2022 218 18 October

Production of strange particles in jets and the UE in pp and p–Pb collisions

ALICE CollaborationALICE Collaboration

The production of strange hadrons (${\rm K}^{0}_{\rm{S}}$, ${\Lambda}$,
$\Xi^{\pm}$, and $\Omega^{\pm}$), baryon-to-meson ratios (${\Lambda}/{\rm
K}^{0}_{\rm{S}}$, $\Xi/{\rm K}^{0}_{\rm{S}}$, and $\Omega/{\rm
K}^{0}_{\rm{S}}$), and baryon-to-baryon ratios ($\Xi/{\Lambda}$,
$\Omega/{\Lambda}$, and $\Omega/\Xi$) associated with jets and the underlying
event were measured as a function of transverse momentum ($p_{\rm T}$) in pp
collisions at $\sqrt{s}=13$ TeV and p$-$Pb collisions at $\sqrt{s_{\rm
NN}}=5.02$ TeV with the ALICE detector at the LHC. The inclusive production of
the same particle species and the corresponding ratios are also reported. The
production of multi-strange hadrons, $\Xi^{\pm}$ and $\Omega^{\pm}$, and their
associated particle ratios in jets and in the underlying event are measured
for the first time. In both pp and p–Pb collisions, the baryon-to-meson and
baryon-to-baryon yield ratios measured in jets differ from the inclusive
particle production for low and intermediate hadron $p_{\rm T}$ (0.6$-$6
GeV/$c$). Ratios measured in the underlying event are in turn similar to those
measured for inclusive particle production. In pp collisions, the particle
production in jets is compared with $\textsc{Pythia}8$ predictions with three
colour-reconnection implementation modes. None of them fully reproduces the
data in the measured hadron transverse momentum region. The maximum deviation
is observed for $\Xi^{\pm}$ and $\Omega^{\pm}$ which reaches a factor of about
six. The event multiplicity dependence is further investigated in p$-$Pb
collisions. In contrast to what is observed in the underlying event, there is
no significant event-multiplicity dependence for particle production in jets.
The presented measurements provide novel constraints on hadronisation and its
Monte Carlo description. In particular, they demonstrate that the
fragmentation of jets alone is insufficient to describe the strange and multi-
strange particle production in hadronic collisions at LHC energies.

##  1 Introduction

High-energy heavy-ion collisions at the LHC create a hot and dense form of
matter called quark$-$gluon plasma (QGP) [1, 2, 3, 4, 5, 6]. The droplet of
QGP created in the collision rapidly expands as a strongly-coupled liquid and
cools down until a temperature near the phase transition at which the
deconfined partons hadronise into ordinary colour-neutral matter [7, 8, 9].
Systematic studies of particle production, transverse momentum spectra and
correlations of identified particles allow to investigate the properties of
the partonic phase and the hadronisation process itself.

The interpretation of heavy-ion results (with hot nuclear matter effects) and
extraction of the QGP properties require studies of particle production in
small collision systems, proton–proton (pp) and proton–nucleus (pA).
Previously, the measurements in these small collision systems were thought of
as a necessary foundation to quantify the initial and final state effects of
the so-called cold nuclear matter. However, during the last decade, the study
of small systems has gained increased interest as a research field in its own
right. In particular, similar effects as those present in heavy-ion collisions
have been observed in pp and p–Pb collisions where the formation of a QGP was
not expected [10, 11, 12, 13, 14, 15, 16]. These include, for example, the
long-range angular correlations [10, 11, 12] and the non-vanishing elliptic
flow coefficient measured using multi-particle cumulant analyses [14, 13]. The
magnitude of these effects increases smoothly with system size and particle
multiplicity from pp, p–Pb to Pb–Pb collisions. Another new feature observed
in high-multiplicity pp and p–Pb collisions is the enhancement of the baryon-
to-meson yield ratios, p$/\pi$ and $\Lambda/{\rm K}^{0}_{\rm{S}}$, at
intermediate transverse momentum $p_{\rm T}$ ($2$–$6$ GeV/$c$) [17, 18, 19,
20], which is qualitatively similar to that observed in Pb–Pb collisions.
Moreover, the strange to non-strange hadron ratio increases continuously as a
function of charged-particle multiplicity density from low-multiplicity pp to
high-multiplicity p–Pb collisions to eventually reach the values observed in
Pb–Pb collisions [21, 20, 18]. These findings suggest the possible existence
of a common underlying mechanism which would determine the chemical
composition of particles produced from small to large collision systems. On
the other hand, measurements of jet production at midrapidity in small systems
do not exhibit nuclear modifications [22, 23, 24, 25, 26, 27, 28, 29].

The enhancement of baryon-to-meson yield ratios in the intermediate $p_{\rm
T}$ region has been related to the interplay of radial flow and parton
recombination [30, 31, 6]. In a recent study, the ALICE Collaboration
investigated baryon-to-meson yield ratios in two separate parts of the event –
inside a jet and in the event portion perpendicular to the jet cone – in pp
collisions at $\sqrt{s}=7$ and $13$ TeV and p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV [32, 33]. The results show that the
enhancement of the $\Lambda/{\rm K}^{0}_{\rm{S}}$ ratio at intermediate
$p_{\rm T}$ obtained from inclusive particle production measurements in Pb–Pb
collisions at $\sqrt{s}~{}=~{}2.76$ TeV [19] and in high-multiplicity pp
collisions [34] is not present in the low-$z$ fragmentation products of jets.
In addition to these effects, one can expect that particle production in this
$p_{\rm T}$ region results from the hard fragmentation of partons of $p_{\rm
T}$ in the $4$–$8$ GeV/$c$ range (momentum fraction $z=p_{\rm T}^{\rm
hadron}/p_{\rm T}^{\rm parton}\approx 0.5$). This is due to the steeply
falling power-law spectrum characteristic for parton production. This so-
called “leading particle effect” was described in terms of a “trigger bias”
[35]. Studying the yield ratios of particles associated with jets allows us to
explore a larger $z$ range, providing new constraints on whether the baryon-
to-meson yield ratio enhancement originates from jet fragmentation.

In this article, the $p_{\rm T}$-differential baryon-to-meson and multi-
strange-to-strange particle ratios are studied in jets reconstructed using the
charged-particle component (charged-particle jets) and in the underlying event
associated to jets. This provides further understanding of the contribution of
soft and hard processes to the enhancement of the baryon-to-meson yield ratios
at intermediate $p_{\rm T}$ and of the strange particle yields as a function
of multiplicity in small systems. In particular, the measurement of the
production of ${\rm K}^{0}_{\rm{S}}$, $\Lambda$ ($\overline{\Lambda}$),
$\Xi^{\pm}$, and $\Omega^{\pm}$ in charged-particle jets and in the underlying
event in pp collisions at $\sqrt{s}~{}=~{}13$ TeV and p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV is reported. Strange particles are
reconstructed in the pseudorapidity range $|\eta|<0.75$. Jets are
reconstructed with a transverse momentum $p_{\rm T,jet}^{\rm ch}>10$ GeV/$c$
and in the pseudorapidity range $\left|\eta_{\rm jet}\right|<0.35$ with a
resolution parameter $R=0.4$ (referred to as jet radius in the following). The
strange particles produced inside a jet are characterised as a function of the
distance between the particle momentum vector and the jet axis in the
$\eta$–$\varphi$ plane, where $\varphi$ is the azimuthal angle.

The results presented in this article surpass the precision of the previous
ALICE $p_{\rm T}$-differential measurements [32] both in pp at $\sqrt{s}=7$
TeV and p–Pb at $\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV collisions. The
studies are extended to the multi-strange sector and the charged-particle
multiplicity dependence is investigated as well. The baryon-to-meson and
baryon-to-baryon yield ratios inside jets are compared to the same ratios
obtained from inclusive events and the underlying event. Results measured in
pp collisions are compared with Pythia $8$ [36] simulations.

The article is structured as follows. In Section 2, the ALICE apparatus and
the data samples used for the analysis are presented. In Section 3, the
methods adopted for charged-particle jet reconstruction, strange particle
reconstruction, and particle–jet matching are described. This section also
includes the estimate of the associated systematic uncertainties. The
measurement of strange hadron $p_{\rm T}$ distributions and the corresponding
yield ratios, together with their comparison with model predictions, are
presented and discussed in Section 4. The paper is summarized in Section 5.

##  2 ALICE detector and data selection

The ALICE apparatus and its performance are described in Refs. [37, 38]. This
analysis mainly relies on the central barrel tracking system and the forward
V0 detector [39]. The central barrel detectors used for this analysis are the
Inner Tracking System (ITS) [40], the Time Projection Chamber (TPC) [41], and
the Time-Of-Flight detector (TOF) [42, 43, 44]. These detectors cover the
pseudorapidity region $|\eta|<0.9$ and are located inside a large solenoidal
magnet providing a 0.5 T magnetic field.

The ITS, the innermost barrel detector, consists of six cylindrical layers of
high spatial resolution silicon detectors using three different technologies.
The two innermost layers (Silicon Pixel Detector) are based on silicon pixel
technology and cover $|\eta|<2.0$ and $|\eta|<1.4$, respectively. The SPD is
used to reconstruct the primary vertex of the collision and short track
segments, which are called "tracklets". The four outer ITS layers consist of
silicon drift (SDD) and strip (SSD) detectors, with the innermost (outermost)
layer having a radius $r=4$ $(43)$ cm. The SDD and SSD are able to measure the
specific ionization energy loss ($\textrm{d}E/\textrm{d}x$) with a relative
resolution of about $10\%$ in the low-$p_{\rm T}$ region (up to $\sim 1$
GeV/$c$) [40]. The ITS is also used to reconstruct and identify low-momentum
particles down to $100$ MeV/$c$ that cannot reach the TPC.

The TPC is a large cylindrical gaseous detector filled with a Ne-CO2 gas
mixture. The radial and longitudinal dimensions of the TPC are about
$85<r<250$ cm and $-250<z<250$ cm, respectively. As the main tracking device,
the TPC provides full azimuthal acceptance for tracks in the region
$|\eta|<0.9$. In addition, it provides charged-hadron identification via the
$\textrm{d}E/\textrm{d}x$ measurement. At low $p_{\rm T}$, the
$\textrm{d}E/\textrm{d}x$ resolution of $5.2\%$ for a minimum ionizing
particle allows track-by-track particle identification [41]. On the other
hand, at intermediate and high $p_{\rm T}$ ($\gtrsim 2.0$ GeV/$c$), the energy
loss distributions of different particle species start to overlap. Therefore,
from there on, particles have to be statistically separated via a multi-
Gaussian fit to the $\textrm{d}E/\textrm{d}x$ distributions.

The TOF, located at a radius of 3.7 m, outside of the TPC, measures the flight
time of the particles. It consists of a cylindrical array of multi-gap
resistive plate chambers with an intrinsic time resolution of $50$ ps. It
covers the range $\left|\eta\right|<0.9$ with full azimuthal acceptance. It
can provide particle identification over a broad $p_{\rm T}$ range
($0.5\lesssim p_{\rm T}\lesssim 2.7$ GeV/$c$). The total time-of-flight
resolution, including the collision time resolution, is about $90$ ps in pp
and p–Pb collisions [34]. The V0 detector, composed of two scintillator
arrays, V0A (covering a pseudorapidity range of $2.8<\eta<5.1$) and V0C
($-3.7<\eta<-1.7$), is utilized for triggering and event classification based
on charged-particle multiplicity.

