2019 096 10 May

Detailed study of the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ interaction with
femtoscopy in small systems

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

This work presents new constraints on the existence and the binding energy of
a possible $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ bound state, the H-dibaryon,
derived from $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ femtoscopic measurements by
the ALICE collaboration. The results are obtained from a new measurement using
the femtoscopy technique in $\mathrm{p\kern-0.50003ptp}$ collisions at
$\sqrt{s}=13$ TeV and $\mathrm{p\mbox{--}Pb}$ collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, combined with previously published results
from $\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=7$ TeV. The
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ scattering parameter space, spanned by
the inverse scattering length $f_{0}^{-1}$ and the effective range $d_{0}$, is
constrained by comparing the measured $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
correlation function with calculations obtained within the Lednický model. The
data are compatible with hypernuclei results and lattice computations, both
predicting a shallow attractive interaction, and permit to test different
theoretical approaches describing the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
interaction. The region in the $(f_{0}^{-1},d_{0})$ plane which would
accommodate a $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ bound state is
substantially restricted compared to previous studies. The binding energy of
the possible $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ bound state is estimated
within an effective-range expansion approach and is found to be
$B_{\Lambda\Lambda}=3.2^{+1.6}_{-2.4}\text{(stat)}^{+1.8}_{-1.0}\text{(syst)}$
MeV.

##  1 Introduction and physics motivation

A detailed characterization of the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
interaction is of fundamental interest since it plays a decisive role in the
quantitative understanding of the hyperon (Y) appearance in dense neutron-rich
matter, in proto-neutron and in neutron stars [1]. If hyperons do appear at
large densities and their fraction becomes sizeable, the Y–Y interaction is
expected to play an important role in the equation of state of the system [2,
3]. Even if the hyperon densities in compact objects are negligible, the
interplay between the average separations and the
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ effective range determine the possible
onset of phenomena such as fermion superfluidity, and hence influence the
transport properties of the system [4, 5, 6].

The characterization of the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ interaction
is still an open issue in experimental nuclear physics. The Nagara event,
recently measured with the emulsion technique [7, 8], reports a clear evidence
for a double-$\Lambda$ hypernucleus $\mathrm{{}_{\Lambda\Lambda}^{6}He}$, with
a small binding energy between the two $\Lambda$s of $\Delta
B_{\Lambda\Lambda}=\,0.67\pm 0.17$ MeV. This value was obtained by comparing
the binding energy of the two $\Lambda$s inside the double hypernucleus
($B_{\Lambda\Lambda}=\,6.91\pm 0.16$ MeV) with the binding energy of a single
$\Lambda$ in a single-hypernucleus, however, it might be influenced by three-
body forces. Nevertheless, this result was used to set a lower limit for the
mass of the predicted but so far not observed H-dibaryon, a possible bound
state composed of six quarks (uuddss) [9]. Several experimental collaborations
have been involved in the search for this state in the decay channels
$\mathrm{H\rightarrow\Lambda p\pi}$ and $\mathrm{H\rightarrow\Lambda\Lambda}$,
in nuclear and elementary ($\mathrm{e^{-}e^{+}}$) collisions, but no evidence
has been found [10, 11, 12], even though an enhanced
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ production near threshold was measured
by E224 and E522 at KEK-PS [13, 14].

Theoretical models constrained to the available nucleon–nucleon and hyperon-
nucleon experimental data, assuming either a soft [15, 16, 17] or a hard [18,
19] repulsive core for the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ interaction,
predict different scattering lengths ($f_{0}$) and effective ranges ($d_{0}$).
Throughout this paper the standard sign convention in femtoscopy is used,
according to which a positive $f_{0}$ corresponds to an attractive
interaction, while a negative scattering length corresponds either to a
repulsive potential ($d_{0}>|f_{0}|/2$) or a bound state ($d_{0}<|f_{0}|/2$).
It was reported that a small variation of the
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ repulsive core parametrization leads to
inverse scattering lengths within
$-0.27\,\,\mathrm{fm}^{-1}<f_{0}^{-1}<4\,\,\mathrm{fm}^{-1}$ and effective
ranges up to 16 fm [20]. Other calculations are directly constrained to the
Nagara event and result in rather small scattering lengths and moderate
effective ranges, like the FG
$(f_{0}^{-1}=\,1.3\,\,\mathrm{fm}^{-1};\,d_{0}=\,6.59\,\,\mathrm{fm})$ [21]
and the HKMYY
$(f_{0}^{-1}=\,1.74\,\,\mathrm{fm}^{-1};\,d_{0}=\,6.45\,\,\mathrm{fm})$ [22]
models. It is clear that more experimental data are needed to study the
problem in a more quantitative and model-independent way.

An alternative method to study hypernuclei is the investigation of momentum
correlations of $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ pairs produced in
hadron–hadron collisions via the femtoscopy technique [23]. The STAR
collaboration reported a $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ scattering
length and effective range of $f_{0}^{-1}=\,-0.91\pm
0.31^{+0.07}_{-0.56}\,\,\mathrm{fm}^{-1}$ and $d_{0}=\,8.52\pm
2.56^{+2.09}_{-0.74}\,\,\mathrm{fm}$, measured in Au–Au collisions at
$\sqrt{s_{\mathrm{NN}}}=200$ GeV [24]. These values correspond to a repulsive
interaction; however, it was shown that the values and the sign of the
scattering parameters strongly depend on the treatment of feed-down
contributions from weak decays to the measured correlation. A re-analysis of
the data outside the STAR collaboration came to different conclusions [20] and
resulted in a shallow attractive interaction.

In a pioneering study [25], the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
interaction was studied employing the femtoscopy technique in
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=7$ TeV. This study
demonstrated that the data are consistent with either a bound state or an
attractive interaction, however, due to the small data sample no quantitative
results were obtained. In this letter, these studies are extended by analyzing
final-state momentum correlations in $\mathrm{p\kern-0.50003ptp}$ collisions
at $\sqrt{s}=13$ TeV and $\mathrm{p\mbox{--}Pb}$ collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, recorded by ALICE during LHC Run 2. The
small system size in $\mathrm{p\kern-0.50003ptp}$ and $\mathrm{p\mbox{--}Pb}$
gives rise to pronounced correlations from strong final-state interactions due
to the small relative distance at which particles are produced. Hence, the
large data sets enable a high-precision study of the
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ strong final-state interaction and
provide new experimental constraints on the scattering parameters and the
existence of a possible bound state.

##  2 Data analysis

The analysis presented in this paper is based on the data samples collected by
ALICE [26] during the Run 2 of the LHC (2015–2018) in
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=$13 TeV and
$\mathrm{p\mbox{--}Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV,
combined with the previously analyzed Run 1 data from
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=$7 TeV [25]. The event
and particle candidate selection criteria follow closely the procedure applied
in the Run 1 analysis [25].

The events are triggered using two V0 detectors, which are small-angle plastic
scintillator arrays placed on either side of the collision vertex at
pseudorapidities $2.8<\eta<5.1$ and $-3.7<\eta<-1.7$ [27]. Minimum bias
$\mathrm{p\kern-0.50003ptp}$ and $\mathrm{p\mbox{--}Pb}$ events are triggered
by the requirement of coincident signals in both V0 detectors, synchronous
with the beam crossing time defined by the LHC clock. The V0 detector is also
used to reject background events stemming from the interaction of beam
particles with the beam pipe materials or beam-gas interactions. Pile-up
events with more than one collision per bunch crossing are rejected by
evaluating the presence of secondary event vertices [27]. Charged particles
are reconstructed by the Inner Tracking System (ITS) [26] and the Time
Projection Chamber (TPC) [28], both immersed in a 0.5 T solenoidal magnetic
field directed along the beam axis. A uniform detector coverage is assured by
requiring the maximal deviation between the reconstructed primary vertex (PV)
and the nominal interaction point to be smaller than 10 cm. The PV can be
reconstructed with the combined information of the ITS and TPC, and
independently with the Silicon Pixel Detector (SPD - one of the three
subdetectors of the ITS). If both methods are available, the difference of the
$z$-coordinate between both vertices is required to be smaller than 5 mm.
After applying these selection criteria the remaining number of events is
$1.0\times 10^{9}$ for the $\mathrm{p\kern-0.50003ptp}$ at $\sqrt{s}=$13 TeV
sample and $6.1\times 10^{8}$ for $\mathrm{p\mbox{--}Pb}$ at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. This corresponds to about 90 % and 84 % of
all processed events in $\mathrm{p\kern-0.50003ptp}$ and
$\mathrm{p\mbox{--}Pb}$.

The $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ interaction is the main focus of the
present study. As will be explained in the next section, the p–p correlation
function is an essential input for the femtoscopic analysis of
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$. Therefore, the reconstruction of both
protons and $\Lambda$ particles will be described in the following paragraphs.
To increase the statistical significance of the result, the anti-particle
pairs are measured as well.

