is the statistical uncertainty of the default value, $\sigma_{\rm
var}$ is the statistical uncertainty of the femtoscopic parameters obtained
using varied analysis criteria, $\rho$ characterizes the correlation between
$y_{0}$ and $y_{\rm var}$.

The systematic uncertainty contribution is taken into account if $B>1$, i.e.
only systematic uncertainties whose statistical significance level exceeds 68%
are included in the total systematic uncertainty value. The systematic
uncertainties $\Delta^{i}_{\rm sys}$ corresponding to each $i^{\rm th}$
variation of the particle selection and fit criteria and having $B>1$ were
added in quadrature to give the total systematic uncertainty $\Delta$ value

$\Delta_{\rm sys}=\sqrt{\sum_{i}\left(\Delta_{\rm sys}^{i}\right)^{2}}.$ (9)

As event selection criterion variation, the sphericity intervals were varied
by $\pm 0.05$ [43], resulting in a systematic uncertainty of up to 10% for the
radii and $\lambda$ parameters for pions and kaons.

The systematic uncertainties related to the track selection ($p_{\rm T}$ and
$\eta$ intervals, $\rm DCA_{\rm transverse}$, $\rm DCA_{\rm longitudinal}$,
the values of the number of track points in TPC) were estimated by varying
each selection criterion (see Tables 1 and 2) with variation limits up to $\pm
20\%$. Another source of systematic uncertainty is the misidentification of
particles and the associated purity correction. The same $\pm 20\%$ variation
of the parameters $n_{\sigma_{\mathrm{TPC}}}$ and $n_{\sigma_{\mathrm{TOF}}}$
used for the purity correction estimation was performed. The purity correction
influences only the $\lambda$ parameter. For pions, single particle purity is
$\sim$ 99% at $p<1.5$ GeV$/c$, so the correction for purity is negligible. For
kaons, it is $<$ 1%. The estimated systematic uncertainty for pions for
spherical events is 2–5% for $R_{\rm inv}$ and $\lambda$, while for jet-like
events it is 1–15% for $R_{\rm inv}$ and 1–20% for $\lambda$. For kaons, it is
$<5$% for spherical events, and 10–20% for jet-like events for both $R_{\rm
inv}$ and $\lambda$.

To minimize the influence of two-track effects, the tracks in this analysis
were required to have the average TPC separation of at least 3 cm. The
systematic uncertainty related to these effects was estimated from comparing
the resulting femtoscopic parameters with those obtained with the average TPC
separation up to 10 cm. This comparison showed that the influence of the two-
track effects on the extracted parameters was negligible.

It is known that usually the extracted femtoscopic parameters noticeably
depend on the fit range if the baseline is not flat, which is the case for CF
in pp collisions. To estimate the related systematic uncertainty, three
different fit ranges are considered: the standard $0<q_{\rm inv}<0.8$ GeV$/c$,
the shorter $0<q_{\rm inv}<0.7$ GeV$/c$, and the longer $0<q_{\rm inv}<0.9$
GeV$/c$ ones. The systematic uncertainty for pion and kaon due to the
variation in fit range is 1–12% for $R_{\rm inv}$ and 5–20% for $\lambda$.

The Coulomb interaction, described by the factor $K$ in Eq. (6), is included
in the default fitting procedure (Eqs. (5)–(7)). The influence of strong
interactions on the extracted femtoscopic observables is estimated using the
factor $K(q_{\mathrm{\rm inv}})=C({\rm QS+Coulomb+strong})/C({\rm QS})$ and is
taken as a systematic uncertainty. The strong interaction for both pions and
kaons was calculated using the fully dynamical lattice QCD result [63]. The
resulting systematic uncertainty for pions is 3–7% for $R_{\rm inv}$ and
$\lambda$ for both spherical and jet-like events. The systematic uncertainty
related to the strong interactions for kaons is 7–15% for radii and
correlation strengths for both spherical and jet-like events.

The systematic uncertainty introduced by the fit range variation was the only
one observed to be fully correlated. For this uncertainty $\rho=1$ in Eq. (8),
while for all other uncertainties $\rho=0$ was used.

##  5 Results and discussion

One of the goals of this work is to compare the kaon and pion radii for
spherical and jet-like events in order to understand if the extracted radii
follow the same $m_{\rm T}$ scaling behavior as observed in heavy-ion
collisions.

To compare the strongly non-Gaussian pion source with the Gaussian kaon one,
the exponential pion radii have to be converted to a Gaussian form. The
Gaussian parametrization assumes a radial Gaussian distribution with the first
moment of the distribution $1/R\sqrt{\pi}$, while the exponential
parametrization assumes a Lorentzian one with the first moment of distribution
$1/R$. Therefore, in order to compare the radii, the exponential radii should
be divided by $\sqrt{\pi}$.

Figure 9: The Gaussian pion (blue circles) and kaon (green crosses) radii for
spherical ($S_{\rm T}>0.7$) and jet-like ($S_{\rm T}<0.3$) events as function
of the average pair transverse mass $m_{\rm T}$ for different multiplicity
intervals. The lines approximating the pion and kaon radii by the linear
function of Eq. (10) are shown for spherical events by dotted blue and green
lines, respectively, and for jet-like events by dotted-dashed lines. The lines
for combined fit for pion and kaon points are shown by black solid and dashed
lines for spherical and jet-like events, respectively. Statistical (bars) and
systematic (boxes) uncertainties are shown. Figure 10: The Gaussian pion (blue
circles) and kaon (green crosses) radii for spherical ($S_{\rm T}>0.7$) and
jet-like ($S_{\rm T}<0.3$) events corrected for the Lorenz boost with factor
in Eq. (11) as function of the average pair transverse mass $m_{\rm T}$ for
different multiplicity intervals. The lines approximating the pion and kaon
radii by the linear function of Eq. (10) are shown for spherical events by
dotted blue and green lines, respectively, and for jet-like events by dotted-
dashed lines. The lines for combined fit for pion and kaon points are shown by
black solid and dashed lines for spherical and jet-like events, respectively.
Statistical (bars) and systematic (boxes) uncertainties are shown.

Figure 9 presents the $m_{\rm T}$ dependence of Gaussian radii for spherical
and jet-like events for pions and kaons in different raw multiplicity
intervals. As discussed in Section 4.2.1, the pion radii for $S_{\rm T}>0.7$,
$N_{\rm trk}<$18 and $k_{\rm T}>0.50$ GeV$/c$ ($m_{\rm T}>~{}0.52$
GeV$/c^{2}$) have to be interpreted with caution because the baseline used to
describe the non-femtoscopic effects was distorted at low $q_{\rm inv}$ (see
Fig. 3) by the $p_{\rm T}>0.5$ GeV$/c$ three-track requirement requested for
the calculation of the transverse sphericity.