Data from pp collisions at $\sqrt{s}~{}=~{}13$ TeV and from p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV are used in this analysis. The pp and
p–Pb data samples were recorded with the ALICE detector in $2016$–$2017$ and
$2016$, respectively. These data were collected with a minimum bias (MB)
trigger requiring at least one hit in both V0A and V0C in coincidence with the
bunch crossing.

Interaction vertices are reconstructed by the extrapolation of ITS tracklets
towards the average beam line. Pileup events, due to multiple interactions in
the triggered bunch crossing, are removed by exploiting the correlation
between the number of SPD hits and tracklets. The coordinate of the primary
vertex along the beam direction is required to be within $\pm 10$ cm with
respect to the nominal position of the ALICE interaction point. After event
selection, the pp sample consists of $1.5$ billion events. The integrated
luminosity of $\mathcal{L}_{\rm int}=9.38\pm 0.47$ nb-1 based on the visible
cross section observed by the V0 trigger was extracted from a van der Meer
scan [45]. About $500$ million events from the p–Pb samples were selected,
which correspond to an integrated luminosity of $\mathcal{L}_{\rm int}=295\pm
11$ $\mu{\rm b}^{-1}$ [46]. The p–Pb events are divided into three
multiplicity classes based on the total charge deposited in the V0A (in the
Pb-going direction). The multiplicity intervals and their corresponding mean
charged-particle density ($\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$) measured
at midrapidity ($\left|\eta\right|<0.5$) are given in Ref. [47].

##  3 Analysis

###  3.1 Charged-particle jet reconstruction

The charged-particle jets are reconstructed using the FastJet package [48]
with the anti-$k_{\rm T}$ algorithm [49] with a resolution parameter $R=0.4$.
Charged particles, which are used as input for jet reconstruction, are
reconstructed by using the ITS and TPC information. Tracks with $p_{\rm
T}>0.15$ GeV/$c$ are accepted over the pseudorapidity range $\left|\eta_{\rm
trk}\right|<0.9$ and with azimuthal angle $0<\varphi<2\pi$.

The reconstructed jet axis pseudorapidity is required to be in the range
$\left|\eta_{\rm jet}\right|<0.35$. This condition ensures that the jet cone
is fully contained within the $\eta$-acceptance for strange particles. A
selection on the charged-particle jet $p_{\rm T}$, $p_{\rm T,jet}^{\rm ch}>10$
GeV/$c$, is applied to ensure that the jet originates from the hard scattering
process [32].

In a hadron–hadron collider event, the two outgoing partons from the hard
scattering are accompanied by particles that arise, e.g. from beam–beam
remnants and multiple parton interactions, which form a background for the jet
production measurement. In pp collisions, the $p_{\rm T}$ density per unit
area in the $\eta$–$\varphi$ plane ($\rho_{\rm bkg}^{\rm ch}$) of this
background is determined from the $k_{\rm T}$ algorithm [50, 51] to be around
$1$ GeV/$c$ rad-1, which is negligible and, hence, not subtracted in this
analysis. Since the background density is larger in p–Pb collisions, the
reconstructed $p_{\rm T}$ of the jet is corrected for the background
contribution [52] using the formula

$p_{\rm T,jet}^{\rm ch}=p_{\rm T,jet}^{\rm rec}-\rho_{\rm bkg}^{\rm ch}\times
A_{\rm jet},$ (1)

where $p_{\rm T,jet}^{\rm rec}$ is the reconstructed jet $p_{\rm T}$ and
$A_{\rm jet}$ is the jet area. $A_{\rm jet}$ is calculated by the active ghost
area method of FastJet, with a ghost area of $0.005$ [53]. The estimation of
the background density $\rho_{\rm bkg}^{\rm ch}$ in sparse systems such as
p–Pb collisions is based on the method described in Ref. [54]. This method
allows to circumvent problems arising from the use of ghost jets applicable to
larger collision systems [54]. Under this method, empty areas are instead
accounted for by applying a correction factor to the background density as
follows

$\rho_{\rm bkg}^{\rm ch}=C\times{\rm median}\left\\{\frac{p_{\rm T,jet}^{\rm
rec}}{A_{\rm jet}}\right\\},~{}{\rm with}~{}C=\frac{\sum_{i}A_{i}}{A_{\rm
acc}},$ (2)

where $A_{i}$ is the area of each $k_{\rm T}$ jet with at least one real
track, i.e. excluding ghosts and $A_{\rm acc}$ is the area of the charged-
particle acceptance, namely $(2\times 0.9)\times 2\pi$. The background
estimate is made more accurate by excluding the two clusters with the largest
$p_{\rm T}$ from the $\rho_{\rm bkg}$ calculation as given by Eq. (2).

Figure 1: Invariant mass distribution for ${\rm K}^{0}_{\rm{S}}$, $\Lambda$,
$\Xi^{-}$, and $\Omega^{-}$ in different $p_{\rm T}$ intervals in MB p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV. The candidates are
reconstructed in $|\eta|<0.75$. The grey areas are used to determine the
background (red dashed lines), see text for details.

###  3.2 Strange particle reconstruction

The strange particles ${\rm K}^{0}_{\rm{S}}$, $\Lambda$, $\overline{\Lambda}$,
$\Xi^{\pm}$, and $\Omega^{\pm}$ are measured at midrapidity
($\left|\eta\right|<0.75$) via the reconstruction of their specific weak decay
topology. The following charged decay channels with the corresponding
branching ratios ($B.R.$) [55] are used:

$\displaystyle{\rm K}^{0}_{\rm{S}}$ $\displaystyle\to\pi^{+}+\pi^{-}$
$\displaystyle B.R.$ $\displaystyle=(69.20\pm 0.05)\%,$
$\displaystyle\Lambda(\overline{\Lambda})$
$\displaystyle\to\mathrm{p}(\rm\overline{p})+\pi^{-}(\pi^{+})$ $\displaystyle
B.R.$ $\displaystyle=(63.9\pm 0.5)\%,$
$\displaystyle\Xi^{-}(\overline{\Xi}^{+})$
$\displaystyle\to\Lambda(\overline{\Lambda})+\pi^{-}(\pi^{+})$ $\displaystyle
B.R.$ $\displaystyle=(99.887\pm 0.035)\%,$
$\displaystyle\Omega^{-}(\overline{\Omega}^{+})$
$\displaystyle\to\Lambda(\overline{\Lambda})+\rm{K}^{-}(\rm{K}^{+})$
$\displaystyle B.R.$ $\displaystyle=(67.8\pm 0.7)\%.$

The proton, pion, and kaon tracks (daughter tracks) are identified via their
measured energy deposition in the TPC [38]. The identification of the ${\rm
V}^{0}$ candidates (${\rm K}^{0}_{\rm{S}}$ and $\Lambda$
($\overline{\Lambda}$) that decay into two oppositely charged daughter
particles) and cascade candidates ($\Xi^{\pm}$ and $\Omega^{\pm}$ that decay
into a bachelor charged meson plus a ${\rm V}^{0}$ decaying particle, giving
the cascade decay topology) follow those presented in earlier ALICE
publications [56, 57, 17, 21, 34, 58]. In addition, the contributions of
pileup collisions outside the trigger bunch crossing (“out-of-bunch pileup”)
are removed. This is achieved by requiring that at least one of the charged
decay tracks matches a hit in a “fast” detector (either the ITS or the TOF
detector). The selections in this analysis are summarized in Tables 5, 6 in
Appendix A.

The signal extraction is performed as a function of $p_{\rm T}$. The invariant
mass distribution in each $p_{\rm T}$ interval is fitted with a Gaussian
function for the signal and a linear function for the combinatorial
background. Examples of the invariant mass distribution fits for all particles
are shown in Fig. 1. This allows for the extraction of the mean ($\mu$) and
width ($\sigma$) of the signal. The “peak” region is defined as that within
$\pm 6\sigma$ for ${\rm V}^{0}$s and $\pm 3\sigma$ ($\pm 4\sigma$) for
cascades in pp (and p–Pb) collisions with respect to $\mu$ for each $p_{\rm
T}$ interval. The “background” regions are defined on both sides of the peak
region (see the gray areas in Fig. 1). The $p_{\rm T}$-differential yields of
strange particles are obtained by subtracting the integral of the background
fit function in the peak region from the total bin count in the same region
(see Ref. [56] for the details).

###  3.3 Matching of strange particles to jets

The strategy for obtaining strange hadrons associated to hard scatterings,
selected by charged-particle jets (JE particles), follows that presented in
Ref. [32]. Particles are defined as located inside the jet cones (JC) if their
distance to the jet axis in the $\eta$–$\varphi$ plane

$R({\rm particle,\,jet})=\sqrt{(\eta_{\rm particle}-\eta_{\rm
jet})^{2}+(\varphi_{\rm particle}-\varphi_{\rm jet})^{2}}$ (3)

is less than a given value $R_{\max}$,

$R({\rm particle,\,jet})<R_{\max},$ (4)

where $R_{\max}=0.4$ to be consistent with the value of the jet resolution
parameter used for the jet reconstruction. The remaining contribution from the
underlying event (UE) in the JC selection, which refers to particles not
associated with jet fragmentation, is estimated in the perpendicular cone (PC)
to the jet axis with radius $R=R_{\rm PC}$. The default value is $R_{\rm
PC}=0.4$.

Since the $\eta$–$\varphi$ acceptance of the JC-selected particles differ from
that for UE estimations, to subtract the UE component from the JC selection, a
density distribution is defined

$\frac{\mathrm{d}\rho}{\mathrm{d}p_{\rm T}}=\frac{1}{N_{\rm
ev}}\times\frac{1}{A_{\rm acc}}\times\frac{\mathrm{d}N}{\mathrm{d}p_{\rm T}},$
(5)

where $\mathrm{d}N/\mathrm{d}p_{\rm T}$ is the $p_{\rm T}$-differential
particle production yield, and $N_{\rm ev}$ and $A_{\rm acc}$ are the number
of events and the area of the $\eta$–$\varphi$ acceptance for a given
selection. For JC and PC selections, $N_{\rm ev}$ corresponds to the number of
events containing at least one jet with $p_{\rm T,jet}^{\rm ch}>10$ GeV/$c$.
The $\eta$–$\varphi$ acceptance area, $A_{\rm acc}$, is calculated via

$A_{\rm acc}=\alpha\pi R^{2},$ (6)

where $R$ is the cone radius for the corresponding selection and $\alpha$ is a
correction factor used to account for the partial geometrical overlap among
jets on the $\eta$–$\varphi$ plane. The $\alpha$ factor is calculated via a
Monte Carlo (MC) sampling approach using measured distributions of strange
particles and jets as inputs. The value of $\alpha$ is around $1.06$ and it is
insensitive to particle species and event multiplicities. It gives a minor
correction on the particle density normalization since the production rate for
jets with $p_{\rm T,jet}^{\rm ch}>10$ GeV/$c$ is low even in high-multiplicity
p–Pb collisions. With the normalization defined in Eq. (5), the $p_{\rm
T}$-differential production density distribution of JE particles is obtained
by subtracting the density distribution of particles with the UE selection
from that with the JC selection, namely:

$\frac{\mathrm{d}\rho^{\rm JE}}{\mathrm{d}p_{\rm T}}=\frac{\mathrm{d}\rho^{\rm
JC}}{\mathrm{d}p_{\rm T}}-\frac{\mathrm{d}\rho^{\rm UE}}{\mathrm{d}p_{\rm
T}}.$ (7)

In addition, to compare with the JE particles, the production yield of
inclusive particles is also normalized according to Eq. (5). For the MB
analysis, $N_{\rm ev}$ corresponds to the number of selected MB events. For
the event-activity differential analysis in p–Pb collisions, $N_{\rm ev}$
corresponds to the number of selected events in the corresponding event
activity interval. The acceptance area, $A_{\rm acc}$, of inclusive particles
is given by

$A_{\rm acc}=\Delta\eta\times\Delta\varphi,$ (8)

where $\Delta\eta=2\times 0.75$ and $\Delta\varphi=2\pi$, correspond to the
$\eta$ and $\varphi$ acceptances of inclusive particles, respectively.

