2019 045 13 March

Measurement of strange baryon–antibaryon interactions

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

Two-particle correlation functions were measured for $\rm p\overline{p}$, $\rm
p\overline{\Lambda}$, $\rm\overline{p}\Lambda$, and
$\Lambda\overline{\Lambda}$ pairs in Pb–Pb collisions at $\sqrt{s_{\rm
NN}}=2.76$ TeV and $\sqrt{s_{\rm NN}}=5.02$ TeV recorded by the ALICE
detector. From a simultaneous fit to all obtained correlation functions, real
and imaginary components of the scattering lengths, as well as the effective
ranges, were extracted for combined $\rm p\overline{\Lambda}$ and
$\rm\overline{p}\Lambda$ pairs and, for the first time, for
$\Lambda\overline{\Lambda}$ pairs. Effective averaged scattering parameters
for heavier baryon–antibaryon pairs, not measured directly, are also provided.
The results reveal similarly strong interaction between measured
baryon–antibaryon pairs, suggesting that they all annihilate in the same
manner at the same pair relative momentum $k^{*}$. Moreover, the reported
significant non-zero imaginary part and negative real part of the scattering
length provide motivation for future baryon–antibaryon bound state searches.

##  1 Introduction

The interaction of baryons is a fundamental aspect of many sub-fields of
nuclear physics. It is investigated extensively with numerous methods, among
which are included the detailed analysis of the properties of atomic nuclei,
the dedicated experiments where beams of one baryon type are scattered on
other baryons bound in atomic nuclei [1, 2, 3, 4, 5, 6], and the femtoscopy
technique [7]. The latter involves the analysis of momentum correlations of
two particles produced in nuclear or elementary collisions [8, 9, 10, 11, 12].
It is especially interesting to probe the interaction in the region of the low
relative momentum of the pair, as it is the most relevant for a precise
extraction of the strong interaction scattering parameters. In particular, the
possible creation of bound states for a given baryon–baryon pair was
investigated extensively [13, 14, 15, 16, 17, 18].

Nuclear collisions at relativistic energies are abundant sources of various
particle species. In particular, the number of baryons and antibaryons created
in each Pb–Pb collision at the Large Hadron Collider (LHC) [19] is of the
order of one hundred each at mid-rapidity [20, 21, 22], which makes it
feasible to study details of their interactions. These particles include
$\Lambda$, $\Sigma$, $\Xi$, and $\Omega$ and an approximately equal amount of
their corresponding antiparticles.

The interactions of baryons are well known for pp pairs and pn pairs.
Measurements were also performed for $\rm p\Lambda$ pairs [23, 24, 25].
Recently, a comparative study of the baryon–baryon and antibaryon–antibaryon
interaction using Au–Au collisions at $\sqrt{s_{\rm NN}}=200$ GeV has been
performed by the STAR experiment at the Relativistic Heavy-Ion Collider and
found that the $\rm\overline{p}\overline{p}$ interaction does not differ from
the pp system [26]. Also, correlation measurements of baryon–baryon pairs in
pp collisions at $\sqrt{s}=7$ TeV and p–Pb collisions at $\sqrt{s_{\rm
NN}}=5.02$ TeV performed by ALICE detector [27] at the LHC provide more
constraints on the interaction of $\rm p\Lambda$ and $\rm\Lambda\Lambda$ [28,
29] as well as $\rm p\Xi^{-}$ [30] at low relative pair momentum.

Concerning proton–antiproton pairs, the strong interaction was studied in
detail [31, 32, 33, 34, 35]. Of particular interest is _protonium_ (or
_antiprotonic hydrogen_) – a proton–antiproton Coulomb bound state, where the
strong interaction also plays a significant role. The protonium atoms are
created by stopping antiprotons in hydrogen and the strong interaction is
studied via shifts in the X-ray spectrum from the expected QED transitions
from excited states. In particular, there is evidence of a contribution from
the strong force to the 1S and 2P states. However, the nature of protonium in
these states, whether it can be considered a nuclear bound state or a result
of the Coulomb interaction, remains an open question. For more details we
refer the reader to the review paper [35].

For baryon–antibaryon pairs with non-zero strangeness there is much less
experimental data available. However, low mass enhancements in the invariant
mass distributions of $\rm p\overline{p}$, $\rm p\overline{\Lambda}$, and
$\Lambda\overline{\Lambda}$ pairs have been observed in charmonium and $\rm B$
meson decays [36, 37, 38, 39]. Those enhancements, except for the $\rm
p\overline{p}$ pair, are sligthly above the mass threshold of the
baryon–antibaryon systems and have widths which are below 200 MeV/$c^{2}$.
Theoretical interpretations of these results predict the existence of various
baryon–antibaryon bound states and propose their classification [36]. Results
presented in this letter might shed new light on this domain.

The baryon–antibaryon scattering parameters, when measured, could be
implemented in the well-established model of heavy-ion collisions, UrQMD [40],
which has the important feature of including rescattering in the hadronic
phase. In particular, recent comparisons of theoretical calculations with the
ALICE data show that a proper description of this phase is critical for the
correct reproduction of a large number of observables, like particle yields,
transverse-momentum spectra, femtoscopy for identified particles, as well as
elliptic flow [41, 42, 43, 44]. The baryon–antibaryon annihilation is a
critical component of the rescattering process. Yet, at the moment, for all
but nucleon-antinucleon pairs, one has to rely on assumptions about the
interaction cross section. Currently it is assumed that all baryon–antibaryon
pairs annihilate in the same way as $\rm p\overline{p}$ pairs at the same
total energy of the pair, $\sqrt{s}$, in the pair rest frame [40].