The selection of the proton candidates follows the analysis strategy used for
the $\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=$7 TeV [25]. The
particle identification (PID) is determined by the number of standard
deviations $n\sigma$ between the hypothesis for a proton and the experimental
measurement of the specific energy loss $\mathrm{d}E/\mathrm{d}x$ in the TPC
or the timing information from the Time-Of-Flight (TOF) detector [29]. The
analyzed tracks are selected within the kinematic range
$0.5<p_{\mathrm{T}}<4.05$ GeV/$c$ and $|\eta|<0.8$. The PID is performed only
with the TPC for tracks with $p<0.75~{}$GeV/$c$, by requiring $|n\sigma|<3$.
To maintain the purity of tracks with $p>0.75~{}$GeV/$c$, the $|n\sigma|$ is
calculated from combining the TPC and TOF information. The contribution of
secondary particles, which stem from electromagnetic and weak decays or the
detector material, are a contamination in the signal. The fractions of primary
and secondary protons are extracted using Monte Carlo (MC) template fits to
the distance of closest approach of the particles to the PV [30]. The MC
distributions are generated using Pythia 8.2 [31] for the
$\mathrm{p\kern-0.50003ptp}$ and DPMJET 3.0.5 [32] for the
$\mathrm{p\mbox{--}Pb}$ case, filtered through the ALICE detector and
reconstruction algorithm [26]. The proton purity in
$\mathrm{p\kern-0.50003ptp}$ ($\mathrm{p\mbox{--}Pb}$) is found to be 99 (97)%
with a primary fraction of 85 (86)%.

The $\mathrm{\Lambda}$ particles are reconstructed via the decay
$\mathrm{\Lambda\rightarrow p\pi^{-}}$, which has a branching ratio of 63.9%
and $c\tau=7.89~{}$cm [33]. For the reconstruction of the $\overline{\Lambda}$
the charge conjugate decay is employed. The interaction rate of the LHC varied
during different periods of the $\mathrm{p\kern-0.50003ptp}$ running. To
maintain a constant purity that is independent of the interaction rate, in
addition to the selection criteria used for the analysis of
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=$7 TeV [25], the charged
decay tracks must either have a hit in one of the SPD or Silicon Strip
Detector (SSD - ITS subdetector) layers or a matched TOF signal. After
applying all selection criteria the final $\Lambda$ and $\overline{\Lambda}$
candidates are selected in a $4$ MeV/$c^{2}$ ($\sim 3\sigma$) mass window
around the nominal mass [33]. The fractions of primary and secondary $\Lambda$
particles are extracted similarly as the protons, while the observable for the
template fits is the cosine of the opening angle $\alpha$ between the
$\Lambda$ momentum and the vector pointing from the PV to the $\Lambda$ decay
vertex. The $\Lambda$ purity in $\mathrm{p\kern-0.50003ptp}$
($\mathrm{p\mbox{--}Pb}$) is found to be 97 (94)% with a primary fraction of
59 (50)%. The exact composition of secondaries, as well as the $\Lambda$ to
$\Sigma^{0}$ ratio, is fixed in the MC simulations, but is model dependent.
Therefore, the systematic uncertainties include a $20\%$ variation of the
ratios of these contributions.

##  3 Analysis of the correlation function

The method used to investigate the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
interaction relies on particle pair correlations measured as a function of
$\vec{k^{*}}$, defined as the single-particle momentum in the pair rest frame
[23]. The observable of interest $C(\vec{p_{1}},\vec{p_{2}})$ is defined as
the ratio of the probability of measuring simultaneously two particles with
momenta $\vec{p_{1}}$ and $\vec{p_{2}}$, to the product of the single-particle
probabilities:

$C(\vec{p_{1}},\vec{p_{2}})=\frac{P(\vec{p_{1}},\vec{p_{2}})}{P(\vec{p_{1}})P(\vec{p_{2}})}.$
(1)

In the absence of correlations, the numerator factorizes and the correlation
function becomes unity. The femtoscopy formalism [23] relates the correlation
function for a pair of particles, to their effective two-particle emitting
source function $S(r)$ and the two-particle wave function
$\Psi(\vec{k^{*}},\vec{r})$:

$C(k^{*})=\int
S(r)\mid\Psi(\vec{k^{*}},\vec{r})\mid^{2}\mathrm{d}^{3}r\xrightarrow{k^{*}\rightarrow\infty}1,$
(2)

where $r$ is the relative distance between the points of emission of the two
particles. This definition of $C(k^{*})$ assumes that the emission source is
not dependent on $k^{*}$, it is spherically symmetric and the emission of all
particles is simultaneous. The EPOS transport model [34] predicts an emission
source that does not fully satisfy the above assumptions. However, it was
verified that the above simplifications result in very mild deviations in the
correlation functions, which are negligible for the present analysis.

For a spherical symmetric potential the angular dependence of the wave-
function is trivially integrated out. Thus the direction of $\vec{k^{*}}$
becomes irrelevant on the left-hand side of Eq. 2. Particles with large
relative momenta $q^{*}=2k^{*}$ are not correlated, leading to
$C(k^{*}\rightarrow\infty)=1$.

The strong interaction has a typical range of a few femtometers and thus a
significant modification of the wave function with respect to its asymptotic
form is expected only for $r\lesssim 2~{}$fm. Consequently, for small emission
sources the correlation function will be particularly sensitive to the strong
interaction potential. Experimentally, a small emission source can be formed
in $\mathrm{p\kern-0.50003ptp}$ and $\mathrm{p\mbox{--}Pb}$ collisions [25,
35]. In the current analysis, it is assumed that the emission profile is
Gaussian and that the p–p and $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ systems
are characterized by a common source size
$r_{0}=r_{\text{p\mbox{--}p}}=r_{\text{$\mathrm{\Lambda}$\mbox{--}$\mathrm{\Lambda}$}}$,
which is determined by fitting the p–p correlation function and then used for
the investigation of the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ interaction. In
$\mathrm{p\kern-0.50003ptp}$ collisions the effect of mini-jets is only
present for baryon correlations between particle and anti-particle [25], hence
the investigated data provide a clean environment to extract the femtoscopic
signal.

Two different frameworks are available for the computation of $C(k^{*})$. The
first tool used in this analysis is the “Correlation Analysis Tool using the
Schrödinger equation” (CATS) [35]. Here, a local potential $V(r)$ is used as
the input to a numerical evaluation of the wave function and the corresponding
correlation function. CATS delivers an exact solution and this tool is used to
model the p–p correlation using a Coulomb and an Argonne $v_{18}$ potential
[36] for the strong interaction. The known p–p interaction allows the source
size $r_{0}$ to be extracted from the fit to the measured correlation
function.

The second tool is the Lednický model [37], which assumes a Gaussian emission
source and evaluates the wave function in the effective-range expansion. In
this approach, the interaction is parameterized in terms of the scattering
length $f_{0}$ and the effective range $d_{0}$. This approach produces a very
accurate approximation for $C(k^{*})$ in case $d_{0}\lesssim r_{0}$, while for
smaller values of $r_{0}$ the approximate solution may become unstable, in
particular for negative values of $f_{0}$ [25]. However, it is known that the
Lednický model can be used to model the p–$\mathrm{\Lambda}$ correlation
function even for a source size of $r_{0}=1.2~{}$fm, with a deviation from the
exact solution of less than $4\%$ [35]. It is therefore expected that this
model can successfully be used to study the
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ interaction, even in small collision
systems. Nevertheless, the validity of the approximation will be further
verified in the next section.

Experimentally, the correlation function is defined as

$C_{\text{exp}}(k^{*})=\mathcal{N}\frac{N_{\text{same}}(k^{*})}{N_{\text{mixed}}(k^{*})}\xrightarrow{k^{*}\rightarrow\infty}1,$
(3)

where $N_{\text{same}}(k^{*})$ and $N_{\text{mixed}}(k^{*})$ are the same and
mixed event distributions, while $\mathcal{N}$ is a normalization constant
determined by the condition that particle pairs with large relative momenta
are not correlated. In small collision systems $C_{\text{exp}}(k^{*})$ often
has a long-range tail due to momentum conservation, and a related
approximately linear non-femtoscopic background extending to low $k^{*}$ [25].
The latter is incorporated by including a linear term in the fit function.

To increase the statistical significance of $C_{\text{exp}}(k^{*})$ the
particle-particle (PP) and antiparticle-antiparticle
($\mathrm{\overline{P}\overline{P}}$) correlations are combined using their
weighted mean
$C_{\text{exp}}(k^{*})=\mathcal{N}_{\text{PP}}C_{\text{exp,PP}}(k^{*})\oplus\mathcal{N}_{\mathrm{\overline{P}\overline{P}}}C_{\mathrm{exp,\overline{P}\overline{P}}}(k^{*})$,
with the normalization performed in the range $240<k^{*}<340$ MeV/$c$, which
is unaffected by femtoscopic correlations. It was verified that
$\mathcal{N}_{\text{PP}}C_{\text{exp,PP}}(k^{*})=\mathcal{N}_{\mathrm{\overline{P}\overline{P}}}C_{\mathrm{exp,\overline{P}\overline{P}}}(k^{*})$
within the statistical uncertainties.

The systematic uncertainties of the experimental correlation function are
evaluated by varying the selection criteria of the proton and $\Lambda$
candidates within 20%, following the procedure used for the analysis of the
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=$7 TeV [25].
Nevertheless, by performing a Barlow test [38], the systematic uncertainties
were found to be insignificant compared to the statistical uncertainties.