The pion and kaon radii for spherical and jet-like events (Figures 9 and 10)
were fitted in each multiplicity interval with a linear function

$f(m_{\rm T})=a+bm_{\rm T},$ (10)

where $a$ and $b$ are free parameters. The results of this fitting are
presented in Tables 4 and 5. The individual fits for pions and kaons are
compared with the combined fit of pion and kaon radii. It should be noted that
for kaons the line is not exactly a fit since there are only two points
available but it illustrates the slope of the radii with $m_{\rm T}$. It
allows quantifying how much the kaon radius data points deviate from this fit
and, thus, how well the approximate $m_{\rm T}$ scaling manifests itself. Both
the spherical ($S_{\rm T}>0.7$) and the jet-like ($S_{\rm T}<0.3$) radii for
pions and kaons decrease with increasing $m_{\rm T}$. The statistical
uncertainties are large, especially for kaons, but there is an indication that
the spherical radii demonstrate a flatter dependence compared to the jet-like
ones for $N_{\rm trk}<30$, while a more pronounced slope appears for $N_{\rm
trk}>30$ (see Table 4). The spherical kaon radii are smaller than the
corresponding spherical pion radii, and the difference increases with
increasing multiplicity. The jet-like pion radii are smaller than spherical
ones, and the difference increases with increasing multiplicity.

Table 4: The parameters of the approximation by the linear function of Eq. 10 of the femtoscopic radii in PRF calculated for pions and kaons for spherical and jet-like events, as a function of pair transverse mass for the different multiplicity intervals from Figure 9. type of fit | $N_{\rm trk}$ | $b$ | $a$ | $\chi^{2}/{\rm NDF}^{{\phantom{1}}^{\phantom{1}}}$
---|---|---|---|---
| 3(1)–18 |  $-0.18\pm$ 0.16 | 1.39 $\pm$ 0.09 | 0.18/3
pions, spherical events | 19–30 |  $-0.55\pm$ 0.14 | 1.74 $\pm$ 0.09 | 1.95/3
| $>30$ |  $-0.69\pm$ 0.14 | 1.98 $\pm$ 0.10 | 1.77/3
| 3(1)–18 |  $-0.76\pm$ 0.20 | 1.50 $\pm$ 0.14 | 0.90/3
pions, jet-like events | 19–30 |  $-0.80\pm$ 0.14 | 1.64 $\pm$ 0.14 | 1.2/3
| $>30$ |  $-0.81\pm$ 0.21 | 1.69 $\pm$ 0.17 | 0.63/3
| 3(1)–18 |  $-0.43\pm$ 0.60 | 1.44 $\pm$ 0.42 | -
kaons, spherical events | 19–30 |  $-0.66\pm$ 0.43 | 1.75 $\pm$ 0.34 | -
| $>30$ |  $-0.85\pm$ 0.38 | 1.99 $\pm$ 0.31 | -
| 3(1)–18 |  $-1.38\pm$ 0.93 | 2.12 $\pm$ 0.78 | -
kaons, jet-like events | 19–30 |  $-1.25\pm$ 1.38 | 2.06 $\pm$ 1.12 | -
| $>30$ | - | - | -
| 3(1)–18 |  $-0.24\pm$ 0.15 | 1.39 $\pm$ 0.09 | 2.10/5
pions and kaons, spherical events | 19–30 |  $-0.56\pm$ 0.14 | 1.72 $\pm$ 0.09 | 2.25/5
| $>30$ |  $-0.69\pm$ 0.14 | 1.97 $\pm$ 0.09 | 2.00/5
| 3(1)–18 |  $-0.67\pm$ 0.16 | 1.47 $\pm$ 0.14 | 1.60/5
pions and kaons, jet-like events | 19–30 |  $-0.78\pm$ 0.17 | 1.63 $\pm$ 0.14 | 1.30/5
| $>30$ | - | - | -

The $m_{\rm T}$ scaling for pions and kaons was predicted in a case of
negligible transverse flow and common freeze-out for 3D radii in the
Longitudinally Co-Moving System (LCMS) [26]), where the pair relative momentum
is decomposed over ($q_{\rm out}$, $q_{\rm side}$, $q_{\rm long}$). Here, the
“long” component goes along the beam direction, “out” – along the pair
transverse momentum, and “side” – perpendicular to the latter in the
transverse plane, while the longitudinal total pair momentum vanishes.
Theoretical calculations within the 3+1D hydrodynamic model coupled with the
statistical hadronization code THERMINATOR-2 taking into account the resonance
contribution showed an effective power-law scaling of 3D LCMS radii over the
pair transverse mass for pions, kaons and protons [25]. The same scaling was
also observed in Ref. [25] for the one-dimensional radii in the RPF. However,
it is often challenging to do measurements in the LCMS due to limited number
of events and, therefore, the measurements are performed in the PRF and then
transformed from the PRF to the LCMS by applying a Lorentz boost in the
direction of the pair transverse momentum with velocity $\beta_{\rm T}=p_{\rm
T}/m_{\rm T}$ as $\gamma_{\rm T}R_{\rm out}$ (where $\gamma_{\rm
T}=\sqrt{1-\beta_{T}^{2}}$). Therefore, the transverse (out) component of the
3D radius changes differently for pions and for kaons due to the different
Lorentz boosts. In Ref. [25], it was shown that the scaling could be restored
if the radii were divided by the following scaling factor

$f=\sqrt{(\sqrt{\gamma}_{\rm T}+2)/3}.$ (11)

After applying these kinematic corrections (Eq. (11)), the authors of Ref.
[25] observed that the one-dimensional $R_{\rm inv}$ correlation radii for
pions, kaons, and protons, as measured by ALICE in Pb–Pb collisions at
$\sqrt{s_{\rm NN}}$ = 2.76 TeV [35], lied on a common curve (with the accuracy
of 10%).

By applying this correction to the radii measured in this work (Fig. 10), the
extracted pion and kaon radii for spherical events become closer to each other
than in the case without such correction (Figure 9) considered above. The
large uncertainties for kaon radii do not allow making any conclusion about
the $m_{\rm T}$ scaling in jet-like events. The understanding of the $m_{\rm
T}$ trend of the jet-like pion and kaon radii requires further study. The
radii shown in Figure 10 were also fitted with the linear function of Eq. 10
(see Table 5). The $\chi^{2}/{\rm NDF}$ for the fit of the uncorrected radii
(Table 4) are larger than for the corrected ones (Table 5) for spherical
events in all multiplicity intervals.