Figure 2: Strange particle reconstruction efficiency in pp collisions at
$\sqrt{s}~{}=~{}13$ TeV (left) and in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV (right) for two selections: inside the
jet cone ($R({\rm par,jet})<0.4$) and for the inclusive case. The vertical
bars represent the statistical uncertainties.

###  3.4 Corrections for strange particle reconstruction and feed-down

The reconstruction efficiencies of each particle are obtained from MC
simulated data. For this purpose, Pythia 8 (for pp collisions) [36] and DPMJet
(for p–Pb collisions) [59] are used and the simulated data are propagated
through the ALICE detector by GEANT3 [60]. Due to differences in the
experimental acceptance for particles associated with jets and the underlying
event, the efficiencies of particles are estimated separately for each case
[32]. Figure 2 shows the reconstruction efficiency of the JC-selected particle
and the inclusive one. The reconstruction efficiencies of inclusive strange
particles and those produced in the underlying event are identical within
uncertainties.

The yields for $\Lambda$ and $\overline{\Lambda}$ are significantly affected
by secondary particles coming from the decays of charged and neutral $\Xi$
baryons. The feed-down fraction is calculated with a data-driven approach
[21]. The inclusive feed-down method was introduced in previous ALICE analyses
[58, 34, 20]. In this work, the feed-down fraction in jet and UE is computed
for each $p_{\rm T}$ interval using the measured spectra of $\Xi^{\pm}$
baryons in jet and UE. The correction of the feed-down contribution from
neutral $\Xi$ baryons is based on the assumption that the production rates of
charged and neutral $\Xi$ baryons are equal. Figure 3 shows the results of the
feed-down fraction for the JC selection compared with the inclusive one.

Figure 3: Fraction of $\Lambda$ yield removed due to the subtraction of feed-
down contributions from charged and neutral $\Xi$ baryons decays in pp
collisions at $\sqrt{s}~{}=~{}13$ TeV (left) and p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV (right). The vertical bars represent
the statistical uncertainties.

###  3.5 Systematic uncertainties

The total systematic uncertainties for ${\rm K}^{0}_{\rm{S}}$, $\Lambda$,
$\overline{\Lambda}$, $\Xi^{\pm}$, and $\Omega^{\pm}$ yields were estimated
separately for each particle and in different $p_{\rm T}$ intervals.
Individual selection criteria are loosened and tightened, in order to estimate
the uncertainty on the discrepancy between data and MC simulations. The main
sources of the systematic uncertainty investigated in this measurement are
related to the knowledge of detector materials, track selections, particle
identification, proper lifetime, topological selections and signal extraction.
All individual uncertainty contributions are listed in Tables 1 and 2 and
finally added in quadrature.

Table 1: Main sources and corresponding relative systematic uncertainties (in %) for ${\rm K}^{0}_{\rm{S}}$, $\Lambda+\overline{\Lambda}$, $\Xi^{-}+\overline{\Xi}^{+}$, and $\Omega^{-}+\overline{\Omega}^{+}$ in pp collisions at $\sqrt{s}~{}=~{}13$ TeV. The values are reported for low, intermediate, and high $p_{\rm T}$. Uncertainty source | ${\rm K}^{0}_{\rm{S}}$ | $\Lambda+\overline{\Lambda}$ | $\Xi^{-}+\overline{\Xi}^{+}$ | $\Omega^{-}+\overline{\Omega}^{+}$
---|---|---|---|---
$p_{\rm T}$ (GeV/$c$) |  0.6 |  2 |  10 |  0.6 |  2 |  10 |  0.6 |  2 |  7 |  1 |  2 |  5
Detector material |  4 |  4 |  4 |  4 |  4 |  4 |  4 |  4 |  4 |  4 |  4 |  4
Competing rejection |  0.16 |  0.1 |  0.2 |  negl. |  0.1 |  3.1 |  - |  - |  - |  - |  - |  -
Track selection |  1.5 |  1.2 |  0.4 |  0.6 |  1.4 |  1.3 |  2.8 |  0.1 |  negl. |  negl. |  1.5 |  0.2
Particle identification |  0.1 |  0.1 |  0.1 |  0.3 |  0.2 |  1.1 |  1.9 |  1.7 |  2.4 |  3.9 |  8.7 |  6
Proper lifetime |  negl. |  0.1 |  negl. |  2.1 |  0.4 |  negl. |  - |  - |  - |  - |  - |  -
Topological |  0.2 |  1.4 |  negl. |  3.9 |  0.8 |  3.9 |  0.6 |  0.9 |  1 |  2.8 |  5.4 |  2.4
Signal extraction |  0.8 |  1.1 |  1.1 |  0.3 |  0.5 |  1.7 |  3 |  1 |  0.5 |  2.3 |  4.6 |  3
Total uncertainty |  4.4 |  4.6 |  4.2 |  6.1 |  4.4 |  6.7 |  6.1 |  4.5 |  4.8 |  6.7 |  12 |  8.2
Table 2: Main sources and corresponding relative systematic uncertainties (in %) for ${\rm K}^{0}_{\rm{S}}$, $\Lambda+\overline{\Lambda}$, $\Xi^{-}+\overline{\Xi}^{+}$, and $\Omega^{-}+\overline{\Omega}^{+}$ in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV. The values are reported for low, intermediate, and high $p_{\rm T}$. Uncertainty source | ${\rm K}^{0}_{\rm{S}}$ | $\Lambda+\overline{\Lambda}$ | $\Xi^{-}+\overline{\Xi}^{+}$ | $\Omega^{-}+\overline{\Omega}^{+}$
---|---|---|---|---
$p_{\rm T}$ (GeV/$c$) |  0.6 |  2 |  10 |  0.6 |  2 |  10 |  0.6 |  2 |  7 |  1 |  2 |  5
Detector material |  4 |  4 |  4 |  4 |  4 |  4 |  4 |  4 |  4 |  4 |  4 |  4
Competing rejection |  0.16 |  0.3 |  0.5 |  0.1 |  negl. |  5.1 |  - |  - |  - |  - |  - |  -
Track selection |  1.4 |  1.7 |  1.8 |  0.2 |  1.3 |  1.4 |  negl. |  negl. |  negl. |  1.3 |  2.5 |  negl.
Particle identification |  0.1 |  0.2 |  0.2 |  0.3 |  0.2 |  1 |  3.1 |  1.2 |  negl. |  8.1 |  13.7 |  5.9
Proper lifetime |  negl. |  negl. |  negl. |  1.6 |  0.3 |  negl. |  0.6 |  0.4 |  negl. |  negl. |  3.3 |  negl.
Topological |  4.4 |  0.6 |  1.9 |  3.9 |  0.9 |  2.7 |  1.3 |  negl. |  2.6 |  1.2 |  4.8 |  3.7
Signal extraction |  0.3 |  2.6 |  1.7 |  0.6 |  0.5 |  2.6 |  5.1 |  0.9 |  2.6 |  negl. |  5.2 |  negl.
Total uncertainty |  6.1 |  5.1 |  5.1 |  5.7 |  4.3 |  6.1 |  7.4 |  4.3 |  5.4 |  9.2 |  16.4 |  8

Material budget. The effect of the incomplete knowledge of the detector
material budget is evaluated by comparing different MC simulations in which
the material budget was increased and decreased by $4.5\%$. This value
corresponds to the uncertainty on the determination of the material budget by
measuring photon conversions [38]. This particular systematic uncertainty is
about $4\%$ [34].

Rejection of competing decays. A ${\rm K}^{0}_{\rm{S}}$ candidate is rejected
if its invariant mass under the hypothesis of a $\Lambda$ or
$\overline{\Lambda}$ lies in the window of $\pm 5$ MeV/$c^{2}$ around the mass
of the $\Lambda$ or $\overline{\Lambda}$, and a $\Lambda$
($\overline{\Lambda}$) candidate is rejected if its invariant mass under the
${\rm K}^{0}_{\rm{S}}$ hypothesis lies in the window of $\pm 10$ MeV/$c^{2}$
around the ${\rm K}^{0}_{\rm{S}}$ mass. To compute the uncertainty due to the
competing selection, the analysis is redone with this rejection at $5$
MeV/$c^{2}$ to $3$ MeV/$c^{2}$ and $6$ MeV/$c^{2}$ for the ${\rm
K}^{0}_{\rm{S}}$. In the case of the $\Lambda$ or $\overline{\Lambda}$, the
rejection is removed entirely.

Track selection. To estimate the systematic uncertainty due to the track
selection, the analysis is redone with an increased number of required
clusters in the TPC from the default $70$ to $80$ clusters out of a maximum of
$159$ clusters.

Particle identification. The TPC $\textrm{d}E/\textrm{d}x$ selection is used
to reduce the combinatorial background in the strange particle invariant mass
distribution. The number of standard deviations $\sigma$ in the identification
of particles using the $\textrm{d}E/\textrm{d}x$ has been varied from
$4\sigma$ to $6\sigma$.

Proper decay length selection. The proper decay length is defined as $mLc/p$,
where $m$ is the mass of the particles, $L$ is the decay length, and $p$ is
the particle’s momentum. The selection on the $mLc/p$ is varied within $12$ to
$40$ cm for ${\rm K}^{0}_{\rm{S}}$, $20$ to $40$ cm for $\Lambda$
$(\overline{\Lambda})$, $10$ to $30$ cm for $\Xi^{\pm}$, and $5$ to $15$ cm
for $\Omega^{\pm}$.

Topological selection. The values of the selection criteria for the
topological variables are varied within ranges resulting in a maximum
variation of $\pm 10\%$ in the raw signal yield around its nominal value. The
observed deviations for each component are summed in quadrature.

Signal extraction. In the same manner as for the topological selection, the
signal extraction has been tested by varying the widths used to define the
“signal” and “background” regions, expressed in terms of the number of
$\sigma$ as defined in Section 3.2. In particular, the width of the peak
region is varied from the default value of $6\sigma$ to $7\sigma$, $5\sigma$,
and $4\sigma$ for ${\rm V}^{0}$ particles and $3\sigma$ to
$4\sigma~{}(3.5\sigma)$ and $2.5\sigma$ for $\Xi~{}(\Omega)$.