Momentum resolution effects modify the correlation function by at most $10\%$
and are accounted for by correcting the theoretical correlation function [25].
The measured experimental correlation function contains not only the
correlation signal of interest, but additionally accumulates residual
contributions from feed-down particles. These are considered in the
theoretical description of the correlation by using the linear decomposition
of the total correlation function into

$C_{\mathrm{tot}}(k^{*})=\sum_{i}\lambda_{i}C_{i}(k^{*}),$ (4)

where the sum runs over all contributions, the $\lambda$ parameters are the
weight factors for the different contributions to the total correlation and
$i=0$ corresponds to the primary correlation. The $\lambda$ coefficients are
determined in a data-driven approach by performing Monte Carlo template fits
to the data, using Pythia and DPMJET in $\mathrm{p\kern-0.50003ptp}$ and
$\mathrm{p\mbox{--}Pb}$ collisions, respectively. The values obtained are
summarized in Table 1. The systematic uncertainties are determined from the
variation of the composition of secondary contributions, and the $\Lambda$ to
$\Sigma^{0}$ ratio.

p–p | p–$\mathrm{\Lambda}$ | p–$\mathrm{\Xi^{-}}$ |  $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
---|---|---|---
Pair |  $\lambda_{i}^{\mathrm{p\kern-0.35002ptp}}$ |  $\lambda_{i}^{\mathrm{p\mbox{--}Pb}}$ | Pair |  $\lambda_{i}^{\mathrm{p\kern-0.35002ptp}}$ |  $\lambda_{i}^{\mathrm{p\mbox{--}Pb}}$ | Pair |  $\lambda_{i}^{\mathrm{p\kern-0.35002ptp}}$ |  $\lambda_{i}^{\mathrm{p\mbox{--}Pb}}$ | Pair |  $\lambda_{i}^{\mathrm{p\kern-0.35002ptp}}$ |  $\lambda_{i}^{\mathrm{p\mbox{--}Pb}}$
(%) |  (%) |  (%) |  (%) |  (%) |  (%) |  (%) |  (%)
pp |  74.8 |  72.8 | p$\Lambda$ |  50.3 |  41.5 | p$\Xi^{-}$ |  55.5 |  50.8 | $\Lambda\Lambda$ |  33.8 |  23.9
ppΛ |  15.1 |  16.1 | p$\Lambda_{\Sigma^{0}}$ |  16.8 |  13.8 | p$\Xi^{-}_{\Xi(1530)^{-}}$ |  8.8 |  8.1 |  |  |
|  |  | p$\Lambda_{\Xi^{-}}$ |  8.3 |  12.1 |  |  |  |  |  |
flat res. |  8.1 |  8.0 | flat res. |  20.4 |  24.9 | flat res. |  30.3 |  28.3 | flat res. |  59.8 |  64.0
fakes |  2.0 |  3.1 | fakes |  4.2 |  7.7 | fakes |  5.4 |  12.8 | fakes |  6.4 |  12.1
Table 1: The weight parameters (Eq. 4)
$\lambda_{i}^{\mathrm{p\kern-0.35002ptp}}$ and
$\lambda_{i}^{\mathrm{p\mbox{--}Pb}}$ of the individual components of the p–p,
p–$\mathrm{\Lambda}$, p–$\mathrm{\Xi^{-}}$ and
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ correlation functions. The sub-indexes
are used to indicate the mother particle in case of feed-down. Only the non-
flat feed-down (residual) contributions are listed individually, while all
other contributions are listed as “flat residuals (res.)”. All misidentified
(fake) pairs are assumed to be uncorrelated, thus resulting in a flat
correlation signal.

The individual contributions $C_{i}(k^{*})$ are modeled either using CATS or
the Lednický model. The non-genuine ($i\neq 0$) contributions include
additional kinematic effects which lead to a smearing of their corresponding
correlation functions [39]. As the correlation strength of these residuals is
strongly damped one can assume that $C_{i\neq 0}(k^{*})\approx 1$ [40]. The
only significant contribution is p–$\mathrm{\Lambda}$$\rightarrow$p–p, where
the p–$\mathrm{\Lambda}$ interaction is modeled using the scattering
parameters from a next-to-leading order (NLO) $\chi$EFT calculation [41] and
the corresponding correlation function is computed using the Lednický model.
The remaining residuals are considered flat, apart from
p–$\mathrm{\Xi^{-}}$$\rightarrow$p–$\mathrm{\Lambda}$,
$\mathrm{p}$–$\Sigma^{0}\rightarrow$p–$\mathrm{\Lambda}$ and
$\mathrm{p}$–$\Xi(1530)^{-}\rightarrow$p–$\mathrm{\Xi^{-}}$, where the
interaction can be modeled. For the p–$\mathrm{\Xi^{-}}$ interaction a recent
lattice QCD potential, from the HAL QCD collaboration [42, 43], is used. The
$\mathrm{p}$–$\Sigma^{0}$ is modeled as in [44], while
$\mathrm{p}$–$\Xi(1530)^{-}$ is evaluated by taking only the Coulomb
interaction into account.

After all corrections have been applied to $C_{\mathrm{tot}}(k^{*})$, the
final fit function is obtained by multiplying it with a linear baseline
$(a+bk^{*})$ describing the normalization and non-femtoscopy background [25]

$C_{\mathrm{fit}}(k^{*})=(a+bk^{*})C_{\mathrm{tot}}(k^{*}).$ (5)

Figure 1 shows an example of the p–p and $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
correlation functions measured in $\mathrm{p\kern-0.50003ptp}$ collisions at
$\sqrt{s}=13$ TeV, together with the fit functions.

Figure 1: Results for the fit of the $\mathrm{p\kern-0.50003ptp}$ data at
$\sqrt{s}=13$ TeV. The p–p correlation function (left panel) is fitted with
CATS (blue line) and the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ correlation
function (right panel) is fitted with the Lednický model (yellow line). The
dashed line represents the linear baseline from Eq. 5, while the dark dashed-
dotted line on top of the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ data shows the
expected correlation based on quantum statistics alone, in case of a strong
interaction potential compatible with zero.

The p–p experimental data show a flat behaviour in the range $200<k^{*}<400$
MeV/$c$, thus by default the slope of the baseline is assumed to be zero
($b=0$) and the correlation is fitted in the range $k^{*}<375$ MeV/$c$. The
resulting $r_{0}$ values are $1.182\pm
0.008\text{(stat)}^{+0.005}_{-0.002}\text{(syst)}$ fm in
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=13$ TeV and $1.427\pm
0.007\text{(stat)}^{+0.001}_{-0.014}\text{(syst)}$ fm in
$\mathrm{p\mbox{--}Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. In
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=7$ TeV the source size is
$r_{0}=1.125\pm 0.018\text{(stat)}^{+0.058}_{-0.035}\text{(syst)}$ fm [25].

The systematic uncertainties of the radius $r_{0}$ are evaluated following the
prescription established during the analysis of $\mathrm{p\kern-0.50003ptp}$
collisions at $\sqrt{s}=$7 TeV [25]. The upper limit of the fit range for the
p–p pairs is varied within $k^{*}\in\\{350,375,400\\}$ MeV/$c$ and the input
to the $\lambda$ parameters is modified by 20%, keeping primary and secondary
fractions constant.

Two further systematic variations are performed for the p–p correlation. The
first concerns the possible effect of non-femtoscopy contributions to the
correlation functions, which can be modeled by a linear baseline (see Eq. 5)
with the inclusion of $b$ as a free fit parameter. The final systematic
variation is to model the p–$\mathrm{\Lambda}$ feed-down contribution by using
a leading-order (LO) [45, 41] computation to model the interaction. The effect
of the latter is negligible, as the transformation to the p–p system smears
the differences observed in the pure p–$\mathrm{\Lambda}$ correlation function
out.

To investigate the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ interaction the
source sizes are fixed to the above results and the
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ correlations from all three data sets
are fitted simultaneously in order to extract the scattering parameters. The
correlation functions show a slight non-flat behaviour at large $k^{*}$,
especially for the $\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=13$
TeV (right panel in Fig. 1). Thus the fit is performed by allowing a non-zero
slope parameter $b$ (see Eq. 5). The fit range is extended to $k^{*}<460$
MeV/$c$ in order to better constrain the linear baseline. Due to the small
primary $\lambda$ parameters (see Table 1) the
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ correlation signal is quite weak and the
fit shows a slight systematic enhancement compared to the expected
$C_{\mathrm{tot}}(k^{*})$ due to quantum statistics only, suggestive of an
attractive interaction. However, the current statistical uncertainties do not
allow the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ scattering parameters to be
extracted from the fit. Therefore, an alternative approach to study the
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ interaction will be presented in the
next section. Systematic uncertainties related to the
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ emission source may arise from several
different effects, which are discussed in the rest of this section.

Previous studies have revealed that the emission source can be elongated along
some of the spatial directions and have a multiplicity or $m_{\mathrm{T}}$
dependence [46, 47]. In the present analysis it is assumed that the
correlation function can be modeled by an effective Gaussian source. The
validity of this statement is verified by a simple toy Monte Carlo, in which a
data-driven multiplicity dependence is introduced into the source function and
the resulting theoretical p–p correlation function computed with CATS. The
deviations between this result and a correlation function obtained with an
effective Gaussian source profile are negligible.

Possible differences in the effective emitting sources of p–p and
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ pairs due to the strong decays of broad
resonances and $m_{\mathrm{T}}$ scaling are evaluated via simulations and
estimated to have at most a $5$% effect on the effective source size $r_{0}$.
This is taken into account by including an additional systematic uncertainty
on the $r_{\text{$\mathrm{\Lambda}$\mbox{--}$\mathrm{\Lambda}$}}$ value
extracted from the fit to the p–p correlation.

##  4 Results

In order to extract the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ scattering
parameters, the correlation functions measured in $\mathrm{p\kern-0.50003ptp}$
collisions at $\sqrt{s}=$7, 13 TeV as well as in $\mathrm{p\mbox{--}Pb}$
collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV are fitted simultaneously. The
right panel in Fig. 1 shows the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
correlation function obtained in $\mathrm{p\kern-0.50003ptp}$ collisions at
$\sqrt{s}=13$ TeV together with the result from the fit.

