Measuring K$^0_{\rm S}$K$^{\rm \pm}$ interactions using Pb-Pb collisions at ${\sqrt{s_{\rm NN}}=2.76}$ TeV

TL;DR

This paper reports the first femtoscopic measurements of K0sK± interactions in Pb-Pb collisions at 2.76 TeV, providing insights into the $a_0(980)$ resonance and its possible tetraquark structure.

Contribution

It introduces the first measurement of femtoscopic correlations between K0s and K± particles in heavy-ion collisions, constraining the properties of the $a_0(980)$ resonance.

Findings

Correlation parameters for K0sK− and K0sK+ are consistent within uncertainties.

Results support the $a_0(980)$ resonance being a tetraquark rather than a diquark.

Mass and coupling parameters of the $a_0$ are constrained by the data.

Abstract

We present the first ever measurements of femtoscopic correlations between the K$^0_{\rm S}$ and K$^{\rm \pm}$ particles. The analysis was performed on the data from Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV measured by the ALICE experiment. The observed femtoscopic correlations are consistent with final-state interactions proceeding via the $a_0(980)$ resonance. The extracted kaon source radius and correlation strength parameters for K$^0_{\rm S}$K$^{\rm -}$ are found to be equal within the experimental uncertainties to those for K$^0_{\rm S}$K$^{\rm +}$. Comparing the results of the present study with those from published identical-kaon femtoscopic studies by ALICE, mass and coupling parameters for the $a_0$ resonance are constrained. Our results are also compatible with the interpretation of the $a_0$ having a tetraquark structure over that of a diquark.

Figures

Tables

Table 1. Table 1: The a 0 subscript 𝑎 0 a_{0} masses and coupling parameters, all in GeV (taken from Ref. [ 2 ] ).

Reference	$m_{a_0}$	${\gamma }_{a_{0}K\overline{K}}$	${\gamma }_{a_0\pi \eta }$
Martin [7]	0.974	0.333	0.222
Antonelli [8]	0.985	0.4038	0.3711
Achasov1 [9]	0.992	0.5555	0.4401
Achasov2 [9]	1.003	0.8365	0.4580

Table 2. Table 2: Fit results for R 𝑅 R and λ 𝜆 \lambda extracted in the present analysis from K S 0 subscript superscript absent 0 S {}^{0}_{\rm S} K ± femtoscopy averaged over K S 0 subscript superscript absent 0 S {}^{0}_{\rm S} K + and K S 0 subscript superscript absent 0 S {}^{0}_{\rm S} K - . Statistical and systematic errors are also shown.

Parameters	$R$ (fm) or $\lambda$	all $k_T$	GeV/$c$	$k_T>0.675$ GeV/$c$
Achasov2	$R$	$5.17\pm 0.16\pm 0.41$	$6.71\pm 0.40\pm 0.42$	$4.75\pm 0.18\pm 0.36$
	$\lambda$	$0.587\pm 0.034\pm 0.051$	$0.651\pm 0.073\pm 0.076$	$0.600\pm 0.040\pm 0.034$
Achasov1	$R$	$4.92\pm 0.15\pm 0.39$	$6.30\pm 0.40\pm 0.43$	$4.49\pm 0.18\pm 0.30$
	$\lambda$	$0.650\pm 0.038\pm 0.056$	$0.723\pm 0.087\pm 0.091$	$0.649\pm 0.048\pm 0.038$
Antonelli	$R$	$4.66\pm 0.17\pm 0.46$	$5.74\pm 0.36\pm 0.26$	$4.07\pm 0.18\pm 0.29$
	$\lambda$	$0.624\pm 0.044\pm 0.058$	$0.703\pm 0.085\pm 0.077$	$0.613\pm 0.052\pm 0.037$
Martin	$R$	$3.29\pm 0.12\pm 0.35$	$4.46\pm 0.25\pm 0.20$	$2.90\pm 0.11\pm 0.41$
	$\lambda$	$0.305\pm 0.020\pm 0.033$	$0.376\pm 0.041\pm 0.037$	$0.296\pm 0.021\pm 0.030$

Table 3. Table 3: Comparisons of R 𝑅 R and λ 𝜆 \lambda from K S 0 subscript superscript absent 0 S {}^{0}_{\rm S} K ± with identical kaon results.

Parameters	${\chi }_R^2/\mathrm{ndf}$	$R$ p-value	${\chi }_{\lambda }^2/\mathrm{ndf}$	$\lambda$ p-value	$⟨\frac{\lambda \left(K_S^0{K}^{\pm }\right)}{\lambda \left(KK\right)}⟩$
Achasov2	0.456	0.713	0.248	0.863	1.04$\pm$0.17
Achasov1	0.583	0.626	0.712	0.545	1.14$\pm$0.20
Antonelli	1.297	0.273	0.302	0.824	1.09$\pm$0.20
Martin	14.0	0.000	22.2	0.000	0.55$\pm$0.10

Equations

$$|{\mathrm{K}}_S^0⟩=\frac{1}{\sqrt{2}}\left(|{\mathrm{K}}^0⟩+|{\overline{\mathrm{K}}}^0⟩\right),$$

$$C(k^{\ast })=A(k^{\ast })/B(k^{\ast })$$

$$k^{\ast }=\sqrt{\frac{(s-m_{{\mathrm{K}}^0}^2-m_{{\mathrm{K}}^{\pm }}^2{)}^2-4m_{{\mathrm{K}}^0}^2{m}_{{\mathrm{K}}^{\pm }}^2}{4s}}$$

$$s=m_{{\mathrm{K}}^0}^2+m_{{\mathrm{K}}^{\pm }}^2+2E_{{\mathrm{K}}^0}{E}_{{\mathrm{K}}^{\pm }}-2{\vec{p}}_{{\mathrm{K}}^0}\cdot {\vec{p}}_{{\mathrm{K}}^{\pm }}$$

$${\Psi }_{-\vec{k}{}^{\ast }}(\vec{r}{}^{\ast })=e^{-i\vec{k}{}^{\ast }\cdot \vec{r}{}^{\ast }}+f(k^{\ast })\frac{e^{i{k}^{\ast }{r}^{\ast }}}{r^{\ast }},$$

$$f(k^{\ast })=\frac{{\gamma }_{a_0\to \mathrm{K}\overline{\mathrm{K}}}}{m_{a_0}^2-s-i({\gamma }_{a_0\to \mathrm{K}\overline{\mathrm{K}}}{k}^{\ast }+{\gamma }_{a_0\to \pi \eta }{k}_{\pi \eta })}.$$

$$C(\vec{k}{}^{\ast })=\int {\mathrm{d}}^3\vec{r}{}^{\ast }S(\vec{r}{}^{\ast }){\left|{\Psi }_{-\vec{k}{}^{\ast }}(\vec{r}{}^{\ast })\right|}^2,$$

$$S(\vec{r}{}^{\ast })\sim e^{-{|\vec{r}{}^{\ast }|}^2/(4R^2)}.$$

$$C(k^{\ast })=1+\lambda \alpha \left[\frac{1}{2}{\left|\frac{f(k^{\ast })}{R}\right|}^2+\frac{2\mathcal{R}f(k^{\ast })}{\sqrt{\pi }R}{F}_1(2k^{\ast }R)-\frac{\mathcal{I}f(k^{\ast })}{R}{F}_2(2k^{\ast }R)\right],$$

$$F_1(z)\equiv \frac{\sqrt{\pi }{e}^{-z^2}\mathrm{erfi}(z)}{2z};F_2(z)\equiv \frac{1-e^{-z^2}}{z}.$$

$$C_{raw}^{fit}(k^{\ast })=a(1-b{k}^{\ast }+c{k}^{\ast 2})C(k^{\ast })$$

$${\chi }_{\omega }^2/\mathrm{ndf}=\frac{1}{\nu }\sum _{i=1}^3\frac{[{\omega }_i(K_{\mathrm{S}}^0{K}^{\pm })-{\omega }_i(KK){]}^2}{{\sigma }_i^2}$$

Full text

\PHyear2017 \PHnumber063 \PHdate06 Apr

\ShortTitleK${}^{0}_{\rm S}$K± interaction using Pb-Pb collisions

\CollaborationALICE Collaboration††thanks: See Appendix A for the list of collaboration members \ShortAuthorALICE Collaboration

We present the first ever measurements of femtoscopic correlations between the K${}^{0}_{\rm S}$ and K± particles. The analysis was performed on the data from Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV measured by the ALICE experiment. The observed femtoscopic correlations are consistent with final-state interactions proceeding 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+. Comparing the results of the present study with those from published identical-kaon femtoscopic studies by ALICE, mass and coupling parameters for the $a_{0}$ resonance are tested. Our results are also compatible with the interpretation of the $a_{0}$ having a tetraquark structure instead of that of a diquark.

1 Introduction

Identical boson femtoscopy, especially of identical charged pions, has been used extensively over the years to study experimentally the space-time geometry of the collision region in high-energy particle and heavy-ion collisions [1]. Identical-kaon femtoscopy studies have also been carried out, recent examples of which are the ones with Au-Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV by the STAR Collaboration [2] (K${}^{0}_{\rm S}$K${}^{0}_{\rm S}$) and with pp at $\sqrt{s}=7$ TeV and Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV by the ALICE Collaboration [3, 4, 5] (K${}^{0}_{\rm S}$K${}^{0}_{\rm S}$ and K*±K±*). The pair-wise interactions between the identical kaons that form the basis for femtoscopy are for K±K± quantum statistics and the Coulomb interaction, and for K${}^{0}_{\rm S}$K${}^{0}_{\rm S}$ quantum statistics and the final-state interaction through the $f_{0}(980)/a_{0}(980)$ threshold resonances.

