2018 234 29 August

K${}^{0}_{\rm S}$K± interaction using pp collisions

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

We present the first measurements of femtoscopic correlations between the
K${}^{0}_{\rm S}$ and K± particles in pp collisions at $\sqrt{s}=7$ TeV
measured by the ALICE experiment. The observed femtoscopic correlations are
consistent with final-state interactions proceeding solely via the
$a_{0}(980)$ resonance. The extracted kaon source radius and correlation
strength parameters for K${}^{0}_{\rm S}$K- are found to be equal within the
experimental uncertainties to those for K${}^{0}_{\rm S}$K+. Results of the
present study are compared with those from identical-kaon femtoscopic studies
also performed with pp collisions at $\sqrt{s}=7$ TeV by ALICE and with a
K${}^{0}_{\rm S}$K± measurement in Pb-Pb collisions at $\sqrt{s_{\rm
NN}}=2.76$ TeV. Combined with the Pb-Pb results, our pp analysis is found to
be compatible with the interpretation of the $a_{0}(980)$ having a tetraquark
structure instead of that of a diquark.

##  1 Introduction

Recently, by using Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV, the ALICE
experiment [1] has published the first-ever study of K${}^{0}_{\rm S}$K±
femtoscopy [2]. K${}^{0}_{\rm S}$K± femtoscopy differs from identical-kaon
femtoscopy, for which a number of studies exist in the literature [3, 4, 5,
6], in that the only pair interaction expected is a final-state interaction
(FSI) through the $a_{0}(980)$ resonance. It was found in that Pb-Pb study
that the FSI in K${}^{0}_{\rm S}$K± proceeds solely through the $a_{0}(980)$
resonance, i.e. with no competing non-resonant channels, and the extracted
kaon source parameters agree with published results from identical-kaon
studies in Pb-Pb collisions. These results were found to be compatible with
the interpretation of the $a_{0}$ resonance as a tetraquark state rather than
a diquark111footnotetext: Note that the term “diquark” will be used in this
paper to indicate a $q_{i}{\overline{q}_{j}}$ quark pair. state [2, 7, 8, 9].
A recent theoretical calculation has shown that the ALICE Pb-Pb results can
indeed be described by a model based on the four-quark model [10].

The argument given in Ref.[2] for a tetraquark $a_{0}$ being compatible with
the Pb-Pb K${}^{0}_{\rm S}$K± result stated above is based on two factors: 1)
the kaon source geometry, and 2) an empirical selection rule (For the sake of
simplicity of notation, “$a_{0}$” will be used for the remainder of this paper
to represent “$a_{0}(980)$.”). For factor 1), the production cross section of
the $a_{0}$ resonance in a reaction channel such as ${\rm K}^{0}{\rm
K}^{-}\rightarrow a^{-}_{0}$ should depend on whether the $a^{-}_{0}$ is
composed of ${\rm d\overline{u}}$ or ${\rm d\overline{s}s\overline{u}}$
quarks, the former requiring the annihilation of the ${\rm\overline{s}s}$ pair
and the latter being a direct transfer of the valence quarks from the kaons to
the $a^{-}_{0}$. Since the femtoscopic size of the 0-10% most central Pb-Pb
collision is measured to be 5–6 fm, the large geometry in these collisions is
favorable for the direct transfer of quarks to the $a_{0}$, whereas not
favorable for the annihilation of the strange quarks due to the short-ranged
nature of the strong interaction. For factor 2), the direct transfer of the
valence quarks from the kaons to the $a^{-}_{0}$ is favored since this is an
“OZI superallowed” reaction [9]. The OZI rule can be stated as “an inhibition
associated with the creation or annihilation of quark lines” [9]. Thus, the
annihilation of the strange quarks is suppressed by the OZI rule. Both of
these factors favor the formation of a tetraquark $a_{0}$ and suppress the
formation of a diquark $a_{0}$. As a result of this, if the $a_{0}$ were a
diquark, one would expect competing non-resonant channels present and/or no
FSI at all, i.e. free-streaming, of the kaon pair thus diluting the strength
of the $a_{0}$ resonant FSI. The fact that this is not seen to be the case in
Pb-Pb collisions favors the tetraquark $a_{0}$ interpretation.

The geometry of the kaon source is seen to be an important factor in the
argument given above, i.e. the large kaon source seen in Pb-Pb collisions
suppresses the annihilation of the strange quarks in the kaon pair and
enhances the direct transfer of quarks to the $a_{0}$. It is interesting to
speculate on the dependence of the strength of the $a_{0}$ resonant FSI on the
size of the kaon source, particularly for a very small source of size $\sim 1$
fm that would be obtained in pp collisions [4, 5]. For a kaon source of size
$\sim 1$ fm, the kaons in a produced kaon pair would be overlapping with each
other at the source, thus giving a geometric enhancement of the strange-quark
annihilation channel that could compete with, or even dominate over, the OZI
rule suppression of quark annihilation. Thus we might expect that the
tetraquark $a_{0}$ resonant FSI could be diluted or completely suppressed by
competing non-resonant annihilation channels that could open up, whereas a
diquark $a_{0}$ resonant FSI, which was not seen to be suppressed by either
geometry or the OZI rule in Pb-Pb, would not be diluted. A femtoscopic
measurement of K${}^{0}_{\rm S}$K± correlations in pp collisions should be
able to test this by determining the strength of the $a_{0}$ FSI by measuring
the femtoscopic $\lambda$ parameter. In more concrete terms, if we were to
compare the $\lambda$ parameters extracted in K${}^{0}_{\rm S}$K± femtoscopic
measurements in pp collisions and Pb-Pb collisions, for a tetraquark $a_{0}$
we would expect $\lambda_{K^{0}_{S}K^{\pm}({\rm
PbPb})}>\lambda_{K^{0}_{S}K^{\pm}({\rm pp})}$ whereas for a diquark $a_{0}$ we
would expect $\lambda_{K^{0}_{S}K^{\pm}({\rm
PbPb})}\sim\lambda_{K^{0}_{S}K^{\pm}({\rm pp})}$. An independent check could
also be made by comparing $\lambda$ from K${}^{0}_{\rm S}$K± femtoscopy in pp
collisions with $\lambda$ from identical-kaon femtoscopy in pp collisions in a
similar way as was done for Pb-Pb collisions [2]. Since we expect identical-
kaon correlations to go solely through quantum statistics (and FSI for neutral
kaons), our expectation for a tetraquark $a_{0}$ would be $\lambda_{KK({\rm
pp})}>\lambda_{K^{0}_{S}K^{\pm}({\rm pp})}$ whereas for a diquark $a_{0}$ we
would expect $\lambda_{KK({\rm pp})}\sim\lambda_{K^{0}_{S}K^{\pm}({\rm pp})}$.

In this Letter, femtoscopic correlations with the particle pair combinations
K${}^{0}_{\rm S}$K± are studied for the first time in pp collisions at
$\sqrt{s}=7$ TeV by the ALICE experiment. The physics goals of the present
K${}^{0}_{\rm S}$K± femtoscopy study are the following: 1) show to what extent
the FSI through the $a_{0}$ resonance describes the correlation functions, 2)
study the K0 and ${\rm\overline{K}^{0}}$ sources to see if there are
differences in the source parameters, 3) compare the results of the extracted
kaon source parameters from the present study with the published results from
Pb-Pb collisions and identical kaon results from pp collisions, and 4) see if
the results from this pp study are compatible with a tetraquark $a_{0}$ as
suggested from the Pb-Pb study.

##  2 Description of experiment and data selection

The ALICE experiment and its performance in the LHC Run 1 $(2009-2013)$ are
described in Ref. [1] and Ref. [11, 12], respectively. About $370\times
10^{6}$ minimum-bias 7 TeV pp collision events taken in 2010 were used in this
analysis. Events were classified using the measured amplitudes in the V0
detectors, which consist of two arrays of scintillators located along the
beamline and covering the full azimuth [13, 14]. Charged particles were
reconstructed and identified with the central barrel detectors located within
a solenoid magnet with a field strength of $B=\pm 0.5$ T. Charged particle
tracking was performed using the Time Projection Chamber (TPC) [15] and the
Inner Tracking System (ITS) [1]. The ITS allowed for high spatial resolution
in determining the primary (collision) vertex. A momentum resolution of less
than 10 MeV/$c$ was typically obtained for the charged tracks of interest in
this analysis [16]. The primary vertex was obtained from the ITS, the position
of the primary vertex being constrained along the beam direction (the
“$z$-position”) to be within $\pm 10$ cm of the center of the ALICE detector.
In addition to the standard track quality selections [16], the selections
based on the quality of track fitting and the number of detected tracking
points in the TPC were used to ensure that only well-reconstructed tracks were
taken in the analysis [11, 15, 16].

Particle identification (PID) for reconstructed tracks was carried out using
both the TPC and the Time-of-Flight (TOF) detectors in the pseudorapidity
range $|\eta|<0.8$ [11, 12]. For the PID signal from both detectors, a value
was assigned to each track denoting the number of standard deviations between
the measured track information and calculated values ($N_{\sigma}$) [6, 11,
12, 16]. For TPC PID, a parametrized Bethe-Bloch formula was used to calculate
the specific energy loss $\left<{\rm d}E/{\rm d}x\right>$ in the detector
expected for a particle with a given mass and momentum. For PID with TOF, the
particle mass was used to calculate the expected time-of-flight as a function
of track length and momentum. This procedure was repeated for four “particle
species hypotheses”, i.e. electron, pion, kaon and proton, and, for each
hypothesis, a different $N_{\sigma}$ value was obtained per detector.