Figure 2: $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ correlations measured in
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=13$ TeV (left panel) and
$\mathrm{p\mbox{--}Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV (right
panel) together with the functions computed by the different models [20]. The
tested potentials are converted to correlation functions using CATS and the
baseline is refitted for each model. The effects of momentum resolution and
residuals are included in the theory curves.

Since the uncertainties of the scattering parameters are large, different
model predictions are tested on the basis of their agreement with the measured
correlation functions.

One option is to use a local potential and obtain $C(k^{*})$ based on the
exact solution from CATS, with the source size fixed to the value obtained
from the fit to the p–p correlations. Many of the existing model predictions
are summarized in [20] and the corresponding potentials $V(r)$ are
parametrized in a local form using a double-Gaussian function. The correlation
function depends on the nature of the underlying interaction and Fig. 2 shows
the experimental $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ correlations measured
in $\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=13$ TeV (left panel)
and $\mathrm{p\mbox{--}Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV
(right panel) together with the correlation functions obtained for different
meson-exchange interaction potentials employing CATS. Models with a strongly
attractive interaction ($f^{-1}_{0}\lesssim 1$ and positive), like the Ehime
[17] potential, result in a large enhancement of the correlation function at
low momenta which overshoots the data significantly both in
$\mathrm{p\kern-0.50003ptp}$ and $\mathrm{p\mbox{--}Pb}$ collisions. The same
is valid for potentials corresponding to a shallow bound state
($f^{-1}_{0}\rightarrow 0$ and negative), e.g. NF44 [19].

The other tested potentials correspond either to a bound state or a shallow
attractive ($f^{-1}_{0}\gtrsim 1$) non-binding interaction. However, those two
very different scenarios result in similar correlations and are difficult to
separate. This is evident from Fig. 2 as all of the ESC08 [48], HKMYY [22] and
Nijmegen ND46 [18] models produce comparable results and are compatible with
the experimental data, even though their scattering parameters are different.
In particular, ND46 predicts a bound state, while the ESC08 and HKMYY models
describe a shallow attractive potential and the latter is consistent with
hypernuclei data [7, 8].

The Lednický model can be used to compute $C(k^{*})$ for any $f^{-1}_{0}$ and
$d_{0}$. Thus a scan over the scattering parameters can be preformed and the
agreement to the experimental data can be quantified. The Lednický model
breaks down for source sizes smaller than the effective range, especially when
dealing with repulsive interactions [25], as it produces unphysical negative
correlation functions. As there are no realistic models predicting such an
interaction, this study is not affected. Nevertheless, all models described in
[20] are explicitly tested by comparing the correlation functions obtained
using the exact solution provided by CATS with the approximate solution
evaluated using the Lednický model. The deviations are on the percent level
and are neglected.

Another assumption, which the Lednický model is based on, is a Gaussian
profile of the source. The EPOS [34] transport model predicts a non-Gaussian
emission profile [35], and the effects of short lived resonances are included.
This source was adopted in CATS, by tuning its width such as to describe the
p–p correlation function, and the predicted $C(k^{*})$ for all of the ND and
NF models, shown in Fig. 3, were compared to the
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ correlation function in
$\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=13$ TeV. The deviations
in $\chi^{2}$ compared to the case of a Gaussian source are within the
uncertainty, justifying the use of a Gaussian source.

Figure 3: Exclusion plot for the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
scattering parameters obtained using the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
correlations from $\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=7$ and
13 TeV as well as $\mathrm{p\mbox{--}Pb}$ collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. The different colors represent the
confidence level of excluding a set of parameters, given in $n\sigma$. The
black hashed region is where the Lednický model produces an unphysical
correlation. The two models denoted by colored stars are compatible with
hypernuclei data, while the red cross corresponds to the preliminary result of
the lattice computation performed by the HAL QCD collaboration. For details
regarding the region at slightly negative $f^{-1}_{0}$ and $d_{0}<4$,
compatible with a bound state, refer to Fig. 4.

To quantify the uncertainties of $f^{-1}_{0}$ and $d_{0}$, and estimate the
confidence level of each parameter set, a Monte Carlo method is used. In the
current work the approach described in [49] is followed, which is closely
related to the Bootstrap method. The strategy is to use the Lednický model to
perform a scan over the parameter space spanned by $f^{-1}_{0}\in[-2,5]$ fm-1
and $d_{0}\in[0,18]$ fm and refit the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
correlation using Eq. 5 when fixing the scattering parameters to a specific
value $(f^{-1}_{0},d_{0})_{i}$. The corresponding $\chi^{2}_{i}$ is evaluated
by taking all data sets ($\mathrm{p\kern-0.50003ptp}$ at $\sqrt{s}=7$ and $13$
TeV and $\mathrm{p\mbox{--}Pb}$ at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV) into
account. The different scattering parameters can be compared by finding the
lowest (best) $\chi^{2}_{\text{best}}$ and evaluating
$\Delta\chi^{2}_{i}=\chi^{2}_{i}-\chi^{2}_{\text{best}}$ for each parameter
set. This observable, and the associated $(f^{-1}_{0},d_{0})_{i}$, can be
directly linked to the confidence level [49]. This can be achieved either by
assuming normally distributed uncertainties of $(f^{-1}_{0},d_{0})$, or
invoking a more sophisticated Monte Carlo study, like the Bootstrap method.
The latter is used in the current analysis.

The resulting exclusion plot is presented in Fig. 3, where the color code
corresponds to the confidence level $n\sigma$ for a specific choice of
scattering parameters. In the computation only the statistical uncertainties
are taken into account, as the systematic uncertainties are negligible
according to the Barlow criterion [38]. The predicted scattering parameters of
all discussed potentials are highlighted with different markers and the phase
space region in which the Lednický model produces an unphysical correlation is
specified by the black hatched area. In this region the effective range
expansion breaks down and the Lednický equation leads to a negative
correlation function. While the STAR result [24] is located in this region,
all theoretical models exclude the possibility of a repulsive
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ interaction with large effective range.
Moreover a re-analysis of the STAR data [20] demonstrated that a more
realistic treatment of the residual correlations leads to an inversion of the
sign of the scattering length, that corresponds to an attractive potential.
The imposed limit on the scattering length is $f_{0}^{-1}>0.8~{}$fm-1 [20].
This result can be tested within the current work, and Fig. 3 demonstrates
that the ALICE data can extend those constraints. In particular the region
corresponding to a strongly attractive or a very weakly binding short-range
interaction (small $|f^{-1}_{0}|$ and small $d_{0}$) is excluded by the data,
while a shallow attractive potential (large $f^{-1}_{0}$) is in very good
agreement with the experimental results obtained from this analysis. A
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ bound state would correspond to negative
$f^{-1}_{0}$ and small $d_{0}$ values. The present data are compatible with
such a scenario, but the available phase space is strongly constrained. The
HKMYY [22], FG [21] and HAL QCD [50] values are of particular interest, as the
first two models are tuned to describe the modern hypernuclei data, while the
latter is the latest state-of-the-art lattice computation from the HAL QCD
collaboration. The lattice results are preliminary and predict the scattering
parameters $f^{-1}_{0}=1.45\pm 0.25$ fm-1 and $d_{0}=5.16\pm 0.82$ fm [50].
All three models are compatible with the ALICE data, providing further support
for a shallow attractive $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ interaction
potential.

Figure 4: The region of the 1$\sigma$ confidence level from Fig. 3, displayed
in the ($B_{\Lambda\Lambda},d_{0}$) plane. The inner (dark) region corresponds
to the statistical uncertainty of the method, while the outer (light) region
includes the systematic variations. The red star corresponds to the parameters
with the lowest $\chi^{2}$.

A possible bound state is investigated within the effective-range expansion by
computing the corresponding binding energy from the relation [51, 52]

$B_{\Lambda\Lambda}=\dfrac{1}{m_{\Lambda}d_{0}^{2}}\left(1-\sqrt{1+2d_{0}f^{-1}_{0}}\right)^{2}.$
(6)

This relation is only valid for bound states, which are characterized by
negative $f^{-1}_{0}$ values. Further, the binding energy has to be a real
number, thus the expression $1+2d_{0}f^{-1}_{0}$ has to be positive, which
implies that at least one of the parameters $f^{-1}_{0}$ or $d_{0}$ has to be
small in absolute value. With these restrictions Eq. 6 transforms the
observables in the exclusion plot (Fig. 3) from $(f^{-1}_{0},d_{0})$ to
$(B_{\Lambda\Lambda},d_{0})$, considering only the parameter space compatible
with a bound state. This is done in Fig. 4, where only the 1$\sigma$
confidence region is shown, as it corresponds to the uncertainty of
$B_{\Lambda\Lambda}$. The dark region marks the statistical uncertainty of the
fit. The allowed binding energy, independent of $d_{0}$, is
$B_{\Lambda\Lambda}=3.2^{+1.6}_{-2.4}\text{(stat)}$ MeV, where the central
value corresponds to the lowest $\chi^{2}$ and the uncertainties are
determined based on the lowest and highest allowed $B_{\Lambda\Lambda}$ values
within the 1$\sigma$ confidence region. However the systematic uncertainties
related to the source sizes are not taken into account, neither any possible
biases related to the fit procedure. Thus the computation of the exclusion
plots (Figs. 3 and 4) was repeated 121 times, where in each re-iteration the
source sizes related to the data sets are varied within the associated
uncertainties, the fit ranges within $k^{*}\in\\{420,460,500\\}~{}$MeV/$c$ and
the bin widths of the experimental correlations are chosen as 12, 16 and 20
MeV/$c$. The resulting fluctuations of the 1$\sigma$ confidence region are
marked in Fig. 4 by the light region and represent the total uncertainty.
Assuming the latter is the quadratic sum of the statistical and systematic
uncertainty, the final result is
$B_{\Lambda\Lambda}=3.2^{+1.6}_{-2.4}\text{(stat)}^{+1.8}_{-1.0}\text{(syst)}$
MeV.