Table 5: The parameters of the approximation by the linear function of Eq. 10 of the femtoscopic radii in the PRF calculated for pions and kaons for spherical and jet-like events, as function of pair transverse mass for the different multiplicity intervals from Figure 10. type of fit | $N_{\rm trk}$ | $b$ | $a$ | $\chi^{2}/{\rm NDF}^{{\phantom{1}}^{\phantom{1}}}$
---|---|---|---|---
| 3(1)–18 |  $-0.40\pm$ 0.13 | 1.36 $\pm$ 0.08 | 0.24/3
pions, spherical events | 19–30 |  $-0.73\pm$ 0.12 | 1.68 $\pm$ 0.08 | 0.81/3
| $>30$ |  $-0.87\pm$ 0.12 | 1.91 $\pm$ 0.09 | 0.69/3
| 3(1)–18 |  $-0.85\pm$ 0.17 | 1.43 $\pm$ 0.13 | 0.39/3
pions, jet-like events | 19–30 |  $-0.90\pm$ 0.16 | 1.55 $\pm$ 0.12 | 0.51/3
| $>30$ |  $-0.91\pm$ 0.19 | 1.61 $\pm$ 0.15 | 0.27/3
| 3(1)–18 |  $-0.55\pm$ 0.56 | 1.50 $\pm$ 0.40 | -
kaons, spherical events | 19–30 |  $-0.79\pm$ 0.42 | 1.81 $\pm$ 0.33 | -
| $>30$ |  $-0.99\pm$ 0.37 | 2.05 $\pm$ 0.31 | -
| 3(1)–18 |  $-1.47\pm$ 0.9 | 2.15 $\pm$ 0.76 | -
kaons, jet-like events | 19–30 |  $-1.35\pm$ 1.35 | 2.10 $\pm$ 0.10 | -
| $>30$ | - | - | -
| 3(1)–18 |  $-0.39\pm$ 0.13 | 1.36 $\pm$ 0.08 | 0.45/5
pions and kaons, spherical events | 19–30 |  $-0.70\pm$ 0.12 | 1.67 $\pm$ 0.08 | 1.25/5
| $>30$ |  $-0.87\pm$ 0.12 | 1.90 $\pm$ 0.09 | 0.75/5
| 3(1)–18 |  $-0.71\pm$ 0.14 | 1.44 $\pm$ 0.12 | 10.1/5
pions and kaons, jet-like events | 19–30 |  $-0.82\pm$ 0.15 | 1.54 $\pm$ 0.12 | 3.10/5
| $>30$ | - | - | -

This suggests an approximate $m_{\rm T}$ scaling for the radii for spherical
events if the differences in Lorentz boosts for pions and kaons are taken into
account.

It is also instructive to consider the difference between the radii with and
without sphericity selection, as shown in Figure 11 for the pion radii for
$S_{\rm T}>0.7$, $S_{\rm T}<0.3$, and without a selection on sphericity. It
can be seen that for large multiplicities ($N_{\rm trk}>18$) the radii
extracted from the data without sphericity selections are close to those
obtained in spherical events. This can be naturally explained by the
experimental sphericity distributions presented in Fig. 1. The figure shows
that all events tend to have large value of $S_{\rm T}$ and that the high-
multiplicity intervals consist mainly of events with $S_{\rm T}>0.7$.
Therefore, the corresponding radii are close to each other within
uncertainties. For $N_{\rm trk}<18$ interval, the fraction of particles with
$S_{\rm T}<0.3$ becomes large, and the radii calculated without sphericity
selection for this multiplicity interval are in between the $S_{\rm T}>0.7$
and $S_{\rm T}<0.3$ sphericity selected results, reflecting some interplay
between all sphericity selected contributions.

Figure 11: The Gaussian pion radii with $S_{\rm T}>0.7$ (open circles),
$S_{\rm T}<0.3$ (solid circles) and without sphericity selection (solid
crosses). Statistical (bars) and systematic (boxes) uncertainties are shown.

Figure 12 demonstrates the $m_{\rm T}$ dependence of the correlation strength
parameters $\lambda$ for pions and kaons both for spherical (left panel) and
jet-like (right panel) events. The $\lambda$ parameters for pions were
converted to a Gaussian form by dividing them by $\sqrt{\pi}$ in the same way
as was done for the radii (see the discussion in the beginning of this
section). The obtained pion $\lambda$ weakly decreases with increasing $m_{\rm
T}$, and this behavior is similar for both sphericity selections. The kaon
$\lambda$ parameters are close to the pion ones, and all of them are in the
range of $\sim$0.4–0.5. The main factors that could decrease the $\lambda$
parameters compared to the ideal case of unity are the non-Gaussian shape of
CFs due to contribution of particles from short-lived (strongly decaying) and
medium-lived ($\omega$ for pions, ${\rm K}^{0}_{\rm S}$ for kaons) resonances
and the $R_{\rm inv}$ distortion in the PRF due to the Lorenz boost in the out
direction resulting in values for $R_{\rm side}$ and $R_{\rm long}$ to be
smaller than $R_{\rm out}$. For pions, the $\lambda$ values are also reduced
due to long-lived resonances such as $\eta$ and $\eta^{{}^{\prime}}$.

Figure 12: The Gaussian pion and kaon $\lambda$ parameters for spherical (left
panel) and jet-like (right panel) events as function of the average pair
transverse mass $m_{\rm T}$ for different multiplicity intervals. The
$\lambda$ parameters are corrected for purity. Statistical (bars) and
systematic (boxes) uncertainties are shown.

The decrease of the pion and kaon sphericity integrated radii with increasing
pair transverse mass in pp collisions was observed at LHC energies before as
an indication of collective behaviour, originating from either initial- or
final-state correlations. However, there was not even an approximate $m_{\rm
T}$ scaling shown. The intriguing analogy with heavy-ion collisions was
interpreted as a possibility of the collective behavior due to quark–gluon
plasma formation [30, 33, 40, 41].

The study presented here demonstrates a similar decrease of radii for both
spherical and jet-like events. There is an indication of an approximate
$m_{\rm T}$ scaling of the radii for pions and kaons in spherical events if
the kinematic correction for these particle species is taken into account.
However, the fact that the decreasing $m_{\rm T}$ dependence and even the
approximate $m_{\rm T}$ scaling are observed in all multiplicity intervals
including the lowest ones suggests that this effect does not support the
hypothesis of collective expansion of hot and dense matter like in heavy-ion
collisions. More realistic looks the hypothesis of common emission conditions
for pions and kaons in pp collisions for the multiplicity intervals studied in
this work, similar to the simplified scenario described in Ref. [25].

##  6 Summary

Correlations of two charged identical pions $\pi^{\pm}\pi^{\pm}$ and kaons
K±K± were measured in pp collisions at $\sqrt{s}=13$ TeV at the LHC. One-
dimensional pion and kaon correlations were classified using the global event-
shape variable, transverse sphericity. For spherical events, the correlation
functions show a strong suppression of mini-jet contributions. On the
contrary, the correlation functions for jet-like events manifest large effects
related to non-femtoscopic correlations at small relative momentum.

The Monte Carlo PYTHIA 8 (Monash) model describes both spherical and jet-like
pion and kaon correlation functions outside the femtoscopic region effect.
Therefore, it was used to subtract non-femtoscopic correlations from the
femtoscopic signal region. The pion correlation functions corrected for mini-
jet contributions as modeled by PYTHIA 8 are described by the exponential
Bowler–Sinyukov function. The Bowler–Sinyukov function using a single Gaussian
was used to describe the kaon correlations. The pion femtoscopic radii
extracted for spherical events are larger than those for jet-like events. Both
pion and kaon radii demonstrate a decreasing trend with increasing pair
transverse mass $m_{\rm T}$.

The Lorentz-boost corrected pion and kaon radii both for spherical and jet-
like events show an approximate scaling behavior with $m_{\rm T}$ in all
multiplicity intervals. The observation of such behavior for small
multiplicity intervals, where the formation of QGP plasma seems to be
impossible, can be interpreted as an indication of the emission occurring
simultaneously for $\pi$ and K in pp collisions for all considered
multiplicities.

## 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), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. In addition, individual groups or members have received support from: European Research Council, Strong 2020 - Horizon 2020 (grant nos. 950692, 824093), European Union; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland.

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##  Appendix A The ALICE Collaboration

S. Acharya 127, D. Adamová 86, G. Aglieri Rinella 33, M. Agnello 30, N.
Agrawal 51, Z. Ahammed 135, S. Ahmad 16, S.U. Ahn 71, I. Ahuja 38, A.
Akindinov 142, M. Al-Turany 97, D. Aleksandrov 142, B. Alessandro 56, H.M.
Alfanda 6, R. Alfaro Molina 67, B. Ali 16, A. Alici 26, N. Alizadehvandchali
115, A. Alkin 33, J. Alme 21, G. Alocco 52, T. Alt 64, A.R. Altamura 50, I.
Altsybeev 95, M.N. Anaam 6, C. Andrei 46, N. Andreou 114, A. Andronic 126, V.
Anguelov 94, F. Antinori 54, P. Antonioli 51, N. Apadula 74, L. Aphecetche
103, H. Appelshäuser 64, C. Arata 73, S. Arcelli 26, M. Aresti 23, R. Arnaldi
56, J.G.M.C.A. Arneiro 110, I.C. Arsene 20, M. Arslandok 139, A. Augustinus
33, R. Averbeck 97, M.D. Azmi 16, H. Baba123, A. Badalà 53, J. Bae 104, Y.W.
Baek 41, X. Bai 119, R. Bailhache 64, Y. Bailung 48, A. Balbino 30, A.
Baldisseri 130, B. Balis 2, D. Banerjee 4, Z. Banoo 91, R. Barbera 27, F.
Barile 32, L. Barioglio 95, M. Barlou78, B. Barman42, G.G. Barnaföldi 138,
L.S. Barnby 85, V. Barret 127, L. Barreto 110, C. Bartels 118, K. Barth 33, E.
Bartsch 64, N. Bastid 127, S. Basu 75, G. Batigne 103, D. Battistini 95, B.
Batyunya 143, D. Bauri47, J.L. Bazo Alba 101, I.G. Bearden 83, C. Beattie 139,
P. Becht 97, D. Behera 48, I. Belikov 129, A.D.C. Bell Hechavarria 126, F.
Bellini 26, R. Bellwied 115, S. Belokurova 142, Y.A.V. Beltran 45, G. Bencedi
138, S. Beole 25, Y. Berdnikov 142, A. Berdnikova 94, L. Bergmann 94, M.G.
Besoiu 63, L. Betev 33, P.P. Bhaduri 135, A. Bhasin 91, M.A. Bhat 4, B.
Bhattacharjee 42, L. Bianchi 25, N. Bianchi 49, J. Bielčík 36, J. Bielčíková
86, J. Biernat 107, A.P. Bigot 129, A. Bilandzic 95, G. Biro 138, S. Biswas 4,
N. Bize 103, J.T. Blair 108, D. Blau 142, M.B. Blidaru 97, N. Bluhme39, C.
Blume 64, G. Boca 22,55, F. Bock 87, T. Bodova 21, A. Bogdanov142, S. Boi 23,
J. Bok 58, L. Boldizsár 138, M. Bombara 38, P.M. Bond 33, G. Bonomi 134,55, H.
Borel 130, A. Borissov 142, A.G. Borquez Carcamo 94, H. Bossi 139, E. Botta
25, Y.E.M. Bouziani 64, L. Bratrud 64, P. Braun-Munzinger 97, M. Bregant 110,
M. Broz 36, G.E. Bruno 96,32, M.D. Buckland 24, D. Budnikov 142, H. Buesching
64, S. Bufalino 30, P. Buhler 102, N. Burmasov 142, Z. Buthelezi 68,122, A.
Bylinkin 21, S.A. Bysiak107, M. Cai 6, H. Caines 139, A. Caliva 29, E. Calvo
Villar 101, J.M.M. Camacho 109, P. Camerini 24, F.D.M. Canedo 110, M. Carabas
125, A.A. Carballo 33, F. Carnesecchi 33, R. Caron 128, L.A.D. Carvalho 110,
J. Castillo Castellanos 130, F. Catalano 33,25, C. Ceballos Sanchez 143, I.
Chakaberia 74, P. Chakraborty 47, S. Chandra 135, S. Chapeland 33, M. Chartier
118, S. Chattopadhyay 135, S. Chattopadhyay 99, T.G. Chavez 45, T. Cheng 97,6,
C. Cheshkov 128, B. Cheynis 128, V. Chibante Barroso 33, D.D. Chinellato 111,
E.S. Chizzali II,95, J. Cho 58, S. Cho 58, P. Chochula 33, D. Choudhury42, P.
Christakoglou 84, C.H. Christensen 83, P. Christiansen 75, T. Chujo 124, M.
Ciacco 30, C. Cicalo 52, F. Cindolo 51, M.R. Ciupek97, G. ClaiIII,51, F.
Colamaria 50, J.S. Colburn100, D. Colella 96,32, M. Colocci 26, M. Concas
IV,33, G. Conesa Balbastre 73, Z. Conesa del Valle 131, G. Contin 24, J.G.
Contreras 36, M.L. Coquet 130, P. Cortese 133,56, M.R. Cosentino 112, F. Costa
33, S. Costanza 22,55, C. Cot 131, J. Crkovská 94, P. Crochet 127, R. Cruz-
Torres 74, P. Cui 6, A. Dainese 54, M.C. Danisch 94, A. Danu 63, P. Das 80, P.
Das 4, S. Das 4, A.R. Dash 126, S. Dash 47, R.M.H. David45, A. De Caro 29, G.
de Cataldo 50, J. de Cuveland39, A. De Falco 23, D. De Gruttola 29, N. De
Marco 56, C. De Martin 24, S. De Pasquale 29, R. Deb 134, R. Del Grande 95, L.
Dello Stritto 29, W. Deng 6, P. Dhankher 19, D. Di Bari 32, A. Di Mauro 33, B.
Diab 130, R.A. Diaz 143,7, T. Dietel 113, Y. Ding 6, J. Ditzel 64, R. Divià
33, D.U. Dixit 19, Ø. Djuvsland21, U. Dmitrieva 142, A. Dobrin 63, B. Dönigus
64, J.M. Dubinski 136, A. Dubla 97, S. Dudi 90, P. Dupieux 127, M. Durkac106,
N. Dzalaiova13, T.M. Eder 126, R.J. Ehlers 74, F. Eisenhut 64, R. Ejima92, D.
Elia 50, B. Erazmus 103, F. Ercolessi 26, F. Erhardt 89, M.R. Ersdal21, B.
Espagnon 131, G. Eulisse 33, D. Evans 100, S. Evdokimov 142, L. Fabbietti 95,
M. Faggin 28, J. Faivre 73, F. Fan 6, W. Fan 74, A. Fantoni 49, M. Fasel 87,
A. Feliciello 56, G. Feofilov 142, A. Fernández Téllez 45, L. Ferrandi 110,
M.B. Ferrer 33, A. Ferrero 130, C. Ferrero 56, A. Ferretti 25, V.J.G.
Feuillard 94, V. Filova 36, D. Finogeev 142, F.M. Fionda 52, F. Flor 115, A.N.
Flores 108, S. Foertsch 68, I. Fokin 94, S. Fokin 142, E. Fragiacomo 57, E.
Frajna 138, U. Fuchs 33, N. Funicello 29, C. Furget 73, A. Furs 142, T.
Fusayasu 98, J.J. Gaardhøje 83, M. Gagliardi 25, A.M. Gago 101, T. Gahlaut47,
C.D. Galvan 109, D.R. Gangadharan 115, P. Ganoti 78, C. Garabatos 97, A.T.
Garcia 131, J.R.A. Garcia 45, E. Garcia-Solis 9, C. Gargiulo 33, P. Gasik 97,
A. Gautam 117, M.B. Gay Ducati 66, M. Germain 103, A. Ghimouz124, C. Ghosh135,
M. Giacalone 51, G. Gioachin 30, P. Giubellino 97,56, P. Giubilato 28, A.M.C.
Glaenzer 130, P. Glässel 94, E. Glimos 121, D.J.Q. Goh76, V. Gonzalez 137, M.
Gorgon 2, K. Goswami 48, S. Gotovac34, V. Grabski 67, L.K. Graczykowski 136,
E. Grecka 86, A. Grelli 59, C. Grigoras 33, V. Grigoriev 142, S. Grigoryan
143,1, F. Grosa 33, J.F. Grosse-Oetringhaus 33, R. Grosso 97, D. Grund 36,
N.A. Grunwald94, G.G. Guardiano 111, R. Guernane 73, M. Guilbaud 103, K.
Gulbrandsen 83, T. Gündem 64, T. Gunji 123, W. Guo 6, A. Gupta 91, R. Gupta
91, R. Gupta 48, S.P. Guzman 45, K. Gwizdziel 136, L. Gyulai 138, C.
Hadjidakis 131, F.U. Haider 91, S. Haidlova 36, H. Hamagaki 76, A. Hamdi 74,
Y. Han 140, B.G. Hanley 137, R. Hannigan 108, J. Hansen 75, M.R. Haque 136,
J.W. Harris 139, A. Harton 9, H. Hassan 116, D. Hatzifotiadou 51, P. Hauer 43,
L.B. Havener 139, S.T. Heckel 95, E. Hellbär 97, H. Helstrup 35, M. Hemmer 64,
T. Herman 36, G. Herrera Corral 8, F. Herrmann126, S. Herrmann 128, K.F.
Hetland 35, B. Heybeck 64, H. Hillemanns 33, B. Hippolyte 129, F.W. Hoffmann
70, B. Hofman 59, G.H. Hong 140, M. Horst 95, A. Horzyk 2, Y. Hou 6, P.
Hristov 33, C. Hughes 121, P. Huhn64, L.M. Huhta 116, T.J. Humanic 88, A.
Hutson 115, D. Hutter 39, R. Ilkaev142, H. Ilyas 14, M. Inaba 124, G.M.
Innocenti 33, M. Ippolitov 142, A. Isakov 84,86, T. Isidori 117, M.S. Islam
99, M. Ivanov13, M. Ivanov 97, V. Ivanov 142, K.E. Iversen 75, M. Jablonski 2,
B. Jacak 74, N. Jacazio 26, P.M. Jacobs 74, S. Jadlovska106, J. Jadlovsky106,
S. Jaelani 82, C. Jahnke 111, M.J. Jakubowska 136, M.A. Janik 136, T.
Janson70, S. Ji 17, S. Jia 10, A.A.P. Jimenez 65, F. Jonas 87, D.M. Jones 118,
J.M. Jowett 33,97, J. Jung 64, M. Jung 64, A. Junique 33, A. Jusko 100, M.J.
Kabus 33,136, J. Kaewjai105, P. Kalinak 60, A.S. Kalteyer 97, A. Kalweit 33,
V. Kaplin 142, A. Karasu Uysal 72, D. Karatovic 89, O. Karavichev 142, T.
Karavicheva 142, P. Karczmarczyk 136, E. Karpechev 142, U. Kebschull 70, R.
Keidel 141, D.L.D. Keijdener59, M. Keil 33, B. Ketzer 43, S.S. Khade 48, A.M.
Khan 119,6, S. Khan 16, A. Khanzadeev 142, Y. Kharlov 142, A. Khatun 117, A.
Khuntia 36, B. Kileng 35, B. Kim 104, C. Kim 17, D.J. Kim 116, E.J. Kim 69, J.
Kim 140, J.S. Kim 41, J. Kim 58, J. Kim 69, M. Kim 19, S. Kim 18, T. Kim 140,
K. Kimura 92, S. Kirsch 64, I. Kisel 39, S. Kiselev 142, A. Kisiel 136, J.P.
Kitowski 2, J.L. Klay 5, J. Klein 33, S. Klein 74, C. Klein-Bösing 126, M.
Kleiner 64, T. Klemenz 95, A. Kluge 33, A.G. Knospe 115, C. Kobdaj 105, T.
Kollegger97, A. Kondratyev 143, N. Kondratyeva 142, E. Kondratyuk 142, J.
Konig 64, S.A. Konigstorfer 95, P.J. Konopka 33, G. Kornakov 136, M. Korwieser
95, S.D. Koryciak 2, A. Kotliarov 86, V. Kovalenko 142, M. Kowalski 107, V.
Kozhuharov 37, I. Králik 60, A. Kravčáková 38, L. Krcal 33,39, M. Krivda
100,60, F. Krizek 86, K. Krizkova Gajdosova 33, M. Kroesen 94, M. Krüger 64,
D.M. Krupova 36, E. Kryshen 142, V. Kučera 58, C. Kuhn 129, P.G. Kuijer 84, T.
Kumaoka124, D. Kumar135, L. Kumar 90, N. Kumar90, S. Kumar 32, S. Kundu 33, P.
Kurashvili 79, A. Kurepin 142, A.B. Kurepin 142, A. Kuryakin 142, S. Kushpil
86, M.J. Kweon 58, Y. Kwon 140, S.L. La Pointe 39, P. La Rocca 27, A.
Lakrathok105, M. Lamanna 33, A.R. Landou 73,114, R. Langoy 120, P. Larionov
33, E. Laudi 33, L. Lautner 33,95, R. Lavicka 102, R. Lea 134,55, H. Lee 104,
I. Legrand 46, G. Legras 126, J. Lehrbach 39, T.M. Lelek2, R.C. Lemmon 85, I.
León Monzón 109, M.M. Lesch 95, E.D. Lesser 19, P. Lévai 138, X. Li10, J. Lien
120, R. Lietava 100, I. Likmeta 115, B. Lim 25, S.H. Lim 17, V. Lindenstruth
39, A. Lindner46, C. Lippmann 97, D.H. Liu 6, J. Liu 118, G.S.S. Liveraro 111,
I.M. Lofnes 21, C. Loizides 87, S. Lokos 107, J. Lomker 59, P. Loncar 34, X.
Lopez 127, E. López Torres 7, P. Lu 97,119, J.R. Luhder 126, M. Lunardon 28,
G. Luparello 57, Y.G. Ma 40, M. Mager 33, A. Maire 129, M.V. Makariev 37, M.
Malaev 142, G. Malfattore 26, N.M. Malik 91, Q.W. Malik20, S.K. Malik 91, L.
Malinina I,VII,143, D. Mallick 131,80, N. Mallick 48, G. Mandaglio 31,53, S.K.
Mandal 79, V. Manko 142, F. Manso 127, V. Manzari 50, Y. Mao 6, R.W. Marcjan
2, G.V. Margagliotti 24, A. Margotti 51, A. Marín 97, C. Markert 108, P.
Martinengo 33, M.I. Martínez 45, G. Martínez García 103, M.P.P. Martins 110,
S. Masciocchi 97, M. Masera 25, A. Masoni 52, L. Massacrier 131, O. Massen 59,
A. Mastroserio 132,50, O. Matonoha 75, S. Mattiazzo 28, A. Matyja 107, C.
Mayer 107, A.L. Mazuecos 33, F. Mazzaschi 25, M. Mazzilli 33, J.E. Mdhluli
122, Y. Melikyan 44, A. Menchaca-Rocha 67, E. Meninno 102,29, A.S. Menon 115,
M. Meres 13, S. Mhlanga113,68, Y. Miake124, L. Micheletti 33, D.L. Mihaylov
95, K. Mikhaylov 143,142, A.N. Mishra 138, D. Miśkowiec 97, A. Modak 4, B.
Mohanty80, M. Mohisin Khan V,16, M.A. Molander 44, S. Monira 136, C. Mordasini
116, D.A. Moreira De Godoy 126, I. Morozov 142, A. Morsch 33, T. Mrnjavac 33,
V. Muccifora 49, S. Muhuri 135, J.D. Mulligan 74, A. Mulliri23, M.G. Munhoz
110, R.H. Munzer 64, H. Murakami 123, S. Murray 113, L. Musa 33, J. Musinsky
60, J.W. Myrcha 136, B. Naik 122, A.I. Nambrath 19, B.K. Nandi 47, R. Nania
51, E. Nappi 50, A.F. Nassirpour 18, A. Nath 94, C. Nattrass 121, M.N.
Naydenov 37, A. Neagu20, A. Negru125, L. Nellen 65, R. Nepeivoda 75, S. Nese
20, G. Neskovic 39, N. Nicassio 50, B.S. Nielsen 83, E.G. Nielsen 83, S.
Nikolaev 142, S. Nikulin 142, V. Nikulin 142, F. Noferini 51, S. Noh 12, P.
Nomokonov 143, J. Norman 118, N. Novitzky 124, P. Nowakowski 136, A. Nyanin
142, J. Nystrand 21, M. Ogino 76, S. Oh 18, A. Ohlson 75, V.A. Okorokov 142,
J. Oleniacz 136, A.C. Oliveira Da Silva 121, A. Onnerstad 116, C. Oppedisano
56, A. Ortiz Velasquez 65, J. Otwinowski 107, M. Oya92, K. Oyama 76, Y.
Pachmayer 94, S. Padhan 47, D. Pagano 134,55, G. Paić 65, A. Palasciano 50, S.
Panebianco 130, H. Park 124, H. Park 104, J. Park 58, J.E. Parkkila 33, Y.
Patley 47, R.N. Patra91, B. Paul 23, H. Pei 6, T. Peitzmann 59, X. Peng 11, M.
Pennisi 25, S. Perciballi 25, D. Peresunko 142, G.M. Perez 7, Y. Pestov142, V.
Petrov 142, M. Petrovici 46, R.P. Pezzi 103,66, S. Piano 57, M. Pikna 13, P.
Pillot 103, O. Pinazza 51,33, L. Pinsky115, C. Pinto 95, S. Pisano 49, M.
Płoskoń 74, M. Planinic89, F. Pliquett64, M.G. Poghosyan 87, B. Polichtchouk
142, S. Politano 30, N. Poljak 89, A. Pop 46, S. Porteboeuf-Houssais 127, V.
Pozdniakov 143, I.Y. Pozos 45, K.K. Pradhan 48, S.K. Prasad 4, S. Prasad 48,
R. Preghenella 51, F. Prino 56, C.A. Pruneau 137, I. Pshenichnov 142, M.
Puccio 33, S. Pucillo 25, Z. Pugelova106, S. Qiu 84, L. Quaglia 25, S. Ragoni
15, A. Rai 139, A. Rakotozafindrabe 130, L. Ramello 133,56, F. Rami 129,
S.A.R. Ramirez 45, T.A. Rancien73, M. Rasa 27, S.S. Räsänen 44, R. Rath 51,
M.P. Rauch 21, I. Ravasenga 84, K.F. Read 87,121, C. Reckziegel 112, A.R.
Redelbach 39, K. Redlich VI,79, C.A. Reetz 97, A. Rehman21, F. Reidt 33, H.A.
Reme-Ness 35, Z. Rescakova38, K. Reygers 94, A. Riabov 142, V. Riabov 142, R.
Ricci 29, M. Richter 20, A.A. Riedel 95, W. Riegler 33, A.G. Riffero 25, C.
Ristea 63, M.V. Rodriguez 33, M. Rodríguez Cahuantzi 45, K. Røed 20, R.
Rogalev 142, E. Rogochaya 143, T.S. Rogoschinski 64, D. Rohr 33, D. Röhrich
21, P.F. Rojas45, S. Rojas Torres 36, P.S. Rokita 136, G. Romanenko 26, F.
Ronchetti 49, A. Rosano 31,53, E.D. Rosas65, K. Roslon 136, A. Rossi 54, A.
