2023 172 21 August

$\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ production in pp collisions at
$\mathrm{\sqrt{\it{s}}}$ = 13 TeV

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

The production yields of the $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$
resonances are measured in pp collisions at $\sqrt{\it{s}}=13$ TeV with ALICE.
The measurements are performed as a function of the charged particle
multiplicity $\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$, which
is related to the energy density produced in the collision. The results
include transverse momentum ($p_{\mathrm{T}}$) distributions,
$p_{\mathrm{T}}$-integrated yields, mean transverse momenta of
$\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$, as well as ratios of the
$p_{\mathrm{T}}$-integrated resonance yields relative to yields of other
hadron species. The $\Sigma(1385)^{\pm}/\pi^{\pm}$ and
$\Xi(1530)^{0}/\pi^{\pm}$ yield ratios are consistent with the trend of the
enhancement of strangeness production from low to high multiplicity pp
collisions, which was previously observed for strange and multi-strange
baryons. The yield ratio between the measured resonances and the long-lived
baryons with the same strangeness content exhibits a hint of a mild increasing
trend at low multiplicity, despite too large uncertainties to exclude the flat
behaviour. The results are compared to predictions from models such as EPOS-
LHC and $\mathrm{PYTHIA\,\,8}$ with Rope shoving. The latter provides the best
description of the multiplicity dependence of the $\Sigma(1385)^{\pm}$ and
$\Xi(1530)^{0}$ production in pp collisions at $\mathrm{\sqrt{\it{s}}}$ = 13
TeV.

##  1 Introduction

Quantum chromodynamics (QCD) [1, 2] predicts an extreme state of nuclear
matter at high temperature and energy density where quarks and gluons are not
confined into hadrons, the quark–gluon plasma (QGP). These conditions are
achieved in ultrarelativistic heavy-ion collisions [3, 4, 5, 6, 7, 8] like
those at at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron
Collider (LHC). As the system created during the collision evolves, the QGP
matter cools down and a transition to a hadron gas occurs when the pseudo-
critical temperature is reached. During the subsequent hadronic phase,
inelastic scatterings among hadrons a priori stop at the chemical freeze-out
and elastic interactions cease at the later time of kinetic freeze-out.

The measurement of the production of strange hadrons has an important role in
the study of the QGP properties [9, 10, 11]. A large abundance of strange
hadrons in nucleus–nucleus (AA) collisions relative to proton–proton (pp)
collisions has manifested itself, without significant initial energy or volume
dependence from RHIC to LHC energies [12, 13, 14]. Strangeness production in
central heavy-ion collisions is described in the frame of statistical
hadronisation models utilising a grand canonical formulation and assuming a
hadron gas in thermal and chemical equilibrium at the chemical freeze-out
stage [15, 16, 17, 18, 19]. Meanwhile, a continuous enhancement of strange
particles relative to pions has been observed with increasing number of
charged particles produced in the final state from pp, p–Pb to peripheral
Pb–Pb collisions [20]. The statistical model with strangeness canonical
suppression [21, 22] and the core-corona superposition model [23, 24] predict
the multiplicity dependence of strangeness production in small systems.

Hadron resonances are powerful tools to study the properties of the late
hadronic phase in ultrarelativistic heavy-ion collisions since the duration of
such a phase is of the same order of magnitude as the resonance lifetimes (few
fm/c) [25]. Such resonances are influenced by interactions in the hadronic
phase. If resonances decay before the kinetic freeze-out, the resonance yield
reconstructed from the kinematics of the decay particles should decrease
relative to the primordial resonance yield due to rescattering of the decay
particles. Conversely, pseudo-elastic scattering of long-lived hadrons
occurring after chemical freeze-out can generate resonances and potentially
increase the observed yield. The balance between rescatterings and
regeneration depends on the scattering cross sections of the decay products,
the density of the produced hadron gas, the lifetime of the resonances, and
the hadronic phase duration [25]. Such a hot and dense medium cannot be
usually expected to be produced in pp collisions, in contrast to ultra-
relativistic heavy-ion collisions. However, recent measurements in high-
multiplicity pp collisions [26, 27, 28] showed some features resembling those
observed in heavy-ion collisions, which are understood as due to the
collective expansion of the medium. Thus, the study of resonance production in
pp collisions depending on the multiplicity of charged particles possibly
provides insight into the role of the hadronic interactions in small systems
[29, 30, 31].

The $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ baryons are good candidates for
the study of single and double-strange resonances with different lifetimes.
These baryonic resonances were previously measured in inelastic pp collisions
at $\mathrm{\sqrt{\it{s}}}$ = 7 TeV [32] and as a function of the charged
particle multiplicity in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02
TeV [33]. The present measurements in pp collisions at $\sqrt{\it{s}}=13$ TeV
extend our knowledge on the production of $\Sigma(1385)^{\pm}$ and
$\Xi(1530)^{0}$ at different centre-of-mass energy and charged particle
multiplicity. Moreover, the measurement reported here provides insight, for
the first time, into the production of these baryonic resonances as a function
of the charged-particle multiplicity, which is related to the energy density
in pp collisions.

##  2 Experimental setup

A detailed description of the ALICE detector can be found in [34, 8], where
the configuration in place during the Run 1 period of the LHC (2009–2013) is
discussed. This configuration is essentially valid also for the Run 2
(2015–2018) when the data used in this analysis were collected. The main
detectors used for the measurement of $\Sigma(1385)^{\pm}$ (also denoted as
$\Sigma^{*\pm}$ in the following) and $\Xi(1530)^{0}$ (denoted as $\Xi^{*0}$)
reported here are briefly discussed below.

The V0 detector [35, 36] consists of two arrays (V0A and V0C) of 32
scintillating counters each. The V0A (V0C) is located at a distance of 329 cm
($-88$ cm) away from the nominal interaction point ($z=0$) along the beam line
that defines the $z$-axis in the coordinate system. The V0A (V0C) covers the
pseudorapidity range $2.8<\eta<5.1$ ($-3.7<\eta<-1.7$) and the full azimuth.
It is used for triggering, for rejection of beam-induced background events,
and for the determination of the multiplicity classes by measuring the sum of
the signals from V0A and V0C forming the V0M signal.

The Inner Tracking System (ITS) [34] is composed of six silicon layers and is
the innermost detector of ALICE. The ITS is used for charged track
reconstruction, and in particular to provide high-precision points in the
vicinity of the primary vertex of the collision. The first two layers of the
ITS consist of the Silicon Pixel Detector (SPD), located at an average radial
distance $\it{r}$ of 3.9 cm and 7.6 cm from the beam line and covering the
pseudorapidity ranges $|\eta|<1.4$ and $|\eta|<2.0$ and the full azimuth
around the interaction point. The SPD is used to reconstruct short track
segments that are called tracklets and to determine the primary vertex of the
collision. Beyond the SPD, there are two layers of Silicon Drift Detectors
(SDD) and two layers of Silicon Strip Detectors (SSD), with the outermost
layer having a radius $r=43$ cm.

The Time Projection Chamber (TPC) [34], located just outside the ITS, is a 90
$\mathrm{m^{3}}$ cylindrical drift chamber filled with a gas mixture and has a
large number of readout channels (557568 [37]). The radial and the
longitudinal dimensions of the TPC are about 85 < $r$ < 250 cm and -250 < $z$
< 250 cm, respectively. The TPC covers the pseudorapidity range $|\eta|<0.9$
and the full azimuthal angle. It provides excellent momentum and spatial
resolution for the reconstruction of charged-particle tracks. Besides its
tracking capability, the TPC is used for particle identification by measuring
the specific ionisation energy loss (d$E$/d$x$) in the gas.

##  3 Data Analysis

The data sample used in this study was collected with the ALICE detector
during the LHC Run 2 (2015–2018) in pp collisions at $\mathrm{\sqrt{\it{s}}}$
= 13 TeV with a minimum bias (MB) trigger, which selects inelastic collisions
based on the requirement of coincident signals in the V0A and V0C detectors.
In addition to the MB trigger requirement, at least one primary charged
particle track in the $|\eta|<1$ range is required in the offline event
selection ($\mathrm{INEL>0}$). The transverse momentum ($p_{\mathrm{T}}$)
thresholds of the V0 and SPD detectors are around 50 MeV/$\it{c}$ [38, 39].
Events with pileup of collisions occurring in different bunch crossings (out-
of-bunch pileup) within the V0 readout time are rejected based on the timing
information of the V0. Events with collision pileup in the same bunch crossing
(in-bunch pileup) are removed based on the presence multiple primary vertices
reconstructed from SPD tracklets [38]. Further background events are rejected
by using the correlation between the number of hits and the number of
tracklets in the SPD. Events having a primary vertex (PV) reconstructed from
global tracks (at least ITS+TPC information), within the range of $\pm$10
$\mathrm{cm}$ with respect to the nominal interaction point along the beam
axis are considered. The total number of minimum bias triggered pp events
analysed is $1.82\times 10^{9}$ corresponding to an integrated luminosity of
$\mathcal{L}_{\mathrm{int}}$ = 31.5 $\mathrm{nb}^{-1}$ [40].

The $\mathrm{INEL>0}$ data sample is split into several event classes denoted
with Roman numerals by measuring the event activity via the total charge
deposited in both V0 detectors, see details in Ref [41]. Table 1 presents the
event classes used in this analysis, their corresponding percentile of the
$\mathrm{INEL>0}$ class, and their mean charged-particle multiplicity density
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$ measured in
$|\eta|<0.5$. Note that some event classes (e.g. I, II, and III) are merged in
this analysis (e.g. I+II+III) to increase the statistical significance. The
detailed information on
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$ distributions and
values in each event class is reported in [42].