##  5 Summary

In this Letter, new data on p–p and $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
correlations in $\mathrm{p\kern-0.50003ptp}$ collisions at $\sqrt{s}=13$ TeV
and $\mathrm{p\mbox{--}Pb}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV
are presented. Together with the results from a pioneering study on two-baryon
correlations in $\mathrm{p\kern-0.50003ptp}$ at $\sqrt{s}=7$ TeV, these data
allow for a detailed study of the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
interaction with unprecedented precision.

Each data set is analyzed separately by extracting the p–p and
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ correlation functions. The former are
used to constrain the size of the source $r_{0}$, which is assumed to be the
same for p–p and $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ pairs. The
$\mathrm{\Lambda}$–$\mathrm{\Lambda}$ interaction is then investigated by
testing the combined compatibility of all data sets to different model
predictions and scattering parameters. The HKMYY and FG models, which are
tuned to hypernuclei data, and the lattice calculations performed by the HAL
QCD collaboration predict a shallow attractive interaction potential. The
ALICE data manifest very good agreement with these predictions. Nevertheless,
the data is also compatible with the existence of a bound state, given a
binding energy of
$B_{\Lambda\Lambda}=3.2^{+1.6}_{-2.4}\text{(stat)}^{+1.8}_{-1.0}\text{(syst)}$
MeV. The Run 3 of the LHC is expected to further increase the statistical
significance of the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$ correlation function
and allow the scattering parameters to be constraint even more precisely in
the future.

## Acknowledgements

The ALICE collaboration is grateful to the HAL QCD collaboration for providing
lattice results regarding the $\mathrm{\Lambda}$–$\mathrm{\Lambda}$
interaction. We are particularly thankful to Prof. Tetsuo Hatsuda and Prof.
Kenji Sasaki for the precious suggestions and stimulating discussions.

The ALICE Collaboration would like to thank all its engineers and technicians
for their invaluable contributions to the construction of the experiment and
the CERN accelerator teams for the outstanding performance of the LHC complex.
The ALICE Collaboration gratefully acknowledges the resources and support
provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG)
collaboration. The ALICE Collaboration acknowledges the following funding
agencies for their support in building and running the ALICE detector: A. I.
Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation
(ANSL), State Committee of Science and World Federation of Scientists (WFS),
Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M
2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung,
Austria; Ministry of Communications and High Technologies, National Nuclear
Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e
Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS),
Financiadora de Estudos e Projetos (Finep) and Fundação de Amparo à Pesquisa
do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of
China (MSTC), National Natural Science Foundation of China (NSFC) and Ministry
of Education of China (MOEC) , China; Croatian Science Foundation and Ministry
of Science and Education, Croatia; Centro de Aplicaciones Tecnológicas y
Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth
and Sports of the Czech Republic, Czech Republic; The Danish Council for
Independent Research — Natural Sciences, the Carlsberg Foundation and Danish
National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics
(HIP), Finland; Commissariat à l’Energie Atomique (CEA), Institut National de
Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National
de la Recherche Scientifique (CNRS) and Région des Pays de la Loire, France;
Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Germany; General Secretariat for Research and
Technology, Ministry of Education, Research and Religions, Greece; National
Research, Development and Innovation Office, Hungary; Department of Atomic
Energy Government of India (DAE), Department of Science and Technology,
Government of India (DST), University Grants Commission, Government of India
(UGC) and Council of Scientific and Industrial Research (CSIR), India;
Indonesian Institute of Science, Indonesia; Centro Fermi - Museo Storico della
Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica
Nucleare (INFN), Italy; Institute for Innovative Science and Technology ,
Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion
of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports,
Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONACYT) y
Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología
(FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA),
Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO),
Netherlands; The Research Council of Norway, Norway; Commission on Science and
Technology for Sustainable Development in the South (COMSATS), Pakistan;
Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher
Education and National Science Centre, Poland; Korea Institute of Science and
Technology Information and National Research Foundation of Korea (NRF),
Republic of Korea; Ministry of Education and Scientific Research, Institute of
Atomic Physics and Ministry of Research and Innovation and Institute of Atomic
Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of
Education and Science of the Russian Federation, National Research Centre
Kurchatov Institute, Russian Science Foundation and Russian Foundation for
Basic Research, Russia; Ministry of Education, Science, Research and Sport of
the Slovak Republic, Slovakia; National Research Foundation of South Africa,
South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg
Foundation (KAW), Sweden; European Organization for Nuclear Research,
Switzerland; National Science and Technology Development Agency (NSDTA),
Suranaree University of Technology (SUT) and Office of the Higher Education
Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy
Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine;
Science and Technology Facilities Council (STFC), United Kingdom; National
Science Foundation of the United States of America (NSF) and United States
Department of Energy, Office of Nuclear Physics (DOE NP), United States of
America.

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##  Appendix A The ALICE Collaboration