###  2.1 Kaon selection

The methods used to select and identify individual K${}^{0}_{\rm S}$ and K±
particles are the same as those used for the ALICE K${}^{0}_{\rm
S}$K${}^{0}_{\rm S}$ [4] and K±K± [5] analyses from $\sqrt{s}=7$ TeV pp
collisions. These are now described below.

####  2.1.1 K${}^{0}_{\rm S}$ selection

The K${}^{0}_{\rm S}$ particles were reconstructed from the decay
K${}^{0}_{\rm S}\rightarrow\pi^{+}\pi^{-}$, with the daughter $\pi^{+}$ and
$\pi^{-}$ tracks detected in the TPC, ITS and TOF detectors. The secondary
vertex finder used to locate the neutral kaon decays employed the “on-the-fly”
reconstruction method [16], which recalculates the daughter track momenta
during the original tracking process under the assumption that the tracks came
from a decay vertex instead of the primary vertex. Pions with $p_{\rm T}>0.15$
GeV/$c$ were accepted (since for lower $p_{\rm T}$ track finding efficiency
drops rapidly) and the distance of closest approach to the primary vertex
(DCA) of the reconstructed K${}^{0}_{\rm S}$ was required to be less than 0.3
cm in all directions. The required $N_{\sigma}$ values for the pions were
$N_{\sigma}^{\rm TPC}<3$ (for all momenta) and $N_{\sigma}^{\rm TOF}<3$ for
$p>0.8$ GeV/$c$. An invariant mass distribution for the $\pi^{+}\pi^{-}$ pairs
was produced and the K${}^{0}_{\rm S}$ was defined to be resulting from a pair
that fell into the invariant mass range $0.480<m_{\pi^{+}\pi^{-}}<0.515$
GeV/$c^{2}$, corresponding to $\pm 4.7\sigma$, where $\sigma=3.7$ MeV/$c^{2}$
is the width of a Gaussian fit to the invariant mass distribution.

####  2.1.2 K± selection

Charged kaon tracks were detected using the TPC and TOF detectors, and were
accepted if they were within the range $0.14<p_{\rm T}<1.2$ GeV/$c$ in order
to obtain good PID. The determination of the momenta of the tracks was
performed using tracks reconstructed with the TPC only and constrained to the
primary vertex. In order to reduce the number of secondary tracks (for
instance the charged particles produced in the detector material, particles
from weak decays, etc.), the primary charged kaon tracks were selected based
on the DCA, such that the DCA transverse to the beam direction was less than
2.4 cm and the DCA along the beam direction was less than 3.2 cm. If the TOF
signal were not available, the required $N_{\sigma}$ values for the charged
kaons were $N_{\sigma}^{\rm TPC}<2$ for $p_{\rm T}<0.5$ GeV/$c$, and the track
was rejected for $p_{\rm T}>0.5$ GeV/$c$. If the TOF signal were also
available and $p_{\rm T}>0.5$ GeV/$c$: $N_{\sigma}^{\rm TPC}<2$ and
$N_{\sigma}^{\rm TOF}<2$ ($0.5<p_{\rm T}<1.2$ GeV/$c$).

The K${}^{0}_{\rm S}$K± experimental pair purity was estimated from a Monte
Carlo (MC) study based on PYTHIA [17] simulations with the Perugia2011 tune
[18], and using GEANT3 [19] to model particle transport through the ALICE
detectors. The purity was determined from the fraction of the reconstructed MC
simulated pairs that were identified as known K${}^{0}_{\rm S}$K± pairs from
PYTHIA. The pair purity was estimated to be $\sim 83$% for all kinematic
regions studied in this analysis. The single-particle purities for
K${}^{0}_{\rm S}$ and K± particles used in this analysis were estimated to be
$\sim 92$% and $\sim 91$%, respectively. The uncertainty in calculating the
pair purity is estimated to be $\pm 1$%.

##  3 Analysis methods

###  3.1 Experimental Correlation Functions

This analysis studies the momentum correlations of K${}^{0}_{\rm S}$K± pairs
using the two-particle correlation function, defined as

$C(k^{*})=\frac{A(k^{*})}{B(k^{*})},$ (1)

where $A(k^{*})$ is the measured distribution of pairs from the same event,
$B(k^{*})$ is the reference distribution of pairs from mixed events, and
$k^{*}$ is the magnitude of the momentum of each of the particles in the pair
rest frame (PRF),

$k^{*}=\sqrt{\frac{(s-m_{\rm K^{0}}^{2}-m_{\rm K^{\pm}}^{2})^{2}-4m_{\rm
K^{0}}^{2}m_{\rm K^{\pm}}^{2}}{4s}}$ (2)

where

$s=m_{\rm K^{0}}^{2}+m_{\rm K^{\pm}}^{2}+2E_{\rm K^{0}}E_{\rm
K^{\pm}}-2\vec{p}_{\rm K^{0}}\cdot\vec{p}_{\rm K^{\pm}}$ (3)

and $m_{\rm K^{0}}$ ($E_{\rm K^{0}}$) and $m_{\rm K^{\pm}}$ ($E_{\rm
K^{\pm}}$) are the rest masses (total energies) of the K${}^{0}_{\rm S}$ and
K±, respectively.

The denominator $B(k^{*})$ was formed by mixing K${}^{0}_{\rm S}$ and K±
particles from each event with K± and K${}^{0}_{\rm S}$ particles,
respectively, from ten other events, where each event has at least both a K±
and a K${}^{0}_{\rm S}$ [2]. The vertices of the mixed events were constrained
to be within 2 cm of each other in the $z$-direction.

Two-track effects, such as the merging of two real tracks into one
reconstructed track and the splitting of one real track into two reconstructed
tracks, is an important issue for femtoscopic studies. This analysis dealt
with these effects using the following method. For each kaon pair, the
distance between the K${}^{0}_{\rm S}$ pion daughter track and the same-
charged K± track was calculated at up to nine points throughout the TPC (every
20 cm from 85 cm to 245 cm) and then averaged. Comparing pairs from the same
event to those from mixed events, one observes a splitting peak for an average
separation of $<11$ cm. To correct for this, this analysis demanded that the
same-charge particles from each kaon pair must have an average TPC separation
of at least 13 cm. Mixed-event tracks were normalized by subtracting the
primary vertex position from each used track point.

Correlation functions were created separately for the two different charge
combinations, K${}^{0}_{\rm S}$K+ and K${}^{0}_{\rm S}$K-, and for three
overlapping/non-exclusive pair transverse momentum $k_{\rm T}=|\vec{p}_{\rm
T,1}+\vec{p}_{\rm T,2}|/2$ ranges: all $k_{\rm T}$, $k_{\rm T}<0.85$ and
$k_{\rm T}>0.85$ GeV/$c$, where $k_{\rm T}=0.85$ GeV/$c$ is the location of
the peak of the $k_{\rm T}$ distribution. The mean $k_{\rm T}$ values for
these three bins were 0.66, 0.49 and 1.17 GeV/$c$, respectively. The raw
K${}^{0}_{\rm S}$K+ correlation functions for these three bins compared with
those generated from PYTHIA simulations with the Perugia2011 tune and using
GEANT3 to model particle transport through the ALICE detectors are shown in
Fig. 1. The PYTHIA correlation functions are normalized to the data in the
vicinity of $k^{*}=0.8$ GeV/$c$. The raw K${}^{0}_{\rm S}$K- correlation
functions look very similar to these. It is seen that although PYTHIA
qualitatively describes the trends of the baseline of the data, it does not
describe it quantitatively such that it could be used to model the baseline
directly. Instead, for the present analysis the strategy for dealing with the
baseline was to describe it with several functional forms to be fitted to the
experimental correlation functions and to use PYTHIA to test the
appropriateness of the proposed baseline functional forms.

Figure 1: Raw K${}^{0}_{\rm S}$K+ correlation functions for the three $k_{T}$
bins compared with those from PYTHIA. The error bars are statistical. The
scale of $C(k^{*})$ is arbitrary. The PYTHIA correlation functions are
normalized to the data in the vicinity of $k^{*}=0.8$ GeV/$c$.

Three functional forms for the baseline were tested with PYTHIA: quadratic,
Gaussian and exponential, given by

$C_{\rm quadratic}(k^{*})=a(1-bk^{*}+ck^{*2})$ (4)

$C_{\rm Gaussian}(k^{*})=a(1+b\exp(-ck^{*2}))$ (5)

$C_{\rm exponential}(k^{*})=a(1+b\exp(-ck^{*}))$ (6)

where $a$, $b$ and $c$ are fit parameters. Fig. 2 shows fits of Eq. (4), Eq.
(5) and Eq. (6) to the PYTHIA correlation functions shown in Fig. 1 for the
three $k_{T}$ ranges used in this analysis. As seen, all three functional
forms do reasonably well in representing the PYTHIA correlation functions.
Thus, all three forms were used in fitting the experimental correlation
function and the different results obtained will be used to estimate the
systematic uncertainty due to the baseline estimation. Of course there are an
infinite number of functions one could try to represent the baseline, but at
least the three that were chosen for this work are simple and representative
of three basic functional forms.

