2021 080 10 May

Kaon–proton scattering in Pb–Pb collisions at the LHC

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

In quantum scattering processes between two particles, aspects characterizing
the strong and Coulomb forces can be observed in kinematic distributions of
the particle pairs. The sensitivity to the interaction potential reaches a
maximum at low relative momentum and vanishing distance between the two
particles. Ultrarelativistic heavy-ion collisions at the LHC provide an
abundant source of many hadron species and can be employed as a measurement
method of scattering parameters that is complementary to scattering
experiments. This study confirms that momentum correlations of particles
produced in Pb–Pb collisions at the LHC provide an accurate measurement of
kaon–proton scattering parameters at low relative momentum, allowing precise
access to the $\rm{K}^{-}p\rightarrow\rm{K}^{-}p$ process. This work also
validates the femtoscopic measurement in ultrarelativistic heavy-ion
collisions as an alternative to scattering experiments and a complementary
tool to the study of exotic atoms with comparable precision. In this work, the
first femtoscopic measurement of momentum correlations of $\rm{K}^{-}\rm{p}\
(\rm{K}^{+}\overline{p})$ and $\rm{K}^{+}\rm{p}\ (\rm{K}^{-}\overline{p})$
pairs in Pb–Pb collisions at centre-of-mass energy per nucleon pair of
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV registered by the ALICE experiment is
reported. The components of the $\rm{K}^{-}\rm{p}$ complex scattering length
are extracted and found to be $\Re
f_{0}=-0.91\pm~{}{0.03}$(stat)${}^{+0.17}_{-0.03}$(syst) and $\Im
f_{0}=0.92\pm~{}{0.05}$(stat)${}^{+0.12}_{-0.33}$(syst). The results are
compared with chiral effective field theory predictions as well as with
existing data from dedicated scattering and exotic kaonic atom experiments.

##  1 Introduction

The study of kaon–nucleon (KN) and antikaon–nucleon ($\overline{\mathrm{K}}$N)
interactions is essential to understand low-energy quantum chromodynamics
(QCD). The Goldstone boson nature of the kaon and its role as an active degree
of freedom within effective field theories are used to describe processes
within the chiral SU(3) dynamics at low energies. Since perturbation theory is
not applicable in this energy regime, experimental data are essential to
constrain the currently available effective theories [1]. In general, three
experimental techniques can be used to access hadron–hadron interaction, such
as $\rm\overline{K}N$, which will be discussed below. Their schematic
illustration is shown in Fig. 1.

Figure 1: Schematic illustration of available experimental techniques for
measuring the interaction among hadrons: a) scattering experiments, b)
measurements of energy shifts from the X-ray de-excitation spectrum of exotic
atoms, c) femtoscopy in small collision systems (pp) with coupled channel
effects shown in green, and in large collision systems (Pb–Pb) with vanishing
coupled channel contributions shown in blue.

A direct measurement of the $\rm\overline{K}N$ interaction was first possible
in scattering experiments with secondary $\rm{K}^{-}$ beams impinging on
hydrogen targets. Such experiments allow the precise control of both the
initial (incoming) and final (outgoing) states, see Fig. 1 a. Furthermore,
polarised beams and targets can be used [2]. However, scattering measurements
can only be performed for pairs of charged and long-lived particles, because
of the technical challenges of creating beams of other particle species,
especially involving strangeness or antimatter [3]. Finally, attaining zero
relative momentum for strange hadrons, such as kaons, is also challenging.
Current $\rm{K}^{-}p$ measurements can only reach a kaon momentum of
approximately $100$ MeV/$c$ with respect to the proton at rest [4, 5, 6, 7, 8,
9, 10]. Therefore, the present accuracy of the $\rm{K}^{-}{\rm p}$ cross
sections and branching ratios at threshold does not sufficiently constrain the
scattering amplitudes.

Another way of studying the low-energy $\rm\overline{K}N$ interaction is by
observing the shifts and widths of energy levels in exotic kaonic atoms [11],
where a negative kaon replaces an electron, see Fig. 1 b. In particular,
kaonic hydrogen and kaonic deuterium can be formed in dedicated experimental
setups and measurements of their X-ray deexcitation spectra provide a link to
the $\rm{K}^{-}p$ strong interaction at zero relative momentum [12]. When the
negative hadron, such as $\rm{K}^{-}$, transits between the lowest energy
states, its wave function overlaps with the nucleus and the presence of the
strong force modifies the energy levels and their widths due to coupling to
intermediate states before absorption [13, 14]. The measurement of the energy
shift and width of the 1S state of the kaonic hydrogen line can be connected
to the $\rm{K}^{-}$p scattering length ($f_{0}$) through the Trueman–Deser
formula [15, 16]. However, it requires model-dependent corrections to account
for the presence of the isospin-breaking couplings and the Coulomb interaction
[16]. The scattering length is a complex number related to both the elastic
and inelastic cross sections of the interaction. The current benchmark result
is from chiral effective field theory ($\chi^{\rm EFT}$ calculations) [17, 18]
anchored to the kaonic hydrogen data [19, 20] collected by the SIDDHARTA
experiment [21] at the DA$\Phi$NE electron–positron collider [22], and
estimates the real part $\Re f_{0}=-0.65\pm 0.10$ fm111The usual femtoscopic
sign convention is used, where a positive $\Re f_{0}$ corresponds to
attractive strong interaction. and the imaginary part $\Im f_{0}=0.81\pm 0.15$
fm of the scattering length. Historically, the scattering parameters extracted
from the kaonic hydrogen experiments pointed to an attractive interaction,
while a repulsive $\rm{K}^{-}p$ scattering length in free space was measured
via scattering experiments. Currently, both results are explained
simultaneously by the presence of the $\Lambda(1405)$ resonance located just
below the $\overline{\mathrm{K}}$N threshold [23]. Similar experiments have
been performed with other hadrons, such as pions [24, 14] and antiprotons
[25], providing precise measurements of the interaction at the kinematic
threshold.

On the other hand, the repulsive nature of the K+p interaction is well
established. It is described by an s-wave [26] scattering length with a
negative real part ($\Re f_{0}=-0.308\pm 0.003$) and the Coulomb interaction
[27, 28].

Scattering experiments are special in that both the initial and final states
are fixed, which implies that only the $\rm{K}^{-}p\rightarrow\rm{K}^{-}p$
process can be accessed. This is not the case for ultrarelativistic particle
collisions since only the $\rm{K}^{-}p$ final state is fixed and different
initial states are allowed, such as $\mathrm{\overline{K}^{0}n}$ and
$\uppi\Sigma$, which are referred to as coupled channels. Collisions of nuclei
at the Large Hadron Collider (LHC) provide an abundant source of various
particle species (including strange hadrons [29]), in both small (pp, p–Pb)
and large (Pb–Pb) systems. In a single central Pb–Pb collision, the number of
produced particles reaches thousands at midrapidity ($|y|<0.5$) [30, 31, 32].
Moreover, since the baryon chemical potential for ultrarelativistic heavy-ion
collisions at LHC energies approaches zero, a nearly equal amount of matter
and antimatter are produced [33]. Therefore, they are an ideal environment for
conducting interaction studies involving both strangeness and antimatter [34,
35, 36], as shown in Fig. 1 c. A recent breakthrough in the field was achieved
by analysing the kaon–proton momentum correlations [37] using the technique of
femtoscopy in high-energy pp collisions at the ALICE experiment [38], showing
clear evidence for the presence of coupled channels in the measured
correlation function. In particular, a clear signature for the opening at the
threshold of the $\mathrm{\overline{K}^{0}n}$ isospin breaking channel is
observed due to the mass difference between the pairs.

In order to reproduce the experimental data, theoretical models need to
describe the Coulomb interaction, the coupled-channels effects, and the
threshold energy difference among the isospin multiplets used in the
calculation [39]. This can be done in a realistic $\overline{\rm
K}$N–$\uppi\Sigma$–$\uppi\Lambda$ coupled-channel potential which can be
constructed starting from chiral SU(3) dynamics [18]. Alternatively, the
$\rm\overline{K}N$ interaction can also be characterized by the
Lednický–Lyuboshitz analytical model where the s-wave scattering parameters
are used to describe the measurements [40, 41].