Femtoscopy allows one to access the baryon–antibaryon interaction at low pair
relative momentum in a way which is complementary to dedicated scattering
experiments. Only the strong interaction is present for
$\rm\mathrm{p}\overline{\Lambda}$ ($\rm\overline{p}\Lambda$) and
$\rm\Lambda\overline{\Lambda}$ pairs, while for $\rm p\overline{p}$ pairs,
where also the Coulomb interaction is present, it is the dominant contribution
[7, 45]. Therefore, the parameters of this interaction, together with the
source function, determine the shape of the correlation function. In addition,
the so-called “residual correlations” effect (presence of an admixture of weak
decay products in the sample of a given baryon–antibaryon pair) results in
non-trivial interconnections between measured correlation functions. The
femtoscopic technique has been employed already to measure $\rm
p\overline{\Lambda}$ and $\rm\overline{p}\Lambda$ scattering parameters by the
STAR experiment [46]. However, the most important limitation of that study is
the fact that no corrections for residual correlations were applied.

In this letter the scattering parameters are extracted for $\rm
p\overline{\Lambda}$, $\rm\overline{p}\Lambda$, and for the first time for
$\Lambda\overline{\Lambda}$ pairs from femtoscopic correlations measured in
Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV and $\sqrt{s_{\rm NN}}=5.02$
TeV registered by the the ALICE experiment at LHC. The residual correlations
are accounted for in the formalism proposed in Ref. [47] which does not
attempt to “correct” for this effect (as proposed in an alternative procedure
in Ref. [48]), but instead uses it to extract information about the strong
interaction potential parameters for the parent particles. Therefore, it
allows for a single and simultaneous fit to all measured correlation
functions. This provides maximum statistical accuracy for the obtained
parameters, minimises the number of fit parameters and provides a non-trivial
internal consistency verification.

Recently, the $\rm p\overline{\Lambda}$ and $\rm\overline{p}\Lambda$
correlations measured by STAR [46] have been reanalysed taking into account
the residual correlations effect [47]. That study suggests that all
baryon–antibaryon pairs might annihilate in a similar way as a function of the
relative momentum of the pair $k^{*}$, instead of the pair centre-of-mass
energy $\sqrt{s}$. This work aims to provide more experimental constraints on
these scenarios.

##  2 Experiment and data analysis

The data sample used in this work was collected in LHC Run 1 (2011) and Run 2
(2015), where two beams of Pb nuclei were brought to collide at the centre-of-
mass energy of $\sqrt{s_{\rm NN}}=2.76$ TeV and $\sqrt{s_{\rm NN}}=5.02$ TeV,
respectively. Products of the collisions were measured by the ALICE detector
[27]. The performance of ALICE is described in Ref. [49].

In this analysis the minimum-bias (MB) trigger was used. It is based on the V0
detector consisting of two arrays of 32 scintillator counters, which are
installed on each side of the interaction point and cover
pseudorapidity111Pseudorapidity is defined as
$\eta=-\ln\left(\tan\left(\theta/2\right)\right)$, where $\theta$ is the polar
angle. ranges $2.8<\eta<5.1$ (V0A) and $-3.7<\eta<-1.7$ (V0C). The MB trigger
required a signal in both V0 detectors within a time window that is consistent
with the collision occurring at the centre of the ALICE detector. The event
centrality was determined by analysing the signal from the V0 detector with
the procedure described in details in Ref. [50].

The position of the collision vertex was reconstructed using the signal from
the Inner Tracking System (ITS) [27]. The ITS is composed of six cylindrical
layers of silicon detectors and covers $|\eta|<0.9$. Its information can be
used for tracking and primary vertex determination. However, in this analysis
it was used only for the latter. The primary vertex for an event was required
to be within $\pm 8$ cm from the centre of the detector.

The analysis was performed in six centrality [51] ranges for both collision
energies. They are listed in Tab. 2 together with their corresponding average
charged-particle multiplicity densities at mid-rapidity
$\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\rangle$ [50, 52].

Table 1: Centrality ranges and corresponding average charged-particle
multiplicity densities at mid-rapidity $\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta\rangle$ for Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$
TeV [50] and $\sqrt{s_{\rm NN}}=5.02$ TeV [52].

Centrality |  $\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\rangle$ $\sqrt{s_{\rm NN}}=2.76$ TeV |  $\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\rangle$ $\sqrt{s_{\rm NN}}=5.02$ TeV
---|---|---
0–5% | $1601\pm 60$ | $1943\pm 53$
5–10% | $1294\pm 49$ | $1586\pm 46$
10–20% | $966\pm 37$ | $1180\pm 31$
20–30% | $649\pm 23$ | $786\pm 20$
30–40% | $426\pm 15$ | $512\pm 15$
40–50% | $261\pm 9$ | $318\pm 12$

Charged-particle trajectory (track) reconstruction for both collision energies
was performed using the Time Projection Chamber (TPC) detector [53]. The TPC
is divided by the central electrode into two halves. Each half is capped with
a readout plane which is composed of 18 sectors (covering the full azimuthal
angle $\varphi$) with 159 padrows placed radially in each sector. A track
signal in the TPC consists of space points (clusters), and each of them is
reconstructed in one of the padrows. A track was required to be composed of at
least 80 clusters to minimise the possibility that a signal left by a single
particle is reconstructed as two tracks. The parameters of the track are
determined by performing a Kalman fit to a set of clusters. The quality of the
fit is determined by calculating the $\chi^{2}$ which was required to be lower
than 4 for every cluster (each cluster has two d.o.f.), in order to select
only well fitted tracks.

The identification of primary protons (antiprotons) was performed using the
combined information from both the TPC and the Time-OF-Flight (TOF) detectors
(a signal from both detectors was required), while the identification of
$\Lambda$ ($\overline{\Lambda}$) decay products (charged secondary pions and
(anti)protons) required information only from the TPC. TOF is a cylindrical
detector composed of Multigap Resistive Proportional Chambers (MRPC) located
at $r\cong 380$ cm from the beam axis. Tracks are propagated from the TPC to
the TOF and matched to hits in this detector. In the case of both TPC and TOF,
the signals (energy loss $\mathrm{d}E/\mathrm{d}x$ for the TPC and the time of
flight for the TOF) were compared to the expected ones for a given particle.
The measured–expected signal deviation was divided by the appropriate detector
resolution $\sigma$. The track was accepted as a proton (pion) if it fell
within $3\sigma$ of combined TPC and TOF expected signals for a proton (pion)
in a given detector.

Tracks were accepted for analysis if their pseudorapidity range was within the
range $|\eta|<0.8$ to avoid regions of the detector with limited acceptance.
The particle identification quality depends on the transverse momentum
$p_{\mathrm{T}}$, thus a $p_{\rm T}\in\left[0.7,\ 4.0\right]$ GeV/$c$ range
was used for primary (anti)protons to assure good purity of the sample. To
make sure that the sample is not significantly contaminated by secondary
particles coming from weak decays and particle–detector interactions, a
selection criterion on the Distance of Closest Approach (DCA) to the primary
vertex was also applied, separately in the transverse plane ($\rm
DCA_{xy}<2.4$ cm) and along the beam axis ($\rm DCA_{z}<3.2$ cm). These
criteria were optimised in order to select a high purity sample of
(anti)protons. The $p_{\mathrm{T}}$-integrated purity, based on Monte Carlo
simulations, of the p ($\rm\overline{p}$) sample was 95.4% (95.2%).

The selection of $\Lambda$ ($\overline{\Lambda}$) is based on their
distinctive decay topology in the decay channel $\Lambda\
(\overline{\Lambda})\rightarrow\mathrm{p}\uppi^{-}\
(\mathrm{\overline{p}}\uppi^{+})$, with a branching ratio of 63.9% [31]. The
reconstruction process, described in Ref. [54], is based on finding candidates
made of two secondary tracks having opposite charge and large impact parameter
with respect to the interaction point. The purity of $\Lambda$ and
$\overline{\Lambda}$ samples is larger than 95% according to the analysis of
the invariant-mass distribution. The $p_{\rm T}$-integrated invariant-mass
distribution of $\Lambda$ ($\overline{\Lambda}$) candidates is shown in Fig.
1.

Figure 1: Raw invariant-mass distribution of $\rm p\uppi^{-}$
($\rm\overline{p}\uppi^{+}$) pairs used to obtain the $\Lambda$
($\overline{\Lambda}$) candidates for Pb–Pb collisions at $\sqrt{s_{\rm
NN}}=5.02$ TeV in the 0–5% centrality range. The dashed lines represent the
selection width used in the analysis.

The femtoscopic correlation is measured as a function of the reduced momentum
difference of the pair
$\vec{k^{*}}=\frac{1}{2}\left(\vec{p_{1}}^{*}-\vec{p_{2}}^{*}\right)$, where
$\vec{p_{1}}^{*}$ and $\vec{p_{2}}^{*}$ denote momenta of the two particles in
the pair rest frame. It is defined as

$C(\vec{k}^{*})=\mathcal{N}\frac{A(\vec{k}^{*})}{B(\vec{k}^{*})}.$ (1)

The distribution $A$, called the “signal”, is constructed from pairs of
particles from the same event. The background distribution $B$ is constructed
from uncorrelated particles measured with the same single-particle acceptance.
In this analysis it was built using the event mixing method with the two
particles coming from two different events for which the vertex positions in
the beam direction agree within $2$ cm and the multiplicities differ by no
more than $1/4$ of the width of the given centrality class for which the
correlation function is calculated. Each particle was correlated with
particles from 10 other events. The parameter $\mathcal{N}$ is a normalisation
factor.

In this work, the analysis is further simplified by performing all
measurements as a function of the magnitude of the relative momentum
$k^{*}=|\vec{k}^{*}|$ only. The $\mathcal{N}$ parameter was calculated during
the background subtraction procedure described in Sec. 3, in a way that the
correlation function approaches unity in $k^{*}\in[0.13,~{}1.5]$ GeV/$c$ for
$\rm p\overline{p}$ pairs and in $k^{*}\in[0.23,~{}1.5]$ GeV/$c$ for $\rm
p\overline{\Lambda}$, $\rm\overline{p}\Lambda$, and
$\Lambda\overline{\Lambda}$ pairs.

##  3 Fitting procedure

The extraction of the scattering parameters from the measured correlation
functions requires a dedicated fitting procedure, which takes into account the
strong and Coulomb interaction, depending on a given pair. The fitting formula
is chosen appropriately for each baryon–antibaryon pair. Afterwards, a
simultaneous fit to all measured pairs, taking into account residual
correlations, is performed. The details of the procedure are described below.

The two-particle correlation function in the pair rest frame is defined as
[55, 56]

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

where $S(\vec{r}^{*})$ is the source emission function,
$\Psi(\vec{k}^{*},\vec{r}^{*})$ is the pair wave function, and $\vec{r}^{*}$
is the relative separation vector. The source is assumed to have a
spherically-symmetric Gaussian distribution according to measurements [12].
The pair wave function depends on the interactions between baryons and
antibaryons. When only the strong interaction is present, the correlation
function can be expressed analytically as a function of the scattering
amplitude $f(k^{*})=\left[\frac{1}{f_{0}}+\frac{1}{2}d_{0}k^{*2}-{\rm
i}k^{*}\right]^{-1}$, and the one-dimensional source size $R$. This
description is called the Lednický–Lyuboshitz analytical model [7] (see
Appendix A for details). In this work, the spin-averaged scattering parameters
are obtained, i.e. $\Re f_{0}$ the real and $\Im f_{0}$ imaginary parts of the
spin-averaged scattering length, and $d_{0}$ for the real part of the spin-
averaged effective range of the interaction. The usual femtoscopic sign
convention is used, where a positive $\Re f_{0}$ corresponds to attractive
strong interaction.

Accounting for residual correlations is an important ingredient of every
correlation function analysis involving baryons. A fraction of observed
(anti)baryons comes from decays of heavier (anti)baryons. This is illustrated
in Fig. 2, where the main contributions to the $\rm p\overline{p}$ correlation
function are marked in blue, to the $\rm p\overline{\Lambda}$ in yellow and to
the $\Lambda\overline{\Lambda}$ in red. In such a case, the correlation
function is built for the daughter particles, while the interaction has taken
place for the parent baryons. To account for this effect, the fitting formula
used in this work contains a sum of correlation functions for each possible
combination of (anti)baryons, weighted by the fraction $\lambda$ of given
residual pairs. One needs to transform the theoretical correlation function of
a pair into the momentum frame of the particles registered in the detector
[47].

The procedure for the correlation function analysis taking into account
residual correlations has been performed before and is described in detail in
Ref. [57]. The same procedure was carried out in this analysis.

The fractions of residual pairs $\lambda$ were calculated based on the AMPT
model [58] after full detector simulation, estimating how many reconstructed
pairs come from primary particles and what is the percentage of those coming
from the given decay. They also take into account other impurities resulting
from misidentification or detector effects. The obtained values of fractions
are listed in Tab. 2. The momentum transformation matrices [47] were generated
using the THERMINATOR 2 model [59] for all residual components of all analysed
systems. The final correlation function for a $xy$ pair is defined as

$C_{xy}(k^{*})=1+\sum_{i}\lambda_{i}\left[C_{i}(k^{*})-1\right],$ (3)

where the sum is over all residual components of the $xy$ pair and
$\lambda_{i}$ and $C_{i}(k^{*})$ are the fraction and the correlation function
of $i$-th pair, respectively [47].

Figure 2: Illustration of the links between different baryon–antibaryon pairs through the residual correlation. Main contributions to the $\rm p\overline{p}$ correlation function are marked in blue, to the $\rm p\overline{\Lambda}$ in yellow and to the $\Lambda\overline{\Lambda}$ in red. Solid lines show connections between studied pairs, while dashed lines present other major residual contributions that are unique for a given system. Table 2: Fractions of residual components of $\rm p\overline{p}$, $\rm p\overline{\Lambda}\oplus\overline{p}\Lambda$, and $\Lambda\overline{\Lambda}$ correlation functions from Monte Carlo events simulated with AMPT model after full detector simulation. The values in parentheses represent fractions obtained with the HIJING model [60] used for evaluation of systematic uncertainties. Fractions are the same for corresponding antipairs.  $\rm p\overline{p}$ | $\rm p\overline{\Lambda}\oplus\overline{p}\Lambda$ | $\Lambda\overline{\Lambda}$
---|---|---
Pair |  $\lambda$ | Pair |  $\lambda$ | Pair |  $\lambda$
$\rm p\overline{p}$ |  0.25 (0.32) | $\rm p\overline{\Lambda}$ |  0.29 (0.28) | $\Lambda\overline{\Lambda}$ |  0.37 (0.24)
$\rm p\overline{\Lambda}$ |  0.12 (0.19) | $\Lambda\overline{\Lambda}$ |  0.08 (0.09) | $\Lambda\overline{\Xi}^{+}$ |  0.04 (0.06)
$\rm p\overline{\Sigma}^{-}$ |  0.04 (0.04) | $\Lambda\overline{\Sigma}^{-}$ |  0.03 (0.02) | $\Lambda\overline{\Xi}^{0}$ |  0.03 (0.05)
$\Lambda\overline{\Lambda}$ |  0.02 (0.03) | $\rm p\overline{\Xi}^{0/+}$ |  0.02 (0.03) | $\Lambda\overline{\Sigma}^{0}$ |  $<0.01$ (0.20)
$\Lambda\overline{\Sigma}^{-}$ |  0.01 (0.01) | $\rm p\overline{\Sigma}^{0}$ |  $<0.01$ (0.12) | $\Sigma^{0}\overline{\Sigma}^{0}$ |  $<0.01$ (0.05)
$\Sigma^{+}\overline{\Sigma}^{-}$ |  $<0.01$ ($<0.01$) | $\Lambda\overline{\Sigma}^{0}$ |  $<0.01$ (0.04) | $\Xi^{0/-}\overline{\Sigma}^{0}$ |  $<0.01$ (0.02)
|  | $\Lambda\overline{\Xi}^{0/+}$ |  $<0.01$ (0.01) | $\Xi^{0/-}\overline{\Xi}^{0/+}$ |  $<0.01$ ($<0.01$)
|  | $\Sigma^{+}\overline{\Sigma}^{0}$ |  $<0.01$ ($<0.01$) |  |
|  | $\Xi^{0/-}\overline{\Sigma}^{+}$ |  $<0.01$ ($<0.01$) |  |

Correlation functions were obtained for four baryon–antibaryon pair systems
$\rm p\overline{p}$, $\rm p\overline{\Lambda}$, $\rm\overline{p}\Lambda$, and
$\Lambda\overline{\Lambda}$. Since the correlation functions $\rm
p\overline{\Lambda}$ and $\rm\overline{p}\Lambda$ were found to be consistent
with each other within the uncertainties, they were always combined and are
further denoted as $\rm p\overline{\Lambda}\oplus\overline{p}\Lambda$. A
simultaneous fit is desirable because of the presence of residual correlations
which link different pairs. Three sets of unknown scattering parameters,
components of the analytical formula (7) used in the fit, were introduced for
$\rm p\overline{\Lambda}\oplus\overline{p}\Lambda$,
$\rm\Lambda\overline{\Lambda}$ as well as heavier, not measured directly,
baryon–antibaryon pairs, further referred to as $\rm B\overline{B}$. The $\rm
p\overline{p}$ system was used as a reference. However, due to the presence of
the Coulomb interaction and coupled channels, the analytical description is no
longer valid in this case (see Appendix A for details). Nevertheless, coupled-
channel effects become negligible for large sources as the ones obtained in
Pb-Pb collision systems. The theoretical $\rm p\overline{p}$ correlation
functions were obtained by generating $\rm p\overline{p}$ pairs with the
THERMINATOR 2 model and by applying weights accounting for the final state
interactions with an approximate treatment of the $\rm n\overline{n}$ coupled
channel, using a numerical model by R. Lednický [7, 11] with experimental
constraints on strong interaction parameters from previous measurements [32,
61, 62].

The source sizes for primary $\rm p\overline{p}$, $\rm
p\overline{\Lambda}\oplus\overline{p}\Lambda$, and $\Lambda\overline{\Lambda}$
pairs were taken from previous measurements of other baryon–baryon and
meson–meson pairs [57]. We assume that the one-dimensional source size $R$,
for each pair, depends on the transverse mass of the pair, $m_{\rm
T}=\sqrt{m^{2}+p_{\rm T}^{2}}$, and on the charged-particle multiplicity
$N_{\rm ch}$ [63] following the relations

$R(m_{\rm T};N_{\rm ch})=a(N_{\rm ch})m_{\rm T}^{\gamma},$ (4)

and

$R(N_{\rm ch};m_{\rm T})=\alpha(m_{\rm T})\sqrt[3]{N_{\rm ch}}+\beta(m_{\rm
T}),$ (5)

where all the parameters and functions are empirical and include the
constraint of the minimum possible source size ($N_{\rm ch}=1$) being equal to
the proton radius, $R_{\rm p}\approx 0.88$ fm [31]. The relations (4) and (5)
are used for all pairs, including those contributing via weak decays.

The experimental correlation function is also affected by phenomena other than
the strong and Coulomb interactions, such as jets and elliptic flow [64, 65,
66]. Those effects are treated as a background. For each experimental
function, a background fit was performed in a $k^{*}$ region where femtoscopic
effects are not prominent. It was found, using the THERMINATOR 2 model, that
the results are not dependent on the $k^{*}$ fit range when the background is
fitted by a third order polynomial. Next, the estimated background was
subtracted from the experimental correlation function. The procedure flattens
the function for higher $k^{*}$ and the slope is larger for less central
collisions, which is consistent with elliptic flow, as it should be more
prominent for semi-central collisions and less for central collisions [64].

As an example, the correlation functions for $\rm p\overline{p}$, $\rm
p\overline{\Lambda}\oplus\overline{p}\Lambda$ and $\Lambda\overline{\Lambda}$
pairs for the 10–20% centrality interval and two collision energies are
represented together with the simultaneous fit in Fig. 3.

Figure 3: Correlation functions of $\rm p\overline{p}$, $\rm
p\overline{\Lambda}\oplus\overline{p}\Lambda$, and $\Lambda\overline{\Lambda}$
pairs for Pb–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV (left) and
$\sqrt{s_{\rm NN}}=2.76$ TeV (right) together with the simultaneous
femtoscopic fit for the 10–20% centrality class.

The momentum resolution effect was investigated with Monte Carlo simulations
by creating a two-dimensional matrix of generated and reconstructed $k^{*}$.
Each slice of the distribution was then fitted with a Gaussian function.
Within the $k^{*}$ region of interest the width of the Gaussian function is
constant; therefore, the fitting function was smeared with a Gaussian with a
width constant in $k^{*}$.

##  4 Results

The strong-interaction scattering parameters $\Re f_{0}$, $\Im f_{0}$, and
$d_{0}$ for $\rm p\overline{p}$, $\rm\overline{p}\Lambda\oplus
p\overline{\Lambda}$, $\Lambda\overline{\Lambda}$, and $\rm B\overline{B}$
pairs resulting from the simultaneous fit are summarised in Tab.
LABEL:tab:multi_fit_summary_2015 and plotted in Fig. 4 together with
statistical (bars) and systematic (ellipses) uncertainties222Details of the
systematic uncertainty estimation are discussed in Appendix B.. Figure 4 also
shows scattering parameters for various baryon–baryon and baryon–antibaryon
pairs extracted in previous studies [67, 68, 69, 70].

As the simultaneous fit yields similar values, within uncertainties, of
parameters for $\rm\overline{p}\Lambda\oplus p\overline{\Lambda}$ and
$\Lambda\overline{\Lambda}$, as well as heavier $\rm B\overline{B}$ pairs, one
can perform a fit assuming a single set of parameters for all systems. By
doing so there is practically no change in the results; in particular, the
reduced $\chi^{2}\approx 1.83$ ($p<0.00001$) of the first fit becomes
$\chi^{2}\approx 1.87$ and other scattering parameters change very slightly,
within systematic uncertainties. This test confirms that the data points can
be correctly described when one assumes that all baryon–antibaryon pairs have
similar values of the scattering length and the effective range of the strong
interaction.

Figure 4: (Top) Comparison of extracted spin-averaged scattering parameters
$\Re f_{0}$ and $\Im f_{0}$ for $\rm
p\overline{\Lambda}\oplus\overline{p}\Lambda$, $\Lambda\overline{\Lambda}$
pairs and for effective $\rm B\overline{B}$ pairs, with previous analyses of
$\rm p\overline{p}$ pairs (singlet) [71, 33, 35, 32]. (Bottom) Comparison of
extracted spin-averaged scattering parameters $\Re f_{0}$ and $d_{0}$ for $\rm
p\overline{\Lambda}\oplus\overline{p}\Lambda$, $\Lambda\overline{\Lambda}$
pairs as well as effective $\rm B\overline{B}$, with selected previous
analyses of other pairs: $\rm pp$ (singlet) [72], $\rm p\overline{p}$
(singlet) [71], $\rm pn$ (singlet) [73], $\rm nn$ (singlet) [73], $\rm
p\Lambda$ (singlet) [68], and $\Lambda\Lambda$ (spin-averaged) [69]. (Note
that the measurement of the $\Lambda\Lambda$ scattering parameters by the STAR
experiment [69] did not account for residual correlations. The recent analysis
of $\Lambda\Lambda$ correlations by the ALICE Collaboration [28], properly
taking into account those correlations, disfavours the STAR results.)

##  5 Discussion

Femtoscopic correlation functions for $\rm p\overline{p}$, $\rm
p\overline{\Lambda}\oplus\overline{p}\Lambda$ and $\Lambda\overline{\Lambda}$
have been measured in Pb–Pb collisions at energies of $\sqrt{s_{\rm NN}}=2.76$
TeV and $\sqrt{s_{\rm NN}}=5.02$ TeV registered by the ALICE experiment. The
analysis was performed in six centrality intervals, yielding 36 correlation
functions in total.

For the first time parameters of the strong interaction, the scattering length
and the effective range, were extracted for $\rm
p\overline{\Lambda}\oplus\overline{p}\Lambda$ and $\Lambda\overline{\Lambda}$
pairs. Moreover, parameters for heavier baryon–antibaryon pairs, which were
not measured directly, were estimated.

Several conclusions can be drawn from the extracted parameters. The real and
imaginary parts of the scattering length, $\Re f_{0}$ and $\Im f_{0}$, and the
effective interaction range, $d_{0}$, have similar values for all
baryon–antibaryon pairs at low $k^{*}$. Therefore, the data can be described
using the same parameters for all studied pairs, which provides a valuable
input for theoretical heavy-ion collisions models. Note that the assumption
used in the UrQMD model, namely that $\Im f_{0}$ is the same for different
baryon–antibaryon pairs as a function of the centre-of-mass energy of the
pair, means that the inelastic cross section would be different at the same
relative pair momentum $k^{*}$.

A significant non-zero imaginary part of the scattering length $\Im f_{0}$
indicates the presence of the inelastic channel of the interaction, which in
the case of baryon–antibaryon includes the annihilation process.

The negative value of the real part of the scattering length, $\Re f_{0}$,
obtained for all baryon–antibaryon pairs may have one of a two meanings:
either the strong interaction is repulsive, or a bound state can be formed.
The significant magnitude of the imaginary part of the scattering length, $\Im
f_{0}$, shows that baryon–antibaryon scattering may occur through inelastic
processes (annihilation). In the UrQMD model, three scenarios can be
considered [47]: i) all baryon–antibaryon pairs annihilate similarly at the
same relative momentum $k^{*}$; ii) $\Im f_{0}$ is the same for all
baryon–antibaryon pairs, but expressed as a function of the pair centre-of-
mass energy, meaning that $\Im f_{0}$ is smaller for baryon–antibaryon pairs
of higher total pair mass; iii) the inelastic cross section is increased for
every matching quark–antiquark pair in the baryon–antibaryon system. In this
scenario, in the specific case of this work, $\Im f_{0}$ for $\rm
p\overline{\Lambda}\oplus\overline{p}\Lambda$ should be lower than for $\rm
p\overline{p}$ and $\Lambda\overline{\Lambda}$, which is not observed. UrQMD
by default uses scenario ii) to model the baryon–antibaryon annihilation,
which in our case would lead to a decrease of $\Im f_{0}$ while going from
$\rm p\overline{p}$ to $\Lambda\overline{\Lambda}$ pairs; however, similar
values of $\Im f_{0}$ for all baryon–antibaryon pairs reported in this work
favour scenario i).

Inelastic scattering is compatible with a bound state, where the baryon and
antibaryon create a short-lived resonance which decays strongly into three
mesons. Evidence for a process in which a particle in the mass range of
2150–2260 MeV/$c^{2}$ decays into a kaon and two pions has been reported by
various experiments in the past and listed by the Particle Data Group (PDG) as
$\rm K_{2}(2250)$ [31]. The reported mass is slightly above the $\rm
p\overline{\Lambda}$ threshold, the width of the resonance is compatible with
a strongly decaying system and the decay products match the valence quark
content of the $\rm p\overline{\Lambda}$ pair. A nucleon–antihyperon system
has also been listed by PDG as $\rm K_{3}(2320)$, with proton and
$\overline{\Lambda}$ in the final state, which corresponds to a bound state
undergoing an elastic scattering. The results presented in this paper support
the existence of baryon–antibaryon bound states such as $\rm K_{2}(2250)$ and
$\rm K_{3}(2320)$. Further studies can provide more evidence on the existence
of those states.

Finally, negative values of the extracted real part of the scattering length
$\Re f_{0}$ show either that the interaction between baryons and antibaryons
is repulsive, or that baryon–antibaryon bound states can be formed. Combined
with the non-zero imaginary part $\Im f_{0}$ which, as mentioned earlier, is
associated with the inelastic processes, it favours the bound states scenario
over the repulsive interaction. In that case a baryon–antibaryon pair would
form a resonance decaying into a group of particles different from the
original ones (for instance, $\mathrm{p}\overline{\Lambda}\rightarrow\rm
X\rightarrow\rm K^{+}\uppi^{+}\uppi^{-}$, where $\rm X$ is the hypothetical
baryon–antibaryon bound state). Further studies will shed more light on
existence of such particles. The scenario of a repulsive interaction is not
completely ruled out, but it would manifest in experiments as a systematic
spatial separation of matter and antimatter, never observed before.

In summary, the strong-interaction cross section parameters (the scattering
length and the effective range) of strange baryon–antibaryon pairs have been
measured at low relative pair momentum using the femtoscopic technique. They
were found to be the same within the systematic uncertainties for all studied
pairs and compatible with the $\rm p\overline{p}$ parameters measured in other
experiments. Therefore, a global picture of the baryon–antibaryon annihilation
proceeding in a very similar way, regardless of the strange-quark content, is
suggested. Finally, the results are consistent with the formation of
baryon–antibaryon bound states. Future searches for such particles will
therefore be of crucial importance.

## Acknowledgements

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

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##  Appendix A Lednický–Lyuboshitz model

The wave function of the pair, $\Psi(\vec{k}^{*},\vec{r}^{*})$, in Eq. (2),
depends on the two-particle interaction. Baryons interact with anti-baryons
via the strong and, if they carry a non-zero electric charge, the Coulomb
force. In such a scenario, the interaction of two non-identical particles is
given by the Bethe–Salpeter amplitude, corresponding to the solution of the
quantum scattering problem taken with the inverse time direction:

$\Psi^{(+)}_{-{\vec{k}^{*}}}({\vec{{r}^{*}},{\vec{k}^{*}}})=\sqrt{A_{\rm
C}(\eta)}\frac{1}{\sqrt{2}}\left[{\rm e}^{-{\rm
i}\vec{k}^{*}\cdot{\vec{r}^{*}}}{\rm F}(-{\rm i}\eta,1,{\rm
i}\zeta^{+})+f_{\rm
C}(\vec{k}^{*})\frac{\tilde{G}(\rho,\eta)}{{r}^{*}}\right],$ (6)

where $A_{\rm C}$ is the Gamow factor,
$\zeta^{\pm}=k^{*}r^{*}(1\pm\cos{\theta^{*}})$, $\eta=1/(k^{*}a_{\rm C})$,
$\rm F$ is the confluent hypergeometric function, and $\tilde{G}$ is the
combination of the regular and singular $\rm S$-wave Coulomb functions.
$\theta^{*}$ is the angle between the pair relative momentum and relative
position in the pair rest frame, while $a_{\rm C}$ is the Bohr radius of the
pair. The component $f_{\rm C}$ is the strong-scattering amplitude, modified
by the Coulomb interaction.

When only the strong interaction is present, the correlation function can be
expressed analytically as a function of the scattering amplitude
$f(k^{*})=\left[\frac{1}{f_{0}}+\frac{1}{2}d_{0}k^{*2}-{\rm
i}k^{*}\right]^{-1}$, and the one-dimensional source size $R$. This
description is called the Lednický–Lyuboshitz analytical model [7]:

$C(k^{*})=1+\sum_{\sigma}\rho_{\sigma}\left[\frac{1}{2}\left|{\frac{f(k^{*})}{R}}\right|^{2}\left(1-\frac{d_{0}^{\sigma}}{2\sqrt{\rm{\uppi}}R}\right)+\frac{2\Re{f(k^{*})}}{\sqrt{\rm{\uppi}}R}F_{1}(2k^{*}R)-\frac{\Im{f(k^{*})}}{R}F_{2}(2k^{*}R)\right],$
(7)

where the sum is over all pair-spin configurations ${\sigma}$, with weights
$\rho_{\sigma}$ (a real number) being $1/4$ and $3/4$ for singlet and triplet
states, respectively, and $F_{1}(z)=\int_{0}^{z}({\rm
e}^{x^{2}-z^{2}}/z)\mathrm{d}x$ and $F_{2}(z)=(1-{\rm e}^{-z^{2}})/z$. When
the Coulomb interaction is also present, e.g., in the $\rm p\overline{p}$
case, the source emission function is numerically integrated with the pair
wave function containing a modified scattering amplitude [45]:

$f_{\rm C}(k^{*})=\left[\frac{1}{f_{0}}+\frac{1}{2}d_{0}k^{*2}-{\rm
i}k^{*}-\frac{2}{a_{\rm C}}h(\eta)-{\rm i}k^{*}A_{\rm C}(\eta)\right]^{-1},$
(8)

where
$h(\eta)=\eta^{2}\sum\limits_{n=1}^{\infty}[n(n^{2}+\eta^{2})]^{-1}-\mathrm{{\upgamma}}-\ln|\eta|$
($\mathrm{{\upgamma}}=0.5772$ is the Euler constant).

The description becomes more complicated when coupled channels (such as $\rm
n\overline{n}\rightarrow p\overline{p}$ in the $\rm p\overline{p}$ system) are
present. For details see Ref. [45, 74].

##  Appendix B Systematic uncertainties

The analysis was also performed on tracks reconstructed using the information
from both the ITS and the TPC, as opposed to using those having the
information from the TPC only. The correlation functions obtained from the
analysis of those tracks were fitted with the procedure described in Sec. 3.
Differences on extracted scattering parameters are between 4% and 17%,
depending on the studied pair and the scattering parameter.

In addition, several components of the fit procedure were varied. Shifting the
correlation function normalisation range in $k^{*}$ by $\pm 0.1$ GeV/$c$
yields almost no change on the extracted scattering parameters (maximum 1%). A
change of the background parametrisation from the third to the fourth-order
polynomial results in differences of up to 19% for $\Im f_{0}$ and below 10%
for other parameters. The second-order polynomial was also tested but it fails
to describe the low $k^{*}$ region and therefore cannot be used to extract
reliable information. Moreover, the use of residual pair fractions calculated
from the HIJING model [60] instead of AMPT resulted in changes of up to 19%
for $d_{0}$, up to 16% for $\Im f_{0}$, and below 10% for $\Re f_{0}$.
Variation of source sizes obtained from transverse-mass and multiplicity
scalings by $\pm 5$% resulted in changes of up to 13% for $\Re f_{0}$, up to
36% for $\Im f_{0}$, and up to 20% for $d_{0}$. Moreover, the width of the
Gaussian distribution accounting for momentum resolution was varied by $\pm
30\%$ which results in systematic uncertainty of up to 11%.

Contributions to the systematic uncertainty on the extracted scattering
parameters are summarised in Tab. 3. Since those components are correlated,
the total systematic uncertainties are represented as covariance ellipses in
the final plots.

Table 3: List of contributions to the systematic uncertainty of the scattering
parameters. Values are averaged over collision energies and centrality ranges.
$\mathrm{p}\overline{\Lambda}\oplus\overline{\mathrm{p}}\Lambda$
---
Uncertainty source |  $\Re{f_{0}}$ (%) |  $\Im{f_{0}}$ (%) |  $d_{0}$ (%)
Normalisation range | $<1$ | $<1$ | $<1$
Background parametrisation | $<1$ | $2$ | 3
Fit range dependence | 3 | 8 | 14
Fractions of residual pairs | 10 | 8 | 19
Momentum resolution correction | 7 | 11 | 4
Track selection | 11 | 14 | 4
Source size variation | 9 | 18 | 20
$\mathrm{\Lambda}\overline{\Lambda}$
Uncertainty source |  $\Re{f_{0}}$ (%) |  $\Im{f_{0}}$ (%) |  $d_{0}$ (%)
Normalisation range | $<1$ | $<1$ | $<1$
Background parametrisation | 6 | 19 | 2
Fit range dependence | 2 | 4 | 5
Fractions of residual pairs | 6 | 15 | 18
Momentum resolution correction | 4 | 7 | 2
Track selection | 7 | 17 | 4
Source size variation | 12 | 35 | 19
$\mathrm{B}\overline{\rm B}$
Uncertainty source |  $\Re{f_{0}}$ (%) |  $\Im{f_{0}}$ (%) |  $d_{0}$ (%)
Normalisation range | $<1$ | 1 | 1
Background parametrisation | 6 | 17 | 6
Fit range dependence | 6 | 12 | 11
Fractions of residual pairs | 7 | 19 | 8
Momentum resolution correction | 3 | 3 | 1
Track selection | 9 | $<1$ | 12
Source size variation | 13 | 36 | 9

S. Acharyaorg141&D. Adamováorg93&S.P. Adhyaorg141&A. Adlerorg74&J.
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Akindinovorg64&M. Al-Turanyorg105&S.N. Alamorg141&D.S.D. Albuquerqueorg122&D.
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Brunoorg33,org104&M.D. Bucklandorg128&D. Budnikovorg107&H. Bueschingorg69&S.
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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.
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Cindoloorg53&J. Cleymansorg125&F. Colamariaorg52&D. Colellaorg52&A.
Colluorg79&M. Colocciorg27&M. Concasorg58orgI&G. Conesa Balbastreorg78&Z.
Conesa del Valleorg61&G. Continorg128&J.G. Contrerasorg37&T.M. Cormierorg94&Y.
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Cuautleorg70&L. Cunqueiroorg94&D. Dabrowskiorg142&T. Dahmsorg103,org117&A.
Daineseorg56&F.P.A. Damasorg137,org114&S. Daniorg66&M.C. Danischorg102&A.
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Dashiorg103&S. Deorg85,org49&A. De Caroorg30&G. de Cataldoorg52&C. de
Contiorg121&J. de Cuvelandorg39&A. De Falcoorg24&D. De Gruttolaorg10&N. De
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Degenhardtorg121&A. Deistingorg102,org105&K.R. Dejaorg142&A. Delofforg84&S.
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Djuvslandorg22&U. Dmitrievaorg62&A. Dobrinorg34,org68&D. Domenicis
Gimenezorg121&B. Dönigusorg69&O. Dordicorg21&A.K. Dubeyorg141&A.
Dublaorg105&S. Dudiorg98&A.K. Duggalorg98&M. Dukhishyamorg85&P.
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Fabbiettiorg117,org103&M. Fagginorg29&J. Faivreorg78&A. Fantoniorg51&M.
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Foertschorg73&P. Fokaorg105&S. Fokinorg87&E. Fragiacomoorg59&A.
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Guittiereorg114&K. Gulbrandsenorg88&T. Gunjiorg132&A. Guptaorg99&R.
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Hamonorg136&R. Hanniganorg119&M.R. Haqueorg63&A. Harlenderovaorg105&J.W.
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Helstruporg36&A. Herghelegiuorg47&E.G. Hernandezorg44&G. Herrera Corralorg9&F.
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Ramelloorg32&F. Ramiorg136&R. Raniwalaorg100&S. Raniwalaorg100&S.S.
Räsänenorg43&B.T. Rascanuorg69&R. Rathorg49&V. Ratzaorg42&I.
Ravasengaorg31&K.F. Readorg94,org130&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.
Rossiorg56,org29&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. Šafaříkorg34,org37&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. Sarkarorg143,org141&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. Schukraftorg88,org34&Y. Schutzorg34,org136&K.
Schwarzorg105&K. Schwedaorg105&G. Scioliorg27&E. Scomparinorg58&M.
Šefčíkorg38&J.E. Segerorg16&Y. Sekiguchiorg132&D. Sekihataorg45&I.
Selyuzhenkovorg91,org105&S. Senyukovorg136&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.
Simonettiorg34,org103&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&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. Tangorg6&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&U. Westerhofforg144&A.M. Whiteheadorg125&E.
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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,org109&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