In addition to the study of the multiplicity dependence of particle production
in the $\mathrm{INEL>0}$ data sample [42], a separate analysis based on the
data from inelastic events (INEL) [38] is carried out. This inelastic (INEL)
analysis differs from the $\mathrm{INEL>0}$ only by the event selection based
on the MB trigger, that does not request the condition that at least one
primary charged particle track in the $|\eta|<1$ range is present. It implies
that the corresponding event normalisation and its corrections differ; for
INEL, the correction on the event normalisation is obtained from the ratio of
the ALICE visible cross section to the total inelastic cross section [40, 43]

Table 1: The event classes [41] used in this analysis, their corresponding multiplicity percentile P $\left(\mathrm{INEL>0}\right)(\%)$ and the mean charged particle multiplicity, $\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$ [41, 43]. The $\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$ in inelastic events is $5.31\pm 0.18$ [44]. Event Class | P $\left(\mathrm{INEL>0}\right)(\%)$ | $\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$
---|---|---
I+II+III |  0–9.29 | $18.16\pm 0.54$
IV+V+VI |  9.29–27.88 | $10.94\pm 0.30$
VII+VIII |  27.88–46.58 |  $7.02\pm 0.15$
IX |  46.58–65.82 |  $4.36\pm 0.06$

###  3.1 Reconstruction of $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$

The properties of the particles involved in this analysis and the decay modes
used for their reconstruction together with the branching ratios are reported
in Table 2.

Table 2:  Quark content, mass, width, lifetime, decay channel used in this analysis and corresponding branching ratio for the $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ resonances as well as for the $\Xi^{-}$ and $\Lambda$ [45] hyperons. Antiparticles are not listed for conciseness. Baryon | Valence | Mass | Width | $\it{c}\rm{\tau}$ | Decay channel | B.R.
---|---|---|---|---|---|---
quarks | (MeV/$c^{2}$) | (MeV/$c^{2}$) | (fm) | (%)
$\Sigma(1385)^{+}$ | uus | $1382.8\pm 0.4$ | $36.0\pm 0.7$ |  $5.5\pm 0.1$ |  $\Lambda+\pi^{+}$ | $87.0\pm 1.5$
$\Sigma(1385)^{-}$ | dds | $1387.2\pm 0.5$ | $39.4\pm 2.1$ |  $5.0\pm 0.3$ |  $\Lambda+\pi^{-}$ | $87.0\pm 1.5$
$\Xi(1530)^{0}$ | uss | $1531.8\pm 0.3$ |  $9.1\pm 0.5$ | $22.0\pm 1.0$ | $\Xi^{-}+\pi^{+}$ | $66.7$
$\Xi^{-}$ | dss | $1321.7\pm 0.1$ |  | $4.91\times 10^{13}$ |  $\Lambda+\pi^{-}$ | $99.9$
$\Lambda$ | uds | $1115.7$ |  | $7.89\times 10^{13}$ |  $\rm{p}+\pi^{-}$ | $63.9\pm 0.5$

The charged $\Sigma(1385)^{\pm}$ and the $\Xi(1530)^{0}$ are reconstructed via
their hadronic decay channels. The two charged states $\Sigma(1385)^{+}$,
$\Sigma(1385)^{-}$ and their anti-particles ($\overline{\Sigma}(1385)^{-}$,
and $\overline{\Sigma}(1385)^{+}$) are separately reconstructed via

$\displaystyle\Sigma(1385)^{+}$
$\displaystyle\rightarrow\Lambda+\pi^{+}\rightarrow(\mathrm{p}+\pi^{-})+\pi^{+}$
(1) $\displaystyle\overline{\Sigma}(1385)^{-}$
$\displaystyle\rightarrow\overline{\Lambda}+\pi^{-}\rightarrow(\overline{\mathrm{p}}+\pi^{+})+\pi^{-}$
$\displaystyle\Sigma(1385)^{-}$
$\displaystyle\rightarrow\Lambda+\pi^{-}\rightarrow(\mathrm{p}+\pi^{-})+\pi^{-}$
$\displaystyle\overline{\Sigma}(1385)^{+}$
$\displaystyle\rightarrow\overline{\Lambda}+\pi^{+}\rightarrow(\overline{\mathrm{p}}+\pi^{+})+\pi^{+}\quad.$

Likewise, $\Xi(1530)^{0}$ and its antiparticle ($\overline{\Xi}(1530)^{0}$)
are reconstructed via

$\displaystyle\Xi(1530)^{0}$
$\displaystyle\rightarrow\Xi^{-}+\pi^{+}\rightarrow(\Lambda+\pi^{-})+\pi^{+}\rightarrow[(\mathrm{p}+\pi^{-})+\pi^{-}]+\pi^{+}$
(2) $\displaystyle\overline{\Xi}(1530)^{0}$
$\displaystyle\rightarrow\overline{\Xi}^{+}+\pi^{-}\rightarrow(\overline{\Lambda}+\pi^{+})+\pi^{-}\rightarrow[(\overline{\mathrm{p}}+\pi^{+})+\pi^{+}]+\pi^{-}\quad.$

The decays are schematically presented in Fig. 1 which illustrates the major
variables used in the selection of decay topologies on a magnified scale for
clarity.

(a) $\Sigma(1385)^{\pm}$

(b) $\Xi(1530)^{0}$

Figure 1: Sketch of the decay modes of $\Sigma(1385)^{\pm}$ and
$\Xi(1530)^{0}$ and depiction of the relevant variables employed for the
selection of displaced decay topologies. The position of the decay vertex of
the resonances is inflated to separate it from the PV for clarity.

The $p_{\mathrm{T}}$-differential yields in inelastic pp collisions are
calculated using the following equation:

$\frac{1}{N_{\mathrm{event}}}\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}=\frac{\epsilon_{\rm{Trig}}\times\epsilon_{\rm{Vertex}}}{N_{\rm{event,raw}}}\frac{N_{\rm{raw}}\times
f_{\rm{S.L.}}}{\Delta p_{\mathrm{T}}\Delta
y}\frac{1}{A\times\epsilon_{\rm{rec}}\times\rm{B.R.}}\quad,$ (3)

where $N_{\mathrm{event,raw}}$ is the total number of analysed events after
the online trigger and the offline selections, $N_{\rm{raw}}$ is the raw yield
of the particles extracted in each $p_{\mathrm{T}}$ and rapidity interval,
with widths of $\Delta p_{\mathrm{T}}$ and $\Delta y$. The factor $\it{A}$ is
the acceptance of the detector, ${\epsilon}_{\rm{rec}}$ is the resonance
reconstruction efficiency, and $\rm{B.R.}$ is the branching ratio of the decay
used for the $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ reconstruction.
$\epsilon_{\rm{Trig}}$ is the trigger efficiency, $\epsilon_{\rm{Vertex}}$ is
the vertex selection efficiency, and both correct the number of events.
$f_{\rm{S.L.}}$ is the $p_{\rm{T}}$-dependent signal loss correction factor
correcting the raw signal yields. The extraction of the raw yield,
$N_{\rm{raw}}$, is discussed in Section 3.3. The correction factors, such as
the $p_{\mathrm{T}}$-dependent $A\times{\epsilon}_{\rm{rec}}\times\rm{B.R.}$,
the multiplicity-dependent $\epsilon_{\rm{Trig}}$ and
$\epsilon_{\rm{Vertex}}$, and $f_{\rm{S.L.}}$ which is dependent on both
$p_{\mathrm{T}}$ and multiplicity, are discussed in Section 3.4.

###  3.2 Track and topological selections

Due to the very short lifetime of the strong decaying $\Sigma(1385)^{\pm}$ and
$\Xi(1530)^{0}$ baryons, pions and hyperons originating from the primary
vertex are considered for the reconstruction of the resonances. Pions from the
primary vertex are required to have $p_{\mathrm{T}}>0.15$ GeV and to be
located in the pseudorapidity range $|\eta|<0.8$ to avoid edge effects in the
TPC acceptance [34]. To ensure a good track reconstruction quality, primary
tracks are required to cross at least 70 out of 159 TPC readout rows with a
normalised $\chi^{2}$ ($\chi^{2}$ per TPC space point) lower than 4. In
addition, tracks are required to have a ratio of crossed readout rows,
$N_{\rm{crossed}}$, to the number of findable clusters,
$N_{\rm{findablecluster}}$, in the TPC larger than 80%. Primary tracks are
also required to have at least one hit in the SPD. The $\chi^{2}_{\rm{ITS-
TPC}}$, calculated by comparing combined ITS+TPC track parameters to those
obtained only from the TPC and constrained to the interaction point, is
required to be lower than 36. $\Xi^{-}$ and $\Lambda$ baryons produced in the
resonance decays are long lived and they are reconstructed from their decay
particles produced in secondary vertices displaced from the primary vertex.
The decay particles produced in these secondary vertices are selected among
tracks with $|\eta|<0.8$ based on a looser selection with respect to the one
for the primary tracks. They are required to cross at least 60 TPC readout
rows, while no request on ITS hits is applied. Finally, the selected pion and
proton candidates are identified by requiring that the specific ionisation
energy loss, $\rm{d}\it{E}/\rm{d}\it{x}$, measured in the TPC lies within
three standard deviations ($\sigma_{\rm{TPC}}$) from the specific energy loss
expected for pions or protons.

The first emitted pion ($\pi^{\pm}_{\,\rm{First}}$ in Fig.1) tracks appear as
if they originate from the primary vertex (PV), so they are selected using the
condition that the distance of closest approach ($\mathrm{DCA}$) to the
primary vertex along the beam axis ($\mathrm{DCA}_{z}$) should be lower than 2
cm and the DCA in the transverse plane ($\mathrm{DCA}_{r}$) lower than
$0.0105+0.035p_{\mathrm{T}}^{-1.1}$ cm, with $p_{\mathrm{T}}$ in units of
GeV/$c$. The primary track selection criteria, which are the standard criteria
used in ALICE analyses, are summarised in Table 3, along with those for
secondary tracks.