Additional systematic uncertainties on the particle yield originate from the
UE subtraction and the jet $p_{\rm T}$ threshold. The systematic uncertainty
due to the UE subtraction is estimated by varying the perpendicular cone
radius from the chosen default value of $R_{\rm PC}=0.4$ to $0.2$ and $0.6$.
From the deviations obtained for different sizes of the PC, the relative
systematic uncertainty of the UE subtraction is estimated. To evaluate the
uncertainty related to the jet $p_{\rm T}$ threshold, the analysis is repeated
varying the jet $p_{\rm T}$ threshold by $\pm 1$ GeV/$c$. The systematic
uncertainties of particles in jets are added to the list of uncertainties in
quadrature. The values are shown in Table 3 and Table 4.

The uncertainties of JE-particle yield ratios ($\Lambda/{\rm K}^{0}_{\rm{S}}$,
$\Xi/{\rm K}^{0}_{\rm{S}}$, $\Omega/{\rm K}^{0}_{\rm{S}}$, $\Xi/\Lambda$,
$\Omega/\Lambda$, and $\Omega/\Xi$) include three sources: the particle
reconstruction, UE subtraction, and the jet $p_{\rm T}$ threshold. The
uncertainty on particle reconstruction is propagated from that obtained for
particle spectra. The systematic uncertainties related to the material budget
are correlated for each particle spectrum and they partially cancel in the
ratios. Uncertainties related to UE subtraction and jet $p_{\rm T}$ threshold
are obtained by varying the same condition for particle spectra in both
numerator and denominator of the corresponding ratios.

Table 3: Main sources and corresponding relative systematic uncertainties (in
%) for particle $p_{\rm T}$-differential density (${\rm K}^{0}_{\rm{S}}$,
$\Lambda+\overline{\Lambda}$, $\Xi^{-}+\overline{\Xi}^{+}$, and
$\Omega^{-}+\overline{\Omega}^{+}$) and particle ratios ($\Lambda/{\rm
K}^{0}_{\rm{S}}$, $\Xi/{\rm K}^{0}_{\rm{S}}$, $\Omega/{\rm K}^{0}_{\rm{S}}$,
$\Xi/\Lambda$, $\Omega/\Lambda$, and $\Omega/\Xi$) in JE in pp collisions at
$\sqrt{s}~{}=~{}13$ TeV. The values are reported for low (0.6 GeV/$c$),
intermediate (2 GeV/$c$), and high (10 GeV/$c$) $p_{\rm T}$.

Uncertainty source | ${\rm K}^{0}_{\rm{S}}$ | $\Lambda+\overline{\Lambda}$ | $\Xi^{-}+\overline{\Xi}^{+}$ | $\Omega^{-}+\overline{\Omega}^{+}$
---|---|---|---|---
$p_{\rm T}$ (GeV/$c$) |  0.6 |  2 |  10 |  0.6 |  2 |  10 |  0.6 |  2 |  7 |  1 |  2 |  5
Particle reconstruction |  1.8 |  0.25 |  negl. |  5.5 |  0.6 |  negl. |  6.7 |  0.9 |  0.1 |  6 |  1.7 |  0.3
UE subtraction |  0.1 |  0.1 |  0.1 |  0.1 |  0.2 |  0.1 |  1.5 |  0.2 |  0.3 |  3.6 |  1.8 |  0.5
Jet $p_{\rm T}$ threshold |  0.6 |  3.1 |  10.9 |  0.6 |  1.1 |  9.9 |  3.5 |  2.4 |  5 |  negl. |  negl. |  negl.
Total uncertainty |  1.8 |  3.1 |  10.9 |  5.6 |  1.2 |  9.9 |  7.7 |  2.6 |  5 |  7.1 |  2.5 |  0.6

Uncertainty source | $(\Lambda+\overline{\Lambda})/(2{\rm K}^{0}_{\rm{S}})$ | $(\Xi^{-}+\overline{\Xi}^{+})/(2{\rm K}^{0}_{\rm{S}})$ | $(\Omega^{-}+\overline{\Omega}^{+})/(2{\rm K}^{0}_{\rm{S}})$
---|---|---|---
$p_{\rm T}$ (GeV/$c$) |  0.6 |  2 |  10 |  0.6 |  2 |  7 |  1 |  2 |  5
Particle reconstruction |  2.4 |  2.8 |  3.3 |  3.4 |  2.8 |  2.8 |  6.7 |  11.4 |  7.3
UE subtraction |  0.8 |  0.2 |  0.4 |  3.5 |  0.2 |  0.1 |  10 |  4 |  2.2
Jet $p_{\rm T}$ threshold |  0.4 |  2.3 |  1 |  1.7 |  1.6 |  3.6 |  1 |  3.3 |  6.4
Total uncertainty |  2.6 |  3.7 |  3.5 |  5.2 |  3.3 |  4.5 |  12.4 |  12.5 |  10

Uncertainty source | $(\Xi^{-}+\overline{\Xi}^{+})/(\Lambda+\overline{\Lambda})$ | $(\Omega^{-}+\overline{\Omega}^{+})/(\Lambda+\overline{\Lambda})$ | $(\Omega^{-}+\overline{\Omega}^{+})/(\Xi^{-}+\overline{\Xi}^{+})$
---|---|---|---
$p_{\rm T}$ (GeV/$c$) |  0.6 |  2 |  7 |  1 |  2 |  5 |  1 |  2 |  5
Particle reconstruction |  3.4 |  3 |  3.2 |  6.7 |  11.5 |  7.5 |  6.8 |  11.5 |  7.4
UE subtraction |  4.4 |  0.4 |  0.2 |  12.4 |  4.2 |  2.3 |  7.8 |  3.8 |  2.7
Jet $p_{\rm T}$ threshold |  0.7 |  0.5 |  1.9 |  0.2 |  0.9 |  3.5 |  0.4 |  1.3 |  3
Total uncertainty |  5.6 |  3 |  3.7 |  14.1 |  12.2 |  8.6 |  10.3 |  12.1 |  8.5

Table 4: Main sources and corresponding relative systematic uncertainties (in
%) for particle $p_{\rm T}$-differential density (${\rm K}^{0}_{\rm{S}}$,
$\Lambda+\overline{\Lambda}$, $\Xi^{-}+\overline{\Xi}^{+}$, and
$\Omega^{-}+\overline{\Omega}^{+}$) and particle yield ratios ($\Lambda/{\rm
K}^{0}_{\rm{S}}$, $\Xi/{\rm K}^{0}_{\rm{S}}$, $\Omega/{\rm K}^{0}_{\rm{S}}$,
$\Xi/\Lambda$, $\Omega/\Lambda$, and $\Omega/\Xi$) in JE in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV. The values are reported for low,
intermediate, and high $p_{\rm T}$.

Uncertainty source | ${\rm K}^{0}_{\rm{S}}$ | $\Lambda+\overline{\Lambda}$ | $\Xi^{-}+\overline{\Xi}^{+}$ | $\Omega^{-}+\overline{\Omega}^{+}$
---|---|---|---|---
$p_{\rm T}$ (GeV/$c$) |  0.6 |  2 |  10 |  0.6 |  2 |  10 |  0.6 |  2 |  7 |  1 |  2 |  5
Particle reconstruction |  5 |  0.8 |  0 |  14.2 |  1.5 |  0 |  24.8 |  2.8 |  0.3 |  8.7 |  3.7 |  0.9
UE subtraction |  0.3 |  0.1 |  0.1 |  0 |  0.1 |  11.2 |  14.1 |  0.8 |  0.7 |  negl. |  negl. |  1.2
Jet $p_{\rm T}$ threshold |  0.3 |  3.5 |  11 |  3.2 |  1.8 |  0.1 |  24.9 |  3 |  4.1 |  3.1 |  10.7 |  7.6
Total uncertainty |  5 |  3.6 |  11 |  14.6 |  2.3 |  11.2 |  37.9 |  4.2 |  4.1 |  9.3 |  11.3 |  7.7

Uncertainty source | $(\Lambda+\overline{\Lambda})/(2{\rm K}^{0}_{\rm{S}})$ | $(\Xi^{-}+\overline{\Xi}^{+})/(2{\rm K}^{0}_{\rm{S}})$ | $(\Omega^{-}+\overline{\Omega}^{+})/(2{\rm K}^{0}_{\rm{S}})$
---|---|---|---
$p_{\rm T}$ (GeV/$c$) |  0.6 |  2 |  10 |  0.6 |  2 |  7 |  1 |  2 |  5
Particle reconstruction |  3.3 |  3.4 |  4.7 |  4.7 |  3.2 |  4 |  9.8 |  1.5 |  7.4
UE subtraction |  0.8 |  0.1 |  0.1 |  9.1 |  1.8 |  1 |  4.1 |  0 |  0.3
Jet $p_{\rm T}$ threshold |  1.4 |  2.6 |  0.1 |  8.6 |  2.4 |  6 |  0.5 |  1.5 |  0.3
Total uncertainty |  3.7 |  4.3 |  4.7 |  13.4 |  4.4 |  7.2 |  10.6 |  15.1 |  7.4

Uncertainty source | $(\Xi^{-}+\overline{\Xi}^{+})/(\Lambda+\overline{\Lambda})$ | $(\Omega^{-}+\overline{\Omega}^{+})/(\Lambda+\overline{\Lambda})$ | $(\Omega^{-}+\overline{\Omega}^{+})/(\Xi^{-}+\overline{\Xi}^{+})$
---|---|---|---
$p_{\rm T}$ (GeV/$c$) |  0.6 |  2 |  10 |  0.6 |  2 |  7 |  1 |  2 |  5
Particle reconstruction |  4.3 |  2.8 |  3.8 |  9.6 |  15 |  7.5 |  10 |  14.9 |  8.6
UE subtraction |  9.9 |  1.9 |  0.8 |  3.6 |  0.1 |  0.3 |  11 |  1.8 |  0.1
Jet $p_{\rm T}$ threshold |  2.7 |  0.6 |  2.6 |  0.4 |  5 |  3 |  0.4 |  3.8 |  1.7
Total uncertainty |  11.1 |  3.4 |  4.7 |  10.3 |  15.8 |  8.1 |  14.9 |  15.5 |  8.7

##  4 Results and discussion

###  4.1 Particle production and yield ratios in pp collisions at
$\sqrt{s}~{}=~{}13$ TeV

Figure 4: $p_{\rm T}$-differential density, $\mathrm{d}\rho/\mathrm{d}p_{\rm
T}$, of ${\rm K}^{0}_{\rm{S}}$ (top left panel), $\Lambda$ (top right panel),
$\Xi$ (bottom left panel), and $\Omega$ (bottom right panel) in pp collisions
at $\sqrt{s}~{}=~{}13$ TeV. The spectra of JE particles (red triangles),
associated with hard scatterings, are compared with that of JC (green squares)
and UE (blue open circles) selections. The results from inclusive measurements
(black closed circles) are presented as well. The statistical uncertainties
are represented by the vertical error bars and the systematic uncertainties by
the boxes. Figure 5: $p_{\rm T}$-dependent strange baryon-to-meson (top) and
baryon-to-baryon (bottom) yield ratios in pp collisions at $\sqrt{s}~{}=~{}13$
TeV. For each case, the results of JE particles (red triangles) are compared
with that of inclusive (black closed circles) and UE (blue open circles)
particles. The statistical uncertainties are represented by the vertical error
bars and the systematic uncertainties by the boxes.