One can also consider the case of non-identical kaon pairs, e.g. K${}^{0}_{\rm S}$K± pairs. Besides the non-resonant channels which may be present, e.g. non-resonant elastic scattering or free-streaming of the kaons from their freeze-out positions to the detector, the other only pair-wise interaction allowed for a K${}^{0}_{\rm S}$K± pair at freeze out from the collision system is a final-state interaction (FSI) through the $a_{0}(980)$ resonance. The other pair-wise interactions present for identical-kaon pairs are not present for K${}^{0}_{\rm S}$K± pairs because: a) there is no quantum statistics enhancement since the kaons are not identical, b) there is no Coulomb effect since one of the kaons is uncharged, and c) there is no strong FSI through the $f_{0}$ resonance since the kaon pair is in an $I=1$ isospin state, as is the $a_{0}$, whereas the $f_{0}$ is an $I=0$ state.

Another feature of the K${}^{0}_{\rm S}$K± FSI through the $a_{0}$ resonance is, due to the $a_{0}$ having strangeness $S=0$ and the K${}^{0}_{\rm S}$ being a linear combination of the K0 and ${\rm\overline{K}^{0}}$,

[TABLE]

only the ${\rm\overline{K}^{0}}$K+ pair from K${}^{0}_{\rm S}$K+ and the K0K- pair from K${}^{0}_{\rm S}$K- have $S=0$ and thus can form the $a_{0}$ resonance. This allows the possibility to study the K0 and ${\rm\overline{K}^{0}}$ sources separately since they are individually selected by studying K${}^{0}_{\rm S}$K- and K${}^{0}_{\rm S}$K+ pairs, respectively. An additional consequence of this feature is that only $50\%$ of either the K${}^{0}_{\rm S}$K- or K${}^{0}_{\rm S}$K+ detected pairs will pass through the $a_{0}$ resonance. This is taken into account in the expression for the model used to fit the correlation functions.

On the other hand, the natural requirement that the source sizes extracted from the K${}^{0}_{\rm S}$K± femtoscopy agree with those obtained for the K${}^{0}_{\rm S}$K${}^{0}_{\rm S}$ and K±K± systems allows one to study the properties of the $a_{0}$ resonance itself. This is interesting in its own right since many studies discuss the possibility that the $a_{0}$, listed by the Particle Data Group as a diquark light unflavored meson state [6], could be a four-quark state, i.e. a tetraquark, or a “${\rm\overline{K}}-$K molecule” [7, 8, 9, 10, 11, 12]. For example, 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 quarks in the kaons to the $a^{-}_{0}$. The results from K${}^{0}_{\rm S}$K- femtoscopy might be sensitive to these two different scenarios.

In this Letter, results from the first study of K${}^{0}_{\rm S}$K± femtoscopy are presented. This has been done for Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV measured by the ALICE experiment at the LHC [13]. 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, and
3. test published $a_{0}$ mass and coupling parameters by comparisons with published identical kaon results [5].

2 Description of experiment and data Selection

The ALICE experiment and its performance in the LHC Run 1 $(2009-2013)$ are described in Ref. [13] and Ref. [14, 15], respectively. About $22\times 10^{6}$ Pb-Pb collision events with [math]–$10\%$ centrality class taken in 2011 were used in this analysis (the average centrality in this range is 4.9% due to a slight trigger inefficiency in the 8-10% range). Events were classified according to their centrality using the measured amplitudes in the V0 detectors, which consist of two arrays of scintillators located along the beamline and covering the full azimuth [16]. Charged particles were reconstructed and identified with the central barrel detectors located within a solenoid magnet with a field strength of $B=0.5$ T. Charged particle tracking was performed using the Time Projection Chamber (TPC) [17] and the Inner Tracking System (ITS) [13]. The ITS allowed for high spatial resolution in determining the primary (collision) vertex. Tracks were reconstructed and their momenta were obtained with the TPC. A momentum resolution of less than 10 MeV/$c$ was typically obtained for the charged tracks of interest in this analysis. 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, the track selections based on the quality of track reconstruction fit and the number of detected tracking points in the TPC were used to ensure that only well-reconstructed tracks were taken in the analysis [14, 15].

Particle identification (PID) for reconstructed tracks was carried out using both the TPC and the Time-of-Flight (TOF) detector in the pseudorapidity range $|\eta|<0.8$ [14, 15]. For each PID method, a value was assigned to each track denoting the number of standard deviations between the measured track information and calculated values ($N_{\sigma}$) [5, 14, 15]. 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”—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 Pb-Pb K${}^{0}_{\rm S}$K${}^{0}_{\rm S}$ and K±K± analyses [5]. 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 and TOF detectors. 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 $N_{\sigma TPC}<3$ and $N_{\sigma TOF}<3$ 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/$c^{2}$.

2.1.2 K± selection

Charged kaon tracks were also detected using the TPC and TOF detectors, and were accepted if they were within the range $0.14<p_{\rm T}<1.5$ GeV/$c$. In order to reduce the number of secondaries (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 $N_{\sigma TPC}<2$ 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/$c$: $N_{\sigma TPC}<3$ and $N_{\sigma TOF}<2$ ($0.5<p_{\rm T}<0.8$ GeV/$c$), $N_{\sigma TOF}<1.5$ ($0.8<p_{\rm T}<1.0$ GeV/$c$), $N_{\sigma TOF}<1$ ($1.0<p_{\rm T}<1.5$ GeV/$c$).

K${}^{0}_{\rm S}$K± experimental pair purity was estimated from a Monte Carlo (MC) study based on HIJING [18] simulations 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 actual K${}^{0}_{\rm S}$K± pairs input from HIJING. The pair purity was estimated to be 88% for all kinematic regions studied in this analysis.

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

[TABLE]

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),

[TABLE]

where,

[TABLE]

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 particles from ten other events. The vertexes of the mixed events were constrained to be within 2 cm of each other in the $z$-direction. A centrality constraint on the mixed events was found not to be necessary for the narrow centrality range, i.e. [math]–$10\%$, used in this analysis. Correlation functions were obtained separately for two different magnetic field orientations in the experiment and then either averaged or fit separately, depending on the fitting method used (see below).

Correlation functions were measured for three overlapping/non-exclusive pair transverse momentum ($k_{\rm T}=|\textbf{p}_{\rm T,1}+\textbf{p}_{\rm T,2}|/2$) bins: all $k_{\rm T}$, $k_{\rm T}<0.675$ and $k_{\rm T}>0.675$ GeV/$c$. The mean $k_{\rm T}$ values for these three bins were 0.675, 0.425 and 0.970 GeV/$c$, respectively. Figure 1 shows sample raw K${}^{0}_{\rm S}$K+ correlation functions for these three bins for one of the magnetic field orientations. One can see the main feature of the femtoscopic correlation function: the suppression due to the strong final-state interactions for small $k^{*}$. In the higher $k^{*}$ region, the effects of the $a_{0}$ appear to not be present and thus could be used as a reference, i.e. “baseline”, for the $a_{0}$-based model fitted to $C(k^{*})$ in order to extract the source parameters. Also shown in the figure are linear fits to the baseline for large $k^{*}$. The effects on $C(k^{*})$ by the $a_{0}$ resonance are mostly seen in the $k^{*}<0.2$ GeV/$c$ region, where the width of the $a_{0}$ region reflects the size of the kaon source (see equations below).

Correlation functions were corrected for momentum resolution effects using HIJING calculations. HIJING was used to create two correlation functions: one in terms of the generator-level $k^{*}$ and one in terms of the simulated detector-level $k^{*}$. Because HIJING does not incorporate final-state interactions, weights were calculated using a 9th-order polynomial fit in $k^{*}$ to an experimental correlation function and were used when filling the same-event distributions. These weights were calculated using $k^{*}$. 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 several percent.

3.2 Final-state interaction model

The K${}^{0}_{\rm S}$K± correlation functions were fit with functions 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, $a_{0}$(980). 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. [2] 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 a plane wave and an outgoing spherical wave,

[TABLE]

where $f(k^{*})$ is the $s$-wave K0K- or $\overline{\rm K}^{0}$K+ scattering amplitude whose contribution is the $s$-wave isovector $a_{0}$ resonance (see Eq. 11 in Ref. [2]),

[TABLE]

In Eq. 6, $m_{a_{0}}$ 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 $\overline{\rm K}^{0}$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 Table 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]

[TABLE]

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

[TABLE]

Equation 7 can be integrated analytically for K${}^{0}_{\rm S}$K± correlations with FSI for the one-dimensional case, with the result

[TABLE]

where

[TABLE]

In the above equations $\alpha$ is the fraction of K${}^{0}_{\rm S}$K*±* pairs that come from the K0K- or $\overline{\rm K}^{0}$K+ system, set to 0.5 assuming symmetry in K0 and $\overline{\rm K}^{0}$ production [2], $R$ is the radius parameter from the spherical Gaussian source distribution given in Eq. 8, 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. Note that the form of the FSI term in Eq. 9 differs from the form of the FSI term for $\rm K^{0}_{S}\rm K^{0}_{S}$ correlations (Eq. 9 of Ref. [2]) 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. 5.

As seen in Eq. 6, the K0K- or $\overline{\rm K}^{0}$K+ s-wave scattering amplitude depends on the $a_{0}$ mass and decay couplings. In the present work, we have taken the values used in Ref. [2] which have been extracted from the analysis of the $a_{0}\rightarrow\pi\eta$ spectra of several experiments [7, 8, 10, 9], shown in Table 1. The extracted $a_{0}$ mass and decay couplings have a range of values for the various references. Except for the Martin reference [7], which extracts the $a_{0}$ values from the reaction 4.2 GeV/$c$ incident momentum K${}^{-}+p\rightarrow\Sigma^{+}(1385)\pi^{-}\eta$ using a two-channel Breit-Wigner formula, the other references extract the $a_{0}$ values from the radiative $\phi$-decay data, i.e. $\phi\rightarrow\pi^{0}\eta\gamma$, from the KLOE collaboration [24]. These latter three references apply a model that assumes, after taking into account the $\phi\rightarrow\pi^{0}\rho^{0}\rightarrow\pi^{0}\eta\gamma$ background process, that the $\phi$ decays to the $\pi^{0}\eta\gamma$ final state through the intermediate processes $\phi\rightarrow{\rm K}^{+}{\rm K}^{-}\gamma\rightarrow a_{0}\gamma$ or $\phi\rightarrow{\rm K}^{+}{\rm K}^{-}\rightarrow a_{0}\gamma$, i.e. the “charged kaon loop model” [9]. The main difference between these analyses is that the Antonelli reference [8] assumes a fixed $a_{0}$ mass in the fit of this model to the $\pi^{0}\eta$ data, whereas the Achasov1 and Achasov2 analyses [9] allow the $a_{0}$ mass to be a free parameter in the two different fits made to the data. It is assumed in the present analysis that these decay couplings will also be valid for K0K- and $\overline{\rm K}^{0}$K+ scattering due to isospin invariance. Correlation functions were fitted with all four of these cases to see the effect on the extracted source parameters.