Figure 2: Comparisons of fits of three possible baseline functional forms with
the PYTHIA correlation functions that were shown in Fig. 1. Fits were made in
the $k^{*}$ range $0-0.8$ GeV/$c$. The scale of $C(k^{*})$ is arbitrary.

Correlation functions were corrected for momentum resolution effects using
PYTHIA calculations. The particle momentum resolution in ALICE for the
relatively low-momentum tracks used in the present analysis was $<10$ MeV/$c$
[1]. Two correlation functions were generated with PYTHIA: one in terms of the
generator-level $k^{*}$ and one in terms of the simulated detector-level
$k^{*}$. Because PYTHIA does not incorporate final-state interactions,
simulated femtoscopic weights were determined using a 9th-order polynomial fit
in $k^{*}$ to the experimental correlation function for the $k_{\rm T}$ range
considered. When filling the same-event distributions, i.e. $A(k^{*})$ in Eq.
1, kaon pairs were individually weighted by this 9th-order fit according to
their generator-level $k^{*}$. Then, the ratio of the “ideal” correlation
function to the “measured” one (for each $k^{*}$ bin) was multiplied to the
data correlation functions before the fit procedure. This correction mostly
affected the lowest $k^{*}$ bins, increasing the extracted source parameters
by $\sim 2\%$.

###  3.2 Final-state interaction model

The final-state interaction model used in the present pp collision analysis
follows the same principles as the ones used for the ALICE Pb-Pb collision
analysis [2]. The measured K${}^{0}_{\rm S}$K± correlation functions were fit
with formulas that include a parameterization which incorporates strong FSI.
It was assumed that the FSI arises in the K${}^{0}_{\rm S}$K± channels due to
the near-threshold resonance, $a_{0}$. This parameterization was introduced by
R. Lednicky and is based on the model by R. Lednicky and V.L. Lyuboshitz [20,
21] (see also Ref. [3] for more details on this parameterization).

Using an equal emission time approximation in the PRF [20], the elastic
K${}^{0}_{\rm S}$K± transition is written as a stationary solution
$\Psi_{-\vec{k}\mkern 2.0mu\vphantom{k}^{*}}(\vec{r}\mkern
2.0mu\vphantom{r}^{*})$ of the scattering problem in the PRF. The quantity
$\vec{r}\mkern 2.0mu\vphantom{r}^{*}$ represents the emission separation of
the pair in the PRF, and the $-\vec{k}\mkern 2.0mu\vphantom{k}^{*}$ subscript
refers to a reversal of time from the emission process. At large distances
this has the asymptotic form of a superposition of an incoming plane wave and
an outgoing spherical wave,

$\Psi_{-\vec{k}\mkern 2.0mu\vphantom{k}^{*}}(\vec{r}\mkern
2.0mu\vphantom{r}^{*})=e^{-i\vec{k}\mkern
2.0mu\vphantom{k}^{*}\cdot\vec{r}\mkern
2.0mu\vphantom{r}^{*}}+f(k^{*})\frac{e^{ik^{*}r^{*}}}{r^{*}}\;,$ (7)

where $f(k^{*})$ is the $s$-wave K0K- or ${\rm\overline{K}^{0}}$K+ scattering
amplitude whose contribution is the $s$-wave isovector $a_{0}$ resonance (see
Eq. (11) in Ref. [3]) and

$f(k^{*})=\frac{\gamma_{a_{0}\rightarrow{\rm
K\overline{K}}}}{m_{a_{0}}^{2}-s-i(\gamma_{a_{0}\rightarrow{\rm
K\overline{K}}}k^{*}+\gamma_{a_{0}\rightarrow\pi\eta}k_{\pi\eta})}\;.$ (8)

In Eq. (8), $m_{a_{0}}$ is the mass of the $a_{0}$ resonance, and
$\gamma_{a_{0}\rightarrow{\rm K\overline{K}}}$ and
$\gamma_{a_{0}\rightarrow\pi\eta}$ are the couplings of the $a_{0}$ resonance
to the K0K- (or ${\rm\overline{K}^{0}}$K+) and $\pi\eta$ channels,
respectively. Also, $s=4(m_{\rm K^{0}}^{2}+k^{*2})$ and $k_{\pi\eta}$ denotes
the momentum in the second decay channel ($\pi\eta$) (see Tab. 1).

The correlation function due to the FSI is then calculated by integrating
$\Psi_{-\vec{k}\mkern 2.0mu\vphantom{k}^{*}}(\vec{r}\mkern
2.0mu\vphantom{r}^{*})$ in the Koonin-Pratt equation [22, 23],

$C_{\rm FSI}(\vec{k}\mkern 2.0mu\vphantom{k}^{*})=\int{\rm
d}^{3}\,\vec{r}\mkern 2.0mu\vphantom{r}^{*}\,S(\vec{r}\mkern
2.0mu\vphantom{r}^{*})\left|\Psi_{-\vec{k}\mkern
2.0mu\vphantom{k}^{*}}(\vec{r}\mkern 2.0mu\vphantom{r}^{*})\right|^{2}\,,$ (9)

where $S(\vec{r}\mkern 2.0mu\vphantom{r}^{*})$ is a one-dimensional Gaussian
source function of the PRF relative distance $\left|\vec{r}\mkern
2.0mu\vphantom{r}^{*}\right|$ with a Gaussian width $R$ of the form

$S(\vec{r}\mkern 2.0mu\vphantom{r}^{*})\sim e^{-\left|\vec{r}\mkern
2.0mu\vphantom{r}^{*}\right|^{2}/(4R^{2})}\;.$ (10)

Equation 9 can be integrated analytically for K${}^{0}_{\rm S}$K± correlations
with FSI for the one-dimensional case, with the result

$C_{\rm
FSI}(k^{*})=1+\lambda\alpha\left[\frac{1}{2}\left|\frac{f(k^{*})}{R}\right|^{2}+\frac{2\mathcal{R}f(k^{*})}{\sqrt{\pi}R}F_{1}(2k^{*}R)-\frac{\mathcal{I}f(k^{*})}{R}F_{2}(2k^{*}R)+\Delta
C\right],$ (11)

where

$F_{1}(z)\equiv\frac{\sqrt{\pi}e^{-z^{2}}\operatorname{erfi}(z)}{2z};\qquad
F_{2}(z)\equiv\frac{1-e^{-z^{2}}}{z}.$ (12)

In the above equations $\alpha$ is the fraction of K${}^{0}_{\rm S}$K± pairs
that come from the K0K- or ${\rm\overline{K}^{0}}$K+ system, set to 0.5
assuming symmetry in K0 and ${\rm\overline{K}^{0}}$ production [3], $R$ is the
radius parameter from the spherical Gaussian source distribution given in Eq.
(10), and $\lambda$ is the correlation strength. The correlation strength is
unity in the ideal case of pure $a_{0}$-resonant FSI, perfect PID, a perfect
Gaussian kaon source and the absence of long-lived resonances which decay into
kaons. The term $\Delta C$ is a calculated correction factor that takes into
account the deviation of the spherical wave assumption used in Eq. (7) in the
inner region of the short-range potential (see the Appendix in Ref. [3]). Its
effect on the extracted $R$ and $\lambda$ parameters is to increase them by
$\sim 14\%$. Note that the form of the FSI term in Eq. (11) differs from the
form of the FSI term for $\rm K^{0}_{S}\rm K^{0}_{S}$ correlations (Eq. (9) of
Ref. [3]) by a factor of $1/2$ due to the non-identical particles in
K${}^{0}_{\rm S}$K± correlations and thus the absence of the requirement to
symmetrize the wavefunction given in Eq. (7).

As seen in Eq. (8), the K0K- or ${\rm\overline{K}^{0}}$K+ s-wave scattering
amplitude depends on the $a_{0}$ mass and decay couplings. From the ALICE Pb-
Pb collision K${}^{0}_{\rm S}$K± study [2], it was found that source
parameters extracted with the “Achasov2” parameters of Ref. [7] agreed best
with the identical kaon measurements, thus in the present pp collision study
only the Achasov2 parameters are used. These parameters are shown in Tab. 1.
Since the correction factor $\Delta C$ is found to mainly depend on
$\gamma_{a_{0}K\bar{K}}$ [3], it is judged that the systematic uncertainty on
the calculation of $\Delta C$ is negligible.

Reference | $m_{a_{0}}$ | $\gamma_{a_{0}\rightarrow{\rm K\overline{K}}}$ | $\gamma_{a_{0}\rightarrow\pi\eta}$
---|---|---|---
Achasov2 [7] | 1.003 | 0.8365 | 0.4580
Table 1: The $a_{0}$ mass and coupling parameters, all in GeV/$c^{2}$, used in
the present study.

The experimental K${}^{0}_{\rm S}$K± correlation functions, calculated using
Eq. (1), were fit with the expression

$C(k^{*})=C_{\rm FSI}(k^{*})C_{\rm baseline}(k^{*}),$ (13)

where $C_{\rm baseline}(k^{*})$ is Eq. (4), Eq. (5) or Eq. (6).