It has been recently predicted that the strength of the coupled channels is
significantly reduced for source sizes larger than 3 fm, because channels
other than $\rm{K}^{-}p$ have a considerable magnitude only around a distance
of 1 fm [39]. It is therefore expected that for larger sources, such as those
created in heavy-ion collisions, their effect on the correlation function
should be significantly reduced or become asymptotically small. Therefore, the
analysis of $\rm{K}^{-}p$ pairs in Pb–Pb collisions, as shown in this work for
the first time, can help to disentangle the
$\rm{K}^{-}p\rightarrow\rm{K}^{-}p$ process from contributions stemming from
on-shell coupled channels at the reaction threshold.

##  2 Experimental setup and particle selection

The ALICE apparatus [38] is designed to measure the particles produced in
proton and lead (Pb) collisions at the LHC [42]. The central barrel consists
of a large solenoid magnet used to generate homogeneous magnetic fields up to
0.5 T along the beam directions and a set of detectors located in the interior
surrounding the beam axis. Additional detectors are located outside the
central barrel in the forward beam direction. A detailed description of the
performance of the ALICE detector can be found in Ref. [43].

In this work, the minimum-bias Pb–Pb data at a collision energy per
nucleon–nucleon pair of $\sqrt{s_{\rm NN}}=5.02$ TeV collected by ALICE in the
LHC Run 2 (2015) are used. The recording of the collisions products was
triggered using the V0 detector consisting of two arrays of 32 scintillator
counters covering pseudorapidity ($\eta$) ranges of 2.8 $<\eta<$ 5.1 (V0A) and
$-3.7<\eta<-1.7$ (V0C). A coincident signal in both detectors consistent with
the collision occurring at the centre of the ALICE detector was required. The
centrality of the collision, expressed in percentages of the total hadronic
cross section, was determined using the amplitudes of the signals in the V0
detectors following the procedure described in Ref. [44] and classified into
six intervals of the Pb–Pb cross section: 0–5%, 5–10%, 10–20%, 20–30%, 30–40%,
and 40–50%. Those intervals together with the corresponding charged-particle
multiplicity densities at midrapidity $\langle\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta\rangle$ are listed in Table 1. Only collisions within $\pm
10$ cm of the nominal interaction point along the beam axis are considered in
this analysis in order to achieve uniform tracking and particle identification
performance.

Table 1: Centrality ranges and corresponding average charged-particle multiplicity densities at midrapidity $\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\rangle$ for Pb–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV [45]. Centrality | $\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\rangle$
---|---
0–5% | $1943\pm 53$
5–10% | $1586\pm 46$
10–20% | $1180\pm 31$
20–30% | $786\pm 20$
30–40% | $512\pm 15$
40–50% | $318\pm 12$

For track reconstruction and hadron identification the analysis uses
information provided by the Inner Tracking System (ITS) [38], the Time
Projection Chamber (TPC) [38, 46], and the Time-of-Flight detector (TOF) [47],
located inside the solenoid magnet.

The ITS is composed of six cylindrical layers of silicon detectors and it is
used to determine the locations of the primary vertex by extrapolation of
primary tracks.

The TPC is a large (volume of 88 $\rm m^{3}$) cylindrical detector filled with
gas and is used as the main tracking and particle identification detector of
ALICE. The central electrode divides the TPC into two halves. At the end of
each half there is a readout plane composed of 18 sectors (with full azimuthal
angle $\varphi$ coverage). Each sector contains 159 padrows arranged radially.
A track signal in the TPC consists of space points (referred to as
_clusters_), each reconstructed in one of the padrows. A Kalman fit is
performed on a set of clusters in order to obtain the parameters of a given
track. In this analysis, the determination of momentum is performed using the
track curvature from the TPC detector only.

TOF is a cylindrical detector composed of Multigap Resistive Plate Chambers
(MRPC) located at $r\cong 380$ cm from the beam axis. They are also arranged
into 18 azimuthal sectors. The detector measures the arrival of particles with
a precision of the order of 50 ps.

Acceptance is restricted to $|\eta|<0.8$. Selected kaons have transverse
momenta of $0.19<p_{\text{T}}<0.45$ GeV$/c$, while for protons the interval is
$0.5<p_{\text{T}}<4.0$ GeV$/c$. The distances of closest approach (DCA) of a
proton track to the primary vertex in the transverse ($\rm DCA_{\text{XY}}$)
and longitudinal ($\rm DCA_{Z}$) directions are required to be less than
$0.0105+0.0350/(p_{\text{T}}/$(GeV/$c)^{-1.1}$) cm and 3.2 cm, respectively.
These selections are imposed to reduce the contamination from secondary tracks
originating from weak decays and from interaction with the detector material.
All selections are summarized in Table 2.

Particle identification is based on energy loss d$E/\text{d}x$ in the TPC and
time of flight in the TOF. The difference between the measured and expected
signals can be expressed in units of detector resolution called $N_{\sigma}$.
For protons, the combined signal from TOF and TPC is allowed to differ from
the expected one by $N_{\sigma}=3\sqrt{2}$. For kaons, five selection criteria
(depending on the momentum $p$) were introduced, as detailed in Table 2. The
selection criteria are optimised to obtain a high-purity sample without
compromising the efficiency. The identification purity of the data sample is
estimated from detailed Monte Carlo (MC) simulations using the HIJING [48]
event generator coupled to the GEANT3 [49] transport package and found to be
above 98.5% for both the kaon and proton samples. The fraction of protons
originating from weak decays is determined to be $5.6\%$ and negligible for
kaons ($<0.05\%$). An additional method based on template fits to the
distributions of the ${{\rm DCA}_{\rm Z}}$ is used to determine the
contribution from weak decays in the proton sample. The fraction of 7.9%
obtained for secondary protons is averaged with the fraction from MC,
resulting in a contamination of 6.5% of weak decays in the sample.

The identified tracks from each event are combined into pairs to form the
distribution $A(k^{*})$. Two-particle detector acceptance effects, including
track splitting, track merging, as well as effects coming from
$\rm\gamma\rightarrow e^{+}e^{-}$ conversion, contribute to the measured
distributions. The following selections are applied to reduce these effects.
For pairs of tracks within the relative pseudorapidity of the two tracks
$|\Delta\eta|<0.01$, an exclusion on the fraction of merged points is
introduced. The merged fraction is defined as the ratio of the number of steps
of $1$ cm considered in the TPC radius range for which the distance between
the tracks is less than $3$ cm, to the total number of steps. Pairs with a
merged fraction above 3% are removed. The $\rm e^{+}e^{-}$ pairs originating
from photon conversions can be misidentified as real kaon–proton pairs and it
is necessary to remove spurious correlations arising from such pairs. These
pairs are removed if their invariant mass, assuming the electron mass for both
particles, is less than 0.002 GeV$/c^{2}$, and the relative polar angle,
$\Delta\theta$, between the two tracks is less than 0.008 rad.

Table 2: Single particle selection criteria for kaons and protons. Track
selection
---
K± $p_{\rm T}$ |  $0.19<p_{\rm T}<0.45$ GeV/$c$
p/$\overline{\rm p}$ $p_{\rm T}$ |  $0.5<p_{\rm T}<4$ GeV/$c$
$|\eta|$ | $<0.8$
$\rm DCA_{\rm z}$ to primary vertex |  $<3.2$ cm
Kaon selection
$N_{\sigma,\rm TPC}$ (for $p<0.4$ GeV/$c$) | $<2$
$N_{\sigma,\rm TPC}$ (for $0.4<p<0.45$ GeV/$c$) | $<1$
$N_{\sigma,\rm TPC}$ (for $p>0.45$ GeV/$c$) | $<3$
$N_{\sigma,\rm TOF}$ (for $0.5<p<0.8$ GeV/$c$) | $<2$
$N_{\sigma,\rm TOF}$ (for $0.8<p<1.0$ GeV/$c$) | $<1.5$
$N_{\sigma,\rm TOF}$ (for $1.0<p<1.5$ GeV/$c$) | $<1$
$\rm DCA_{\rm xy}$ to primary vertex | 2.4 cm
Proton selection
$\sqrt{N_{\sigma,\rm TPC}^{2}+N_{\sigma,\rm TOF}^{2}}$ (for $p_{\rm T}>0.5$ GeV/$c$) | $<3\sqrt{2}$
$\rm DCA_{\rm xy}$ to primary vertex |  $0.0105+0.0350/(p_{\text{T}}/$(GeV/$c)^{-1.1}$) cm

##  3 Data analysis

The femtoscopic measurements are based on the sensitivity of two-particle
correlations at low relative momentum to the space–time separation of the
particle emitters due to the effects of quantum statistics and/or final state
interactions (FSI), i.e. Coulomb and strong forces, depending on the pair
under consideration [50, 51]. The femtoscopic correlation function, as shown
in Fig. 1 c, in the pair rest frame (PRF) can be written as [52, 53]