3.3 Fitting methods

In order to estimate the systematic errors in the fitting method used to extract $R$ and $\lambda$ using Eq. 9, two different methods, judged to be equally valid, have been used to handle the effects of the baseline: 1) a separate linear fit to the “baseline region,” followed by fitting Eq. 9 to the correlation function divided by the linear fit to extract the source parameters, and 2) a combined fit of Eq. 9 and a quadratic function describing the baseline where the source parameters and the parameters of the quadratic function are fitted simultaneously. The source parameters are extracted for each case from both methods and averaged, the symmetric systematic error for each case due to the fitting method being one-half of the difference between the two methods. Both fitting methods will now be described in more detail.

3.3.1 Linear baseline method

In the “linear baseline method,” for the all $k_{\rm T}$, $k_{\rm T}<0.675$ and $k_{\rm T}>0.675$ GeV/$c$ bins the $a_{0}$ regions were taken to be $k^{*}<0.3$, $k^{*}<0.2$ and $k^{*}<0.4$ GeV/$c$, respectively. In the higher $k^{*}$ region it was assumed that effects of the $a_{0}$ were not present and thus can be used as a reference, i.e. “baseline”, for the $a_{0}$-based model fitted to $C(k^{*})$, which was averaged over the two magnetic field orientations used in the experiment, to extract the source parameters. For the three $k_{\rm T}$ bins, linear fits were made in the $k^{*}$ ranges $0.3$–$0.45$, $0.2$–$0.45$ and $0.4$–$0.6$ GeV/$c$, respectively, and the correlation functions were divided by these fits to remove baseline effects extending into the low-$k^{*}$ region. These ranges were taken to define the baselines since the measured correlation functions were found to be linear here. For larger values of $k^{*}$ the correlation functions became non-linear. The baseline was studied using HIJING MC calculations which take into account the detector characteristics as described earlier. The $C(k^{*})$ distributions obtained from HIJING do not show suppressions at low $k^{*}$ as seen in Fig. 1 but rather show linear distributions over the entire ranges in $k^{*}$ shown in the figure. HIJING also shows the baseline becoming non-linear for larger values of $k^{*}$, as seen in the measurements. The MC generator code AMPT [25] was also used to study the baseline. AMPT is similar to HIJING but also includes final-state rescattering effects. AMPT calculations also showed linear baselines in the $k^{*}$ ranges used in the present analysis, becoming non-linear for larger $k^{*}$. Both HIJING and AMPT qualitatively show the same direction of changes in the slopes of the baseline vs. $k_{\rm T}$ as seen in the data, but AMPT more accurately described the slope values themselves, suggesting that final-state rescattering plays a role in the $k_{\rm T}$ dependence of the baseline slope. The systematic uncertainties on the extracted source parameters due to the assumption of linearity in these $k^{*}$ regions were estimated from HIJING to be less than 1%.

Figure 2 shows examples of K${}^{0}_{\rm S}$K+ and K${}^{0}_{\rm S}$K- correlation functions divided by linear fits to the baseline with Eq. 9 using the Achasov2 parameters. One can see the main feature of the femtoscopic correlation function: the suppression due to the strong final-state interactions for small $k^{*}$. As seen, the $a_{0}$ FSI parameterization gives an excellent representation of the “signal region” of the data, i.e. the suppression of the correlation functions in the $k^{*}$ range 0 to about 0.15 GeV/$c$.

3.3.2 Quadratic baseline method

In the “quadratic baseline method,” $R$ and $\lambda$ are extracted assuming a quadratic baseline function by fitting the product of a quadratic function and the Lednicky equation, Eq. 9, to the raw correlation functions for each of the two magnetic field orientations used in the experiment, such as shown in Fig. 1, i.e. ,

[TABLE]

where $C(k^{*})$ is given by Eq. 9, and $a$, $b$ and $c$ are fit parameters. Eq. 11 is fit to the same $k^{*}$ ranges as shown in Fig. 1, i.e. [math]–$0.45$ GeV/$c$ for all $k_{\rm T}$ and $k_{\rm T}<0.675$ GeV/$c$, and [math]–$0.6$ GeV/$c$ for $k_{\rm T}>0.675$ GeV/$c$. The fits to the experimental correlation functions are found to be of similar good quality as seen for the linear baseline method fits shown in Fig. 2.

3.4 Systematic uncertainties

Systematic uncertainties on the extracted source parameters were estimated by varying the ranges of kinematic and PID cut values on the data by $\pm 10\%$ and $\pm 20\%$, as well as from MC simulations. The main systematic uncertainties on the extracted values of $R$ and $\lambda$ due to various sources, not including the baseline fitting method, are: a) $k^{*}$ fitting range: 2%, b) single-particle and pair cuts (e.g. DCA cuts, PID cuts, pair separation cuts): $2\%$–$4\%$ for $R$ and $3\%$–$8\%$ for $\lambda$, and c) pair purity: 1% on $\lambda$. Combining the individual systematic uncertainties in quadrature, the total systematic uncertainties on the extracted source parameters, not including the baseline fitting method contribution, are in the ranges $3\%$–$5\%$ for $R$ and $4\%$–$8\%$ for $\lambda$.

As mentioned earlier, for the two fitting methods, the source parameters are extracted for each case from both methods and averaged, the symmetric systematic error for each case due to the fitting method being one-half of the difference between the two methods. The baseline fitting method systematic error thus obtained is added in quadrature with the systematic errors given above. It is found that the size of the baseline fitting method systematic errors are about 50% larger for $R$ and of similar magnitude for $\lambda$ as those quoted above for the non-fitting-method systematic errors.

4 Results and discussion

Figure 3 shows sample results for the $R$ and $\lambda$ parameters extracted in the present analysis from K${}^{0}_{\rm S}$K± femtoscopy using the Achasov1 parameters. The left column compares K${}^{0}_{\rm S}$K+ and K${}^{0}_{\rm S}$K- results from the quadratic baseline fit method, and the right column compares results averaged over K${}^{0}_{\rm S}$K+ and K${}^{0}_{\rm S}$K- for the quadratic baseline fits and the linear baseline fits. As it is usually the case in femtoscopic analyses, the fitted $R$ and $\lambda$ parameters are correlated. The fitting (statistical) uncertainties are taken to be the extreme values of the $1\sigma$ fit contours in $R$ vs. $\lambda$. Statistical uncertainties are plotted for all results. It is seen in the figure that the $R$ and $\lambda$ values for K${}^{0}_{\rm S}$K- have a slight tendency to be larger than those for K${}^{0}_{\rm S}$K+. Such a difference could result from the K- – nucleon scattering cross section being larger than that for K+ – nucleon (see Fig. 51.9 of Ref. [6]), possibly resulting in more final-state rescattering for the K-. Since the difference is not significant once systematic uncertainties are taken into account, K${}^{0}_{\rm S}$K+ and K${}^{0}_{\rm S}$K- are averaged over in the final results. The difference in the extracted parameters between the two baseline fitting methods is also seen to be small, and is accounted for as a systematic error, as described earlier.

The results for the $R$ and $\lambda$ parameters extracted in the present analysis from K${}^{0}_{\rm S}$K± femtoscopy, averaged over the two baseline fit methods and averaged over K${}^{0}_{\rm S}$K+ and K${}^{0}_{\rm S}$K-, are presented in Table 2 and in Figs. 4 and 5. Fit results are shown for all four parameter sets given in Table 1. Figs. 4 and 5 also show comparisons with identical kaon results for the same collision system and energy from ALICE from Ref. [5]. Statistical and total uncertainties are shown for all results.

As shown in Fig. 4, both Achasov parameter sets, with the larger $a_{0}$ masses and decay couplings, appear to give $R$ values that agree best with those obtained from identical-kaon femtoscopy. The Antonelli parameter set appears to give slightly lower values. Comparing the measured $R$ values between K${}^{0}_{\rm S}$K${}^{0}_{\rm S}$ and K*±K±* in Fig. 4 they are seen to agree with each other within the uncertainties. In fact, the only reason for the femtoscopic K${}^{0}_{\rm S}$K± radii to be different from the K${}^{0}_{\rm S}$K${}^{0}_{\rm S}$ and K*±K±* ones would be if the K${}^{0}_{\rm S}$ and K*±* sources were displaced with respect to each other. This is not expected because the collision dynamics is governed by strong interactions for which the isospin symmetry applies.

The results for the correlation strength parameters $\lambda$ are shown in Fig. 5. The $\lambda$ parameters from K${}^{0}_{\rm S}$K± and K*±K±* are corrected for experimental purity [5].The K${}^{0}_{\rm S}$K${}^{0}_{\rm S}$ pairs have a high purity of $>90\%$, so the corresponding correction was neglected [5](see the earlier discussion on purity). Statistical and total uncertainties are shown for all results.

The K${}^{0}_{\rm S}$K± $\lambda$ values, with the exception of the Martin parameters, appear to be in agreement with the $\lambda$ values for the identical kaons. All of the $\lambda$ values are seen to be measured to be about 0.6, i.e. less than the ideal value of unity, which can be due to the contribution of kaons from K∗ decay ($\Gamma\sim 50$ MeV, where $\Gamma$ is the decay width) and from other long-lived resonances (such as the $D$-meson) distorting the spatial kaon source distribution away from the ideal Gaussian which is assumed in the fit function [26]. One would expect that the K${}^{0}_{\rm S}$K± $\lambda$ values agree with those from the identical kaons if the FSI for the K${}^{0}_{\rm S}$K± went solely through the $a_{0}$ resonant channel since this analysis should see the same source distribution.

In order to obtain a more quantitative comparison of the present results for $R$ and $\lambda$ with the identical kaon results, the $\chi^{2}/{\rm ndf}$ is calculated for $R$ and $\lambda$ for each parameter set,

[TABLE]

where $\omega$ is either $R$ or $\lambda$, $i$ runs over the three $k_{T}$ values, the number of degrees of freedom taken is ${\rm ndf}=3$ and $\sigma_{i}$ is the sum of the statistical and systematic uncertainties on the $i^{th}$ K${}^{0}_{\rm S}$K± extracted parameter (Note that the all $k_{\rm T}$ bin indeed contains the kaon pairs that make up the $k_{\rm T}<0.675$ GeV/$c$ and $k_{\rm T}>0.675$ GeV/$c$ bins, but in addition it contains an equal number of new pair combinations between the kaons in the $k_{\rm T}<0.675$ GeV/$c$ and $k_{\rm T}>0.675$ GeV/$c$ bins. So for the purposes of this simple comparison, we approximate the all $k_{\rm T}$ bin as being independent). The linear sum of the statistical and systematic uncertainties is used for $\sigma_{i}$ to be consistent with the linear sum of the statistical and systematic uncertainties plotted on the points in Figs. 4 and  5. The quantity $\omega_{i}(KK)$ is determined by fitting a quadratic to the identical kaon results and evaluating the fit at the average $k_{T}$ values of the K${}^{0}_{\rm S}$K± measurements. Table 3 summarizes the results for each parameter set and the extracted p-values. As seen, the Achasov2, Achasov1 and Antonelli parameter sets are consistent with the identical kaon results for both $R$ and $\lambda$. The Martin parameter set is seen to have vanishingly small p-values for both $R$ and $\lambda$ and is thus in clear disagreement with the identical kaon results, as can easily be seen by examining Figs. 4 and 5.

In order to quantitatively estimate the size of the non-resonant channel present, the ratio $\left\langle\frac{\lambda(K^{0}_{\rm S}K^{\rm\pm})}{\lambda(KK)}\right\rangle$ has been calculated for each parameters set, where the average is over the three $k_{T}$ values and the uncertainty is calculated from the average of the statistical+systematic uncertainties on the K${}^{0}_{\rm S}$K± parameters. These values are shown in the last column of Table 3. Disregarding the Martin value, the smallest value this ratio can take within the uncertainties is 0.87 (from the Achasov2 paramters) which would thus allow at most a 13% non-resonant contribution.

The results of this study presented above clearly show that the measured K${}^{0}_{\rm S}$K± have dominantly undergone a FSI through the $a_{0}$ resonance. This is remarkable considering that we measure in Pb-Pb collisions the average separation between the two kaons at freeze out to be $\sim 5$ fm, and due to the short-ranged nature of the strong interaction of $\sim 1$ fm this would seem to not encourage a FSI but rather encourage free-streaming of the kaons to the detector resulting in a “flat” correlation function. A dominant FSI is what might be expected if the $a_{0}$ would be a four-quark, i.e. tetraquark, state or a “${\rm\overline{K}}-$K molecule.” There appears to be no calculations in the literature for the tetraquark vs. diquark production cross sections for the interaction ${\rm K\overline{K}}\rightarrow a_{0}$, but qualitative arguments compatible with the $a_{0}$ being a four–quark state can be made based on the present measurements. The main argument in favor of this is that the reaction channel ${\rm K}^{0}{\rm K}^{-}\rightarrow a^{-}_{0}$ ($\overline{\rm K}^{0}$K${}^{+}\rightarrow a^{+}_{0}$) is strongly favored if the $a^{-}_{0}$ ($a^{+}_{0}$) is composed of ${\rm d\overline{s}s\overline{u}}$ (${\rm\overline{d}s\overline{s}u}$) quarks such that a direct transfer of the quarks in the kaons to the $a^{-}_{0}$ ($a^{+}_{0}$) has taken place, since this is an “OZI superallowed” reaction [12]. The “OZI rule” can be stated as “an inhibition associated with the creation or annihilation of quark lines” [12]. Thus, a diquark $a_{0}$ final state is less favored according to the OZI rule since it would require the annihilation of the strange quarks in the kaon interaction. This would allow for the possibility of a significant non-resonant or free-streaming channel for the kaon interaction that would result in a $\lambda$ value below the identical-kaon value by diluting the $a_{0}$ signal. As mentioned above, the collision geometry itself also suppresses the annihilation of the strange quarks due to the large separation between the kaons at freeze out. Note that this assumes that the $C(k^{*})$ distribution of a non-resonant channel would be mostly “flat” or “monotonic” in shape and not showing a strong resonant-like signal as seen for the $a_{0}$ in Fig. 1 and Fig. 2. This assumption is clearly true in the free-streaming case, which is assumed in Eq. 9 in setting $\alpha=0.5$ due to the non-resonant kaon combinations. A similar argument, namely that the success of the “charged kaon loop model” in describing the radiative $\phi$-decay data favors the $a_{0}$ as a tetraquark state, is given in Ref. [9].

5 Summary

In summary, femtoscopic correlations with K${}^{0}_{\rm S}$K± pairs have been studied for the first time. This new femtoscopic method was applied to data from central Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV by the LHC ALICE experiment. Correlations in the K${}^{0}_{\rm S}$K± pairs are produced by final-state interactions which proceed through the a0(980) resonance. The $a_{0}$ resonant FSI is seen to give an excellent representation of the shape of the signal region in the present study. The differences between ${\rm\overline{K}^{0}}$K+ and K0K- for the extracted $R$ and $\lambda$ values are found to be insignificant within the uncertainties of the present study. The three larger $a_{0}$ mass and decay parameter sets are favored by the comparison with the identical kaon results. The present results are also compatible with the interpretation of the $a_{0}$ resonance as a tetraquark state. This work should provide a constraint on models that are used to predict kaon-kaon interactions [27, 28]. It will be interesting to apply K${}^{0}_{\rm S}$K± femtoscopy to other collision energies, e.g. the higher LHC energies now available, and bombarding species, e.g. proton-proton collisions, since the different source sizes encountered in these cases will probe the interaction of the K${}^{0}_{\rm S}$ with the K± in different sensitivity ranges (i.e. see the $R$ dependence in Eq. 9).

Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of China (MSTC), National Natural Science Foundation of China (NSFC) and Ministry of Education of China (MOEC) , China; Ministry of Science, Education and Sport and Croatian Science Foundation, Croatia; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research — Natural Sciences, the Carlsberg Foundation and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE) and Council of Scientific and Industrial Research (CSIR), New Delhi, India; Indonesian Institute of Science, Indonesia; Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education and National Science Centre, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Romanian National Agency for Science, Technology and Innovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation and National Research Centre Kurchatov Institute, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba, Ministerio de Ciencia e Innovacion and Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Spain; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; National Science and Technology Development Agency (NSDTA), Suranaree University of Technology (SUT) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.

Appendix A The ALICE Collaboration

S. Acharya${}^{\textrm{\scriptsize 139}}$, D. Adamová${}^{\textrm{\scriptsize 96}}$, J. Adolfsson${}^{\textrm{\scriptsize 34}}$, M.M. Aggarwal${}^{\textrm{\scriptsize 101}}$, G. Aglieri Rinella${}^{\textrm{\scriptsize 35}}$, M. Agnello${}^{\textrm{\scriptsize 31}}$, N. Agrawal${}^{\textrm{\scriptsize 48}}$, Z. Ahammed${}^{\textrm{\scriptsize 139}}$, N. Ahmad${}^{\textrm{\scriptsize 17}}$, S.U. Ahn${}^{\textrm{\scriptsize 80}}$, S. Aiola${}^{\textrm{\scriptsize 143}}$, A. Akindinov${}^{\textrm{\scriptsize 65}}$, S.N. Alam${}^{\textrm{\scriptsize 139}}$, J.L.B. Alba${}^{\textrm{\scriptsize 114}}$, D.S.D. Albuquerque${}^{\textrm{\scriptsize 125}}$, D. Aleksandrov${}^{\textrm{\scriptsize 92}}$, B. Alessandro${}^{\textrm{\scriptsize 59}}$, R. Alfaro Molina${}^{\textrm{\scriptsize 75}}$, A. Alici${}^{\textrm{\scriptsize 54}}$,${}^{\textrm{\scriptsize 12}}$,${}^{\textrm{\scriptsize 27}}$, A. Alkin${}^{\textrm{\scriptsize 3}}$, J. Alme${}^{\textrm{\scriptsize 22}}$, T. Alt${}^{\textrm{\scriptsize 71}}$, L. Altenkamper${}^{\textrm{\scriptsize 22}}$, I. Altsybeev${}^{\textrm{\scriptsize 138}}$, C. Alves Garcia Prado${}^{\textrm{\scriptsize 124}}$, M. An${}^{\textrm{\scriptsize 7}}$, C. Andrei${}^{\textrm{\scriptsize 89}}$, D. Andreou${}^{\textrm{\scriptsize 35}}$, H.A. Andrews${}^{\textrm{\scriptsize 113}}$, A. Andronic${}^{\textrm{\scriptsize 109}}$, V. Anguelov${}^{\textrm{\scriptsize 106}}$, C. Anson${}^{\textrm{\scriptsize 99}}$, T. Antičić${}^{\textrm{\scriptsize 110}}$, F. Antinori${}^{\textrm{\scriptsize 57}}$, P. Antonioli${}^{\textrm{\scriptsize 54}}$, R. Anwar${}^{\textrm{\scriptsize 127}}$, L. Aphecetche${}^{\textrm{\scriptsize 117}}$, H. Appelshäuser${}^{\textrm{\scriptsize 71}}$, S. Arcelli${}^{\textrm{\scriptsize 27}}$, R. Arnaldi${}^{\textrm{\scriptsize 59}}$, O.W. Arnold${}^{\textrm{\scriptsize 107}}$,${}^{\textrm{\scriptsize 36}}$, I.C. Arsene${}^{\textrm{\scriptsize 21}}$, M. Arslandok${}^{\textrm{\scriptsize 106}}$, B. Audurier${}^{\textrm{\scriptsize 117}}$, A. Augustinus${}^{\textrm{\scriptsize 35}}$, R. Averbeck${}^{\textrm{\scriptsize 109}}$, M.D. Azmi${}^{\textrm{\scriptsize 17}}$, A. Badalà${}^{\textrm{\scriptsize 56}}$, Y.W. Baek${}^{\textrm{\scriptsize 79}}$,${}^{\textrm{\scriptsize 61}}$, S. Bagnasco${}^{\textrm{\scriptsize 59}}$, R. Bailhache${}^{\textrm{\scriptsize 71}}$, R. Bala${}^{\textrm{\scriptsize 103}}$, A. Baldisseri${}^{\textrm{\scriptsize 76}}$, M. Ball${}^{\textrm{\scriptsize 45}}$, R.C. Baral${}^{\textrm{\scriptsize 68}}$, A.M. Barbano${}^{\textrm{\scriptsize 26}}$, R. Barbera${}^{\textrm{\scriptsize 28}}$, F. Barile${}^{\textrm{\scriptsize 53}}$,${}^{\textrm{\scriptsize 33}}$, L. Barioglio${}^{\textrm{\scriptsize 26}}$, G.G. Barnaföldi${}^{\textrm{\scriptsize 142}}$, L.S. Barnby${}^{\textrm{\scriptsize 113}}$,${}^{\textrm{\scriptsize 95}}$, V. Barret${}^{\textrm{\scriptsize 82}}$, P. Bartalini${}^{\textrm{\scriptsize 7}}$, K. Barth${}^{\textrm{\scriptsize 35}}$, J. Bartke${}^{\textrm{\scriptsize 121}}$\Aref0, E. Bartsch${}^{\textrm{\scriptsize 71}}$, M. Basile${}^{\textrm{\scriptsize 27}}$, N. Bastid${}^{\textrm{\scriptsize 82}}$, S. Basu${}^{\textrm{\scriptsize 139}}$,${}^{\textrm{\scriptsize 141}}$, B. Bathen${}^{\textrm{\scriptsize 72}}$, G. Batigne${}^{\textrm{\scriptsize 117}}$, A. Batista Camejo${}^{\textrm{\scriptsize 82}}$, B. Batyunya${}^{\textrm{\scriptsize 78}}$, P.C. Batzing${}^{\textrm{\scriptsize 21}}$, I.G. Bearden${}^{\textrm{\scriptsize 93}}$, H. Beck${}^{\textrm{\scriptsize 106}}$, C. Bedda${}^{\textrm{\scriptsize 64}}$, N.K. Behera${}^{\textrm{\scriptsize 61}}$, I. Belikov${}^{\textrm{\scriptsize 135}}$, F. Bellini${}^{\textrm{\scriptsize 27}}$, H. Bello Martinez${}^{\textrm{\scriptsize 2}}$, R. Bellwied${}^{\textrm{\scriptsize 127}}$, L.G.E. Beltran${}^{\textrm{\scriptsize 123}}$, V. Belyaev${}^{\textrm{\scriptsize 85}}$, G. Bencedi${}^{\textrm{\scriptsize 142}}$, S. Beole${}^{\textrm{\scriptsize 26}}$, A. Bercuci${}^{\textrm{\scriptsize 89}}$, Y. Berdnikov${}^{\textrm{\scriptsize 98}}$, D. Berenyi${}^{\textrm{\scriptsize 142}}$, R.A. Bertens${}^{\textrm{\scriptsize 130}}$, D. Berzano${}^{\textrm{\scriptsize 35}}$, L. Betev${}^{\textrm{\scriptsize 35}}$, A. Bhasin${}^{\textrm{\scriptsize 103}}$, I.R. Bhat${}^{\textrm{\scriptsize 103}}$, A.K. Bhati${}^{\textrm{\scriptsize 101}}$, B. Bhattacharjee${}^{\textrm{\scriptsize 44}}$, J. Bhom${}^{\textrm{\scriptsize 121}}$, L. Bianchi${}^{\textrm{\scriptsize 127}}$, N. Bianchi${}^{\textrm{\scriptsize 51}}$, C. Bianchin${}^{\textrm{\scriptsize 141}}$, J. Bielčík${}^{\textrm{\scriptsize 39}}$, J. Bielčíková${}^{\textrm{\scriptsize 96}}$, A. Bilandzic${}^{\textrm{\scriptsize 36}}$,${}^{\textrm{\scriptsize 107}}$, R. Biswas${}^{\textrm{\scriptsize 4}}$, S. Biswas${}^{\textrm{\scriptsize 4}}$, J.T. Blair${}^{\textrm{\scriptsize 122}}$, D. Blau${}^{\textrm{\scriptsize 92}}$, C. Blume${}^{\textrm{\scriptsize 71}}$, G. Boca${}^{\textrm{\scriptsize 136}}$, F. Bock${}^{\textrm{\scriptsize 84}}$,${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 106}}$, A. Bogdanov${}^{\textrm{\scriptsize 85}}$, L. Boldizsár${}^{\textrm{\scriptsize 142}}$, M. Bombara${}^{\textrm{\scriptsize 40}}$, G. Bonomi${}^{\textrm{\scriptsize 137}}$, M. Bonora${}^{\textrm{\scriptsize 35}}$, J. Book${}^{\textrm{\scriptsize 71}}$, H. Borel${}^{\textrm{\scriptsize 76}}$, A. Borissov${}^{\textrm{\scriptsize 19}}$, M. Borri${}^{\textrm{\scriptsize 129}}$, E. Botta${}^{\textrm{\scriptsize 26}}$, C. Bourjau${}^{\textrm{\scriptsize 93}}$, P. Braun-Munzinger${}^{\textrm{\scriptsize 109}}$, M. Bregant${}^{\textrm{\scriptsize 124}}$, T.A. Broker${}^{\textrm{\scriptsize 71}}$, T.A. Browning${}^{\textrm{\scriptsize 108}}$, M. Broz${}^{\textrm{\scriptsize 39}}$, E.J. Brucken${}^{\textrm{\scriptsize 46}}$, E. Bruna${}^{\textrm{\scriptsize 59}}$, G.E. Bruno${}^{\textrm{\scriptsize 33}}$, D. Budnikov${}^{\textrm{\scriptsize 111}}$, H. Buesching${}^{\textrm{\scriptsize 71}}$, S. Bufalino${}^{\textrm{\scriptsize 31}}$, P. Buhler${}^{\textrm{\scriptsize 116}}$, P. Buncic${}^{\textrm{\scriptsize 35}}$, O. Busch${}^{\textrm{\scriptsize 133}}$, Z. Buthelezi${}^{\textrm{\scriptsize 77}}$, J.B. Butt${}^{\textrm{\scriptsize 15}}$, J.T. Buxton${}^{\textrm{\scriptsize 18}}$, J. Cabala${}^{\textrm{\scriptsize 119}}$, D. Caffarri${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 94}}$, H. Caines${}^{\textrm{\scriptsize 143}}$, A. Caliva${}^{\textrm{\scriptsize 64}}$, E. Calvo Villar${}^{\textrm{\scriptsize 114}}$, P. Camerini${}^{\textrm{\scriptsize 25}}$, A.A. Capon${}^{\textrm{\scriptsize 116}}$, F. Carena${}^{\textrm{\scriptsize 35}}$, W. Carena${}^{\textrm{\scriptsize 35}}$, F. Carnesecchi${}^{\textrm{\scriptsize 27}}$,${}^{\textrm{\scriptsize 12}}$, J. Castillo Castellanos${}^{\textrm{\scriptsize 76}}$, A.J. Castro${}^{\textrm{\scriptsize 130}}$, E.A.R. Casula${}^{\textrm{\scriptsize 24}}$,${}^{\textrm{\scriptsize 55}}$, C. Ceballos Sanchez${}^{\textrm{\scriptsize 9}}$, P. Cerello${}^{\textrm{\scriptsize 59}}$, S. Chandra${}^{\textrm{\scriptsize 139}}$, B. Chang${}^{\textrm{\scriptsize 128}}$, S. Chapeland${}^{\textrm{\scriptsize 35}}$, M. Chartier${}^{\textrm{\scriptsize 129}}$, J.L. Charvet${}^{\textrm{\scriptsize 76}}$, S. Chattopadhyay${}^{\textrm{\scriptsize 139}}$, S. Chattopadhyay${}^{\textrm{\scriptsize 112}}$, A. Chauvin${}^{\textrm{\scriptsize 107}}$,${}^{\textrm{\scriptsize 36}}$, M. Cherney${}^{\textrm{\scriptsize 99}}$, C. Cheshkov${}^{\textrm{\scriptsize 134}}$, B. Cheynis${}^{\textrm{\scriptsize 134}}$, V. Chibante Barroso${}^{\textrm{\scriptsize 35}}$, D.D. Chinellato${}^{\textrm{\scriptsize 125}}$, S. Cho${}^{\textrm{\scriptsize 61}}$, P. Chochula${}^{\textrm{\scriptsize 35}}$, K. Choi${}^{\textrm{\scriptsize 19}}$, M. Chojnacki${}^{\textrm{\scriptsize 93}}$, S. Choudhury${}^{\textrm{\scriptsize 139}}$, T. Chowdhury${}^{\textrm{\scriptsize 82}}$, P. Christakoglou${}^{\textrm{\scriptsize 94}}$, C.H. Christensen${}^{\textrm{\scriptsize 93}}$, P. Christiansen${}^{\textrm{\scriptsize 34}}$, T. Chujo${}^{\textrm{\scriptsize 133}}$, S.U. Chung${}^{\textrm{\scriptsize 19}}$, C. Cicalo${}^{\textrm{\scriptsize 55}}$, L. Cifarelli${}^{\textrm{\scriptsize 12}}$,${}^{\textrm{\scriptsize 27}}$, F. Cindolo${}^{\textrm{\scriptsize 54}}$, J. Cleymans${}^{\textrm{\scriptsize 102}}$, F. Colamaria${}^{\textrm{\scriptsize 33}}$, D. Colella${}^{\textrm{\scriptsize 66}}$,${}^{\textrm{\scriptsize 35}}$, A. Collu${}^{\textrm{\scriptsize 84}}$, M. Colocci${}^{\textrm{\scriptsize 27}}$, M. Concas${}^{\textrm{\scriptsize 59}}$\Arefidp1835040, G. Conesa Balbastre${}^{\textrm{\scriptsize 83}}$, Z. Conesa del Valle${}^{\textrm{\scriptsize 62}}$, M.E. Connors${}^{\textrm{\scriptsize 143}}$\Arefidp1854432, J.G. Contreras${}^{\textrm{\scriptsize 39}}$, T.M. Cormier${}^{\textrm{\scriptsize 97}}$, Y. Corrales Morales${}^{\textrm{\scriptsize 59}}$, I. Cortés Maldonado${}^{\textrm{\scriptsize 2}}$, P. Cortese${}^{\textrm{\scriptsize 32}}$, M.R. Cosentino${}^{\textrm{\scriptsize 126}}$, F. Costa${}^{\textrm{\scriptsize 35}}$, S. Costanza${}^{\textrm{\scriptsize 136}}$, J. Crkovská${}^{\textrm{\scriptsize 62}}$, P. Crochet${}^{\textrm{\scriptsize 82}}$, E. Cuautle${}^{\textrm{\scriptsize 73}}$, L. Cunqueiro${}^{\textrm{\scriptsize 72}}$, T. Dahms${}^{\textrm{\scriptsize 36}}$,${}^{\textrm{\scriptsize 107}}$, A. Dainese${}^{\textrm{\scriptsize 57}}$, M.C. Danisch${}^{\textrm{\scriptsize 106}}$, A. Danu${}^{\textrm{\scriptsize 69}}$, D. Das${}^{\textrm{\scriptsize 112}}$, I. Das${}^{\textrm{\scriptsize 112}}$, S. Das${}^{\textrm{\scriptsize 4}}$, A. Dash${}^{\textrm{\scriptsize 90}}$, S. Dash${}^{\textrm{\scriptsize 48}}$, S. De${}^{\textrm{\scriptsize 124}}$,${}^{\textrm{\scriptsize 49}}$, A. De Caro${}^{\textrm{\scriptsize 30}}$, G. de Cataldo${}^{\textrm{\scriptsize 53}}$, C. de Conti${}^{\textrm{\scriptsize 124}}$, J. de Cuveland${}^{\textrm{\scriptsize 42}}$, A. De Falco${}^{\textrm{\scriptsize 24}}$, D. De Gruttola${}^{\textrm{\scriptsize 30}}$,${}^{\textrm{\scriptsize 12}}$, N. De Marco${}^{\textrm{\scriptsize 59}}$, S. De Pasquale${}^{\textrm{\scriptsize 30}}$, R.D. De Souza${}^{\textrm{\scriptsize 125}}$, H.F. Degenhardt${}^{\textrm{\scriptsize 124}}$, A. Deisting${}^{\textrm{\scriptsize 109}}$,${}^{\textrm{\scriptsize 106}}$, A. Deloff${}^{\textrm{\scriptsize 88}}$, C. Deplano${}^{\textrm{\scriptsize 94}}$, P. Dhankher${}^{\textrm{\scriptsize 48}}$, D. Di Bari${}^{\textrm{\scriptsize 33}}$, A. Di Mauro${}^{\textrm{\scriptsize 35}}$, P. Di Nezza${}^{\textrm{\scriptsize 51}}$, B. Di Ruzza${}^{\textrm{\scriptsize 57}}$, I. Diakonov${}^{\textrm{\scriptsize 138}}$, M.A. Diaz Corchero${}^{\textrm{\scriptsize 10}}$, T. Dietel${}^{\textrm{\scriptsize 102}}$, P. Dillenseger${}^{\textrm{\scriptsize 71}}$, R. Divià${}^{\textrm{\scriptsize 35}}$, Ø. Djuvsland${}^{\textrm{\scriptsize 22}}$, A. Dobrin${}^{\textrm{\scriptsize 35}}$, D. Domenicis Gimenez${}^{\textrm{\scriptsize 124}}$, B. Dönigus${}^{\textrm{\scriptsize 71}}$, O. Dordic${}^{\textrm{\scriptsize 21}}$, L.V.V. Doremalen${}^{\textrm{\scriptsize 64}}$, T. Drozhzhova${}^{\textrm{\scriptsize 71}}$, A.K. Dubey${}^{\textrm{\scriptsize 139}}$, A. Dubla${}^{\textrm{\scriptsize 109}}$, L. Ducroux${}^{\textrm{\scriptsize 134}}$, A.K. Duggal${}^{\textrm{\scriptsize 101}}$, P. Dupieux${}^{\textrm{\scriptsize 82}}$, R.J. Ehlers${}^{\textrm{\scriptsize 143}}$, D. Elia${}^{\textrm{\scriptsize 53}}$, E. Endress${}^{\textrm{\scriptsize 114}}$, H. Engel${}^{\textrm{\scriptsize 70}}$, E. Epple${}^{\textrm{\scriptsize 143}}$, B. Erazmus${}^{\textrm{\scriptsize 117}}$, F. Erhardt${}^{\textrm{\scriptsize 100}}$, B. Espagnon${}^{\textrm{\scriptsize 62}}$, S. Esumi${}^{\textrm{\scriptsize 133}}$, G. Eulisse${}^{\textrm{\scriptsize 35}}$, J. Eum${}^{\textrm{\scriptsize 19}}$, D. Evans${}^{\textrm{\scriptsize 113}}$, S. Evdokimov${}^{\textrm{\scriptsize 115}}$, 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R. Russo${}^{\textrm{\scriptsize 26}}$, A. Rustamov${}^{\textrm{\scriptsize 91}}$, E. Ryabinkin${}^{\textrm{\scriptsize 92}}$, Y. Ryabov${}^{\textrm{\scriptsize 98}}$, A. Rybicki${}^{\textrm{\scriptsize 121}}$, S. Saarinen${}^{\textrm{\scriptsize 46}}$, S. Sadhu${}^{\textrm{\scriptsize 139}}$, S. Sadovsky${}^{\textrm{\scriptsize 115}}$, K. Šafařík${}^{\textrm{\scriptsize 35}}$, S.K. Saha${}^{\textrm{\scriptsize 139}}$, B. Sahlmuller${}^{\textrm{\scriptsize 71}}$, B. Sahoo${}^{\textrm{\scriptsize 48}}$, P. Sahoo${}^{\textrm{\scriptsize 49}}$, R. Sahoo${}^{\textrm{\scriptsize 49}}$, S. Sahoo${}^{\textrm{\scriptsize 68}}$, P.K. Sahu${}^{\textrm{\scriptsize 68}}$, J. Saini${}^{\textrm{\scriptsize 139}}$, S. Sakai${}^{\textrm{\scriptsize 51}}$,${}^{\textrm{\scriptsize 133}}$, M.A. Saleh${}^{\textrm{\scriptsize 141}}$, J. Salzwedel${}^{\textrm{\scriptsize 18}}$, S. Sambyal${}^{\textrm{\scriptsize 103}}$, V. Samsonov${}^{\textrm{\scriptsize 85}}$,${}^{\textrm{\scriptsize 98}}$, A. Sandoval${}^{\textrm{\scriptsize 75}}$, D. Sarkar${}^{\textrm{\scriptsize 139}}$, N. Sarkar${}^{\textrm{\scriptsize 139}}$, P. Sarma${}^{\textrm{\scriptsize 44}}$, M.H.P. Sas${}^{\textrm{\scriptsize 64}}$, E. Scapparone${}^{\textrm{\scriptsize 54}}$, F. Scarlassara${}^{\textrm{\scriptsize 29}}$, R.P. Scharenberg${}^{\textrm{\scriptsize 108}}$, H.S. Scheid${}^{\textrm{\scriptsize 71}}$, C. Schiaua${}^{\textrm{\scriptsize 89}}$, R. Schicker${}^{\textrm{\scriptsize 106}}$, C. Schmidt${}^{\textrm{\scriptsize 109}}$, H.R. Schmidt${}^{\textrm{\scriptsize 105}}$, M.O. Schmidt${}^{\textrm{\scriptsize 106}}$, M. Schmidt${}^{\textrm{\scriptsize 105}}$, S. Schuchmann${}^{\textrm{\scriptsize 106}}$, J. Schukraft${}^{\textrm{\scriptsize 35}}$, Y. Schutz${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 135}}$,${}^{\textrm{\scriptsize 117}}$, K. Schwarz${}^{\textrm{\scriptsize 109}}$, K. Schweda${}^{\textrm{\scriptsize 109}}$, G. Scioli${}^{\textrm{\scriptsize 27}}$, E. Scomparin${}^{\textrm{\scriptsize 59}}$, R. Scott${}^{\textrm{\scriptsize 130}}$, M. Šefčík${}^{\textrm{\scriptsize 40}}$, J.E. Seger${}^{\textrm{\scriptsize 99}}$, Y. Sekiguchi${}^{\textrm{\scriptsize 132}}$, D. Sekihata${}^{\textrm{\scriptsize 47}}$, I. Selyuzhenkov${}^{\textrm{\scriptsize 109}}$,${}^{\textrm{\scriptsize 85}}$, K. Senosi${}^{\textrm{\scriptsize 77}}$, S. Senyukov${}^{\textrm{\scriptsize 3}}$,${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 135}}$, E. Serradilla${}^{\textrm{\scriptsize 75}}$,${}^{\textrm{\scriptsize 10}}$, P. Sett${}^{\textrm{\scriptsize 48}}$, A. Sevcenco${}^{\textrm{\scriptsize 69}}$, A. Shabanov${}^{\textrm{\scriptsize 63}}$, A. Shabetai${}^{\textrm{\scriptsize 117}}$, R. Shahoyan${}^{\textrm{\scriptsize 35}}$, W. Shaikh${}^{\textrm{\scriptsize 112}}$, A. Shangaraev${}^{\textrm{\scriptsize 115}}$, A. Sharma${}^{\textrm{\scriptsize 101}}$, A. Sharma${}^{\textrm{\scriptsize 103}}$, M. Sharma${}^{\textrm{\scriptsize 103}}$, M. Sharma${}^{\textrm{\scriptsize 103}}$, N. Sharma${}^{\textrm{\scriptsize 130}}$,${}^{\textrm{\scriptsize 101}}$, A.I. Sheikh${}^{\textrm{\scriptsize 139}}$, K. Shigaki${}^{\textrm{\scriptsize 47}}$, Q. Shou${}^{\textrm{\scriptsize 7}}$, K. Shtejer${}^{\textrm{\scriptsize 26}}$,${}^{\textrm{\scriptsize 9}}$, Y. Sibiriak${}^{\textrm{\scriptsize 92}}$, S. Siddhanta${}^{\textrm{\scriptsize 55}}$, K.M. Sielewicz${}^{\textrm{\scriptsize 35}}$, T. Siemiarczuk${}^{\textrm{\scriptsize 88}}$, D. Silvermyr${}^{\textrm{\scriptsize 34}}$, C. Silvestre${}^{\textrm{\scriptsize 83}}$, G. Simatovic${}^{\textrm{\scriptsize 100}}$, G. Simonetti${}^{\textrm{\scriptsize 35}}$, R. Singaraju${}^{\textrm{\scriptsize 139}}$, R. Singh${}^{\textrm{\scriptsize 