For the strange hadrons discussed in this paper, the ratios of yields for
particles and antiparticles are consistent with unity within uncertainties, as
expected at LHC energies in the midrapidity region [34, 58, 16]. Therefore,
all the spectra and the corresponding ratios shown in the following are
reported after summing particles and antiparticles, when a distinct
antiparticle state exists. The sums of particles and antiparticles,
$\Lambda+\overline{\Lambda}$, $\Xi^{-}+\overline{\Xi}^{+}$, and
$\Omega^{-}+\overline{\Omega}^{+}$ are simply denoted as $\Lambda$, $\Xi$, and
$\Omega$, unless explicitly written.

Figure 4 shows the fully corrected $p_{\rm T}$-differential densities,
$\mathrm{d}\rho/\mathrm{d}p_{\rm T}$ defined by Eq. (5), of ${\rm
K}^{0}_{\rm{S}}$, $\Lambda$, $\Xi$, and $\Omega$ associated with charged-
particle jets and the underlying event in pp collisions at $\sqrt{s}~{}=~{}13$
TeV. For particles matched to the jet cone, the JC-selected particles defined
by Eq. (4), the UE component estimated using the PC selection is mainly
concentrated at low $p_{\rm T}$ in the region of $p_{\rm T}<1$–$2$ GeV/$c$.
The UE fraction is higher for $\Lambda$, $\Xi$, and $\Omega$ baryons than for
${\rm K}^{0}_{\rm{S}}$ mesons. In the high-$p_{\rm T}$ region ($p_{\rm T}>5$
GeV/$c$), JC-selected particle production is dominated by the products from
hard scatterings – the JE particles defined by Eq. (7). The density
distribution of UE particles rapidly decreases with $p_{\rm T}$, reaching
values about one order of magnitude lower than that with the JC selection for
particle $p_{\rm T}$ exceeding $4$ GeV/$c$. This is consistent with the
expectation that the high-$p_{\rm T}$ particles originate from jet
fragmentation. The density distributions of the inclusive particles obtained
in MB events are also compared with that of the JE and UE particles in Fig. 4.
Since the density of JE particles is obtained from events triggered by
charged-particle jets, its $p_{\rm T}$-dependence is considerably less steep
than that of inclusive particles. The density of UE particles is higher than
that of inclusive particles since the UE is obtained from events containing
jets with $p_{\rm T,jet}^{\rm ch}>10$ GeV/$c$. This is due to the well
established jet pedestal effect [61]. The underlying event density increases
with the leading track $p_{\rm T}$ and then saturates at high $p_{\rm T}$. The
$p_{\rm T}$ dependence of the inclusive particle density is qualitatively
similar to that for UE particles, which shows a steeply falling distribution
with increasing $p_{\rm T}$.

Figure 6: $p_{\rm T}$-differential density distributions for inclusive (left)
and within jets (right) ${\rm K}^{0}_{\rm{S}}$ (black closed circles),
$\Lambda$ (red open circles), $\Xi$ (blue squares), and $\Omega$ (green
inverted triangles) in pp collisions at $\sqrt{s}~{}=~{}13$ TeV. The spectra
in data are compared with Pythia $8$ CR-BLC simulations. Three modes, labeled
as mode $0$ (solid line), $2$ (dashed line), and $3$ (dash-dotted line) are
adopted in the simulations. The Pythia-to-data ratios are shown in the four
bottom panels where the spread of the three Pythia $8$ CR-BLC implementation
modes are presented as bands. For clarity, some of the spectra were scaled
with the factors indicated in the legends. The statistical uncertainties are
represented by the vertical error bars and the systematic uncertainties by the
boxes.

The yield ratios of $\Lambda$, $\Xi$, and $\Omega$ baryons to ${\rm
K}^{0}_{\rm{S}}$ mesons as a function of $p_{\rm T}$ in pp collisions at
$\sqrt{s}~{}=~{}13$ TeV are shown in the top three panels of Fig. 5 for
different selection criteria. The yield ratios of the UE selected particles
given by the PC selection are consistent with that of inclusive particles
within uncertainties. These ratios show an enhancement in the $p_{\rm T}$
region $1$–$5$ GeV/$c$ with respect to those for the JE particles. The yield
ratios of the JE selected particles are approximately independent of $p_{\rm
T}$ in the region beyond $2$ GeV/$c$, in particular, they do not show a
maximum at intermediate $p_{\rm T}$. Clearly the enhancement of the baryon-to-
meson yield ratio seen in the inclusive measurement is not present within
jets. It is worth noting that the $\Lambda/{\rm K}^{0}_{\rm{S}}$ ratio of
inclusive particles becomes consistent with that of JE particles within
uncertainties for $p_{\rm T}>6$ GeV/$c$ as the high-$p_{\rm T}$ inclusive
particles originate predominantly from jet fragmentation. The results for JE
particles are consistent with those in Ref. [32] for pp collisions at
$\sqrt{s}~{}=~{}7$ TeV, showing no dependence on the collision energy. For the
$\Xi$/${\rm K}^{0}_{\rm{S}}$ and $\Omega$/${\rm K}^{0}_{\rm{S}}$ ratios, even
with limited $p_{\rm T}$ coverage, the trends imply that the results of
inclusive measurements are expected to converge to that of JE particles at
higher $p_{\rm T}$.

The strange baryon-to-baryon yield ratios, $\Xi$/$\Lambda$,
$\Omega$/$\Lambda$, and $\Omega$/$\Xi$, as a function of $p_{\rm T}$ are
presented in the bottom three panels of Fig. 5. For each case, the numerator
always contains at least one more strange quark than the denominator, and the
results obtained from JE, UE and inclusive selections are compared. Similarly
to the baryon-to-meson yield ratios shown in the upper three panels of the
same figure, the baryon-to-baryon yield ratios from the UE are consistent with
that from the inclusive measurements within uncertainties. In the measured
$p_{\rm T}$ range, they increase with $p_{\rm T}$ up to $4$ GeV/$c$. For
$p_{\rm T}>2$ GeV/$c$, the $\Xi$/$\Lambda$ ratio of JE particles is almost
independent of $p_{\rm T}$, and shows a strong suppression by a factor of
about two with respect to the inclusive measurements. However, the
$\Omega$/$\Lambda$ and $\Omega$/$\Xi$ ratios for particles associated with
jets show a similar $p_{\rm T}$ dependence as the inclusive particles. The
$\Omega$/$\Lambda$ ratio of JE particles is systematically lower than the
inclusive measurement, but with a smaller suppression than that observed for
$\Xi/\Lambda$. For the $\Omega$/$\Xi$ ratio, the results of JE particles are
compatible with that of inclusive particles within uncertainties. These
findings suggest that the production mechanism of $\Omega$ baryons, as
strange-quark triplets, in jets may be similar to that in the UE. This
conclusion can be further confirmed in future measurements using a larger data
sample.

The $p_{\rm T}$-differential densities of inclusive ${\rm K}^{0}_{\rm{S}}$,
$\Lambda$, $\Xi$, and $\Omega$ are compared with simulations with Pythia $8$
event generator [36] in the left panels of Fig. 6. The Pythia $8$ Monte Carlo
simulation studies are performed with the CR-BLC model [62], in which the
minimisation of the string potential is implemented considering the SU($3$)
multiplet structure of QCD, allowing for the formation of “baryonic”
configurations where two colours can combine coherently to form anti-colours.
From the CR-BLC model [62], three modes (labeled as mode $0$, $2$, and $3$)
are suggested by the authors – each applying different constraints on the
allowed reconnections among the colour sources. In particular, considerations
are given to the causal connections among strings involved in the reconnection
and to the time dilation caused by relative boosts of the strings. The density
spectra using Pythia $8$ are normalized in the same way as data described in
Section 3.3. The left-bottom panels of Fig. 6 show the ratios between Pythia
$8$ simulations and data. Since for each particle species the three CR-BLC
modes give almost identical $p_{\rm T}$-differential density spectra, the
results corresponding to different CR-BLC modes are presented as bands (unless
explicitly stated otherwise).

The inclusive density spectra obtained with Pythia $8$ underestimate the data
for all particle species and the $p_{\rm T}$ dependence follows a power-law
trend, which does not reproduce the moderate peaks on the spectra around
$p_{\rm T}=2$ GeV/$c$ present in data. This results in a “valley” structure in
Pythia-to-data ratios in the interval of $1<p_{\rm T}<4$ GeV/$c$. For ${\rm
K}^{0}_{\rm{S}}$ and $\Lambda$, the value of the MC/data ratio reaches the
minimum of around $0.4$ at $p_{\rm T}\simeq 2$ GeV/$c$, then it increases with
$p_{\rm T}$ for $p_{\rm T}>2$ GeV/$c$ and shows a saturation trend with a
value that rises to $0.8$ at $p_{\rm T}>6$ GeV/$c$. For the multi-strange
baryons, $\Xi$ and $\Omega$, the ratio decreases with strange-quark content
and baryon mass. The minimum values of the ratio are around $0.2$ and $0.1$
for $\Xi$ and $\Omega$, respectively.

In analogy with the left panel of Fig. 6, the right panel shows the
comparisons of $p_{\rm T}$-differential densities for JE particles with the
corresponding Pythia $8$ simulations for the different CR-BLC modes. The JE-
particle density spectra from Pythia $8$ are obtained following the same
approach applied to data as detailed in Section 3.3. Pythia $8$ simulations
overestimate the density of ${\rm K}^{0}_{\rm{S}}$ mesons and $\Lambda$
baryons in jets for $p_{\rm T}<2$ GeV/$c$, while, in general, a better
agreement is observed for $p_{\rm T}>2$ GeV/$c$. The MC/data ratio for those
two particle species are almost identical, as seen in the lower panels of Fig.
6. But, in general, the $p_{\rm T}$-differential density obtained from the
generator is softer than that in the data. For $\Xi$ baryons, Pythia $8$
overestimates their production associated with jets over the measured $p_{\rm
T}$ range, $0.9<p_{\rm T}<8$ GeV/$c$, by a factor of around three to six
depending on $p_{\rm T}$. A possible explanation is that the strings
containing partons produced in the hard scattering processes in Pythia
fragmentation have higher string tension. It is likely that in Pythia $8$ the
ss-diquark string production rate is much higher than that within the jet
fragmentation found in data. Moreover, since the probability for an ss-diquark
combining with another single s-quark to form an $\Omega$ baryon is lower than
the probability combining with u- and d-quarks to form a $\Xi$ baryon, the
density of $\Omega$ produced in jets is underestimated. For $p_{\rm T}>2$
GeV/$c$, the corresponding $\Omega$ MC/data ratio reaches about $0.5$ with
mild dependence on $p_{\rm T}$. This is indicative of the vastly overestimated
production density of $\Xi$ baryons in jets within the generator.

Figure 7: $p_{\rm T}$-dependent strange baryon-to-meson (top) and baryon-to-
baryon (bottom) ratios in pp collisions at $\sqrt{s}~{}=~{}13$ TeV. For each
case, the results of JE (red triangles) and inclusive (black closed circles)
particles are compared with Pythia $8$ CR-BLC simulations. The bands
correspond to the combination of simulations, where the spread of the three
different CR-BLC implementation modes. The statistical uncertainties are
represented by the vertical error bars and the systematic uncertainties by the
boxes.