S. Acharyaorg141&D. Adamováorg93&S.P. Adhyaorg141&A. Adlerorg74&J.
Adolfssonorg80&M.M. Aggarwalorg98&G. Aglieri Rinellaorg34&M. Agnelloorg31&N.
Agrawalorg10&Z. Ahammedorg141&S. Ahmadorg17&S.U. Ahnorg76&S. Aiolaorg146&A.
Akindinovorg64&M. Al-Turanyorg105&S.N. Alamorg141&D.S.D. Albuquerqueorg122&D.
Aleksandrovorg87&B. Alessandroorg58&H.M. Alfandaorg6&R. Alfaro Molinaorg72&B.
Aliorg17&Y. Aliorg15&A. Aliciorg10,org53,org27&A. Alkinorg2&J. Almeorg22&T.
Altorg69&L. Altenkamperorg22&I. Altsybeevorg112&M.N. Anaamorg6&C.
Andreiorg47&D. Andreouorg34&H.A. Andrewsorg109&A. Andronicorg144&M.
Angelettiorg34&V. Anguelovorg102&C. Ansonorg16&T. Antičićorg106&F.
Antinoriorg56&P. Antonioliorg53&R. Anwarorg126&N. Apadulaorg79&L.
Aphecetcheorg114&H. Appelshäuserorg69&S. Arcelliorg27&R. Arnaldiorg58&M.
Arratiaorg79&I.C. Arseneorg21&M. Arslandokorg102&A. Augustinusorg34&R.
Averbeckorg105&S. Azizorg61&M.D. Azmiorg17&A. Badalàorg55&Y.W. Baekorg40&S.
Bagnascoorg58&X. Baiorg105&R. Bailhacheorg69&R. Balaorg99&A.
Baldisseriorg137&M. Ballorg42&R.C. Baralorg85&R. Barberaorg28&L.
Barioglioorg26&G.G. Barnaföldiorg145&L.S. Barnbyorg92&V. Barretorg134&P.
Bartaliniorg6&K. Barthorg34&E. Bartschorg69&F. Baruffaldiorg29&N.
Bastidorg134&S. Basuorg143&G. Batigneorg114&B. Batyunyaorg75&P.C.
Batzingorg21&D. Bauriorg48&J.L. Bazo Albaorg110&I.G. Beardenorg88&C.
Beddaorg63&N.K. Beheraorg60&I. Belikovorg136&F. Belliniorg34&R.
Bellwiedorg126&V. Belyaevorg91&G. Bencediorg145&S. Beoleorg26&A.
Bercuciorg47&Y. Berdnikovorg96&D. Berenyiorg145&R.A. Bertensorg130&D.
Berzanoorg58&M.G. Besoiuorg68&L. Betevorg34&A. Bhasinorg99&I.R. Bhatorg99&H.
Bhattorg48&B. Bhattacharjeeorg41&A. Bianchiorg26&L. Bianchiorg126,org26&N.
Bianchiorg51&J. Bielčíkorg37&J. Bielčíkováorg93&A. Bilandzicorg117,org103&G.
Biroorg145&R. Biswasorg3&S. Biswasorg3&J.T. Blairorg119&D. Blauorg87&C.
Blumeorg69&G. Bocaorg139&F. Bockorg94,org34&A. Bogdanovorg91&L.
Boldizsárorg145&A. Bolozdynyaorg91&M. Bombaraorg38&G. Bonomiorg140&H.
Borelorg137&A. Borissovorg144,org91&M. Borriorg128&H. Bossiorg146&E.
Bottaorg26&C. Bourjauorg88&L. Bratrudorg69&P. Braun-Munzingerorg105&M.
Bregantorg121&T.A. Brokerorg69&M. Brozorg37&E.J. Bruckenorg43&E.
Brunaorg58&G.E. Brunoorg33,org104&M.D. Bucklandorg128&D. Budnikovorg107&H.
Bueschingorg69&S. Bufalinoorg31&O. Bugnonorg114&P. Buhlerorg113&P.
Buncicorg34&Z. Butheleziorg73&J.B. Buttorg15&J.T. Buxtonorg95&D.
Caffarriorg89&A. Calivaorg105&E. Calvo Villarorg110&R.S. Camachoorg44&P.
Cameriniorg25&A.A. Caponorg113&F. Carnesecchiorg10&J. Castillo
Castellanosorg137&A.J. Castroorg130&E.A.R. Casulaorg54&F. Catalanoorg31&C.
Ceballos Sanchezorg52&P. Chakrabortyorg48&S. Chandraorg141&B. Changorg127&W.
Changorg6&S. Chapelandorg34&M. Chartierorg128&S. Chattopadhyayorg141&S.
Chattopadhyayorg108&A. Chauvinorg24&C. Cheshkovorg135&B. Cheynisorg135&V.
Chibante Barrosoorg34&D.D. Chinellatoorg122&S. Choorg60&P. Chochulaorg34&T.
Chowdhuryorg134&P. Christakoglouorg89&C.H. Christensenorg88&P.
Christiansenorg80&T. Chujoorg133&C. Cicaloorg54&L. Cifarelliorg10,org27&F.
Cindoloorg53&J. Cleymansorg125&F. Colamariaorg52&D. Colellaorg52&A.
Colluorg79&M. Colocciorg27&M. Concasorg58orgI&G. Conesa Balbastreorg78&Z.
Conesa del Valleorg61&G. Continorg59,org128&J.G. Contrerasorg37&T.M.
Cormierorg94&Y. Corrales Moralesorg58,org26&P. Corteseorg32&M.R.
Cosentinoorg123&F. Costaorg34&S. Costanzaorg139&J. Crkovskáorg61&P.
Crochetorg134&E. Cuautleorg70&L. Cunqueiroorg94&D. Dabrowskiorg142&T.
Dahmsorg103,org117&A. Daineseorg56&F.P.A. Damasorg137,org114&S. Daniorg66&M.C.
Danischorg102&A. Danuorg68&D. Dasorg108&I. Dasorg108&S. Dasorg3&A.
Dashorg85&S. Dashorg48&A. Dashiorg103&S. Deorg85,org49&A. De Caroorg30&G. de
Cataldoorg52&C. de Contiorg121&J. de Cuvelandorg39&A. De Falcoorg24&D. De
Gruttolaorg10&N. De Marcoorg58&S. De Pasqualeorg30&R.D. De Souzaorg122&S.
Deborg49&H.F. Degenhardtorg121&K.R. Dejaorg142&A. Delofforg84&S.
Delsantoorg131,org26&P. Dhankherorg48&D. Di Bariorg33&A. Di Mauroorg34&R.A.
Diazorg8&T. Dietelorg125&P. Dillensegerorg69&Y. Dingorg6&R. Diviàorg34&Ø.
Djuvslandorg22&U. Dmitrievaorg62&A. Dobrinorg34,org68&B. Dönigusorg69&O.
Dordicorg21&A.K. Dubeyorg141&A. Dublaorg105&S. Dudiorg98&M. Dukhishyamorg85&P.
Dupieuxorg134&R.J. Ehlersorg146&D. Eliaorg52&H. Engelorg74&E. Eppleorg146&B.
Erazmusorg114&F. Erhardtorg97&A. Erokhinorg112&M.R. Ersdalorg22&B.
Espagnonorg61&G. Eulisseorg34&J. Eumorg18&D. Evansorg109&S. Evdokimovorg90&L.
Fabbiettiorg117,org103&M. Fagginorg29&J. Faivreorg78&A. Fantoniorg51&M.
Faselorg94&P. Fecchioorg31&L. Feldkamporg144&A. Felicielloorg58&G.
Feofilovorg112&A. Fernández Téllezorg44&A. Ferreroorg137&A. Ferrettiorg26&A.
Festantiorg34&V.J.G. Feuillardorg102&J. Figielorg118&S. Filchaginorg107&D.
Finogeevorg62&F.M. Fiondaorg22&G. Fiorenzaorg52&F. Flororg126&S.
Foertschorg73&P. Fokaorg105&S. Fokinorg87&E. Fragiacomoorg59&U.
Frankenfeldorg105&G.G. Fronzeorg26&U. Fuchsorg34&C. Furgetorg78&A.
Fursorg62&M. Fusco Girardorg30&J.J. Gaardhøjeorg88&M. Gagliardiorg26&A.M.
Gagoorg110&A. Galorg136&C.D. Galvanorg120&P. Ganotiorg83&C. Garabatosorg105&E.
Garcia-Solisorg11&K. Gargorg28&C. Gargiuloorg34&K. Garnerorg144&P.
Gasikorg103,org117&E.F. Gaugerorg119&M.B. Gay Ducatiorg71&M. Germainorg114&J.
Ghoshorg108&P. Ghoshorg141&S.K. Ghoshorg3&P. Gianottiorg51&P.
Giubellinoorg105,org58&P. Giubilatoorg29&P. Glässelorg102&D.M. Goméz
Coralorg72&A. Gomez Ramirezorg74&V. Gonzalezorg105&P. González-Zamoraorg44&S.
Gorbunovorg39&L. Görlichorg118&S. Gotovacorg35&V. Grabskiorg72&L.K.
Graczykowskiorg142&K.L. Grahamorg109&L. Greinerorg79&A. Grelliorg63&C.
Grigorasorg34&V. Grigorievorg91&A. Grigoryanorg1&S. Grigoryanorg75&O.S.
Groettvikorg22&J.M. Gronefeldorg105&F. Grosaorg31&J.F. Grosse-
Oetringhausorg34&R. Grossoorg105&R. Guernaneorg78&B. Guerzoniorg27&M.
Guittiereorg114&K. Gulbrandsenorg88&T. Gunjiorg132&A. Guptaorg99&R.
Guptaorg99&I.B. Guzmanorg44&R. Haakeorg34,org146&M.K. Habiborg105&C.
Hadjidakisorg61&H. Hamagakiorg81&G. Hamarorg145&M. Hamidorg6&R.
Hanniganorg119&M.R. Haqueorg63&A. Harlenderovaorg105&J.W. Harrisorg146&A.
Hartonorg11&J.A. Hasenbichlerorg34&H. Hassanorg78&D.
Hatzifotiadouorg10,org53&P. Hauerorg42&S. Hayashiorg132&S.T. Heckelorg69&E.
Hellbärorg69&H. Helstruporg36&A. Herghelegiuorg47&E.G. Hernandezorg44&G.
Herrera Corralorg9&F. Herrmannorg144&K.F. Hetlandorg36&T.E. Hildenorg43&H.
Hillemannsorg34&C. Hillsorg128&B. Hippolyteorg136&B. Hohlwegerorg103&D.
Horakorg37&S. Hornungorg105&R. Hosokawaorg133&P. Hristovorg34&C. Huangorg61&C.
Hughesorg130&P. Huhnorg69&T.J. Humanicorg95&H. Hushnudorg108&L.A.
Husovaorg144&N. Hussainorg41&S.A. Hussainorg15&T. Hussainorg17&D.
Hutterorg39&D.S. Hwangorg19&J.P. Iddonorg128,org34&R. Ilkaevorg107&M.
Inabaorg133&M. Ippolitovorg87&M.S. Islamorg108&M. Ivanovorg105&V.
Ivanovorg96&V. Izucheevorg90&B. Jacakorg79&N. Jacazioorg27&P.M.
Jacobsorg79&M.B. Jadhavorg48&S. Jadlovskaorg116&J. Jadlovskyorg116&S.
Jaelaniorg63&C. Jahnkeorg121&M.J. Jakubowskaorg142&M.A. Janikorg142&M.
Jercicorg97&O. Jevonsorg109&R.T. Jimenez Bustamanteorg105&M. Jinorg126&F.
Jonasorg144,org94&P.G. Jonesorg109&A. Juskoorg109&P. Kalinakorg65&A.
Kalweitorg34&J.H. Kangorg147&V. Kaplinorg91&S. Karorg6&A. Karasu Uysalorg77&O.
Karavichevorg62&T. Karavichevaorg62&P. Karczmarczykorg34&E. Karpechevorg62&U.
Kebschullorg74&R. Keidelorg46&M. Keilorg34&B. Ketzerorg42&Z.
Khabanovaorg89&A.M. Khanorg6&S. Khanorg17&S.A. Khanorg141&A.
Khanzadeevorg96&Y. Kharlovorg90&A. Khatunorg17&A. Khuntiaorg118,org49&B.
Kilengorg36&B. Kimorg60&B. Kimorg133&D. Kimorg147&D.J. Kimorg127&E.J.
Kimorg13&H. Kimorg147&J. Kimorg147&J.S. Kimorg40&J. Kimorg102&J. Kimorg147&J.
Kimorg13&M. Kimorg102&S. Kimorg19&T. Kimorg147&T. Kimorg147&S. Kirschorg39&I.
Kiselorg39&S. Kiselevorg64&A. Kisielorg142&J.L. Klayorg5&C. Kleinorg69&J.
Kleinorg58&S. Kleinorg79&C. Klein-Bösingorg144&S. Klewinorg102&A.
Klugeorg34&M.L. Knichelorg34&A.G. Knospeorg126&C. Kobdajorg115&M.K.
Köhlerorg102&T. Kolleggerorg105&A. Kondratyevorg75&N. Kondratyevaorg91&E.
Kondratyukorg90&P.J. Konopkaorg34&L. Koskaorg116&O. Kovalenkoorg84&V.
Kovalenkoorg112&M. Kowalskiorg118&I. Králikorg65&A. Kravčákováorg38&L.
Kreisorg105&M. Krivdaorg109,org65&F. Krizekorg93&K. Krizkova Gajdosovaorg37&M.
Krügerorg69&E. Kryshenorg96&M. Krzewickiorg39&A.M. Kuberaorg95&V.
Kučeraorg60&C. Kuhnorg136&P.G. Kuijerorg89&L. Kumarorg98&S. Kumarorg48&S.
Kunduorg85&P. Kurashviliorg84&A. Kurepinorg62&A.B. Kurepinorg62&S.
Kushpilorg93&J. Kvapilorg109&M.J. Kweonorg60&J.Y. Kwonorg60&Y. Kwonorg147&S.L.
La Pointeorg39&P. La Roccaorg28&Y.S. Laiorg79&R. Langoyorg124&K.
Lapidusorg34,org146&A. Lardeuxorg21&P. Larionovorg51&E. Laudiorg34&R.
Lavickaorg37&T. Lazarevaorg112&R. Leaorg25&L. Leardiniorg102&S. Leeorg147&F.
Lehasorg89&S. Lehnerorg113&J. Lehrbachorg39&R.C. Lemmonorg92&I. León
Monzónorg120&E.D. Lesserorg20&M. Lettrichorg34&P. Lévaiorg145&X. Liorg12&X.L.
Liorg6&J. Lienorg124&R. Lietavaorg109&B. Limorg18&S. Lindalorg21&V.