90}}$, V. Singhal${}^{\textrm{\scriptsize 139}}$, T. Sinha${}^{\textrm{\scriptsize 112}}$, B. Sitar${}^{\textrm{\scriptsize 38}}$, M. Sitta${}^{\textrm{\scriptsize 32}}$, T.B. Skaali${}^{\textrm{\scriptsize 21}}$, M. Slupecki${}^{\textrm{\scriptsize 128}}$, N. Smirnov${}^{\textrm{\scriptsize 143}}$, R.J.M. Snellings${}^{\textrm{\scriptsize 64}}$, T.W. Snellman${}^{\textrm{\scriptsize 128}}$, J. Song${}^{\textrm{\scriptsize 19}}$, M. Song${}^{\textrm{\scriptsize 144}}$, F. Soramel${}^{\textrm{\scriptsize 29}}$, S. Sorensen${}^{\textrm{\scriptsize 130}}$, F. Sozzi${}^{\textrm{\scriptsize 109}}$, E. Spiriti${}^{\textrm{\scriptsize 51}}$, I. Sputowska${}^{\textrm{\scriptsize 121}}$, B.K. Srivastava${}^{\textrm{\scriptsize 108}}$, J. Stachel${}^{\textrm{\scriptsize 106}}$, I. Stan${}^{\textrm{\scriptsize 69}}$, P. Stankus${}^{\textrm{\scriptsize 97}}$, E. Stenlund${}^{\textrm{\scriptsize 34}}$, D. Stocco${}^{\textrm{\scriptsize 117}}$, P. Strmen${}^{\textrm{\scriptsize 38}}$, A.A.P. Suaide${}^{\textrm{\scriptsize 124}}$, T. Sugitate${}^{\textrm{\scriptsize 47}}$, C. Suire${}^{\textrm{\scriptsize 62}}$, M. Suleymanov${}^{\textrm{\scriptsize 15}}$, M. Suljic${}^{\textrm{\scriptsize 25}}$, R. Sultanov${}^{\textrm{\scriptsize 65}}$, M. Šumbera${}^{\textrm{\scriptsize 96}}$, S. Sumowidagdo${}^{\textrm{\scriptsize 50}}$, K. Suzuki${}^{\textrm{\scriptsize 116}}$, S. Swain${}^{\textrm{\scriptsize 68}}$, A. Szabo${}^{\textrm{\scriptsize 38}}$, I. Szarka${}^{\textrm{\scriptsize 38}}$, A. Szczepankiewicz${}^{\textrm{\scriptsize 140}}$, U. Tabassam${}^{\textrm{\scriptsize 15}}$, J. Takahashi${}^{\textrm{\scriptsize 125}}$, G.J. Tambave${}^{\textrm{\scriptsize 22}}$, N. Tanaka${}^{\textrm{\scriptsize 133}}$, M. Tarhini${}^{\textrm{\scriptsize 62}}$, M. Tariq${}^{\textrm{\scriptsize 17}}$, M.G. Tarzila${}^{\textrm{\scriptsize 89}}$, A. Tauro${}^{\textrm{\scriptsize 35}}$, G. Tejeda Muñoz${}^{\textrm{\scriptsize 2}}$, A. Telesca${}^{\textrm{\scriptsize 35}}$, K. Terasaki${}^{\textrm{\scriptsize 132}}$, C. Terrevoli${}^{\textrm{\scriptsize 29}}$, B. Teyssier${}^{\textrm{\scriptsize 134}}$, D. Thakur${}^{\textrm{\scriptsize 49}}$, S. Thakur${}^{\textrm{\scriptsize 139}}$, D. Thomas${}^{\textrm{\scriptsize 122}}$, R. Tieulent${}^{\textrm{\scriptsize 134}}$, A. Tikhonov${}^{\textrm{\scriptsize 63}}$, A.R. Timmins${}^{\textrm{\scriptsize 127}}$, A. Toia${}^{\textrm{\scriptsize 71}}$, S. Tripathy${}^{\textrm{\scriptsize 49}}$, S. Trogolo${}^{\textrm{\scriptsize 26}}$, G. Trombetta${}^{\textrm{\scriptsize 33}}$, L. Tropp${}^{\textrm{\scriptsize 40}}$, V. Trubnikov${}^{\textrm{\scriptsize 3}}$, W.H. Trzaska${}^{\textrm{\scriptsize 128}}$, B.A. Trzeciak${}^{\textrm{\scriptsize 64}}$, T. Tsuji${}^{\textrm{\scriptsize 132}}$, A. Tumkin${}^{\textrm{\scriptsize 111}}$, R. Turrisi${}^{\textrm{\scriptsize 57}}$, T.S. Tveter${}^{\textrm{\scriptsize 21}}$, K. Ullaland${}^{\textrm{\scriptsize 22}}$, E.N. Umaka${}^{\textrm{\scriptsize 127}}$, A. Uras${}^{\textrm{\scriptsize 134}}$, G.L. Usai${}^{\textrm{\scriptsize 24}}$, A. Utrobicic${}^{\textrm{\scriptsize 100}}$, M. Vala${}^{\textrm{\scriptsize 66}}$,${}^{\textrm{\scriptsize 119}}$, J. Van Der Maarel${}^{\textrm{\scriptsize 64}}$, J.W. Van Hoorne${}^{\textrm{\scriptsize 35}}$, M. van Leeuwen${}^{\textrm{\scriptsize 64}}$, T. Vanat${}^{\textrm{\scriptsize 96}}$, P. Vande Vyvre${}^{\textrm{\scriptsize 35}}$, D. Varga${}^{\textrm{\scriptsize 142}}$, A. Vargas${}^{\textrm{\scriptsize 2}}$, M. Vargyas${}^{\textrm{\scriptsize 128}}$, R. Varma${}^{\textrm{\scriptsize 48}}$, M. Vasileiou${}^{\textrm{\scriptsize 87}}$, A. Vasiliev${}^{\textrm{\scriptsize 92}}$, A. Vauthier${}^{\textrm{\scriptsize 83}}$, O. Vázquez Doce${}^{\textrm{\scriptsize 107}}$,${}^{\textrm{\scriptsize 36}}$, V. Vechernin${}^{\textrm{\scriptsize 138}}$, A.M. Veen${}^{\textrm{\scriptsize 64}}$, A. Velure${}^{\textrm{\scriptsize 22}}$, E. Vercellin${}^{\textrm{\scriptsize 26}}$, S. Vergara Limón${}^{\textrm{\scriptsize 2}}$, R. Vernet${}^{\textrm{\scriptsize 8}}$, R. Vértesi${}^{\textrm{\scriptsize 142}}$, L. Vickovic${}^{\textrm{\scriptsize 120}}$, S. Vigolo${}^{\textrm{\scriptsize 64}}$, J. Viinikainen${}^{\textrm{\scriptsize 128}}$, Z. Vilakazi${}^{\textrm{\scriptsize 131}}$, O. Villalobos Baillie${}^{\textrm{\scriptsize 113}}$, A. Villatoro Tello${}^{\textrm{\scriptsize 2}}$, A. Vinogradov${}^{\textrm{\scriptsize 92}}$, L. Vinogradov${}^{\textrm{\scriptsize 138}}$, T. Virgili${}^{\textrm{\scriptsize 30}}$, V. Vislavicius${}^{\textrm{\scriptsize 34}}$, A. Vodopyanov${}^{\textrm{\scriptsize 78}}$, M.A. Völkl${}^{\textrm{\scriptsize 106}}$,${}^{\textrm{\scriptsize 105}}$, K. Voloshin${}^{\textrm{\scriptsize 65}}$, S.A. Voloshin${}^{\textrm{\scriptsize 141}}$, G. Volpe${}^{\textrm{\scriptsize 33}}$, B. von Haller${}^{\textrm{\scriptsize 35}}$, I. Vorobyev${}^{\textrm{\scriptsize 36}}$,${}^{\textrm{\scriptsize 107}}$, D. Voscek${}^{\textrm{\scriptsize 119}}$, D. Vranic${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 109}}$, J. Vrláková${}^{\textrm{\scriptsize 40}}$, B. Wagner${}^{\textrm{\scriptsize 22}}$, J. Wagner${}^{\textrm{\scriptsize 109}}$, H. Wang${}^{\textrm{\scriptsize 64}}$, M. Wang${}^{\textrm{\scriptsize 7}}$, D. Watanabe${}^{\textrm{\scriptsize 133}}$, Y. Watanabe${}^{\textrm{\scriptsize 132}}$, M. Weber${}^{\textrm{\scriptsize 116}}$, S.G. Weber${}^{\textrm{\scriptsize 109}}$, D.F. Weiser${}^{\textrm{\scriptsize 106}}$, S.C. Wenzel${}^{\textrm{\scriptsize 35}}$, J.P. Wessels${}^{\textrm{\scriptsize 72}}$, U. Westerhoff${}^{\textrm{\scriptsize 72}}$, A.M. Whitehead${}^{\textrm{\scriptsize 102}}$, J. Wiechula${}^{\textrm{\scriptsize 71}}$, J. Wikne${}^{\textrm{\scriptsize 21}}$, G. Wilk${}^{\textrm{\scriptsize 88}}$, J. Wilkinson${}^{\textrm{\scriptsize 106}}$, G.A. Willems${}^{\textrm{\scriptsize 72}}$, M.C.S. Williams${}^{\textrm{\scriptsize 54}}$, E. Willsher${}^{\textrm{\scriptsize 113}}$, B. Windelband${}^{\textrm{\scriptsize 106}}$, W.E. Witt${}^{\textrm{\scriptsize 130}}$, S. Yalcin${}^{\textrm{\scriptsize 81}}$, K. Yamakawa${}^{\textrm{\scriptsize 47}}$, P. Yang${}^{\textrm{\scriptsize 7}}$, S. Yano${}^{\textrm{\scriptsize 47}}$, Z. Yin${}^{\textrm{\scriptsize 7}}$, H. Yokoyama${}^{\textrm{\scriptsize 133}}$,${}^{\textrm{\scriptsize 83}}$, I.-K. Yoo${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 19}}$, J.H. Yoon${}^{\textrm{\scriptsize 61}}$, V. Yurchenko${}^{\textrm{\scriptsize 3}}$, V. Zaccolo${}^{\textrm{\scriptsize 59}}$,${}^{\textrm{\scriptsize 93}}$, A. Zaman${}^{\textrm{\scriptsize 15}}$, C. Zampolli${}^{\textrm{\scriptsize 35}}$, H.J.C. Zanoli${}^{\textrm{\scriptsize 124}}$, N. Zardoshti${}^{\textrm{\scriptsize 113}}$, A. Zarochentsev${}^{\textrm{\scriptsize 138}}$, P. Závada${}^{\textrm{\scriptsize 67}}$, N. Zaviyalov${}^{\textrm{\scriptsize 111}}$, H. Zbroszczyk${}^{\textrm{\scriptsize 140}}$, M. Zhalov${}^{\textrm{\scriptsize 98}}$, H. Zhang${}^{\textrm{\scriptsize 22}}$,${}^{\textrm{\scriptsize 7}}$, X. Zhang${}^{\textrm{\scriptsize 7}}$, Y. Zhang${}^{\textrm{\scriptsize 7}}$, C. Zhang${}^{\textrm{\scriptsize 64}}$, Z. Zhang${}^{\textrm{\scriptsize 7}}$,${}^{\textrm{\scriptsize 82}}$, C. Zhao${}^{\textrm{\scriptsize 21}}$, N. Zhigareva${}^{\textrm{\scriptsize 65}}$, D. Zhou${}^{\textrm{\scriptsize 7}}$, Y. Zhou${}^{\textrm{\scriptsize 93}}$, Z. Zhou${}^{\textrm{\scriptsize 22}}$, H. Zhu${}^{\textrm{\scriptsize 22}}$, J. Zhu${}^{\textrm{\scriptsize 117}}$,${}^{\textrm{\scriptsize 7}}$, X. Zhu${}^{\textrm{\scriptsize 7}}$, A. Zichichi${}^{\textrm{\scriptsize 12}}$,${}^{\textrm{\scriptsize 27}}$, A. Zimmermann${}^{\textrm{\scriptsize 106}}$, M.B. Zimmermann${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 72}}$, G. Zinovjev${}^{\textrm{\scriptsize 3}}$, J. Zmeskal${}^{\textrm{\scriptsize 116}}$, S. Zou${}^{\textrm{\scriptsize 7}}$