The $p_{\rm T}$-differential particle ratios from the JE and the inclusive
selections are compared with the Pythia $8$ simulations in Fig. 7. Pythia $8$
CR-BLC tunes generally agree with the $\Lambda$/${\rm K}^{0}_{\rm{S}}$ ratios
for both JE particles and inclusive measurements, despite that the simulations
do not reproduce the individual density spectra neither in jets nor in the
inclusive sample. Large discrepancies between data and the MC model are
observed for all the other cases containing multi-strange hadrons in the
numerator over the measured $p_{\rm T}$ acceptance. As stated in Ref. [63],
although the string junction mechanism applied in Pythia $8$ CR-BLC tunes
increases the baryon production probabilities, the ss-diquark is disfavoured
in the Pythia fragmentation due to the phase-space constraint on high
invariant mass strings. This results in Pythia $8$ largely underestimating the
inclusive particle ratios containing multi-strange hadrons in the numerator.
Since the density of $\Xi$ in jets is overestimated by Pythia $8$, then the
$\Xi$/${\rm K}^{0}_{\rm{S}}$ and $\Xi$/$\Lambda$ ratios given by Pythia $8$
increase dramatically with $p_{\rm T}$ and raise to unrealistic large values.
At the same time, the $\Omega$/$\Xi$ ratio in jets is suppressed in Pythia $8$
generated events. It seems that Pythia $8$ qualitatively reproduces the
$p_{\rm T}$ dependence for $\Omega$/${\rm K}^{0}_{\rm{S}}$ and
$\Omega$/$\Lambda$ ratios in jets. However, this may be due to the unrealistic
enhancement of the ss-diquark produced by strings containing partons from hard
scatterings in the model. It is worth noticing that the colour rope mechanism
[64], in which the strange particle production is enhanced via interactions
between strings [63], vastly overestimates the $\Xi$ and $\Omega$ production
in jets at high $p_{\rm T}$ (see the illustration shown in Fig. 10 in Appendix
B). The enhancement of the multi-strange production in colour rope predictions
results from the higher local energy density in the region where an energetic
jet is present. In summary, the measurements presented in this section provide
important constraints on the production mechanisms of particles, especially
for the multi-strange baryon, associated with hard partons.

Figure 8: $p_{\rm T}$-differential density, $\mathrm{d}\rho/\mathrm{d}p_{\rm
T}$, of ${\rm K}^{0}_{\rm{S}}$ (top left panel), $\Lambda$ (top right panel),
$\Xi$ (bottom left panel), and $\Omega$ (bottom right panel) in p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV. The spectra of JE
particles (red triangles), associated with hard scatterings, are compared with
that of JC (green squares) and UE (blue open circles) selections. The results
from inclusive measurements (black closed circles) are presented as well. The
statistical uncertainties are represented by the vertical error bars and the
systematic uncertainties by the boxes.

###  4.2 Production and ratios of JE particles in p–Pb collisions at
${\bf\sqrt{s_{\bf\rm NN}}=5.02}$ TeV

The proton to $\pi^{\pm}$ ratios and strange baryon-to-meson yield ratios
measured at high multiplicity in small collision systems (pp and p–Pb) [65,
21, 18, 66, 34, 20, 17] exhibit an enhancement at intermediate $p_{\rm T}\sim
3$ GeV/$c$ with respect to the low-multiplicity events, qualitatively
reminiscent of that measured in Pb–Pb collisions [67, 68, 19, 69]. In the
latter, the enhancement is considered as the fingerprint of hydrodynamic
evolution of the colour-deconfined matter state, the quark–gluon plasma,
created under extreme conditions of high temperature and energy density. To
further constrain the particle production mechanisms in small collision
systems, the study of strange particle production within charged-particle jets
is extended to p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV in
both MB events and in events selected in various multiplicity intervals.

Figure 8 shows the $p_{\rm T}$-differential densities of ${\rm
K}^{0}_{\rm{S}}$, $\Lambda$, $\Xi$, and $\Omega$ in MB p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV. For each case, the density
distribution of JE particles is compared with that from JC and UE selections,
and that of inclusive particles. In general, the particle densities measured
in p–Pb collisions have the same order of magnitude as the corresponding ones
in pp collisions shown in Fig. 4. Similar to the case in pp collisions, the
density of JC-selected particles is dominated by those associated with hard
scattering at high $p_{\rm T}$ ($p_{\rm T}>3$ GeV/$c$). As in pp, the $p_{\rm
T}$-dependent density of JE particles is considerably less steep than the
inclusive ones. The UE component given by the PC selection is mainly located
in the low-$p_{\rm T}$ region but the contribution is larger than in pp
collisions. The UE fractions are $61.3\%$ ($47.0\%$), $80.4\%$ ($65.5\%$),
$90.0\%$ ($73.4\%$) and $61.4\%$ ($62.0\%$) for ${\rm K}^{0}_{\rm{S}}$,
$\Lambda$, and $\Xi$ in the interval of $0.9<p_{\rm T}<1.6$ GeV/$c$ and for
$\Omega$ in the interval of $0.9<p_{\rm T}<2.2$ GeV/$c$ in p–Pb (pp)
collisions, respectively. This follows the expectation that the multiplicity
of particles within the UE is correlated with the number of nucleon$-$nucleon
interactions and the energy density of the system. The $p_{\rm T}$-dependent
densities of ${\rm K}^{0}_{\rm{S}}$ mesons and $\Lambda$ and $\Xi$ baryons
with different selections are also measured for various event multiplicity
classes, presented in Figs. 11, 12, and 13 in Appendix C. The magnitude of the
density increases with the event multiplicity, and the results in the low
multiplicity class become almost identical to those in pp collisions.

Figure 9: $p_{\rm T}$-dependent strange baryon-to-meson (top) and baryon-to-
baryon (bottom) ratios for particles produced within jets in p–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV. For each case, the results for
different event multiplicity classes are compared with that in pp collisions
at $\sqrt{s}~{}=~{}13$ TeV. The statistical uncertainties are represented by
the vertical error bars and the systematic uncertainties by the boxes. See the
text for details.

The ratios of JE particles measured in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV are shown in Fig. 9. The results of
$\Lambda$/${\rm K}^{0}_{\rm{S}}$, $\Xi$/${\rm K}^{0}_{\rm{S}}$, and
$\Xi$/$\Lambda$ ratios are presented in three event multiplicity classes, from
high ($0$–$10\%$), intermediate ($10$–$40\%$) to low ($40$–$100\%$)
multiplicities, and compared with that in MB events. Since the multiplicity
differential analysis is challenging for $\Omega$ baryons due to the low
number of candidates the ratios of $\Omega$/${\rm K}^{0}_{\rm{S}}$,
$\Omega$/$\Lambda$ and $\Omega$/$\Xi$ are only given for the MB events. All
ratios are also compared with the corresponding measurements in pp collisions
at $\sqrt{s}~{}=~{}13$ TeV. Similar to what is observed in Ref. [32], the
$\Lambda$/${\rm K}^{0}_{\rm{S}}$ ratio obtained in p–Pb collisions is
systematically higher than that in pp collisions for $2<p_{\rm T}<4$ GeV/$c$:
in this $p_{\rm T}$ interval the ratio in p–Pb collisions also increases with
the event multiplicity. The differences are quantified in terms of standard
deviations considering statistical and systematic uncertainties. The
differences are $0.8\sigma$ between MB p–Pb collisions and pp collisions and
$1.1\sigma$ between high- ($0$–$10\%$) and low-multiplicity ($40$–$100\%$)
p–Pb collisions. A similar behavior is observed in ratios between other
particle species. However, due to substantial uncertainties, variations
between collision systems or among different event multiplicity classes for
p–Pb collisions are much less significant than for the $\Lambda$/${\rm
K}^{0}_{\rm{S}}$ ratio. The observed deviations remain to be studied with
better statistical precision.

The comparisons of the ratios for JE particles to those for inclusive and UE
particles for different event multiplicity classes are shown in Figs. 14, 15,
and 16 in Appendix C for $\Lambda$/${\rm K}^{0}_{\rm{S}}$, $\Xi$/${\rm
K}^{0}_{\rm{S}}$, and $\Xi$/$\Lambda$, respectively. Similar to what is
observed in pp collisions, in each event multiplicity class, the $p_{\rm T}$
dependence of the ratio for UE particles is consistent with that of inclusive
particles within uncertainties. Furthermore, the enhancement of particle
ratios at intermediate $p_{\rm T}$ is not observed in jets, suggesting that
the enhancement of particle ratios observed at high multiplicity in small
systems is only present in the UE and not a feature of jet fragmentation.

##  5 Summary

The production of ${\rm K}^{0}_{\rm{S}}$ mesons and $\Lambda$, $\Xi$, and
$\Omega$ baryons is measured separately for particles associated with hard
scatterings and the underlying event for the first time at the LHC in pp
collisions at $\sqrt{s}~{}=~{}13$ TeV and p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV. The results in pp collisions are
compared with Pythia $8$ CR-BLC simulations. Pythia $8$ simulations reproduce
fairly well the $\Lambda$/${\rm K}^{0}_{\rm{S}}$ ratio in data. However, large
discrepancies between data and simulations are observed in the ratios
including multi-strange baryons. In p–Pb collisions, the strange baryon-to-
meson and baryon-to-baryon yield ratios associated with jets for different
event multiplicity classes have a similar trend. Better statistical precision
is required to clarify their multiplicity and collision system dependence. The
enhancement in the ratio at intermediate $p_{\rm T}$ found in the inclusive
particle measurements in high-multiplicity p–Pb and Pb–Pb collisions is not
present for particles associated with hard scatterings selected by jets
reconstructed from charged particles for $p_{\rm T,jet}^{\rm ch}>10$ GeV/$c$.
Moreover, as the enhancement has been linked to the interplay of radial flow
and parton recombination at intermediate $p_{\rm T}$, its absence within the
jet cone demonstrates that these effects are indeed limited to the soft
particle production processes.

## References

  * [1] E. V. Shuryak, “Theory and phenomenology of the QCD vacuum”, Phys. Rept. 115 (1984) 151.
  * [2] J. Cleymans, R. Gavai, and E. Suhonen, “Quarks and Gluons at High Temperatures and Densities”, Phys. Rept. 130 (1986) 217.
  * [3] S. Bass, M. Gyulassy, H. Stoecker, and W. Greiner, “Signatures of quark gluon plasma formation in high-energy heavy ion collisions: A Critical review”, J. Phys. G 25 (1999) R1–R57, arXiv:hep-ph/9810281.
  * [4] H. Satz, “Color deconfinement in nuclear collisions”, Rept. Prog. Phys. 63 (2000) 1511, arXiv:hep-ph/0007069.
  * [5] B. V. Jacak and B. Muller, “The exploration of hot nuclear matter”, Science 337 (2012) 310–314.
  * [6] B. Muller, J. Schukraft, and B. Wyslouch, “First Results from Pb+Pb collisions at the LHC”, Ann. Rev. Nucl. Part. Sci. 62 (2012) 361–386, arXiv:1202.3233 [hep-ex].
  * [7] S. Borsanyi, G. Endrodi, Z. Fodor, A. Jakovac, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo, “The QCD equation of state with dynamical quarks”, JHEP 11 (2010) 077, arXiv:1007.2580 [hep-lat].
  * [8] T. Bhattacharya et al., “QCD Phase Transition with Chiral Quarks and Physical Quark Masses”, Phys. Rev. Lett. 113 (2014) 082001, arXiv:1402.5175 [hep-lat].
  * [9] P. Braun-Munzinger, V. Koch, T. Schäfer, and J. Stachel, “Properties of hot and dense matter from relativistic heavy ion collisions”, Phys. Rept. 621 (2016) 76–126, arXiv:1510.00442 [nucl-th].
  * [10] ATLAS Collaboration, G. Aad et al., “Observation of Long-Range Elliptic Azimuthal Anisotropies in $\sqrt{s}=$13 and 2.76 TeV $pp$ Collisions with the ATLAS Detector”, Phys. Rev. Lett. 116 (2016) 172301, arXiv:1509.04776 [hep-ex].
  * [11] ALICE Collaboration, B. Abelev et al., “Long-range angular correlations on the near and away side in p$-$Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV”, Phys. Lett. B719 (2013) 29–41, arXiv:1212.2001 [nucl-ex].
  * [12] ALICE Collaboration, B. Abelev et al., “Long-range angular correlations of $\rm\pi$, K and p in p-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV”, Phys. Lett. B726 (2013) 164–177, arXiv:1307.3237 [nucl-ex].
  * [13] CMS Collaboration, V. Khachatryan et al., “Evidence for Collective Multiparticle Correlations in p-Pb Collisions”, Phys. Rev. Lett. 115 (2015) 012301, arXiv:1502.05382 [nucl-ex].
  * [14] ALICE Collaboration, S. Acharya et al., “Investigations of Anisotropic Flow Using Multiparticle Azimuthal Correlations in pp, p-Pb, Xe-Xe, and Pb-Pb Collisions at the LHC”, Phys. Rev. Lett. 123 (2019) 142301, arXiv:1903.01790 [nucl-ex].
  * [15] ALICE Collaboration, B. Abelev et al., “$K^{*}(892)^{0}$ and $\phi(1020)$ production in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV”, Phys. Rev. C91 (2015) 024609, arXiv:1404.0495 [nucl-ex].
  * [16] ALICE Collaboration, J. Adam et al., “Multi-strange baryon production in p–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV”, Phys. Lett. B758 (2016) 389–401, arXiv:1512.07227 [nucl-ex].
  * [17] ALICE Collaboration, S. Acharya et al., “Multiplicity dependence of light-flavor hadron production in pp collisions at $\sqrt{s}$ = 7 TeV”, Phys. Rev. C99 (2019) 024906, arXiv:1807.11321 [nucl-ex].
  * [18] CMS Collaboration, V. Khachatryan et al., “Multiplicity and rapidity dependence of strange hadron production in pp, p–Pb, and Pb–Pb collisions at the LHC”, Phys. Lett. B768 (2017) 103–129, arXiv:1605.06699 [nucl-ex].
  * [19] ALICE Collaboration, B. Abelev et al., “${\rm K^{0}_{S}}$ and $\Lambda$ production in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV”, Phys. Rev. Lett. 111 (2013) 222301, arXiv:1307.5530 [nucl-ex].
  * [20] ALICE Collaboration, J. Adam et al., “Enhanced production of multi-strange hadrons in high-multiplicity proton–proton collisions”, Nature Phys. 13 (2017) 535–539, arXiv:1606.07424 [nucl-ex].
  * [21] ALICE Collaboration, B. Abelev et al., “Multiplicity Dependence of Pion, Kaon, Proton and Lambda Production in p-Pb Collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV”, Phys. Lett. B728 (2014) 25–38, arXiv:1307.6796 [nucl-ex].
  * [22] ALICE Collaboration, S. Acharya et al., “Measurements of inclusive jet spectra in pp and central Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV”, Phys. Rev. C101 (2020) 034911, arXiv:1909.09718 [nucl-ex].
  * [23] ALICE Collaboration, S. Acharya et al., “Measurement of charged jet cross section in $pp$ collisions at ${\sqrt{s}=5.02}$ TeV”, Phys. Rev. D100 (2019) 092004, arXiv:1905.02536 [nucl-ex].
  * [24] ALICE Collaboration, B. Abelev et al., “Charged jet cross sections and properties in proton-proton collisions at $\sqrt{s}=7$ TeV”, Phys. Rev. D91 (2015) 112012, arXiv:1411.4969 [nucl-ex].
  * [25] ALICE Collaboration, B. Abelev et al., “Measurement of the inclusive differential jet cross section in $pp$ collisions at $\sqrt{s}=2.76$ TeV”, Phys. Lett. B722 (2013) 262–272, arXiv:1301.3475 [nucl-ex].
  * [26] ALICE Collaboration, S. Acharya et al., “Charged jet cross section and fragmentation in proton-proton collisions at $\sqrt{s}$ = 7 TeV”, Phys. Rev. D99 (2019) 012016, arXiv:1809.03232 [nucl-ex].
  * [27] ALICE Collaboration, S. Acharya et al., “Constraints on jet quenching in p-Pb collisions at $\mathbf{\sqrt{s_{NN}}}$ = 5.02 TeV measured by the event-activity dependence of semi-inclusive hadron-jet distributions”, Phys. Lett. B783 (2018) 95–113, arXiv:1712.05603 [nucl-ex].
  * [28] ALICE Collaboration, J. Adam et al., “Measurement of dijet $k_{\rm T}$ in p–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV”, Phys. Lett. B746 (2015) 385–395, arXiv:1503.03050 [nucl-ex].
  * [29] ALICE Collaboration, J. Adam et al., “Centrality dependence of charged jet production in p–Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV”, Eur. Phys. J. C76 (2016) 271, arXiv:1603.03402 [nucl-ex].
  * [30] R. J. Fries, B. Muller, C. Nonaka, and S. A. Bass, “Hadronization in heavy ion collisions: Recombination and fragmentation of partons”, Phys. Rev. Lett. 90 (2003) 202303, arXiv:nucl-th/0301087.
  * [31] P. Bozek, “Hydrodynamic flow from RHIC to LHC”, Acta Phys. Polon. B43 (2012) 689, arXiv:1111.4398 [nucl-th].
  * [32] ALICE Collaboration, S. Acharya et al., “Production of $\Lambda$ and K${}^{0}_{\rm S}$ in jets in p–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and pp collisions at $\sqrt{s}=7$ TeV”, Phys. Lett. B827 (2022) 136984, arXiv:2105.04890 [nucl-ex].
  * [33] ALICE Collaboration, S. Acharya et al., “K${}_{\rm S}^{0}$\- and (anti-)$\Lambda$-hadron correlations in pp collisions at $\sqrt{s}=13$ TeV”, Eur. Phys. J. C81 (2021) 945, arXiv:2107.11209 [nucl-ex].
  * [34] ALICE Collaboration, S. Acharya et al., “Production of light-flavor hadrons in pp collisions at $\sqrt{s}=7$ and $\sqrt{s}=13$ TeV”, Eur. Phys. J. C81 (2021) 256, arXiv:2005.11120 [nucl-ex].
  * [35] S. D. Ellis, M. Jacob, and P. V. Landshoff, “Jets and Correlations in Large p(T) Reactions”, Nucl. Phys. B108 (1976) 93.
  * [36] T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O. Rasmussen, and P. Z. Skands, “An introduction to PYTHIA 8.2”, Comput. Phys. Commun. 191 (2015) 159–177, arXiv:1410.3012 [hep-ph].
  * [37] ALICE Collaboration, K. Aamodt et al., “The ALICE experiment at the CERN LHC”, JINST 3 (Aug, 2008) S08002.
  * [38] ALICE Collaboration, B. Abelev et al., “Performance of the ALICE Experiment at the CERN LHC”, Int. J. Mod. Phys. A29 (2014) 1430044, arXiv:1402.4476 [nucl-ex].
  * [39] ALICE Collaboration, E. Abbas et al., “Performance of the ALICE VZERO system”, JINST 8 (2013) P10016, arXiv:1306.3130 [nucl-ex].
  * [40] ALICE Collaboration, K. Aamodt et al., “Alignment of the ALICE Inner Tracking System with cosmic-ray tracks”, JINST 5 (2010) P03003, arXiv:1001.0502 [physics.ins-det].
  * [41] J. Alme et al., “The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events”, Nucl. Instrum. Meth. A622 (2010) 316–367, arXiv:1001.1950 [physics.ins-det].
  * [42] ALICE TOF Collaboration, A. Akindinov et al., “Particle identification with the ALICE TOF detector at very high particle multiplicity”, Eur. Phys. J. C32S1 (2004) 165–177.
  * [43] A. Akindinov et al., “The ALICE Time-Of-Flight system: Construction, assembly and quality tests”, Nuovo Cim. B124 (2009) 235–253.
  * [44] A. Akindinov et al., “Results of the ALICE time-of-flight detector from the 2009 cosmic-ray data taking”, Eur. Phys. J. C68 (2010) 601–607.
  * [45] ALICE Collaboration, “ALICE 2016-2017-2018 luminosity determination for pp collisions at $\mathbf{\sqrt{{\textit{s}}}}$ = 13 TeV.” ALICE-PUBLIC-2021-005.  http://cds.cern.ch/record/2776672.
  * [46] ALICE Collaboration, S. Acharya et al., “Azimuthal correlations of prompt D mesons with charged particles in pp and p–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV”, Eur. Phys. J. C80 (2020) 979, arXiv:1910.14403 [nucl-ex].
  * [47] ALICE Collaboration, J. Adam et al., “Pseudorapidity and transverse-momentum distributions of charged particles in proton-proton collisions at $\sqrt{s}=$ 13 TeV”, Phys. Lett. B753 (2016) 319–329, arXiv:1509.08734 [nucl-ex].
  * [48] M. Cacciari, G. P. Salam, and G. Soyez, “FastJet User Manual”, Eur. Phys. J. C72 (2012) 1896, arXiv:1111.6097 [hep-ph].
  * [49] M. Cacciari, G. P. Salam, and G. Soyez, “The anti-$k_{t}$ jet clustering algorithm”, JHEP 2004 (2008) 063, arXiv:0802.1189 [hep-ph].
  * [50] S. Catani, Y. L. Dokshitzer, M. H. Seymour, and B. R. Webber, “Longitudinally invariant $K_{t}$ clustering algorithms for hadron hadron collisions”, Nucl. Phys. B406 (1993) 187–224.
  * [51] S. D. Ellis and D. E. Soper, “Successive combination jet algorithm for hadron collisions”, Phys. Rev. D48 (1993) 3160–3166, arXiv:hep-ph/9305266.
  * [52] M. Cacciari and G. P. Salam, “Pileup subtraction using jet areas”, Phys. Lett. B659 (2008) 119–126, arXiv:0707.1378 [hep-ph].
  * [53] M. Cacciari, G. P. Salam, and G. Soyez, “The Catchment Area of Jets”, JHEP 2004 (2008) 005, arXiv:0802.1188 [hep-ph].
  * [54] CMS Collaboration, S. Chatrchyan et al., “Measurement of the underlying event activity in $pp$ collisions at $\sqrt{s}=0.9$ and 7 TeV with the novel jet-area/median approach”, JHEP 08 (2012) 130, arXiv:1207.2392 [hep-ex].
  * [55] Particle Data Group Collaboration, R. L. Workman et al., “Review of Particle Physics”, PTEP 2022 (2022) 083C01.
  * [56] ALICE Collaboration, K. Aamodt et al., “Strange particle production in proton-proton collisions at sqrt(s) = 0.9 TeV with ALICE at the LHC”, Eur. Phys. J. C71 (2011) 1594, arXiv:1012.3257 [hep-ex].
  * [57] ALICE Collaboration, B. Abelev et al., “Multi-strange baryon production in pp collisions at $\sqrt{s}=7$ TeV with ALICE”, Phys. Lett. B712 (2012) 309–318, arXiv:1204.0282 [nucl-ex].
  * [58] ALICE Collaboration, S. Acharya et al., “Multiplicity dependence of (multi-)strange hadron production in proton-proton collisions at $\sqrt{s}$ = 13 TeV”, Eur. Phys. J. C80 (2020) 167, arXiv:1908.01861 [nucl-ex].
  * [59] S. Roesler, R. Engel, and J. Ranft, “The Monte Carlo event generator DPMJET-III”, in International Conference on Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications (MC 2000), pp. 1033–1038.  12, 2000.  arXiv:hep-ph/0012252.
  * [60] R. Brun, F. Bruyant, F. Carminati, S. Giani, M. Maire, A. McPherson, G. Patrick, and L. Urban, “GEANT: Detector Description and Simulation Tool.” Cern-w5013, cern-w-5013, w5013, w-5013, 10, 1994.  https://cds.cern.ch/record/1082634.
  * [61] ALICE Collaboration, S. Acharya et al., “Underlying Event properties in pp collisions at $\sqrt{s}=13$ TeV”, JHEP 2004 (2020) 192, arXiv:1910.14400 [nucl-ex].
  * [62] J. R. Christiansen and P. Z. Skands, “String Formation Beyond Leading Colour”, JHEP 2008 (2015) 003, arXiv:1505.01681 [hep-ph].
  * [63] C. Bierlich and J. R. Christiansen, “Effects of color reconnection on hadron flavor observables”, Phys. Rev. D92 (2015) 094010, arXiv:1507.02091 [hep-ph].
  * [64] C. Bierlich, G. Gustafson, L. Lönnblad, and A. Tarasov, “Effects of Overlapping Strings in pp Collisions”, JHEP 03 (2015) 148, arXiv:1412.6259 [hep-ph].
  * [65] ALICE Collaboration, S. Acharya et al., “Production of charged pions, kaons, and (anti-)protons in Pb–Pb and inelastic pp collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV”, Phys. Rev. C101 (2020) 044907, arXiv:1910.07678 [nucl-ex].
  * [66] ALICE Collaboration, J. Adam et al., “Multiplicity dependence of charged pion, kaon, and (anti)proton production at large transverse momentum in p-Pb collisions at $\mathbf{\sqrt{{\textit{s}}_{\rm NN}}}$ = 5.02 TeV”, Phys. Lett. B760 (2016) 720–735, arXiv:1601.03658 [nucl-ex].
  * [67] ALICE Collaboration, B. Abelev et al., “Pion, Kaon, and Proton Production in Central Pb–Pb Collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV”, Phys. Rev. Lett. 109 (2012) 252301, arXiv:1208.1974 [hep-ex].
  * [68] ALICE Collaboration, B. Abelev et al., “Centrality dependence of $\pi$, K, p production in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV”, Phys. Rev. C88 (2013) 044910, arXiv:1303.0737 [hep-ex].
  * [69] ALICE Collaboration, B. Abelev et al., “Multi-strange baryon production at mid-rapidity in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV”, Phys. Lett. B728 (2014) 216–227, arXiv:1307.5543 [nucl-ex]. [Erratum: Phys.Lett.B 734, 409–410 (2014)].
  * [70] C. Bierlich et al., “A comprehensive guide to the physics and usage of PYTHIA 8.3”, arXiv:2203.11601 [hep-ph].