Lindenstruthorg39&S.W. Lindsayorg128&C. Lippmannorg105&M.A. Lisaorg95&V.
Litichevskyiorg43&A. Liuorg79&S. Liuorg95&W.J. Llopeorg143&I.M. Lofnesorg22&V.
Loginovorg91&C. Loizidesorg94&P. Loncarorg35&X. Lopezorg134&E. López
Torresorg8&P. Luettigorg69&J.R. Luhderorg144&M. Lunardonorg29&G.
Luparelloorg59&M. Lupiorg74&A. Maevskayaorg62&M. Magerorg34&S.M.
Mahmoodorg21&T. Mahmoudorg42&A. Maireorg136&R.D. Majkaorg146&M.
Malaevorg96&Q.W. Malikorg21&L. Malininaorg75orgII&D. Mal’Kevichorg64&P.
Malzacherorg105&A. Mamonovorg107&V. Mankoorg87&F. Mansoorg134&V.
Manzariorg52&Y. Maoorg6&M. Marchisoneorg135&J. Marešorg67&G.V.
Margagliottiorg25&A. Margottiorg53&J. Marguttiorg63&A. Marínorg105&C.
Markertorg119&M. Marquardorg69&N.A. Martinorg102&P. Martinengoorg34&J.L.
Martinezorg126&M.I. Martínezorg44&G. Martínez Garcíaorg114&M. Martinez
Pedreiraorg34&S. Masciocchiorg105&M. Maseraorg26&A. Masoniorg54&L.
Massacrierorg61&E. Massonorg114&A. Mastroserioorg52,org138&A.M.
Mathisorg103,org117&P.F.T. Matuokaorg121&A. Matyjaorg118&C. Mayerorg118&M.
Mazzilliorg33&M.A. Mazzoniorg57&A.F. Mechlerorg69&F. Meddiorg23&Y.
Melikyanorg91&A. Menchaca-Rochaorg72&E. Meninnoorg30&M. Meresorg14&S.
Mhlangaorg125&Y. Miakeorg133&L. Michelettiorg26&M.M. Mieskolainenorg43&D.L.
Mihaylovorg103&K. Mikhaylovorg64,org75&A. Mischkeorg63org*&A.N. Mishraorg70&D.
Miśkowiecorg105&C.M. Mituorg68&N. Mohammadiorg34&A.P. Mohantyorg63&B.
Mohantyorg85&M. Mohisin Khanorg17orgIII&M. Mondalorg141&M.M. Mondalorg66&C.
Mordasiniorg103&D.A. Moreira De Godoyorg144&L.A.P. Morenoorg44&S.
Morettoorg29&A. Morrealeorg114&A. Morschorg34&T. Mrnjavacorg34&V.
Mucciforaorg51&E. Mudnicorg35&D. Mühlheimorg144&S. Muhuriorg141&J.D.
Mulliganorg79,org146&M.G. Munhozorg121&K. Münningorg42&R.H. Munzerorg69&H.
Murakamiorg132&S. Murrayorg73&L. Musaorg34&J. Musinskyorg65&C.J.
Myersorg126&J.W. Myrchaorg142&B. Naikorg48&R. Nairorg84&B.K. Nandiorg48&R.
Naniaorg10,org53&E. Nappiorg52&M.U. Naruorg15&A.F. Nassirpourorg80&H. Natal da
Luzorg121&C. Nattrassorg130&R. Nayakorg48&T.K. Nayakorg85,org141&S.
Nazarenkoorg107&R.A. Negrao De Oliveiraorg69&L. Nellenorg70&S.V. Nesboorg36&G.
Neskovicorg39&B.S. Nielsenorg88&S. Nikolaevorg87&S. Nikulinorg87&V.
Nikulinorg96&F. Noferiniorg10,org53&P. Nomokonovorg75&G. Noorenorg63&J.
Normanorg78&P. Nowakowskiorg142&A. Nyaninorg87&J. Nystrandorg22&M.
Oginoorg81&A. Ohlsonorg102&J. Oleniaczorg142&A.C. Oliveira Da Silvaorg121&M.H.
Oliverorg146&C. Oppedisanoorg58&R. Oravaorg43&A. Ortiz Velasquezorg70&A.
Oskarssonorg80&J. Otwinowskiorg118&K. Oyamaorg81&Y. Pachmayerorg102&V.
Pacikorg88&D. Paganoorg140&G. Paićorg70&P. Palniorg6&J. Panorg143&A.K.
Pandeyorg48&S. Panebiancoorg137&V. Papikyanorg1&P. Pareekorg49&J.
Parkorg60&J.E. Parkkilaorg127&S. Parmarorg98&A. Passfeldorg144&S.P.
Pathakorg126&R.N. Patraorg141&B. Paulorg24,org58&H. Peiorg6&T.
Peitzmannorg63&X. Pengorg6&L.G. Pereiraorg71&H. Pereira Da Costaorg137&D.
Peresunkoorg87&G.M. Perezorg8&E. Perez Lezamaorg69&V. Peskovorg69&Y.
Pestovorg4&V. Petráčekorg37&M. Petroviciorg47&R.P. Pezziorg71&S. Pianoorg59&M.
Piknaorg14&P. Pillotorg114&L.O.D.L. Pimentelorg88&O. Pinazzaorg53,org34&L.
Pinskyorg126&S. Pisanoorg51&D.B. Piyarathnaorg126&M. Płoskońorg79&M.
Planinicorg97&F. Pliquettorg69&J. Plutaorg142&S. Pochybovaorg145&M.G.
Poghosyanorg94&B. Polichtchoukorg90&N. Poljakorg97&W. Poonsawatorg115&A.
Poporg47&H. Poppenborgorg144&S. Porteboeuf-Houssaisorg134&V.
Pozdniakovorg75&S.K. Prasadorg3&R. Preghenellaorg53&F. Prinoorg58&C.A.
Pruneauorg143&I. Pshenichnovorg62&M. Puccioorg34,org26&V. Puninorg107&K.
Puranapandaorg141&J. Putschkeorg143&R.E. Quishpeorg126&S. Ragoniorg109&S.
Rahaorg3&S. Rajputorg99&J. Rakorg127&A. Rakotozafindrabeorg137&L.
Ramelloorg32&F. Ramiorg136&R. Raniwalaorg100&S. Raniwalaorg100&S.S.
Räsänenorg43&B.T. Rascanuorg69&R. Rathorg49&V. Ratzaorg42&I.
Ravasengaorg31&K.F. Readorg130,org94&K. Redlichorg84orgIV&A. Rehmanorg22&P.
Reicheltorg69&F. Reidtorg34&X. Renorg6&R. Renfordtorg69&A. Reshetinorg62&J.-P.
Revolorg10&K. Reygersorg102&V. Riabovorg96&T. Richertorg80,org88&M.
Richterorg21&P. Riedlerorg34&W. Rieglerorg34&F. Riggiorg28&C. Risteaorg68&S.P.
Rodeorg49&M. Rodríguez Cahuantziorg44&K. Røedorg21&R. Rogalevorg90&E.
Rogochayaorg75&D. Rohrorg34&D. Röhrichorg22&P.S. Rokitaorg142&F.
Ronchettiorg51&E.D. Rosasorg70&K. Roslonorg142&P. Rosnetorg134&A.
Rossiorg29&A. Rotondiorg139&F. Roukoutakisorg83&A. Royorg49&P. Royorg108&O.V.
Ruedaorg80&R. Ruiorg25&B. Rumyantsevorg75&A. Rustamovorg86&E.
Ryabinkinorg87&Y. Ryabovorg96&A. Rybickiorg118&H. Rytkonenorg127&S.
Saarinenorg43&S. Sadhuorg141&S. Sadovskyorg90&K. Šafaříkorg37,org34&S.K.
Sahaorg141&B. Sahooorg48&P. Sahooorg49&R. Sahooorg49&S. Sahooorg66&P.K.
Sahuorg66&J. Sainiorg141&S. Sakaiorg133&S. Sambyalorg99&V.
Samsonovorg96,org91&A. Sandovalorg72&A. Sarkarorg73&D. Sarkarorg141,org143&N.
Sarkarorg141&P. Sarmaorg41&V.M. Sartiorg103&M.H.P. Sasorg63&E.
Scapparoneorg53&B. Schaeferorg94&J. Schambachorg119&H.S. Scheidorg69&C.
Schiauaorg47&R. Schickerorg102&A. Schmahorg102&C. Schmidtorg105&H.R.
Schmidtorg101&M.O. Schmidtorg102&M. Schmidtorg101&N.V. Schmidtorg94,org69&A.R.
Schmierorg130&J. Schukraftorg34,org88&Y. Schutzorg34,org136&K.
Schwarzorg105&K. Schwedaorg105&G. Scioliorg27&E. Scomparinorg58&M.
Šefčíkorg38&J.E. Segerorg16&Y. Sekiguchiorg132&D. Sekihataorg45&I.
Selyuzhenkovorg105,org91&S. Senyukovorg136&D. Serebryakovorg62&E.
Serradillaorg72&P. Settorg48&A. Sevcencoorg68&A. Shabanovorg62&A.
Shabetaiorg114&R. Shahoyanorg34&W. Shaikhorg108&A. Shangaraevorg90&A.
Sharmaorg98&A. Sharmaorg99&M. Sharmaorg99&N. Sharmaorg98&A.I. Sheikhorg141&K.
Shigakiorg45&M. Shimomuraorg82&S. Shirinkinorg64&Q. Shouorg111&Y.
Sibiriakorg87&S. Siddhantaorg54&T. Siemiarczukorg84&D. Silvermyrorg80&G.
Simatovicorg89&G. Simonettiorg103,org34&R. Singhorg85&R. Singhorg99&V.K.
Singhorg141&V. Singhalorg141&T. Sinhaorg108&B. Sitarorg14&M. Sittaorg32&T.B.
Skaaliorg21&M. Slupeckiorg127&N. Smirnovorg146&R.J.M. Snellingsorg63&T.W.
Snellmanorg127&J. Sochanorg116&C. Sonccoorg110&J. Songorg60,org126&A.
Songmoolnakorg115&F. Soramelorg29&S. Sorensenorg130&I. Sputowskaorg118&J.
Stachelorg102&I. Stanorg68&P. Stankusorg94&P.J. Steffanicorg130&E.
Stenlundorg80&D. Stoccoorg114&M.M. Storetvedtorg36&P. Strmenorg14&A.A.P.
Suaideorg121&T. Sugitateorg45&C. Suireorg61&M. Suleymanovorg15&M.
Suljicorg34&R. Sultanovorg64&M. Šumberaorg93&S. Sumowidagdoorg50&K.
Suzukiorg113&S. Swainorg66&A. Szaboorg14&I. Szarkaorg14&U. Tabassamorg15&G.
Taillepiedorg134&J. Takahashiorg122&G.J. Tambaveorg22&S. Tangorg134,org6&M.
Tarhiniorg114&M.G. Tarzilaorg47&A. Tauroorg34&G. Tejeda Muñozorg44&A.
Telescaorg34&C. Terrevoliorg126,org29&D. Thakurorg49&S. Thakurorg141&D.
Thomasorg119&F. Thoresenorg88&R. Tieulentorg135&A. Tikhonovorg62&A.R.
Timminsorg126&A. Toiaorg69&N. Topilskayaorg62&M. Toppiorg51&F. Torales-
Acostaorg20&S.R. Torresorg120&S. Tripathyorg49&T. Tripathyorg48&S.
Trogoloorg26,org29&G. Trombettaorg33&L. Tropporg38&V. Trubnikovorg2&W.H.
Trzaskaorg127&T.P. Trzcinskiorg142&B.A. Trzeciakorg63&T. Tsujiorg132&A.
Tumkinorg107&R. Turrisiorg56&T.S. Tveterorg21&K. Ullalandorg22&E.N.
Umakaorg126&A. Urasorg135&G.L. Usaiorg24&A. Utrobicicorg97&M.
Valaorg116,org38&N. Valleorg139&S. Valleroorg58&N. van der Kolkorg63&L.V.R.
van Doremalenorg63&M. van Leeuwenorg63&P. Vande Vyvreorg34&D. Vargaorg145&M.
Varga-Kofaragoorg145&A. Vargasorg44&M. Vargyasorg127&R. Varmaorg48&M.
Vasileiouorg83&A. Vasilievorg87&O. Vázquez Doceorg117,org103&V.
Vecherninorg112&A.M. Veenorg63&E. Vercellinorg26&S. Vergara Limónorg44&L.
Vermuntorg63&R. Vernetorg7&R. Vértesiorg145&L. Vickovicorg35&J.
Viinikainenorg127&Z. Vilakaziorg131&O. Villalobos Baillieorg109&A. Villatoro
Telloorg44&G. Vinoorg52&A. Vinogradovorg87&T. Virgiliorg30&V.
Vislaviciusorg88&A. Vodopyanovorg75&B. Volkelorg34&M.A. Völklorg101&K.
Voloshinorg64&S.A. Voloshinorg143&G. Volpeorg33&B. von Hallerorg34&I.
Vorobyevorg103,org117&D. Voscekorg116&J. Vrlákováorg38&B. Wagnerorg22&Y.
Watanabeorg133&M. Weberorg113&S.G. Weberorg105&A. Wegrzynekorg34&D.F.
Weiserorg102&S.C. Wenzelorg34&J.P. Wesselsorg144&E. Widmannorg113&J.
Wiechulaorg69&J. Wikneorg21&G. Wilkorg84&J. Wilkinsonorg53&G.A.
Willemsorg34&E. Willsherorg109&B. Windelbandorg102&W.E. Wittorg130&Y.
Wuorg129&R. Xuorg6&S. Yalcinorg77&K. Yamakawaorg45&S. Yangorg22&S.
Yanoorg137&Z. Yinorg6&H. Yokoyamaorg63&I.-K. Yooorg18&J.H. Yoonorg60&S.
Yuanorg22&A. Yuncuorg102&V. Yurchenkoorg2&V. Zaccoloorg58,org25&A.
Zamanorg15&C. Zampolliorg34&H.J.C. Zanoliorg121&N. Zardoshtiorg34&A.
Zarochentsevorg112&P. Závadaorg67&N. Zaviyalovorg107&H. Zbroszczykorg142&M.
Zhalovorg96&X. Zhangorg6&Z. Zhangorg6,org134&C. Zhaoorg21&V.
Zherebchevskiiorg112&N. Zhigarevaorg64&D. Zhouorg6&Y. Zhouorg88&Z.
Zhouorg22&J. Zhuorg6&Y. Zhuorg6&A. Zichichiorg27,org10&M.B. Zimmermannorg34&G.
Zinovjevorg2&N. Zurloorg140&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