$C(\vec{k}^{*})=\int
S(\vec{r}^{*})~{}\left|{\Psi(\vec{k}^{*},\vec{r}^{*})}\right|^{2}\mathrm{d}^{3}{r}^{*},$
(1)

where $|\vec{k^{*}}|=k^{*}$ is half the kaon–proton pair relative momentum,
which is equal to the momentum of the first particle in the PRF, where the
pair centre of mass is at rest ($\vec{p_{1}}=-\vec{p_{2}}$). The two-particle
emitting source function is denoted as $S(\vec{r}^{*})$,
$\Psi(\vec{k}^{*},\vec{r}^{*})$ is the pair wave function, and $\vec{r}^{*}$
is the relative separation vector. The pair wave function depends on the
interactions between the two hadrons [40, 41]. In the case of equal emission
time in the PRF, the Bethe–Salpeter amplitude in the Lednický–Lyuboshitz
formalism [40, 41, 54], described in detail in Appendix A.1, coincides with a
stationary solution of the scattering problem with reversed time direction in
the emission process. The interaction then depends only on the scattering
length, $f_{0}$, and the effective range of the interaction, $d_{0}$. In this
work, the spin-averaged scattering parameters are obtained, i.e. the real and
imaginary parts, $\Re f_{0}$ and $\Im f_{0}$, respectively, of the scattering
length. Moreover, the zero-effective-range approximation ($d_{0}=0$) is used
in the analysis.

The experimental correlation function,
$C(k^{*})=\mathcal{N}~{}A(k^{*})/B(k^{*})$, is constructed as a ratio between
the measured distribution of pair relative momenta $A(k^{*})$ and the
uncorrelated distribution $B(k^{*})$ obtained using the mixed-event technique
[55, 56], where $\mathcal{N}$ is a free normalization factor which is
constrained by $C(k^{*})=1$ at $300<k^{*}<800$ MeV$/c$. Effects of the
scattering length as well as of the size of the femtoscopic source are studied
in the region of $k^{*}<150~{}{\rm{MeV}}/c$. Deviations from unity of
$C(k^{*})$ in this region indicate the presence of an interaction between the
studied particles. In general, the attractive or repulsive forces manifest
themselves in values of the correlation function greater or smaller than one,
respectively [57].

The femtoscopic correlation functions for $\rm{K}^{-}p$ and $\rm{K}^{+}p$
pairs and their charge conjugates $\rm{K}^{+}\overline{p}$ and
$\rm{K}^{-}\overline{p}$ are measured in six centrality intervals [44]. The
centrality intervals and the corresponding charged-particle multiplicity
densities at midrapidity $\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\rangle$
are listed in Table 1. Since no deviations, apart from statistical ones,
between pairs and corresponding charge conjugate pairs are observed, they are
combined and denoted as $\rm{K}^{+}p\oplus\rm{K}^{-}\overline{p}$ for same-
and $\rm{K}^{-}p\oplus\rm{K}^{+}\overline{p}$ for opposite-charge
combinations, respectively.

In Pb–Pb collisions, particles are also correlated due to the collective
expansion of the system. This generates a slope in the correlation function
[58] which appears to be well described by both hydrodynamic simulations [59]
coupled to the statistical hadronisation code THERMINATOR 2 [60] or using the
AMPT model [61]. These background correlations are therefore subtracted before
fitting the correlation functions by employing a first-order polynomial fit to
the AMPT simulated data in the first two centrality intervals (0–10%) and a
fit to the THERMINATOR 2 simulated data for the remaining centrality classes
(10–50%). The fixed value of the impact parameter used for 0–10% centrality
interval in THERMINATOR 2 was not reproducing the distribution of measured
average charged-particle multiplicity.

The extraction of the scattering length parameters of
$\rm{K}^{-}p\oplus\rm{K}^{+}\overline{p}$ pairs from the measured correlation
functions uses a dedicated fitting procedure based on the Lednický–Lyuboshitz
formalism. A simultaneous fit to all measured pairs in the six centrality
classes is performed in the range up to $k^{*}=175~{}{\rm{MeV}}/c$. The final
values of the fitted parameters are obtained from the comparison of the
experimental correlation functions to the set of precomputed model functions
and based on the lowest $\chi^{2}$/ndf.

The assumption for the source function $S(\vec{r}^{*})$ is that, for each
centrality, it is a three-dimensional spheroid with a Gaussian density profile
in the PRF [62, 56, 63] with a common width parameter for same- and opposite-
charge pairs $R_{\rm Kp}$, referred to as the source size or femtoscopic
radius. This assumption is based on hydrodynamic models [64, 65] of the matter
produced in ultrarelativistic heavy-ion collisions which provide quantitative
agreement [66] with collective phenomena [67], particle transverse-momentum
spectra [68], and femtoscopy of both identical [69, 56] and non-identical
particles [63]. The femtoscopic radii follow the previously observed linear
scaling with $\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\rangle^{1/3}$ and the
transverse-mass scaling behaviour [70, 71, 72, 73, 69]. This allows one to fix
the source functional form in Eq. (1) and use the Lednický–Lyuboshitz
formalism for measurements of the interaction between any pair of particles
that can be detected in the final state. Moreover, the fit is further
constrained by using the measured scattering length values for
$\rm{K}^{+}p\oplus\rm{K}^{-}\overline{p}$ pairs, established from a partial
wave analysis to be $\Re f_{0}=-0.308\pm 0.003$ fm [28]. Finally, there are
six different femtoscopic radii corresponding to each centrality class and
two, real and imaginary, components of the
$\rm{K}^{-}p\oplus\rm{K}^{+}\overline{p}$ scattering length. In a simultaneous
fit to all measured correlation functions, the fitting procedure determines
the six radii from the $\rm{K}^{+}p$ correlations and the real and imaginary
parameters of the strong interaction scattering length from the $\rm{K}^{-}p$
correlations.

The fitting procedure also accounts for the purity of the sample, defined as
the percentage of properly identified primary particle pairs originating from
the three-dimensional Gaussian profile of the source, following the method
described in Ref. [74]. This method was successfully employed in the pion–kaon
femtoscopic analysis by ALICE [63]. The value for the purity parameter was
estimated to be 87% and depends on the misidentification, secondary
contamination from weak decays, and percentage of kaons and protons that come
from strongly decaying resonances constituting the long tails in the source
distribution, outside the Gaussian core.

The measured correlation function is also affected by the finite momentum
resolution of the ALICE detector. The detector response matrix is obtained
using a detailed Monte Carlo simulation of the detector based on HIJING [48]
coupled to GEANT3 [49] transport code and is used to smear the theoretical
calculations.

##  4 Systematic uncertainties

The final systematic uncertainties are the maximum and minimum deviations from
the reference values obtained for different variations of the analysis. The
relative values of the important sources of uncorrelated systematic
uncertainty are listed in Table 3. One of the most significant sources of
uncertainty comes from background estimation. The analysis considers two
variations of the default option. The first one (Background 1) defines the
background as a first-order polynomial fit to the raw data in the $k^{*}$
region 0.35–0.6 GeV/$c$ instead of predictions from the AMPT model in the
first two centrality intervals. The second one (Background 2) estimates the
background from the average of the first-order polynomial fit to the raw data
and the AMPT prediction in the first two centrality intervals and the average
of functions provided by the THERMINATOR 2 code and the AMPT model in the
other four centrality intervals. The pair purity value used for scaling data
points is also varied. The default value equals 87%, the effect of possible
additional sources of impurities is evaluated and found to be smaller than 7%.
The systematic effect of the finite resolution of the detectors is evaluated
using an alternative technique based on a smoothed detector response matrix.
Another variation of the default analysis is obtained by using a different
sample of kaons. The default data contain kaons in the transverse-momentum
range between 0.19–0.45 GeV/$c$, while the variations cover the regions of
0.5–1.5 GeV/$c$ as well as 0.19–1.5 GeV/$c$. The sample with high $p_{\rm T}$
is the most significant source of the uncertainty of the real and imaginary
parts of the scattering length due to the change in the average pair
transverse mass $m_{\rm T}$ (the changes of radii are expected and should not
be treated as systematic uncertainty). The systematic uncertainty related to
the DCA is evaluated using an alternative selection of a $p_{\rm T}$ dependent
${\rm DCA}_{\rm Z}<0.418-0.372\times p_{\rm T}^{0.66}$ cm and a constant value
of $\rm DCA_{\rm XY}<2.4$ cm, preserving the integrated proton purity.
Additionally, results from the combined fit to both kaon selections are also
taken into account where the high $p_{\rm T}$ kaon sample radii are scaled to
the low-$p_{\rm T}$ according to the average pair $m_{\rm T}$. Variations of
the fitting range and track reconstruction have a negligible contribution
compared with other sources.

Table 3: Components of the systematic uncertainty expressed as relative uncertainties from various sources. For a detailed description of each variation see the text.  |  $\Delta R_{\rm Kp}$ (%) |  |
---|---|---|---
Variation | Centrality |  $\Delta\Re f_{0}$ (%) |  $\Delta\Im f_{0}$ (%)
| 0–5% | 5–10% | 10–20% | 20–30% | 30–40% | 40–50% |  |
Background 1 | 4 |  $<$1 |  $<$1 |  $<$1 |  $<$1 |  $<$1 | 3 | 1
Background 2 | 3 | 3 | 4 | 3 | 1 | 3 | 6 | 13
Pair purity $-3$% |  $-$3 |  $-$4 |  $-$3 |  $-$3 |  $-$3 |  $-$3 |  $+$1 |  $-$5
Pair purity +3% |  $+$6 |  $+$4 |  $+$7 |  $+$4 |  $+$4 |  $+$4 |  $-$2 |  $+$11
Momentum | $-$14 | $-$13 | $-$9 | $-$11 | $-$10 | $-$10 | $+$19 | $-$27
resolution
Fit range | 5 | 2 | 1 | 1 | $<$1 | $<$1 | 2 | $<$1
0–0.2 GeV$/c$
Fit range | 3 | 3 | 8 | $<$1 | $<$1 | $<$1 | 4 | 1
0.005–0.150 GeV$/c$
Alternative DCA | 8 | 6 | 4 | 6 | $<$1 | 7 | 1 | 5
selection
Kaon selection | $-$11 | $-$8 | $-$8 | $-$13 | $-$5 | $-$4 | $+$16 | $-$10
(low and high $p_{\rm T}$)
Kaon selection | Does not apply | $+$19 | $-$35
(high $p_{\rm T}$ only)

##  5 Results

Figure 2:  The $\rm K^{-}p\oplus K^{+}\overline{p}$ correlation functions in
the six centrality classes, with the corresponding Lednický–Lyuboshitz fits
(denoted as “L–L”) and Kyoto model calculations shown as light cyan and orange
bands, respectively. The width of the bands corresponds to the 1-$\sigma$
uncertainties. The inserts show the $\rm K^{+}p\oplus K^{-}\overline{p}$
correlation functions with Lednický–Lyuboshitz fits as light cyan bands. The
bottom panels show the difference between data and the fit (model) normalised
by the statistical uncertainty of the data $\sigma_{\rm stat}$. The average
pair transverse mass $\langle m_{\rm T}\rangle$ is $0.92\pm 0.03$ GeV/$c^{2}$
for all centrality intervals. The statistical and systematic uncertainties are
added in quadrature and shown as vertical bars.

Figure 3: Left: scattering parameters obtained from the Lednický–Lyuboshitz
fit compared with available world data and theoretical calculations.
Statistical uncertainties are represented as bars and systematic
uncertainties, if provided, as boxes. Right: experimental femtoscopic
correlation function for $\rm{K}^{-}p\oplus\rm{K}^{+}\overline{p}$ pairs in
the 30–40% centrality interval, together with various Lednický–Lyuboshitz
calculations obtained using the scattering length parameters from Refs. [75,
76, 77, 17, 18, 78, 79] and the source radius from this analysis. The
statistical and systematic uncertainties of the measured data points are added
in quadrature and shown as vertical bars.

The correlation functions for opposite-charge particle pairs
($\rm{K}^{-}\rm{p}\oplus\rm{K}^{+}\overline{p}$), after division by the AMPT
or THERMINATOR 2 baselines, are shown in Fig. 2. The correlation functions for
same-charge particle pairs ($\rm{K}^{+}\rm{p}\oplus\rm{K}^{-}\overline{p}$)
are presented as inserts. The cyan band represents the result of the
simultaneous fit to all obtained correlation functions with the
Lednický–Lyuboshitz model [40, 41]. The orange band corresponds to predictions
from $\rm\chi^{EFT}$ calculations. These are computed using the Kyoto model
[39] and evaluated with the CATS framework [80]. The Kyoto model is based on a
chiral effective SU(3) calculation in which all coupled channels, such as
$\rm\overline{K}^{0}$n and $\uppi\Sigma$ are included. At present, this model
is able to describe both the ALICE results from proton–proton collisions [37]
and the SIDDHARTA measurement [18]. The bottom panels of Fig. 2 show the
difference between the data and the fit (model) divided by the statistical
uncertainty of the data, $\rm\sigma_{\rm stat}$.

The following effects can be observed: the
$\rm{K}^{-}\rm{p}\oplus\rm{K}^{+}\overline{p}$ pairs show an attractive
Coulomb interaction for small $k^{*}$. The effect is opposite for
$\rm{K}^{+}\rm{p}\oplus\rm{K}^{-}\overline{p}$ pairs. The influence of the
repulsive strong interaction manifests as correlation functions reaching
values below unity in the region of $k^{*}\approx 20-50$ MeV$/c$ and becomes
more pronounced towards more peripheral events, i.e., smaller source sizes. As
predicted in Ref. [39], features of the correlation function related to the
coupled channels, observed in the analysis of pp collisions [37], are
negligible here. Neither the cusp structure at 58 MeV/$c$ due to the presence
of the isospin-breaking channel ${\rm K}^{0}\rm{n}\rightarrow\rm{K}^{-}\rm{p}$
nor the enhancement due to the coupled channels below threshold enhancing the
correlation above unity in the intermediate $k^{*}$ range are visible in the
correlation function in Pb–Pb.

The common femtoscopic radii $R_{\rm Kp}$ for same- and opposite-charge pairs
obtained from the Lednický–Lyuboshitz fit are provided in Fig. 2 as well. They
increase from around 5 fm for peripheral events to almost 9 fm for central
events, and all are larger than 3 fm where the predicted effect of coupled
channels is reduced or negligible [39]. The radii scale linearly with the cube
root of the mean charged-particle multiplicity density
$\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\rangle^{1/3}$, as observed for
pion–pion [73], kaon–kaon [56], and pion–kaon [63] pairs. The scattering
length parameters obtained from the fit are $\Re
f_{0}=-0.91\pm~{}0.03$(stat)${}^{+0.17}_{-0.03}$(syst) fm and $\Im
f_{0}=0.92\pm~{}0.05$(stat)${}^{+0.12}_{-0.33}$(syst) fm.

The obtained parameters of the scattering length are compared with the
available experimental values as well as model calculations [75, 76, 77, 18,
78, 79] in the left panel of Fig. 3. Numerical values of those parameters are
also provided in Tab. 4. The ALICE results are compatible with them within
uncertainties222Note that systematic uncertainties are not provided for some
of the older results.. Up until this point, the world’s best experimental data
on Kp scattering are mainly from exotic kaonic atoms, where the interaction at
the threshold is measured, and from scattering experiments. Theory predictions
and calculations are based on $\rm\chi^{EFT}$ models.

Moreover, the Lednický–Lyuboshitz formalism is also used to compute
femtoscopic correlation functions using scattering length parameters from
previous measurements and theory predictions. They are then compared with the
experimental data and the deviations in units of $\chi^{2}/\mathrm{ndf}$ are
obtained. The result of such a procedure is shown in Fig. 3 (right), while the
$\chi^{2}/\mathrm{ndf}$ values are presented in Table 4. The Kyoto model,
which captures well the structures related to coupled channels in pp
collisions, reproduces the data trends in all measured Pb–Pb centrality
intervals, confirming that the coupled channels are fundamental in the
description of small sources but have a negligible influence on correlation
functions at large source sizes [39]. However, the model still requires
further development as the resulting $\chi^{2}/\mathrm{ndf}=2.8$ is slightly
worse than the best calculations using the Lednický–Lyuboshitz analytical
approach.

Table 4: Values of the scattering parameters and the $\chi^{2}/\mathrm{ndf}$ for the deviation between the ALICE data and available model calculations and previous measurements for $\rm{K}^{-}$p pairs at low relative momentum. Model calculation: |  $\Re f_{0}$ (fm) |  $\Im f_{0}$ (fm) | $\chi^{2}/{\text{ndf}}$
---|---|---|---
Lednický–Lyuboshitz fit to data |  $\ -$0.91$\pm~{}0.03$(stat)${}^{+0.17}_{-0.03}$(syst) |  0.92$\pm~{}0.05$(stat)${}^{+0.12}_{-0.33}$(syst) | 1.4
Kyoto [39, 80] | – | – | 2.8
Lednický–Lyuboshitz with fixed parameters from:
Kaonic deuterium (Hoshino et al.) [78] |  $-$0.66 | 0.89 | 2.0
Scattering experiments (Martin) [75] |  $-$0.67$\pm$0.1 |  0.64$\pm$0.1 | 3.3
Chiral SU(3) (Ikeda et al.) [17, 18] |  $-$0.7 | 0.89 | 1.9
SIDDHARTA chiral SU(3) [17, 18] |  $-$0.65$\pm$0.1 |  0.81$\pm$0.15 | 2.3
Hamiltonian EFT (Liu et al.) [77] |  $-$0.75 | 0.80 | 1.9
Kaonic hydrogen (Ito et al.) [76] |  $-$0.78$\pm$0.15 |  0.49$\pm$0.25 | 4.2
Chiral SU(3) (Borasoy et al.) [79] |  $-$1.05$\pm$0.5 |  0.75$\pm$0.4 | 1.6

##  6 Summary

In this work, we present the first measurement of non-identical particle
femtoscopy of $\rm{K}^{-}p\oplus\rm{K}^{+}\overline{p}$ and
$\rm{K}^{+}p\oplus\rm{K}^{-}\overline{p}$ pairs performed in Pb–Pb collisions
at $\sqrt{s_{\text{NN}}}~{}=$ 5.02 TeV in six centrality intervals. Up to now,
the existing experimental data on $\rm{K}^{-}p$ scattering allowed us to study
the interaction at a fixed range, either in the asymptotic regime, where the
effect of the coupled channels is not present, or at very small ranges
($R_{\mathrm{Kp}}\sim 1$ fm) where they are dominant and difficult to
disentangle from the $\rm{K}^{-}p\rightarrow\rm{K}^{-}p$ channel. The analysis
of the Pb–Pb data with the ALICE detector addresses these issues by testing
the $\rm{K}^{-}p$ interaction as a function of the source size in the range
$R_{\mathrm{Kp}}\in(4.9,8.9)$ fm. In femtoscopy, a precise knowledge of the
source from which hadrons are emitted is needed to measure the interaction
using quantum scattering theory. In the case of pp collisions, where this is
of the order of 1 fm, very short interaction distances are probed. In Pb–Pb
collisions, the larger average distance of several fm between the hadrons
probes the asymptotic form of the two-particle wave function, as demonstrated
in this work. The obtained values of $R_{\rm Kp}$ follow a linear scaling with
the cube root of averaged charged-particle multiplicity density and the
transverse-mass scaling. This is in agreement with other femtoscopic
measurements in heavy-ion collisions, as expected from the hydrodynamic
models. The resulting correlation functions are fitted simultaneously to
extract the complex scattering length whose components are $\Re f_{0}=-0.91\pm
0.03$(stat)${}^{+0.17}_{-0.03}$(syst) fm and $\Im f_{0}=0.92\pm
0.05$(stat)${}^{+0.12}_{-0.33}$(syst) fm. The obtained result is consistent
with existing data from scattering experiments. Moreover, theoretical
computations based on $\chi^{\rm EFT}$ (the Kyoto model) provide a comparably
good description across all centrality intervals, providing further
confirmation on the validity of the model.

## 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), 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; 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; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Institute of Applied Science (IIST), 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 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; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA) and Office of the Higher Education Commission under NRU project of Thailand, 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.

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##  Appendix A The ALICE Collaboration

