2023 215 27 September

Particle production in pp at $\sqrt{s}$ = 13 TeV Vs transverse spherocity

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

Results on the transverse spherocity dependence of light-flavor particle
production ($\pi$, K, p, $\phi$, ${\rm K^{*0}}$, ${\rm K}^{0}_{\rm{S}}$,
$\Lambda$, $\Xi$) at midrapidity in high-multiplicity pp collisions at
$\sqrt{s}=13$ TeV were obtained with the ALICE apparatus. The transverse
spherocity estimator ($S_{\text{O}}^{p_{\rm T}=1}$) categorizes events by
their azimuthal topology. Utilizing narrow selections on $S_{\text{O}}^{p_{\rm
T}=1}$, it is possible to contrast particle production in collisions dominated
by many soft initial interactions with that observed in collisions dominated
by one or more hard scatterings. Results are reported for two multiplicity
estimators covering different pseudorapidity regions. The
$S_{\text{O}}^{p_{\rm T}=1}$ estimator is found to effectively constrain the
hardness of the events when the midrapidity ($\left|\eta\right|<0.8$)
estimator is used.

The production rates of strange particles are found to be slightly higher for
soft isotropic topologies, and severely suppressed in hard jet-like
topologies. These effects are more pronounced for hadrons with larger mass and
strangeness content, and observed when the topological selection is done
within a narrow multiplicity interval. This demonstrates that an important
aspect of the universal scaling of strangeness enhancement with final-state
multiplicity is that high-multiplicity collisions are dominated by soft,
isotropic processes. On the contrary, strangeness production in events with
jet-like processes is significantly reduced.

The results presented in this article are compared with several QCD-inspired
Monte Carlo event generators. Models that incorporate a two-component
phenomenology, either through mechanisms accounting for string density, or
thermal production, are able to describe the observed strangeness enhancement
as a function of $S_{\text{O}}^{p_{\rm T}=1}$.

##  1 Introduction

Studies of high-multiplicity proton–proton (pp) and proton–lead (p–Pb)
collisions have revealed that small collision systems exhibit signatures
previously considered unique features of heavy-ion collisions. Some of these
signatures, such as the enhanced production of strange hadrons [1], and
collective flow [2, 3], can be explained by the formation of a strongly
interacting medium. However, the formation of a medium in these small systems
challenges current theoretical frameworks, because their initial small volumes
imply lifetimes so short that it is unclear to what degree the systems can
equilibrate (see Ref. [4] and references therein).

The observation of collective flow, as well as strangeness enhancement in
particular, implies that pp collisions at LHC and RHIC energies can no longer
be described as semi-incoherent sums of parton–parton collisions, an idea that
has been central to most general-purpose quantum chromodynamics (QCD)-inspired
Monte-Carlo event generators, such as PYTHIA [5] and Herwig [6]. “Jet
Universality” is another long-standing idea for the phenomenological
understanding of QCD assuming that, while the partonic processes vary with
system and beam energy, the produced color fields and their hadronization are
universal. In the context of Lund strings, this implies that the string
tension and string-fragmentation parameters are the same regardless of
collision system. For a recent discussion, we refer to Ref. [7]. The discovery
of strangeness enhancement scaling with the multiplicity [8][9] violates the
assumptions of jet universality, and for this reason QCD-inspired generators
have incorporated additional phenomenological final-state pre-hadronization
mechanisms, such as string percolation [10], color ropes [11], baryon
junctions [12] and/or new types of baryon-favored color reconnection [13].
Furthermore, charm fragmentation fractions in pp collisions also differ
significantly from the values measured in $\textrm{e}^{+}\textrm{e}^{-}$
collisions [14].

In contrast, quark–gluon plasma (QGP)-inspired models include a system
evolution with volume and multiplicity and so the qualitative features of both
collective flow and strangeness enhancement are expected. EPOS-LHC is an event
generator where the initial interactions lead to a two-phase state
(core–corona) consisting of a dense core of QGP, and a diluted corona [15].
Strangeness enhancement in EPOS-LHC is due to a change in the relative
contribution of the corona (low strangeness production from pomerons) and core
(high thermal strangeness production from QGP) with multiplicity.

As can be seen from the previous discussion, strange-particle production
appears to be a powerful probe for QGP-like effects in small systems, and the
origin of the strangeness enhancement constitutes an important open question.
Therefore, results on strangeness production in small systems can facilitate
progress in the understanding of both QCD dynamics and hadronization, in
addition to putting constraints on phenomenological models.

ALICE has previously reported that strangeness enhancement as a function of
the average multiplicity at midrapidity does not depend on the collision
system nor center-of-mass energy per nucleon–nucleon collision, ranging from
pp to p–Pb and $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV to $\sqrt{s}$ =13 TeV [16].
This universality implies a strong correlation between the underlying physics
processes that drive both the enhancement and the multiplicity. In this
article, we have tested if the observed universality can be broken by
contrasting high-multiplicity events dominated by one or more hard
scatterings, with events dominated by multiple softer interactions.

At high transverse momentum ($p_{\rm T}$), strangeness production in hadronic
collisions tends to originate from “hard”, perturbative QCD processes. These
hadrons are either produced directly through flavor creation ($\rm
XX\rightarrow\rm s\bar{s}$) or flavor excitation
($\rm{s}X\rightarrow\rm{s}X$), or indirectly as a result of radiation and/or
hadronization associated with hard processes, e.g., through gluon splitting
following the partonic evolution ($\rm g\rightarrow s\bar{s}$). In contrast,
the production of “soft”, low-$p_{\rm T}$ strange hadrons ($p_{\rm T}\leq
2~{}{\rm GeV}/c$) is dominated by non-perturbative QCD processes, where novel
QCD dynamics could be found. The final-state azimuthal topology is expected to
reflect which of these QCD processes are primarily driving particle production
for a given event. Events dominated by one or more hard scatterings will
presumably lead to pronounced back-to-back jet structures, while events that
contain several softer scatterings will result in isotropic distributions. We
note that previous results obtained by ALICE, both utilizing the same event
shape estimator [17] and a similar one, the transverse sphericity [18], found
evidence for this behavior in the way that $\langle p_{\mathrm{T}}\rangle$
would depend on the event topology.

To identify the final-state azimuthal topology, we will here use a modified
variant of the transverse spherocity ($S_{\text{O}}$) estimator proposed in
Ref. [17], for being more sensitive to the underlying processes. The lower
bound of $S_{\text{O}}$ aims to distinguish “Jet-like” events, which in this
study are events characterized by an azimuthal topology similar to a pair of
back-to-back jets (implying a tight clustering of particles with a difference
in azimuthal angle $\Delta\phi\approx 0$ or $\pi$ [17]), which on average
produces a larger number of high-$p_{\rm T}$ hadrons compared with the
$S_{\text{O}}$–integrated distribution, thereby “hardening” the $p_{\rm
T}$-differential spectra. Conversely, the upper bound of $S_{\text{O}}$
selects “Isotropic” events, defined by an azimuthal topology which is close to
symmetric, with an absence of preferred direction. The hypothesis is that
$S_{\text{O}}$, by contrasting events with these different topologies, can be
used to control the degree of QGP-like effects, like strangeness enhancement
and radial flow, in high-multiplicity pp collisions [19, 20].

In this article, we present the first results on strangeness production in
high-multiplicity pp collisions at $\sqrt{s}=13\text{\,TeV}$ as a function of
the transverse spherocity. The results obtained for the light-flavor hadrons
are presented as the sum of particles and anti-particles, explicitly as
$\pi^{+}$ \+ $\pi^{-}$, $\rm{K}^{+}$ \+ $\rm{K}^{-}$, $\rm K^{*0}$ \+
$\rm{\overline{K^{*0}}}$, p + $\rm\overline{p}$, $\Lambda$ \+
$\overline{\Lambda}$, $\Xi^{-}$ \+ $\Xi^{+}$ where the exceptions are ${\rm
K}^{0}_{\rm{S}}$ and $\phi$. Hereinafter, the sum of particle and anti-
particles will be referred to as $\pi$, K, ${\rm K}^{0}_{\rm{S}}$, $\rm
K^{*0}$, p, $\phi$, $\Lambda$, and $\Xi$, unless otherwise explicitly
mentioned.

The article is organized as follows. The ALICE main detectors used in this
analysis are detailed in Section 2. Section 2.1 describes the high-
multiplicity definitions used throughout this article. The transverse
spherocity observable, along with caveats, is defined in Section 3. The
details concerning particle identification (PID), yield extraction, and
correction procedures are discussed in Section 4. The details regarding
experimental corrections and systematic uncertainties are discussed in
Sections 5 and 6, respectively. The results are reported in Section 7, and
finally the summary and conclusions of our study are discussed in Section 8.

##  2 Experimental setup and event selection

A detailed description of the ALICE apparatus in its Run 1 and 2
configuration, as well as its performance, can be found in Refs. [21, 22].
This section will briefly describe the main ALICE detectors used for the event
selection, $S_{\text{O}}^{p_{\rm T}=1}$ determination, and extraction of
particle spectra. All radii in the following are given as distances from the
beam axis.

The detectors of the ALICE apparatus can be grouped as follows: the central
barrel at midrapidity, the muon arm at forward rapidity, and the forward
global detectors. To be able to efficiently trigger on inelastic pp
collisions, ALICE employs two forward scintillator arrays, V0A and V0C, with a
pseudorapidity coverage of $2.8<\eta<5.1$ and $-3.7<\eta<-1.7$, respectively.

Both $S_{\text{O}}^{p_{\rm T}=1}$ and particle yields are determined by using
tracks in the central barrel. The main detectors for tracking in the central
barrel are the Inner Tracking System (ITS) and the Time Projection Chamber
(TPC). The ITS detector is composed of six layers of cylindrical silicon
detectors with full azimuthal acceptance, where the radius of the innermost
(outermost) layer is $3.9$ cm ($43$ cm). The innermost layers consist of two
arrays of hybrid silicon pixel detectors (SPD), whose fine granularity
provides high precision tracking closest to the primary vertex. The SPD is
also used to reconstruct tracklets, short two-point track segments covering
the pseudorapidity region $\left|\eta\right|~{}<~{}1.4$. The tracklets provide
both efficient primary vertex determination and a precise estimate of the
charged-particle multiplicity. The remaining layers of the ITS are only used
for tracking in the analyses presented here. The TPC is the primary tracking
device in ALICE that provides a full three-dimensional trajectory for each
track. It is a large cylindrical detector that surrounds the ITS detector with
an inner and outer radii of 85 cm and 250 cm, respectively. It has full
azimuthal acceptance and a pseudorapidity coverage of $-0.9<\eta<0.9$ for
full-length tracks. The ITS and TPC are situated inside the solenoidal L3
magnet with a uniform magnetic field of 0.5 T. For global tracks, where the
full information of the ITS and TPC are used together, a momentum resolution
of 1–10 % is achieved for momenta ranging from 0.05 to $100\text{\,GeV/$c$}$.

The ALICE apparatus utilizes a broad range of different particle
identification techniques to identify the mass of each analyzed particle. For
weakly-decaying $V^{0}$ (${\rm K}^{0}_{\rm{S}}$, $\Lambda$) and Cascades
($\Xi$), the TPC tracking is able to provide with topological track matching
of the decay products, where particles are then identified through peaks in
invariant mass distributions. For the other particles, the PID is provided by
the specific energy loss, d$E$/d$x$, measured in the TPC and the particle’s
velocity (given a measured momentum in the TPC) is provided by the Time-of-
flight (TOF) detector. The TOF consists of Multi-Gap Resistive Plate Chambers
(MRPC), which are used for the particle identification by measuring the total
time of flight of the identified hadrons. It is located at about 3.7 m from
the interaction point, with a full azimuthal acceptance and has a
pseudorapidity coverage of $-0.9<\eta<0.9$. Details of the particle
identification procedure are given in Sec. 4.

###  2.1 Event selection

Data used in this analysis were collected with a minimum bias trigger, which
requires one or more hits in both V0 scintillator arrays in coincidence with
proton beams from both directions. The contamination from beam-induced
background is removed offline by using the timing information in the V0
detectors and taking into account the correlation between tracklets and
clusters in the SPD detector, as discussed in detail in [22]. The primary
vertex is reconstructed by correlating hits in the two SPD layers and only
events with a primary vertex within $\pm$10 cm of the nominal interaction
point along the beam direction are accepted for this analysis. Due to the fast
readout time of the SPD, any contamination from out-of-bunch pile-up is
rejected. The contamination from in-bunch pile-up events is removed offline by
excluding events with multiple vertices reconstructed in the SPD. Any
remaining pile-up will be from collisions which produce little or no
particles. Due to the required high-multiplicity event-selection, this will
have a negligible impact on the final results presented in this article,

The measurements reported here were performed on minimum-bias triggered events
that additionally have at least one charged particle measured in the
pseudorapidity interval $|\eta|<1$ ($\text{INEL}>0$) [23], corresponding to
about 75 % of the total inelastic cross section. Two different multiplicity
estimators are used, the total charge deposited in the V0 detectors (V0M), and
the number of SPD tracklets within $\mbox{$\left|\eta\right|~{}<~{}0$}.8$
($N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$). For each of these estimators,
the multiplicity is classified as a percentile, where 0% corresponds to the
highest and 100% to the lowest multiplicity. The high-multiplicity events used
throughout this article include the top-1% (10%) multiplicity percentile, with
a minimum of 10 reconstructed charged primary tracks at midrapidity
($\left|\eta\right|~{}<~{}0$.8).

##  3 Unweighted transverse spherocity $S_{\text{O}}^{p_{\rm T}=1}$

In this analysis, the unweighted transverse spherocity $S_{\text{O}}^{p_{\rm
T}=1}$ is used to quantify the topology in the azimuthal plane. It is
calculated as

$\centering S_{\text{O}}^{p_{\rm
T}=1}=\frac{\pi^{2}}{4}\min_{\hat{n}}\left(\frac{\Sigma_{i}|\hat{p_{\textrm{T},i}}\times\hat{n}|}{N_{\textrm{trks}}}\right)^{2}.\@add@centering$
(1)

The sum is calculated over all charged particles with $p_{\rm
T}>0.15\text{\,GeV/$c$}$, where $\hat{p_{\textrm{T}}}$ represents the
transverse momentum unit vector, $N_{\textrm{trks}}$ is the number of charged
particles in a given event and $\hat{n}$ is the unit vector that minimizes
$S_{\text{O}}^{p_{\rm T}=1}$.

Loose selection criteria were chosen for primary tracks to ensure a high
efficiency and uniform azimuthal acceptance over the full TPC volume. At least
50 or more measured clusters are required for a track in the TPC. Furthermore,
the TPC tracks must be matched to hits in the ITS, but, to ensure homogeneous
azimuthal acceptance, the tracks are not explicitly required to have hits in
the SPD. These requirements improve the tracking precision, and reject tracks
from out-of-bunch pile-up. Finally, selections of distance of closest approach
(DCA) along the beam axis ($|\rm DCA_{\it{z}}|<3.2$ cm), and in the xy-plane
($|\rm DCA_{\it{xy}}|<2.4$ cm) are applied, ensuring that the reconstructed
TPC track points to the primary vertex.

Unlike the traditional transverse spherocity estimator discussed in [24], the
transverse momentum ($p_{\rm T}$) of each track in this article is normalized
to 1 ($p_{\rm T}=1$) when measuring the $S_{\text{O}}^{p_{\rm T}=1}$. This
modification was required to have similar sensitivity between neutral and
charged particles. Otherwise, there would be significant differences between
the production of neutral and charged kaons in jet-like events. This can be
understood considering that for the traditional spherocity, a single
high-$p_{\rm T}$ track will have a large weight in the spherocity calculation,
which can occur for a charged kaon but never for a neutral kaon. By assigning
the same weight to all measured primary charged tracks, one reduces the
possible charged-vs-neutral biases.

However, this also means that results obtained with the two different
spherocity estimators (traditional and unweighted) can only be qualitatively
compared. Furthermore, as $S_{\text{O}}^{p_{\rm T}=1}$ is independent of the
$p_{\rm T}$ of the particles, it requires a substantial amount of particles to
be a good measure of the event topology. For this reason, the number of
charged tracks is required to be greater or equal to 10 for events included in
this analysis, which limits the applicability of the unweighted spherocity
estimator to high-multiplicity pp collisions.

The values of $S_{\text{O}}^{p_{\rm T}=1}$ will, by construction, lie between
0 and 1. Having events with $S_{\text{O}}^{p_{\rm T}=1}\approx 0$ imply that
$|\hat{p_{\textrm{T}}}\times\hat{n}|\approx 0$ for all tracks, which indicates
that all tracks are parallel in the azimuthal plane, suggesting that the event
is dominated by a single back-to-back dijet. Events where
$S_{\text{O}}^{p_{\rm T}=1}$ $\rightarrow$ 1 imply that all particles are
uniformly distributed azimuthally, suggesting the absence of a preferred
direction. Note that part of the isotropy of the event can be affected by
anisotropic flow [2]. The unfolded $S_{\text{O}}^{p_{\rm T}=1}$ distributions
are presented in Fig. 1, along with model predictions, for the three different
multiplicity selections used in this article. The correction of the
$S_{\text{O}}^{p_{\rm T}=1}$ distributions is based on the Bayesian unfolding
technique [25]. The same unfolding method used in previous ALICE publications
[26] is applied here.

A key aspect of the analysis presented in this article is the capability to
compare the measured results with MC generator predictions. Extensive studies
were performed to understand and mitigate any experimental biases due to the
$S_{\text{O}}^{p_{\rm T}=1}$ selection. The experimental bias is evaluated by
generating PYTHIA 8 111The fully simulated PYTHIA events are the same used to
obtain the tracking efficiency correction discussed in Sec. 4. We refer to
this section for technical details on the simulation. events, that are
propagated through a full ALICE simulation of the experimental apparatus.

The $S_{\text{O}}^{p_{\rm T}=1}$ definition has been constructed to require
that the generated events agree with the reconstructed simulated events, where
the $p_{\rm T}$ spectra have been corrected for the minimum bias
reconstruction efficiency222Secondary particles were rejected using MC
information.. This ensures that the measured and generated results are
directly comparable. The experimental uncertainty is minimized by adopting the
following criteria, making $S_{\text{O}}^{p_{\rm T}=1}$ a robust and model-
independent observable:

  * •

$S_{\text{O}}^{p_{\rm T}=1}$ selection in quantiles.
One major source of experimental bias is the smearing of the measured
$S_{\text{O}}^{p_{\rm T}=1}$ distribution by detector effects. It was verified
through MC studies that one can minimize the effect of the smearing by
measuring $S_{\text{O}}^{p_{\rm T}=1}$ in quantiles, similar to how
multiplicity classes are defined in ALICE [17]. The stability of the quantiles
is due to the fact that spherocity distribution does not have large gradients.
A robust model-to-data comparison is achieved by calculating the model
comparison in measured percentiles, rather than for the numerical
$S_{\text{O}}^{p_{\rm T}=1}$ ranges we report in this article.

  * •

Exclusion of neutral decay modes for resonance particles
The decay daughters of both $\phi$ and $\rm K^{*0}$ meet the standard ALICE
definition of primary particles [27], subsequently leading to the resonance
daughters entering the measurement of $S_{\text{O}}^{p_{\rm T}=1}$ for a given
event. These daughters will contribute to the multiplicity estimate if
measured at midrapidity, and as both the $\phi$ and $\rm K^{*0}$ resonances
have charged and neutral decay modes, the branching ratio for the charged
decay mode will artificially inflate in high-multiplicity events. This bias
can be completely avoided by only including (and correcting for) the following
charged decay modes for resonance particles in the resulting spectra: $\phi$
$\rightarrow$ $K^{+}K^{-}$ and $\rm K^{*0}$ $\rightarrow$ K$\pi$.

  * •

Contamination of secondary particles
There is an effect that comes from the loose selection criteria for primary
tracks used in this analysis. The loose DCA selections, which are there to
maintain a full azimuthal acceptance, consequently lead to some decay
daughters from $V^{0}$s and cascades to be incorrectly reconstructed as
primary particles. To minimize the experimental bias from this effect, we
include the primary $\Lambda$, $\rm K^{0}_{S}$, and $\Xi$ directly into the
calculation of $S_{\text{O}}^{p_{\rm T}=1}$ for the generated MC predictions.
The inclusion of these particles at the generator level makes the results
presented in this article directly comparable to model predictions.

Note that the $S_{\text{O}}^{p_{\rm T}=1}$ distribution is the same across all
presented particle species in this article. The implementation of these
corrections reduce the experimental bias to a few percent, presented in Table
1, which lists the remaining fractional systematic uncertainties due to the
$S_{\text{O}}^{p_{\rm T}=1}$ selection. The only exception is for low $p_{\rm
T}$ $\Lambda$ ($\bar{\Lambda}$) and $\rm K^{0}_{S}$, where we do not present
results for $p_{\rm T}<1\text{\,GeV/$c$}$. Our understanding is that for these
very low $p_{\rm T}$ tracks, the azimuthal angles of the decay daughters that
enter the $S_{\text{O}}^{p_{\rm T}=1}$ measurement are too different from
their mother to give a precise result. Charged pions, kaons and (anti)protons
are the most abundant particles, as well as the particles that enter directly
into the $S_{\text{O}}^{p_{\rm T}=1}$ measurement, ensuring that these
particle species are more robust against experimental biases.