The fitting strategy used was to carry out a 5-parameter fit of Eq. (13) to
the K${}^{0}_{\rm S}$K± experimental correlation functions to extract $R$,
$\lambda$, $a$, $b$ and $c$ for each of the six ($k_{T}$ range)-(charge state)
combinations. For each of these six combinations, the three baseline
functional forms, and two $k^{*}$ fit ranges, (0.0-0.6 GeV/$c$) and (0.0-0.8
GeV/$c$), were fit, giving six $R$ and six $\lambda$ parameter values for each
combination. These six values were then averaged and the variance calculated
to obtain the final values for the parameters and an estimate of the combined
systematic uncertainties from the baseline assumptions and fit range,
respectively.

##  4 Results and discussion

###  4.1 Fits to the experimental correlation functions

Figure 3 shows sample correlation functions divided by the quadratic baseline
function with fits of Eq. (13) for K${}^{0}_{\rm S}$K± and the $k^{*}$ fit
range ($0.0-0.6$ GeV/$c$) for the three $k_{T}$ bins. The fits using the other
baseline assumptions and to the wider range of ($0.0-0.8$ GeV/$c$) are similar
in quality. Comparing with the quadratic baseline, using the Gaussian baseline
tends to give $\sim 10-20$% smaller source parameters whereas using the
exponential baseline tends to give $\sim 10-20$% larger source parameters. The
average $\chi^{2}/{\rm ndf}$ and p-value over all of the fits are 1.554 and
0.172, respectively. Statistical (lines) and the quadratic sum of the
statistical and systematic (boxes) uncertainties are shown. The systematic
uncertainties were determined by varying cuts on the data (See the discussion
of the “cut systematic uncertainty” in the section below on “Systematic
Uncertainties for more details.”). Fig. 4 shows sample raw correlation
functions for K${}^{0}_{\rm S}$K+ for the three $k_{T}$ bins and the quadratic
baseline function, Eq. 4, that was fit corresponding to the 5-parameter fits
of Eq. 13 to the K${}^{0}_{\rm S}$K+ data presented in Fig. 3. Statistical
uncertainties on the fit parameters were obtained by constructing the
1$\sigma$ $\lambda$ vs. $R$ contour and taking the errors to be at the extreme
extents of the contour. A typical value of the correlation coefficient is
0.642. This method gives the most conservative estimates of the statistical
uncertainties.

Figure 3: Correlation functions divided by one of the baseline functions with
fits from Eq. (13) for K${}^{0}_{\rm S}$K+ and K${}^{0}_{\rm S}$K- and $k^{*}$
fit range (0.0-0.6 GeV/$c$) for the three $k_{T}$ bins and the quadratic
baseline function assumption. Statistical (lines) and the quadratic sum of the
statistical and systematic (boxes) uncertainties are shown. For $k^{*}>0.05$
GeV/$c$, the systematic uncertainties become negligible and the boxes are no
longer shown. Figure 4: Sample raw correlation functions for K${}^{0}_{\rm
S}$K+ showing the fitted quadratic baseline function, Eq. 4. Statistical
uncertainties are shown. The scale of $C(k^{*})$ is arbitrary.

The Achasov2 $a_{0}$ FSI parameterization coupled with the various baseline
assumptions gives a good representation of the signal region of the data, i.e.
reproducing the enhancement in the $k^{*}$ region $0.0-0.1$ GeV/$c$ and the
small dip in the region $0.1-0.3$ GeV/$c$. A good representation of the signal
region was also seen to be the case for the Pb-Pb analysis with the Achasov2
parameterization, which has a qualitatively different $k^{*}$ dependence of
the correlation function that is dominated by a dip at low $k^{*}$ (Compare
present Fig. 3 with Fig. 2 from Ref. [2]). The enhancement seen for the
small-$R$ system at low $k^{*}$ is expected from Eq. (11) as a consequence of
the first term in the brackets that goes as $1/R^{2}$. This demonstrates the
ability of Eq. (11) to describe the FSI in both the small and large size
regimes as going through the $a_{0}$ resonance.

###  4.2 Extracted $R$ and $\lambda$ parameters

The results for the extracted average $R$ and $\lambda$ parameters and the
statistical and systematic uncertainties on these for the present analysis of
K${}^{0}_{\rm S}$K± femtoscopy from 7 TeV pp collisions are shown in Tab. 2.
The statistical uncertainties given are the averages over the 6 fits for each
case. As can be seen, $R$ and $\lambda$ for K${}^{0}_{\rm S}$K+ agree within
the statistical uncertainties with those for K${}^{0}_{\rm S}$K- in all cases.

R or $\lambda$ [+/-] |  $k_{\rm T}$ cut | fit | statistical | fit | cut | total | total
---|---|---|---|---|---|---|---
(GeV/$c$) | value | uncert. | systematic | systematic | systematic | quadratic
|  |  | uncert. | uncert. | uncert. | uncert.
R[+] (fm) | $k_{\rm T}<0.85$ | 0.905 | 0.063 | 0.243 | 0.033 | 0.245 | 0.253
$k_{\rm T}>0.85$ | 0.788 | 0.077 | 0.168 | 0.031 | 0.171 | 0.188
All $k_{\rm T}$ | 0.922 | 0.048 | 0.188 | 0.038 | 0.192 | 0.198
$\lambda$[+] | $k_{\rm T}<0.85$ | 0.189 | 0.046 | 0.070 | 0.012 | 0.071 | 0.085
$k_{\rm T}>0.85$ | 0.222 | 0.080 | 0.066 | 0.015 | 0.068 | 0.105
All $k_{\rm T}$ | 0.242 | 0.046 | 0.066 | 0.020 | 0.069 | 0.083
R[-] (fm) | $k_{\rm T}<0.85$ | 1.039 | 0.060 | 0.244 | 0.039 | 0.247 | 0.254
$k_{\rm T}>0.85$ | 0.786 | 0.082 | 0.145 | 0.032 | 0.148 | 0.169
All $k_{\rm T}$ | 0.995 | 0.046 | 0.185 | 0.041 | 0.190 | 0.195
$\lambda$[-] | $k_{\rm T}<0.85$ | 0.253 | 0.044 | 0.096 | 0.016 | 0.097 | 0.107
$k_{\rm T}>0.85$ | 0.208 | 0.084 | 0.038 | 0.016 | 0.042 | 0.094
All $k_{\rm T}$ | 0.277 | 0.038 | 0.074 | 0.023 | 0.078 | 0.087
Table 2: Fit results for average R and $\lambda$ showing statistical and
systematic uncertainties from K${}^{0}_{\rm S}$K± femtoscopy with pp
collisions at $\sqrt{s}=7$ TeV. The “[+/-]” in the first column refers to
K${}^{0}_{\rm S}$K+ or K${}^{0}_{\rm S}$K-. See the text for the definitions
of the various uncertainties.

###  4.3 Systematic uncertainties

Table 2 shows the total systematic uncertainties on the extracted $R$ and
$\lambda$ parameters. As is seen, for most cases the total systematic
uncertainty is larger than the statistical uncertainty. The total systematic
uncertainty is broken down in Tab. 2 into two main contributions, the “fit
systematic uncertainty” and the “cut systematic uncertainty”, and is the
quadratic sum of these. The fit systematic uncertainty is the combined
systematic uncertainty due to the various baseline assumptions and varying the
$k^{*}$ fit range, as described earlier. The cut systematic uncertainty is the
systematic uncertainty related to the various cuts made in the data analysis.
To determine this, single particle cuts were varied by $\sim 10$%, and the
value chosen for the minimum separation distance of same-sign tracks was
varied by $\sim 20$%. Taking the upper-limit values of the variations to be
conservative, this led to additional errors of $4\%$ for $R$ and $8\%$ for
$\lambda$. As seen in the table, the fit systematic uncertainty dominates over
the cut systematic uncertainty in all cases, demonstrating the large
uncertainties in determining the non-femtoscopic baseline in pp collisions.
The “total quadratic uncertainty” is the quadratic sum of the “statistical
uncertainty” column and the “total systematic uncertainty” column.