Table 3: Summary of the track selection criteria applied to primary and
secondary tracks. Secondary track selection
---
$|\eta|$ | $<0.8$
$N_{\rm{crossed}}$ | $>60$
TPC $\rm{d}\it{E}/\rm{d}\it{x}$ | $<3\sigma$
Primary track selection
$|\eta|$ | $<0.8$
$p_{\mathrm{T}}$ |  $>0.15$ GeV/$c$
$N_{\rm{crossed}}$ | $>70$
$N_{\rm{crossed}}/N_{\rm{findablecluster}}$ | $>0.8$
$\chi^{2}$/cluster in TPC | $<4$
$\chi^{2}$ of ITS-TPC track fit | $<36$
$\mathrm{DCA}_{z}$ to PV |  $<2$ cm
$\mathrm{DCA}_{r}$ to PV |  $<0.0105+0.035p_{\mathrm{T}}^{-1.1}$ cm
number of SPD points | $\geq 1$
TPC $\rm{d}\it{E}/\rm{d}\it{x}$ | $<3\sigma$

The secondary vertices of $\Lambda$ and $\Xi^{-}$ are reconstructed via their
decay mode into p+$\pi^{-}$ and $\Lambda$+$\pi^{-}$ (and charge conjugates)
respectively, by applying a similar strategy as the one used in [43, 41, 32,
33]. The applied geometrical selections on the displaced decay-vertex topology
are summarised in Table 4.

The $\Lambda$($\overline{\Lambda}$) from $\Sigma(1385)^{\pm}$ decays are
selected if the DCA between the two daughter tracks (DCA $\Lambda$ daughters
in Fig.1(a)) is smaller than 1.6 cm and the DCA of the $\Lambda$ in the
$xy$-plane to the PV ($r(\Lambda)$ in Fig.1(a)) is larger than 0.02 cm to
ensure that those tracks are not primary charged particles coming from the PV.
In addition, the DCA of $\Lambda$ to the PV is required to be lower than 0.3
cm to reject the $\Lambda$ baryons from $\Xi^{-}$ or $\overline{\Xi}^{+}$
[32]. The invariant mass of the $m_{\mathrm{p\pi^{-}}}$ pair is required to be
within $\pm 10$ MeV/$c^{2}$ with respect to the world-average $\Lambda$ mass
value [45], i.e. within a mass window which is at least about 4 times the
reconstructed mass resolution for $\Lambda$ [46]. The cosine of the pointing
angle ($\theta_{\Lambda}$) between the direction of the momentum of the
$\Lambda$ and the line connecting the secondary to the primary vertex is
required to be larger than 0.98 to reject any potential secondary $\Lambda$
from other particle decays.

Table 4: Summary of the selection criteria for $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ candidates. See the text and Fig. 1 for the details. Selection criteria | $\Sigma(1385)^{\pm}$ | $\Xi(1530)^{0}$
---|---|---
DCA $\Lambda$ daughters (cm) | $<1.6$ | $<1.4$
DCA $\Lambda$ to PV (cm) | $<0.3$ | $>0.07$
DCA $\pi$ to PV (cm) | $>0.05$ | $>0.05$
DCA $\rm{p}$ to PV (cm) | $>0.05$ | $>0.05$
$\cos{\theta_{\Lambda}}$ | $>0.98$ | $>0.97$
$r$($\Lambda$) (cm) | $1.4<r<100$ | $0.2<r<100$
$|m_{\mathrm{p\pi}}-m_{\Lambda,\rm{PDG}}|$ (MeV/$c^{2}$) | $<10$ | $<7$
$\mathrm{DCA}_{r}$ of pions decaying from $\Xi^{-}$ to the PV (cm) |  | $>0.015$
DCA $\Xi^{-}$ daughters (cm) |  | $<1.6$
$\cos{\theta_{\Xi}}$ |  | $>0.97$
$r$($\Xi$) (cm) |  | $0.2<r<100$
$|m_{\mathrm{\Lambda\pi}}-m_{\Xi,\rm{PDG}}|$ (MeV/$c^{2}$) |  | $<7$
$|y|$ of reconstructed resonance | $<0.5$

The $\Xi^{-}$ from $\Xi(1530)^{0}$ decays are selected by requiring that the
accompanying pion called "bachelor" pion, $\pi^{-}_{\rm{Bach}}$, and the
$\Lambda$ baryon stem from a common point in space by imposing that the DCA
between $\Xi^{-}$ daughters is < 1.6 cm (see Fig.1(b)) and further demanding
the $\pi^{-}_{\rm{Bach}}$ from $\Xi^{-}$ to be a secondary particle, i.e. a
track sufficiently apart from the primary vertex
($\mathrm{DCA}\leavevmode\nobreak\ \pi^{-}_{\rm{Bach}}$ to PV > 0.015 cm). The
DCA between the $\Lambda$ decay products, $\pi$ and p ($\rm{DCA}$ $\Lambda$
$\rm{daughters}$ in Fig.1(b)) is required to be lower than 1.4 cm. The
$\Lambda$ baryon itself is a secondary decay product in the decay topology,
hence the $\rm{DCA}$ of $\Lambda$ to the PV ($\rm{DCA}$ $\Lambda$ $\rm{to}$
$\rm{PV}$ in Fig.1(b)) is required to be larger than 0.07 cm. Selections on
the invariant masses of the daughter particles, the cosine of the pointing
angles ($\theta_{\Lambda}$ and $\theta_{\Xi}$), and the transverse distance
from PV $r$($\Lambda$) and $r$($\Xi$) are applied to optimise the balance
between purity and efficiency of each particle species. The selection criteria
for $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ are listed in Table 4.

Finally, all reconstructed resonances are required to be in the rapidity
interval ($|y|<0.5$).

###  3.3 Signal extraction

(a)

(b)

(c)

(d)

Figure 2: The invariant mass distribution of
$\Lambda\pi^{+}+\overline{\Lambda}\pi^{-}$ pairs (a) and the charge conjugates
(c) in $|y|<0.5$ produced in pp collisions at $\sqrt{s}=13$ TeV for
$1.8<p_{\mathrm{T,\,\Lambda\pi}}<2.0$ GeV/$c$ and the I+II+III multiplicity
class (full black circles). The combinatorial background estimated with the
event mixing technique is shown as open red squares in the (a) and (c) panels,
whereas the invariant mass distributions after combinatorial background
subtraction are shown in the (b) and (d) panels together with the fits to the
signal and the residual background contributions. The solid red curves are the
results of the combined fit and the dashed black lines represent the residual
background.

The selected hyperons and primary pions from the same event are combined into
pairs to compute the invariant mass in given $p_{\mathrm{T}}$ intervals and in
the region $|y|<0.5$. The invariant mass distributions of $\Lambda\pi^{+}$
($\overline{\Lambda}\pi^{-}$) and $\Lambda\pi^{-}$
($\overline{\Lambda}\pi^{+}$) pairs for $1.8<p_{\mathrm{T}}<2.0$ GeV/$c$ and
$\Xi^{-}\pi^{+}$ ($\Xi^{+}\pi^{-}$) pairs for $1.6<p_{\mathrm{T}}<2.0$ GeV/$c$
are shown in Figs. 2 and 3, respectively. In order to increase the
significance of the signal, the invariant mass distributions of
$\Sigma(1385)^{+}$ and $\overline{\Sigma}(1385)^{-}$ are summed together in
Fig. 2a and 2b. Similarly, the distributions for $\Sigma(1385)^{-}$ and
$\overline{\Sigma}(1385)^{+}$ (Fig. 2c and 2d), as well as $\Xi(1530)^{0}$ and
$\overline{\Xi}(1530)^{0}$, are also summed (Fig. 3). The combinatorial
background distributions in the figures are estimated through an event-mixing
technique where $\Lambda\pi$ ($\Xi\pi$) pairs are formed by combining
$\Lambda$ ($\Xi$) candidates from one event with $\pi$ from different events.
Each event is combined with nine others. To minimise distortions due to the
different positions of the PV and to ensure a similar event structure, the
events entering the pool for mixing are requested to i) have a similar PV
position in the $z$ direction ($|\Delta z_{\mathrm{PV}}|<1$ cm) and ii) belong
to the same multiplicity class.

(a)

(b)

Figure 3:  The invariant mass distribution of $\Xi^{-}\pi^{+}+\Xi^{+}\pi^{-}$
pairs in $|y|<0.5$ produced in pp collisions at $\sqrt{s}=13$ TeV for
$1.6<p_{\mathrm{T,\,\Lambda\pi}}<2.0$ GeV/$c$ and the I+II+III multiplicity
class (full black circles). The combinatorial background estimated with the
event mixing technique is shown as open red squares in panel (a), whereas the
invariant mass distribution after combinatorial background subtraction is
shown in panel (b) together with the fits to the signal and the residual
background contributions. The solid red curve is the result of the combined
fit and the dashed black line represents the residual background.

The mixed-event background and the same-event distributions are normalised in
an invariant mass interval where they are supposed to overlap, away from the
signal peak. The normalisation regions are $1.7<M_{\Lambda\pi}<1.9$
GeV/$c^{2}$ and $1.65<M_{\Xi\pi}<1.75$ GeV/$c^{2}$ for $\Lambda\pi$ and
$\Xi\pi$ invariant mass distributions, respectively.

The mixed-event background is subtracted from the same-event invariant mass
distribution producing the histograms for $\Sigma(1385)^{+}$
($\overline{\Sigma}(1385)^{-}$), $\Sigma(1385)^{-}$
($\overline{\Sigma}(1385)^{+}$) and $\Xi(1530)^{0}$
($\overline{\Xi}(1530)^{0}$) candidates, which are reported in the right
panels of Figs. 2 and 3. These distributions are fitted with a combination of
a non-relativistic Breit-Wigner function or a Voigtian function to describe
the signal peak and a function to describe the residual background of
correlated pairs that remain after the subtraction of the combinatorial
background estimated with the mixed-event technique. The Breit-Wigner function
is used to describe the signal peak of $\Sigma(1385)^{\pm}$ and the Voigtian
function is used for $\Xi(1530)^{0}$. The Voigtian function is the convolution
of a Breit-Wigner function to the line shape of the resonance and a Gaussian
function to account for the detector resolution that for $\Xi(1530)^{0}$ is
not negligible in comparison to the width of the resonance. The fitting ranges
are $1.28<M_{\Lambda\pi}<1.54$ GeV/$c^{2}$ for $\Sigma(1385)$ and
$1.47<M_{\Xi\pi}<1.65$ GeV/$c^{2}$ for $\Xi(1530)^{0}$, as in previous
analysis at $\sqrt{s}$ = 7 TeV [32].