Table 1: The fractional systematic uncertainties used to estimate the experimental bias introduced when triggering on $S_{\text{O}}^{p_{\rm T}=1}$. The uncertainties are $p_{\rm T}$-independent, and are applied to both jet-like and isotropic event selections, unless otherwise specified. | $\pi$ | K | p |  $\mathrm{\phi}$ and $\mathrm{K}^{*}$ |  $\rm K^{0}_{S}$ and $\Lambda$ | $\Xi$
---|---|---|---|---|---|---
|  |  |  |  |  $p_{\rm T}$ $>1$ GeV/$c$ |
$S_{\text{O}}^{p_{\rm T}=1}$ $p_{\rm T}$ spectra | 0% | 0% | 0% | 3% | Isotropic: 1% | 3%
|  |  |  |  | jet-like: 4% |
|  |  |  |  |  $p_{\rm T}$ $>1$ GeV/$c$ |
$S_{\text{O}}^{p_{\rm T}=1}$ h/$\pi$ ratio | N/A | 0% | 0% | 3% | Isotropic: 1% | 3%
|  |  |  |  | jet-like: 4% |

The quantiles used for the experimental measurements are listed in Table 2.
The roman numerals represent the multiplicity labels for these percentiles
reported in earlier ALICE publications [17][26]. It is important to stress
that the $S_{\text{O}}^{p_{\rm T}=1}$ selections for the model comparisons
presented throughout this article are done on their corresponding
$S_{\text{O}}^{p_{\rm T}=1}$ quantiles.

Table 2: Values corresponding to the $S_{\text{O}}^{p_{\rm T}=1}$ range of the different quantiles obtained from the uncorrected $S_{\text{O}}^{p_{\rm T}=1}$ distribution used for the event selections in this analysis. Multiplicity: |  $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ I–III (0–10%) |  $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ I (0–1%) | V0M I (0–1%)
---|---|---|---
Jet-like
$S_{\text{O}}^{p_{\rm T}=1}$ 0–1% | $<0.408$ | $<0.487$ | $<0.433$
$S_{\text{O}}^{p_{\rm T}=1}$ 0–5% | $<0.508$ | $<0.577$ | $<0.535$
$S_{\text{O}}^{p_{\rm T}=1}$ 0–10% | $<0.561$ | $<0.624$ | $<0.589$
$S_{\text{O}}^{p_{\rm T}=1}$ 0–20% | $<0.625$ | $<0.680$ | $<0.651$
Isotropic
$S_{\text{O}}^{p_{\rm T}=1}$ 80–100% | $>0.833$ | $>0.859$ | $>0.846$
$S_{\text{O}}^{p_{\rm T}=1}$ 90–100% | $>0.871$ | $>0.892$ | $>0.882$
$S_{\text{O}}^{p_{\rm T}=1}$ 95–100% | $>0.896$ | $>0.913$ | $>0.905$
$S_{\text{O}}^{p_{\rm T}=1}$ 99–100% | $>0.930$ | $>0.942$ | $>0.936$

Figure 1: Upper panels: The measured and fully corrected $S_{\text{O}}^{p_{\rm
T}=1}$ distributions. Lower panels: Ratio between model calculations and
experimental data. These are presented for
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ 0–1% (top), 0–10% (middle) and
V0M 0–1% (bottom). The curves represent different model predictions, where the
shaded area represents the statistical uncertainty of the models. The relative
systematic uncertainty is shown as a gray area around unity in the lower
panels.

##  4 Measurements of transverse momentum spectra

In this section, the procedure for the $p_{\rm T}$ spectra measurements will
be presented. First, the analyses utilizing only primary charged tracks are
discussed in Section 4.1, followed in Section 4.2 by the analyses which
utilize the weak decay topology, reconstructed via secondary tracks. All
particle spectra are measured in the exact same pseudorapidity interval
($|\eta|<0.8$) for which the $S_{\text{O}}^{p_{\rm T}=1}$ is defined, to
ensure maximal correlation between event topology and particle production.
This allows for a clear, one-to-one comparison between MC generators and data.

###  4.1 Particle identification utilizing primary charged tracks

This subsection discusses analyses regarding the production of $\pi,{\rm
K},{\rm p}$, and the resonances $\phi$ and $\rm K^{*0}$. For these analyses,
global tracks are reconstructed using the combined information from the ITS
and TPC to achieve high precision. Track selection criteria are applied to
limit the contamination from secondary particles, to maximize tracking
efficiency and to improve the $\text{d}E/\text{d}x$ and momentum resolution
for primary charged particles. The number of crossed pad rows in the TPC is
required to be at least 70 (out of a maximum of 159); the ratio of the number
of crossed pad rows to the number of findable clusters (the number of
geometrically possible clusters which can be assigned to a track) is
restricted to be greater than 0.8, see Ref. [22] for details. The goodness-of-
fit values $\chi^{2}$ per cluster ($\chi^{2}/N_{\rm clusters}$) of the track
fits in the TPC must be less than 4. Tracks must be associated with at least
one cluster in the SPD, and the $\chi^{2}$ values per cluster in the ITS are
restricted in order to select high-quality tracks. The DCA to the primary
vertex in the plane perpendicular to the beam axis (DCAxy) is required to be
less than seven times the resolution of this quantity; this selection is
$p_{\rm T}$ dependent, i.e. DCAxy $<7\times(0.0015\pm 0.05p_{\rm T})$ cm. A
loose selection criterion is also applied for the DCA in the beam direction
(DCAz), by rejecting tracks with DCA${}_{z}>$ 2 cm, to remove tracks from
possible residual pileup events. The transverse momentum of each track must be
greater than 0.15 GeV/$c$ and the pseudorapidity is restricted to the range
$|\eta|<$ 0.8 to avoid edge effects in the TPC acceptance. Additionally,
tracks produced by the reconstructed weak decays of pions and kaons (the
“kink" decay topology) are rejected.

The Particle Identification (PID) technique adopted for these analyses is
based on a selection on the $n\sigma$ distributions, which are defined as

$\displaystyle
n\sigma=\frac{\text{Signal}_{\textrm{measured}}-\langle\text{Signal}_{\textrm{expected}}\rangle}{\sigma},$

where the Signal can be either the measured $\text{d}E/\text{d}x$ in the TPC,
or the extracted 1/$\beta$ in the TOF, and $\sigma$ is the corresponding
resolution.

####  4.1.1 Charged pions, kaons and (anti)protons

Primary $\pi,{\rm K},{\rm p}$ are measured in the range of
0.3–$20.0\text{\,GeV/$c$}$, and yields are extracted following standard
particle identification techniques reported in previous ALICE publications
[26][28]. At low $p_{\rm T}$ the particles are identified with high purity
through the TPC $\text{d}E/\text{d}x$ by fitting the $n\sigma$ distributions
[29]. In this $p_{\rm T}$ range, the large separation power between $\pi$–K
and p–K allows for a particle identification on a track-by-track basis. The
relative particle abundances are obtained by fitting the $n\sigma$
distributions in narrow intervals of transverse momentum. For the kaons a two-
Gaussian parameterization is used to correct for contamination of electrons.

At intermediate $p_{\rm T}$, the TOF detector is used for identification by
fitting the $\beta$ distribution [30]. Particle identification in this $p_{\rm
T}$ range is also performed on a track-by-track basis, by fitting the
convolution of a Gaussian parameterization and an exponential function to the
$\beta$ distribution. Similarly to low $p_{\rm T}$, the identified particle
yield is extracted through the $n\sigma$ of these fits.

Finally, the TPC $\text{d}E/\text{d}x$ is used to identify the relativistic
high-$p_{\rm T}$ particles (rTPC), with a technique described in Ref. [31].
Unlike the methods used for lower $p_{\rm T}$ intervals, this technique does
not allow for track-by-track identification of $\pi,{\rm K},{\rm p}$. Instead,
the relative particle abundances are measured by fitting a four-Gaussian
parameterization to the $\text{d}E/\text{d}x$ distributions, in $\eta$ and
momentum intervals, where each Gaussian corresponds to the signal of $\pi,{\rm
K},{\rm p}$ and electrons. The fractional yields in each Gaussian are then
used to extract the identified particle abundances from the full charged
primary particle $p_{\rm T}$ spectra in $\eta$ and momentum intervals. The
explicit momentum intervals for each particle identification technique are
found in Table. 3.

Table 3: A breakdown of the momentum intervals for the different PID techniques used in the $\pi,{\rm K},{\rm p}$ analysis. Analysis | PID technique |  $p_{\rm T}$ ranges (${\rm GeV}/c$)
---|---|---
|  |  $\pi$ K p
TPC | n$\sigma$ fits | 0.3–0.7 0.3–0.6 0.45–1.0
TOF |  $\beta$ fits | 0.7–3.0 0.6–3.0 1.0–3.0
rTPC |  $\text{d}E/\text{d}x$ fits | 3.0–20 3.0–20 3.0–20

####  4.1.2 Resonance particles $\phi$ and $\rm K^{*0}$

Resonance particles cannot be directly detected by the experimental apparatus,
but one can extract their yield by analyzing the invariant mass
$M_{\text{inv}}$ distribution, obtained by correlating all pairs of possible
decay daughters. For the analyses presented here, the relevant decays are:

$\displaystyle\phi$ $\displaystyle\rightarrow\rm K^{+}+K^{-}$
$\displaystyle\rm B.R.~{}=(49.2\pm 0.5)\%,$ $\displaystyle\rm K^{*0}(\bar{\rm
K^{*0}})$ $\displaystyle\rightarrow\rm K^{+}(K^{-})+\pi^{-}(\pi^{+})$
$\displaystyle\rm B.R.~{}=(66.503\pm 0.014)\%.$ (2)

The extraction technique summarized in the following is similar to previously
published procedures, see for example Ref. [32] for further details.

The $M_{\text{inv}}$ distribution is constructed utilizing $\pi$ and $K$
hadrons, identified via selections on the TPC and TOF n$\sigma$ distributions.
This is critical to reduce the contamination of pions in the kaons sample. The
combinatorial background is estimated by creating a mixed-event
$M_{\text{inv}}$ sample for each resonance decay channel. The $M_{\text{inv}}$
is then calculated for pairs of daughter candidates originating from different
events, which is then subtracted from the signal distribution. The precision
with which the mixed-event distribution can describe the combinatorial
background depends significantly on the event topology. For events with jet-
like topologies, this description is very poor, as the mixed events have a
completely different event topology if the “jet axes” are not aligned. One can
easily understand this by expressing the $M_{\text{inv}}$ (with masses
$m_{1,2}$ and momentum $p_{1,2}$, and energies $E_{1,2}$) in terms of the
angle between the two momentum vectors, $\theta$,

$M_{\textrm{inv}}^{2}=m_{1}^{2}+m_{2}^{2}+2E_{1}E_{2}-2|\vec{p_{1}}||\vec{p_{2}}|\cos{(\theta)}.$
(3)

By similar reasoning one can deduce that the description of the combinatorial
background in isotropic events is very good. Therefore, one needs significant
statistics to precisely estimate the remaining background, so that the yield
extraction is accurate. Relative to the other analyses presented in this
article, the resonance analyses are consequently limited in terms of how
narrow one is able to make $S_{\text{O}}^{p_{\rm T}=1}$ event selection. This
also results in a significant $S_{\text{O}}^{p_{\rm T}=1}$ dependence of the
systematic uncertainty.

The reconstructed resonance particle yield is extracted, in $p_{\rm
T}$-differential intervals, using a Voigtian peak function for the signal and
a 2nd-degree polynomial for the remaining combinatorial background. The yield
extractions for $\phi$ and $\rm K^{*0}$ are then performed in two separate
steps: First, by counting the entries after subtraction of the 2nd-degree
polynomial in the invariant mass ranges 0.995–1.07 ${\rm GeV}/c$ and 0.76–1.12
${\rm GeV}/c$, respectively. Second, the Voigtian tails are integrated outside
the aforementioned counted mass intervals to correct for the missing tails,
which represents a minor fraction of the total yield. The final yields are
obtained by the summation of the bin counted estimate and the integrated
Voigtian tails.

###  4.2 Particle identification utilizing weak decay topology

The details regarding the reconstruction of the weakly decaying particles,
${\rm K}^{0}_{\rm{S}}$, $\Lambda$, and $\Xi$, which utilize secondary tracks,
are reported here. The relevant decays are:

$\displaystyle{\rm K}^{0}_{\rm{S}}$
$\displaystyle\rightarrow\rm\pi^{+}\pi^{-}$ $\displaystyle\rm
B.R.~{}=(69.20\pm 0.05)\%,$ $\displaystyle\Lambda(\bar{\Lambda})$
$\displaystyle\rightarrow\rm p(\bar{p})+\pi^{-}(\pi^{+})$ $\displaystyle\rm
B.R.~{}=(63.9\pm 0.5)\%,$ $\displaystyle\Xi^{-}(\overline{\Xi}^{+})$
$\displaystyle\rightarrow\rm\Lambda(\bar{\Lambda})+\pi^{-}(\pi^{+})$
$\displaystyle\rm B.R.~{}=(99.887\pm 0.035)\%.$ (4)

As a substantial fraction of secondary particles from the decays are produced
outside the ITS, the track criteria are different for these secondary tracks
than for primary particles: no ITS information is required, and the tracks are
required to _not_ point directly back to the collision vertex. The data sample
used in these analyses contained a significant contribution of out-of-bunch
pile up that had to be accounted for.

The topological constraints, as well as the track quality requirements, are
summarized in Table 4 and Table 5 for $V^{0}$ and $\Xi$ candidates,
respectively. Topological constraints are applied on the reconstructed decay
geometry to reduce background, specifically the distances of the daughters to
the primary vertex (PV), the DCA of the daughters to the secondary vertex, and
the pointing angle of the $V^{0}$ candidate with respect to the PV. The
topological identification starts with the formation of $V^{0}$ candidates,
consisting of two secondary tracks that:

  * •

do not point to the PV (DCA of daughters to PV),

  * •

appear to share the same secondary production vertex ($V^{0}$ DCA),

  * •

do point back to the PV (from the secondary vertex) when the momentum vectors
are summed up (pointing angle).

To calculate the $M_{\text{inv}}$, the masses of the secondary tracks are
assigned based on Eq. 4.2 after testing the PID consistency. This yields up to
three different hypotheses, ${\rm K}^{0}_{\rm{S}}$, $\Lambda$, and
$\bar{\Lambda}$, for the $M_{\text{inv}}$ of each $V^{0}$. If a $V^{0}$
candidate has its invariant mass compatible to other $V^{0}$ masses under the
respective competing hypotheses, it is rejected. Additionally, for $\Lambda$
and $\bar{\Lambda}$, a selection on an experimental estimate of the particle’s
proper lifetime is also used to reduce the background. All selection criteria
used are summarized in Table. 4.

Table 4: Topological selection criteria used in the identification of the $\rm K^{0}_{S}$, $\Lambda$, and $\bar{\Lambda}$ particles. Selection variable | Selection criteria for $\rm K^{0}_{S}$ ($\Lambda$, $\bar{\Lambda}$)
---|---
Topology
DCA between daughters | $<1.0~{}\mathrm{cm}$
Cosine of pointing angle | $>0.97(0.995)$
Transverse decay radius $R_{xy}$ | $>0.5~{}\mathrm{cm}$
Daughter tracks selection
DCA of daughters to PV |  $>0.06$ cm
TPC PID of daughters | $<5\,\sigma$
Track pseudorapidity |  $\left|\eta\right|~{}<~{}0$.8
TPC crossed rows | $N_{\mathrm{cr}}>70$
TPC crossed rows to findable ratio | $N_{\mathrm{cr}}/N_{\mathrm{f}}>0.8$
Candidate selection
$V^{0}$ pseudorapidity |  $\left|\eta\right|~{}<~{}0$.8
Transverse momentum |  $1.0<p_{\rm T}<25.0$ ${\rm GeV}/c$
Proper lifetime (transverse) |  $(\,R_{xy}\times m_{(\Lambda,\bar{\Lambda})}/p_{\mathrm{T}}\,)<30$ cm
Competing mass | $>4\,\sigma$

For cascades ($\Xi$), secondary $V^{0}$ candidates are matched to secondary
bachelor tracks and by assuming the relevant masses one can test the cascade
hypothesis for a $\Xi$. Secondary $V^{0}$ are identified by means of a
selection on the distance of the PV from the pointing direction of the
candidate.

Table 5: Summary of the topological selection values used for the $\Xi$ candidate selection. All impact parameter requirements on tracks are 2D ($xy$). Selection variable | Selection criteria
---|---
Topology of $\Xi$
DCA between daughters ($V^{0}$ and $\pi$) |  $<1.6$ cm
Cosine of pointing angle | $>0.97$
Cascade transverse decay radius |  $>0.8$ cm
DCA of bachelor to PV |  $>0.05$ cm
Topology of secondary $\Lambda$
DCA between daughters (p and $\pi$) |  $<1.6$ cm
$V^{0}$ impact parameter |  $>0.07$ cm
$V^{0}$ transverse decay radius |  $>1.4$ cm
Window around $\Lambda$ mass |  $<0.006$ (GeV/$c^{2}$)
DCA of daughters to PV |  $>0.04$ cm
Common bachelor/daughter track selection
Track pseudorapidity |  $\left|\eta\right|~{}<~{}0$.8
TPC clusters |  $>$ 70
TPC PID of daughters | $<5\,\sigma$

As the TPC is a relatively slow detector with a readout time of
${\approx}100\,\mu$s, it is possible to accidentally accept secondary tracks
from $V^{0}$ or cascades produced in earlier or later events. To reject these
candidates, we require that at least one decay daughter is either associated
to a cluster in the ITS or is matched to a hit in the TOF detector.

##  5 Corrections

The $p_{\rm T}$ spectra of $\phi$, $\rm K^{*0}$, and $\Xi$ are only corrected
for acceptance and tracking efficiencies, while the study of $\pi,{\rm K},{\rm
p}$, $\Lambda$, and ${\rm K}^{0}_{\rm{S}}$ requires more sophisticated
corrections to account for the contamination from secondary particles. The
$p_{\rm T}$ spectra of $\pi$, K and p are corrected for acceptance,
reconstruction inefficiency, TPC–TOF matching efficiency (only in the TOF
analysis) and secondary particle contamination. The reconstruction
efficiencies are obtained from event simulations using the PYTHIA8
(Monash-2013 tune) Monte Carlo event generator [33]. Then, the propagation of
the simulated events through the ALICE apparatus is described with GEANT 3.21
[34]. Finally, the simulated events are reconstructed and analyzed using the
same procedure as for data. This study found that the reconstruction
efficiencies are independent of the multiplicity and spherocity selections.
Thus, the values from the minimum-bias sample were applied. In addition, since
low-momentum interactions of $\mathrm{K}^{-}$ and $\mathrm{\overline{p}}$ with
the detector material are not completely described by GEANT 3, an additional
correction to the reconstruction efficiencies of these two particles is
estimated with GEANT 4 [35] and FLUKA [36].

The secondary particle contamination correction takes into account the
contamination to the $p_{\rm T}$ spectra of $\pi$ and $\mathrm{p}$ from weak
decays: ${\rm
K}^{0}_{\rm{S}}\rightarrow\pi^{+}+\pi^{-},\Lambda\rightarrow\mathrm{p}+\pi^{+},\Sigma^{+}\rightarrow\mathrm{p}+\pi^{0}$
(and charge conjugates) and material interactions. This correction is
estimated from a multi-template fit to data distributions of the transverse
distance-of-closest approach $(\mathrm{DCA}_{xy})$ [37]. Three templates that
represent the expected shapes of $\mathrm{DCA}_{xy}$ distributions of primary
and secondary (from weak decays) particles, and of particles from interactions
with the detector material are used. The fits are constrained in the interval
$\pm 3~{}\mathrm{cm}$. Since the TPC and TOF analyses employ different track
selections, these corrections are estimated separately for the TPC and TOF
analyses. At $p_{\rm T}=0.45~{}\rm{GeV}/\it{c}$ the contribution from non-
primary $\pi^{+}(\rm{p})$ was found to be about $4\%(20\%)$, while at $p_{\rm
T}=2.0~{}\rm{GeV}/\it{c}$ it decreases to about $1\%(4\%)$. Since this
correction decreases asymptotically, an extrapolation from the TOF measurement
is applied in the rTPC analysis.

Secondary production of $\Lambda$ ($\bar{\Lambda}$) from $\Xi^{\pm}$ and
$\Xi^{0}$ baryons were determined from measured $\Xi^{\pm}$ spectra in data
and the feed-down matrix obtained from MC simulations, which gives the
probabilities of $\Xi^{\pm}$ and $\Xi^{0}$ decaying into $\Lambda$
($\bar{\Lambda}$) at given transverse momenta. The feed-down matrix is
calculated in minimum bias events and the $\Xi^{\pm}$ $p_{\rm T}$ spectra used
for the final correction come from the same high-multiplicity and spherocity
event selections. The secondary yields do not exceed 25% of the total yields
across the entire $p_{\rm T}$-range.

##  6 Systematic uncertainties

The estimation of the total systematic uncertainties for each
$S_{\text{O}}^{p_{\rm T}=1}$ distribution is performed using the methods
described in Ref. [26]. Two sources of systematic uncertainty are considered,
and the total uncertainty is given as the sum in quadrature of the two
components:

  * •

Monte Carlo non-closure: PYTHIA8 with Monash tune is the default model used to
generate the spherocity response matrix and $S_{\text{O}}^{p_{\rm T}=1}$
distributions with and without the detector efficiency losses. The generated
$S_{\text{O}}^{p_{\rm T}=1}$ distributions are defined as previously described
in Sec. 3. The unfolded $S_{\text{O}}^{p_{\rm T}=1}$ spectrum from the
simulation is compared to the generated one. Thus, any statistically
significant difference between the generated and unfolded distributions is
referred to as MC non-closure and is added in quadrature to the total
systematic uncertainty. This uncertainty is within $2\%$.

  * •

Dependence on the choice of the MC model: EPOS-LHC is used as the alternative
model to generate a different spherocity response matrix. This response matrix
is used to unfold the $S_{\text{O}}^{p_{\rm T}=1}$ distributions. The ratio
between the final unfolded distributions using PYTHIA8 and EPOS-LHC was
quantified and added to the total systematic uncertainty. This uncertainty has
a spherocity dependence. While in the interval $S_{\text{O}}^{p_{\rm
T}=1}>0.8$ this uncertainty is about $3\%$, for the interval
$S_{\text{O}}^{p_{\rm T}=1}<0.6$ the uncertainty is of about $5.8\%$.

Similar to prior sections, the systematic uncertainties for analyses depending
on primary charged particles are discussed in Section 6.1. Likewise, the
systematic uncertainties for longer-lived particles are discussed in Section
6.2. We note that in all cases, careful studies in the spirit of Ref. [38]
were performed to remove possible statistical effects from the systematic
uncertainties.

###  6.1 Systematic uncertainties for analyses utilizing primary charged
particles

The total systematic uncertainty on the $p_{\rm T}$ spectra of $\pi,{\rm
K},{\rm p}$ is divided into two categories. The first class includes the
uncertainties that are common among the different PID techniques: the track
selection criteria, the ITS–TPC and TPC–TOF matching efficiencies. These
uncertainties are species and $p_{\rm T}$ dependent. The second class includes
systematic uncertainties that are technique dependent: signal extraction
method and the estimation of the secondary particle correction. This study
utilizes the same methods used in previous ALICE analyses [26, 30, 29, 31].
Most of the systematic uncertainties cancel in the $p_{\rm T}$-differential
particle ratios $(\mathrm{K}/\pi$ and $\mathrm{p}/\pi)$ except the ones
attributed to the signal extraction and feed-down correction. Moreover, at
high transverse momentum (rTPC analysis) the procedure described in [31] is
used to extract the signal extraction systematic uncertainty on the
$\mathrm{K}/\pi$ and $\mathrm{p}/\pi$ ratios directly from fits to the
$\text{d}E/\text{d}x$ distributions. Table 6 shows a summary of the relative
systematic uncertainties on the $p_{\rm T}$ spectra of $\pi$, K, p, and the
particle ratios. The results are shown for the spherocity classes: Jet-like
and Isotropic [0–1]%, and the $S_{\text{O}}^{p_{\rm T}=1}$ unbiased case. The
multiplicity class corresponds to
$N_{\mathrm{tracklets}}^{|\eta|<0.8}\,\mathrm{I{-}III}$. Similar results are
obtained for the other multiplicity classes.

Table 6: Summary of the relative systematic uncertainties on the $p_{\rm T}$
spectra of $\pi$, K, p, and the particle ratios. The uncertainties are
reported as percentage values. The intervals represent the minimum and maximum
values in the respective interval of identification. They are given for the
spherocity classes: Jet-like and Isotropic [0-1]%, and the
$S_{\text{O}}^{p_{\rm T}=1}$ unbiased case. The multiplicity class corresponds
to $N_{\mathrm{tracklets}}^{|\eta|<0.8}\,\mathrm{I{-}III}$.

Source $\pi$ $\mathrm{K}$ $\mathrm{p}$ Jet-like Isotropic HM Jet-like
Isotropic HM Jet-like Isotropic HM Common ITS–TPC matching efficiency 0.7 – 3
0.7 – 3 0.7 – 3 0.7 – 3 0.7 – 3 0.7 – 3 0.7 – 3 0.7 – 3 0.7 – 3 Track
selection 0.13 – 1 0.13 – 1 0.13 – 1 0.13 – 2 0.13 – 2 0.13 – 2 0.13 – 2.7
0.13 – 2.7 0.13 – 3 TPC PID 0.2 – 1.8 0.2 – 1.9 0.2 – 1.8 2.8 – 6 2.8 – 6 2.8
– 6 1.6 – 9.8 1.6 – 10 1.6 – 9.9 $N_{\mathrm{cl}}$ 0.5 – 0.7 0.6 – 0.7 0.6 –
0.7 0.02 – 0.8 0.03 – 0.7 0 – 0.5 0.7 – 1.5 0.7 – 1.4 0.7 – 1.3 Feed-Down 0.3
– 0.9 0.3 – 0.9 0.3 – 0.9 – – – 1.1 – 10 1.1 – 10 1.1 – 10 TOF PID 0.03 – 2.9
0.03 – 1.8 0.02 – 2.1 0.3 – 8.7 0.3 – 4.2 0.2 – 4.8 0.08 – 4.8 0.08 – 6.9 0.09
– 5.4 Feed-Down 0 – 0.2 0 – 0.2 0 – 0.2 – – – 0.2 – 0.9 0.2 – 0.9 0.2 – 0.9
TPC–TOF matching efficiency 3 3 3 6 6 6 4 4 4 rTPC PID 0.65 – 2.8 0.68 – 2.9
0.67 – 2.8 2.7 – 10.7 2.5 – 10.7 2.5 – 10.3 4.6 – 15.0 4.8 – 14.9 4.7 – 14.1
$N_{\mathrm{cl}}$ 0.5 – 1.5 0.4 – 1.6 0.6 – 1.5 0.04 – 0.7 0.05 – 0.5 0.03 –
0.7 0.08 – 1.4 0.5 – 1.7 0.1 – 1.4 Feed-Down Negl. Negl. Negl. – – – 0 – 0.2 0
– 0.2 0 – 0.2 Total 1.2 – 4.4 1.2 – 4.5 1.5 – 5 3.1 – 10.9 3.1 – 10.9 3 – 11
3.1 – 15.7 3 – 15.3 3 – 15 Particle ratios $\mathrm{K}/\pi$ $\mathrm{p}/\pi$
Total – – – 0.3 – 11 0.3 – 11.4 0.4 – 11 0.8 – 15 0.7 – 14.6 1 – 14

The main contributions to the systematic uncertainty on the spectra of the
resonance particles are listed in Table 7. The uncertainties are evaluated in
groups, where each group contains sources of systematic uncertainties that
cannot be evaluated individually. The systematic uncertainties are $p_{\rm
T}$-dependent, and the ranges listed in the table represent the minimum and
maximum values. The maximum uncertainties for $\phi$ and $\rm K^{*0}$ are
obtained at low $p_{\rm T}$ ($p_{\rm T}<1.5$ GeV/$c$), with the uncertainties
reaching local minima at intermediate $p_{\rm T}$ ($1.5<p_{\rm T}<4.0$
GeV/$c$), and then approaching towards the maximum value at high $p_{\rm T}$
($p_{\rm T}>4.0$ GeV/$c$). Both the correlated and uncorrelated sources
defined in Tab 7 are used to account for the uncertainty in the $p_{\rm
T}$-differential particle spectra, but only the uncorrelated sources are
considered for the $S_{\text{O}}^{p_{\rm T}=1}$-dependent-
to-$S_{\text{O}}^{p_{\rm T}=1}$-integrated ratios.

The uncertainties related to signal extraction are estimated through
variations of the fit range, constraints to the peak fit, and variations of
the residual background function. “Track selection & PID” consists of varying
the $n\sigma$ requirements for valid resonance daughter candidates, as well as
variations in the track quality criteria. This includes variations of the
required crossed rows in the TPC, the initial vertex position along the beam
axis, and the DCA along the beam axis (DCAz). Finally, the background
estimation includes changes in how the combinatorial background is evaluated
(event-mixing, reflected mass hypothesis, like-charge pairs).

Table 7: The most relevant systematic uncertainties for the resonance analysis as a function of $S_{\text{O}}^{p_{\rm T}=1}$. “HM” in this table represents the $S_{\text{O}}^{p_{\rm T}=1}$-integrated spectra. Uncertainties are $p_{\rm T}$-dependent, and ranges listed represent the minimum and maximum values presented in the final spectra (see text for details).  Hadron: |  | $\phi$ |  |  | $\rm K^{*0}$ |
---|---|---|---|---|---|---
Topology: | Jet-like | HM | Iso | Jet-like | HM | Iso
Uncorrelated sources |  |  |  |  |  |
Signal extraction | 1–3% | 1–2% | 1.5–2.5% | 3–7% | 2–4% | 1–5%
Track selection & PID | 2–6% | 1–5% | 1–5% | 1–5% | 1–4% | 1–4%
Background estimation | 1–3% | 0–1% | 1–2% | 1–3% | 1–4% | 1–4%
Correlated sources |  |  |  |  |  |
Tracking efficiency |  | 2% |  |  | 2% |
Branching ratio |  | 1% |  |  | 2% |
Hadronic interaction |  | 2–3% |  |  | 0–2% |
Material budget |  | 0–5% |  |  | 0–5% |
Total uncertainty | 5–9% | 5–8% | 5–8% | 5–9% | 4–8% | 4–8%
Table 8: The most relevant systematic uncertainties for the long-lived particles ${\rm K}^{0}_{\rm{S}}$, $\Lambda$ ($\bar{\Lambda}$), and $\Xi$, as a function of $S_{\text{O}}^{p_{\rm T}=1}$. “HM” in this table represents the $S_{\text{O}}^{p_{\rm T}=1}$-unbiased spectra. Uncertainties are $p_{\rm T}$-dependent, and ranges listed represent the minimum and maximum values presented in the final spectra (see text for details).  Topology: | Jet-like | Iso | HM | Jet-like/HM | Iso/HM
---|---|---|---|---|---
K${}^{0}_{\mathrm{S}}$
Selection cuts | 3% | 3–4% | 3–4% | Negl. | 1%
Track pile–up | 1% | 1–3% | 1% | 0–2% | 0–2%
Signal extraction | 1–3% | 1–3% | 1–3% | Negl. | Negl.
Efficiency | 2% | 2% | 2% | 2% | 2%
Material budget | 4% | 4% | 4% | – | –
Experimental bias | 4% | 1% | – | 4% | 1%
Total uncertainty | 7% | 6–7%% | 5–6% | 5% | 2–3%
$\Lambda$($\overline{\Lambda})$
Selection cuts | 1–5% | 2–6% | 4–5% | 0–1% | 0–3%
Track pile–up | 4–5% | 5% | 3–5% | 0–1.5% | 0–1%
Signal extraction | 2–6% | 2–6% | 2–6% | 0–2% | 0–1%
Feed-down correction | 1.0–1.5% | 1.0–1.5% | 1.0–1.5% | Negl. | Negl.
Efficiency | 2% | 2% | 2% | 2% | 2%
Material budget | 4% | 4% | 4% | – | –
Experimental bias | 4% | 1% | – | 4% | 1%
Total uncertainty | 8–10% | 8–9% | 7–9% | 5% | 3–4%
$\Xi^{\pm}$
Selection cuts | 0–1% | 0–1% | 0–1% | Negl. | Negl.
Track pile–up | 2–3% | 2–3% | 2–3% | 2% | Negl.
Signal extraction | 0–1% | 0–1% | 0–1% | 1% | Negl.
Efficiency | 2% | 2% | 2% | 2% | 2%
Material budget | 1–9% | 1–9% | 1–9% | – | –
Experimental bias | 3% | 3% | – | 3% | 3%
Total uncertainty | 5–10% | 5–10% | 4–10% | 4% | 3.5%

The correlated sources apply equally across the different
$S_{\text{O}}^{p_{\rm T}=1}$ selections, and cancel in the ratio. The hadronic
interaction and material budget represent the uncertainties in interactions
between particles and the ALICE detector, and the uncertainty in the hadronic
interaction cross section of particles traversing material in ALICE.

###  6.2 Systematic uncertainties on analyses of long-lived particles

The systematic uncertainties on long-lived weakly decaying particles, $\rm
K^{0}_{S}$, $\Lambda$ ($\bar{\Lambda}$), and $\Xi$, are reported in Table 8
and have similar components for all particle species:

  * •

Selection criteria: estimated by carrying out the analysis using looser and
tighter variations of the selections in Tables 4 and 5.

  * •

Track pile-up: assigned due to the requirement that at least one daughter (or
bachelor track for $\Xi$) has a fast-detector signal (ITS or TOF), see Sec.
4.2. This systematic uncertainty was found by varying the number of required
tracks and fast signals, and reflects how well these conditions are modelled
in the MC simulation.

  * •

Signal extraction: estimated by varying the range in $M_{\text{inv}}$ for
signal and background and the shape of the background.

  * •

Efficiency: accounts for possible variations of the tracking efficiency with
multiplicity. The same uncertainty, 2%, as used in a previous detailed study
of multiplicity-dependent strangeness production in $\sqrt{s}$ = 13 TeV pp
collisions [8] is assigned here.

  * •

Material budget: estimated by varying parameters in the Monte Carlo
description of the ALICE apparatus, see Ref. [22] for details.

  * •

Experimental bias: taken from Table 1. See discussion in Sec. 3 for details.

In addition to the above-mentioned uncertainties, there is also a contribution
from evaluating the secondary yields for $\Lambda$ ($\bar{\Lambda}$)
particles. It was determined by varying $\Xi$ yields within their
uncertainties, using an alternative method of constructing the feed-down
matrix only from charged $\Xi$ baryons, as well as a flat systematic
uncertainty to account for the possible multiplicity dependence of the matrix
(shown in Table8 as “Feed-down correction").

Finally, we note that some of the systematic uncertainties cancel when we
compare results in the same multiplicity class but with various
$S_{\text{O}}^{p_{\rm T}=1}$ selections. This uncertainty is shown in Table 8
as “jet-like/HM" and “Iso/HM" and was estimated by doing the systematic
variations for a jet-like selection and an unbiased (same multiplicity)
selection in parallel and comparing the ratios of $p_{\rm T}$ spectra with and
without the variation. The studies were performed for various
$S_{\text{O}}^{p_{\rm T}=1}$ and multiplicity selections. No strong dependence
was found inside the relevant selections (e.g. for tighter or looser jet-like
selections). However, one should note that such a dependence is hard to pin
down with good precision due to the limited number of candidates for very
tight selections.

##  7 Results and discussion

The results presented in this section include the transverse momentum spectra,
integrated yields, $\left<\mathrm{d}N/\mathrm{d}y\right>$, and mean transverse
momentum, $\left<p_{\rm T}\right>$, as a function of $S_{\text{O}}^{p_{\rm
T}=1}$, as well as $p_{\rm T}$-differential ratios between particle species
(mainly with respect to pions), and the $p_{\rm T}$-differential ratios-
to-$\pi$ relative to the $S_{\text{O}}^{p_{\rm T}=1}$ unbiased baseline
(referred to as the “double ratio”). Finally, the strangeness enhancement as a
function of $S_{\text{O}}^{p_{\rm T}=1}$ is investigated.

In the following, the $\left<\mathrm{d}N/\mathrm{d}y\right>$ and $\left<p_{\rm
T}\right>$ are calculated in the measured kinematic range, and corrected for
the limited range by extrapolating the spectra to the unmeasured $p_{\rm T}$
regions using Levy–Tsallis fits. To account for the additional systematic
uncertainties arising from this procedure, modified fit ranges and alternative
parameterization of the spectra such as Boltzmann, $m_{\rm T}$-exponential,
$p_{\rm T}$-exponential, Fermi-Dirac (only for fermions) and Bose–Einstein
statistics (only for bosons), and Boltzmann–Gibbs blast-wave functions are
used as variations. The resulting differences are added in quadrature to the
systematic uncertainties obtained from the measured $p_{\rm T}$ ranges to get
the final systematic uncertainties for the
$\left<\mathrm{d}N/\mathrm{d}y\right>$ and $\left<p_{\rm T}\right>$. More
details about this procedure can be found in Ref. [8].

The experimental measurements will be compared with a broad selection of pp MC
models, namely PYTHIA 8.2 [7] (both the default Monash tune and a rope
hadronization tune), Herwig 7.2 [6], and EPOS-LHC [15]. PYTHIA 8.2 is a QCD-
inspired model that is built around the Lund-string model for hadronization
[33]. The default Monash tune is unable to describe the strangeness
enhancement in small systems, while the rope extension (layers of overlapping
strings that increase the string tension) of the Lund-string model [11] has
been introduced to accommodate this. For the PYTHIA 8.2 Ropes, note that this
article only utilizes the "Flavour Ropes" for the model predictions, without
the string-shoving mechanism [39] incorporated in the rope hadronization
framework. Similarly, Herwig is a QCD-inspired pp generator centered around a
cluster hadronization model [6], which has recently been extended to be able
to describe the strangeness enhancement [40]. On the contrary, EPOS-LHC is a
two-component core-corona model, which incorporates QGP features in the core
to explain the strangeness enhancement.

The effect of the $S_{\text{O}}^{p_{\rm T}=1}$ selection is discussed in Sec.
7.1 for the two multiplicity estimators. It is shown that the spherocity
selection for the events with the highest midrapidity multiplicity, 0–1%
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$, gives the best control of the
event “hardness”, i.e. select events with a large $\left<p_{\rm T}\right>$.
Results obtained using this estimator are therefore first presented in Secs.
7.2– 7.4, followed by results obtained using other multiplicity estimators in
Sec. 7.5.

###  7.1 High-multiplicity estimators and $S_{\text{O}}^{p_{\rm T}=1}$

If one considers a high-multiplicity pp collision to be built up from
independent subcollisions (a traditional MPI picture [41]), then there will be
a trivial isotropization with increasing multiplicity. As previous ALICE
measurements indicate a strong correlation between multiplicity and QGP-like
effects, such as strangeness production [1], it is important for the study
presented here to disentangle this possible trivial bias from the underlying
physical properties of interest. To understand the impact of this on the
$S_{\text{O}}^{p_{\rm T}=1}$ selection, the $\left<p_{\rm T}\right>$ and the
average pion yield $\langle\rm{d}\it{N}_{\pi}/\rm{d}\it{y}\rangle$, with
different multiplicity and spherocity selection criteria are shown in Fig. 2.
Results are shown for both the forward (V0M) and midrapidity
($N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$) multiplicity estimators
(described in Sec. 2.1). A clear distinction is observed with respect to how
the different multiplicity estimators relate to the $S_{\text{O}}^{p_{\rm
T}=1}$ selection. This effect is solely driven by the rapidity region where
the multiplicity is estimated, and not by properties of the ALICE apparatus.

Figure 2: Correlation between $\langle p_{\rm{T}}\rangle$ and
$\langle\rm{d}N_{\pi}/\rm{d}y\rangle$ as a function of $S_{\text{O}}^{p_{\rm
T}=1}$, in the 0–10% and 0–1% V0M and
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ multiplicity classes. The total
systematic uncertainties are represented by empty boxes. The statistical
uncertainty is smaller than the reported marker sizes.

It is observed that the V0M multiplicity selection maintains a similar
$\left<p_{\rm T}\right>$, but contains large variations in
$\left<\mathrm{d}N_{\mathrm{\pi}}/\mathrm{d}y\right>$ for the different
$S_{\text{O}}^{p_{\rm T}=1}$ selections. In contrast, the
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ selected events are characterized
by large differences in $\left<p_{\rm T}\right>$ among the event classes,
selecting events according to their hardness. The implicit multiplicity
dependence of $S_{\text{O}}^{p_{\rm T}=1}$ is minimized by sharply
constraining the multiplicity using a midrapidity multiplicity estimation.
This implies that the $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$
multiplicity estimator, in tandem with a $S_{\text{O}}^{p_{\rm T}=1}$
selection, is best at separating events based on their hardness.

Moreover, PYTHIA 8.2 model studies of the correlation between the average
transverse momentum transfer of the hardest parton–parton interaction,
$\left<\hat{p}_{\rm T}\right>$, and the average number of multi-parton
interactions $\left<n\textrm{MPI}\right>$ is presented in Fig. 3 for
multiplicity and $S_{\text{O}}^{p_{\rm T}=1}$ intervals of 0–1%. For each
estimator, the multiplicity is calculated as the number of primary charged
particles in the pseudorapidity interval(s) covered by that estimator. Figure
3 shows that the hardest scattering for the events in the jet-like
$S_{\text{O}}^{p_{\rm T}=1}$ 0–1% event category is significantly harder than
for the $S_{\text{O}}^{p_{\rm T}=1}$-integrated, high-multiplicity reference.
This is observed both for the default PYTHIA 8.2 Monash, and with the rope
hadronization framework enabled. This feature is present when the multiplicity
is estimated both in the $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ and V0M
pseudorapidity regions, but the effect is particularly strong when the
multiplicity is estimated at midrapidity. Furthermore, the isotropic
$S_{\text{O}}^{p_{\rm T}=1}$ 99–100% events are slightly softer than overall
high-multiplicity events. In conjunction with the softer $\left<p_{\rm
T}\right>$ presented in Fig. 2, these findings suggest that the isotropic
topologies are formed by multiple softer interactions, while the jet-like
topologies have at least one hard scattering that is significantly harder than
for the $S_{\text{O}}^{p_{\rm T}=1}$-integrated selection.

Figure 3: PYTHIA 8.2 correlation study between $\left<\hat{p}_{\rm T}\right>$
and $\left<n\textrm{MPI}\right>$ as a function of $S_{\text{O}}^{p_{\rm
T}=1}$, in 0–1% V0M and $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$
multiplicity classes. The default PYTHIA 8.2 Monash variation is compared to
PYTHIA 8.2 with color rope hadronization. The total systematic and statistical
uncertainties are smaller than the marker sizes. The grey band is an
interpolation between the points, to more clearly illustrate the trend of each
multiplicity and model variation.

In the following, a complete set of results will be presented using
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ 0–1% to highlight the impact on
the QCD dynamics of the extreme event topologies, while minimizing the effects
of any trivial multiplicity (system size) dependence. The results are first
presented for jet-like and isotropic events, utilizing a 0–10% and 90–100%
$S_{\text{O}}^{p_{\rm T}=1}$ selection, respectively, to have a complete set
of particle spectra. Furthermore, selected results are also presented for the
most extreme 1% percentiles of $S_{\text{O}}^{p_{\rm T}=1}$.

###  7.2 Results of $S_{\text{O}}^{p_{\rm T}=1}$-differential $p_{\rm T}$
spectra at $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ 0–1%

The $p_{\rm T}$ spectra for jet-like and isotropic events are presented in
Figures 4 and 5 for $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ 0–1% together
with the $S_{\text{O}}^{p_{\rm T}=1}$ unbiased reference. The trends of the
spectral shapes are consistent between all observed particle species,
showcasing a significant hardening (softening) of the $p_{\rm T}$ in the low
(high) $S_{\text{O}}^{p_{\rm T}=1}$ selection, relative to the inclusive high-
multiplicity event class, respectively. These trends are also well reflected
in the model predictions. The PYTHIA 8.2 default Monash tune can describe the
qualitative trends of the $S_{\text{O}}^{p_{\rm T}=1}$ selection. However, a
large quantitative deviation from data is observed in the $p_{\rm T}$
differential production of light-flavor hadrons, in particular the non-strange
hadrons. The PYTHIA 8.2 rope tune is able to describe the measured data for
strange hadrons very well, but overestimates the total amount of produced non-
strange hadrons. These large deviations are well known from previous studies
[16].

Figure 4: Transverse momentum distribution of $\pi,{\rm K},{\rm p}$, $\rm
K^{*0}$, $\phi$, $\rm K^{0}_{S}$, $\Lambda$ and $\Xi$ for
$S_{\text{O}}^{p_{\rm T}=1}$ classes selected for events at high-multiplicity,
determined by events in the top 1% of
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$. The lower panels present the
ratio between the $S_{\text{O}}^{p_{\rm T}=1}$-integrated and
$S_{\text{O}}^{p_{\rm T}=1}$-differential events. Statistical and total
systematic uncertainties are shown by error bars and boxes, respectively. The
curves represent PYTHIA 8.2 model predictions of the same measurement.

Figure 5: Transverse momentum distribution of $\pi,{\rm K},{\rm p}$, $\rm
K^{*0}$, $\phi$, $\rm K^{0}_{S}$, $\Lambda$ and $\Xi$ for
$S_{\text{O}}^{p_{\rm T}=1}$ classes selected for events at high-multiplicity,
determined by events in the top 1% of
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$. The lower panels present the
ratio between the $S_{\text{O}}^{p_{\rm T}=1}$-integrated and
$S_{\text{O}}^{p_{\rm T}=1}$-differential events. Statistical and total
systematic uncertainties are shown by error bars and boxes, respectively. Fig.
4 and Fig. 5 both show the same experimental data. The curves represent Herwig
7.2 and EPOS-LHC predictions of the same measurement.

Figure 6: The $\left<p_{\rm T}\right>$ and
$\left<\mathrm{d}N/\mathrm{d}y\right>$ as a function of particle masses
obtained for the various particle species in $S_{\text{O}}^{p_{\rm T}=1}$
classes selected for high-multiplicity events, determined by the events in the
0–1% of $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$. Upper (lower) panels
show the $\left<p_{\rm T}\right>$ ($\left<\mathrm{d}N/\mathrm{d}y\right>$).
The total systematic uncertainty is represented by the shaded regions. The
measured data is compared to predictions from PYTHIA8 Monash, PYTHIA8 Rope,
EPOS-LHC, and Herwig 7.2.

The $S_{\text{O}}^{p_{\rm T}=1}$-differential average $p_{\rm T}$
($\left<p_{\rm T}\right>$) and yield $\left<\mathrm{d}N/\mathrm{d}y\right>$
are reported in Fig 6 as a function of the extracted particle masses. The
measured $\left<p_{\rm T}\right>$ values confirms what is qualitatively
observed in the $p_{\rm T}$-differential spectra: there is a significant
$p_{\rm T}$-hardening in jet-like events, and this trend is consistent across
all measured light-flavor particle species. Furthermore, the $\left<p_{\rm
T}\right>$ of the integrated $S_{\text{O}}^{p_{\rm T}=1}$ high-multiplicity
events are consistent with the $\left<p_{\rm T}\right>$ of the isotropic
sample. This observation indicates that average high-multiplicity events and
$S_{\text{O}}^{p_{\rm T}=1}$ selected isotropic events are dominated by
similar underlying physics processes. This shows that the
$S_{\text{O}}^{p_{\rm T}=1}$-integrated event class is not the arithmetic
average of the jet-like and isotropic subsamples, indicating that jet-like
events are rare outliers of a much more homogeneous group of high-multiplicity
events. This observation is of particular interest, and we will focus on
exploring it in further detail in the following. Furthermore, it also suggests
that the isotropic events are similar to the average high-multiplicity events
before $S_{\text{O}}^{p_{\rm T}=1}$ selection and, contrarily, that the jet-
like events are rare outliers dominated by jet-like physics, and that QGP-like
effects, such as radial flow and strangeness enhancement, are therefore
suppressed for jet-like events.

The bottom panels of Fig. 6 show that the top-1%
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ estimator constrains the variance
in $\left<\mathrm{d}N/\mathrm{d}y\right>$ between the different
$S_{\text{O}}^{p_{\rm T}=1}$ classes, for all measured particles. Hence, any
observed deviations in comparisons between
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ 0–1% jet-like and isotropic
events are unlikely to be driven by a trivial difference in multiplicity. This
is not only true for the $\pi$ mesons as reported in Section 7.1, but across
all measured particle masses as a function of $S_{\text{O}}^{p_{\rm T}=1}$.

Most of the presented models overestimate the $\left<p_{\rm T}\right>$ for all
particle species except $\rm K^{*0}$, however, this effect can be partially
explained by the fact that the models and data are compared at different
midrapidity charged particle multiplicities [40]. Moreover, the models give a
reasonable description of the particle specie differences when one normalizes
the $\left<p_{\rm T}\right>$ relative to that of pions. Furthermore, one can
note that the PYTHIA 8.2 predictions, in particular with the enabled color
rope framework, overestimates the production of protons and pions, but
qualitatively describes the production of most strange hadrons. Moreover, the
color rope framework seems to primarily affect the baryons, as the resonance
particles show only a small difference in the integrated yield between PYTHIA
8.2 color rope framework and the default PYTHIA 8.2 Monash, in particular for
the $\rm K^{*0}$. In contrast, EPOS-LHC describes the production rates of most
particles within the uncertainties of the data, but is unable to capture the
trend seen for charged kaons. Herwig 7.2 is unable to capture most of the
trends observed in the measured data.

###  7.3 Particle ratios for $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ 0–1%

QGP-like effects, such as collective flow and strangeness enhancement, affect
hadrons of heavier species distinctly. Collective flow will boost heavier
particles to larger $p_{\rm T}$ than lighter particles, and strangeness
enhancement in previous measurements was found to scale with the number of
strange quarks [1][8]. Due to its low mass, abundant production and lack of
strangeness, the pion constitutes a good reference for the QCD physics we are
less interested in. Therefore, by studying the $p_{\rm T}$-differential
particle-to-pion ratios, we can potentially identify QGP-like features in the
data.

To be able to observe the quantitative trends with the highest precision, we
construct double ratio (DR), as defined in Eq. 5

$\centering\left(\frac{{\rm d}N/{\rm d}p_{\rm T}}{{\rm d}N_{\pi}/{\rm d}p_{\rm
T}}\right)_{S_{\text{O}}^{p_{\rm T}=1}}\bigg{/}\left(\frac{{\rm d}N/{\rm
d}p_{\rm T}}{{\rm d}N_{\pi}/{\rm d}p_{\rm
T}}\right)_{\scaleto{\int}{15pt}S_{\text{O}}^{p_{\rm T}=1}},\@add@centering$
(5)

where the denominator represents the $S_{\text{O}}^{p_{\rm T}=1}$-integrated,
high-multiplicity event sample. The advantage of the double ratio from an
experimental standpoint is that most of the systematic uncertainties will
cancel in the ratio between the $S_{\text{O}}^{p_{\rm T}=1}$-differential and
$S_{\text{O}}^{p_{\rm T}=1}$-integrated spectra, for the same species. The
double ratios therefore have the best precision in terms of systematic
uncertainties of all the data presented in this section. For the comparison
with MC models, the DR means that focus can be shifted away from the large
discrepancies between data and model that exists for most particle species, to
test if the quantitative relative trends are the same in data and MC.
Therefore, we advocate that these comparisons are the ones that are most
sensitive to the physics of $S_{\text{O}}^{p_{\rm T}=1}$ selection.

The $p_{\rm T}$-differential relative yield of identified light-flavor hadrons
to $\pi$ mesons, as well as the DR, for the
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ 0–1% multiplicity events are
presented for the 10% $S_{\text{O}}^{p_{\rm T}=1}$ percentiles in Fig. 7 and
Fig. 8, compared with PYTHIA 8.2 predictions in the former, and EPOS-LHC and
Herwig 7.2 predictions in the latter.