Affiliation notes

{Authlist}

\Adef

0Deceased

\Adef

idp1835040Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy

\Adef

idp1854432Also at: Georgia State University, Atlanta, Georgia, United States

\Adef

idp4144160Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia

\Adef

idp4502608Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India

\Adef

idp5486048Also at: Institute of Theoretical Physics, University of Wroclaw, Poland

Collaboration Institutes

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

2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

4Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India

5Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

7Central China Normal University, Wuhan, China

8Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France

9Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba

10Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain

11Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico

12Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi’, Rome, Italy

13Chicago State University, Chicago, Illinois, United States

14China Institute of Atomic Energy, Beijing, China

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

16Departamento de Física de Partículas and IGFAE, Universidad de Santiago de Compostela, Santiago de Compostela, Spain

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

18Department of Physics, Ohio State University, Columbus, Ohio, United States

19Department of Physics, Pusan National University, Pusan, South Korea

20Department of Physics, Sejong University, Seoul, South Korea

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

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

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

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

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

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

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

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

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

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

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

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

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

34Division of Experimental High Energy Physics, University of Lund, Lund, Sweden

35European Organization for Nuclear Research (CERN), Geneva, Switzerland

36Excellence Cluster Universe, Technische Universität München, Munich, Germany

37Faculty of Engineering, Bergen University College, Bergen, Norway

38Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia

39Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic

40Faculty of Science, P.J. Šafárik University, Košice, Slovakia

41Faculty of Technology, Buskerud and Vestfold University College, Tonsberg, Norway

42Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany

43Gangneung-Wonju National University, Gangneung, South Korea

44Gauhati University, Department of Physics, Guwahati, India

45Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany

46Helsinki Institute of Physics (HIP), Helsinki, Finland

47Hiroshima University, Hiroshima, Japan

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

49Indian Institute of Technology Indore, Indore, India

50Indonesian Institute of Sciences, Jakarta, Indonesia

51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

52INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy

53INFN, Sezione di Bari, Bari, Italy

54INFN, Sezione di Bologna, Bologna, Italy

55INFN, Sezione di Cagliari, Cagliari, Italy

56INFN, Sezione di Catania, Catania, Italy

57INFN, Sezione di Padova, Padova, Italy

58INFN, Sezione di Roma, Rome, Italy

59INFN, Sezione di Torino, Turin, Italy

60INFN, Sezione di Trieste, Trieste, Italy

61Inha University, Incheon, South Korea

62Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, CNRS-IN2P3, Orsay, France

63Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

64Institute for Subatomic Physics of Utrecht University, Utrecht, Netherlands

65Institute for Theoretical and Experimental Physics, Moscow, Russia

66Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia

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

68Institute of Physics, Bhubaneswar, India

69Institute of Space Science (ISS), Bucharest, Romania

70Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany

71Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany

72Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, Münster, Germany

73Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico

74Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil

75Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico

76IRFU, CEA, Université Paris-Saclay, Saclay, France

77iThemba LABS, National Research Foundation, Somerset West, South Africa

78Joint Institute for Nuclear Research (JINR), Dubna, Russia

79Konkuk University, Seoul, South Korea

80Korea Institute of Science and Technology Information, Daejeon, South Korea

81KTO Karatay University, Konya, Turkey

82Laboratoire de Physique Corpusculaire (LPC), Clermont Université, Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

83Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

84Lawrence Berkeley National Laboratory, Berkeley, California, United States

85Moscow Engineering Physics Institute, Moscow, Russia

86Nagasaki Institute of Applied Science, Nagasaki, Japan

87National and Kapodistrian University of Athens, Physics Department, Athens, Greece, Athens, Greece

88National Centre for Nuclear Studies, Warsaw, Poland

89National Institute for Physics and Nuclear Engineering, Bucharest, Romania

90National Institute of Science Education and Research, Bhubaneswar, India

91National Nuclear Research Center, Baku, Azerbaijan

92National Research Centre Kurchatov Institute, Moscow, Russia

93Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

94Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam, Netherlands

95Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom

96Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež u Prahy, Czech Republic

97Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

98Petersburg Nuclear Physics Institute, Gatchina, Russia

99Physics Department, Creighton University, Omaha, Nebraska, United States

100Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia

101Physics Department, Panjab University, Chandigarh, India

102Physics Department, University of Cape Town, Cape Town, South Africa

103Physics Department, University of Jammu, Jammu, India

104Physics Department, University of Rajasthan, Jaipur, India

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

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

107Physik Department, Technische Universität München, Munich, Germany

108Purdue University, West Lafayette, Indiana, United States

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

110Rudjer Bošković Institute, Zagreb, Croatia

111Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

112Saha Institute of Nuclear Physics, Kolkata, India

113School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom

114Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru

115SSC IHEP of NRC Kurchatov institute, Protvino, Russia

116Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

117SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France

118Suranaree University of Technology, Nakhon Ratchasima, Thailand

119Technical University of Košice, Košice, Slovakia

120Technical University of Split FESB, Split, Croatia

121The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland

122The University of Texas at Austin, Physics Department, Austin, Texas, United States

123Universidad Autónoma de Sinaloa, Culiacán, Mexico

124Universidade de São Paulo (USP), São Paulo, Brazil

125Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

126Universidade Federal do ABC, Santo Andre, Brazil

127University of Houston, Houston, Texas, United States

128University of Jyväskylä, Jyväskylä, Finland

129University of Liverpool, Liverpool, United Kingdom

130University of Tennessee, Knoxville, Tennessee, United States

131University of the Witwatersrand, Johannesburg, South Africa

132University of Tokyo, Tokyo, Japan

133University of Tsukuba, Tsukuba, Japan

134Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, Lyon, France

135Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France

136Università degli Studi di Pavia, Pavia, Italy

137Università di Brescia, Brescia, Italy

138V. Fock Institute for Physics, St. Petersburg State University, St. Petersburg, Russia

139Variable Energy Cyclotron Centre, Kolkata, India

140Warsaw University of Technology, Warsaw, Poland

141Wayne State University, Detroit, Michigan, United States

142Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest, Hungary

143Yale University, New Haven, Connecticut, United States

144Yonsei University, Seoul, South Korea

145Zentrum für Technologietransfer und Telekommunikation (ZTT), Fachhochschule Worms, Worms, Germany