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

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

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

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

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

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

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

org6Central China Normal University, Wuhan, China

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

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

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

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

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Chonbuk National University, Jeonju, Republic of Korea

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

org15COMSATS University Islamabad, Islamabad, Pakistan

org16Creighton University, Omaha, Nebraska, United States

org17Department of Physics, Aligarh Muslim University, Aligarh, India

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

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

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

org21Department of Physics, University of Oslo, Oslo, Norway

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

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

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

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

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

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

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

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

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

org31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

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

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

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

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

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

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

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

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

org40Gangneung-Wonju National University, Gangneung, Republic of Korea

org41Gauhati University, Department of Physics, Guwahati, India

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

org43Helsinki Institute of Physics (HIP), Helsinki, Finland

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

org45Hiroshima University, Hiroshima, Japan

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

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

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

org49Indian Institute of Technology Indore, Indore, India

org50Indonesian Institute of Sciences, Jakarta, Indonesia

org51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org52INFN, Sezione di Bari, Bari, Italy

org53INFN, Sezione di Bologna, Bologna, Italy

org54INFN, Sezione di Cagliari, Cagliari, Italy

org55INFN, Sezione di Catania, Catania, Italy

org56INFN, Sezione di Padova, Padova, Italy

org57INFN, Sezione di Roma, Rome, Italy

org58INFN, Sezione di Torino, Turin, Italy

org59INFN, Sezione di Trieste, Trieste, Italy

org60Inha University, Incheon, Republic of Korea

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

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

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

org64Institute for Theoretical and Experimental Physics, Moscow, Russia

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

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

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

org68Institute of Space Science (ISS), Bucharest, Romania

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

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

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

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

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

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

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

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

org77KTO Karatay University, Konya, Turkey

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

org79Lawrence Berkeley National Laboratory, Berkeley, California, United
States

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

org81Nagasaki Institute of Applied Science, Nagasaki, Japan

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

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

org84National Centre for Nuclear Research, Warsaw, Poland

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

org86National Nuclear Research Center, Baku, Azerbaijan

org87National Research Centre Kurchatov Institute, Moscow, Russia

org88Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org89Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org90NRC Kurchatov Institute IHEP, Protvino, Russia

org91NRNU Moscow Engineering Physics Institute, Moscow, Russia

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

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

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

org95Ohio State University, Columbus, Ohio, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

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

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Jammu, Jammu, India

org100Physics Department, University of Rajasthan, Jaipur, India

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

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

org103Physik Department, Technische Universität München, Munich, Germany

org104Politecnico di Bari, Bari, Italy

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

org106Rudjer Bošković Institute, Zagreb, Croatia

org107Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

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

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

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

org111Shanghai Institute of Applied Physics, Shanghai, China

org112St. Petersburg State University, St. Petersburg, Russia

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

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

org115Suranaree University of Technology, Nakhon Ratchasima, Thailand

org116Technical University of Košice, Košice, Slovakia

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

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

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

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

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

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University College of Southeast Norway, Tonsberg, Norway

org125University of Cape Town, Cape Town, South Africa

org126University of Houston, Houston, Texas, United States

org127University of Jyväskylä, Jyväskylä, Finland

org128University of Liverpool, Liverpool, United Kingdom

org129University of Science and Techonology of China, Hefei, China

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

org134Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

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

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

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

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

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

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

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

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

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea