2024 133 21 May

Strangeness enhancement in pp collisions using angular correlations

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

A study of strange hadron production associated with hard scattering processes
and with the underlying event is conducted to investigate the origin of the
enhanced production of strange hadrons in small collision systems
characterised by large charged-particle multiplicities. For this purpose, the
production of the single-strange meson ${\rm K}^{0}_{\rm{S}}$ and the double-
strange baryon $\Xi^{\pm}$ is measured, in each event, in the azimuthal
direction of the highest-$p_{\rm T}$ particle (“trigger" particle), related to
hard scattering processes, and in the direction transverse to it in azimuth,
associated with the underlying event, in pp collisions at $\sqrt{s}=5.02$ TeV
and $\sqrt{s}=13$ TeV using the ALICE detector at the LHC. The per-trigger
yields of ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ are dominated by the
transverse-to-leading production (i.e., in the direction transverse to the
trigger particle), whose contribution relative to the toward-leading
production is observed to increase with the event charged-particle
multiplicity. The transverse-to-leading and the toward-leading
$\Xi^{\pm}$/${\rm K}^{0}_{\rm{S}}$ yield ratios increase with the multiplicity
of charged particles, suggesting that strangeness enhancement with
multiplicity is associated with both hard scattering processes and the
underlying event. The relative production of $\Xi^{\pm}$ with respect to ${\rm
K}^{0}_{\rm{S}}$ is higher in transverse-to-leading processes over the whole
multiplicity interval covered by the measurement. The ${\rm K}^{0}_{\rm{S}}$
and $\Xi^{\pm}$ per-trigger yields and yield ratios are compared with
predictions of three different phenomenological models, namely Pythia8.2 with
the Monash tune, Pythia8.2 with ropes and EPOS LHC. The comparison shows that
none of them can quantitatively describe either the transverse-to-leading or
the toward-leading yields of ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$.

##  1 Introduction

The enhancement of strange hadron production in heavy-ion collisions with
respect to minimum bias pp collisions was one of the first predicted
signatures of quark–gluon plasma (QGP) formation [1, 2, 3]. This strangeness
enhancement was first observed at the SPS [4, 5, 6, 7, 8, 9] and was later
measured in Au–Au collisions at RHIC [10] and in Pb–Pb collisions at the LHC
[11]. The ALICE Collaboration further studied the production of strange
hadrons in smaller collision systems, such as p–Pb [12, 13] and pp collisions
[14, 15, 16, 17]. The results show that the ratios of (multi-)strange to non-
strange hadron yields increase with the multiplicity of charged particles
produced in the collision, reaching in high-multiplicity pp collisions values
compatible with those measured in peripheral Pb–Pb collisions [18].

The smooth evolution of the ratios with multiplicity across different
collision systems implies a common particle production mechanism in the
different systems. This is also supported by other observables, such as
“ridge”-like structures in the two-particle angular correlations at large
pseudorapidity difference [19, 20] and non-vanishing anisotropic flow
coefficients [21, 22, 23], which suggest the presence of collective effects in
small collision systems [15]. These observations challenge the current
understanding of hadronic collisions, as different particle production
mechanisms are expected to be involved in the different collision systems [1].

Several theoretical approaches have attempted to describe the strange hadron
production in hadronic collisions. A qualitative description of the
experimental results has been achieved with different event generators, such
as Pythia8 with colour ropes [24], HERWIG [25, 26] and EPOS LHC [27], which
combine perturbative Quantum Chromodynamics (pQCD) calculations with
phenomenological models for the description of hard and soft processes,
respectively. A qualitative description of strange hadron production is also
provided by the statistical hadronisation model, whereby what is usually
described as strangeness enhancement in A–A collisions can be in fact
understood as a strangeness suppression in pp: the relative abundances of
strange hadrons with respect to lighter flavours can be diminished in small
systems by a canonical suppression of the strangeness quantum numbers [28, 29,
30, 31]. However, none of these theoretical approaches provides a consistent
quantitative description of the multiplicity dependence of the hadron-to-pion
ratios [14, 18, 32], indicating that the microscopic origin of strangeness
enhancement with multiplicity in small collision systems remains an open
issue.

One way to investigate this phenomenon consists in studying the strange hadron
production associated with hard scattering processes and with the underlying
event. Hard scattering processes are associated with high-energy parton shower
(jet) hadronization, whereas the underlying event consists of all the
processes different from the hardest partonic interaction. The ALICE
Collaboration has recently studied the $p_{\rm T}$ spectra of different
(multi-)strange hadron yields in jets and in the underlying event in minimum
bias pp collisions at $\sqrt{s}=7$ TeV and $\sqrt{s}=13$ TeV and in p–Pb at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV [33, 34], using the anti-$k_{\mathrm{T}}$
algorithm [35, 36] for jet reconstruction. The results indicate that jet
fragmentation alone is not sufficient to describe strange particle production
in hadronic collisions at LHC energies and suggest that the baryon-over-meson
yield ratios increase with multiplicity at intermediate $p_{\rm T}$ values
[15] might be driven by particle production in the underlying event.

This paper presents a complementary measurement of strange hadron production
associated with hard scattering processes and the underlying event as a
function of the charged-particle multiplicity in pp collisions. The $p_{\rm
T}$ spectra and the $p_{\rm T}$-integrated yields of ${\rm K}^{0}_{\rm{S}}$
and $\Xi^{\pm}$ are measured at central rapidities in pp collisions at
$\sqrt{s}=5.02$ TeV and at $\sqrt{s}=13$ TeV in the direction of the leading
particle (trigger particle), which is considered to be a proxy for the jet
axis, and in the direction transverse to the trigger particle, which is
associated with the underlying event and might also receive a contribution
from low-$p_{\rm T}$ jets (mini-jets). For this purpose, the angular
correlations between trigger particles and ${\rm K}^{0}_{\rm{S}}$
($\Xi^{\pm}$) are exploited. The single-strange meson ${\rm K}^{0}_{\rm{S}}$
and the double-strange baryon $\Xi^{\pm}$ are studied as they have a different
strangeness content and therefore a different sensitivity to strangeness
enhancement. In addition, these species receive a negligible feed-down from
other particles, which simplifies the measurement of their yields. The ${\rm
K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ per-trigger yields per unit
$\Delta\eta\Delta\varphi$ are reported as a function of the charged-particle
multiplicity and are compared with the predictions of three different
phenomenological models, namely Pythia8.2 with the Monash 2013 tune [37],
Pythia8.2 with ropes [24] and EPOS LHC [27].

The paper is organised as follows. Section 2 outlines the experimental setup
and the data sample used for this measurement, Sec. 3 presents the
experimental details of the analysis, and Sec. 4 shows the per-trigger $p_{\rm
T}$ spectra and $p_{\rm T}$-integrated yields of ${\rm K}^{0}_{\rm{S}}$ and
$\Xi^{\pm}$ as a function of the charged-particle multiplicity, together with
their comparison with model predictions. Finally, the conclusions are drawn in
Sec. 5.

##  2 Experimental setup and data selection

The ALICE apparatus [38, 39] consists of central barrel detectors covering the
pseudorapidity interval $|\eta|<0.9$, a muon spectrometer covering
$-4.0<\eta<-2.5$, and a set of detectors at forward and backward rapidities
used for triggering and event characterisation purposes. The central barrel
detectors are positioned inside a solenoidal magnet providing a 0.5 T magnetic
field along the beam axis and are used for primary vertex (PV) reconstruction,
track reconstruction and charged-particle identification. The main detectors
used for the analysis presented in this paper are the Inner Tracking System
(ITS) [40], the Time Projection Chamber (TPC) [41], the Time Of Flight (TOF)
detector [42], and the V0 detectors [43]. The ITS is the innermost detector of
the ALICE experiment. The ITS used during the LHC Run 2 consisted of six
cylindrical layers of silicon tracking detectors placed at a radial distance
from the beam pipe between 3.9 and 43.0 cm. The two innermost layers of the
ITS were equipped with Silicon Pixel Detectors (SPD), the two intermediate
layers consisted of Silicon Drift Detectors (SDD), and the two outermost
layers of Silicon Strip Detectors (SSD). The SPD was used to reconstruct the
PV of the collision and the tracklets, short two-point track segments covering
the pseudorapidity region $|\eta|<1.2$. The other main functions of the ITS
are the reconstruction of secondary vertices from weak decays and the tracking
and identification of particles with momentum smaller than 200 MeV/c. The TPC
is the main tracking detector of the central barrel. It is used for the
identification of charged particles by measuring the specific ionisation
energy loss $\textrm{d}E/\textrm{d}x$. The TPC has a cylindrical shape with an
inner radius of 85 cm, an outer radius of 250 cm and an overall length along
the beam direction of 5 m. It is filled with nearly $\mathrm{90~{}m^{3}}$ of
gas mixture, consisting of $\mathrm{Ar/CO_{2}}$ (88/12) in 2016 and 2018 and
$\mathrm{Ne/CO_{2}/N_{2}}$ (90/10/5) in 2017. It covers the pseudorapidity
region of $\mathrm{|\eta|<0.9}$ for tracks with full radial length and
provides full azimuthal acceptance. The TPC is radially segmented into “pad
rows": tracks reconstructed with the TPC may consist of up to 159 points, each
corresponding to one crossed pad row. The TOF detector is an array of multigap
resistive plate chambers (MRPCs) covering the pseudorapidity range of
$|\eta|\lesssim 0.9$ and providing full azimuthal acceptance. Its primary
purpose is the identification of particles with intermediate momentum via the
measurement of their time of flight. The V0 detector consists of two arrays of
scintillation counters, V0A and V0C, placed at forward rapidity. The V0A is
located at $+$3.3 m from the interaction point and covers the pseudorapidity
range of $\mathrm{2.8<\eta<5.1}$, whereas the V0C is placed on the opposite
side at $-$0.9 m from the interaction point and covers the pseudorapidity
range of $\mathrm{-3.7<\eta<-1.7}$. The V0 detector provides the minimum bias
trigger in pp, p–Pb and Pb–Pb collisions. It is used to classify pp collisions
in multiplicity percentile classes based on the total deposited charge (V0M
amplitude).

The analysis presented in this paper was performed using pp collisions at
$\sqrt{s}=5.02$ TeV and $\sqrt{s}=13$ TeV collected by the ALICE experiment
during the LHC Run 2 data-taking campaign (2015–2018). Two samples of pp
collisions at $\sqrt{s}=13$ TeV were used: one collected with the minimum bias
(MB) trigger, the other collected with the high multiplicity (HM) trigger. The
MB trigger is provided by the combined signals in the V0A and V0C detectors.
The HM trigger is activated online when the amplitude of the signal in the V0
detectors is above a predefined threshold and allows for the selection of
events characterised by approximately 30 charged particles produced at
midrapidity, i.e., four times more than those collected in minimum bias events
($\approx$ 7). The sample of pp collisions at $\sqrt{s}=5.02$ TeV was
collected with the MB trigger, and consists of events characterised by
approximately 6 charged particles produced at midrapidity.

To ensure uniform detector acceptance, the reconstructed PV position must lie
within $\pm$10 cm from the nominal interaction point in the beam direction.
The contamination from in-bunch pileup events is removed by excluding events
with multiple vertices reconstructed with the SPD. The background from beam-
gas events is removed by using the timing information in the V0 detectors and
the correlation between SPD tracklets and SPD clusters, as discussed in detail
in Ref. [39].

The MB events used for the trigger particle-${\rm K}^{0}_{\rm{S}}$ correlation
analysis were collected in 2016 and 2017 and amount to about $1\times 10^{9}$
good quality events. All MB events collected in 2016, 2017 and 2018 were used
for the trigger particle-$\Xi^{\pm}$ correlation analysis, corresponding to
$1.6\times 10^{9}$ events after the quality selections. The sample of HM
events at $\sqrt{s}=13$ TeV consists of $4\times 10^{8}$ selected events
collected in 2016, 2017 and 2018. The sample of MB pp collisions at
$\sqrt{s}=5.02$ TeV consists of $9\times 10^{8}$ good events recorded in 2017.

##  3 Analysis details

The selected events are divided into V0M multiplicity percentile classes
defined starting from the distribution of the sum of the signal amplitudes
measured with the two V0 detectors. Minimum bias events at $\sqrt{s}=13$ TeV
are divided into five multiplicity classes (0–5%, 5–10%, 10–30%, 30–50%,
50–100%): the 0–5% class, for example, contains the 5% of events with the
highest V0M amplitude, while the 70–100% class contains the 30% of events with
the smallest V0M amplitude. Once corrected for the trigger efficiency, these
ranges represent fractional intervals of the cross section of
$\mathrm{INEL>0}$ events, defined as events having at least one charged
particle produced in the pseudorapidity interval $|\eta|<1$. The corrected
intervals are respectively: 0–4.57%, 4.57–9.15%, 9.15–27.50%, 27.50–46.12%,
46.12–100%, respectively. The details about the correction procedure can be
found in Ref. [44]. High multiplicity events at $\sqrt{s}=13$ TeV are selected
in the multiplicity range 0–0.1%, which includes the 0.1% of the MB events
characterised by the highest V0M amplitude. These events are further divided
into three multiplicity classes: 0–0.01%, 0.01–0.05% and 0.05–0.1%, with the
first one corresponding to 0–0.0091% of the $\mathrm{INEL>0}$ cross section,
and the sum of the other two classes to 0.0091–0.0915%. The available number
of MB events at $\sqrt{s}~{}=~{}5.02$ TeV allows for the analysis to be
performed only in two multiplicity classes (0–10%, 10–100%, corresponding to
0–9.15% and 9.15–100% of the $\mathrm{INEL>0}$ cross section, respectively),
as at this energy the sample of MB events is smaller and the average strange
hadron yields per event are smaller than those at $\sqrt{s}=13$ TeV. For each
V0M percentile class, the average multiplicity of charged particles produced
at midrapidity in events containing a trigger particle,
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5,\
p_{\rm{T,trigg}}>3\ \mathrm{GeV}/c}$, is computed using the technique
described in Ref. [44].

###  3.1 Trigger particle identification

In this analysis, a trigger particle is defined as the charged particle with
the highest-$p_{\rm T}$ in a given event (leading particle), coming from the
PV, produced in the pseudorapidity interval $|\eta|<0.8$ and within the
transverse momentum range $3<p_{\mathrm{T}}<15$ GeV/c. The minimum $p_{\rm T}$
threshold is applied to select particles originating from the hadronisation of
hard scattering processes. An increase of the threshold value above 3 GeV/c
would reduce the contribution from particles not originating from hard
scattering processes. However, it would also decrease the number of events
with a trigger particle, limiting the possibility of performing a multiplicity
dependent measurement of the angular correlation between trigger particles and
$\Xi^{\pm}$ baryons. The trigger particles are selected starting from the
tracks reconstructed using the TPC and constrained to the PV. Only tracks in
the $\mathrm{|\eta|<0.8}$ acceptance region, where full track reconstruction
is provided, are accepted. Standard selections are applied: tracks are
required to cross at least 80 out of 159 TPC pad rows and to be formed by more
than 70 TPC clusters, where a cluster is the signal induced by the passage of
the particle in a crossed pad row. In order not to have large gaps in the
number of expected tracking points in the radial direction, the ratio of
crossed pad rows $N_{\mathrm{crossed}}$ over findable clusters
$N_{\mathrm{findable}}$ is required to be greater than 0.8. In order to reject
the low-resolution tracks which pass through the edges of the TPC sectors,
tracks with radial lengths smaller than 90 cm are discarded, and the ratio
between the number of crossed pad rows and the radial track length is required
to be greater than 0.8 $\mathrm{cm}^{-1}$. In addition, a maximum $p_{\rm T}$
threshold of 15 GeV/c is applied to retain only tracks with $p_{\rm T}$
resolution better than 2%. Finally, the goodness-of-fit $\chi^{2}$ per TPC
cluster of the track fit in the TPC is required to be smaller than 4. To
discard charged particles not originating from the PV, a selection on the
distance of closest approach (DCA) of the track to the PV is applied both
along the beam direction $z$ ($\mathrm{DCA}_{z}$) and in the perpendicular
plane ($\mathrm{DCA}_{xy}$):

$\mathrm{|DCA_{\emph{z}}|<0.04~{}cm\;,\>|DCA_{\emph{xy}}|<\left(0.0105+\frac{0.035}{[\textit{p}_{T}/(GeV/\textit{c})]^{1.1}}\right)~{}cm}.$

The $p_{\rm T}$-dependent selection on the $\mathrm{DCA}_{xy}$ allows for
selecting tracks within 7$\sigma$ from the interaction vertex in the
transverse plane, where $\sigma$ is the resolution with which the
$\mathrm{DCA}_{xy}$ is measured.
The fraction of good-quality events containing a trigger particle increases
with the event multiplicity, from approximately 2% in the 50–100% V0M class to
50% in the highest multiplicity class 0–0.01%, as it is more likely to find a
high-$p_{\rm T}$ track in events characterised by a larger multiplicity of
charged particles.

###  3.2 Identification of ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$

The strange hadrons ${\rm K}^{0}_{\rm{S}}$, $\Xi^{-}$ and $\Xi^{+}$ (in the
following $\Xi^{\pm}$) are identified in the pseudorapidity range of
$|\eta|<0.8$ via invariant mass analysis techniques, exploiting the topology
of their weak decays into charged hadrons [45]:

$\displaystyle\mathrm{K^{0}_{S}}\rightarrow\pi^{+}\pi^{-}$
$\displaystyle\Xi^{-}\rightarrow\Lambda\pi^{-}\rightarrow\mathrm{p}\pi^{-}\pi^{-}(\Xi^{+}\rightarrow\overline{\Lambda}\pi^{+}\rightarrow\mathrm{\overline{p}}\pi^{+}\pi^{+})$

$\displaystyle\mathrm{B.R.=(69.20\pm 0.05)}\%$
$\displaystyle\mathrm{B.R.(\Xi^{-}\rightarrow\Lambda\pi^{-})=(99.887\pm
0.035)}\%$ $\displaystyle\mathrm{B.R.(\Lambda\rightarrow p\pi^{-})=(63.9\pm
0.5)}\%.$

The charged daughter tracks of ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$
candidates are selected in the pseudorapidity range of $|\eta|<0.8$, and are
required to satisfy the same track quality criteria applied for the trigger
particle selection. Daughter tracks in the whole $p_{\rm T}$ interval are
identified by requiring the specific ionisation energy loss
$\mathrm{d}E/\mathrm{d}x$ measured in the TPC to be compatible with the
expected theoretical value within $\pm 3\sigma$, where $\sigma$ is related to
the resolution with which $\mathrm{d}E/\mathrm{d}x$ is measured. In addition,
daughter tracks are required not to be associated with a “kink topology" [46],
which is characteristic of the decay of charged kaons. The combinatorial
background is suppressed by applying standard topological selections (see ref.
[17]), listed in Table 1.

Table 1: Daughter-track quality selections, topological and kinematic
selections applied to ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ candidates. The
symbol $\theta_{\mathrm{P}}$ stands for the pointing angle, i.e. the angle
between the reconstructed momentum vector of the ${\rm K}^{0}_{\rm{S}}$ and
$\Xi^{\pm}$ candidates and the line connecting the primary to the secondary
vertex. All other symbols are explained in the text.  Daughter-track
selections
---
Number of TPC clusters |  $>$ 70
$\chi^{2}$/ndf |  $<$ 4
Number of TPC crossed pad rows $N_{\mathrm{crossed}}$ |  $>$ 80
$N_{\mathrm{crossed}}/N_{\mathrm{findable}}$ |  $>$ 0.8
Track length $l_{\mathrm{TPC}}$ in the TPC |  $>$ 90 cm
$N_{\mathrm{crossed}}/l_{\mathrm{TPC}}$ |  $>$ 0.8 $\mathrm{cm}^{-1}$
Rejection of kink topology | Yes
$|\eta|$ |  $<$ 0.8
$\mathrm{d}E/\mathrm{d}x$ measured in the TPC | $<3\sigma$
At least one daughter track has a hit in the SPD or in the TOF | Yes
$\mathbf{K^{0}_{S}}$-topological-variable selections
DCA daughter tracks to PV |  $>$ 0.06 cm
DCA between daughter tracks |  $<$ 1$\sigma$
$\mathrm{cos(\theta_{P})}$ |  $>$ 0.995
DCA ${\rm K}^{0}_{\rm{S}}$ to PV |  $<$ 0.5 cm
${\rm K}^{0}_{\rm{S}}$ decay radius |  $>$ 0.5 cm
$\Xi^{\pm}$-topological-variable selections
DCA meson daughter to PV |  $>$ 0.04 cm
DCA baryon daughter to PV |  $>$ 0.03 cm
DCA bachelor to PV |  $>$ 0.04 cm
DCA between daughter tracks of the $\Lambda$ |  $<$ 1.5$\sigma$
$\mathrm{cos(\theta_{P})}$ (of $\Xi^{\pm}$ to PV) |  $>$ 0.995
$\mathrm{cos(\theta_{P})}$ (of (anti-)$\Lambda$ to $\Xi^{\pm}$ decay vertex) |  $>$ 0.97
DCA between bachelor and (anti-)$\Lambda$ |  $<$ 0.8 cm
DCA $\Lambda$ to PV |  $>$ 0.06 cm
(anti-)$\Lambda$ decay radius |  $>$ 1.1 cm
$\Xi^{\pm}$ decay radius |  $>$ 0.5 cm
$\mathbf{K^{0}_{S}}$-candidate selections
$|\eta_{V^{0}}|$ |  $<$ 0.8
$\mathrm{|m_{\pi p}-m_{\Lambda}|}$ |  $>5$ MeV/$c^{2}$
Proper lifetime $\tau$ |  $<20$ cm/c ($\simeq 7.5\langle\tau_{{\rm K}^{0}_{\rm{S}}}\rangle$)
$\Xi^{\pm}$-candidate selections
$|\eta_{\Xi^{\pm}}|$ |  $<$ 0.8
$\mathrm{|m_{\pi p}-m_{\Lambda}|}$ |  $<6$ MeV/$c^{2}$
$\mathrm{|m_{K\Lambda}-m_{\Omega}|}$ |  $>5$ MeV/$c^{2}$
Proper lifetime $\tau$ |  $<14.73$ cm/c (= 3$\langle\tau_{\Xi^{\pm}}\rangle$)

A selection on the proper lifetime $\tau$ of ${\rm K}^{0}_{\rm{S}}$ and
$\Xi^{\pm}$ candidates is also applied. The proper lifetime is calculated as
$\tau=d\times m/|\vec{p}|$, where $m$ is the nominal mass of the considered
particle, $|\vec{p}|$ is the magnitude of the reconstructed momentum, and $d$
is the distance of the reconstructed secondary decay vertex from the primary
one. In order to identify $\Xi^{\pm}$, the invariant mass of the daughter
(anti-)$\Lambda$ is required to differ from the nominal mass value of the
$\Lambda$ by less than 6 MeV/$c^{2}$, according to the (anti-)$\Lambda$
invariant mass resolution. The background of (anti-)$\Lambda$ in the ${\rm
K}^{0}_{\rm{S}}$ sample is suppressed by rejecting the ${\rm K}^{0}_{\rm{S}}$
candidates whose invariant mass calculated under the p$\pi$ assumption for the
daughter tracks lies within $\pm 5$ MeV/$c^{2}$ from the nominal $\Lambda$
mass. Similarly, the background of $\Omega^{\pm}$ in the cascade sample is
tackled by rejecting the cascade candidates whose invariant mass calculated
under the $\Lambda\mathrm{K}$ assumption for the daughter particles lies
within $\pm 5$ MeV/$c^{2}$ from the nominal $\Omega$ mass. The width of the
rejected region is determined according to the invariant mass resolution
$\sigma$ of the competing candidate, and corresponds to approximately $\pm
3\sigma$. Finally, to reduce the out-of-bunch pileup background caused by
tracks from other bunch crossings within the TPC integration time, at least
one of the daughter tracks is required to have a hit in the TOF or the SPD.

The signal extraction is performed as a function of $p_{\rm T}$. The invariant
mass distributions of ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ candidates are
fitted with the sum of two Gaussian functions, used to take into account the
invariant mass resolution of the signal peak, and a first-degree polynomial,
used to describe the background. A “peak" region is defined within $\pm
4\sigma$ from $\mu$, where $\mu$ and $\sigma$ are the average mean value and
width of the two Gaussian functions, respectively. For each candidate,
“sideband" regions are defined: the sidebands of the ${\rm K}^{0}_{\rm{S}}$
($\Xi^{\pm}$) invariant mass distributions are defined as the intervals
$\mu-10\sigma<m_{\pi^{+}\pi^{-}}(m_{\pi\Lambda})<\mu-4\sigma$ and
$\mu+4\sigma<m_{\pi^{+}\pi^{-}}(m_{\pi\Lambda})<\mu+10\sigma$. The purity of
the ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ candidates samples, defined as the
ratio between the signal and the total number of candidates in the invariant
mass range within $\pm 4\sigma$ from $\mu$, is larger than 0.95 and 0.89 for
${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$, respectively.

###  3.3 The angular correlation function

The angular correlation between trigger particles, denoted as “h", and
associated particles, i.e. the ${\rm K}^{0}_{\rm{S}}$ ($\Xi^{\pm}$) candidates
with an invariant mass within 4$\sigma$ from the average mean value $\mu$ of
the Gaussian fit functions, is expressed as a function of the pseudorapidity
difference $\Delta\eta$ and the azimuthal angle difference $\Delta\varphi$
between the trigger and associated particles. An example of angular
correlation distribution
$\mathrm{d}^{2}{N_{\mathrm{assoc}}}(\Delta\eta,\Delta\varphi)/\mathrm{d}\Delta\eta\mathrm{d}\Delta\varphi$
of h-$\rm{K}^{0}_{\rm{S}}$ pairs produced in pp collisions at $\sqrt{s}=13$
TeV is shown in the left panel of Fig. 1. The distribution shows a near-side
peak centred at ($\Delta\eta$, $\Delta\varphi$) = (0, 0) which is associated
with h-${\rm K}^{0}_{\rm{S}}$ pairs fragmented within the same jet. The
distribution is corrected by the efficiency$\times$acceptance$\times$B.R. of
associated particles $\epsilon_{\mathrm{assoc}}$ computed using a Monte Carlo
simulation based on Pythia8.2 with the Monash 2013 tune [37] for the
generation of events and on Geant 4 [47] for the description of the
propagation of particles through the material of the detector. The term
$\epsilon_{\mathrm{assoc}}$ is calculated in events with a trigger particle
identified by applying the selections described in Sec. 3.1. It increases with
$p_{\rm T}$, reaching a saturation value of about 35% and 25% at
$p_{\mathrm{T}}=3$ and 4 GeV/c for ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$,
respectively. For ${\rm K}^{0}_{\rm{S}}$, $\epsilon_{\mathrm{assoc}}$
increases with decreasing charged-particle multiplicity, varying by about 10%
from the 0–5% to the 50–100% V0M multiplicity classes, whereas for
$\Xi^{\pm}$, because of the different decay topology, it does not depend on
multiplicity. For both particles, $\epsilon_{\mathrm{assoc}}$ is computed in
each multiplicity class and as a function of $\eta$ and $p_{\rm T}$, and is
applied as a weight factor to each entry of the angular correlation
distribution.

The angular correlation distribution (left panel of Fig. 1) exhibits a
triangular shape in $\Delta\eta$, which is related to the geometrical
acceptance of the trigger–associated particle pairs. It is corrected for by
the pair acceptance $\epsilon_{\mathrm{pair}}$, calculated with the mixed-
event method, which correlates the trigger particle found in one event with
the associated particles produced in different events. These events are
required to have similar characteristics, namely to lie in the same
multiplicity class, to have the z-coordinate of the PV differing by less than
2 cm, and to contain a trigger particle. Each entry of the mixed-event angular
correlation distribution is weighed with $1/\epsilon_{\mathrm{assoc}}$, to
take into account the $\eta$ dependence of the associated particle efficiency.
As shown in the central plot of Fig. 1, the mixed-event angular correlation
distribution has a triangular shape in $\Delta\eta$, determined by the $\eta$
acceptance. In contrast, it shows no dependence on $\Delta\varphi$, as a
consequence of the cylindrical symmetry of the detector. To obtain the pair
acceptance, the mixed-event distribution is normalised to unity at
$\Delta\eta\simeq 0$, where all particle pairs are assumed to be accepted. The
raw angular correlation distributions are divided by the pair acceptance to
retain the genuine physical correlations in such pair-acceptance window
$\mathrm{d}^{2}{N^{\mathrm{corrected}}_{\mathrm{assoc}}}(\Delta\eta,\Delta\varphi)/\mathrm{d}\Delta\eta\mathrm{d}\Delta\varphi$,
shown in the right panel of Fig. 1. The pair acceptance is computed in each
multiplicity class. Since the h-$\Xi^{\pm}$acceptance does not show any
multiplicity dependence within the statistical uncertainty, the correction is
performed using the pair acceptance computed in the 0-100% multiplicity class,
in order to reduce statistical fluctuations.

Figure 1: (left) Example of angular correlation distribution between trigger
and ${\rm K}^{0}_{\rm{S}}$ found in the same collision. (centre) Acceptance
correction of trigger-${\rm K}^{0}_{\rm{S}}$ pairs. (right) Angular
correlation distribution divided by the pair acceptance.

###  3.4 Evaluation of the $p_{\rm T}$ spectra and integrated yields

The corrected angular correlation distributions
$\mathrm{d}^{2}{N^{\mathrm{corrected}}_{\mathrm{assoc}}}(\Delta\eta,\Delta\varphi)/\mathrm{d}\Delta\eta\mathrm{d}\Delta\varphi$
(right panel of Fig. 1) are projected onto the $\Delta\varphi$ axis. The
$\Delta\varphi$ projections are corrected for the contribution of the
combinatorial background due to candidates which are not ${\rm
K}^{0}_{\rm{S}}$ ($\Xi^{\pm}$). The standard procedure, which is applied to
${\rm K}^{0}_{\rm{S}}$ in all samples and to $\Xi^{\pm}$ in the HM sample,
consists of subtracting the angular correlations obtained using ${\rm
K}^{0}_{\rm{S}}$ ($\Xi^{\pm}$) candidates in the “sidebands" of the invariant
mass distributions from those obtained from the peak region. Before
subtraction, the angular correlation obtained from the sidebands is divided by
the integral of the invariant mass distribution in the sidebands regions and
multiplied by the integral of the background fit function in the signal region
in order to take into account the purity of the ${\rm K}^{0}_{\rm{S}}$ and
$\Xi^{\pm}$ samples. A different procedure is applied to take into account the
contribution of misidentified $\Xi^{\pm}$ in minimum bias pp collisions at
$\sqrt{s}=13$ TeV and at $\sqrt{s}=5.02$ TeV, since these samples do not
contain enough events to compute the h-$\Xi^{\pm}$angular correlation
distributions from the sidebands regions. In this case, the $\Delta\varphi$
projections are multiplied by the purity of the sample of $\Xi^{\pm}$
candidates. This procedure assumes that the angular correlation distributions
for background candidates have the same shape as for signal candidates. A
systematic uncertainty is applied to take into account any difference with
respect to the standard procedure, as described in Sec. 3.5.

In addition, the $\Delta\varphi$ projections are corrected for the fraction of
feed-down ${\rm K}^{0}_{\rm{S}}$ ($\Xi^{\pm}$). For this purpose, the
distributions are multiplied by ($1-F_{\mathrm{NP}}$), where $F_{\mathrm{NP}}$
is the fraction of non-primary ${\rm K}^{0}_{\rm{S}}$ ($\Xi^{\pm}$) calculated
using Monte Carlo simulations. This procedure is based on the assumption that
the angular correlation for feed-down particles has the same shape as the
angular correlation for primary strange hadrons. This correction has a
negligible impact since in the $p_{\rm T}$ ranges considered in this analysis
$F_{\mathrm{NP}}\sim 0.5\%$ for $\Xi^{\pm}$ and $F_{\mathrm{NP}}<0.05\%$ for
${\rm K}^{0}_{\rm{S}}$.

The associated particle yields are computed by integrating the $\Delta\varphi$
projections and are divided by the width of the $\Delta\eta\Delta\varphi$
region from which they are extracted. The toward-leading production is
extracted from the region ($|\Delta\eta|<0.86$, $|\Delta\varphi|<1.1$), chosen
to include the whole near-side peak. The transverse-to-leading production is
extracted from ($0.86<|\Delta\eta|<1.2$, $0.96<\Delta\varphi<1.8$): this
region is chosen to exclude the away-side peak associated with the recoil jet,
whose contribution is situated around $\Delta\varphi\sim\pi$ and is elongated
over the whole $\Delta\eta$ interval, and to exclude any possible residual
near-side peak contribution in the region around $\Delta\varphi\sim 0$.
Finally, the full yield is obtained from the whole $\Delta\eta\Delta\varphi$
region ($|\Delta\eta|<1.2$, $-\pi/2<\Delta\varphi<3/2\pi$).

To obtain the toward-leading yield, the contribution of the underlying event
is subtracted from the toward-leading $\Delta\varphi$ projections. An estimate
of the underlying event contribution is provided by the long-range
$\Delta\varphi$ projections obtained from the $0.86<|\Delta\eta|<1.2$ region
and scaled to take into account the different $\Delta\eta$ widths of the two
regions. This procedure cannot be applied to extract the toward-leading yield
of $\Xi^{\pm}$ with $p_{\rm T}$ $\lesssim$ 2 GeV/c in the minimum bias samples
because of the large statistical uncertainties affecting the transverse-to-
leading $\Delta\varphi$ projections. To overcome this issue, the angular
correlation between charged particles with $0.15<p_{\mathrm{T}}<2.5$ GeV/c and
$\Xi^{\pm}$ candidates is computed, and the $\Delta\varphi$ projections
obtained from the $0.86<|\Delta\eta|<1.2$ region are used as estimates of the
underlying event, after being scaled in order to match the $|\Delta\eta|<0.86$
projections in the interval $1\lesssim\Delta\varphi\lesssim 2$. These
projections do not suffer from large statistical errors. They are observed to
be compatible within uncertainties with the default distributions in the
$-\pi/2<\Delta\varphi<\pi/2$ interval, where the near-side peak lies. A
systematic uncertainty related to this procedure is evaluated as described in
Sec. 3.5.

The per-trigger yields per unit $\Delta\eta\Delta\varphi$, from now on
referred to as “yields", are corrected by an additional normalisation factor
$C_{\mathrm{norm}}$ in order to obtain the fully corrected $p_{\rm T}$ spectra
$\left(\frac{1}{N_{\mathrm{trigg}}}\frac{1}{\Delta\eta\Delta\varphi}\frac{\mathrm{d}N}{\mathrm{d}p_{\mathrm{T}}}\right)$
in the three different regions:

$\frac{1}{N_{\mathrm{trigg}}}\frac{1}{\Delta\eta\Delta\varphi}\frac{\mathrm{d}N}{\mathrm{d}p_{\mathrm{T}}}\
=\frac{1}{N_{\mathrm{trigg}}}\frac{1}{\Delta\eta\Delta\varphi}\frac{1}{\Delta
p_{\mathrm{T}}}C_{\mathrm{norm}}\int_{\Delta\varphi}\frac{\mathrm{d}N^{\mathrm{corrected}}_{\mathrm{assoc}}}{\mathrm{d\Delta\varphi}}\mathrm{d\Delta\varphi},$
(1)

where $N_{\mathrm{trigg}}$ is the number of trigger particles in a given V0M
multiplicity class and $C_{\mathrm{norm}}$ considers the efficiency with which
events with a trigger particle are selected. The normalisation factor
$C_{\mathrm{norm}}$ is computed using a Monte Carlo simulation and depends on
the efficiency of trigger particle reconstruction and the difference between
the ${\rm K}^{0}_{\rm{S}}$ ($\Xi^{\pm}$) spectra measured in events with a
reconstructed trigger particle and events with a generated trigger particle.
This correction factor is compatible with one for the toward-leading spectra,
whereas it decreases with $p_{\rm T}$ for full and transverse-to-leading
spectra, reaching a saturation value of about 0.98 at $p_{\mathrm{T}}>3$ GeV/c
for both ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$.

To compute the $p_{\rm T}$-integrated yields, the spectra are fitted with four
different functions used to extrapolate the yield in the unmeasured $p_{\rm
T}$ interval. The extrapolated yield is the average obtained from the four
different fit functions: the Lévi-Tsallis [48], the Boltzmann, the Fermi-
Dirac, and the $m_{\mathrm{T}}$-exponential functions [17]. The extrapolated
fraction of the ${\rm K}^{0}_{\rm{S}}$ yield amounts up to approximately 1% of
the total yield for full and transverse-to-leading production and to
approximately 8% for toward-leading production. The extrapolated fraction of
the $\Xi^{\pm}$ yield varies between 10% and 40% for full and transverse-to-
leading production and between 20% and 35% for toward-leading production,
depending on the multiplicity class.

###  3.5 Systematic uncertainties

Several systematic uncertainties affecting the measurement of the full,
transverse-to-leading and toward-leading $p_{\rm T}$ spectra are investigated.
All the considered sources of systematic uncertainties are reported in Table 2
for ${\rm K}^{0}_{\rm{S}}$ (top) and $\Xi^{\pm}$ (bottom) $p_{\rm T}$ spectra,
together with the relative uncertainty associated with each of the sources at
three different $p_{\rm T}$ values in minimum bias pp collisions at
$\sqrt{s}=13$ TeV.

Table 2: Summary of the relative systematic uncertainties of the ${\rm
K}^{0}_{\rm{S}}$ (top) and $\Xi^{\pm}$ (bottom) $p_{\rm T}$ spectra measured
in pp collisions at $\sqrt{s}=13$ TeV in the V0M multiplicity class 0-100%.
The values in parentheses refer to the toward-leading spectra and are reported
only when a difference from the transverse-to-leading and full spectra is
observed. No systematic uncertainty for the toward-leading $\Xi^{\pm}$ spectra
is reported in the lowest $p_{\rm T}$ interval, as the measurement is
performed for $p_{\mathrm{T}}>1.5(2)$ GeV/c, depending on the multiplicity
class. No significant centre-of-mass energy dependence is observed. The three
sources of uncertainty marked with an asterisk are observed to be partially
uncorrelated across multiplicity, whereas all the other sources are fully
correlated across multiplicity. See text for details.

Hadron | $\mathrm{K^{0}_{S}}$
---|---
$p_{\mathrm{T}}$ (GeV/c) |  $\approx$0.6 |  $\approx$1.8 |  $\approx$3.5
Topological selections:* |  |  |
Full |  0.3% |  0.3% |  0.3%
Transverse-to-leading |  0.5% |  0.5% |  0.5%
Toward-leading |  2% |  2% |  1%
Trigger particle $\mathrm{DCA}_{z}$ selection |  0.1% |  0.07% |  0.05%
Choice of $\Delta\eta$ region* |  0.3% (2%) |  0.5% (1.2%) |  0.7% (0.7%)
Choice of $\Delta\varphi$ region* |  0.7% (2.5%) |  0.7% (0.7%) |  1.2% (0.2%)
Background fit function |  0.1% |  0.3% |  0.5%
Choice of Monte Carlo |  1% |  1% |  1%
Material budget |  2% |  0.2% |  0.4%
Residual in-bunch pileup |  2% |  2% |  2%
Out-of-bunch pileup track rejection |  1.2% |  1.2% |  1.2%
Total |  3% (5%) |  3% (3.5%) |  2.5% (3%)
Hadron | $\Xi^{\pm}$
$p_{\mathrm{T}}$ (GeV/c) |  $\approx$0.6 |  $\approx$1.8 |  $\approx$3.5
Topological selections:* |  |  |
Full |  1% |  0.1% |  0.2%
Transverse-to-leading |  3.0% |  0.6% |  0.5%
Toward-leading |  – |  5% |  3%
Trigger particle $\mathrm{DCA}_{z}$ selection |  0.1% |  0.07% |  0.05%
Choice of $\Delta\eta$ region* |  2% |  1% (2%) |  1% (1%)
Choice of $\Delta\varphi$ region* |  0.9% |  1% (–) |  1.2% (–)
Background fit function |  0.5% |  0.5% |  0.5%
Misidentified $\Xi^{\pm}$ subtraction |  0.8% |  0.4% (2.5%) |  0.3% (1.2%)
Out–of–jet subtraction |  – |  5% |  –
Material budget |  2% |  2% |  2%
Residual in-bunch pileup |  2% |  2% |  2%
Out-of-bunch pileup track rejection |  2% |  2% |  2%
Total |  5% |  3% (8%) |  3% (4%)

The topological selections are varied to take into account the differences
between the distributions of the topological variables in the data and in the
Monte Carlo simulation used to compute the ${\rm K}^{0}_{\rm{S}}$ and
$\Xi^{\pm}$ acceptance$\times$efficiencies. The systematic uncertainty is
evaluated from the distribution of the fully corrected yields obtained by
randomly changing the topological selections within ranges leading to a
maximum variation of about $\pm 2$% in the raw signal yields when one single
topological variable is varied. The relative systematic uncertainty depends on
the multiplicity class. Overall, it is smaller than 2% (4%) for the
transverse-to-leading and full $p_{\rm T}$ spectra of ${\rm K}^{0}_{\rm{S}}$
($\Xi^{\pm}$). For the toward-leading spectra of ${\rm K}^{0}_{\rm{S}}$
($\Xi^{\pm}$) it reaches values up to 8% at $p_{\mathrm{T}}<1$ (2) GeV/c,
decreasing with increasing $p_{\rm T}$. This source of uncertainty represents
the dominant one for the toward-leading spectra.

The effect of a different fraction of non-primary charged particles in the
sample of trigger particles is evaluated by varying the selection applied to
the $\mathrm{DCA}_{z}$ of the trigger particles. The systematic uncertainty is
extracted from the distribution of the fully corrected yields obtained by
randomly changing the $\mathrm{DCA}_{z}$ selection within the $(0,2)$ cm
range. The relative uncertainty associated with this source is smaller than
0.2% for full and transverse-to-leading production, and smaller than 0.5% for
toward-leading production: it represents the smallest contribution to the
total systematic uncertainty.