S. Acharya143, D. Adamová98, A. Adler76, J. Adolfsson83, G. Aglieri Rinella35,
M. Agnello31, N. Agrawal55, Z. Ahammed143, S. Ahmad16, S.U. Ahn78, I. Ahuja39,
Z. Akbar52, A. Akindinov95, M. Al-Turany110, S.N. Alam41, D. Aleksandrov91, B.
Alessandro61, H.M. Alfanda7, R. Alfaro Molina73, B. Ali16, Y. Ali14, A.
Alici26, N. Alizadehvandchali127, A. Alkin35, J. Alme21, T. Alt70, L.
Altenkamper21, I. Altsybeev115, M.N. Anaam7, C. Andrei49, D. Andreou93, A.
Andronic146, M. Angeletti35, V. Anguelov107, F. Antinori58, P. Antonioli55, C.
Anuj16, N. Apadula82, L. Aphecetche117, H. Appelshäuser70, S. Arcelli26, R.
Arnaldi61, I.C. Arsene20, M. Arslandok148,107, A. Augustinus35, R.
Averbeck110, S. Aziz80, M.D. Azmi16, A. Badalà57, Y.W. Baek42, X. Bai131,110,
R. Bailhache70, Y. Bailung51, R. Bala104, A. Balbino31, A. Baldisseri140, B.
Balis2, M. Ball44, D. Banerjee4, R. Barbera27, L. Barioglio108,25, M.
Barlou87, G.G. Barnaföldi147, L.S. Barnby97, V. Barret137, C. Bartels130, K.
Barth35, E. Bartsch70, F. Baruffaldi28, N. Bastid137, S. Basu83, G.
Batigne117, B. Batyunya77, D. Bauri50, J.L. Bazo Alba114, I.G. Bearden92, C.
Beattie148, I. Belikov139, A.D.C. Bell Hechavarria146, F. Bellini26,35, R.
Bellwied127, S. Belokurova115, V. Belyaev96, G. Bencedi71, S. Beole25, A.
Bercuci49, Y. Berdnikov101, A. Berdnikova107, D. Berenyi147, L. Bergmann107,
M.G. Besoiu69, L. Betev35, P.P. Bhaduri143, A. Bhasin104, I.R. Bhat104, M.A.
Bhat4, B. Bhattacharjee43, P. Bhattacharya23, L. Bianchi25, N. Bianchi53, J.
Bielčík38, J. Bielčíková98, J. Biernat120, A. Bilandzic108, G. Biro147, S.
Biswas4, J.T. Blair121, D. Blau91, M.B. Blidaru110, C. Blume70, G. Boca29,59,
F. Bock99, A. Bogdanov96, S. Boi23, J. Bok63, L. Boldizsár147, A.
Bolozdynya96, M. Bombara39, P.M. Bond35, G. Bonomi142,59, H. Borel140, A.
Borissov84, H. Bossi148, E. Botta25, L. Bratrud70, P. Braun-Munzinger110, M.
Bregant123, M. Broz38, G.E. Bruno109,34, M.D. Buckland130, D. Budnikov111, H.
Buesching70, S. Bufalino31, O. Bugnon117, P. Buhler116, Z. Buthelezi74,134,
J.B. Butt14, S.A. Bysiak120, D. Caffarri93, M. Cai28,7, H. Caines148, A.
Caliva110, E. Calvo Villar114, J.M.M. Camacho122, R.S. Camacho46, P.
Camerini24, F.D.M. Canedo123, F. Carnesecchi35,26, R. Caron140, J. Castillo
Castellanos140, E.A.R. Casula23, F. Catalano31, C. Ceballos Sanchez77, P.
Chakraborty50, S. Chandra143, S. Chapeland35, M. Chartier130, S.
Chattopadhyay143, S. Chattopadhyay112, A. Chauvin23, T.G. Chavez46, C.
Cheshkov138, B. Cheynis138, V. Chibante Barroso35, D.D. Chinellato124, S.
Cho63, P. Chochula35, P. Christakoglou93, C.H. Christensen92, P.
Christiansen83, T. Chujo136, C. Cicalo56, L. Cifarelli26, F. Cindolo55, M.R.
Ciupek110, G. ClaiII,55, J. CleymansI,126, F. Colamaria54, J.S. Colburn113, D.
Colella109,54,34,147, A. Collu82, M. Colocci35,26, M. ConcasIII,61, G. Conesa
Balbastre81, Z. Conesa del Valle80, G. Contin24, J.G. Contreras38, M.L.
Coquet140, T.M. Cormier99, P. Cortese32, M.R. Cosentino125, F. Costa35, S.
Costanza29,59, P. Crochet137, E. Cuautle71, P. Cui7, L. Cunqueiro99, A.
Dainese58, F.P.A. Damas117,140, M.C. Danisch107, A. Danu69, I. Das112, P.
Das89, P. Das4, S. Das4, S. Dash50, S. De89, A. De Caro30, G. de Cataldo54, L.
De Cilladi25, J. de Cuveland40, A. De Falco23, D. De Gruttola30, N. De
Marco61, C. De Martin24, S. De Pasquale30, S. Deb51, H.F. Degenhardt123, K.R.
Deja144, L. Dello Stritto30, S. Delsanto25, W. Deng7, P. Dhankher19, D. Di
Bari34, A. Di Mauro35, R.A. Diaz8, T. Dietel126, Y. Ding138,7, R. Divià35,
D.U. Dixit19, Ø. Djuvsland21, U. Dmitrieva65, J. Do63, A. Dobrin69, B.
Dönigus70, O. Dordic20, A.K. Dubey143, A. Dubla110,93, S. Dudi103, M.
Dukhishyam89, P. Dupieux137, N. Dzalaiova13, T.M. Eder146, R.J. Ehlers99, V.N.
Eikeland21, D. Elia54, B. Erazmus117, F. Ercolessi26, F. Erhardt102, A.
Erokhin115, M.R. Ersdal21, B. Espagnon80, G. Eulisse35, D. Evans113, S.
Evdokimov94, L. Fabbietti108, M. Faggin28, J. Faivre81, F. Fan7, A. Fantoni53,
M. Fasel99, P. Fecchio31, A. Feliciello61, G. Feofilov115, A. Fernández
Téllez46, A. Ferrero140, A. Ferretti25, V.J.G. Feuillard107, J. Figiel120, S.
Filchagin111, D. Finogeev65, F.M. Fionda56,21, G. Fiorenza35,109, F. Flor127,
A.N. Flores121, S. Foertsch74, P. Foka110, S. Fokin91, E. Fragiacomo62, E.
Frajna147, U. Fuchs35, N. Funicello30, C. Furget81, A. Furs65, J.J.
Gaardhøje92, M. Gagliardi25, A.M. Gago114, A. Gal139, C.D. Galvan122, P.
Ganoti87, C. Garabatos110, J.R.A. Garcia46, E. Garcia-Solis10, K. Garg117, C.
Gargiulo35, A. Garibli90, K. Garner146, P. Gasik110, E.F. Gauger121, A.
Gautam129, M.B. Gay Ducati72, M. Germain117, J. Ghosh112, P. Ghosh143, S.K.
Ghosh4, M. Giacalone26, P. Gianotti53, P. Giubellino110,61, P. Giubilato28,
A.M.C. Glaenzer140, P. Glässel107, D.J.Q. Goh85, V. Gonzalez145, L.H.
González-Trueba73, S. Gorbunov40, M. Gorgon2, L. Görlich120, S. Gotovac36, V.
Grabski73, L.K. Graczykowski144, L. Greiner82, A. Grelli64, C. Grigoras35, V.
Grigoriev96, A. GrigoryanI,1, S. Grigoryan77,1, O.S. Groettvik21, F.
Grosa35,61, J.F. Grosse-Oetringhaus35, R. Grosso110, G.G. Guardiano124, R.
Guernane81, M. Guilbaud117, K. Gulbrandsen92, T. Gunji135, A. Gupta104, R.
Gupta104, I.B. Guzman46, S.P. Guzman46, L. Gyulai147, M.K. Habib110, C.
Hadjidakis80, G. Halimoglu70, H. Hamagaki85, G. Hamar147, M. Hamid7, R.
Hannigan121, M.R. Haque144,89, A. Harlenderova110, J.W. Harris148, A.
Harton10, J.A. Hasenbichler35, H. Hassan99, D. Hatzifotiadou55, P. Hauer44,
L.B. Havener148, S. Hayashi135, S.T. Heckel108, E. Hellbär70, H. Helstrup37,
T. Herman38, E.G. Hernandez46, G. Herrera Corral9, F. Herrmann146, K.F.
Hetland37, H. Hillemanns35, C. Hills130, B. Hippolyte139, B. Hofman64, B.
Hohlweger93,108, J. Honermann146, G.H. Hong149, D. Horak38, S. Hornung110, A.
Horzyk2, R. Hosokawa15, P. Hristov35, C. Huang80, C. Hughes133, P. Huhn70,
T.J. Humanic100, H. Hushnud112, L.A. Husova146, A. Hutson127, D. Hutter40,
J.P. Iddon35,130, R. Ilkaev111, H. Ilyas14, M. Inaba136, G.M. Innocenti35, M.
Ippolitov91, A. Isakov38,98, M.S. Islam112, M. Ivanov110, V. Ivanov101, V.
Izucheev94, M. Jablonski2, B. Jacak82, N. Jacazio35, P.M. Jacobs82, S.
Jadlovska119, J. Jadlovsky119, S. Jaelani64, C. Jahnke124,123, M.J.
Jakubowska144, M.A. Janik144, T. Janson76, M. Jercic102, O. Jevons113, F.
Jonas99,146, P.G. Jones113, J.M. Jowett 35,110, J. Jung70, M. Jung70, A.
Junique35, A. Jusko113, J. Kaewjai118, P. Kalinak66, A. Kalweit35, V.
Kaplin96, S. Kar7, A. Karasu Uysal79, D. Karatovic102, O. Karavichev65, T.
Karavicheva65, P. Karczmarczyk144, E. Karpechev65, A. Kazantsev91, U.
Kebschull76, R. Keidel48, D.L.D. Keijdener64, M. Keil35, B. Ketzer44, Z.
Khabanova93, A.M. Khan7, S. Khan16, A. Khanzadeev101, Y. Kharlov94, A.
Khatun16, A. Khuntia120, B. Kileng37, B. Kim17,63, D. Kim149, D.J. Kim128,
E.J. Kim75, J. Kim149, J.S. Kim42, J. Kim107, J. Kim149, J. Kim75, M. Kim107,
S. Kim18, T. Kim149, S. Kirsch70, I. Kisel40, S. Kiselev95, A. Kisiel144, J.P.
Kitowski2, J.L. Klay6, J. Klein35, S. Klein82, C. Klein-Bösing146, M.
Kleiner70, T. Klemenz108, A. Kluge35, A.G. Knospe127, C. Kobdaj118, M.K.
Köhler107, T. Kollegger110, A. Kondratyev77, N. Kondratyeva96, E.
Kondratyuk94, J. Konig70, S.A. Konigstorfer108, P.J. Konopka35,2, G.
Kornakov144, S.D. Koryciak2, L. Koska119, A. Kotliarov98, O. Kovalenko88, V.
Kovalenko115, M. Kowalski120, I. Králik66, A. Kravčáková39, L. Kreis110, M.
Krivda113,66, F. Krizek98, K. Krizkova Gajdosova38, M. Kroesen107, M.
Krüger70, E. Kryshen101, M. Krzewicki40, V. Kučera35, C. Kuhn139, P.G.
Kuijer93, T. Kumaoka136, D. Kumar143, L. Kumar103, N. Kumar103, S. Kundu35,89,
P. Kurashvili88, A. Kurepin65, A.B. Kurepin65, A. Kuryakin111, S. Kushpil98,
J. Kvapil113, M.J. Kweon63, J.Y. Kwon63, Y. Kwon149, S.L. La Pointe40, P. La
Rocca27, Y.S. Lai82, A. Lakrathok118, M. Lamanna35, R. Langoy132, K.
Lapidus35, P. Larionov53, E. Laudi35, L. Lautner35,108, R. Lavicka38, T.
Lazareva115, R. Lea142,24,59, J. Lee136, J. Lehrbach40, R.C. Lemmon97, I. León
Monzón122, E.D. Lesser19, M. Lettrich35,108, P. Lévai147, X. Li11, X.L. Li7,
J. Lien132, R. Lietava113, B. Lim17, S.H. Lim17, V. Lindenstruth40, A.
Lindner49, C. Lippmann110, A. Liu19, J. Liu130, I.M. Lofnes21, V. Loginov96,
C. Loizides99, P. Loncar36, J.A. Lopez107, X. Lopez137, E. López Torres8, J.R.
Luhder146, M. Lunardon28, G. Luparello62, Y.G. Ma41, A. Maevskaya65, M.
Mager35, T. Mahmoud44, A. Maire139, M. Malaev101, Q.W. Malik20, L.
MalininaIV,77, D. Mal’Kevich95, N. Mallick51, P. Malzacher110, G.
Mandaglio33,57, V. Manko91, F. Manso137, V. Manzari54, Y. Mao7, J. Mareš68,
G.V. Margagliotti24, A. Margotti55, A. Marín110, C. Markert121, M. Marquard70,
N.A. Martin107, P. Martinengo35, J.L. Martinez127, M.I. Martínez46, G.
Martínez García117, S. Masciocchi110, M. Masera25, A. Masoni56, L.
Massacrier80, A. Mastroserio141,54, A.M. Mathis108, O. Matonoha83, P.F.T.
Matuoka123, A. Matyja120, C. Mayer120, A.L. Mazuecos35, F. Mazzaschi25, M.
Mazzilli35, M.A. Mazzoni60, J.E. Mdhluli134, A.F. Mechler70, F. Meddi22, Y.
Melikyan65, A. Menchaca-Rocha73, E. Meninno116,30, A.S. Menon127, M. Meres13,
S. Mhlanga126,74, Y. Miake136, L. Micheletti61,25, L.C. Migliorin138, D.L.
Mihaylov108, K. Mikhaylov77,95, A.N. Mishra147, D. Miśkowiec110, A. Modak4,
A.P. Mohanty64, B. Mohanty89, M. Mohisin Khan16, Z. Moravcova92, C.
Mordasini108, D.A. Moreira De Godoy146, L.A.P. Moreno46, I. Morozov65, A.
Morsch35, T. Mrnjavac35, V. Muccifora53, E. Mudnic36, D. Mühlheim146, S.
Muhuri143, J.D. Mulligan82, A. Mulliri23, M.G. Munhoz123, R.H. Munzer70, H.
Murakami135, S. Murray126, L. Musa35, J. Musinsky66, C.J. Myers127, J.W.
Myrcha144, B. Naik134,50, R. Nair88, B.K. Nandi50, R. Nania55, E. Nappi54,
M.U. Naru14, A.F. Nassirpour83, A. Nath107, C. Nattrass133, A. Neagu20, L.
Nellen71, S.V. Nesbo37, G. Neskovic40, D. Nesterov115, B.S. Nielsen92, S.
Nikolaev91, S. Nikulin91, V. Nikulin101, F. Noferini55, S. Noh12, P.
Nomokonov77, J. Norman130, N. Novitzky136, P. Nowakowski144, A. Nyanin91, J.
Nystrand21, M. Ogino85, A. Ohlson83, V.A. Okorokov96, J. Oleniacz144, A.C.
Oliveira Da Silva133, M.H. Oliver148, A. Onnerstad128, C. Oppedisano61, A.
Ortiz Velasquez71, T. Osako47, A. Oskarsson83, J. Otwinowski120, K. Oyama85,
Y. Pachmayer107, S. Padhan50, D. Pagano142,59, G. Paić71, A. Palasciano54, J.
Pan145, S. Panebianco140, P. Pareek143, J. Park63, J.E. Parkkila128, S.P.
Pathak127, R.N. Patra104,35, B. Paul23, J. Pazzini142,59, H. Pei7, T.
Peitzmann64, X. Peng7, L.G. Pereira72, H. Pereira Da Costa140, D. Peresunko91,
G.M. Perez8, S. Perrin140, Y. Pestov5, V. Petráček38, M. Petrovici49, R.P.
Pezzi72, S. Piano62, M. Pikna13, P. Pillot117, O. Pinazza55,35, L. Pinsky127,
C. Pinto27, S. Pisano53, M. Płoskoń82, M. Planinic102, F. Pliquett70, M.G.
Poghosyan99, B. Polichtchouk94, S. Politano31, N. Poljak102, A. Pop49, S.
Porteboeuf-Houssais137, J. Porter82, V. Pozdniakov77, S.K. Prasad4, R.
Preghenella55, F. Prino61, C.A. Pruneau145, I. Pshenichnov65, M. Puccio35, S.
Qiu93, L. Quaglia25, R.E. Quishpe127, S. Ragoni113, A. Rakotozafindrabe140, L.
Ramello32, F. Rami139, S.A.R. Ramirez46, A.G.T. Ramos34, T.A. Rancien81, R.
Raniwala105, S. Raniwala105, S.S. Räsänen45, R. Rath51, I. Ravasenga93, K.F.
Read99,133, A.R. Redelbach40, K. RedlichV,88, A. Rehman21, P. Reichelt70, F.
Reidt35, H.A. Reme-ness37, R. Renfordt70, Z. Rescakova39, K. Reygers107, A.
Riabov101, V. Riabov101, T. Richert83,92, M. Richter20, W. Riegler35, F.
Riggi27, C. Ristea69, S.P. Rode51, M. Rodríguez Cahuantzi46, K. Røed20, R.
Rogalev94, E. Rogochaya77, T.S. Rogoschinski70, D. Rohr35, D. Röhrich21, P.F.
Rojas46, P.S. Rokita144, F. Ronchetti53, A. Rosano33,57, E.D. Rosas71, A.
Rossi58, A. Rotondi29,59, A. Roy51, P. Roy112, S. Roy50, N. Rubini26, O.V.
Rueda83, R. Rui24, B. Rumyantsev77, P.G. Russek2, A. Rustamov90, E.
Ryabinkin91, Y. Ryabov101, A. Rybicki120, H. Rytkonen128, W. Rzesa144, O.A.M.
Saarimaki45, R. Sadek117, S. Sadovsky94, J. Saetre21, K. Šafařík38, S.K.
Saha143, S. Saha89, B. Sahoo50, P. Sahoo50, R. Sahoo51, S. Sahoo67, D. Sahu51,
P.K. Sahu67, J. Saini143, S. Sakai136, S. Sambyal104, V. SamsonovI,101,96, D.
Sarkar145, N. Sarkar143, P. Sarma43, V.M. Sarti108, M.H.P. Sas148, J.
Schambach99,121, H.S. Scheid70, C. Schiaua49, R. Schicker107, A. Schmah107, C.
Schmidt110, H.R. Schmidt106, M.O. Schmidt107, M. Schmidt106, N.V.
Schmidt99,70, A.R. Schmier133, R. Schotter139, J. Schukraft35, Y. Schutz139,
K. Schwarz110, K. Schweda110, G. Scioli26, E. Scomparin61, J.E. Seger15, Y.
Sekiguchi135, D. Sekihata135, I. Selyuzhenkov110,96, S. Senyukov139, J.J.
Seo63, D. Serebryakov65, L. Šerkšnytė108, A. Sevcenco69, T.J. Shaba74, A.
Shabanov65, A. Shabetai117, R. Shahoyan35, W. Shaikh112, A. Shangaraev94, A.
Sharma103, H. Sharma120, M. Sharma104, N. Sharma103, S. Sharma104, O.
Sheibani127, K. Shigaki47, M. Shimomura86, S. Shirinkin95, Q. Shou41, Y.
Sibiriak91, S. Siddhanta56, T. Siemiarczuk88, T.F. Silva123, D. Silvermyr83,
G. Simonetti35, B. Singh108, R. Singh89, R. Singh104, R. Singh51, V.K.
Singh143, V. Singhal143, T. Sinha112, B. Sitar13, M. Sitta32, T.B. Skaali20,
G. Skorodumovs107, M. Slupecki45, N. Smirnov148, R.J.M. Snellings64, C.
Soncco114, J. Song127, A. Songmoolnak118, F. Soramel28, S. Sorensen133, I.
Sputowska120, J. Stachel107, I. Stan69, P.J. Steffanic133, S.F.
Stiefelmaier107, D. Stocco117, I. Storehaug20, M.M. Storetvedt37, C.P.
Stylianidis93, A.A.P. Suaide123, T. Sugitate47, C. Suire80, M. Suljic35, R.
Sultanov95, M. Šumbera98, V. Sumberia104, S. Sumowidagdo52, S. Swain67, A.
Szabo13, I. Szarka13, U. Tabassam14, S.F. Taghavi108, G. Taillepied137, J.
Takahashi124, G.J. Tambave21, S. Tang137,7, Z. Tang131, M. Tarhini117, M.G.
Tarzila49, A. Tauro35, G. Tejeda Muñoz46, A. Telesca35, L. Terlizzi25, C.
Terrevoli127, G. Tersimonov3, S. Thakur143, D. Thomas121, R. Tieulent138, A.
Tikhonov65, A.R. Timmins127, M. Tkacik119, A. Toia70, N. Topilskaya65, M.
Toppi53, F. Torales-Acosta19, T. Tork80, R.C. Torres82, S.R. Torres38, A.
Trifiró33,57, S. Tripathy55,71, T. Tripathy50, S. Trogolo35,28, G.
Trombetta34, V. Trubnikov3, W.H. Trzaska128, T.P. Trzcinski144, B.A.
Trzeciak38, A. Tumkin111, R. Turrisi58, T.S. Tveter20, K. Ullaland21, A.
Uras138, M. Urioni59,142, G.L. Usai23, M. Vala39, N. Valle59,29, S. Vallero61,
N. van der Kolk64, L.V.R. van Doremalen64, M. van Leeuwen93, P. Vande Vyvre35,
D. Varga147, Z. Varga147, M. Varga-Kofarago147, A. Vargas46, M. Vasileiou87,
A. Vasiliev91, O. Vázquez Doce108, V. Vechernin115, E. Vercellin25, S. Vergara
Limón46, L. Vermunt64, R. Vértesi147, M. Verweij64, L. Vickovic36, Z.
Vilakazi134, O. Villalobos Baillie113, G. Vino54, A. Vinogradov91, T.
Virgili30, V. Vislavicius92, A. Vodopyanov77, B. Volkel35, M.A. Völkl107, K.
Voloshin95, S.A. Voloshin145, G. Volpe34, B. von Haller35, I. Vorobyev108, D.
Voscek119, N. Vozniuk65, J. Vrláková39, B. Wagner21, C. Wang41, D. Wang41, M.
Weber116, R.J.G.V. Weelden93, A. Wegrzynek35, S.C. Wenzel35, J.P. Wessels146,
J. Wiechula70, J. Wikne20, G. Wilk88, J. Wilkinson110, G.A. Willems146, B.
Windelband107, M. Winn140, W.E. Witt133, J.R. Wright121, W. Wu41, Y. Wu131, R.
Xu7, S. Yalcin79, Y. Yamaguchi47, K. Yamakawa47, S. Yang21, S. Yano47,140, Z.
Yin7, H. Yokoyama64, I.-K. Yoo17, J.H. Yoon63, S. Yuan21, A. Yuncu107, V.
Zaccolo24, A. Zaman14, C. Zampolli35, H.J.C. Zanoli64, N. Zardoshti35, A.
Zarochentsev115, P. Závada68, N. Zaviyalov111, H. Zbroszczyk144, M. Zhalov101,
S. Zhang41, X. Zhang7, Y. Zhang131, V. Zherebchevskii115, Y. Zhi11, D. Zhou7,
Y. Zhou92, J. Zhu7,110, Y. Zhu7, A. Zichichi26, G. Zinovjev3, N. Zurlo142,59

Affiliation Notes

I Deceased

II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy

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

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

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

Collaboration Institutes

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

2 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 Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

7 Central China Normal University, Wuhan, China

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

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

10 Chicago State University, Chicago, Illinois, United States

11 China Institute of Atomic Energy, Beijing, China

12 Chungbuk National University, Cheongju, Republic of Korea

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

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 dell’Università ’La Sapienza’ and Sezione INFN,
Rome, 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 Nucleare e Teorica, Università di Pavia, Pavia,
Italy

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

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

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

33 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy

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

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

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

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

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

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

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

41 Fudan University, Shanghai, China

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

43 Gauhati University, Department of Physics, Guwahati, India

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

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

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

47 Hiroshima University, Hiroshima, Japan

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

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

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

51 Indian Institute of Technology Indore, Indore, India

52 Indonesian Institute of Sciences, Jakarta, Indonesia

53 INFN, Laboratori Nazionali di Frascati, Frascati, Italy

54 INFN, Sezione di Bari, Bari, Italy

55 INFN, Sezione di Bologna, Bologna, Italy

56 INFN, Sezione di Cagliari, Cagliari, Italy

57 INFN, Sezione di Catania, Catania, Italy

58 INFN, Sezione di Padova, Padova, Italy

59 INFN, Sezione di Pavia, Pavia, Italy

60 INFN, Sezione di Roma, Rome, Italy

61 INFN, Sezione di Torino, Turin, Italy

62 INFN, Sezione di Trieste, Trieste, Italy

63 Inha University, Incheon, Republic of Korea

64 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands

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

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

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

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

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

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

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

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

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

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

75 Jeonbuk National University, Jeonju, Republic of Korea

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

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

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

79 KTO Karatay University, Konya, Turkey

80 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France

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

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

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

84 Moscow Institute for Physics and Technology, Moscow, Russia

85 Nagasaki Institute of Applied Science, Nagasaki, Japan

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

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

88 National Centre for Nuclear Research, Warsaw, Poland

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

90 National Nuclear Research Center, Baku, Azerbaijan

91 National Research Centre Kurchatov Institute, Moscow, Russia

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

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

94 NRC Kurchatov Institute IHEP, Protvino, Russia

95 NRC «Kurchatov»Institute - ITEP, Moscow, Russia

96 NRNU Moscow Engineering Physics Institute, Moscow, Russia

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

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

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

100 Ohio State University, Columbus, Ohio, United States

101 Petersburg Nuclear Physics Institute, Gatchina, Russia

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

103 Physics Department, Panjab University, Chandigarh, India

104 Physics Department, University of Jammu, Jammu, India

105 Physics Department, University of Rajasthan, Jaipur, India

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

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

108 Physik Department, Technische Universität München, Munich, Germany

109 Politecnico di Bari and Sezione INFN, Bari, Italy

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

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

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

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

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

115 St. Petersburg State University, St. Petersburg, Russia

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

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

118 Suranaree University of Technology, Nakhon Ratchasima, Thailand

119 Technical University of Košice, Košice, Slovakia

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

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

122 Universidad Autónoma de Sinaloa, Culiacán, Mexico

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

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

125 Universidade Federal do ABC, Santo Andre, Brazil

126 University of Cape Town, Cape Town, South Africa

127 University of Houston, Houston, Texas, United States

128 University of Jyväskylä, Jyväskylä, Finland

129 University of Kansas, Lawrence, Kansas, United States

130 University of Liverpool, Liverpool, United Kingdom

131 University of Science and Technology of China, Hefei, China

132 University of South-Eastern Norway, Tonsberg, Norway

133 University of Tennessee, Knoxville, Tennessee, United States

134 University of the Witwatersrand, Johannesburg, South Africa

135 University of Tokyo, Tokyo, Japan

136 University of Tsukuba, Tsukuba, Japan

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

138 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon
, Lyon, France

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

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

141 Università degli Studi di Foggia, Foggia, Italy

142 Università di Brescia, Brescia, Italy

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

144 Warsaw University of Technology, Warsaw, Poland

145 Wayne State University, Detroit, Michigan, United States

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

147 Wigner Research Centre for Physics, Budapest, Hungary

148 Yale University, New Haven, Connecticut, United States

149 Yonsei University, Seoul, Republic of Korea

###  A.1 Lednický–Lyuboshitz formalism

The pair wave function in Eq. (1), $\Psi(\vec{k}^{*},\vec{r}^{*})$, depends on
the two-particle interaction. Kaons interact with protons via the strong and,
for charged kaons, also 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 in the
inverse time direction333The inverse time direction is manifested by the “$-$”
sign in front of $k^{*}$.:

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

where $A_{\rm C}$ is the Gamow factor,
$\zeta^{\pm}=k^{*}r^{*}(1\pm\cos{\theta^{*}})$, $\varepsilon=1/(k^{*}a_{\rm
C})$, $\rm F$ is the confluent hypergeometric function, and $\tilde{G}$ is the
combination of the regular and singular s-wave Coulomb functions. The angle
$\theta^{*}$ is defined between the pair relative momentum and relative
position in the pair rest frame, while $a_{\rm C}$ is the Bohr radius of the
pair ($a_{C}=-83.59$ fm for $\rm{K}^{-}p$ pairs). The component $f_{\rm
C}(k^{*})$ is the strong-interaction scattering amplitude, modified by the
Coulomb component:

$f^{-1}_{C}(k^{*})=\frac{1}{f_{0}}+\frac{1}{2}d_{0}{k^{*}}^{2}-\frac{2}{a_{C}}h(k^{*}a_{C})-\text{i}k^{*}a_{C},$
(3)

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

Moreover, the description becomes more complicated when coupled channels are
present. For details, see Refs. [51, 81].

The correlation function is obtained by numerical integration of the source
function $S(r^{*})$, parameterised by a three-dimensional Gaussian in the PRF,
with the Bethe–Salpeter amplitude given in Eq. (2) and with the Coulomb-
modified scattering amplitude defined in Eq. (3) [74, 82].