2023 106 30 May

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

The interaction between $\Lambda$ baryons and kaons/antikaons is a crucial
ingredient for the strangeness $S=0$ and $S=-2$ sector of the meson–baryon
interaction at low energies. In particular, the
$\Lambda{\mathrm{\overline{K}}}$ might help in understanding the origin of
states such as the $\Xi\mathrm{(1620)}$, whose nature and properties are still
under debate. Experimental data on $\Lambda\mbox{--}{\mathrm{K}}$ and
$\Lambda\mbox{--}{\mathrm{\overline{K}}}$ systems are scarce, leading to large
uncertainties and tension between the available theoretical predictions
constrained by such data. In this Letter we present the measurements of
$\Lambda\mbox{--}$K${}^{+}\oplus\overline{\Lambda}\mbox{--}$K- and
$\Lambda\mbox{--}$K${}^{-}\oplus\overline{\Lambda}\mbox{--}$K+ correlations
obtained in the high-multiplicity triggered data sample in pp collisions at
$\sqrt{s}\leavevmode\nobreak\ =\leavevmode\nobreak\ 13$ TeV recorded by ALICE
at the LHC. The correlation function for both pairs is modeled using the
Lednický–Lyuboshits analytical formula and the corresponding scattering
parameters are extracted. The
$\Lambda\mbox{--}$K${}^{-}\oplus\overline{\Lambda}\mbox{--}$K+ correlations
show the presence of several structures at relative momenta $k^{*}$ above 200
MeV$/c$, compatible with the $\Omega$ baryon, the $\Xi\mathrm{(1690)}$, and
$\Xi\mathrm{(1820)}$ resonances decaying into $\Lambda\mbox{--}$K- pairs. The
low $k^{*}$ region in the
$\Lambda\mbox{--}$K${}^{-}\oplus\overline{\Lambda}\mbox{--}$K+ also exhibits
the presence of the $\Xi\mathrm{(1620)}$ state, expected to strongly couple to
the measured pair. The presented data allow to access the $\Lambda$K+ and
$\Lambda$K- strong interaction with an unprecedented precision and deliver the
first experimental observation of the $\Xi\mathrm{(1620)}$ decaying into
$\Lambda$K- .

##  1 Introduction

Measurements of correlations of particle pairs in the relative momentum space
performed in small colliding systems at the Large Hadron Collider (LHC), such
as proton–proton (pp) and p–Pb collisions, have proven to be a sensitive
experimental tool to investigate hadron–hadron interactions. In recent years,
this so-called femtoscopy technique [1] was employed by the ALICE
Collaboration to deliver a large amount of high-precision data on interactions
involving strange baryons and antibaryons [2, 3, 4, 5, 6, 7, 8, 9]. This made
it possible to validate for the first time state-of-the-art lattice QCD
predictions at the physical point and to provide crucial experimental tests
for low-energy effective field theories. Lately, the same technique was
applied to meson–baryon pairs giving the possibility to access the interaction
of protons with $\phi$, charm D mesons, and kaons [10, 11, 12, 13]. In the
strangeness $S=-1$ meson–baryon sector, the measurement of the $\rm{K}^{-}$p
correlation function in different colliding systems [12, 14, 13] provided a
detailed picture of the $\rm{K}^{-}$p strong interaction above threshold and
novel constraints on the coupling strength to the $\rm\overline{K}^{0}$n and
$\uppi\Sigma$ channels. These femtoscopic correlations delivered the most
precise data on the $\rm{K}^{-}$p interaction and a crucial input to pin down
the $\rm\overline{K}N$–$\uppi\Sigma$ dynamics, responsible for the formation
of the $\Lambda(1405)$ resonance [15, 16, 17], which currently is the only
accepted molecular state in the hadronic spectrum.

States with a similar nature, namely arising dynamically in multi-channel
interactions, are predicted to exist also in the $S=-2$ meson–baryon sector in
which antikaons ($\rm\overline{K}$) interact with the strange $\Lambda$
baryon. Theoretical calculations based on chiral unitary frameworks [18, 19,
20, 21, 22, 23], Bethe-Salpeter approaches [24], and meson-exchange models
[25] indicate that several $\Xi$ resonances, such as the $\Xi\mathrm{(1620)}$
and the $\Xi\mathrm{(1690)}$, might indeed originate from the coupling between
the $\Lambda\mbox{--}{\mathrm{\overline{K}}}$ system and other $S=-2$
channels, like $\uppi\Xi$ and $\Sigma\mathrm{\overline{K}}$. The knowledge on
these low-lying $\Xi$ resonances is rather scarce. Several measurements are
available [26, 27, 28, 29, 30] but not all quantum numbers and branching
ratios for the different decay channels can be estimated [31]. Both resonances
are too light to be accomodated in most quark models [32, 33] and,
particularly for the $\Xi\mathrm{(1620)}$ state, only the decay in the neutral
$\uppi\Xi$ channel has recently been observed by the Belle Collaboration [28],
confirming the first experimental evidence in the same channel obtained in the
1970s [26, 27, 34]. Due to the lack of experimental data, the nature and the
properties of the $\Xi\mathrm{(1620)}$ are still open for discussion and its
theoretical modeling is far away from being settled. Since this state can in
principle couple to the $\Lambda\mbox{--}{\mathrm{\overline{K}}}$ system, the
possibility to access the $\Lambda{\mathrm{\overline{K}}}$ interaction with
the femtoscopy technique opens a new road in the study of double-strange
resonances.
By considering the interaction between a $\Lambda$ and a kaon, the $S=0$
meson–baryon dynamics can be probed, in which, as for the
$\Lambda\mbox{--}{\mathrm{\overline{K}}}$ system, many inelastic channels are
present (such as $\uppi$N, $\Sigma\mathrm{K}$). Effective Lagrangians
describing the coupled-channel $S=0$ system are mainly anchored to the large
database on elastic $\uppi$N scattering [35, 36, 37, 38], which leads to a
detailed understanding of most of the light-flavor baryonic resonances known
today, such as $N^{\ast}$ and $\Delta$. However, there might also be states
which strongly couple to inelastic channels with no net strangeness, such as
$\Lambda{\mathrm{K}}$ [20, 39]. Providing experimental constraints on the
$\Lambda{\mathrm{K}}$ interaction can hence contribute to improve the
knowledge of the light hadronic spectrum.

Additional data on the interaction between $\Lambda$ baryons and strange
mesons is also important in view of the recent efforts in going beyond the
non-interacting picture of hadrons in the statistical approaches applied in
heavy-ion collisions (HIC) [40, 41, 42]. The proton-to-pion ratio [43], which
was not properly reproduced within the basic assumption of thermal models
describing the hadronic phase as a non-interacting system, found its
explanation in the inclusion of the $\uppi$N scattering parameters in a more
sophisticated recent statistical approach [44]. Since $\Lambda$ and
kaons/antikaons are the most abundant strange hadrons produced in HICs, the
interaction between them can be used as an input for these new calculations
within the thermal model and help to shed light on the role of strangeness in
the hadronization process [45].
Correlations of all the neutral and charged combinations between $\Lambda$ and
kaons ($\Lambda\mbox{--}{\mathrm{K}}$,
$\Lambda\mbox{--}{\mathrm{\overline{K}}}$,
$\Lambda\mbox{--}{\mathrm{K^{0}_{S}}}$) have been published by the ALICE
Collaboration in Pb–Pb collisions at a center-of-mass energy per
nucleon–nucleon collision $\sqrt{s_{\mathrm{NN}}}\leavevmode\nobreak\
=\leavevmode\nobreak\ 2.76$ TeV [46], and delivered the first scattering
parameters on the underlying interaction, being repulsive for
$\Lambda\mbox{--}{\mathrm{K}}$ and attractive for the remaining pairs. A
similar measurement on $\Lambda\mbox{--}{\mathrm{K^{0}_{S}}}$ has also been
conducted recently by the CMS Collaboration in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}\leavevmode\nobreak\ =\leavevmode\nobreak\ 5.02$ TeV
[47], in which a different treatment of feed-down contributions is used.

In this Letter, we study the $\Lambda{\mathrm{K}}$ and
$\Lambda{\mathrm{\overline{K}}}$ interaction via the measurement of the
correlations for the charged combinations
$\Lambda\mbox{--}$K${}^{+}\oplus\overline{\Lambda}\mbox{--}$K- and
$\Lambda\mbox{--}$K${}^{-}\oplus\overline{\Lambda}\mbox{--}$K+ in pp
collisions at $\sqrt{s}\leavevmode\nobreak\ =\leavevmode\nobreak\ 13$ TeV [48,
49].
In order to enhance the number of
$\Lambda\mbox{--}$K${}^{+}\oplus\overline{\Lambda}\mbox{--}$K- and
$\Lambda\mbox{--}$K${}^{-}\oplus\overline{\Lambda}\mbox{--}$K+ pairs, the
analysis is performed in the high-multiplicity (HM) data sample in which an
enhanced yield of strange particles, as $\Lambda$ and kaons, is observed [50].
Note that the correlation functions of $\Lambda\mbox{--}$K+
($\Lambda\mbox{--}$K- ) pairs and $\overline{\Lambda}\mbox{--}$K-
($\overline{\Lambda}\mbox{--}$K+ ) pairs are added together in order to
enhance the statistical significance of the results. The results are obtained
by comparing the experimental data to the modeled correlation using the
Lednický–Lyuboshits analytical formula, from which scattering parameters and
properties of the $\Xi\mathrm{(1620)}$ are extracted.

##  2 Data analysis

The data sample studied in this work was collected by ALICE [51] at the LHC in
pp collisions at $\sqrt{s}=13$ TeV during the Run 2 period. All analyzed
events passed a HM trigger, based on the measured amplitude in the V0 detector
system, consisting of two arrays of plastic scintillators located at forward
($2.8<\eta<5.1$) and backward ($-3.7<\eta<-1.7$) pseudorapidities [52]. The
selected events correspond to the inelastic pp collisions with the top 0.17%
of the measured signal amplitudes, with at least one charged particle in the
range $|\eta|<1$ (referred to as INEL $>$ 0) [48, 49]. The resulting data
sample contains events with an average of 30 produced charged particles in the
pseudorapidity interval $\left|\eta\right|\leavevmode\nobreak\
<\leavevmode\nobreak\ 0.5$ [5].Approximately $1.0\times 10^{9}$ HM events are
selected by adopting the procedure described in Refs. [4, 5, 53].

The Monte Carlo simulated data used in this analysis are obtained from the
PYTHIA 8.2 event generator [54]. The transport through the ALICE detector is
simulated using GEANT 3 [55] and the reconstruction follows the dedicated
ALICE reconstruction algorithm [48]. An additional selection on large charged-
particle multiplicities, which mimics the effect of the HM trigger, is
applied.

The primary vertex (PV) of the collision is measured using the charged-
particle tracks reconstructed from the Inner Tracking System (ITS) [56] and
the Time Projection Chamber (TPC) [57]. A maximal displacement of the PV with
respect to the nominal interaction point of 10 cm along the beam axis is
required in order to ensure a uniform acceptance. Charged particles are
identified using information provided by the TPC [57] and the Time-of-Flight
(TOF) detector [58]. The ITS, TPC, and TOF detectors, used for charged-
particle tracking and identification, cover the full azimuthal angle and the
pseudorapidity interval $\left|\eta\right|\leavevmode\nobreak\
<\leavevmode\nobreak\ 0.9$, and are embedded in a uniform magnetic field of
0.5 T along the beam axis.

The information provided by these detectors is used to extract the kinematic
and topological quantities needed to reconstruct the K ($\rm\overline{K}$) and
$\Lambda$ ($\overline{\Lambda}$) candidates. The selection on these variables
is varied to evaluate the related systematic uncertainties. In the following,
the systematic variations of the selections specifically mentioned in the text
are enclosed in parentheses.

The identification of kaons (antikaons) is conducted employing both the TPC
and TOF detectors by applying a strict selection on the deviation $n_{\sigma}$
between the measured quantities ($\textrm{d}E/\textrm{d}x$, time-of-flight)
and the signal hypothesis for a kaon, electron, or pion, normalized by the
detector resolution $\sigma$. The $n_{\sigma}$ thresholds are chosen so as to
remove possible contamination from electrons and pions to the kaon sample. The
kaon candidates are selected within a transverse momentum range of $p_{\rm T}$
$\in$ [0.15 (0.1, 0.2), 4.0] GeV$/c$ and a pseudorapidity range of
$|\eta|<0.8\,(0.75,0.85)$, to avoid regions of the detector with limited
acceptance. To significantly improve the amount of primary kaons with respect
to secondary particles coming from weak decays and particle–detector
interactions, a selection criterion on the Distance of Closest Approach (DCA)
to the primary vertex is applied, both in the transverse plane
($\mathrm{DCA}_{xy}<0.1$ cm) and along the direction of the beam
($\mathrm{DCA}_{z}<0.2$ cm). The purity, referring to the fraction of
correctly identified kaon and antikaon candidates, is around 99.5% and the
primary fraction is estimated to be 57.6%, using the same procedure described
in Ref. [59].

The kinematic and topological selection criteria related to the reconstruction
of $\Lambda$ and $\overline{\Lambda}$, as well as the associated systematic
uncertainties, are the same as described in Ref. [53]. Due to their charge
neutrality and their short lifetime, the $\Lambda$ candidates are
reconstructed through the weak decay $\mathrm{\Lambda\rightarrow p\pi^{-}}$,
which has a branching ratio of BR = (63.9 $\pm$ 0.5)$\%$ and a decay length of
$\mathrm{c\tau=(7.89\pm 0.06)}$ cm [31]. The charge-conjugate decay is used
for the $\overline{\Lambda}$ reconstruction. The candidates are then
identified within a p$\pi^{-}$ invariant mass window of
$|M_{\mathrm{p}\pi}-M_{\Lambda}|<4$ MeV$/c$ 2 (corresponding to about
3$\sigma$), with the nominal mass $M_{\Lambda}=1116$ MeV$/c$ 2 [31]. This
leads to purities of $P_{\Lambda}$ = $94.2\%$, $P_{\overline{\Lambda}}$ =
$95.1\%$ for $\Lambda$ and $\overline{\Lambda}$, respectively. A primary
fraction of 57.6% is extracted following the procedure described in Ref. [60].
Secondary contributions from weak decays of neutral and charged $\Xi$ baryons
account for $23.2\%$ of the candidate sample. The remaining 19.2% are
attributed to $\Sigma^{0}$ particles.

##  3 Analysis of the correlation function

The observable of this analysis is the two-particle correlation function
$C(k^{*})$, defined as [1]

$\displaystyle
C(k^{*})=\mathcal{N}\times\frac{N_{\rm{same}}(k^{*})}{N_{\rm{mixed}}(k^{*})},$
(1)

where $k^{*}=\frac{1}{2}\times|\mathbf{p}^{*}_{1}-\mathbf{p}^{*}_{2}|$ is the
relative momentum of the pair in its rest frame. Here
$N_{\mathrm{same}}(k^{*})$ is the $k^{*}$ distribution of pairs measured in
the same event, $N_{\mathrm{mixed}}(k^{*})$ is the reference distribution of
uncorrelated pairs sampled from different (mixed) events. The mixed-event
sample is obtained by pairing particles stemming from events with a similar
number of charged particles at midrapidity and a close-by primary vertex
position along the beam direction, following [4, 12, 5]. The constant
$\mathcal{N}$ is a normalization parameter determined by assuming particle
pairs with large $k^{*}$ to be uncorrelated, which corresponds to a flat
$C(k^{*})=1$ [1]. This normalization constant $\mathcal{N}$ is evaluated in
$k^{*}$ $\in$ $\mathrm{[240-340]}$ MeV$/c$ for
$\Lambda\mbox{--}$K${}^{+}\oplus\overline{\Lambda}\mbox{--}$K- and in the
region $\mathrm{[500-800]}$ MeV$/c$ for
$\Lambda\mbox{--}$K${}^{-}\oplus\overline{\Lambda}\mbox{--}$K+, where no
resonances are present.

A total of $4.45\text{\times}{10}^{6}$
$\Lambda\mbox{--}$K${}^{+}\oplus\overline{\Lambda}\mbox{--}$K- and
$4.38\text{\times}{10}^{6}$
$\Lambda\mbox{--}$K${}^{-}\oplus\overline{\Lambda}\mbox{--}$K+ pairs
contribute to the correlation signal for $k^{*}<200$ MeV$/c$. For brevity, in
the following $\Lambda\mbox{--}$K+ denotes the combination
$\Lambda\mbox{--}$K${}^{+}\oplus\overline{\Lambda}\mbox{--}$K- and
$\Lambda\mbox{--}$K- is used for
$\Lambda\mbox{--}$K${}^{-}\oplus\overline{\Lambda}\mbox{--}$K+. The resulting
experimental correlation functions are shown in the upper panel of Fig. 1 and
in Fig. 2.

The measured correlations are fitted with a correlation function:

$\displaystyle C_{\mathrm{tot}}(k^{*})=$ $\displaystyle N_{D}\times
C_{\mathrm{model}}(k^{*})\times C_{\mathrm{background}}(k^{*}),$ (2)

where $N_{D}$ is a normalization constant, free to vary in the fit. The
default fit range is $0<k^{*}<500$ MeV$/c$. A variation of $\pm 10\%$ to the
upper limit of the default fit range is applied for evaluating the systematic
uncertainties. The term $C_{\mathrm{background}}$ is related to a possible
residual background, which can still be present in the femtoscopic
correlation. Its modeling is addressed in details later in this section. The
term $C_{\rm{model}}(k^{*})=1+\sum_{i}\lambda_{i}\times(C_{i}(k^{*})-1)$
includes the genuine correlation ($i=\mathrm{gen}$), which arises from final
state interaction among the two particles of interest, as well as residual
contributions involving secondary particles from weak or electromagnetic
decays and misidentified ones. Each of these contributions is weighted by the
corresponding $\lambda_{i}$ parameter, evaluated as the product of the
purities and fractions (primary or secondary) of the particles composing the
$i$ pair [2]. The latter are reported for kaons and $\Lambda$ baryons in Sec.
2.

The genuine contribution for $\Lambda\mbox{--}$K+ and $\Lambda\mbox{--}$K-
pairs amounts to $\lambda_{\mathrm{gen}}=51\%$; the residual correlations
between kaons (antikaons) and $\Lambda$ ($\overline{\Lambda}$) from the decay
of $\Xi$ ($\overline{\Xi}$) contribute each with a weight of
$\lambda_{\Lambda_{\Xi}K}=10\%$. The correlations for the charged combinations
(e.g $\Xi^{\pm}\mbox{--}\mathrm{K^{\pm}}$) are modeled with the CATS framework
[61] assuming Coulomb-only interaction. The presence of a residual strong
interaction between $\Xi$ and kaons is neglected in this analysis since
currently no experimental data are available and the corresponding theoretical
predictions are hence not validated yet [62, 63]. Similarly, residual
correlations involving $\Xi^{0}$ and $\Sigma^{0}$ are considered to be flat
due to the absence of Coulomb interaction. Such residual contributions, along
with correlations involving misidentified particles, amount to
$\lambda_{\mathrm{flat}}=39\%$ of the measured signal. The systematic
uncertainties related to the $\lambda_{i}$ parameters are estimated based on
the purities obtained for each varied set of kinematic and topological cuts,
as well as by varying the values of secondary fractions by $\pm 10\%$. In
addition to the feed-down contributions, a correction for the finite
experimental momentum resolution is taken into account for a direct comparison
with data [2].

The last factor in Eq. 2, $C_{\mathrm{background}}$, accounts for the non-
femtoscopic background visible in both measured correlations [2]. In
particular, the $\Lambda\mbox{--}$K+ data are affected by the presence of the
so-called mini-jet contributions, typically associated to the initial hard
processes occurring at the parton level during the collision [64]. This type
of background has already been observed in several meson–meson[65, 66, 67,
68], meson–baryon [10, 12], and baryon–antibaryon femtoscopic analyses [9] and
it is particularly enhanced when the net-charges, such as baryon number,
electric charge and strangeness, are zero for the pair at hand. The mini-jet
term included in the $C_{\rm{background}}(k^{*})$ for $\Lambda\mbox{--}$K+ is
modeled using Monte Carlo simulated data and following the same procedure
adopted in Ref. [9]. A polynomial of second order is added as baseline to the
mini-jet part of the background to take into account energy–momentum
conservation effects developing at large $k^{*}$[2], which lead to an
enhancement of the correlation function in this momentum region. The
coefficients of the polynomial are fixed by a prefit of
$C_{\mathrm{background}}(k^{*})$ to the $\Lambda\mbox{--}$K+ data in the
region of $400<k^{*}<2000$ MeV$/c$. A variation of $\pm 10\%$ in the lower and
upper limit of this range range is included to estimate the systematic
uncertainty related to the total background. In the case of
$\Lambda\mbox{--}$K- , the mini-jet background is much less pronounced since
the the net-strangeness of the pair is not zero. The measured
$\Lambda\mbox{--}$K- correlation function outside the femtoscopic region of
$k^{*}>200$ MeV$/c$ is well reproduced by Monte Carlo simulated data and no
additional baselines are required to describe the large $k^{*}$ region. Hence,
the total $C_{\mathrm{background}}(k^{*})$ in the $\Lambda\mbox{--}$K- case is
modeled using only the simulated correlation, parametrized by a third-order
polynomial constrained to be flat at $k^{*}\rightarrow 0$ since no signal is
expected to arise from the background [6, 8] at low $k^{*}$. The coefficients
of the polynomial are fixed by fitting the Monte Carlo simulated data in the
range $k^{*}$ $\in$ $[0,600]$ MeV$/c$, with systematic variations of the upper
limit of $\pm 10\%$.

Besides the background, which shifts the data upwards with respect to unity in
the region of relative momenta above 200 MeV$/c$, there are several structures
present in the measured $\Lambda\mbox{--}$K- correlation (upper panel in Fig.
1), related to resonances decaying into $\Lambda\mbox{--}$K- pairs. In the
lower panel of Fig. 1, the invariant mass of $\Lambda\mbox{--}$K- pairs,
expressed in $k^{*}$, is shown in order to better visualize the location of
these three resonances. The $\Lambda\mbox{--}$K- invariant mass spectrum in
$k^{*}$ is obtained using the same- and mixed-event distributions in Eq. 1 and
by following the same approach employed in resonance analyses [69]. The
uncorrelated mixed-event distribution, normalized to the signal outside the
resonance region ($k^{*}$ $\in$ $[500,800]$ MeV$/c$), is subtracted from the
same-event $\Lambda\mbox{--}$K- signal. After this subtraction, a residual
background is still present, corresponding to the
$C_{\mathrm{background}}(k^{*})$ contribution in the measured correlation
function shown above. This remaining background in the invariant mass
distribution can be modeled as well using Monte Carlo data, fitted with a
fourth-order polynomial, and it can be finally subtracted from the measured
spectrum in order to investigate in more details the $\Lambda\mbox{--}$K-
dynamics at low $k^{*}$. The peak appearing at $k^{*}\approx 211$ MeV$/c$
(green dashed line) corresponds to the $\Omega$ baryon decaying weakly into
$\Lambda$K- with a branching ratio of $(67.8\pm 0.7)\%$ [31]. The $\Xi(1690)$
and $\Xi(1820)$ resonances can be associated to the second and third peaks in
the correlation. The negative counts in the region $100<k^{*}<200$ MeV$/c$ of
the $\Lambda\mbox{--}$K- invariant mass are due to the presence of a residual
non-resonant interaction, which will be discussed in detail in Sec. 4.

Figure 1: (Color online) Upper: measured correlation function for
$\Lambda\mbox{--}$K- pairs (empty points) with statistical (line) and
systematic (gray boxes) uncertainties. Lower: invariant mass spectrum of
$\Lambda\mbox{--}$K- pairs used to build the measured correlation function.
Only the statistical uncertainties are shown. The upper x-axis indicates the
energy at rest
$E=\sqrt{(k^{*})^{2}+m_{\Lambda}^{2}}+\sqrt{(k^{*})^{2}+m_{K}^{2}}$ of the
pair written as a function of the relative momentum of the
$\Lambda\mbox{--}$K- pair. The quantity $E$ corresponds to the invariant mass
$M$ of the $\Lambda\mbox{--}$K- pairs. The colored vertical dashed lines
indicate the values of the relative momentum $k^{*}$ (upper panel) and the
value of the energy $E$ at rest of each resonance (lower panel) corresponding
to its nominal mass extracted in the final femtoscopic fit.

Currently the branching ratios of the strong decays of these states into
$\Lambda$K- are not precisely known [31]. In the upper x-axis of the bottom
panel of Fig. 1, the corresponding mass of the resonance obtained from the
kinematic relation
$E=\sqrt{(k^{*})^{2}+m_{\Lambda}^{2}}+\sqrt{(k^{*})^{2}+m_{K}^{2}}$, is shown.
In order to properly model the background outside the femtoscopic range, these
three resonances must be taken into account. The total background correlation
for $\Lambda\mbox{--}$K- can hence be written as

$\displaystyle
C_{\mathrm{background}}^{\Lambda\mathrm{K}^{-}}(k^{*})=\alpha_{\mathrm{pol3}}(1+bk^{*}{{}^{2}}+ck^{*}{{}^{3}})+\alpha_{\Omega}f_{\mathrm{G}}(M_{\Omega},\sigma_{\Omega})+\sum_{i}\alpha_{i}f_{\mathrm{BW}}(M_{i},\Gamma_{i}),$
(3)

in which a Gaussian distribution $f_{\mathrm{G}}$ is used for the $\Omega$
baryon decaying weakly to $\Lambda\mbox{--}$K- , and a typical Breit-Wigner
one $f_{\mathrm{BW}}$ for the two excited $\Xi$ resonances, having broader
widths due to the strong decay to $\Lambda\mbox{--}$K- . In order to help the
convergence of the final femtoscopic fit, a fit of the total
$C_{\mathrm{background}}(k^{*})$ correlation to the data is performed in the
$k^{*}$ region of $190-600$ MeV$/c$ to estimate the weights $\alpha_{\Omega}$,
$\alpha_{i}$ as well as the masses and widths of the resonances. A change of
$\pm 10\%$ in the upper limit of the prefit range is included in the
evaluation of the final systematic uncertainties. These parameters are then
kept free in the final femtoscopic fit of $C_{\mathrm{tot}}(k^{*})$ to the
data and the values obtained for the masses and widths are found to be
compatible with the available PDG values [31] and recent measurements [30,
29]. The orange band in Figs. 2 and 3 shows the total
$C_{\mathrm{background}}(k^{*})$ correlation function extracted in the final
femtoscopic fit, multiplied by the normalization factor $N_{D}$, for
$\Lambda\mbox{--}$K+ and $\Lambda\mbox{--}$K- pairs, respectively.

The last ingredient needed to model the data is the strong interaction of the
$\Lambda\mbox{--}$K+ and $\Lambda\mbox{--}$K- pairs entering in the
$C_{\rm{model}}(k^{*})$ in Eq. 2 via the genuine correlation function
$C_{\mathrm{gen}}(k^{*})$. This is modeled for both pairs using the
Lednický–Lyuboshits analytical formula [70], following the approach used in
Ref. [46],

$\displaystyle
C(k^{*})_{\mathrm{LL}}=1+\Bigg{[}\frac{1}{2}\Bigg{|}\frac{f(k^{*})}{R}\Bigg{|}^{2}\Bigg{(}1-\frac{d_{0}}{2\sqrt{\pi}R}\Bigg{)}+\frac{2\Re
f(k^{*})}{\sqrt{\pi}R}F_{1}(2k^{*}R)-\frac{\Im
f(k^{*})}{R}F_{2}(2k^{*}R)\Bigg{]}.$ (4)

The scattering amplitude $f(k^{*})$ is the quantity embedding the scattering
parameters and providing information on the underlying interaction. Typically,
$f(k^{*})$ is expressed via the effective-range expansion (ERE)
$f(k^{*})=\left(\frac{1}{f_{0}}+\frac{1}{2}d_{0}k^{\ast^{2}}-ik^{*}\right)^{-1}$,
in which $f_{0}$ is the scattering length and $d_{0}$ is the effective range.
The parameter $R$ is the size of the emitting source with a Gaussian profile.
In this work it was fixed using the core-resonance model taken from Ref. [53],
already employed in several previous femtoscopic analyses performed in small
colliding systems as pp collisions and anchored to $\rm{p}\mbox{--}\rm{p}$
correlations. The core radius for $\Lambda\mbox{--}$K+ and
$\Lambda\mbox{--}$K- pairs is
$r_{\mathrm{core}}(\left<m_{\mathrm{T}}\right>=1.35\,\,\mathrm{Ge\kern-1.99997ptV/}c^{2})=1.11\pm
0.04\leavevmode\nobreak\ $ fm. In order to use the core-resonance total source
in Eq. 4, this must be parametrized with a Gaussian distribution. The presence
of long-lived strong resonances feeding to $\Lambda$ and kaons introduces a
significant exponential tail for large $r^{*}$, which cannot be described with
a single Gaussian [6, 5, 8, 10, 13]. The total source is hence modeled with a
weighted sum of two Gaussians, leading to an effective emitting source
$S_{\mathrm{eff}}(r^{*})=\lambda_{S}[\omega_{S}S_{1}(r^{*})+(1-\omega_{S})S_{2}(r^{*})]$,
in which $r_{1}=1.202^{+0.043}_{-0.042}$ fm , $r_{2}=2.330^{+0.050}_{-0.045}$
fm, $\lambda_{S}=0.9806^{+0.0006}_{-0.0008}$, and
$\omega_{S}=0.7993^{+0.0037}_{-0.0027}$. As systematic variation of the source
function, these values are varied within the uncertainties. Due to the
additive property of correlation functions, the final genuine correlation is
then taken as the sum of two correlations evaluated with the two properly
weighted Gaussian sources. To preserve the correct normalization of the
emitting source and the unitarity of the $\lambda$ parameters [2] in
$C_{\mathrm{model}}(k^{*})$, a (1$-\lambda_{S}$) contribution is added.