Roy 48, S. Roy 47, N. Rubini 26, D. Ruggiano 136, R. Rui 24, P.G. Russek 2, R.
Russo 84, A. Rustamov 81, E. Ryabinkin 142, Y. Ryabov 142, A. Rybicki 107, H.
Rytkonen 116, J. Ryu 17, W. Rzesa 136, O.A.M. Saarimaki 44, S. Sadhu 32, S.
Sadovsky 142, J. Saetre 21, K. Šafařík 36, P. Saha42, S.K. Saha 4, S. Saha 80,
B. Sahoo 47, B. Sahoo 48, R. Sahoo 48, S. Sahoo61, D. Sahu 48, P.K. Sahu 61,
J. Saini 135, K. Sajdakova38, S. Sakai 124, M.P. Salvan 97, S. Sambyal 91, D.
Samitz 102, I. Sanna 33,95, T.B. Saramela110, P. Sarma 42, V. Sarritzu 23,
V.M. Sarti 95, M.H.P. Sas 139, J. Schambach 87, H.S. Scheid 64, C. Schiaua 46,
R. Schicker 94, A. Schmah97, C. Schmidt 97, H.R. Schmidt93, M.O. Schmidt 33,
M. Schmidt93, N.V. Schmidt 87, A.R. Schmier 121, R. Schotter 129, A. Schröter
39, J. Schukraft 33, K. Schweda 97, G. Scioli 26, E. Scomparin 56, J.E. Seger
15, Y. Sekiguchi123, D. Sekihata 123, M. Selina 84, I. Selyuzhenkov 97, S.
Senyukov 129, J.J. Seo 94,58, D. Serebryakov 142, L. Šerkšnytė 95, A. Sevcenco
63, T.J. Shaba 68, A. Shabetai 103, R. Shahoyan33, A. Shangaraev 142, A.
Sharma90, B. Sharma 91, D. Sharma 47, H. Sharma 54,107, M. Sharma91, S. Sharma
76, S. Sharma 91, U. Sharma 91, A. Shatat 131, O. Sheibani115, K. Shigaki 92,
M. Shimomura77, J. Shin12, S. Shirinkin 142, Q. Shou 40, Y. Sibiriak 142, S.
Siddhanta 52, T. Siemiarczuk 79, T.F. Silva 110, D. Silvermyr 75, T.
Simantathammakul105, R. Simeonov 37, B. Singh91, B. Singh 95, K. Singh 48, R.
Singh 80, R. Singh 91, R. Singh 48, S. Singh 16, V.K. Singh 135, V. Singhal
135, T. Sinha 99, B. Sitar 13, M. Sitta 133,56, T.B. Skaali20, G. Skorodumovs
94, M. Slupecki 44, N. Smirnov 139, R.J.M. Snellings 59, E.H. Solheim 20, J.
Song 115, C. Sonnabend 33,97, F. Soramel 28, A.B. Soto-hernandez 88, R.
Spijkers 84, I. Sputowska 107, J. Staa 75, J. Stachel 94, I. Stan 63, P.J.
Steffanic 121, S.F. Stiefelmaier 94, D. Stocco 103, I. Storehaug 20, P.
Stratmann 126, S. Strazzi 26, A. Sturniolo 31,53, C.P. Stylianidis84, A.A.P.
Suaide 110, C. Suire 131, M. Sukhanov 142, M. Suljic 33, R. Sultanov 142, V.
Sumberia 91, S. Sumowidagdo 82, S. Swain61, I. Szarka 13, M. Szymkowski 136,
S.F. Taghavi 95, G. Taillepied 97, J. Takahashi 111, G.J. Tambave 80, S. Tang
6, Z. Tang 119, J.D. Tapia Takaki 117, N. Tapus125, L.A. Tarasovicova 126,
M.G. Tarzila 46, G.F. Tassielli 32, A. Tauro 33, G. Tejeda Muñoz 45, A.
Telesca 33, L. Terlizzi 25, C. Terrevoli 115, S. Thakur 4, D. Thomas 108, A.
Tikhonov 142, A.R. Timmins 115, M. Tkacik106, T. Tkacik 106, A. Toia 64, R.
Tokumoto92, K. Tomohiro92, N. Topilskaya 142, M. Toppi 49, T. Tork 131, V.V.
Torres 103, A.G. Torres Ramos 32, A. Trifiró 31,53, A.S. Triolo 33,31,53, S.
Tripathy 51, T. Tripathy 47, S. Trogolo 33, V. Trubnikov 3, W.H. Trzaska 116,
T.P. Trzcinski 136, A. Tumkin 142, R. Turrisi 54, T.S. Tveter 20, K. Ullaland
21, B. Ulukutlu 95, A. Uras 128, G.L. Usai 23, M. Vala38, N. Valle 22, L.V.R.
van Doremalen59, M. van Leeuwen 84, C.A. van Veen 94, R.J.G. van Weelden 84,
P. Vande Vyvre 33, D. Varga 138, Z. Varga 138, M. Vasileiou 78, A. Vasiliev
142, O. Vázquez Doce 49, O. Vazquez Rueda 115, V. Vechernin 142, E. Vercellin
25, S. Vergara Limón45, R. Verma47, L. Vermunt 97, R. Vértesi 138, M. Verweij
59, L. Vickovic34, Z. Vilakazi122, O. Villalobos Baillie 100, A. Villani 24,
A. Vinogradov 142, T. Virgili 29, M.M.O. Virta 116, V. Vislavicius75, A.
Vodopyanov 143, B. Volkel 33, M.A. Völkl 94, K. Voloshin142, S.A. Voloshin
137, G. Volpe 32, B. von Haller 33, I. Vorobyev 95, N. Vozniuk 142, J.
Vrláková 38, J. Wan40, C. Wang 40, D. Wang40, Y. Wang 40, Y. Wang 6, A.
Wegrzynek 33, F.T. Weiglhofer39, S.C. Wenzel 33, J.P. Wessels 126, S.L.
Weyhmiller 139, J. Wiechula 64, J. Wikne 20, G. Wilk 79, J. Wilkinson 97, G.A.
Willems 126, B. Windelband 94, M. Winn 130, J.R. Wright 108, W. Wu40, Y. Wu
119, R. Xu 6, A. Yadav 43, A.K. Yadav 135, S. Yalcin 72, Y. Yamaguchi 92, S.
Yang21, S. Yano 92, Z. Yin 6, I.-K. Yoo 17, J.H. Yoon 58, H. Yu12, S. Yuan21,
A. Yuncu 94, V. Zaccolo 24, C. Zampolli 33, F. Zanone 94, N. Zardoshti 33, A.
Zarochentsev 142, P. Závada 62, N. Zaviyalov142, M. Zhalov 142, B. Zhang 6, C.
Zhang 130, L. Zhang 40, S. Zhang 40, X. Zhang 6, Y. Zhang119, Z. Zhang 6, M.
Zhao 10, V. Zherebchevskii 142, Y. Zhi10, D. Zhou 6, Y. Zhou 83, J. Zhu 97,6,
Y. Zhu6, S.C. Zugravel 56, N. Zurlo 134,55