###  4.4 Comparisons with K${}^{0}_{\rm S}$K± results from Pb-Pb collisions at
$\sqrt{s_{\rm NN}}=2.76$ TeV and identical-kaon results from pp collisions at
$\sqrt{s}=7$ TeV

In this section comparisons of the present results for $R$ and $\lambda$ with
K${}^{0}_{\rm S}$K± measurements from ALICE 2.76 TeV Pb-Pb collisions for
$0-10$% centrality [2], and with identical-kaon measurements from ALICE 7 TeV
pp collisions [4, 5] are presented. Since it is seen in Tab. 2 that the
extracted parameters for K${}^{0}_{\rm S}$K+ agree within the statistical
uncertainties with those for K${}^{0}_{\rm S}$K- in all cases, these are
averaged over weighted by the statistical uncertainties in the following
figures

Figure 5 shows the comparison with the ALICE Pb-Pb collision K${}^{0}_{\rm
S}$K± measurements. The $\lambda$ parameters have been divided by the pair
purity for each case, i.e. 83% for the present pp collisions and 88% for the
Pb-Pb collisions [2], so that they can be compared on the same basis. It is
seen that $R$ for $0-10$% centrality Pb-Pb is $\sim 5$ fm, and is
significantly larger than the $R\sim 1$ fm measured for pp collisions. This is
expected since $R$ reflects the geometric size of the interaction region of
the collision. It is somewhat surprising that $\lambda$ for pp collisions is
seen to be significantly less than that for Pb-Pb collisions. There are two
main factors effecting the value of the $\lambda$ parameter: 1) the degree to
which a Gaussian fits the correlation function and 2) the effect of long-lived
resonances diluting the kaon sample. For 1), it is seen in Fig. 3 for pp and
in Fig. 2 of Ref. [2] for Pb-Pb that the Gaussian function used in the
Ledincky equation, Eqs. 10 and 11, fits both colliding systems well,
minimizing the effect of 1). For 2), the K∗ decay ($\Gamma\sim 50$ MeV) has
the largest influence on diluting the kaon sample, and it is unlikely that the
multiplicity ratio of K/K∗ changes dramatically in going from 2.76 TeV to 7
TeV. From these arguments we might naively expect $\lambda$ to be similar in
the pp and Pb-Pb cases.

Figure 5: $R$ and $\lambda$ parameters extracted in the present analysis from
K${}^{0}_{\rm S}$K± femtoscopy averaged over K${}^{0}_{\rm S}$K+ and
K${}^{0}_{\rm S}$K-, along with a comparison with K${}^{0}_{\rm S}$K± results
from ALICE 2.76 TeV Pb-Pb collisions for $0-10$% centrality [2]. The quadratic
sum of the statistical and systematic uncertainties is plotted for all results
as boxes and the statistical uncertainties are given as lines. The $\lambda$
parameters have been divided by their respective pair purities to facilitate
their comparison.

In order to properly compare the present results with the ALICE pp collision
identical-kaon measurements, we must take the weighted average (weighted by
their statistical uncertainties) over the multiplicity bins used in Refs. [4,
5] since our present results are summed over all multiplicity. Figure 6 shows
the comparison between the present results for $R$ and $\lambda$ and
measurements from the identical-kaon femtoscopy in 7 TeV pp collisions. The
$R$ values are seen to agree between the present analysis and the identical
kaon analyses within the uncertainties. The $\lambda$ parameters shown in Fig.
6 are each divided by their respective pair purities. Going from the lowest to
the highest $k_{\rm T}$ points, for the neutral-kaon pairs the purities are
0.88 and 0.84 [4], and for the charge-kaon pairs the purities are 0.84, 0.61,
0.79 and 1.0 [5], respectively. The purity-normalized $\lambda$ parameters for
the identical kaons are seen to scatter in a wide range between values of
$0.3-0.7$, whereas the K${}^{0}_{\rm S}$K± values are seen to lie in the
narrower range of $0.25-0.30$.

Figure 6: $R$ and purity-normalized $\lambda$ parameters extracted in the
present analysis from K${}^{0}_{\rm S}$K± femtoscopy averaged over
K${}^{0}_{\rm S}$K+ and K${}^{0}_{\rm S}$K-, along with comparisons with
identical kaon results from ALICE 7 TeV pp collisions averaged over event
multiplicity. The quadratic sum of the statistical and systematic
uncertainties is plotted for all results as boxes and the statistical
uncertainties are given as lines. Also plotted as a blue dashed line is the
simple average of the identical-kaon purity-normalized $\lambda$ parameters.

In order to help to clarify the comparison between the purity-normalized
$\lambda$ values from K${}^{0}_{\rm S}$K± and the identical-kaon results, the
simple average over the identical kaon purity-normalized $\lambda$ parameters
is plotted as a blue dashed line in Fig. 6. As seen, the K${}^{0}_{\rm S}$K±
values tend to be smaller than the average of the identical kaons, as was more
significantly the case for the comparison with the purity-normalized $\lambda$
values from Pb-Pb seen in Fig. 5, however the large scatter of the identical
kaons makes it difficult to draw any strong conclusions from this comparison.

###  4.5 Implications from the present results for the $a_{0}$ to be a
tetraquark state

The K${}^{0}_{\rm S}$K± FSI is described well by assuming it is due to the
$a_{0}$ resonance for both pp and Pb-Pb collisions, as seen in Fig. 3 of the
present work and in Fig. 2 of Ref. [2]. The $R$ parameters extracted from this
method are also seen to agree within uncertainties with the identical-kaon
measurements for each of these collision systems. For Pb-Pb collisions, it was
found that the $\lambda$ parameters extracted from K${}^{0}_{\rm S}$K± also
agree with the corresponding identical-kaon measurements for Pb-Pb collisions
indicating that the FSI between the kaons goes solely through the $a_{0}$
resonance. The present pp collision results for $\lambda$, which are
significantly lower than the K${}^{0}_{\rm S}$K± values from Pb-Pb collisions
seen in Fig. 5 and which tend to be lower than the corresponding identical-
kaon values in pp collisions seen in Fig. 6, imply that the FSI for these
collisions does not go solely through the $a_{0}$ resonance, i.e. non-resonant
elastic channels and/or free-streaming are also present. From the arguments
given in the Introduction, this is the geometric effect that would be expected
in the case of a tetraquark $a_{0}$ since competing annihilation channels
could open up in the smaller system and compete with the FSI through the
$a_{0}$, whereas for a diquark $a_{0}$ the FSI should still go solely through
the $a_{0}$. The pp collision results are thus compatible with the conclusion
from the Pb-Pb collision measurement [2] that favors the interpretation of the
$a_{0}$ resonance to be a tetraquark state.