The residual background consists of $\Lambda\pi$ ($\Xi\pi$) pairs originating
from the decays of other particles.

For $\Sigma(1385)^{\pm}$, a template function is implemented for the residual
background based on Monte Carlo simulations (see [32] for a detailed
description). In Fig. 2c and 2d the peak from
$\Xi^{-}\rightarrow\Lambda+\pi^{-}$ ($\overline{\Xi}^{+}$
$\rightarrow\overline{\Lambda}+\pi^{+}$) is visible: this physical background
is accounted for by an additional component entering the residual background
for $\Sigma(1385)^{-}$ ($\overline{\Sigma}(1385)^{+}$) decays. For
$\Xi(1530)^{0}$, a second-order polynomial is used.

In each $p_{\mathrm{T}}$ interval, the raw yield of $\Sigma(1385)^{\pm}$ and
$\Xi(1530)^{0}$ is obtained by integrating the Breit-Wigner function and
Voigtian function, respectively.

###  3.4 Corrections and normalisation

The raw yields of $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ resonances for each
$p_{\mathrm{T}}$ interval are corrected for the geometrical acceptance and the
reconstruction efficiency of the detector, and normalised for the branching
ratios of the considered decay channels.

The correction factors are estimated from Monte Carlo simulations based on the
PYTHIA 8 event generator [47] with the Monash 2013 tune [48] and on GEANT 3
[49] (v2-4-14) for the transport of particles through the ALICE detector. The
$\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ resonances from the simulation are
reconstructed and selected by applying the same track quality, topological,
and particle identification criteria as for the data. The generated and
reconstructed resonances in $\mathrm{PYTHIA\,\,8}$ are used to calculate the
correction factors. The corrections, including acceptance, efficiency, and
total branching ratio, $A\times\epsilon_{\rm{rec}}\times\rm{B.R.}$, for
$\mathrm{INEL>0}$ events are shown in Fig. 4. Since no strong multiplicity
dependence of the efficiency is observed as in Ref [41], the values from the
$\mathrm{INEL>0}$ events are used for the correction of the raw yields of all
the multiplicity classes, and a $2\%$ systematic uncertainty, constant across
$p_{\mathrm{T}}$ bins, is assigned to account for residual differences.

All selected events are required to have at least one charged particle track
in the pseudorapidity interval $|\eta|<1$ ($\mathrm{INEL>0}$). However, due to
the inefficiency of the trigger, some $\mathrm{INEL>0}$ events are not
selected and, in turn, all the $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$
resonances produced in those events are not counted as well. A signal-loss
correction, $f_{\rm{S.L.}}$, is thus applied, which accounts for resonances in
non-triggered events. This is evaluated using the same simulations used to
estimate the acceptance and efficiency. To calculate this correction factor,
the simulated resonance $p_{\mathrm{T}}$ spectrum before triggering and event
selection is divided by the corresponding $p_{\mathrm{T}}$ spectrum after
those selections for each multiplicity class. This correction is more
important for the lower multiplicity classes (10% correction for class X,
while only 1% for class I+II+III).

Along with the correction of the yield, the number of events needs to be
corrected for the inefficiencies of the trigger and the event selections, such
as the primary vertex selection. The trigger efficiency $\epsilon_{\rm{Trig}}$
and the vertex selection efficiency $\epsilon_{\rm{Vertex}}$ are about 88% and
98%, respectively, for the lower-multiplicity classes and reach almost 100%
for the higher-multiplicity classes [41, 50]. In the case of inelastic
collisions, a global normalisation factor,
$\epsilon_{\rm{Trig}}\times\epsilon_{\rm{Vertex}}=0.74$ with a relative
uncertainty of $2.5\%$ [43] is applied.

Figure 4:  The product of geometrical acceptance ($A$), reconstruction
efficiency of the detector ($\epsilon_{\rm{rec}}$) and branching ratio (B.R.)
for $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ resonances as a function of
$p_{\mathrm{T}}$ in $|y|<0.5$ obtained with simulations based on event
generation with $\mathrm{PYTHIA\,\,8}$ Monash 2013 [48] and particle
transported with GEANT 3 [49].

##  4 Systematic uncertainties

Table 5: Summary of systematic uncertainties on the differential yield $\rm{d}^{2}\it{N}/\rm{d}\it{p}_{\rm{T}}\rm{d}\it{y}$ for the $\mathrm{INEL>0}$ event class. Negligible contributions are noted as negl. Source of uncertainty | $\Sigma(1385)^{+}$ | $\Sigma(1385)^{-}$ | $\Xi(1530)^{0}$
---|---|---|---
$p_{\mathrm{T}}$-dependent |
Signal extraction | 4–10% | 8–15% | 1–17%
Topological selection | 1–10% | 1–10% | 1–3%
TPC particle identification | 1–3% | 1–3% | 1–3%
Material budget | 0.8–8.3% | 0.8–8.3% | 1.2–5.1%
$p_{\mathrm{T}}$-independent |
ITS–TPC matching | 3% | 3% | 3%
Dependence of efficiency on multiplicity | 2% | 2% | 2%
Branching Ratio | 1.1% | 1.1% | 0.3%
Signal loss correction | negl. | negl. | negl.
Trigger efficiency | negl. | negl. | negl.
Vertex selection efficiency | negl. | negl. | negl.
Total | 6–17% | 9–20% | 4–19%

Different sources of systematic uncertainty on the measured
$\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ observables
($\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}$,
$\frac{\mathrm{d}N}{\mathrm{d}y}$, $\langle p_{\mathrm{T}}\rangle$) were
considered: the sources are essentially associated with the global tracking
efficiency, track quality and topological selections, particle identification,
signal extraction, and knowledge of the ALICE material budget. The systematic
uncertainties are determined by varying the fit range and the selection
criteria. The procedure applies to both $p_{\mathrm{T}}$-dependent and
$p_{\mathrm{T}}$-independent uncertainties and is reconsidered for each
$p_{\mathrm{T}}$ interval and multiplicity class. The list of sources is given
in Table 5 together with the range of values estimated for each of them.

The signal extraction uncertainty includes the uncertainty from the fitting
procedure quantified by varying the fit range, and the normalisation range of
the invariant mass distributions of the mixed-event background. The signal
extraction is the main contribution to the total systematic uncertainty for
$\Sigma(1385)^{\pm}$, originating from the bump structure located on the left
side of the signal peak (see Fig. 2 (b)). The signal extraction uncertainty on
the $\Sigma(1385)^{+}$ is around 10% in most of the $p_{\mathrm{T}}$ and
multiplicity intervals while the one of the $\Sigma(1385)^{-}$ is around 15%
due to the effect of the additional $\Xi^{-}$ peak in the background. The
signal extraction uncertainty of the $\Xi(1530)^{0}$ is around 5–6 % on
average and reaches up to 17%, but only in the case of the first
$p_{\mathrm{T}}$ bin in the highest multiplicity event (I+II+III) case caused
by the poor significance of the signal. The systematic uncertainty originating
from an imperfect description in the simulation of the variables utilised in
the selection of displaced decay topologies are estimated by varying the
criteria on the DCA and the cosine of the pointing angle of the particle decay
products $\Lambda$ and $\Xi^{-}$, and their mass windows. Variations are
performed around the nominal values of the selection variables one at a time,
while fixing all the other ones. $\Sigma(1385)^{\pm}$ show a relatively higher
uncertainty for the topological selection than the one of $\Xi(1530)^{0}$,
given that the $\Sigma(1385)$ family is indeed further affected by the
residual background (see Fig. 2). The systematic uncertainty associated with
particle identification is determined by using a tighter and a looser
requirement on the TPC d$E$/d$x$. The uncertainty from the material budget of
the ALICE detector is taken from the studies performed for the reconstruction
of $\Lambda$ and $\Xi^{-}$ hyperons reported in [43]. Finally, the systematic
uncertainty on ITS–TPC matching efficiency of the first emitted pion from the
resonances ($\pi_{\rm{first}}$ in Fig. 1) was defined from the difference in
the prolongation probability of TPC tracks to ITS points between data and
Monte Carlo simulations. The matching efficiency uncertainty and the tiny
variation of the reconstruction efficiency in different multiplicity classes
are considered as fully $p_{\mathrm{T}}$-correlated uncertainties. Other
uncertainties such as the ones on signal loss correction, trigger efficiency,
and vertex selection efficiency have a negligible contribution to this study.

The total uncertainty is calculated as the quadratic sum of the uncertainties
from the different sources. The $p_{\mathrm{T}}$-independent uncertainties are
considered but as a separate group for
$\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}$ spectra and
$\langle p_{\mathrm{T}}\rangle$ quantities, since they do not affect the
$p_{\mathrm{T}}$ shape of the spectra but just their overall magnitude. On the
other hand, such uncertainties are of special concern for
$p_{\mathrm{T}}$-integrated quantities such as
$\frac{\mathrm{d}N}{\mathrm{d}y}$. For quantities given along
$\mathrm{d}N_{\text{ch}}/\mathrm{d}\eta$, a special investigation was
conducted to quantify the level of correlation of all systematic uncertainties
along event multiplicity.

##  5 Results

The $p_{\mathrm{T}}$-differential yields ($p_{\mathrm{T}}$ spectra) for
$\Sigma(1385)^{+}$, $\Sigma(1385)^{-}$, and $\Xi(1530)^{0}$ (and their
antiparticles) in the various multiplicity classes, as well as the ratios of
these spectra to the inclusive INEL$>0$ spectrum, are shown in Fig. 5. The
$p_{\mathrm{T}}$ spectra of $\Sigma(1385)^{+}$ and $\Sigma(1385)^{-}$ are
identical within uncertainties.