The systematic uncertainty associated with the choice of the $\Delta\eta$
region is assessed by changing the default boundaries of the $\Delta\eta$
regions by about $\pm$10%. The results are compared with those obtained with
the default ranges. The variations are significant according to the Barlow
criterion [49], with a $2\sigma$ threshold in at least four out of ten
$\Delta\varphi$ intervals, indicating that they are not compatible with
statistical fluctuations. For both ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$, the
relative systematic uncertainty of the transverse-to-leading spectra is
smaller than 2%, whereas for the toward-leading spectra it decreases with
$p_{\rm T}$ from at most 6% for $p_{\mathrm{T}}<1(2)$ GeV/c for ${\rm
K}^{0}_{\rm{S}}$ ($\Xi^{\pm}$) to less than 2% for $p_{\mathrm{T}}>3$ GeV/c.
The full yield, which by definition is obtained from the region
($|\Delta\eta|<1.2$, $-\pi/2<\Delta\varphi<3/2\pi$), is not affected by this
source of systematic uncertainty.

Similarly, the systematic uncertainty related to the choice of the
$\Delta\varphi$ interval is assessed by changing the default boundaries of the
$\Delta\varphi$ regions by about $\pm 10$%. For both ${\rm K}^{0}_{\rm{S}}$
and $\Xi^{\pm}$, the variations of the transverse-to-leading $\Delta\varphi$
interval are significant according to the Barlow check with a $2\sigma$
threshold in at least three $p_{\rm T}$ intervals. The relative uncertainty,
computed taking into account only the significant variations, increases with
$p_{\rm T}$ up to 2% for both particles. The variations of the toward-leading
yields are significant for ${\rm K}^{0}_{\rm{S}}$ in minimum bias pp
collisions at $\sqrt{s}=13$ TeV: the relative uncertainty decreases with
$p_{\rm T}$ from about 2% down to $\sim 0.1\%$ for $p_{\mathrm{T}}>4$ GeV/c.
On the contrary, the variations are not significant for $\Xi^{\pm}$ toward-
leading spectra. As for the choice of the $\Delta\eta$ region, this source
does not affect the full yields.

The relative uncertainties associated with the topological selections and the
choice of the $\Delta\eta$ and $\Delta\varphi$ intervals mildly depend on the
multiplicity class.

Another systematic effect is related to the choice of the function used to fit
the background of the invariant mass distributions of ${\rm K}^{0}_{\rm{S}}$
and $\Xi^{\pm}$ candidates. To quantify it, the fit to the background is
performed with a second-degree polynomial and the invariant mass interval in
which the fit is performed is varied. The results obtained in this way are
compared with the default ones. For ${\rm K}^{0}_{\rm{S}}$, the relative
systematic uncertainty increases with $p_{\rm T}$ up to 1.5%. For $\Xi^{\pm}$,
the relative systematic uncertainty equals 0.5% in all $p_{\rm T}$ intervals.
No dependence on the multiplicity class is observed.

To account for the simplified procedure applied to the subtraction of the
contribution of misidentified $\Xi^{\pm}$ in the minimum bias samples, the
$\Xi^{\pm}$ spectra measured in the 0–100% multiplicity class of pp collisions
at $\sqrt{s}=13$ TeV are compared with those obtained using the method based
on the sidebands of the invariant mass distribution. The difference between
the spectra obtained with the two methods is significant according to the
Barlow criterion with a $2\sigma$ threshold in at least three $p_{\rm T}$
intervals, and their relative half-difference is assigned as a systematic
uncertainty to the $\Xi^{\pm}$ spectra in all multiplicity classes in minimum
bias events. The relative uncertainty decreases with increasing $p_{\rm T}$,
it is smaller than 1% for full and transverse-to-leading production and
smaller than 3% for toward-leading production.

Since the ${\rm K}^{0}_{\rm{S}}$ efficiency depends on the multiplicity, a
systematic uncertainty is assigned to ${\rm K}^{0}_{\rm{S}}$ spectra in order
to account for possible differences between the multiplicity distribution in
the data and in the Monte Carlo simulation used to compute the efficiency
correction. To assess this uncertainty, the default ${\rm K}^{0}_{\rm{S}}$
efficiencies, computed using a Monte Carlo distribution based on Pythia8, are
compared with those obtained using a different Monte Carlo simulation based on
EPOS LHC [27], and a 1% uncertainty is added to account for the differences.

Another source of uncertainty for the $\Xi^{\pm}$ toward-leading spectra is
related to the method applied to subtract the contribution of the underlying
event in the low-$p_{\rm T}$ intervals ($p_{\mathrm{T}}<2.5$ GeV/c) where the
standard method cannot be applied due to large statistical uncertainties. To
evaluate this uncertainty, the $\Xi^{\pm}$ toward-leading spectra are compared
with those obtained using the standard procedure in the [2.0-2.5) GeV/c
interval, where the number of $\Xi^{\pm}$ candidates is large enough to allow
for the application of both methods. The systematic uncertainty, which amounts
to 5–10% depending on the multiplicity class, is also assigned to the lower
$p_{\rm T}$ intervals where the extraction procedure of the toward-leading
yield differs from the standard one.

To take into account the imperfect reproduction of the detector material
budget in the Monte Carlo simulation, the ${\rm K}^{0}_{\rm{S}}$ and
$\Xi^{\pm}$ efficiencies are compared with those obtained using a Monte Carlo
with a different dependence of the material budget on the radial distance from
the interaction point. For ${\rm K}^{0}_{\rm{S}}$, the uncertainty associated
with the material budget decreases with $p_{\rm T}$ from a maximum of 2% and
shows a similar trend in all multiplicity classes. For $\Xi^{\pm}$, this
systematic uncertainty amounts to 2% and is independent of multiplicity and
$p_{\rm T}$.

The systematic uncertainties related to pileup rejection are inherited from
the analysis of (multi-)strange hadron production in pp collisions at
$\sqrt{s}=13$ TeV [17]. To account for a residual contamination from in-bunch
pileup, a relative systematic uncertainty of 2% is assigned to both ${\rm
K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ $p_{\rm T}$ spectra. The systematic
uncertainty due to out-of-bunch pileup, evaluated in Ref. [17] by changing the
matching scheme of the decay tracks with the ITS and TOF detectors, amounts to
1.2% (2%) for ${\rm K}^{0}_{\rm{S}}$ ($\Xi^{\pm}$) spectra in all $p_{\rm T}$
intervals and multiplicity classes.

Finally, another source of systematic uncertainty affecting the $p_{\rm
T}$-integrated yield is associated with choosing the fit function used to
extrapolate the $p_{\rm T}$-spectra. The uncertainty is given by the half-
difference between the maximum and the minimum extrapolated yields obtained
with the four different fit functions. This uncertainty amounts at most to
0.5% (4%) for full and transverse-to-leading yields of ${\rm K}^{0}_{\rm{S}}$
($\Xi^{\pm}$), and to 2% (4%) for toward-leading yields of ${\rm
K}^{0}_{\rm{S}}$ ($\Xi^{\pm}$).

Most of the sources of systematic uncertainties considered in this analysis
are fully correlated across multiplicity, as they determine a shift of the
yields in the same direction in all multiplicity classes. Three sources of
uncertainty, namely the selections applied to identify ${\rm K}^{0}_{\rm{S}}$
and $\Xi^{\pm}$ candidates and the choices of the $\Delta\varphi$ and
$\Delta\eta$ intervals, are observed to be partially uncorrelated across
multiplicity. For each of these sources, in order to determine the fraction of
uncertainty which is uncorrelated across multiplicity, the ratio $R_{var}^{m}$
is computed:

$R_{\mathrm{var}}^{m}=\frac{y_{\mathrm{var}}^{\mathrm{m}}/y_{\mathrm{def}}^{\mathrm{m}}}{y_{\mathrm{var}}^{0-100\%}/y_{\mathrm{def}}^{0-100\%}}.$
(2)

Here $y_{\mathrm{def}}^{\mathrm{m}}$ and $y_{\mathrm{def}}^{0-100\%}$ are the
default yields measured in a given $p_{\rm T}$ interval in the multiplicity
class $m$ and 0–100%, respectively, and $y_{\mathrm{var}}^{\mathrm{m}}$ and
$y_{\mathrm{var}}^{0-100\%}$ are the yields obtained by applying a systematic
variation. If a source of uncertainty is fully correlated across multiplicity,
$R_{\mathrm{var}}^{\mathrm{m}}\sim 1$. For each source of systematic
uncertainty, the uncorrelated relative uncertainty across multiplicity is
computed as the maximum deviation of $R_{\mathrm{var}}^{\mathrm{m}}$ from
unity.

On average, the uncorrelated fraction of the total systematic uncertainty for
${\rm K}^{0}_{\rm{S}}$ ($\Xi^{\pm}$) amounts to approximately 3%(5%), 10%(20%)
and 25%(25%) for the full, transverse-to-leading and toward-leading
production, respectively.

##  4 Results

The full, toward-leading and transverse-to-leading $p_{\rm T}$ distributions
of ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ per unit $\Delta\eta\Delta\varphi$
area are shown for the different multiplicity classes in Figs. 2 and 3 for pp
collisions at $\sqrt{s}=13$ TeV and Figs. 4 and 5 for pp collisions at
$\sqrt{s}=5.02$ TeV. The bottom panels show the ratios to the spectra measured
in the 0–100% multiplicity class. In all multiplicity classes and at both
centre-of-mass energies, the toward-leading spectra (right panels) are harder,
i.e. have a larger average $p_{\rm T}$, than the transverse-to-leading
(central panels) and full (left panels) spectra, as expected from the fact
that the production in the direction of the trigger particle is associated
with hard scattering processes. As shown in the bottom panels of Figs. 2–5,
the transverse-to-leading and full $p_{\rm T}$ spectra increase with
multiplicity in all $p_{\rm T}$ intervals, becoming harder as the multiplicity
increases. This behaviour was already reported for strange hadron spectra
measured inclusively, i.e. in all events, in Pb–Pb [11], p–Pb [12] and pp
collisions [15, 17]. In Pb–Pb collisions this behaviour is more pronounced
than in small collision systems and is interpreted as an indication of the
presence of radial flow. In contrast to the full and transverse-to-leading
spectra, the toward-leading spectra show a much smaller dependence on the
multiplicity.

Figure 2: Transverse momentum distributions of ${\rm K}^{0}_{\rm{S}}$ per unit
$\Delta\eta\Delta\varphi$ area in pp collisions at $\sqrt{s}=13$ TeV. The
left, central and right panels refer to full, transverse-to-leading and
toward-leading production, respectively. Different colours refer to different
multiplicity classes selected using the V0 detector, as indicated in the
legend. The spectra are scaled by different factors to improve the visibility.
The bottom panels display the ratios to the spectra measured in the 0–100%
multiplicity class. The statistical errors are represented by the error bars,
the systematic uncertainties by the empty boxes. Error bars are smaller than
the marker size and are therefore not visible. Figure 3: Transverse momentum
distributions of $\Xi^{\pm}$ per unit $\Delta\eta\Delta\varphi$ area in pp
collisions at $\sqrt{s}=13$ TeV. The left, central and right panels refer to
full, transverse-to-leading and toward-leading production, respectively.
Different colours refer to different multiplicity classes selected using the
V0 detector, as indicated in the legend. The spectra are scaled by different
factors to improve the visibility. The bottom panels display the ratios to the
spectra measured in the 0–100% multiplicity class. The statistical errors are
represented by the error bars, the systematic uncertainties by the empty
boxes. Error bars are smaller than the marker size and are therefore not
visible.  Figure 4: Transverse momentum distributions of ${\rm
K}^{0}_{\rm{S}}$ per unit $\Delta\eta\Delta\varphi$ area in pp collisions at
$\sqrt{s}=5.02$ TeV. The left, central and right panels refer to full,
transverse-to-leading and toward-leading production, respectively. Different
colours refer to different multiplicity classes selected using the V0
detector, as indicated in the legend. The spectra are scaled by different
factors to improve the visibility. The bottom panels display the ratios to the
spectra measured in the 0–100% multiplicity class. The statistical errors are
represented by the error bars, the systematic uncertainties by the empty
boxes. Error bars are smaller than the marker size and are therefore not
visible.  Figure 5: Transverse momentum distributions of $\Xi^{\pm}$ per unit
$\Delta\eta\Delta\varphi$ area in pp collisions at $\sqrt{s}=5.02$ TeV. The
left, central and right panels refer to full, transverse-to-leading and
toward-leading production, respectively. Different colours refer to different
multiplicity classes selected using the V0 detector, as indicated in the
legend. The spectra are scaled by different factors to improve the visibility.
The bottom panels display the ratios to the spectra measured in the 0–100%
multiplicity class. The statistical errors are represented by the error bars,
the systematic uncertainties by the empty boxes. Error bars are smaller than
the marker size and are therefore not visible.

The full, transverse-to-leading and toward-leading $p_{\rm T}$-integrated
yields of ${\rm K}^{0}_{\rm{S}}$ ($\Xi^{\pm}$) per unit
$\Delta\eta\Delta\varphi$ area are shown in Fig. 6 (7) as a function of the
charged-particle multiplicity measured at midrapidity in events with a trigger
particle $\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5,\
p_{\rm{T,trigg}}>3\ \mathrm{GeV}/c}$, in the following abbreviated with
$\langle\mathrm{d}N/\mathrm{d}\eta\rangle_{\mathrm{trigg}}$. The yields show
no dependence on the centre-of-mass energy, as observed in previously
published results [17]. The full and transverse-to-leading yields of both
${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ increase with multiplicity faster than
the toward-leading yields. For better visibility, the toward-leading $p_{\rm
T}$-integrated yields of ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ per unit
$\Delta\eta\Delta\varphi$ area are separately shown in Fig. 8, where the
$\Xi^{\pm}$ yields are scaled such that the lowest-multiplicity $\Xi^{\pm}$
yield matches the ${\rm K}^{0}_{\rm{S}}$ one. Both the ${\rm K}^{0}_{\rm{S}}$
and $\Xi^{\pm}$ yields are not compatible with a flat trend with multiplicity
with a $5\sigma$ confidence level. The relative increase of the ${\rm
K}^{0}_{\rm{S}}$ yield from the lowest to the highest multiplicity is
($1.22\pm 0.04$), where the uncertainty is given by the sum in quadrature of
the statistical and the systematic uncertainty uncorrelated in multiplicity.
The relative increase of the $\Xi^{\pm}$ yield ($1.93\pm 0.17$) is
significantly larger than the ${\rm K}^{0}_{\rm{S}}$ one.

Figure 6: Upper panel: full (blue), transverse-to-leading (green) and toward-
leading (red) ${\rm K}^{0}_{\rm{S}}$ yields per unit $\Delta\eta\Delta\varphi$
area as a function of the charged-particle multiplicity measured in events
with a trigger particle. The data points are drawn with markers, the model
predictions with lines of different styles, as indicated in the legend.
Statistical and systematic uncertainties of the data points are shown by error
bars and empty boxes, respectively. Shadowed boxes represent systematic
uncertainties uncorrelated across multiplicity. The sum in quadrature of
statistical and systematic uncertainties of the model predictions are shown by
error bars, too small to be visible in the plot. Bottom panel: ratio between
the model predictions and the cubic spline fitted to the data points. The
shaded band around one represents the sum in quadrature of the statistical and
systematic uncertainties of the data points. Figure 7: Upper panel: full
(blue), transverse-to-leading (green) and toward-leading (red) $\Xi^{\pm}$
yields per unit $\Delta\eta\Delta\varphi$ area as a function of the charged-
particle multiplicity measured in events with a trigger particle. The data
points are drawn with markers, the model predictions with lines of different
styles, as indicated in the legend. Statistical and systematic uncertainties
of the data points are shown by error bars and empty boxes, respectively.
Shadowed boxes represent systematic uncertainties uncorrelated across
multiplicity. The sum in quadrature of statistical and systematic
uncertainties of the model predictions are shown by error bars, too small to
be visible in the plot. Bottom panel: ratio between the model predictions and
the cubic spline fitted to the data points. The shaded band around one
represents the sum in quadrature of the statistical and systematic
uncertainties of the data points. Figure 8: Upper panel: toward-leading ${\rm
K}^{0}_{\rm{S}}$ (magenta) and $\Xi^{\pm}$ (light blue) yields per unit
$\Delta\eta\Delta\varphi$ area as a function of the charged-particle
multiplicity measured in events with a trigger particle. The $\Xi^{\pm}$
yields are scaled such that the lowest-multiplicity $\Xi^{\pm}$ yield matches
the ${\rm K}^{0}_{\rm{S}}$ one. The data points are drawn with markers, the
model predictions with lines of different styles, as indicated in the legend.
Statistical and systematic uncertainties of the data points are shown by error
bars and empty boxes, respectively. Shadowed boxes represent systematic
uncertainties uncorrelated across multiplicity. The width of the bands
represents the sum in quadrature of statistical and systematic uncertainties
of the model predictions. Bottom panel: ratio between the model predictions
and the cubic spline fitted to the data points. The shaded band around one
represents the sum in quadrature of the statistical and systematic
uncertainties of the data points.

The yields are compared with the predictions of three different
phenomenological models, namely Pythia8.2 with the Monash 2013 tune [37],
Pythia8.2 with ropes [24] and EPOS LHC [27]. Pythia is based on the Lund
string hadronisation model [50]. As shown in Ref. [18], Pythia8.2 with the
Monash 2013 tune cannot describe the strangeness enhancement with multiplicity
in $\mathrm{INEL>0}$ pp collisions: it underestimates the ratios between
strange hadron and pion yields and does not reproduce their increase with
multiplicity. The description is improved if overlapping strings are allowed
to interact with each other, forming the so-called “colour ropes" [24].
Indeed, Pythia8 with colour ropes can qualitatively describe the strangeness
enhancement with multiplicity in pp collisions, as shown in Ref. [18].
Finally, the EPOS LHC [27] event generator implements the core-corona model
[51], according to which strings in a low-density area form the corona and
hadronise normally, while strings in a high-density area form the core and
undergo collective hadronisation. As shown in Ref. [14], EPOS LHC can
reasonably well describe the $\mathrm{K^{0}_{S}}/\pi$ ratio measured in
$\mathrm{INEL>0}$ pp collisions, while it overestimates the strangeness
enhancement with multiplicity for the $\Lambda$, $\Xi^{\pm}$ and
$\Omega^{\pm}$ baryons.

The bottom panels of Figs. 6-7-8 display the ratios between the model
predictions and the cubic splines fitted to the data points. All the models
underestimate the full and the transverse-to-leading ${\rm K}^{0}_{\rm{S}}$
yields (Fig. 6). The underestimation is more significant at low multiplicity
($\langle\mathrm{d}N/\mathrm{d}\eta\rangle\sim 10$), where all models
underestimate the yields by about 30%. At high multiplicity
($\langle\mathrm{d}N/\mathrm{d}\eta\rangle\sim 30$), both Pythia8
implementations underestimate the yields by about 15%, while EPOS LHC predicts
values compatible with the measured ones. The increase with multiplicity of
the toward-leading yield of ${\rm K}^{0}_{\rm{S}}$ (Fig. 8) is not reproduced
by any of the three models: both Pythia8 implementations overestimate the
yields and show a hint of decrease with multiplicity, whereas EPOS LHC
predicts a decrease of the toward-leading yield with multiplicity. The
deviation of the models from the full and transverse-to-leading $\Xi^{\pm}$
yields (Fig. 7) is larger than the deviation from those of the ${\rm
K}^{0}_{\rm{S}}$ (Fig. 6). Both Pythia8 implementations underestimate the
yields: Pythia8 Monash underestimates them by approximately 70% over the whole
multiplicity interval, whereas Pythia8 with ropes underestimates them by about
50% at low multiplicity and 20% at high multiplicity. EPOS LHC underestimates
the yield at low multiplicity by about 50% and overestimates it by about 20%
at high multiplicity, predicting an increase of the transverse-to-leading and
full yields with multiplicity larger than the one observed in the data. The
increase with multiplicity of the $\Xi^{\pm}$ toward-leading yield (Fig. 8) is
not described by Pythia8 Monash, which predicts a nearly flat trend with
multiplicity. On the contrary, Pythia8 with ropes and EPOS LHC can
qualitatively reproduce the increasing trend. These models, however,
overestimate the toward-leading yields over the whole multiplicity interval.