##  5 Summary

In summary, femtoscopic correlations with the particle pair combinations
K${}^{0}_{\rm S}$K± are studied in pp collisions at $\sqrt{s}=7$ TeV for the
first time by the LHC ALICE experiment. Correlations in the K${}^{0}_{\rm
S}$K± pairs are produced by final-state interactions which proceed through the
$a_{0}$ resonance. It is found that the $a_{0}$ final-state interaction
describes the shape of the measured K${}^{0}_{\rm S}$K± correlation functions
well. The extracted radius and $\lambda$ parameters for K${}^{0}_{\rm S}$K-
are found to be equal within the experimental uncertainties to those for
K${}^{0}_{\rm S}$K+. Results of the present study are compared with those from
identical-kaon femtoscopic studies also performed with pp collisions at
$\sqrt{s}=7$ TeV by ALICE and with a recent ALICE K${}^{0}_{\rm S}$K±
measurement in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV. These
comparisons suggest that non-resonant elastic scattering channels are present
in pp collisions, unlike in Pb-Pb collisions. It is our conclusion that the
present results, in combination with the ALICE Pb-Pb collision measurements,
favor the interpretation of the $a_{0}$ to be a tetraquark state.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians
for their invaluable contributions to the construction of the experiment and
the CERN accelerator teams for the outstanding performance of the LHC complex.
The ALICE Collaboration gratefully acknowledges the resources and support
provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG)
collaboration. The ALICE Collaboration acknowledges the following funding
agencies for their support in building and running the ALICE detector: A. I.
Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation
(ANSL), State Committee of Science and World Federation of Scientists (WFS),
Armenia; Austrian Academy of Sciences and Nationalstiftung für Forschung,
Technologie und Entwicklung, Austria; Ministry of Communications and High
Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional
de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do
Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil;
Ministry of Science & Technology of China (MSTC), National Natural Science
Foundation of China (NSFC) and Ministry of Education of China (MOEC) , China;
Ministry of Science 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) and Institut
National de Physique Nucléaire et de Physique des Particules (IN2P3) and
Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium
für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat
for Research and Technology, Ministry of Education, Research and Religions,
Greece; National Research, Development and Innovation Office, Hungary;
Department of Atomic Energy Government of India (DAE), 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 Romanian National Agency
for Science, Technology and Innovation, Romania; Joint Institute for Nuclear
Research (JINR), Ministry of Education and Science of the Russian Federation
and National Research Centre Kurchatov Institute, Russia; Ministry of
Education, Science, Research and Sport of the Slovak Republic, Slovakia;
National Research Foundation of South Africa, South Africa; 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. Acharya139, F.T.-. Acosta20, D. Adamová93, A. Adler74, J. Adolfsson80, M.M.
Aggarwal98, G. Aglieri Rinella34, M. Agnello31, N. Agrawal48, Z. Ahammed139,
S.U. Ahn76, S. Aiola144, A. Akindinov64, M. Al-Turany104, S.N. Alam139, D.S.D.
Albuquerque121, D. Aleksandrov87, B. Alessandro58, H.M. Alfanda6, R. Alfaro
Molina72, Y. Ali15, A. Alici10,27,53, A. Alkin2, J. Alme22, T. Alt69, L.
Altenkamper22, I. Altsybeev111, M.N. Anaam6, C. Andrei47, D. Andreou34, H.A.
Andrews108, A. Andronic104,142, M. Angeletti34, V. Anguelov102, C. Anson16, T.
Antičić105, F. Antinori56, P. Antonioli53, R. Anwar125, N. Apadula79, L.
Aphecetche113, H. Appelshäuser69, S. Arcelli27, R. Arnaldi58, M. Arratia79,
I.C. Arsene21, M. Arslandok102, A. Augustinus34, R. Averbeck104, M.D. Azmi17,
A. Badalà55, Y.W. Baek40,60, S. Bagnasco58, R. Bailhache69, R. Bala99, A.
Baldisseri135, M. Ball42, R.C. Baral85, A.M. Barbano26, R. Barbera28, F.
Barile52, L. Barioglio26, G.G. Barnaföldi143, L.S. Barnby92, V. Barret132, P.
Bartalini6, K. Barth34, E. Bartsch69, N. Bastid132, S. Basu141, G. Batigne113,
B. Batyunya75, P.C. Batzing21, J.L. Bazo Alba109, I.G. Bearden88, H. Beck102,
C. Bedda63, N.K. Behera60, I. Belikov134, F. Bellini34, H. Bello Martinez44,
R. Bellwied125, L.G.E. Beltran119, V. Belyaev91, G. Bencedi143, S. Beole26, A.
Bercuci47, Y. Berdnikov96, D. Berenyi143, R.A. Bertens128, D. Berzano34,58, L.
Betev34, P.P. Bhaduri139, A. Bhasin99, I.R. Bhat99, H. Bhatt48, B.
Bhattacharjee41, J. Bhom117, A. Bianchi26, L. Bianchi26,125, N. Bianchi51, J.
Bielčík37, J. Bielčíková93, A. Bilandzic103,116, G. Biro143, R. Biswas3, S.
Biswas3, J.T. Blair118, D. Blau87, C. Blume69, G. Boca137, F. Bock34, A.
Bogdanov91, L. Boldizsár143, A. Bolozdynya91, M. Bombara38, G. Bonomi138, M.
Bonora34, H. Borel135, A. Borissov102,142, M. Borri127, E. Botta26, C.
Bourjau88, L. Bratrud69, P. Braun-Munzinger104, M. Bregant120, T.A. Broker69,
M. Broz37, E.J. Brucken43, E. Bruna58, G.E. Bruno33,34, D. Budnikov106, H.
Buesching69, S. Bufalino31, P. Buhler112, P. Buncic34, O. BuschI,131, Z.
Buthelezi73, J.B. Butt15, J.T. Buxton95, J. Cabala115, D. Caffarri89, H.
Caines144, A. Caliva104, E. Calvo Villar109, R.S. Camacho44, P. Camerini25,
A.A. Capon112, W. Carena34, F. Carnesecchi10,27, J. Castillo Castellanos135,
A.J. Castro128, E.A.R. Casula54, C. Ceballos Sanchez8, S. Chandra139, B.
Chang126, W. Chang6, S. Chapeland34, M. Chartier127, S. Chattopadhyay139, S.
Chattopadhyay107, A. Chauvin24, C. Cheshkov133, B. Cheynis133, V. Chibante
Barroso34, D.D. Chinellato121, S. Cho60, P. Chochula34, T. Chowdhury132, P.
Christakoglou89, C.H. Christensen88, P. Christiansen80, T. Chujo131, S.U.
Chung18, C. Cicalo54, L. Cifarelli10,27, F. Cindolo53, J. Cleymans124, F.
Colamaria52, D. Colella52, A. Collu79, M. Colocci27, M. ConcasII,58, G. Conesa
Balbastre78, Z. Conesa del Valle61, J.G. Contreras37, T.M. Cormier94, Y.
Corrales Morales58, P. Cortese32, M.R. Cosentino122, F. Costa34, S.
Costanza137, J. Crkovská61, P. Crochet132, E. Cuautle70, L. Cunqueiro94,142,
D. Dabrowski140, T. Dahms103,116, A. Dainese56, F.P.A. Damas113,135, S.
Dani66, M.C. Danisch102, A. Danu68, D. Das107, I. Das107, S. Das3, A. Dash85,
S. Dash48, S. De49, A. De Caro30, G. de Cataldo52, C. de Conti120, J. de
Cuveland39, A. De Falco24, D. De Gruttola10,30, N. De Marco58, S. De
Pasquale30, R.D. De Souza121, H.F. Degenhardt120, A. Deisting102,104, A.
Deloff84, S. Delsanto26, C. Deplano89, P. Dhankher48, D. Di Bari33, A. Di
Mauro34, B. Di Ruzza56, R.A. Diaz8, T. Dietel124, P. Dillenseger69, Y. Ding6,
R. Divià34, Ø. Djuvsland22, A. Dobrin34, D. Domenicis Gimenez120, B.
Dönigus69, O. Dordic21, A.K. Dubey139, A. Dubla104, L. Ducroux133, S. Dudi98,
A.K. Duggal98, M. Dukhishyam85, P. Dupieux132, R.J. Ehlers144, D. Elia52, E.
Endress109, H. Engel74, E. Epple144, B. Erazmus113, F. Erhardt97, A.
Erokhin111, M.R. Ersdal22, B. Espagnon61, G. Eulisse34, J. Eum18, D. Evans108,
S. Evdokimov90, L. Fabbietti103,116, M. Faggin29, J. Faivre78, A. Fantoni51,
M. Fasel94, L. Feldkamp142, A. Feliciello58, G. Feofilov111, A. Fernández
Téllez44, A. Ferretti26, A. Festanti34, V.J.G. Feuillard102, J. Figiel117,
M.A.S. Figueredo120, S. Filchagin106, D. Finogeev62, F.M. Fionda22, G.
Fiorenza52, F. Flor125, M. Floris34, S. Foertsch73, P. Foka104, S. Fokin87, E.
Fragiacomo59, A. Francescon34, A. Francisco113, U. Frankenfeld104, G.G.
Fronze26, U. Fuchs34, C. Furget78, A. Furs62, M. Fusco Girard30, J.J.
Gaardhøje88, M. Gagliardi26, A.M. Gago109, K. Gajdosova88, M. Gallio26, C.D.
Galvan119, P. Ganoti83, C. Garabatos104, E. Garcia-Solis11, K. Garg28, C.
Gargiulo34, K. Garner142, P. Gasik103,116, E.F. Gauger118, M.B. Gay Ducati71,
M. Germain113, J. Ghosh107, P. Ghosh139, S.K. Ghosh3, P. Gianotti51, P.
Giubellino58,104, P. Giubilato29, P. Glässel102, D.M. Goméz Coral72, A. Gomez
Ramirez74, V. Gonzalez104, P. González-Zamora44, S. Gorbunov39, L. Görlich117,
S. Gotovac35, V. Grabski72, L.K. Graczykowski140, K.L. Graham108, L.
Greiner79, A. Grelli63, C. Grigoras34, V. Grigoriev91, A. Grigoryan1, S.
Grigoryan75, J.M. Gronefeld104, F. Grosa31, J.F. Grosse-Oetringhaus34, R.
Grosso104, R. Guernane78, B. Guerzoni27, M. Guittiere113, K. Gulbrandsen88, T.
Gunji130, A. Gupta99, R. Gupta99, I.B. Guzman44, R. Haake34,144, M.K.
Habib104, C. Hadjidakis61, H. Hamagaki81, G. Hamar143, M. Hamid6, J.C.
Hamon134, R. Hannigan118, M.R. Haque63, A. Harlenderova104, J.W. Harris144, A.
Harton11, H. Hassan78, D. Hatzifotiadou10,53, P. Hauer42, S. Hayashi130, S.T.
Heckel69, E. Hellbär69, H. Helstrup36, A. Herghelegiu47, E.G. Hernandez44, G.
Herrera Corral9, F. Herrmann142, K.F. Hetland36, T.E. Hilden43, H.
Hillemanns34, C. Hills127, B. Hippolyte134, B. Hohlweger103, D. Horak37, S.
Hornung104, R. Hosokawa78,131, J. Hota66, P. Hristov34, C. Huang61, C.
Hughes128, P. Huhn69, T.J. Humanic95, H. Hushnud107, N. Hussain41, T.
Hussain17, D. Hutter39, D.S. Hwang19, J.P. Iddon127, R. Ilkaev106, M.
Inaba131, M. Ippolitov87, M.S. Islam107, M. Ivanov104, V. Ivanov96, V.
Izucheev90, B. Jacak79, N. Jacazio27, P.M. Jacobs79, M.B. Jadhav48, S.
Jadlovska115, J. Jadlovsky115, S. Jaelani63, C. Jahnke116,120, M.J.