##  Appendix A Particle candidate selection criteria

Table 5: ${\rm K}^{0}_{\rm{S}}$ ($\Lambda$ and $\overline{\Lambda}$) candidate selection criteria of topological variables, daughter tracks and ${\rm V}^{0}$ candidates. The DCA stands for the “distance of closest approach”, PV represents the “primary collision vertex” and CPA is the “cosine pointing angle between the momentum vector of the reconstructed ${\rm V}^{0}$ and the displacement vector between the decay and primary vertices”. Topological variable |  pp |  p–Pb
---|---|---
${\rm V}^{0}$ transverse decay radius |  $>0.5$ cm |  $>0.5$ cm
DCA of ${\rm V}^{0}$ daughter track to PV |  $>0.06$ cm |  $>0.06$ cm
DCA between ${\rm V}^{0}$ daughter tracks |  $<1.0\sigma$ |  $<1\sigma$
CPA of ${\rm V}^{0}$ |  $>0.97$ ($0.995$) |  $>0.97$ ($0.995$)
Track selection |  |
Daughter track pseudorapidity interval |  $|\eta|<0.8$ |  $\left|\eta\right|<0.8$
Daughter track $N_{\rm crossed~{}rows}$ |  $\geq 70$ |  $\geq$ 70
Daughter track $N_{\rm crossed~{}rows}/N_{\rm findable}$ |  $\geq 0.8$ |  $\geq$ 0.8
TPC $\textrm{d}E/\textrm{d}x$ |  $<5\sigma$ |  $<5\sigma$
Candidate selection |  |
Pseudorapidity interval |  $|\eta|<0.75$ |  $|\eta|<0.75$
Proper lifetime ($mL/p$) |  $<20$ (30) cm |  $<20$ (30) cm
Competing mass |  $>0.005$ (0.010) GeV/$c^{2}$ |  $>0.005$ (0.010) GeV/$c^{2}$
Table 6: $\Xi^{\pm}$ ($\Omega^{\pm}$) candidate selection criteria of topological variables, daughter tracks and cascade candidates. Topological variable |  pp |  p–Pb
---|---|---
Cascade transverse decay radius |  $>0.8(0.6)$ cm |  $>0.6$ cm
${\rm V}^{0}$ transverse decay radius |  $>1.4$ cm |  $>1.2$ cm
DCA (bachelor to PV) |  $>0.05$ cm |  $>0.04$ cm
DCA (${\rm V}^{0}$ to PV) |  $>0.07$ cm |  $>0.06$ cm
DCA (positive / negative track to PV) |  $>0.04(0.03)$ cm |  $>0.03$ cm
DCA between ${\rm V}^{0}$ daughter tracks |  $<1.6\sigma$ |  $<1.5\sigma$
DCA (bachelor to ${\rm V}^{0}$) |  $<1.6(1.0)$ cm |  $<1.3$ cm
CPA of Cascade |  $>0.97$ |  $>0.97$
CPA of ${\rm V}^{0}$ |  $>0.97$ |  $>0.97$
${\rm V}^{0}$ invariant mass window |  $\pm 0.006$ GeV/$c^{2}$ |  $\pm 0.008$ GeV/$c^{2}$
Track selection |  |
Daughter track pseudorapidity interval |  $|\eta|<0.8$ |  $|\eta|<0.8$
Daughter track $N_{\rm crossed~{}rows}$ |  $\geq 70$ |  $\geq$ 70
Daughter track $N_{\rm crossed~{}rows}/N_{\rm findable}$ |  $\geq 0.8$ |  $\geq$ 0.8
TPC $\textrm{d}E/\textrm{d}x$ |  $<5\sigma$ |  $<4\sigma$
Candidate selection |  |
Pseudorapidity interval |  $|\eta|<0.75$ |  $|\eta|<0.75$
Proper lifetime ($mL/p$) |  |  $<3\times c\tau$
Competing mass |  $8$ MeV/$c^{2}$ |  $8$ MeV/$c^{2}$

##  Appendix B Comparison of $\Xi$/$\Lambda$ and $\Omega^{-}$/$\Lambda$ ratios
to colour-rope predictions in pp collisions at $\sqrt{s}~{}=~{}13$ TeV

Figure 10: $p_{\rm T}$-dependent $\Xi$/$\Lambda$ (left panel) and
$\Omega^{-}$/$\Lambda$ (right panel) ratios in pp collisions at
$\sqrt{s}~{}=~{}13$ TeV. For each case, the results of JE particles (red
inverted-triangle) are compared with that of inclusive (black closed circles).
The corresponding colour-rope predictions [64] implemented in the Pythia $8$
event generator [70] are compared to data as well.

##  Appendix C $p_{\rm T}$-differential particle density and ratios for event
multiplicity classes in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$
TeV

Figure 11: $p_{\rm T}$-differential density, $\mathrm{d}\rho/\mathrm{d}p_{\rm
T}$, of ${\rm K}^{0}_{\rm{S}}$ (left panel), $\Lambda$ (middle panel) and
$\Xi$ (right panel) for the $0$–$10\%$ event multiplicity class in p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV. The spectra of JE
particles (red inverted-triangle), associated with hard scatterings, are
compared with that of JC (green squares) and UE (blue open circles)
selections. The results from inclusive measurements (black closed circles) are
presented as well. The statistical uncertainties are represented by the
vertical error bars and the systematic uncertainties by the boxes. Figure 12:
$p_{\rm T}$-differential density, $\mathrm{d}\rho/\mathrm{d}p_{\rm T}$, of
${\rm K}^{0}_{\rm{S}}$ (left panel), $\Lambda$ (middle panel) and $\Xi$ (right
panel) for the $10$–$40\%$ event multiplicity class in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV. The spectra of JE particles (red
inverted-triangle), associated with hard scatterings, are compared with that
of JC (green squares) and UE (blue open circles) selections. The results from
inclusive measurements (black closed circles) are presented as well. The
statistical uncertainties are represented by the vertical error bars and the
systematic uncertainties by the boxes. Figure 13: $p_{\rm T}$-differential
density, $\mathrm{d}\rho/\mathrm{d}p_{\rm T}$, of ${\rm K}^{0}_{\rm{S}}$ (left
panel), $\Lambda$ (middle panel) and $\Xi$ (right panel) for the $40$–$100\%$
event multiplicity class in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV. The spectra of JE particles (red
inverted-triangle), associated with hard scatterings, are compared with that
of JC (green squares) and UE (blue open circles) selections. The results from
inclusive measurements (black closed circles) are presented as well. The
statistical uncertainties are represented by the vertical error bars and the
systematic uncertainties by the boxes. Figure 14: $p_{\rm T}$-dependent
$\Lambda$/${\rm K}^{0}_{\rm{S}}$ ratio for $0$–$10\%$ (left panel),
$10$–$40\%$ (middle panel) and $40$–$100\%$ (right panel) event multiplicity
classes. For each case, the results of JE particles (red inverted-triangle)
are compared with that of inclusive (black closed circles) and UE (blue open
circles) particles. The statistical uncertainties are represented by the
vertical error bars and the systematic uncertainties by the boxes. Figure 15:
$p_{\rm T}$-dependent $\Xi$/${\rm K}^{0}_{\rm{S}}$ ratio for $0$–$10\%$ (left
panel), $10$–$40\%$ (middle panel) and $40$–$100\%$ (right panel) event
multiplicity classes. For each case, the results of JE particles (red
inverted-triangle) are compared with that of inclusive (black closed circles)
and UE (blue open circles) particles. The statistical uncertainties are
represented by the vertical error bars and the systematic uncertainties by the
boxes. Figure 16: $p_{\rm T}$-dependent $\Xi$/$\Lambda$ ratio for $0$–$10\%$
(left panel), $10$–$40\%$ (middle panel) and $40$–$100\%$ (right panel) event
multiplicity classes. For each case, the results of JE particles (red
inverted-triangle) are compared with that of inclusive (black closed circles)
and UE (blue open circles) particles. The statistical uncertainties are
represented by the vertical error bars and the systematic uncertainties by the
boxes.