For $p_{\mathrm{T}}<4$ GeV/$c$, a hardening of the $p_{\mathrm{T}}$ spectra
from low to high-multiplicity events is clearly visible, while at higher
$p_{\mathrm{T}}$ the spectra have the same shape regardless of the
multiplicity class, indicating that the processes that affect the shape of the
$p_{\mathrm{T}}$ spectra depending on the multiplicity of particles produced
in the collision are dominant at low $p_{\mathrm{T}}$. A similar behaviour was
reported for other species, in collisions at the same energy [51].

(a)

(b)

(c)

Figure 5: Transverse momentum spectra of $\Sigma(1385)^{+}$ (a),
$\Sigma(1385)^{-}$ (b) and $\Xi(1530)^{0}$ (c) in pp collisions at
$\mathrm{\sqrt{\it{s}}}$ = 13 TeV in multiplicity classes and for the
inclusive case ($\mathrm{INEL>0}$). Statistical and total systematic
uncertainties are shown by error bars and boxes, respectively. The bottom
panels show the ratios of the multiplicity-dependent spectra to the
$\mathrm{INEL>0}$ distributions. The systematic uncertainties on the ratios
are obtained by considering only contributions of multiplicity-uncorrelated
uncertainties described in Table 5. The dashed lines represent the fits to the
spectra with the Lévy–Tsallis function.

(a)

(b)

Figure 6: Ratios of transverse momentum spectra of $\Sigma(1385)^{\pm}$ (a)
and $\Xi(1530)^{0}$ (b) in inelastic pp collisions at $\mathrm{\sqrt{\it{s}}}$
= 13 TeV to the ones in inelastic pp collisions $\mathrm{\sqrt{\it{s}}}$ = 7
TeV [32] compared with those of $\Xi^{-}$, $\Lambda$ and $\pi^{\pm}$ [52, 43].
The statistical and systematic uncertainties are shown as vertical error bars
and boxes, respectively. In the present measurement, the shaded boxes
represent the multiplicity-uncorrelated uncertainties.

Figure 6 shows the ratios of the transverse momentum spectra for inelastic pp
collisions at $\mathrm{\sqrt{\it{s}}}\leavevmode\nobreak\
=\leavevmode\nobreak\ 13$ TeV to those at
$\mathrm{\sqrt{\it{s}}}\leavevmode\nobreak\ =\leavevmode\nobreak\ 7$ TeV for
$\Sigma(1385)^{\pm}$ (left) and $\Xi(1530)^{0}$ (right). For both
$\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$, the yield ratios at low
$p_{\mathrm{T}}$ ($p_{\mathrm{T}}<2$ GeV/$c$) are slightly larger than unity,
even though they are compatible with unity within the systematic
uncertainties. The yield ratios are also consistent with being independent of
$p_{\mathrm{T}}$ at low $p_{\mathrm{T}}$. These considerations suggest that
the production mechanism of these resonances in the soft scattering regime is
only mildly dependent on the collision energy in the measured energy range.
For $p_{\mathrm{T}}>2$ GeV/$c$, the ratios are observed to depart from unity,
indicating a hardening of the $p_{\mathrm{T}}$ spectra at
$\mathrm{\sqrt{\it{s}}}\leavevmode\nobreak\ =\leavevmode\nobreak\ 13$ TeV as
compared to $\mathrm{\sqrt{\it{s}}}\leavevmode\nobreak\ =\leavevmode\nobreak\
7$ TeV. A similar behaviour was observed for the yield ratios of $\pi^{\pm}$,
$\Lambda$ and $\Xi^{-}$ [43] which are shown in Figure 6 overlaid to the
$\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ results. The slope of the
$\Xi(1530)^{0}$ yield ratios in Figure 6 (b) is compatible within
uncertainties with the slope of $\Xi^{\mp}$ yield ratios and the rapid
increase of $\Xi(1530)^{0}$ for $p_{\mathrm{T}}>3$ GeV/$c$ needs to be
confirmed in the higher $p_{\mathrm{T}}$ region with more precise measurements
on larger data samples for further interpretations on any distinction.

To calculate the total yields of $\Sigma(1385)^{\pm}$, and $\Xi(1530)^{0}$
integrated over $p_{\mathrm{T}}$ (d$N$/d$y$) and their mean transverse
momentum $\langle p_{\mathrm{T}}\rangle$, the measured $p_{\mathrm{T}}$
differential spectra are fitted with a Lévy–Tsallis function [53] defined as:

$\frac{1}{N_{\mathrm{event}}}\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}=p_{\mathrm{T}}N^{\prime}\frac{(n-1)(n-2)}{nC\left[nC+m_{0}(n-2)\right]}\left[1+\frac{\sqrt{p^{2}_{\rm{T}}+m^{2}_{0}}-m_{0}}{nC}\right]^{-n},$
(4)

where $N_{\rm{event}}$ is the number of events in a given multiplicity class,
$m_{0}$ is the world-average mass of the particle, and $n$, $C$, and the
integrated yield $N^{\prime}$ are free parameters of the fit. This function is
successfully used to describe most of the identified particle spectra in pp
collisions [41, 43]. The Lévy–Tsallis functions obtained by fitting the
$p_{\mathrm{T}}$ spectra in the different multiplicity classes are shown as
dashed lines in Fig. 5.

The value of d$N$/d$y$ is obtained by integrating the measured spectrum from
$p_{\mathrm{T}}$ = 0.7 (0.8) to 6.0 (8.8) GeV/$c$ for $\Sigma(1385)^{\pm}$
($\Xi(1530)^{0}$) and the extrapolated fitting curve in the unmeasured regions
down to $p_{\mathrm{T}}=0$ and up to $p_{\mathrm{T}}=10$ GeV/$c$. Similarly,
the $\langle p_{\mathrm{T}}\rangle$ is computed using the measured spectra in
the $p_{\mathrm{T}}$ interval of the measurement and the Lévy–Tsallis function
outside this range. The values of d$N$/d$y$ and $\langle
p_{\mathrm{T}}\rangle$ are reported in Table 6.

The fractions of extrapolated particle yield at low $p_{\mathrm{T}}$ for
different multiplicity classes are 26–43% and 21–43% depending on the
multiplicity class for $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$, respectively.
The extrapolated yields in the high-$p_{\mathrm{T}}$ region are negligible.
Alternative functions such as the Boltzmann, Fermi–Dirac,
$m_{\rm{T}}$-exponential, $p_{\mathrm{T}}$-exponential, and blast-wave
functions are employed to estimate the systematic uncertainty of this
extrapolation, which amounts to about 3–4% for both resonances. The fit
functions used for the systematic study are listed in Appendix A. As reported
in Table 6, the relative uncertainties of the INEL results are larger than
those of the $\mathrm{INEL>0}$ results due to the propagation of the
uncertainty on the normalisations, $\epsilon_{\rm{Trig}}$,
$\epsilon_{\rm{Vertex}}$, and $f_{\rm{S.L.}}$ which are slightly different for
the INEL and the $\mathrm{INEL>0}$ samples.

Table 6: The values of d$N$/d$y$ and $\langle p_{\mathrm{T}}\rangle$ for multiplicity-integrated spectra (INEL, $\mathrm{INEL>0}$) and for each multiplicity class. Statistical (first one), total systematic (second one) and multiplicity-uncorrelated systematic (third one, in brackets) uncertainties are quoted. The multiplicity-uncorrelated systematic uncertainties are not an additional source here but must be considered as a component of the total systematic uncertainties. Baryon | Event Class | d$N$/d$y$ ($\times 10^{-3}$) |  $\langle p_{\mathrm{T}}\rangle$ (GeV/$c$)
---|---|---|---
$\Xi(1530)^{0}$ | $\mathrm{INEL>0}$ |  $4.29\pm 0.05\pm 0.20\,(0.16$) |  $1.44\pm 0.01\pm 0.06\,(0.05$)
I+II+III | $14.29\pm$0.15$\pm$0.70$\,($0.52$)$ | $1.64\pm$0.01$\pm$0.06$\,($0.06$)$
IV+V+VI | $7.96\pm$0.10$\pm$0.38$\,($0.29$)$ | $1.44\pm$0.01$\pm$0.06$\,($0.05$)$
VII+VIII | $4.42\pm$0.08$\pm$0.27$\,($0.16$)$ | $1.30\pm$0.01$\pm$0.05$\,($0.05$)$
IX | $2.14\pm$0.05$\pm$0.11$\,($0.08$)$ | $1.23\pm$0.01$\pm$0.05$\,($0.04$)$
X | $0.85\pm$0.05$\pm$0.05$\,($0.03$)$ | $1.05\pm$0.03$\pm$0.04$\,($0.04$)$
INEL | $2.98\pm$0.07$\pm$0.15$\,($0.11$)$ | $1.45\pm$0.02$\pm$0.06$\,($0.05$)$
$\Sigma(1385)^{\pm}$ | $\mathrm{INEL>0}$ | $14.68\pm 0.11\pm 0.80\,(0.55)$ | $1.28\pm 0.01\pm 0.05\,(0.05)$
I+II+III | $45.11\pm 0.53\pm 2.40\,(1.70)$ | $1.51\pm 0.01\pm 0.07\,(0.05)$
IV+V+VI | $26.37\pm 0.34\pm 1.40\,(1.00)$ | $1.33\pm 0.01\pm 0.06\,(0.05)$
VII+VIII | $15.11\pm 0.23\pm 0.83\,(0.57)$ | $1.19\pm 0.01\pm 0.05\,(0.05)$
IX | $8.67\pm 0.18\pm 0.51\,(0.33)$ | $1.07\pm 0.01\pm 0.04\,(0.04)$
X | $3.75\pm 0.01\pm 0.28\,(0.14)$ | $0.91\pm 0.01\pm 0.04\,(0.03)$
INEL | $11.04\pm$0.20$\pm$0.60$\,($0.42$)$ | $1.27\pm$0.01$\pm$0.05$\,($0.05$)$
Figure 7: The $p_{\mathrm{T}}$-integrated yields as a function of charged-
particle pseudorapidity density
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle_{|\eta|<0.5}$ for
$\Sigma(1385)^{\pm}$ (left) and $\Xi(1530)^{0}$ (right) compared with the
measurements in pp collisions at $\sqrt{\it{s}}=7$ TeV [32] and p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}\leavevmode\nobreak\
=\leavevmode\nobreak\ 5.02$ TeV [33]. The open and shaded boxes represent the
total and multiplicity-uncorrelated systematic uncertainties, respectively.
The measured points are compared to predictions from different event
generators, namely EPOS-LHC [54], $\mathrm{PYTHIA\,\,8}$ with Monash 2013
tuning [48], and $\mathrm{PYTHIA\,\,8}$ with Rope shoving [55, 56, 57, 58].
(Appendix B). The predictions are obtained for pp collisions at
$\sqrt{\it{s}}=13$ TeV on $\mathrm{INEL>0}$ events. Figure 8: The $\langle
p_{\mathrm{T}}\rangle$ as a function of charged-particle pseudorapidity
density for $\Sigma(1385)^{\pm}$ (left) and $\Xi(1530)^{0}$ (right) compared
with the measurements in pp collisions at $\sqrt{\it{s}}=7$ TeV [32] and p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}\leavevmode\nobreak\
=\leavevmode\nobreak\ 5.02$ TeV [33]. The open and shaded boxes represent the
total and multiplicity-uncorrelated systematic uncertainties, respectively.
The measured points are compared to predictions from different event
generators, namely EPOS-LHC [54], $\mathrm{PYTHIA\,\,8}$ with Monash 2013
tuning [48], and $\mathrm{PYTHIA\,\,8}$ with Rope shoving [55, 56, 57, 58].
(Appendix B). The predictions are obtained for pp collisions at
$\sqrt{\it{s}}=13$ TeV, based on $\mathrm{INEL>0}$ events.