The ratios between $\Xi^{\pm}$ and ${\rm K}^{0}_{\rm{S}}$ yields as a function
of $\langle\mathrm{d}N/\mathrm{d}\eta\rangle$ are shown in the top panel of
Fig. 9, together with the model predictions. In the data, the ratio of full
yields increases with multiplicity: this could be related to the larger
strangeness content of the $\Xi^{\pm}$ with respect to the ${\rm
K}^{0}_{\rm{S}}$. Indeed, the enhanced production of strange hadrons with
increasing multiplicity was observed to be higher for particles with larger
strangeness content [14]. The ratio of transverse-to-leading yields increases
with the multiplicity by a factor $(1.75\pm 0.16)$, with the error given by
the sum in quadrature of the statistical and systematic uncertainty
uncorrelated across multiplicity. It is compatible with the ratio of full
yields, because the full yield is dominated by transverse-to-leading
production, as shown in Figs. 6 and 7. Also the toward-leading ratio increases
with multiplicity: a flat behaviour with multiplicity is excluded since a
zero-degree polynomial is not able to describe the ratio within the
uncertainties uncorrelated across multiplicity. The increase of the toward-
leading ratio from the lowest to the highest multiplicity interval equals a
factor ($1.58\pm 0.15$). As shown by the double ratio between the toward-
leading and the transverse-to-leading $\Xi^{\pm}$/${\rm K}^{0}_{\rm{S}}$
ratios displayed in the bottom panel of Fig. 9, the toward-leading ratio is
approximately 40% smaller than the transverse-to-leading ratio, suggesting
that the production of $\Xi^{\pm}$ with respect to ${\rm K}^{0}_{\rm{S}}$ is
favoured in transverse-to-leading processes over the whole multiplicity
interval where the measurement was performed. The double ratio is well
described by a zero-degree polynomial with a $\chi^{2}/\mathrm{ndf}=6.6/7$,
indicating that the transverse-to-leading and toward-leading yield ratios
increase with multiplicity in a similar way.

The central panel of Fig. 9 displays the ratio between the model predictions
and the data points. Pythia8 Monash underestimates the ratios in the whole
multiplicity interval, due to the large underestimation of the full and
transverse-to-leading $\Xi^{\pm}$ yields and of the overestimation of the
${\rm K}^{0}_{\rm{S}}$ toward-leading yield. The toward-leading ratio does not
describe the increase observed in the data. The full and transverse-to-leading
ratios show instead an increase with multiplicity, which is smaller than the
one observed in the data, as suggested by the decrease of the model over data
ratio from about 0.5 at low multiplicity to about 0.4 at high multiplicity.
Pythia8 with ropes can qualitatively describe the increase of the ratios with
multiplicity observed in the data. However, the full and transverse-to-leading
ratios are underestimated in the whole multiplicity interval, and particularly
at low multiplicity, where the underestimation of the $\Xi^{\pm}$ yields is
larger. The toward-leading ratio is in qualitative agreement with the data,
but its increase with multiplicity is slightly overestimated: this fair
agreement is resulting from the overestimation of both the ${\rm
K}^{0}_{\rm{S}}$ and the $\Xi^{\pm}$ toward-leading yields. Finally, EPOS LHC
overestimates the increase with multiplicity of the full and transverse-to-
leading ratios, as a consequence of the overestimation of the increase with
multiplicity of $\Xi^{\pm}$ yields. In particular, the full and transverse-to-
leading ratios are underestimated by about 30% at low multiplicity and
overestimated by about 20% at high multiplicity. The toward-leading ratio is
instead overestimated in the whole multiplicity interval, mainly as a
consequence of the overestimation of the $\Xi^{\pm}$ toward-leading yield.
Moreover, its increase with multiplicity is larger than the one observed in
the data because the ${\rm K}^{0}_{\rm{S}}$ toward-leading yields predicted by
EPOS LHC decrease with multiplicity. As shown in the bottom panel of Fig. 9,
the three models predict a larger double ratio than the one measured in the
data, i.e. they overestimate the toward-leading $\Xi^{\pm}$/${\rm
K}^{0}_{\rm{S}}$ production with respect to the transverse-to-leading one. The
double ratios predicted by Pythia8 with ropes and EPOS LHC are smaller than
unity and can be described with a zero-degree polynomial. On the contrary, the
double ratio predicted by Pythia8 Monash is compatible with one in the lowest
multiplicity class and decreases to about 0.8 in the highest multiplicity
class.

Figure 9:  Top panel: full (blue), transverse-to-leading (green) and toward-
leading (red) $\Xi^{\pm}$/${\rm K}^{0}_{\rm{S}}$ yield ratios as a function of
the charged-particle multiplicity measured at midrapidity in events with a
trigger particle. The data points are drawn with markers, and their
statistical and systematic uncertainties are shown by error bars and empty
boxes, respectively. Shadowed boxes represent systematic uncertainties
uncorrelated across multiplicity. The model predictions are drawn with lines
of different styles. The width of the bands represents the sum in quadrature
of statistical and systematic uncertainties of the model predictions, and is
visible only for toward-leading production. Central panel: ratio between the
model predictions and the cubic spline fitted to the data points. The shaded
band around unity represents the sum in quadrature of the statistical and
systematic uncertainties of the data points. Bottom panel: double ratio
between the toward-leading and the transverse-to-leading $\Xi^{\pm}$/${\rm
K}^{0}_{\rm{S}}$ ratio.

The comparison of the Monte Carlo model predictions with the data suggests
that none of the considered models describes strange hadron production in hard
scattering processes or in the underlying event.

##  5 Summary and outlook

The production of ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ in pp collisions at
$\sqrt{s}=5.02$ TeV and at $\sqrt{s}=13$ TeV was measured in the direction of
the highest-$p_{\rm T}$ charged particle (trigger particle) and in the
direction transverse to it. The toward-leading $p_{\rm T}$ spectra are harder
than the transverse-to-leading ones, as expected from the fact that the
production in the direction of the trigger particle is associated with hard
scattering processes, whereas the production in the transverse-to-leading
direction is related to the underlying event.

The $p_{\rm T}$-integrated yields per unit $\Delta\eta\Delta\varphi$ of ${\rm
K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ are dominated by transverse-to-leading
production and increase with the multiplicity of charged particles produced at
midrapidity. The toward-leading yields show instead a milder dependence on the
multiplicity, indicating that the contribution of transverse-to-leading
processes relative to toward-leading ones increases with the multiplicity. The
${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ yields do not show any significant
centre-of-mass energy dependence.

The ratio between the $\Xi^{\pm}$ and the ${\rm K}^{0}_{\rm{S}}$ yields
provides insight into the strangeness enhancement effect, since the
strangeness content of the $\Xi^{\pm}$ ($|S|$=2) is larger than the ${\rm
K}^{0}_{\rm{S}}$ one ($|S|$=1). Both the transverse-to-leading and the toward-
leading $\Xi^{\pm}$/${\rm K}^{0}_{\rm{S}}$ yield ratios increase with the
multiplicity of charged particles. The transverse-to-leading ratio is larger
than the toward-leading one, suggesting that the relative production of
$\Xi^{\pm}$ with respect to ${\rm K}^{0}_{\rm{S}}$ is favoured in transverse-
to-leading processes.

None of the considered models, namely Pythia8 Monash tune, Pythia8 with ropes
and EPOS LHC, can quantitatively describe the transverse-to-leading and
toward-leading yields of ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$. Both Pythia8
implementations underestimate the full and the transverse-to-leading ${\rm
K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ yields, with the largest underestimation
observed for the $\Xi^{\pm}$ yields. The increase of the full and transverse-
to-leading $\Xi^{\pm}$ yields with multiplicity is overestimated by both
Pythia8 with ropes and EPOS LHC, leading to an overestimation of the increase
of the full and transverse-to-leading $\Xi^{\pm}$/${\rm K}^{0}_{\rm{S}}$ yield
ratios with multiplicity. The increase of the toward-leading yield of ${\rm
K}^{0}_{\rm{S}}$ with multiplicity is not reproduced by any of the three
models. On the contrary, the increase of the $\Xi^{\pm}$ toward-leading yield
with multiplicity is qualitatively reproduced by Pythia8 with ropes and EPOS
LHC, while Pythia8 Monash predicts a flat trend with multiplicity. Overall,
the comparison with the data indicates that the strange hadron production
associated with both hard scattering processes and the underlying event is not
properly described by any of the considered models. Additionally, other models
such as the most recent implementation of the core-corona approach EPOS4 [52]
could be tested.

Further investigation of the origin of the enhanced production of strange
hadrons in high-multiplicity pp collisions with respect to low-multiplicity
ones will be possible thanks to the huge sample of pp collisions that is being
collected during the ongoing Run 3, which is expected to be three orders of
magnitude larger than the Run 2 one. With Run 3 data, the study of the
dependence of the toward-leading and transverse-to-leading $\Xi^{\pm}$ yields
on the minimum $p_{\rm T}$ of the trigger particle and the measurement of the
toward-leading and transverse-to-leading $\Omega^{\pm}$ yields as a function
of the charged-particle multiplicity will become feasible and will help
improve the current understanding of strange hadron production mechanisms.

## 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; 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; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education, 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 Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, 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) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), 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: Czech Science Foundation (grant no. 23-07499S), Czech Republic; European Research Council (grant no. 950692), European Union; ICSC - Centro Nazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, European Union - NextGenerationEU; 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 86, A. Agarwal135, G. Aglieri Rinella 32, L.
Aglietta24, M. Agnello 29, N. Agrawal 25, Z. Ahammed 135, S. Ahmad 15, S.U.
Ahn 71, I. Ahuja 37, A. Akindinov 141, V. Akishina38, M. Al-Turany 97, D.
Aleksandrov 141, B. Alessandro 56, H.M. Alfanda 6, R. Alfaro Molina 67, B. Ali
15, A. Alici 25, N. Alizadehvandchali 116, A. Alkin 104, J. Alme 20, G. Alocco
52, T. Alt 64, A.R. Altamura 50, I. Altsybeev 95, J.R. Alvarado 44, M.N. Anaam
6, C. Andrei 45, N. Andreou 115, A. Andronic 126, E. Andronov 141, V. Anguelov
94, F. Antinori 54, P. Antonioli 51, N. Apadula 74, L. Aphecetche 103, H.
Appelshäuser 64, C. Arata 73, S. Arcelli 25, M. Aresti 22, R. Arnaldi 56,
J.G.M.C.A. Arneiro 110, I.C. Arsene 19, M. Arslandok 138, A. Augustinus 32, R.
Averbeck 97, M.D. Azmi 15, H. Baba124, A. Badalà 53, J. Bae 104, Y.W. Baek 40,
X. Bai 120, R. Bailhache 64, Y. Bailung 48, R. Bala 91, A. Balbino 29, A.
Baldisseri 130, B. Balis 2, D. Banerjee 4, Z. Banoo 91, V. Barbasova37, F.
Barile 31, L. Barioglio 56, M. Barlou78, B. Barman41, G.G. Barnaföldi 46, L.S.
Barnby 115, E. Barreau 103, V. Barret 127, L. Barreto 110, C. Bartels 119, K.
Barth 32, E. Bartsch 64, N. Bastid 127, S. Basu 75, G. Batigne 103, D.
Battistini 95, B. Batyunya 142, D. Bauri47, J.L. Bazo Alba 101, I.G. Bearden
83, C. Beattie 138, P. Becht 97, D. Behera 48, I. Belikov 129, A.D.C. Bell
Hechavarria 126, F. Bellini 25, R. Bellwied 116, S. Belokurova 141, L.G.E.
Beltran 109, Y.A.V. Beltran 44, G. Bencedi 46, A. Bensaoula116, S. Beole 24,
Y. Berdnikov 141, A. Berdnikova 94, L. Bergmann 94, M.G. Besoiu 63, L. Betev
32, P.P. Bhaduri 135, A. Bhasin 91, B. Bhattacharjee 41, L. Bianchi 24, N.
Bianchi 49, J. Bielčík 35, J. Bielčíková 86, A.P. Bigot 129, A. Bilandzic 95,
G. Biro 46, S. Biswas 4, N. Bize 103, J.T. Blair 108, D. Blau 141, M.B.
Blidaru 97, N. Bluhme38, C. Blume 64, G. Boca 21,55, F. Bock 87, T. Bodova 20,
J. Bok 16, L. Boldizsár 46, M. Bombara 37, P.M. Bond 32, G. Bonomi 134,55, H.
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24, Y.E.M. Bouziani 64, L. Bratrud 64, P. Braun-Munzinger 97, M. Bregant 110,
M. Broz 35, G.E. Bruno 96,31, V.D. Buchakchiev 36, M.D. Buckland 23, D.
Budnikov 141, H. Buesching 64, S. Bufalino 29, P. Buhler 102, N. Burmasov 141,
Z. Buthelezi 68,123, A. Bylinkin 20, S.A. Bysiak107, J.C. Cabanillas Noris
109, M.F.T. Cabrera116, M. Cai 6, H. Caines 138, A. Caliva 28, E. Calvo Villar
101, J.M.M. Camacho 109, P. Camerini 23, F.D.M. Canedo 110, S.L. Cantway 138,
M. Carabas 113, A.A. Carballo 32, F. Carnesecchi 32, R. Caron 128, L.A.D.
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Cattaruzzi 23, C. Ceballos Sanchez 142, R. Cerri24, I. Chakaberia 74, P.
Chakraborty 136,47, S. Chandra 135, S. Chapeland 32, M. Chartier 119, S.
Chattopadhay135, S. Chattopadhyay 135, S. Chattopadhyay 99, M. Chen39, T.
Cheng 97,6, C. Cheshkov 128, V. Chibante Barroso 32, D.D. Chinellato 111, E.S.
Chizzali II,95, J. Cho 58, S. Cho 58, P. Chochula 32, Z.A. Chochulska136, D.
Choudhury41, P. Christakoglou 84, C.H. Christensen 83, P. Christiansen 75, T.
Chujo 125, M. Ciacco 29, C. Cicalo 52, M.R. Ciupek97, G. ClaiIII,51, F.
Colamaria 50, J.S. Colburn100, D. Colella 31, M. Colocci 25, M. Concas 32, G.
Conesa Balbastre 73, Z. Conesa del Valle 131, G. Contin 23, J.G. Contreras 35,
M.L. Coquet 103,130, P. Cortese 133,56, M.R. Cosentino 112, F. Costa 32, S.
Costanza 21,55, C. Cot 131, J. Crkovská 94, P. Crochet 127, R. Cruz-Torres 74,
P. Cui 6, M.M. Czarnynoga136, A. Dainese 54, G. Dange38, M.C. Danisch 94, A.
Danu 63, P. Das 80, P. Das 4, S. Das 4, A.R. Dash 126, S. Dash 47, A. De Caro
28, G. de Cataldo 50, J. de Cuveland38, A. De Falco 22, D. De Gruttola 28, N.
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L. Dello Stritto 32, W. Deng 6, K.C. Devereaux18, P. Dhankher 18, D. Di Bari
31, A. Di Mauro 32, B. Diab 130, R.A. Diaz 142,7, T. Dietel 114, Y. Ding 6, J.
Ditzel 64, R. Divià 32, Ø. Djuvsland20, U. Dmitrieva 141, A. Dobrin 63, B.
Dönigus 64, J.M. Dubinski 136, A. Dubla 97, P. Dupieux 127, N. Dzalaiova13,
T.M. Eder 126, R.J. Ehlers 74, F. Eisenhut 64, R. Ejima92, D. Elia 50, B.
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Evdokimov 141, L. Fabbietti 95, M. Faggin 23, J. Faivre 73, F. Fan 6, W. Fan
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141, F.M. Fionda 52, E. Flatland32, F. Flor 138,116, A.N. Flores 108, S.
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Fusayasu 98, J.J. Gaardhøje 83, M. Gagliardi 24, A.M. Gago 101, T. Gahlaut47,
C.D. Galvan 109, D.R. Gangadharan 116, P. Ganoti 78, C. Garabatos 97, J.M.
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H.M. Gaur38, A. Gautam 118, M.B. Gay Ducati 66, M. Germain 103, C. Ghosh135,
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H. Helstrup 34, M. Hemmer 64, T. Herman 35, S.G. Hernandez116, G. Herrera
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B. Hippolyte 129, F.W. Hoffmann 70, B. Hofman 59, G.H. Hong 139, M. Horst 95,
A. Horzyk 2, Y. Hou 6, P. Hristov 32, P. Huhn64, L.M. Huhta 117, T.J. Humanic
88, A. Hutson 116, D. Hutter 38, M.C. Hwang 18, R. Ilkaev141, M. Inaba 125,
G.M. Innocenti 32, M. Ippolitov 141, A. Isakov 84, T. Isidori 118, M.S. Islam
99, S. Iurchenko141, M. Ivanov13, M. Ivanov 97, V. Ivanov 141, K.E. Iversen
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119, J.M. Jowett 32,97, J. Jung 64, M. Jung 64, A. Junique 32, A. Jusko 100,
J. Kaewjai105, P. Kalinak 60, A. Kalweit 32, A. Karasu Uysal V,72, D.
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Y. Kharlov 141, A. Khatun 118, A. Khuntia 35, Z. Khuranova 64, B. Kileng 34,
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35, E. Kryshen 141, V. Kučera 58, C. Kuhn 129, P.G. Kuijer 84, T. Kumaoka125,
D. Kumar135, L. Kumar 90, N. Kumar90, S. Kumar 31, S. Kundu 32, P. Kurashvili
79, A. Kurepin 141, A.B. Kurepin 141, A. Kuryakin 141, S. Kushpil 86, V.
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Langoy 121, P. Larionov 32, E. Laudi 32, L. Lautner 32,95, R.A.N. Laveaga109,
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M.M. Lesch 95, E.D. Lesser 18, P. Lévai 46, M. Li6, X. Li10, B.E. Liang-gilman
18, J. Lien 121, R. Lietava 100, I. Likmeta 116, B. Lim 24, S.H. Lim 16, V.
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Q.W. Malik19, S.K. Malik 91, L. Malinina I,VIII,142, D. Mallick 131, N.
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## Affiliation Notes

I Deceased
II Also at: Max-Planck-Institut fur Physik, Munich, Germany
III Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
IV Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
V Also at: Yildiz Technical University, Istanbul, Türkiye
VI Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
VII Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VIII 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 Krakow, 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 Creighton University, Omaha, Nebraska, United States
15 Department of Physics, Aligarh Muslim University, Aligarh, India
16 Department of Physics, Pusan National University, Pusan, Republic of Korea
17 Department of Physics, Sejong University, Seoul, Republic of Korea
18 Department of Physics, University of California, Berkeley, California,
United States
19 Department of Physics, University of Oslo, Oslo, Norway
20 Department of Physics and Technology, University of Bergen, Bergen, Norway
21 Dipartimento di Fisica, Università di Pavia, Pavia, Italy
22 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy
23 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy
24 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy
25 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy
26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy
27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy
28 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy
29 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy
30 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy
31 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy
32 European Organization for Nuclear Research (CERN), Geneva, Switzerland
33 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia
34 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway
35 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic
36 Faculty of Physics, Sofia University, Sofia, Bulgaria
37 Faculty of Science, P.J. Šafárik University, Košice, Slovak Republic
38 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany
39 Fudan University, Shanghai, China
40 Gangneung-Wonju National University, Gangneung, Republic of Korea
41 Gauhati University, Department of Physics, Guwahati, India
42 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany
43 Helsinki Institute of Physics (HIP), Helsinki, Finland
44 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico
45 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania
46 HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
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 Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France
74 Lawrence Berkeley National Laboratory, Berkeley, California, United States
75 Lund University Department of Physics, Division of Particle Physics, Lund,
Sweden
76 Nagasaki Institute of Applied Science, Nagasaki, Japan
77 Nara Women’s University (NWU), Nara, Japan
78 National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece
79 National Centre for Nuclear Research, Warsaw, Poland
80 National Institute of Science Education and Research, Homi Bhabha National
Institute, Jatni, India
81 National Nuclear Research Center, Baku, Azerbaijan
82 National Research and Innovation Agency - BRIN, Jakarta, Indonesia
83 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
84 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands
85 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
86 Nuclear Physics Institute of the Czech Academy of Sciences, Husinec-Řež,
Czech Republic
87 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
88 Ohio State University, Columbus, Ohio, United States
89 Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia
90 Physics Department, Panjab University, Chandigarh, India
91 Physics Department, University of Jammu, Jammu, India
92 Physics Program and International Institute for Sustainability with Knotted
Chiral Meta Matter (SKCM2), Hiroshima University, Hiroshima, Japan
93 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany
94 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
95 Physik Department, Technische Universität München, Munich, Germany
96 Politecnico di Bari and Sezione INFN, Bari, Italy
97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Darmstadt, Germany
98 Saga University, Saga, Japan
99 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata,
India
100 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom
101 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru
102 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
103 SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France
104 Sungkyunkwan University, Suwon City, Republic of Korea
105 Suranaree University of Technology, Nakhon Ratchasima, Thailand
106 Technical University of Košice, Košice, Slovak Republic
107 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland
108 The University of Texas at Austin, Austin, Texas, United States
109 Universidad Autónoma de Sinaloa, Culiacán, Mexico
110 Universidade de São Paulo (USP), São Paulo, Brazil
111 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
112 Universidade Federal do ABC, Santo Andre, Brazil
113 Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti,
Bucharest, Romania
114 University of Cape Town, Cape Town, South Africa
115 University of Derby, Derby, United Kingdom
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 Universität Münster, Institut für Kernphysik, Münster, Germany
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 Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
132 Università degli Studi di Foggia, Foggia, Italy
133 Università del Piemonte Orientale, Vercelli, Italy
134 Università di Brescia, Brescia, Italy
135 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata,
India
136 Warsaw University of Technology, Warsaw, Poland
137 Wayne State University, Detroit, Michigan, United States
138 Yale University, New Haven, Connecticut, United States
139 Yonsei University, Seoul, Republic of Korea
140 Zentrum für Technologie und Transfer (ZTT), Worms, Germany
141 Affiliated with an institute covered by a cooperation agreement with CERN
142 Affiliated with an international laboratory covered by a cooperation
agreement with CERN.