Jakubowska140, M.A. Janik140, C. Jena85, M. Jercic97, O. Jevons108, R.T.
Jimenez Bustamante104, M. Jin125, P.G. Jones108, A. Jusko108, P. Kalinak65, A.
Kalweit34, J.H. Kang145, V. Kaplin91, S. Kar6, A. Karasu Uysal77, O.
Karavichev62, T. Karavicheva62, P. Karczmarczyk34, E. Karpechev62, U.
Kebschull74, R. Keidel46, D.L.D. Keijdener63, M. Keil34, B. Ketzer42, Z.
Khabanova89, A.M. Khan6, S. Khan17, S.A. Khan139, A. Khanzadeev96, Y.
Kharlov90, A. Khatun17, A. Khuntia49, M.M. Kielbowicz117, B. Kileng36, B.
Kim131, D. Kim145, D.J. Kim126, E.J. Kim13, H. Kim145, J.S. Kim40, J. Kim102,
J. Kim13, M. Kim60,102, S. Kim19, T. Kim145, T. Kim145, K. Kindra98, S.
Kirsch39, I. Kisel39, S. Kiselev64, A. Kisiel140, J.L. Klay5, C. Klein69, J.
Klein58, C. Klein-Bösing142, S. Klewin102, A. Kluge34, M.L. Knichel34, A.G.
Knospe125, C. Kobdaj114, M. Kofarago143, M.K. Köhler102, T. Kollegger104, N.
Kondratyeva91, E. Kondratyuk90, A. Konevskikh62, P.J. Konopka34, M.
Konyushikhin141, L. Koska115, O. Kovalenko84, V. Kovalenko111, M. Kowalski117,
I. Králik65, A. Kravčáková38, L. Kreis104, M. Krivda65,108, F. Krizek93, M.
Krüger69, E. Kryshen96, M. Krzewicki39, A.M. Kubera95, V. Kučera60,93, C.
Kuhn134, P.G. Kuijer89, J. Kumar48, L. Kumar98, S. Kumar48, S. Kundu85, P.
Kurashvili84, A. Kurepin62, A.B. Kurepin62, S. Kushpil93, J. Kvapil108, M.J.
Kweon60, Y. Kwon145, S.L. La Pointe39, P. La Rocca28, Y.S. Lai79, I.
Lakomov34, R. Langoy123, K. Lapidus144, A. Lardeux21, P. Larionov51, E.
Laudi34, R. Lavicka37, R. Lea25, L. Leardini102, S. Lee145, F. Lehas89, S.
Lehner112, J. Lehrbach39, R.C. Lemmon92, I. León Monzón119, P. Lévai143, X.
Li12, X.L. Li6, J. Lien123, R. Lietava108, B. Lim18, S. Lindal21, V.
Lindenstruth39, S.W. Lindsay127, C. Lippmann104, M.A. Lisa95, V.
Litichevskyi43, A. Liu79, H.M. Ljunggren80, W.J. Llope141, D.F. Lodato63, V.
Loginov91, C. Loizides79,94, P. Loncar35, X. Lopez132, E. López Torres8, P.
Luettig69, J.R. Luhder142, M. Lunardon29, G. Luparello59, M. Lupi34, A.
Maevskaya62, M. Mager34, S.M. Mahmood21, A. Maire134, R.D. Majka144, M.
Malaev96, Q.W. Malik21, L. MalininaIII,75, D. Mal’Kevich64, P. Malzacher104,
A. Mamonov106, V. Manko87, F. Manso132, V. Manzari52, Y. Mao6, M.
Marchisone129,133, J. Mareš67, G.V. Margagliotti25, A. Margotti53, J.
Margutti63, A. Marín104, C. Markert118, M. Marquard69, N.A. Martin102,104, P.
Martinengo34, J.L. Martinez125, M.I. Martínez44, G. Martínez García113, M.
Martinez Pedreira34, S. Masciocchi104, M. Masera26, A. Masoni54, L.
Massacrier61, E. Masson113, A. Mastroserio52,136, A.M. Mathis103,116, P.F.T.
Matuoka120, A. Matyja117,128, C. Mayer117, M. Mazzilli33, M.A. Mazzoni57, F.
Meddi23, Y. Melikyan91, A. Menchaca-Rocha72, E. Meninno30, M. Meres14, S.
Mhlanga124, Y. Miake131, L. Micheletti26, M.M. Mieskolainen43, D.L.
Mihaylov103, K. Mikhaylov64,75, A. Mischke63, A.N. Mishra70, D. Miśkowiec104,
J. Mitra139, C.M. Mitu68, N. Mohammadi34, A.P. Mohanty63, B. Mohanty85, M.
Mohisin KhanIV,17, D.A. Moreira De Godoy142, L.A.P. Moreno44, S. Moretto29, A.
Morreale113, A. Morsch34, T. Mrnjavac34, V. Muccifora51, E. Mudnic35, D.
Mühlheim142, S. Muhuri139, M. Mukherjee3, J.D. Mulligan144, M.G. Munhoz120, K.
Münning42, R.H. Munzer69, H. Murakami130, S. Murray73, L. Musa34, J.
Musinsky65, C.J. Myers125, J.W. Myrcha140, B. Naik48, R. Nair84, B.K. Nandi48,
R. Nania10,53, E. Nappi52, A. Narayan48, M.U. Naru15, A.F. Nassirpour80, H.
Natal da Luz120, C. Nattrass128, S.R. Navarro44, K. Nayak85, R. Nayak48, T.K.
Nayak139, S. Nazarenko106, R.A. Negrao De Oliveira34,69, L. Nellen70, S.V.
Nesbo36, G. Neskovic39, F. Ng125, M. Nicassio104, J. Niedziela34,140, B.S.
Nielsen88, S. Nikolaev87, S. Nikulin87, V. Nikulin96, F. Noferini10,53, P.
Nomokonov75, G. Nooren63, J.C.C. Noris44, J. Norman78, A. Nyanin87, J.
Nystrand22, M. Ogino81, H. Oh145, A. Ohlson102, J. Oleniacz140, A.C. Oliveira
Da Silva120, M.H. Oliver144, J. Onderwaater104, C. Oppedisano58, R. Orava43,
M. Oravec115, A. Ortiz Velasquez70, A. Oskarsson80, J. Otwinowski117, K.
Oyama81, Y. Pachmayer102, V. Pacik88, D. Pagano138, G. Paić70, P. Palni6, J.
Pan141, A.K. Pandey48, S. Panebianco135, V. Papikyan1, P. Pareek49, J. Park60,
J.E. Parkkila126, S. Parmar98, A. Passfeld142, S.P. Pathak125, R.N. Patra139,
B. Paul58, H. Pei6, T. Peitzmann63, X. Peng6, L.G. Pereira71, H. Pereira Da
Costa135, D. Peresunko87, E. Perez Lezama69, V. Peskov69, Y. Pestov4, V.
Petráček37, M. Petrovici47, C. Petta28, R.P. Pezzi71, S. Piano59, M. Pikna14,
P. Pillot113, L.O.D.L. Pimentel88, O. Pinazza34,53, L. Pinsky125, S. Pisano51,
D.B. Piyarathna125, M. Płoskoń79, M. Planinic97, F. Pliquett69, J. Pluta140,
S. Pochybova143, P.L.M. Podesta-Lerma119, M.G. Poghosyan94, B. Polichtchouk90,
N. Poljak97, W. Poonsawat114, A. Pop47, H. Poppenborg142, S. Porteboeuf-
Houssais132, V. Pozdniakov75, S.K. Prasad3, R. Preghenella53, F. Prino58, C.A.
Pruneau141, I. Pshenichnov62, M. Puccio26, V. Punin106, K. Puranapanda139, J.
Putschke141, S. Raha3, S. Rajput99, J. Rak126, A. Rakotozafindrabe135, L.
Ramello32, F. Rami134, R. Raniwala100, S. Raniwala100, S.S. Räsänen43, B.T.
Rascanu69, R. Rath49, V. Ratza42, I. Ravasenga31, K.F. Read94,128, K.
RedlichV,84, A. Rehman22, P. Reichelt69, F. Reidt34, X. Ren6, R. Renfordt69,
A. Reshetin62, J.-P. Revol10, K. Reygers102, V. Riabov96, T. Richert63,80,88,
M. Richter21, P. Riedler34, W. Riegler34, F. Riggi28, C. Ristea68, S.P.
Rode49, M. Rodríguez Cahuantzi44, K. Røed21, R. Rogalev90, E. Rogochaya75, D.
Rohr34, D. Röhrich22, P.S. Rokita140, F. Ronchetti51, E.D. Rosas70, K.
Roslon140, P. Rosnet132, A. Rossi29,56, A. Rotondi137, F. Roukoutakis83, C.
Roy134, P. Roy107, O.V. Rueda70, R. Rui25, B. Rumyantsev75, A. Rustamov86, E.
Ryabinkin87, Y. Ryabov96, A. Rybicki117, S. Saarinen43, S. Sadhu139, S.
Sadovsky90, K. Šafařík34, S.K. Saha139, B. Sahoo48, P. Sahoo49, R. Sahoo49, S.
Sahoo66, P.K. Sahu66, J. Saini139, S. Sakai131, M.A. Saleh141, S. Sambyal99,
V. Samsonov91,96, A. Sandoval72, A. Sarkar73, D. Sarkar139, N. Sarkar139, P.
Sarma41, M.H.P. Sas63, E. Scapparone53, F. Scarlassara29, B. Schaefer94, H.S.
Scheid69, C. Schiaua47, R. Schicker102, C. Schmidt104, H.R. Schmidt101, M.O.
Schmidt102, M. Schmidt101, N.V. Schmidt69,94, J. Schukraft34, Y. Schutz34,134,
K. Schwarz104, K. Schweda104, G. Scioli27, E. Scomparin58, M. Šefčík38, J.E.
Seger16, Y. Sekiguchi130, D. Sekihata45, I. Selyuzhenkov91,104, S.
Senyukov134, E. Serradilla72, P. Sett48, A. Sevcenco68, A. Shabanov62, A.
Shabetai113, R. Shahoyan34, W. Shaikh107, A. Shangaraev90, A. Sharma98, A.
Sharma99, M. Sharma99, N. Sharma98, A.I. Sheikh139, K. Shigaki45, M.
Shimomura82, S. Shirinkin64, Q. Shou6,110, Y. Sibiriak87, S. Siddhanta54, K.M.
Sielewicz34, T. Siemiarczuk84, D. Silvermyr80, G. Simatovic89, G.
Simonetti34,103, R. Singaraju139, R. Singh85, R. Singh99, V. Singhal139, T.
Sinha107, B. Sitar14, M. Sitta32, T.B. Skaali21, M. Slupecki126, N.
Smirnov144, R.J.M. Snellings63, T.W. Snellman126, J. Sochan115, C. Soncco109,
J. Song18,60, A. Songmoolnak114, F. Soramel29, S. Sorensen128, F. Sozzi104, I.
Sputowska117, J. Stachel102, I. Stan68, P. Stankus94, E. Stenlund80, D.
Stocco113, M.M. Storetvedt36, P. Strmen14, A.A.P. Suaide120, T. Sugitate45, C.
Suire61, M. Suleymanov15, M. Suljic34, R. Sultanov64, M. Šumbera93, S.
Sumowidagdo50, K. Suzuki112, S. Swain66, A. Szabo14, I. Szarka14, U.
Tabassam15, J. Takahashi121, G.J. Tambave22, N. Tanaka131, M. Tarhini113, M.G.
Tarzila47, A. Tauro34, G. Tejeda Muñoz44, A. Telesca34, C. Terrevoli29, B.
Teyssier133, D. Thakur49, S. Thakur139, D. Thomas118, F. Thoresen88, R.
Tieulent133, A. Tikhonov62, A.R. Timmins125, A. Toia69, N. Topilskaya62, M.
Toppi51, S.R. Torres119, S. Tripathy49, S. Trogolo26, G. Trombetta33, L.
Tropp38, V. Trubnikov2, W.H. Trzaska126, T.P. Trzcinski140, B.A. Trzeciak63,
T. Tsuji130, A. Tumkin106, R. Turrisi56, T.S. Tveter21, K. Ullaland22, E.N.
Umaka125, A. Uras133, G.L. Usai24, A. Utrobicic97, M. Vala115, L. Valencia
Palomo44, N. Valle137, N. van der Kolk63, L.V.R. van Doremalen63, J.W. Van
Hoorne34, M. van Leeuwen63, P. Vande Vyvre34, D. Varga143, A. Vargas44, M.
Vargyas126, R. Varma48, M. Vasileiou83, A. Vasiliev87, O. Vázquez Doce103,116,
V. Vechernin111, A.M. Veen63, E. Vercellin26, S. Vergara Limón44, L.
Vermunt63, R. Vernet7, R. Vértesi143, L. Vickovic35, J. Viinikainen126, Z.
Vilakazi129, O. Villalobos Baillie108, A. Villatoro Tello44, A. Vinogradov87,
T. Virgili30, V. Vislavicius80,88, A. Vodopyanov75, M.A. Völkl101, K.
Voloshin64, S.A. Voloshin141, G. Volpe33, B. von Haller34, I. Vorobyev103,116,
D. Voscek115, D. Vranic34,104, J. Vrláková38, B. Wagner22, M. Wang6, Y.
Watanabe131, M. Weber112, S.G. Weber104, A. Wegrzynek34, D.F. Weiser102, S.C.
Wenzel34, J.P. Wessels142, U. Westerhoff142, A.M. Whitehead124, J. Wiechula69,
J. Wikne21, G. Wilk84, J. Wilkinson53, G.A. Willems34,142, M.C.S. Williams53,
E. Willsher108, B. Windelband102, W.E. Witt128, R. Xu6, S. Yalcin77, K.
Yamakawa45, S. Yano45,135, Z. Yin6, H. Yokoyama78,131, I.-K. Yoo18, J.H.
Yoon60, S. Yuan22, V. Yurchenko2, V. Zaccolo58, A. Zaman15, C. Zampolli34,
H.J.C. Zanoli120, N. Zardoshti108, A. Zarochentsev111, P. Závada67, N.
Zaviyalov106, H. Zbroszczyk140, M. Zhalov96, X. Zhang6, Y. Zhang6, Z.
Zhang6,132, C. Zhao21, V. Zherebchevskii111, N. Zhigareva64, D. Zhou6, Y.
Zhou88, Z. Zhou22, H. Zhu6, J. Zhu6, Y. Zhu6, A. Zichichi10,27, M.B.
Zimmermann34, G. Zinovjev2, J. Zmeskal112

Affiliation Notes

I Deceased

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

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

IV Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India

V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland

Collaboration Institutes

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

2 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine

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

4 Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

6 Central China Normal University, Wuhan, China

7 Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France

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

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

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

11 Chicago State University, Chicago, Illinois, United States

12 China Institute of Atomic Energy, Beijing, China

13 Chonbuk National University, Jeonju, Republic of Korea

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

15 COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

16 Creighton University, Omaha, Nebraska, United States

17 Department of Physics, Aligarh Muslim University, Aligarh, India

18 Department of Physics, Pusan National University, Pusan, Republic of Korea

19 Department of Physics, Sejong University, Seoul, Republic of Korea

20 Department of Physics, University of California, Berkeley, California,
United States

21 Department of Physics, University of Oslo, Oslo, Norway

22 Department of Physics and Technology, University of Bergen, Bergen, Norway

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

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

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

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

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

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

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

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

31 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

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

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

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

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

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

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

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

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

40 Gangneung-Wonju National University, Gangneung, Republic of Korea

41 Gauhati University, Department of Physics, Guwahati, India

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

43 Helsinki Institute of Physics (HIP), Helsinki, Finland

44 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

45 Hiroshima University, Hiroshima, Japan

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

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

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

49 Indian Institute of Technology Indore, Indore, India

50 Indonesian Institute of Sciences, Jakarta, Indonesia

51 INFN, Laboratori Nazionali di Frascati, Frascati, Italy

52 INFN, Sezione di Bari, Bari, Italy

53 INFN, Sezione di Bologna, Bologna, Italy

54 INFN, Sezione di Cagliari, Cagliari, Italy

55 INFN, Sezione di Catania, Catania, Italy

56 INFN, Sezione di Padova, Padova, Italy

57 INFN, Sezione di Roma, Rome, Italy

58 INFN, Sezione di Torino, Turin, Italy

59 INFN, Sezione di Trieste, Trieste, Italy

60 Inha University, Incheon, Republic of Korea

61 Institut 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

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

63 Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht,
Netherlands

64 Institute for Theoretical and Experimental Physics, Moscow, Russia

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

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

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

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

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

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

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

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

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

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

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

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

77 KTO Karatay University, Konya, Turkey

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

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

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

81 Nagasaki Institute of Applied Science, Nagasaki, Japan

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

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

84 National Centre for Nuclear Research, Warsaw, Poland

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

86 National Nuclear Research Center, Baku, Azerbaijan

87 National Research Centre Kurchatov Institute, Moscow, Russia

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

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

90 NRC Kurchatov Institute IHEP, Protvino, Russia

91 NRNU Moscow Engineering Physics Institute, Moscow, Russia

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

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

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

95 Ohio State University, Columbus, Ohio, United States

96 Petersburg Nuclear Physics Institute, Gatchina, Russia

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

98 Physics Department, Panjab University, Chandigarh, India

99 Physics Department, University of Jammu, Jammu, India

100 Physics Department, University of Rajasthan, Jaipur, India

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

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

103 Physik Department, Technische Universität München, Munich, Germany

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

105 Rudjer Bošković Institute, Zagreb, Croatia

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

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

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

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

110 Shanghai Institute of Applied Physics, Shanghai, China

111 St. Petersburg State University, St. Petersburg, Russia

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

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

114 Suranaree University of Technology, Nakhon Ratchasima, Thailand

115 Technical University of Košice, Košice, Slovakia

116 Technische Universität München, Excellence Cluster ’Universe’, Munich,
Germany

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

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

119 Universidad Autónoma de Sinaloa, Culiacán, Mexico

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

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

122 Universidade Federal do ABC, Santo Andre, Brazil

123 University College of Southeast Norway, Tonsberg, Norway

124 University of Cape Town, Cape Town, South Africa

125 University of Houston, Houston, Texas, United States

126 University of Jyväskylä, Jyväskylä, Finland

127 University of Liverpool, Liverpool, United Kingdom

128 University of Tennessee, Knoxville, Tennessee, United States

129 University of the Witwatersrand, Johannesburg, South Africa

130 University of Tokyo, Tokyo, Japan

131 University of Tsukuba, Tsukuba, Japan

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

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

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

135 Université Paris-Saclay Centre d¿Études de Saclay (CEA), IRFU, Department
de Physique Nucléaire (DPhN), Saclay, France

136 Università degli Studi di Foggia, Foggia, Italy

137 Università degli Studi di Pavia and Sezione INFN, Pavia, Italy

138 Università di Brescia and Sezione INFN, Brescia, Italy

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

140 Warsaw University of Technology, Warsaw, Poland

141 Wayne State University, Detroit, Michigan, United States

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

143 Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

144 Yale University, New Haven, Connecticut, United States

145 Yonsei University, Seoul, Republic of Korea