Figure 7 shows the $p_{\mathrm{T}}$-integrated yields, d$N$/d$y$, as a
function of the charged-particle pseudorapidity density at midrapidity and in
comparison with the values previously measured in pp collisions at
$\mathrm{\sqrt{\it{s}}}=7$ TeV [32] and in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV [33] by the ALICE Collaboration. The
comparison suggests that the integrated yields depend only on the
multiplicity, irrespective of the collision energy and system. This is
consistent with previous results at the LHC [41, 51], highlighting the fact
that the mechanisms of particle production are related essentially to the
event properties that determine the multiplicity. The measurements are
compared with the predictions of different event generators, namely EPOS-LHC
[54], $\mathrm{PYTHIA\,\,8}$ with Monash 2013 tuning [48], and
$\mathrm{PYTHIA\,\,8}$ with Rope shoving [55, 56, 57, 58]. Both EPOS-LHC and
PYTHIA8 are QCD-inspired event generators. The EPOS-LHC includes a modelling
of the collective behaviour implemented via a core-corona approach [59].
Instead, $\mathrm{PYTHIA\,\,8}$ with Monash 2013 does not include a collective
expansion and is based on the Lund string fragmentation model.
$\mathrm{PYTHIA\,\,8}$ with Rope shoving describes multiparton interactions by
allowing nearby strings to shove each other and form a colour "rope" from
overlapping strings. The model predictions are reported for pp collisions at
$\mathrm{\sqrt{\it{s}}}=13$ TeV. The increasing trend of the
$\mathrm{d}N/\mathrm{d}y$ of $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ with
increasing $\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$ for pp
collisions is qualitatively reproduced by the different event generator
models. However, $\mathrm{PYTHIA\,\,8}$ with Monash 2013 tuning (green dashed
curve) predicts a much milder increase for both resonances, whereas EPOS-LHC
(blue solid curve) and $\mathrm{PYTHIA\,\,8}$ with Rope shoving (purple dotted
curve, see details of the tune settings in Appendix B) describe the measured
$\mathrm{d}N/\mathrm{d}y$ of both resonances within the uncertainties, with
possibly a small tension between the EPOS-LHC prediction and the
$\Xi(1530)^{0}$ data in the highest multiplicity interval.

Figure 8 shows the mean transverse momentum $\langle p_{\mathrm{T}}\rangle$
for $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ as a function of the charged-
particle pseudorapidity density. The values obtained in pp collisions at
$\mathrm{\sqrt{\it{s}}}=7$ TeV [32] and in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV [33] are reported in the same figure. The
increasing trend of the $\langle p_{\mathrm{T}}\rangle$ as a function of
multiplicity in pp collisions is steeper than the one in p–Pb collisions for
both $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$, consistent with what is
observed for unidentified charged particles in pp collisions at
$\mathrm{\sqrt{\it{s}}}$ = 7 TeV and p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV [60]. The increasing trend and the
measured values are well described by EPOS-LHC. Both $\mathrm{PYTHIA\,\,8}$
with Monash 2013 tuning and $\mathrm{PYTHIA\,\,8}$ with Rope shoving predict
an increasing trend, however, they underestimate the data in the full range of
the pp measurements.

Figure 9: Ratio of the resonance to pion $p_{\mathrm{T}}$-integrated yield as
a function of the charged-particle pseudorapidity density for
$\Sigma(1385)^{\pm}$ (left) and $\Xi(1530)^{0}$ (right). The open and shaded
boxes represent the total and multiplicity-uncorrelated systematic
uncertainties, respectively. The measured points are compared to predictions
from different event generators, namely EPOS-LHC [54], $\mathrm{PYTHIA\,\,8}$
with Monash 2013 tuning [48], and $\mathrm{PYTHIA\,\,8}$ with Rope shoving
[55, 56, 57, 58]. (Appendix B). The predictions are obtained for pp collisions
at $\sqrt{\it{s}}=13$ TeV, based on $\mathrm{INEL>0}$ events.

The ratios of the $p_{\mathrm{T}}$-integrated yield ratios of
$\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ hyperons to those of pions are shown
in Fig. 9 as a function of the charged-particle pseudorapidity density and
they are compared to the ratios measured in pp collisions at
$\mathrm{\sqrt{\it{s}}}$ = 7 TeV and p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV [53, 32, 33, 43]. They provide insight
into the evolution of strangeness production with increasing multiplicity. The
results show a smooth increasing trend as a function of multiplicity without
energy and collision system dependence. The yields of $\Sigma(1385)^{\pm}$ and
$\Xi(1530)^{0}$ relative to those of pions increase by 60% and 120%,
respectively, from the lowest to highest multiplicity pp collisions considered
in this work. The increase depends on the strangeness content of the
resonance; with $\Sigma^{*\pm}$ having a strangeness content (S) of 1 and
$\Xi^{*0}$ having S=2. These results are consistent with previous measurements
of ground-state hyperons to pion ratios with ALICE [41]. EPOS-LHC and
$\mathrm{PYTHIA\,\,8}$ with Rope shoving predict an increasing trend with
multiplicity for both resonances. EPOS-LHC describes fairly well the measured
$\Sigma(1385)^{\pm}$/$\pi$ ratios, while $\mathrm{PYTHIA\,\,8}$ Rope
overestimates them. Both EPOS-LHC and $\mathrm{PYTHIA\,\,8}$ Rope tend to
overestimate the increasing trend of $\Xi(1530)^{0}$/$\pi$ ratios.

Figure 10: Yield ratio of the resonances to the ground states having the same
quark content as a function of the charged-particle pseudorapidity density for
$\Sigma(1385)^{\pm}$ (left) and $\Xi(1530)^{0}$ (right). The open and shaded
boxes represent the total and multiplicity-uncorrelated systematic
uncertainties, respectively. The measured points are compared to predictions
from different event generators, namely EPOS-LHC [54], $\mathrm{PYTHIA\,\,8}$
with Monash 2013 tuning [48], and $\mathrm{PYTHIA\,\,8}$ with Rope shoving
[55, 56, 57, 58]. (Appendix B). The predictions are obtained for pp collisions
at $\sqrt{\it{s}}=13$ TeV, based on $\mathrm{INEL>0}$ events.

The integrated yield ratios of excited to ground-state hyperons [32, 33, 41]
with the same strangeness content are shown in Fig. 10. They are drawn for
different collision systems and centre-of-mass energies as a function of
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$. The measured
$\Sigma(1385)^{\pm}$/$\Lambda$ and $\Xi(1530)^{0}$/$\Xi^{-}$ ratios are
compatible either with a flat behaviour as a function of multiplicity or with
a mild multiplicity dependence, even though no firm conclusion can be drawn
considering the magnitude of the systematic uncertainties and the fact that
they are partly uncorrelated across multiplicity intervals. The EPOS-LHC and
$\mathrm{PYTHIA\,\,8}$ with Rope shoving predict a slight increase of the
$\Sigma(1385)^{\pm}$/$\Lambda$ and $\Xi(1530)^{0}$/$\Xi^{-}$ ratios with
increasing multiplicity at low multiplicities. They describe the data within
the experimental uncertainties. The $\mathrm{PYTHIA\,\,8}$ Monash 2013
prediction exhibits a flat behaviour and it underestimates the overall
magnitude of the ratios by about a factor of two. Note that a decreasing trend
was observed in the EPOS-LHC model prediction for the K${}^{*}/$K ratio
($c\tau$(K∗) = $4.16$ fm/$c$ [45]), apparently describing the measurements in
pp and p–Pb collisions [31, 61]. Despite similar lifetimes, K∗ and
$\Sigma(1385)^{\pm}$ exhibit different yield trends in pp collisions, hinting
at the nuanced interplay of rescattering and regeneration effects within a
potential hadronic stage. While the decreasing yield of K∗ could be attributed
to decay product rescattering, the stable yield of $\Sigma(1385)^{\pm}$ might
suggest a more pronounced regeneration effect. Conversely, the longer-lived
$\Xi(1530)^{0}$, seemingly unaffected by these hadronic stage effects,
provides a contrasting reference.

##  6 Conclusions

In this article, the $p_{\mathrm{T}}$-differential yields of
$\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$ in inelastic pp collisions at
$\mathrm{\sqrt{\it{s}}}$ = 13 TeV are reported and compared with previous
ALICE measurements in pp collisions at $\mathrm{\sqrt{\it{s}}}$ = 7 TeV,
revealing a hardening of the $p_{\mathrm{T}}$ spectra as the collision energy
increases. The hardening is more pronounced for $p_{\mathrm{T}}>2$ GeV/$c$.
Going from low to high multiplicity events in pp collisions at
$\mathrm{\sqrt{\it{s}}}$ = 13 TeV, a clear hardening is observed that affects
the shape of the lowest $p_{\mathrm{T}}$ part of the spectra.

The $p_{\mathrm{T}}$-integrated yield, d$N$/d$y$ of $\Sigma(1385)^{\pm}$, and
$\Xi(1530)^{0}$ is found to increase with charged-particle pseudorapidity
density, with a trend that does not depend on collision energy and is the same
for pp and p–Pb collisions. This is consistent with previous findings at the
LHC [41], highlighting the fact that the mechanisms of particle production are
related primarily to the conditions that determine multiplicity. On the other
hand, the increasing trend of the $\langle p_{\mathrm{T}}\rangle$ as a
function of $\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$ in pp
collisions is slightly steeper than the one in p–Pb collisions for both
$\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$, as observed for charged particles
and other light-flavour hadrons in pp collisions at different energies and
p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV.

An increasing trend with multiplicity is found for the
$\Sigma(1385)^{\pm}$/$\pi^{\pm}$ and $\Xi(1530)^{0}$/$\pi^{\pm}$ ratios. The
enhancement is more pronounced for $\Xi(1530)^{0}$ ($S$=2) than
$\Sigma(1385)^{\pm}$ ($S$=1), confirming that strangeness enhancement
predominantly depends on the strangeness content, rather than on the hyperon
mass [20]. The integrated yields of $\Sigma(1385)^{\pm}$ and $\Xi(1530)^{0}$
show a scaling with multiplicity consistent within uncertainties with that of
the ground-state hyperons with the same strangeness content, indicating that
the strange-baryon resonance production and its ground state have a similar
increase on multiplicity. These results, when combined with other resonance
studies in small systems, can provide valuable contributions to our
understanding of a possible hadronic stage in pp collisions and on the role of
rescattering and regeneration effects in such stage.

## 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; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA), Thailand Science Research and Innovation (TSRI) and National Science, Research and Innovation Fund (NSRF), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. In addition, individual groups or members have received support from: European Research Council, Strong 2020 - Horizon 2020 (grant nos. 950692, 824093), European Union; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland.

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##  Appendix A Fitting functions used in this paper

####  $p_{\mathrm{T}}$ exponential function

$\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}=Ap_{\mathrm{T}}e^{-p_{\mathrm{T}}/T},$
(5)

with normalisation factor $A$ and temperature $T$ as fit parameters.

####  $m_{\mathrm{T}}$ exponential function

$\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}=Ap_{\mathrm{T}}e^{-\mbox{$m_{\mathrm{T}}$}/T},$
(6)

where $\mbox{$m_{\mathrm{T}}$}=\sqrt{p_{\mathrm{T}}^{2}+m_{0}^{2}}$ while
$m_{0}$ is the rest mass of the particle. The normalisation factor $A$ and
temperature $T$ are the fit parameters.

#### Fermi–Dirac function

[62]

$\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}=p_{\mathrm{T}}A\frac{1}{\rm{e}^{(\sqrt{\it{p_{\mathrm{T}}}^{2}+\it{m}^{2}}/\it{T})}+1},$
(7)

with $A$ and $T$ as fit parameters and $m$ the mass of the particle under
study.

#### Boltzmann distribution

[62]

$\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}=Ap_{\mathrm{T}}\mbox{$m_{\mathrm{T}}$}e^{-\mbox{$m_{\mathrm{T}}$}/T},$
(8)

where $m_{\mathrm{T}}$ is $\sqrt{p_{\mathrm{T}}^{2}+m_{0}^{2}}$ while $m_{0}$
is the rest mass of the particle. The normalisation factor $A$ and temperature
$T$ are the fit parameters.

#### Lévy–Tsallis distribution

[53]

$\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}=p_{\mathrm{T}}N^{\prime}\frac{(n-1)(n-2)}{nC\left[nC+m_{0}(n-2)\right]}\left[1+\frac{\mbox{$m_{\mathrm{T}}$}-m_{0}}{nC}\right]^{-n}\quad,$
(9)

where $\mbox{$m_{\mathrm{T}}$}=\sqrt{p_{\mathrm{T}}^{2}+m_{0}^{2}}$ while
$m_{0}$ is the rest mass of the particle, and $n$, $C$ and the integrated
yield $N^{\prime}$ are free parameters of the fit.

#### Blast-wave distribution

[63]

$\frac{1}{p_{\mathrm{T}}}\frac{\mathrm{d}^{2}N}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}\propto\int^{R}_{0}rm_{\mathrm{T}}I_{0}\left(\frac{p_{\mathrm{T}}\sinh\rho}{T_{\mathrm{kin}}}\right)K_{1}\left(\frac{m_{\mathrm{T}}\cosh\rho}{T_{\mathrm{kin}}}\right)\mathrm{d}r,$
(10)

where $I_{0}$ and $K_{1}$ are the modified Bessel functions, $r$ is the
distance from the centre of the expanding system, $R$ is the limiting radius
of the system expansion, $T_{\mathrm{kin}}$ is the temperature of the kinetic
freeze–out and $\rho=\rm{arctanh}\,\beta$ defines the velocity profile.

##  Appendix B PYTHIA8 Rope Shoving Parameters

Parameters below are additional parameters to the default Monash tune 2013
(Tune ID = 14 in v8.243).

    MultiPartonInteractions:pT0Ref = 2.15
    BeamRemnants:remnantMode = 1
    BeamRemnants:saturation = 5
    ColourReconnection:mode = 1
    ColourReconnection:allowDoubleJunRem = off
    ColourReconnection:m0 = 0.3
    ColourReconnection:allowJunctions = on
    ColourReconnection:junctionCorrection = 1.2
    ColourReconnection:timeDilationMode = 2
    ColourReconnection:timeDilationPar = 0.18
    Ropewalk:RopeHadronization = on
    Ropewalk:doShoving = on
    Ropewalk:tInit = 1.5
    Ropewalk:deltat = 0.05
    Ropewalk:tShove 0.1
    Ropewalk:gAmplitude = 0.
    Ropewalk:doFlavour = on
    Ropewalk:r0 = 0.5
    Ropewalk:m0 = 0.2
    Ropewalk:beta = 0.1
    PartonVertex:setVertex = on
    PartonVertex:protonRadius = 0.7
    PartonVertex:emissionWidth = 0.1