The understanding of the $\Lambda$K- interaction, particularly in the low
$k^{*}$ region, is strictly connected to the $\Xi\mathrm{(1620)}$ state. In
principle, since $\Xi\mathrm{(1620)}$ shares the same quantum numbers as the
$\Lambda\mbox{--}$K- pair, the two systems can couple strongly. The Belle
collaboration recently published the observation of the $\Xi\mathrm{(1620)}$
state in the $\Xi\uppi$ decay channel
($E_{\mathrm{thr.1}}=m_{\uppi}+m_{\Xi}=1461.3$ MeV$/c^{2}$) [28]. The reported
mass and widths in Ref. [28] are $M_{\Xi\mathrm{(1620)}}=1610.4\pm 6.0$
MeV$/c^{2}$, $\Gamma_{\Xi\mathrm{(1620)}}=60.0\pm 4.8$ MeV, which indicates
that the decay of $\Xi\mathrm{(1620)}$ into $\Lambda$K-
($E_{\mathrm{thr.2}}=m_{\mathrm{K^{-}}}+m_{\Lambda}=1609.4$ MeV$/c^{2}$) is
kinematically allowed. No experimental evidence of this decay channel has been
observed so far. The presented work provides quantitative evidence of this
process.

The $\Xi\mathrm{(1620)}$ state can be clearly seen in the peak at
$k^{*}\approx 80$ MeV$/c$ in the lower panel of Fig. 1. Hence, to model the
$\Lambda$K- interaction at low $k^{*}$, the $\Xi\mathrm{(1620)}$ must be taken
into account in the Lednický–Lyuboshits approach. Similar scenarios, with
resonances contributing to the signal in the low $k^{*}$ region, were observed
in $\mathrm{K^{0}_{S}-K^{\pm}}$ correlations measured in pp and Pb–Pb
collisions, in which the interaction mainly goes through the formation of the
$a_{0}$ resonance. A way to properly include such a resonant interaction is to
write the scattering amplitude in Eq. 4 in terms of the probability
distribution describing the state. Due to the vicinity of the $\Lambda$K-
decay-channel threshold, the $\Xi\mathrm{(1620)}$ resonance must be described
with a Flatté-like distribution [71] such as the Sill distribution used in
Ref. [72]. The corresponding scattering amplitude can be written as

$\displaystyle f(k^{*})=$
$\displaystyle\dfrac{-2\tilde{\Gamma}_{\mathrm{\Lambda
K^{-}}}}{E^{2}-M^{2}+i\tilde{\Gamma}_{\mathrm{\Xi\uppi}}\sqrt{E^{2}-E_{\mathrm{thr.\mathrm{\Xi\uppi}}}^{2}}+i\tilde{\Gamma}_{\mathrm{\Lambda
K^{-}}}\sqrt{E^{2}-E_{\mathrm{thr.\mathrm{\Lambda K^{-}}}}^{2}}}$ (5)

in which $M$ is the mass of the $\Xi\mathrm{(1620)}$ state,
$\tilde{\Gamma}_{i=\mathrm{\Xi\uppi},\mathrm{\Lambda K^{-}}}$ are the
effective partial widths as defined in Ref. [72], and
$E_{\mathrm{thr}.i=\mathrm{\Xi\uppi},\mathrm{\Lambda K^{-}}}$ are the
threshold energies for the two channels, as defined above.

Besides the interaction between $\Lambda$ and antikaons through the
$\Xi\mathrm{(1620)}$ state, a non-resonant strong interaction is present in
the measured correlation function, which can be explicitly seen in the lower
panel of Fig. 1 for $100<k^{*}<200$ MeV$/c$. In this $k^{*}$ region the data,
corrected by the background contribution as described above, go below zero
indicating a depletion in the measured $\Lambda\mbox{--}$K- pairs arising from
the underlying non-resonant component of the interaction. Since there are no
theoretical approaches available at the moment in which the $\Lambda$K-
interaction is composed of a resonant part, through the $\Xi\mathrm{(1620)}$
state above the $\Lambda$K- threshold, and a non-resonant one, an effective
modeling of these two contributions will be adopted employing the
Lednický–Lyuboshits formula. The non-resonant
$C_{\mathrm{LL}}^{\mathrm{non\text{-}res}}(k^{*})$ and resonant
$C_{\mathrm{LL}}^{\mathrm{res}}(k^{*})$ correlations are modeled using Eq. 4:
for $C_{\mathrm{LL}}^{\mathrm{non\text{-}res}}(k^{*})$ an ERE scattering
amplitude is assumed, while for $C_{\mathrm{LL}}^{\mathrm{res}}(k^{*})$ a Sill
amplitude is employed, according to Eq. 5. Taking both interactions into
account, the final genuine correlation for $\Lambda\mbox{--}$K- is composed of
a weighted sum of a correlation including the resonant process and another one
responsible for the non-resonant part

$\displaystyle C_{\mathrm{gen}}(k^{*})=\omega
C_{\mathrm{LL}}^{\mathrm{non\text{-}res}}(k^{*})+(1-\omega)C_{\mathrm{LL}}^{\mathrm{res}}(k^{*}).$
(6)

The remaining free parameters to be extracted in the final femtoscopic fit of
$C_{\mathrm{tot}}(k^{*})$ to the data are the weight $\omega$ for non-resonant
scattering parameters $(\Re f_{0},\Im f_{0},d_{0})$, the mass $M$, the partial
widths $\tilde{\Gamma}_{i=1,2}$ of the $\Xi\mathrm{(1620)}$ state, and the
masses and widths of the $\Omega$, $\Xi\mathrm{(1690)}$, and
$\Xi\mathrm{(1820)}$.

Figure 2: (Color online) Measured correlation function of $\Lambda\mbox{--}$K+
pairs. Statistical (bars) and systematic (boxes) uncertainties are shown
separately. The light cyan band represents the total fit obtained using Eq. 2
from which the normalization $N_{D}$, and the scattering parameters ($\Re
f_{0}$,$\Im f_{0}$, and $d_{0}$) are extracted. The orange band represents the
$C_{\mathrm{background}}(k^{*})$ contribution, modeled as described in Section
3, and multiplied by the constant $N_{D}$. Lower panel: $n_{\sigma}$ deviation
between data and model in terms of numbers of standard deviations.

##  4 Results

The results for $\Lambda\mbox{--}$K+ and $\Lambda\mbox{--}$K- systems are
shown in Figs. 2 and 3, respectively. The lower panels in each plot show the
deviation between data and model in terms of number of standard deviations
$n_{\sigma}$. The width of the band represents the total uncertainty of the
fit, including the statistical and the systematic uncertainties. The gray
boxes correspond to the systematic uncertainties of the data and they
maximally amount to 3$\%$–4$\%$ in the lowest $k^{*}$ interval for each pair.
The measured $\Lambda\mbox{--}$K+ correlation function, shown in Fig. 2, is
below unity at low $k^{*}$, indicating a repulsive strong interaction between
$\Lambda$ and kaons, in agreement with the femtoscopic results obtained in
Pb–Pb collisions [46]. The behavior of the data is well reproduced by the fit
using Eq. 2 with an average reduced $\chi^{2}/$NDF of 3.9 estimated in the
default fit range.

Figure 3: (Color online) Measured correlation function of $\Lambda\mbox{--}$K-
pairs. Statistical (bars) and systematic (boxes) uncertainties are shown
separately. The light cyan band represents the total fit obtained using Eq. 2
from which the normalization $N_{D}$, the non-resonant scattering parameters
($\Re f_{0}$,$\Im f_{0}$ and $d_{0}$) and the properties of the
$\Xi\mathrm{(1620)}$ state are extracted. The violet band represents the
$C_{\mathrm{LL}}^{\mathrm{res}}(k^{*})$ correlation multiplied by the
corresponding weight $(1-\omega)$, while the olive green band is the $\omega
C_{\mathrm{LL}}^{\mathrm{non-res}}(k^{*})$. The orange band represents the
$C_{\mathrm{background}}(k^{*})$ modeled using the Monte Carlo simulations
multiplied by the constant $N_{D}$. Lower panel: $n_{\sigma}$ deviation
between data and model in terms of numbers of standard deviations.

In Fig. 3, the results for the $\Lambda\mbox{--}$K- system are presented. The
light cyan band represents the total correlation function (Eq. 2) with the
genuine interaction modeled, including a non-resonant and a resonant
contribution through the formation of the $\Xi\mathrm{(1620)}$. The fit well
describes the data and the reduced $\chi^{2}/$NDF, evaluated within the fit
range, is 2.9. The obtained weight $\omega$ in Eq. 6 is found to be $0.950\pm
0.005\mathrm{(stat.)}\pm 0.006\mathrm{(syst.)}$, indicating that a dominant
contribution from the non-resonant interaction is needed to reproduce the
data. However, the approach taking into account both contributions, which is
used in this work, should be considered as a phenomenological approach and
more theoretical investigations are needed in order to provide a better
description of the interplay between resonant and non-resonant processes. The
two additional bands reported in Fig. 3 correspond to the weighted correlation
functions obtained from the fit, which represent the resonant (violet) and
non-resonant (olive) $\Lambda$K- interaction, respectively.

The $\Lambda\mbox{--}$K- pairs interacting through the resonance lead to a
rather flat correlation profile at low $k^{*}$, which peaks at the mass of the
observed $\Xi\mathrm{(1620)}$ ($k^{*}\approx 80$ MeV$/c$) and then quickly
reaches unity. The extracted values of mass and partial effective widths for
the $\Xi\mathrm{(1620)}$ from the femtoscopic fit are also reported in Fig. 3.
The mass $M_{\Xi\mathrm{(1620)}}=1618.49\pm 0.28\mathrm{(stat.)}\pm
0.21\mathrm{(syst.)}$ MeV$/c^{2}$ obtained from the fit, as stated in Sec. 3,
is in agreement with the Belle measurement [28]. The numerical values of
$\tilde{\Gamma}_{\mathrm{\Xi\uppi}}=1.01\pm 0.14\mathrm{(stat.)}\pm
0.39\mathrm{(syst.)}$ MeV and $\tilde{\Gamma}_{\mathrm{\Lambda
K^{-}}}=115.99\pm 8.56\mathrm{(stat.)}\pm 4.08\mathrm{(syst.)}$ MeV, obtained
from the fit using a Flatté-like distribution, should not be taken literally
since mainly the ratio between the two coupling constants to these channels is
constrained by near-threshold data [73]. Nevertheless, the large
$\tilde{\Gamma}_{\mathrm{\Lambda K^{-}}}$ indicates a strong coupling of the
$\Xi\mathrm{(1620)}$ state to the $\Lambda$K- channel. To provide a
qualitative comparison between the results obtained in this work and the total
width reported by Belle, the determination of the poles for the Sill
scattering amplitude in Eq. 5 is performed. By inserting the values of the
extracted mass and widths in the denominator and searching for its zeros, the
pole position for the $\Xi\mathrm{(1620)}$ resonance corresponds to a state
with a mass $M=1616.34^{+0.01}_{-0.05}$ MeV$/c^{2}$ and a total width of
$\Gamma=12.00\pm 1.24$ MeV. The total uncertainty reported is propagated in
the calculation from the quadratic sum of the statistical and systematic error
on the mass and widths obtained from the femtoscopic fit. The value of the
mass obtained from the pole is compatible with the results reported by Belle,
while the width $\Gamma$ is smaller. This discrepancy can arise, as mentioned
above, from the presence of a close-by threshold and the typical
interpretation of the mass and in particular of the width obtained directly
from the energy of the pole might not hold for a near-threshold resonance, as
the $\Xi\mathrm{(1620)}$ in this case.

The ERE of the scattering amplitude $f(k^{*})$ in the Lednický–Lyuboshits
formula allows the scattering parameters $\Re f_{0}$, $\Im f_{0}$, and $d_{0}$
to be extracted. The results for $\Lambda$K+ (red diamonds) and for the non-
resonant $\Lambda$K- interaction (red circles) are shown in Fig. 4 with
statistical (bars) and systematic (shaded areas) uncertainties, and summarized
in Table 1. The left panel of Fig. 4 shows the real part of the scattering
length $\Re f_{0}$ (x-axis) as a function of the imaginary part $\Im f_{0}$
(y-axis) obtained in this work and its comparison to the measurements in Pb–Pb
collisions (blue markers) [46]. The available theoretical predictions for $\Re
f_{0}$ and $\Im f_{0}$, also presented in Fig. 4, are based on unitarized
chiral perturbation theory at leading order (LO) (green open circles [18],
light-cyan open circles [22, 23]) and on the standard chiral perturbation
theory at next-to-leading order (NLO) (orange open squares [35], magenta open
markers [36]). The output of these chiral calculations strongly depends on the
so-called low-energy and subtraction constants, parameters of the model which
need as input the experimental data to be fixed. In particular, the results
obtained in Ref. [35, 36] arise from a full treatment of the $SU(3)$ flavor
meson–baryon interaction and are hence anchored to large $|S|=0$ pion–nucleon
database. Moreover, to reduce the number of input parameters, isospin symmetry
is assumed, and then the crossing symmetry leads to almost identical
scattering parameters for the $\Lambda$K+ and $\Lambda$K- interaction. In the
unitarized framework of [18, 22, 23], the $\Xi\mathrm{(1620)}$ is dynamically
generated, meaning that the state is not introduced in the Lagrangian
investigated at LO, but it appears in the scattering amplitude due to the
meson–baryon interaction dynamics. The results in Ref. [18] were published
before the Belle measurement on $\Xi\mathrm{(1620)}$ [28], hence the model
parameters were constrained mainly by symmetry assumptions and by experimental
data on the antikaon–nucleon interaction. The scattering amplitude obtained
within this work has been studied in Ref. [22, 23], allowing for variations in
the subtraction constants of the model in order to reproduce the
$\Xi\mathrm{(1620)}$ properties measured by Belle. An agreement with the
measured $\Xi\mathrm{(1620)}$ mass and width is achieved only with very large
values of these constants, in contrast with the typical trend seen in similar
works. Such discrepancy might arise from the inclusion of only LO
contributions in the interaction and it can be investigated in the future with
an updated version of the chiral potentials in Ref. [74] at NLO that recently
became available. The studies in Ref. [18, 22, 23] show that the $\Lambda$K-
interaction is crucial in the understanding of the $\Xi\mathrm{(1620)}$ state
and it must be properly taken into account in the dynamics.

The negative value of $\Re f_{0}$ obtained in this work for
$\Lambda\mbox{--}$K+ pairs is compatible with the Pb–Pb results [46],
confirming the presence of a repulsive interaction. This is in tension with
the chiral calculations [35, 36], indicating an overall attraction. The
extracted $\Lambda$K+ $\Im f_{0}$ is in agreement within 1$\sigma$ with the
value obtained from the Pb–Pb measurements and it is in line with the
available predictions. The non-negligible value (roughly $1/3$ of the $\Re
f_{0}$), reported in Table 1, indicates the presence of inelastic channels in
the measured interaction. The $d_{0}$ is shown in the right panel of Fig. 4
and it can be seen that, for both $\Lambda\mbox{--}$K+ and
$\Lambda\mbox{--}$K- systems, the values extracted in pp and Pb–Pb colliding
systems are in agreement within uncertainties.

The $\Lambda\mbox{--}$K- pairs undergoing the non-resonant interaction in Fig.
3 (olive green bands) show an attractive interaction with a depletion in the
region $100<k^{*}<200$ MeV$/c$ (as seen in the lower panel of Fig. 1) given by
a non-negligible $\Im f_{0}$. The $\Re f_{0}$ lies in the positive side of the
x-axis, hence indicating an attractive $\Lambda$K- strong interaction as
observed in Pb–Pb collisions. Similarly, the $\Im f_{0}$ is compatible within
uncertainties with Pb–Pb results. The agreement between the non-resonant
$\Lambda$K- scattering parameters obtained in this work and the ones obtained
in Pb–Pb collisions is expected since in large colliding systems the effect of
resonances, such as the $\Xi\mathrm{(1620)}$, on the measured correlation
function is suppressed. Hence, the femtoscopic signal will be driven by the
non-resonant contribution. The theoretical models currently available on the
$\Lambda$K- interaction are far from converging to a common description of
this system, as can be seen in the predicted values of scattering parameters
in Fig. 4. As mentioned above, the tension mainly arises from the extremely
scarce amount of data available on this system. The work presented in this
Letter will significantly improve the knowledge on the interactions between
$\Lambda$ and antikaons and shed light on the role played by the
$\Xi\mathrm{(1620)}$ state, observed for the first time in this decay channel.

Figure 4: (Color online) Left: extracted $\Re f_{0}$ and $\Im f_{0}$ for the $\Lambda$K+ (red diamonds) and $\Lambda$K- (red dots) interaction in pp collisions, compared to Pb–Pb results (blue) [46] and available models (orange [35], magenta [36], green [18], and light cyan [22, 23]). For [18], the scattering parameters obtained for different sets of input parameters are reported. Statistical (bars) and systematic (boxes) uncertainties are shown. Right: extracted effective range $d_{0}$ obtained in this work (red) and in Pb–Pb collisions (blue) [46]. Table 1: Extracted scattering parameters for $\Lambda$K+ interaction and for the non-resonant part of $\Lambda$K- interaction in pp collisions. Statistical and systematic uncertainties are reported. Pair |  $\Lambda\mbox{--}$K+ |  $\Lambda\mbox{--}$K-
---|---|---
$\Re f_{0}$ (fm) | $-0.61\pm 0.03(\mathrm{stat})\pm 0.03(\mathrm{syst})$ | $0.33\pm 0.03(\mathrm{stat})\pm 0.02(\mathrm{syst})$
$\Im f_{0}$ (fm) | $0.23\pm 0.06(\mathrm{stat})\pm 0.04(\mathrm{syst})$ | $0.46\pm 0.03(\mathrm{stat})\pm 0.02(\mathrm{syst})$
$d_{0}$ (fm) | $0.80\pm 0.19(\mathrm{stat})\pm 0.18(\mathrm{syst})$ | $-5.47\pm 0.36(\mathrm{stat})\pm 0.26(\mathrm{syst})$

##  5 Summary

The two-particle correlation technique is used to access the strong
interaction between $\Lambda$ hyperons and charged kaons. This is achieved by
measuring the $\Lambda\mbox{--}$K+ and $\Lambda\mbox{--}$K- correlation
functions in pp collisions, down to zero momenta. The results presented in
this work provide the most precise data on these interactions. The $\Lambda$K+
interaction is found to be repulsive, with a non-negligible $\Im f_{0}$,
indicating that inelastic channels are present. The measured
$\Lambda\mbox{--}$K- correlation function shows a signal above unity at low
$k^{*}$, pointing to an overall attractive interaction, as well as several
resonances at different $k^{*}$ values above 200 MeV$/c$. The masses and
widths of these states, extracted from the fit to the correlation function,
are compatible with the $\Omega$ baryon and with two excited $\Xi$ states: the
$\Xi\mathrm{(1690)}$ and the $\Xi\mathrm{(1820)}$. The invariant mass spectrum
of the $\Lambda\mbox{--}$K- pairs, obtained from the same- and mixed-event
distributions entering the measured correlation function shows an additional
peak at $k^{*}\approx 80$ MeV$/c$. This structure corresponds to the
$\Xi\mathrm{(1620)}$ state, expected to couple to the $\Lambda\mbox{--}$K-
system. The $\Xi\mathrm{(1620)}$ is observed so far only in the $\Xi\uppi$
channel [28, 26, 27], hence these data represent the first experimental
evidence of the decay of the $\Xi\mathrm{(1620)}$ into $\Lambda\mbox{--}$K-
pairs. The measurements performed in this work show that the
$\Xi\mathrm{(1620)}$ plays an important role at the level of the strong
$\Lambda$K- interaction. To reproduce the measured $\Lambda\mbox{--}$K-
correlation two contributions must be taken into account in the genuine
interaction: a resonant term, in which $\Lambda\mbox{--}$K- pairs interact
through the formation of $\Xi\mathrm{(1620)}$ and modeled via a Sill
distribution [72], and a residual non-resonant part. Both contributions are
modeled using the Lednický–Lyuboshits analytical formula with different
scattering amplitudes $f(k^{*})$. The extracted mass and partial widths for
the $\Xi\mathrm{(1620)}$ state are expressed in terms of poles of the Sill
scattering amplitude. The mass is found to be consistent with the recent Belle
measurements in the $\Xi\uppi$ decay channel. The extracted scattering
parameters for the $\Lambda$K+ and the $\Lambda$K- (non-resonant) interaction
are in agreement with the femtoscopic measurements of the same pairs performed
by the ALICE collaboration in Pb–Pb collisions.

The presented data provide important experimental constraints for low-energy
effective theories, aiming at describing the strangeness $S=0$ and $S=-2$
sectors of the meson–baryon interaction, and show the possibility to
investigate the role of still not established resonances, such as the
$\Xi\mathrm{(1620)}$, in hadron–hadron interactions.

## Acknowledgements

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

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##  Appendix A The ALICE Collaboration

S. Acharya 127, D. Adamová 87, A. Adler70, G. Aglieri Rinella 33, M. Agnello
30, N. Agrawal 51, Z. Ahammed 134, S. Ahmad 16, S.U. Ahn 71, I. Ahuja 38, A.
Akindinov 142, M. Al-Turany 98, D. Aleksandrov 142, B. Alessandro 56, H.M.
Alfanda 6, R. Alfaro Molina 67, B. Ali 16, A. Alici 26, N. Alizadehvandchali
116, A. Alkin 33, J. Alme 21, G. Alocco 52, T. Alt 64, A.R. Altamura 50, I.
Altsybeev 96, M.N. Anaam 6, C. Andrei 46, A. Andronic 137, V. Anguelov 95, F.
Antinori 54, P. Antonioli 51, N. Apadula 75, L. Aphecetche 105, H.
Appelshäuser 64, C. Arata 74, S. Arcelli 26, M. Aresti 52, R. Arnaldi 56,
J.G.M.C.A. Arneiro 112, I.C. Arsene 20, M. Arslandok 139, A. Augustinus 33, R.
Averbeck 98, M.D. Azmi 16, H. Baba124, A. Badalà 53, J. Bae 106, Y.W. Baek 41,
X. Bai 120, R. Bailhache 64, Y. Bailung 48, A. Balbino 30, A. Baldisseri 130,
B. Balis 2, D. Banerjee 4, Z. Banoo 92, R. Barbera 27, F. Barile 32, L.
Barioglio 96, M. Barlou79, G.G. Barnaföldi 138, L.S. Barnby 86, V. Barret 127,
L. Barreto 112, C. Bartels 119, K. Barth 33, E. Bartsch 64, N. Bastid 127, S.
Basu 76, G. Batigne 105, D. Battistini 96, B. Batyunya 143, D. Bauri47, J.L.
Bazo Alba 103, I.G. Bearden 84, C. Beattie 139, P. Becht 98, D. Behera 48, I.
Belikov 129, A.D.C. Bell Hechavarria 137, F. Bellini 26, R. Bellwied 116, S.
Belokurova 142, G. Bencedi 138, S. Beole 25, A. Bercuci 46, Y. Berdnikov 142,
A. Berdnikova 95, L. Bergmann 95, M.G. Besoiu 63, L. Betev 33, P.P. Bhaduri
134, A. Bhasin 92, M.A. Bhat 4, B. Bhattacharjee 42, L. Bianchi 25, N. Bianchi
49, J. Bielčík 36, J. Bielčíková 87, J. Biernat 109, A.P. Bigot 129, A.
Bilandzic 96, G. Biro 138, S. Biswas 4, N. Bize 105, J.T. Blair 110, D. Blau
142, M.B. Blidaru 98, N. Bluhme39, C. Blume 64, G. Boca 22,55, F. Bock 88, T.
Bodova 21, A. Bogdanov142, S. Boi 23, J. Bok 58, L. Boldizsár 138, M. Bombara
38, P.M. Bond 33, G. Bonomi 133,55, H. Borel 130, A. Borissov 142, A.G.
Borquez Carcamo 95, H. Bossi 139, E. Botta 25, Y.E.M. Bouziani 64, L. Bratrud
64, P. Braun-Munzinger 98, M. Bregant 112, M. Broz 36, G.E. Bruno 97,32, M.D.
Buckland 24, D. Budnikov 142, H. Buesching 64, S. Bufalino 30, P. Buhler 104,
N. Burmasov 142, Z. Buthelezi 68,123, A. Bylinkin 21, S.A. Bysiak109, M. Cai
6, H. Caines 139, A. Caliva 29, E. Calvo Villar 103, J.M.M. Camacho 111, P.
Camerini 24, F.D.M. Canedo 112, M. Carabas 126, A.A. Carballo 33, F.
Carnesecchi 33, R. Caron 128, L.A.D. Carvalho 112, J. Castillo Castellanos
130, F. Catalano 33,25, C. Ceballos Sanchez 143, I. Chakaberia 75, P.
Chakraborty 47, S. Chandra 134, S. Chapeland 33, M. Chartier 119, S.
Chattopadhyay 134, S. Chattopadhyay 101, T.G. Chavez 45, T. Cheng 98,6, C.
Cheshkov 128, B. Cheynis 128, V. Chibante Barroso 33, D.D. Chinellato 113,
E.S. Chizzali I,96, J. Cho 58, S. Cho 58, P. Chochula 33, P. Christakoglou 85,
C.H. Christensen 84, P. Christiansen 76, T. Chujo 125, M. Ciacco 30, C. Cicalo
52, F. Cindolo 51, M.R. Ciupek98, G. ClaiII,51, F. Colamaria 50, J.S.
Colburn102, D. Colella 97,32, M. Colocci 26, G. Conesa Balbastre 74, Z. Conesa
del Valle 73, G. Contin 24, J.G. Contreras 36, M.L. Coquet 130, P. Cortese
132,56, M.R. Cosentino 114, F. Costa 33, S. Costanza 22,55, C. Cot 73, J.
Crkovská 95, P. Crochet 127, R. Cruz-Torres 75, P. Cui 6, A. Dainese 54, M.C.
Danisch 95, A. Danu 63, P. Das 81, P. Das 4, S. Das 4, A.R. Dash 137, S. Dash
47, R.M.H. David45, A. De Caro 29, G. de Cataldo 50, J. de Cuveland39, A. De
Falco 23, D. De Gruttola 29, N. De Marco 56, C. De Martin 24, S. De Pasquale
29, R. Deb133, S. Deb 48, R. Del Grande 96, L. Dello Stritto 29, W. Deng 6, P.
Dhankher 19, D. Di Bari 32, A. Di Mauro 33, B. Diab 130, R.A. Diaz 143,7, T.
Dietel 115, Y. Ding 6, R. Divià 33, D.U. Dixit 19, Ø. Djuvsland21, U.
Dmitrieva 142, A. Dobrin 63, B. Dönigus 64, J.M. Dubinski 135, A. Dubla 98, S.
Dudi 91, P. Dupieux 127, M. Durkac108, N. Dzalaiova13, T.M. Eder 137, R.J.
Ehlers 75, F. Eisenhut 64, R. Ejima93, D. Elia 50, B. Erazmus 105, F.
Ercolessi 26, F. Erhardt 90, M.R. Ersdal21, B. Espagnon 73, G. Eulisse 33, D.
Evans 102, S. Evdokimov 142, L. Fabbietti 96, M. Faggin 28, J. Faivre 74, F.
Fan 6, W. Fan 75, A. Fantoni 49, M. Fasel 88, P. Fecchio30, A. Feliciello 56,
G. Feofilov 142, A. Fernández Téllez 45, L. Ferrandi 112, M.B. Ferrer 33, A.
Ferrero 130, C. Ferrero 56, A. Ferretti 25, V.J.G. Feuillard 95, V. Filova 36,
D. Finogeev 142, F.M. Fionda 52, F. Flor 116, A.N. Flores 110, S. Foertsch 68,
I. Fokin 95, S. Fokin 142, E. Fragiacomo 57, E. Frajna 138, U. Fuchs 33, N.
Funicello 29, C. Furget 74, A. Furs 142, T. Fusayasu 100, J.J. Gaardhøje 84,
M. Gagliardi 25, A.M. Gago 103, T. Gahlaut47, C.D. Galvan 111, D.R.
Gangadharan 116, P. Ganoti 79, C. Garabatos 98, A.T. Garcia 73, J.R.A. Garcia
45, E. Garcia-Solis 9, C. Gargiulo 33, K. Garner137, P. Gasik 98, A. Gautam
118, M.B. Gay Ducati 66, M. Germain 105, A. Ghimouz125, C. Ghosh134, M.
Giacalone 51, G. Gioachin 30, P. Giubellino 98,56, P. Giubilato 28, A.M.C.
Glaenzer 130, P. Glässel 95, E. Glimos 122, D.J.Q. Goh77, V. Gonzalez 136, M.
Gorgon 2, K. Goswami 48, S. Gotovac34, V. Grabski 67, L.K. Graczykowski 135,
E. Grecka 87, A. Grelli 59, C. Grigoras 33, V. Grigoriev 142, S. Grigoryan
143,1, F. Grosa 33, J.F. Grosse-Oetringhaus 33, R. Grosso 98, D. Grund 36,
G.G. Guardiano 113, R. Guernane 74, M. Guilbaud 105, K. Gulbrandsen 84, T.
Gundem 64, T. Gunji 124, W. Guo 6, A. Gupta 92, R. Gupta 92, R. Gupta 48, S.P.
Guzman 45, K. Gwizdziel 135, L. Gyulai 138, C. Hadjidakis 73, F.U. Haider 92,
H. Hamagaki 77, A. Hamdi 75, Y. Han 140, B.G. Hanley 136, R. Hannigan 110, J.
Hansen 76, M.R. Haque 135, J.W. Harris 139, A. Harton 9, H. Hassan 88, D.
Hatzifotiadou 51, P. Hauer 43, L.B. Havener 139, S.T. Heckel 96, E. Hellbär
98, H. Helstrup 35, M. Hemmer 64, T. Herman 36, G. Herrera Corral 8, F.
Herrmann137, S. Herrmann 128, K.F. Hetland 35, B. Heybeck 64, H. Hillemanns
33, B. Hippolyte 129, F.W. Hoffmann 70, B. Hofman 59, G.H. Hong 140, M. Horst
96, A. Horzyk 2, Y. Hou 6, P. Hristov 33, C. Hughes 122, P. Huhn64, L.M. Huhta
117, T.J. Humanic 89, A. Hutson 116, D. Hutter 39, T. Hyodo III,99, R.
Ilkaev142, H. Ilyas 14, M. Inaba 125, G.M. Innocenti 33, M. Ippolitov 142, A.
Isakov 85,87, T. Isidori 118, M.S. Islam 101, M. Ivanov13, M. Ivanov 98, V.
Ivanov 142, K.E. Iversen 76, M. Jablonski 2, B. Jacak 75, N. Jacazio 26, P.M.
Jacobs 75, S. Jadlovska108, J. Jadlovsky108, S. Jaelani 83, C. Jahnke 113,
M.J. Jakubowska 135, M.A. Janik 135, T. Janson70, S. Ji 17, S. Jia 10, A.A.P.
Jimenez 65, F. Jonas 88, D.M. Jones 119, J.M. Jowett 33,98, J. Jung 64, M.
Jung 64, A. Junique 33, A. Jusko 102, M.J. Kabus 33,135, J. Kaewjai107, P.
Kalinak 60, A.S. Kalteyer 98, A. Kalweit 33, Y. Kamiya IV,99, V. Kaplin 142,
A. Karasu Uysal 72, D. Karatovic 90, O. Karavichev 142, T. Karavicheva 142, P.
Karczmarczyk 135, E. Karpechev 142, U. Kebschull 70, R. Keidel 141, D.L.D.
Keijdener59, M. Keil 33, B. Ketzer 43, S.S. Khade 48, A.M. Khan 120,6, S. Khan
16, A. Khanzadeev 142, Y. Kharlov 142, A. Khatun 118, A. Khuntia 36, M.B.
Kidson115, B. Kileng 35, B. Kim 106, C. Kim 17, D.J. Kim 117, E.J. Kim 69, J.
Kim 140, J.S. Kim 41, J. Kim 58, J. Kim 69, M. Kim 19, S. Kim 18, T. Kim 140,
K. Kimura 93, S. Kirsch 64, I. Kisel 39, S. Kiselev 142, A. Kisiel 135, J.P.
Kitowski 2, J.L. Klay 5, J. Klein 33, S. Klein 75, C. Klein-Bösing 137, M.
Kleiner 64, T. Klemenz 96, A. Kluge 33, A.G. Knospe 116, C. Kobdaj 107, T.
Kollegger98, A. Kondratyev 143, N. Kondratyeva 142, E. Kondratyuk 142, J.
Konig 64, S.A. Konigstorfer 96, P.J. Konopka 33, G. Kornakov 135, S.D.
Koryciak 2, A. Kotliarov 87, V. Kovalenko 142, M. Kowalski 109, V. Kozhuharov
37, I. Králik 60, A. Kravčáková 38, L. Krcal 33,39, M. Krivda 102,60, F.
Krizek 87, K. Krizkova Gajdosova 33, M. Kroesen 95, M. Krüger 64, D.M. Krupova
36, E. Kryshen 142, V. Kučera 58, C. Kuhn 129, P.G. Kuijer 85, T. Kumaoka125,
D. Kumar134, L. Kumar 91, N. Kumar91, S. Kumar 32, S. Kundu 33, P. Kurashvili
80, A. Kurepin 142, A.B. Kurepin 142, A. Kuryakin 142, S. Kushpil 87, M.J.
Kweon 58, Y. Kwon 140, S.L. La Pointe 39, P. La Rocca 27, A. Lakrathok107, M.
Lamanna 33, R. Langoy 121, P. Larionov 33, E. Laudi 33, L. Lautner 33,96, R.
Lavicka 104, R. Lea 133,55, H. Lee 106, I. Legrand 46, G. Legras 137, J.
Lehrbach 39, T.M. Lelek2, R.C. Lemmon 86, I. León Monzón 111, M.M. Lesch 96,
E.D. Lesser 19, P. Lévai 138, X. Li10, X.L. Li6, J. Lien 121, R. Lietava 102,
I. Likmeta 116, B. Lim 25, S.H. Lim 17, V. Lindenstruth 39, A. Lindner46, C.
Lippmann 98, A. Liu 19, D.H. Liu 6, J. Liu 119, G.S.S. Liveraro 113, I.M.
Lofnes 21, C. Loizides 88, S. Lokos 109, J. Lomker 59, P. Loncar 34, X. Lopez
127, E. López Torres 7, P. Lu 98,120, J.R. Luhder 137, M. Lunardon 28, G.
Luparello 57, Y.G. Ma 40, M. Mager 33, A. Maire 129, M.V. Makariev 37, M.
Malaev 142, G. Malfattore 26, N.M. Malik 92, Q.W. Malik20, S.K. Malik 92, L.
Malinina VII,143, D. Mallick 73,81, N. Mallick 48, G. Mandaglio 31,53, S.K.
Mandal 80, V. Manko 142, F. Manso 127, V. Manzari 50, Y. Mao 6, R.W. Marcjan
2, G.V. Margagliotti 24, A. Margotti 51, A. Marín 98, C. Markert 110, P.
Martinengo 33, M.I. Martínez 45, G. Martínez García 105, M.P.P. Martins 112,
S. Masciocchi 98, M. Masera 25, A. Masoni 52, L. Massacrier 73, O. Massen 59,
A. Mastroserio 131,50, O. Matonoha 76, S. Mattiazzo 28, P.F.T. Matuoka112, A.
Matyja 109, C. Mayer 109, A.L. Mazuecos 33, F. Mazzaschi 25, M. Mazzilli 33,
J.E. Mdhluli 123, A.F. Mechler64, Y. Melikyan 44, A. Menchaca-Rocha 67, E.
Meninno 104,29, A.S. Menon 116, M. Meres 13, S. Mhlanga115,68, Y. Miake125, L.
Micheletti 33, L.C. Migliorin128, D.L. Mihaylov 96, K. Mikhaylov 143,142, A.N.
Mishra 138, D. Miśkowiec 98, A. Modak 4, A.P. Mohanty 59, B. Mohanty81, M.
Mohisin Khan V,16, M.A. Molander 44, S. Monira 135, Z. Moravcova 84, C.
Mordasini 117, D.A. Moreira De Godoy 137, I. Morozov 142, A. Morsch 33, T.
Mrnjavac 33, V. Muccifora 49, S. Muhuri 134, J.D. Mulligan 75, A. Mulliri23,
M.G. Munhoz 112, R.H. Munzer 64, H. Murakami 124, S. Murray 115, L. Musa 33,
J. Musinsky 60, J.W. Myrcha 135, B. Naik 123, A.I. Nambrath 19, B.K. Nandi 47,
R. Nania 51, E. Nappi 50, A.F. Nassirpour 18,76, A. Nath 95, C. Nattrass 122,
M.N. Naydenov 37, A. Neagu20, A. Negru126, L. Nellen 65, R. Nepeivoda 76, S.
Nese 20, G. Neskovic 39, B.S. Nielsen 84, E.G. Nielsen 84, S. Nikolaev 142, S.
Nikulin 142, V. Nikulin 142, F. Noferini 51, S. Noh 12, P. Nomokonov 143, J.
Norman 119, N. Novitzky 125, P. Nowakowski 135, A. Nyanin 142, J. Nystrand 21,
M. Ogino 77, S. Oh 18, A. Ohlson 76, V.A. Okorokov 142, J. Oleniacz 135, A.C.
Oliveira Da Silva 122, M.H. Oliver 139, A. Onnerstad 117, C. Oppedisano 56, A.
Ortiz Velasquez 65, J. Otwinowski 109, M. Oya93, K. Oyama 77, Y. Pachmayer 95,
S. Padhan 47, D. Pagano 133,55, G. Paić 65, A. Palasciano 50, S. Panebianco
130, H. Park 125, H. Park 106, J. Park 58, J.E. Parkkila 33, Y. Patley 47,
R.N. Patra92, B. Paul 23, H. Pei 6, T. Peitzmann 59, X. Peng 11, M. Pennisi
25, S. Perciballi 25, D. Peresunko 142, G.M. Perez 7, Y. Pestov142, V. Petrov
142, M. Petrovici 46, R.P. Pezzi 105,66, S. Piano 57, M. Pikna 13, P. Pillot
105, O. Pinazza 51,33, L. Pinsky116, C. Pinto 96, S. Pisano 49, M. Płoskoń 75,
M. Planinic90, F. Pliquett64, M.G. Poghosyan 88, B. Polichtchouk 142, S.
Politano 30, N. Poljak 90, A. Pop 46, S. Porteboeuf-Houssais 127, V.
Pozdniakov 143, I.Y. Pozos 45, K.K. Pradhan 48, S.K. Prasad 4, S. Prasad 48,
R. Preghenella 51, F. Prino 56, C.A. Pruneau 136, I. Pshenichnov 142, M.
Puccio 33, S. Pucillo 25, Z. Pugelova108, S. Qiu 85, L. Quaglia 25, R.E.
Quishpe116, S. Ragoni 15, A. Rakotozafindrabe 130, L. Ramello 132,56, F. Rami
129, S.A.R. Ramirez 45, T.A. Rancien74, M. Rasa 27, S.S. Räsänen 44, R. Rath
51, M.P. Rauch 21, I. Ravasenga 85, K.F. Read 88,122, C. Reckziegel 114, A.R.
Redelbach 39, K. Redlich VI,80, C.A. Reetz 98, A. Rehman21, F. Reidt 33, H.A.
Reme-Ness 35, Z. Rescakova38, K. Reygers 95, A. Riabov 142, V. Riabov 142, R.
Ricci 29, M. Richter 20, A.A. Riedel 96, W. Riegler 33, A.G. Riffero 25, C.
Ristea 63, M.V. Rodriguez 33, M. Rodríguez Cahuantzi 45, K. Røed 20, R.
Rogalev 142, E. Rogochaya 143, T.S. Rogoschinski 64, D. Rohr 33, D. Röhrich
21, P.F. Rojas45, S. Rojas Torres 36, P.S. Rokita 135, G. Romanenko 26, F.
Ronchetti 49, A. Rosano 31,53, E.D. Rosas65, K. Roslon 135, A. Rossi 54, A.
Roy 48, S. Roy 47, N. Rubini 26, O.V. Rueda 116, D. Ruggiano 135, R. Rui 24,
P.G. Russek 2, R. Russo 85, A. Rustamov 82, E. Ryabinkin 142, Y. Ryabov 142,
A. Rybicki 109, H. Rytkonen 117, J. Ryu 17, W. Rzesa 135, O.A.M. Saarimaki 44,
S. Sadhu 32, S. Sadovsky 142, J. Saetre 21, K. Šafařík 36, P. Saha42, S.K.
Saha 4, S. Saha 81, B. Sahoo 47, B. Sahoo 48, R. Sahoo 48, S. Sahoo61, D. Sahu
48, P.K. Sahu 61, J. Saini 134, K. Sajdakova38, S. Sakai 125, M.P. Salvan 98,
S. Sambyal 92, D. Samitz 104, I. Sanna 33,96, T.B. Saramela112, D. Sarkar 136,
P. Sarma 42, V. Sarritzu 23, V.M. Sarti 96, M.H.P. Sas 139, J. Schambach 88,
H.S. Scheid 64, C. Schiaua 46, R. Schicker 95, A. Schmah98, C. Schmidt 98,
H.R. Schmidt94, M.O. Schmidt 33, M. Schmidt94, N.V. Schmidt 88, A.R. Schmier
122, R. Schotter 129, A. Schröter 39, J. Schukraft 33, K. Schweda 98, G.
Scioli 26, E. Scomparin 56, J.E. Seger 15, Y. Sekiguchi124, D. Sekihata 124,
M. Selina 85, I. Selyuzhenkov 98, S. Senyukov 129, J.J. Seo 95,58, D.
Serebryakov 142, L. Šerkšnytė 96, A. Sevcenco 63, T.J. Shaba 68, A. Shabetai
105, R. Shahoyan33, A. Shangaraev 142, A. Sharma91, B. Sharma 92, D. Sharma
47, H. Sharma 54,109, M. Sharma 92, S. Sharma 77, S. Sharma 92, U. Sharma 92,
A. Shatat 73, O. Sheibani116, K. Shigaki 93, M. Shimomura78, J. Shin12, S.
Shirinkin 142, Q. Shou 40, Y. Sibiriak 142, S. Siddhanta 52, T. Siemiarczuk
80, T.F. Silva 112, D. Silvermyr 76, T. Simantathammakul107, R. Simeonov 37,
B. Singh92, B. Singh 96, K. Singh 48, R. Singh 81, R. Singh 92, R. Singh 48,
S. Singh 16, V.K. Singh 134, V. Singhal 134, T. Sinha 101, B. Sitar 13, M.
Sitta 132,56, T.B. Skaali20, G. Skorodumovs 95, M. Slupecki 44, N. Smirnov
139, R.J.M. Snellings 59, E.H. Solheim 20, J. Song 116, A. Songmoolnak107, C.
Sonnabend 33,98, F. Soramel 28, A.B. Soto-hernandez 89, R. Spijkers 85, I.
Sputowska 109, J. Staa 76, J. Stachel 95, I. Stan 63, P.J. Steffanic 122, S.F.
Stiefelmaier 95, D. Stocco 105, I. Storehaug 20, P. Stratmann 137, S. Strazzi
26, A. Sturniolo 31,53, C.P. Stylianidis85, A.A.P. Suaide 112, C. Suire 73, M.
Sukhanov 142, M. Suljic 33, R. Sultanov 142, V. Sumberia 92, S. Sumowidagdo
83, S. Swain61, I. Szarka 13, M. Szymkowski 135, S.F. Taghavi 96, G.
Taillepied 98, J. Takahashi 113, G.J. Tambave 81, S. Tang 6, Z. Tang 120, J.D.
Tapia Takaki 118, N. Tapus126, L.A. Tarasovicova 137, M.G. Tarzila 46, G.F.
Tassielli 32, A. Tauro 33, G. Tejeda Muñoz 45, A. Telesca 33, L. Terlizzi 25,
C. Terrevoli 116, S. Thakur 4, D. Thomas 110, A. Tikhonov 142, A.R. Timmins
116, M. Tkacik108, T. Tkacik 108, A. Toia 64, R. Tokumoto93, K. Tomohiro93, N.
Topilskaya 142, M. Toppi 49, T. Tork 73, V.V. Torres 105, A.G. Torres Ramos
32, A. Trifiró 31,53, A.S. Triolo 33,31,53, S. Tripathy 51, T. Tripathy 47, S.
Trogolo 33, V. Trubnikov 3, W.H. Trzaska 117, T.P. Trzcinski 135, A. Tumkin
142, R. Turrisi 54, T.S. Tveter 20, K. Ullaland 21, B. Ulukutlu 96, A. Uras
128, G.L. Usai 23, M. Vala38, N. Valle 22, L.V.R. van Doremalen59, M. van
Leeuwen 85, C.A. van Veen 95, R.J.G. van Weelden 85, P. Vande Vyvre 33, D.
Varga 138, Z. Varga 138, M. Vasileiou 79, A. Vasiliev 142, O. Vázquez Doce 49,
V. Vechernin 142, E. Vercellin 25, S. Vergara Limón45, R. Verma47, L. Vermunt
98, R. Vértesi 138, M. Verweij 59, L. Vickovic34, Z. Vilakazi123, O.
Villalobos Baillie 102, A. Villani 24, G. Vino 50, A. Vinogradov 142, T.
Virgili 29, M.M.O. Virta 117, V. Vislavicius76, A. Vodopyanov 143, B. Volkel
33, M.A. Völkl 95, K. Voloshin142, S.A. Voloshin 136, G. Volpe 32, B. von
Haller 33, I. Vorobyev 96, N. Vozniuk 142, J. Vrláková 38, J. Wan40, C. Wang
40, D. Wang40, Y. Wang 40, Y. Wang 6, A. Wegrzynek 33, F.T. Weiglhofer39, S.C.
Wenzel 33, J.P. Wessels 137, S.L. Weyhmiller 139, J. Wiechula 64, J. Wikne 20,
G. Wilk 80, J. Wilkinson 98, G.A. Willems 137, B. Windelband 95, M. Winn 130,
J.R. Wright 110, W. Wu40, Y. Wu 120, R. Xu 6, A. Yadav 43, A.K. Yadav 134, S.
Yalcin 72, Y. Yamaguchi 93, S. Yang21, S. Yano 93, Z. Yin 6, I.-K. Yoo 17,
J.H. Yoon 58, H. Yu12, S. Yuan21, A. Yuncu 95, V. Zaccolo 24, C. Zampolli 33,
F. Zanone 95, N. Zardoshti 33, A. Zarochentsev 142, P. Závada 62, N.
Zaviyalov142, M. Zhalov 142, B. Zhang 6, C. Zhang 130, L. Zhang 40, S. Zhang
40, X. Zhang 6, Y. Zhang120, Z. Zhang 6, M. Zhao 10, V. Zherebchevskii 142, Y.
Zhi10, D. Zhou 6, Y. Zhou 84, J. Zhu 98,6, Y. Zhu6, S.C. Zugravel 56, N. Zurlo
133,55

## Affiliation Notes

I Also at: Max-Planck-Institut für Physik, Munich, Germany
II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
III Also at: Department of Physics, Tokyo Metropolitan University, Hachioji,
Japan
IV Also at: Helmholtz Institut für Strahlen- und Kernphysik and Bethe Center
for Theoretical Physics, Universität Bonn, Bonn, Germany
V Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
VI Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VII Also at: An institution covered by a cooperation agreement with CERN

## Collaboration Institutes

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