## Affiliation Notes

I Deceased
II Also at: Max-Planck-Institut für Physik, Munich, Germany
III Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
IV Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
V Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
VI Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VII Also at: An institution covered by a cooperation agreement with CERN

## Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia
2 AGH University of Krakow, Cracow, Poland
3 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine
4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India
5 California Polytechnic State University, San Luis Obispo, California, United
States
6 Central China Normal University, Wuhan, China
7 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba
8 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and
Mérida, Mexico
9 Chicago State University, Chicago, Illinois, United States
10 China Institute of Atomic Energy, Beijing, China
11 China University of Geosciences, Wuhan, China
12 Chungbuk National University, Cheongju, Republic of Korea
13 Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovak Republic
14 COMSATS University Islamabad, Islamabad, Pakistan
15 Creighton University, Omaha, Nebraska, United States
16 Department of Physics, Aligarh Muslim University, Aligarh, India
17 Department of Physics, Pusan National University, Pusan, Republic of Korea
18 Department of Physics, Sejong University, Seoul, Republic of Korea
19 Department of Physics, University of California, Berkeley, California,
United States
20 Department of Physics, University of Oslo, Oslo, Norway
21 Department of Physics and Technology, University of Bergen, Bergen, Norway
22 Dipartimento di Fisica, Università di Pavia, Pavia, Italy
23 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy
24 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy
25 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy
26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy
27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy
28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy
29 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy
30 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy
31 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy
32 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy
33 European Organization for Nuclear Research (CERN), Geneva, Switzerland
34 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia
35 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway
36 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic
37 Faculty of Physics, Sofia University, Sofia, Bulgaria
38 Faculty of Science, P.J. Šafárik University, Košice, Slovak Republic
39 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany
40 Fudan University, Shanghai, China
41 Gangneung-Wonju National University, Gangneung, Republic of Korea
42 Gauhati University, Department of Physics, Guwahati, India
43 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany
44 Helsinki Institute of Physics (HIP), Helsinki, Finland
45 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico
46 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania
47 Indian Institute of Technology Bombay (IIT), Mumbai, India
48 Indian Institute of Technology Indore, Indore, India
49 INFN, Laboratori Nazionali di Frascati, Frascati, Italy
50 INFN, Sezione di Bari, Bari, Italy
51 INFN, Sezione di Bologna, Bologna, Italy
52 INFN, Sezione di Cagliari, Cagliari, Italy
53 INFN, Sezione di Catania, Catania, Italy
54 INFN, Sezione di Padova, Padova, Italy
55 INFN, Sezione di Pavia, Pavia, Italy
56 INFN, Sezione di Torino, Turin, Italy
57 INFN, Sezione di Trieste, Trieste, Italy
58 Inha University, Incheon, Republic of Korea
59 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands
60 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovak Republic
61 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India
62 Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic
63 Institute of Space Science (ISS), Bucharest, Romania
64 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
65 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico
66 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil
67 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico
68 iThemba LABS, National Research Foundation, Somerset West, South Africa
69 Jeonbuk National University, Jeonju, Republic of Korea
70 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany
71 Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea
72 KTO Karatay University, Konya, Turkey
73 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France
74 Lawrence Berkeley National Laboratory, Berkeley, California, United States
75 Lund University Department of Physics, Division of Particle Physics, Lund,
Sweden
76 Nagasaki Institute of Applied Science, Nagasaki, Japan
77 Nara Women’s University (NWU), Nara, Japan
78 National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece
79 National Centre for Nuclear Research, Warsaw, Poland
80 National Institute of Science Education and Research, Homi Bhabha National
Institute, Jatni, India
81 National Nuclear Research Center, Baku, Azerbaijan
82 National Research and Innovation Agency - BRIN, Jakarta, Indonesia
83 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
84 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands
85 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
86 Nuclear Physics Institute of the Czech Academy of Sciences, Husinec-Řež,
Czech Republic
87 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
88 Ohio State University, Columbus, Ohio, United States
89 Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia
90 Physics Department, Panjab University, Chandigarh, India
91 Physics Department, University of Jammu, Jammu, India
92 Physics Program and International Institute for Sustainability with Knotted
Chiral Meta Matter (SKCM2), Hiroshima University, Hiroshima, Japan
93 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany
94 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
95 Physik Department, Technische Universität München, Munich, Germany
96 Politecnico di Bari and Sezione INFN, Bari, Italy
97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Darmstadt, Germany
98 Saga University, Saga, Japan
99 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata,
India
100 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom
101 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru
102 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
103 SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France
104 Sungkyunkwan University, Suwon City, Republic of Korea
105 Suranaree University of Technology, Nakhon Ratchasima, Thailand
106 Technical University of Košice, Košice, Slovak Republic
107 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland
108 The University of Texas at Austin, Austin, Texas, United States
109 Universidad Autónoma de Sinaloa, Culiacán, Mexico
110 Universidade de São Paulo (USP), São Paulo, Brazil
111 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
112 Universidade Federal do ABC, Santo Andre, Brazil
113 University of Cape Town, Cape Town, South Africa
114 University of Derby, Derby, United Kingdom
115 University of Houston, Houston, Texas, United States
116 University of Jyväskylä, Jyväskylä, Finland
117 University of Kansas, Lawrence, Kansas, United States
118 University of Liverpool, Liverpool, United Kingdom
119 University of Science and Technology of China, Hefei, China
120 University of South-Eastern Norway, Kongsberg, Norway
121 University of Tennessee, Knoxville, Tennessee, United States
122 University of the Witwatersrand, Johannesburg, South Africa
123 University of Tokyo, Tokyo, Japan
124 University of Tsukuba, Tsukuba, Japan
125 University Politehnica of Bucharest, Bucharest, Romania
126 Universität Münster, Institut für Kernphysik, Münster, Germany
127 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
128 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de
Lyon, Lyon, France
129 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France,
Strasbourg, France
130 Université Paris-Saclay, Centre d’Etudes de Saclay (CEA), IRFU, Départment
de Physique Nucléaire (DPhN), Saclay, France
131 Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
132 Università degli Studi di Foggia, Foggia, Italy
133 Università del Piemonte Orientale, Vercelli, Italy
134 Università di Brescia, Brescia, Italy
135 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata,
India
136 Warsaw University of Technology, Warsaw, Poland
137 Wayne State University, Detroit, Michigan, United States
138 Wigner Research Centre for Physics, Budapest, Hungary
139 Yale University, New Haven, Connecticut, United States
140 Yonsei University, Seoul, Republic of Korea
141 Zentrum für Technologie und Transfer (ZTT), Worms, Germany
142 Affiliated with an institute covered by a cooperation agreement with CERN
143 Affiliated with an international laboratory covered by a cooperation
agreement with CERN.