##  Appendix C The ALICE Collaboration

S. Acharya 126, D. Adamová 86, G. Aglieri Rinella 33, M. Agnello 30, N.
Agrawal 51, Z. Ahammed 134, S. Ahmad 16, S.U. Ahn 71, I. Ahuja 38, A.
Akindinov 142, M. Al-Turany 97, D. Aleksandrov 142, B. Alessandro 56, H.M.
Alfanda 6, R. Alfaro Molina 67, B. Ali 16, A. Alici 26, N. Alizadehvandchali
115, A. Alkin 33, J. Alme 21, G. Alocco 52, T. Alt 64, A.R. Altamura 50, I.
Altsybeev 95, M.N. Anaam 6, C. Andrei 46, N. Andreou 114, A. Andronic 137, V.
Anguelov 94, F. Antinori 54, P. Antonioli 51, N. Apadula 74, L. Aphecetche
103, H. Appelshäuser 64, C. Arata 73, S. Arcelli 26, M. Aresti 23, R. Arnaldi
56, J.G.M.C.A. Arneiro 110, I.C. Arsene 20, M. Arslandok 139, A. Augustinus
33, R. Averbeck 97, M.D. Azmi 16, H. Baba123, A. Badalà 53, J. Bae 104, Y.W.
Baek 41, X. Bai 119, R. Bailhache 64, Y. Bailung 48, A. Balbino 30, A.
Baldisseri 129, B. Balis 2, D. Banerjee 4, Z. Banoo 91, R. Barbera 27, F.
Barile 32, L. Barioglio 95, M. Barlou78, B. Barman42, G.G. Barnaföldi 138,
L.S. Barnby 85, V. Barret 126, L. Barreto 110, C. Bartels 118, K. Barth 33, E.
Bartsch 64, N. Bastid 126, S. Basu 75, G. Batigne 103, D. Battistini 95, B.
Batyunya 143, D. Bauri47, J.L. Bazo Alba 101, I.G. Bearden 83, C. Beattie 139,
P. Becht 97, D. Behera 48, I. Belikov 128, A.D.C. Bell Hechavarria 137, F.
Bellini 26, R. Bellwied 115, S. Belokurova 142, Y.A.V. Beltran 45, G. Bencedi
138, S. Beole 25, Y. Berdnikov 142, A. Berdnikova 94, L. Bergmann 94, M.G.
Besoiu 63, L. Betev 33, P.P. Bhaduri 134, A. Bhasin 91, M.A. Bhat 4, B.
Bhattacharjee 42, L. Bianchi 25, N. Bianchi 49, J. Bielčík 36, J. Bielčíková
86, J. Biernat 107, A.P. Bigot 128, A. Bilandzic 95, G. Biro 138, S. Biswas 4,
N. Bize 103, J.T. Blair 108, D. Blau 142, M.B. Blidaru 97, N. Bluhme39, C.
Blume 64, G. Boca 22,55, F. Bock 87, T. Bodova 21, A. Bogdanov142, S. Boi 23,
J. Bok 58, L. Boldizsár 138, M. Bombara 38, P.M. Bond 33, G. Bonomi 133,55, H.
Borel 129, A. Borissov 142, A.G. Borquez Carcamo 94, H. Bossi 139, E. Botta
25, Y.E.M. Bouziani 64, L. Bratrud 64, P. Braun-Munzinger 97, M. Bregant 110,
M. Broz 36, G.E. Bruno 96,32, M.D. Buckland 24, D. Budnikov 142, H. Buesching
64, S. Bufalino 30, P. Buhler 102, N. Burmasov 142, Z. Buthelezi 68,122, A.
Bylinkin 21, S.A. Bysiak107, M. Cai 6, H. Caines 139, A. Caliva 29, E. Calvo
Villar 101, J.M.M. Camacho 109, P. Camerini 24, F.D.M. Canedo 110, M. Carabas
125, A.A. Carballo 33, F. Carnesecchi 33, R. Caron 127, L.A.D. Carvalho 110,
J. Castillo Castellanos 129, F. Catalano 33,25, C. Ceballos Sanchez 143, I.
Chakaberia 74, P. Chakraborty 47, S. Chandra 134, S. Chapeland 33, M. Chartier
118, S. Chattopadhyay 134, S. Chattopadhyay 99, T.G. Chavez 45, T. Cheng 97,6,
C. Cheshkov 127, B. Cheynis 127, V. Chibante Barroso 33, D.D. Chinellato 111,
E.S. Chizzali I,95, J. Cho 58, S. Cho 58, P. Chochula 33, D. Choudhury42, P.
Christakoglou 84, C.H. Christensen 83, P. Christiansen 75, T. Chujo 124, M.
Ciacco 30, C. Cicalo 52, F. Cindolo 51, M.R. Ciupek97, G. ClaiII,51, F.
Colamaria 50, J.S. Colburn100, D. Colella 96,32, M. Colocci 26, M. Concas
III,33, G. Conesa Balbastre 73, Z. Conesa del Valle 130, G. Contin 24, J.G.
Contreras 36, M.L. Coquet 129, P. Cortese 132,56, M.R. Cosentino 112, F. Costa
33, S. Costanza 22,55, C. Cot 130, J. Crkovská 94, P. Crochet 126, R. Cruz-
Torres 74, P. Cui 6, A. Dainese 54, M.C. Danisch 94, A. Danu 63, P. Das 80, P.
Das 4, S. Das 4, A.R. Dash 137, S. Dash 47, R.M.H. David45, A. De Caro 29, G.
de Cataldo 50, J. de Cuveland39, A. De Falco 23, D. De Gruttola 29, N. De
Marco 56, C. De Martin 24, S. De Pasquale 29, R. Deb 133, R. Del Grande 95, L.
Dello Stritto 29, W. Deng 6, P. Dhankher 19, D. Di Bari 32, A. Di Mauro 33, B.
Diab 129, R.A. Diaz 143,7, T. Dietel 113, Y. Ding 6, J. Ditzel 64, R. Divià
33, D.U. Dixit 19, Ø. Djuvsland21, U. Dmitrieva 142, A. Dobrin 63, B. Dönigus
64, J.M. Dubinski 135, A. Dubla 97, S. Dudi 90, P. Dupieux 126, M. Durkac106,
N. Dzalaiova13, T.M. Eder 137, R.J. Ehlers 74, F. Eisenhut 64, R. Ejima92, D.
Elia 50, B. Erazmus 103, F. Ercolessi 26, F. Erhardt 89, M.R. Ersdal21, B.
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M. Faggin 28, J. Faivre 73, F. Fan 6, W. Fan 74, A. Fantoni 49, M. Fasel 87,
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115, A.N. Flores 108, S. Foertsch 68, I. Fokin 94, S. Fokin 142, E. Fragiacomo
57, E. Frajna 138, U. Fuchs 33, N. Funicello 29, C. Furget 73, A. Furs 142, T.
Fusayasu 98, J.J. Gaardhøje 83, M. Gagliardi 25, A.M. Gago 101, T. Gahlaut47,
C.D. Galvan 109, D.R. Gangadharan 115, P. Ganoti 78, C. Garabatos 97, A.T.
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A. Gautam 117, M.B. Gay Ducati 66, M. Germain 103, A. Ghimouz124, C. Ghosh134,
M. Giacalone 51, G. Gioachin 30, P. Giubellino 97,56, P. Giubilato 28, A.M.C.
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Gorgon 2, K. Goswami 48, S. Gotovac34, V. Grabski 67, L.K. Graczykowski 135,
E. Grecka 86, A. Grelli 59, C. Grigoras 33, V. Grigoriev 142, S. Grigoryan
143,1, F. Grosa 33, J.F. Grosse-Oetringhaus 33, R. Grosso 97, D. Grund 36,
N.A. Grunwald94, G.G. Guardiano 111, R. Guernane 73, M. Guilbaud 103, K.
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J.W. Harris 139, A. Harton 9, H. Hassan 116, D. Hatzifotiadou 51, P. Hauer 43,
L.B. Havener 139, S.T. Heckel 95, E. Hellbär 97, H. Helstrup 35, M. Hemmer 64,
T. Herman 36, G. Herrera Corral 8, F. Herrmann137, S. Herrmann 127, K.F.
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70, B. Hofman 59, G.H. Hong 140, M. Horst 95, A. Horzyk2, Y. Hou 6, P. Hristov
33, C. Hughes 121, P. Huhn64, L.M. Huhta 116, T.J. Humanic 88, A. Hutson 115,
D. Hutter 39, R. Ilkaev142, H. Ilyas 14, M. Inaba 124, G.M. Innocenti 33, M.
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A. Kurepin 142, A.B. Kurepin 142, A. Kuryakin 142, S. Kushpil 86, M.J. Kweon
58, Y. Kwon 140, S.L. La Pointe 39, P. La Rocca 27, A. Lakrathok105, M.
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G.M. Perez 7, Y. Pestov142, V. Petrov 142, M. Petrovici 46, R.P. Pezzi 103,66,
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97, G. Scioli 26, E. Scomparin 56, J.E. Seger 15, Y. Sekiguchi123, D. Sekihata
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## Affiliation Notes

I Also at: Max-Planck-Institut für Physik, Munich, Germany
II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
IV Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VI 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 COMSATS University Islamabad, Islamabad, Pakistan
15 Creighton University, Omaha, Nebraska, United States
16 Department of Physics, Aligarh Muslim University, Aligarh, India
17 Department of Physics, Pusan National University, Pusan, Republic of Korea
18 Department of Physics, Sejong University, Seoul, Republic of Korea
19 Department of Physics, University of California, Berkeley, California,
United States
20 Department of Physics, University of Oslo, Oslo, Norway
21 Department of Physics and Technology, University of Bergen, Bergen, Norway
22 Dipartimento di Fisica, Università di Pavia, Pavia, Italy
23 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy
24 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy
25 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy
26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy
27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy
28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy
29 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy
30 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy
31 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy
32 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy
33 European Organization for Nuclear Research (CERN), Geneva, Switzerland
34 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia
35 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway
36 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic
37 Faculty of Physics, Sofia University, Sofia, Bulgaria
38 Faculty of Science, P.J. Šafárik University, Košice, Slovak Republic
39 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany
40 Fudan University, Shanghai, China
41 Gangneung-Wonju National University, Gangneung, Republic of Korea
42 Gauhati University, Department of Physics, Guwahati, India
43 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany
44 Helsinki Institute of Physics (HIP), Helsinki, Finland
45 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico
46 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania
47 Indian Institute of Technology Bombay (IIT), Mumbai, India
48 Indian Institute of Technology Indore, Indore, India
49 INFN, Laboratori Nazionali di Frascati, Frascati, Italy
50 INFN, Sezione di Bari, Bari, Italy
51 INFN, Sezione di Bologna, Bologna, Italy
52 INFN, Sezione di Cagliari, Cagliari, Italy
53 INFN, Sezione di Catania, Catania, Italy
54 INFN, Sezione di Padova, Padova, Italy
55 INFN, Sezione di Pavia, Pavia, Italy
56 INFN, Sezione di Torino, Turin, Italy
57 INFN, Sezione di Trieste, Trieste, Italy
58 Inha University, Incheon, Republic of Korea
59 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands
60 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovak Republic
61 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India
62 Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic
63 Institute of Space Science (ISS), Bucharest, Romania
64 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
65 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico
66 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil
67 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico
68 iThemba LABS, National Research Foundation, Somerset West, South Africa
69 Jeonbuk National University, Jeonju, Republic of Korea
70 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany
71 Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea
72 KTO Karatay University, Konya, Turkey
73 Laboratoire de Physique 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 University of Cape Town, Cape Town, South Africa
114 University of Derby, Derby, United Kingdom
115 University of Houston, Houston, Texas, United States
116 University of Jyväskylä, Jyväskylä, Finland
117 University of Kansas, Lawrence, Kansas, United States
118 University of Liverpool, Liverpool, United Kingdom
119 University of Science and Technology of China, Hefei, China
120 University of South-Eastern Norway, Kongsberg, Norway
121 University of Tennessee, Knoxville, Tennessee, United States
122 University of the Witwatersrand, Johannesburg, South Africa
123 University of Tokyo, Tokyo, Japan
124 University of Tsukuba, Tsukuba, Japan
125 University Politehnica of Bucharest, Bucharest, Romania
126 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
127 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de
Lyon, Lyon, France
128 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France,
Strasbourg, France
129 Université Paris-Saclay, Centre d’Etudes de Saclay (CEA), IRFU, Départment
de Physique Nucléaire (DPhN), Saclay, France
130 Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
131 Università degli Studi di Foggia, Foggia, Italy
132 Università del Piemonte Orientale, Vercelli, Italy
133 Università di Brescia, Brescia, Italy
134 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata,
India
135 Warsaw University of Technology, Warsaw, Poland
136 Wayne State University, Detroit, Michigan, United States
137 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany
138 Wigner Research Centre for Physics, Budapest, Hungary
139 Yale University, New Haven, Connecticut, United States
140 Yonsei University, Seoul, Republic of Korea
141 Zentrum für Technologie und Transfer (ZTT), Worms, Germany
142 Affiliated with an institute covered by a cooperation agreement with CERN
143 Affiliated with an international laboratory covered by a cooperation
agreement with CERN.