The DR is presented in the lower panels, showcasing a clear enhancement of
strangeness yield in isotropic topologies, and a suppression in jet-like
topologies. Remarkably, the DR for all presented particle species decrease
significantly for jet-like events. This can be interpreted as most particle
ratios being shifted towards higher $p_{\rm T}$ in jet-like events, i.e. as
the $p_{\rm T}$ of the partonic sub-collisions increase, the same hadrons will
be produced with larger $p_{\rm T}$. The hadron-to-$\pi$ ratios exhibit a
small enhancement of strange-hadron ratios in isotropic events, and a
pronounced suppression in jet-like events. This suggests that strange particle
production is favored in isotropic topologies.

In Fig. 7, the default Monash tune of PYTHIA 8.2 quantitatively predicts the
interplay between the $S_{\text{O}}^{p_{\rm T}=1}$-integrated high-
multiplicity events and the $S_{\text{O}}^{p_{\rm T}=1}$-differential event
classes, but shows large quantitative deviation for most of the measured data.
The rope tune does slightly better, in particular for baryons, but the
deviation is for both tunes particularly large for the two resonance particles
$\phi$ and $\rm K^{*0}$. In contrast, neither Herwig 7.2 or EPOS-LHC are able
to quantitatively describe the $p_{\rm T}$-differential particle-to-$\pi$
ratios, as seen in Fig. 8.

The PYTHIA 8.2 Monash tune and the rope hadronization framework are both able
to qualitatively capture the trend between isotropic and jet-like topologies
in the DR for all presented light-flavor particles. Remarkably, there is no
difference between the PYTHIA 8.2 Monash and the PYTHIA 8.2 Rope curves. Even
though the production rates of light-flavor hadrons are different, both
variations are able to describe the trends presented for the
$S_{\text{O}}^{p_{\rm T}=1}$ characterized events. EPOS-LHC and Herwig 7.2 are
able to qualitatively describe some trends, but are not able to describe the
full evolution, mainly towards larger $p_{\rm T}$.

By utilizing a narrower event selection, we present the $p_{\rm
T}$-differential relative yield of identified light-flavor hadrons to $\pi$
mesons, as well as the DR, for the
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ 0–1% multiplicity with 1%
$S_{\text{O}}^{p_{\rm T}=1}$ percentiles in Fig. 9 and Fig. 10. The resonances
are excluded from this measurement due to the low number of events in the
narrow $S_{\text{O}}^{p_{\rm T}=1}$ and multiplicity selection. This is an
experimental challenge that particularly affects both $\phi$ and $\rm K^{*0}$,
as the signals are contaminated by large combinatorial backgrounds. Likewise,
the large fluctuations in the MC predictions present in Fig. 9 and Fig. 10 are
driven by an insufficient amount of events in the double-differential
selection, compounded by the low production rate of the rare particle yields
in the various models.

For all measured particles, the effect of the enhancement and suppression of
light-flavor particles relative to pions is stronger when approaching more
extreme topologies, in particular the suppression of yield in jet-like events.
This is clearly seen both through the single particle-to-$\pi$ ratio, and in
the DR, contrasting Fig. 7 with Fig. 9. In particular, one can note a large
suppression of strange hadrons across the entire measured $p_{\rm T}$ range
for events with jet-like topologies. This novel feature suggests that the
abundance of strange hadrons in high-multiplicity events are produced in
events that are associated to soft physics in terms of the azimuthal topology.
This observation also implies that there is a significant amount of high-
multiplicity events that reflect the same rates of strangeness production
found in low-multiplicity events. ALICE has previously published studies of
differential $\Lambda$/${\rm K}^{0}_{\rm{S}}$ production in jets relative to
the underlying event (UE), where it was found that the ratio in the jet was
far below that of the ratio in the UE [42]. This is qualitatively similar to
what we observe for the most extreme jet-like events in this study. One could
therefore understand the results obtained here as a generalization to jet-
dominated events.

The $\rm p/\pi$ peak present for the 99–100% most isotropic events, as well as
in the average 0–1% high-multiplicity events, is significantly suppressed in
0–1% jet-like event sample. In conjunction with strangeness suppression, this
hints towards a decrease of QGP-like effects in events with extremely jetlike
topologies. Furthermore, the discrepancy between the $\rm p/\pi$ and $\rm
K/\pi$ ratios at high-$p_{\rm T}$ is interesting to note, where the
isotropic/jet-like ratios meet for the $\rm p/\pi$ while diverging for the
$\rm K/\pi$. The underlying mechanism of this effect is currently not fully
understood.

Figure 7: Top panels show hadron-to-$\pi$ ratios for 0–10%
$S_{\text{O}}^{p_{\rm T}=1}$ classes selected for the 0–1%
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ multiplicity events. Bottom
panels present the hadron-to-$\pi$ double ratios of $S_{\text{O}}^{p_{\rm
T}=1}$ classes relative to $S_{\text{O}}^{p_{\rm T}=1}$ integrated high-
multiplicity events. Statistical and systematic uncertainties are shown by
bars and boxes, respectively. Experimental results are compared with
predictions from PYTHIA 8.2 Monash and Ropes.

Figure 8: Top panels show hadron-to-$\pi$ ratios for 0–10%
$S_{\text{O}}^{p_{\rm T}=1}$ classes selected for the 0–1%
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ multiplicity events. Figure 7 and
Fig. 8 both contain the same experimental data, but the vertical ranges are
modified to accommodate the model predictions. Bottom panels present the
hadron-to-$\pi$ double ratios of $S_{\text{O}}^{p_{\rm T}=1}$ classes relative
to $S_{\text{O}}^{p_{\rm T}=1}$ integrated high-multiplicity events.
Statistical and systematic uncertainties are shown by bars and boxes,
respectively. Experimental results are compared with predictions from Herwig
7.2 and EPOS-LHC

Figure 9: Top panels show hadron-to-$\pi$ ratios for 0–1%
$S_{\text{O}}^{p_{\rm T}=1}$ classes selected for the 0–1%
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ multiplicity events. Bottom
panels present the hadron-to-$\pi$ double ratios of $S_{\text{O}}^{p_{\rm
T}=1}$ classes relative to $S_{\text{O}}^{p_{\rm T}=1}$ integrated high-
multiplicity events. Statistical and systematic uncertainties are shown by
bars and boxes, respectively. Experimental results are compared with
predictions from PYTHIA 8.2 Monash and Ropes.

Figure 10: Top panels show hadron-to-$\pi$ ratios for 0–1%
$S_{\text{O}}^{p_{\rm T}=1}$ classes selected for the 0–1%
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ multiplicity events. Figure 9 and
Fig. 10 both contain the same experimental data, but the vertical ranges are
modified to accommodate the model predictions. Bottom panels present the
hadron-to-$\pi$ double ratios of $S_{\text{O}}^{p_{\rm T}=1}$ classes relative
to $S_{\text{O}}^{p_{\rm T}=1}$ integrated high-multiplicity events.
Statistical and systematic uncertainties are shown by bars and boxes,
respectively. Data are compared with PYTHIA 8.2 Monash predictions, and the
PYTHIA 8.2 rope hadronization framework. The large fluctuations present in the
Herwig 7.2 predictions are due to statistical limitations.

In Fig. 9, the two PYTHIA 8.2 predictions are qualitatively able to describe
some of the particle-to-$\pi$ ratios for the 1% $S_{\text{O}}^{p_{\rm T}=1}$
percentiles, but remarkably underestimate the $p_{\rm T}$-differential
production of $\Xi$ baryons, as well as the isotropic production of both
charged and neutral kaons. However, PYTHIA 8.2 is still able to qualitatively
describe the interplay between high-multiplicity events, isotropic and jet-
like topologies in the DR. Similar to what was observed in Fig. 8 for the
broader $S_{\text{O}}^{p_{\rm T}=1}$ selection, EPOS-LHC and Herwig 7.2 are
unable to accurately capture the interplay of the DR towards larger $p_{\rm
T}$. EPOS-LHC and Herwig 7.2 are both able to qualitatively describe most of
the observed trends for the charged and neutral kaons in Fig. 10, with a
slight underestimation of the absolute production rates. However, both model
predictions are unable to describe the observed trends for the presented
baryons.

In Fig. 11, baryon-to-meson ratios are presented for p/$\pi$, $\Lambda$/${\rm
K}^{0}_{\rm{S}}$ and $\Xi$/$\phi$. These ratios are known to be interesting
observables, able to highlight features of radial flow and possible
recombination [28]. While the $\Xi$/$\phi$ ratio is not usually associated to
measurements of radial flow, phenomenological models have different views of
the effective net-strangeness of the $\phi$ meson. In Lund-string-like models,
such as PYTHIA 8.2, the $\phi$ meson is produced from the fragmentation of
$\textrm{s}\bar{\textrm{s}}$ pairs, making it effectively double strange. On
the other hand, statistical thermal models typically treats the $\phi$ meson
as having no strangeness, where the production instead is driven by the hadron
mass.

The overall trends among the three ratios are qualitatively similar, even as
the strangeness content increases from p ($|S|=0$) to $\Xi$ ($|S|=2$).
Furthermore, one can apply a traditional hypothesis of radial flow in larger
collision systems, i.e., that a radial expansion of the system boosts heavier
baryons out to high $p_{\rm T}$, resulting in a depletion of baryons at
low-$p_{\rm T}$. In this context, Fig. 11 highlights an abundance or
suppression of isotropic (jet-like) protons at intermediate $p_{\rm T}$ in the
$p/\pi$ ratio, without the depletion (enhancement) of isotropic (jet-like)
protons at low $p_{\rm T}$. The origin for the difference in the low-$p_{\rm
T}$ behavior is still unclear, but we suspect that there is an interplay
between soft radial flow and the hard suppression in the ratios to pions,
observed in the jet-like events through Figs. 7– 10. One should keep in mind
that the relative systematic uncertainties are smaller than the total
systematic uncertainties reported in Fig. 11, c.f., Sec. 6 for further
discussion.

Similar trends are observed in the $\Lambda$/${\rm K}^{0}_{\rm{S}}$ ratio,
although systematic uncertainties in the lower panel does not allow for a
clear conclusion on the interplay between jet-like and isotropic events. The
$\Xi$/$\phi$ ratio suggests that there is a constant enhancement of $\Xi$
baryons relative to produced $\phi$ mesons, within systematic uncertainties.

Figure 11: p/$\pi$, $\Lambda$/$K$ and $\Xi$/$\phi$ ratios for different
$S_{\text{O}}^{p_{\rm T}=1}$ classes are obtained for $0-1\%$ events measured
by the $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$. Lower panels show the
ratio to $S_{\text{O}}^{p_{\rm T}=1}$-integrated event selection. Statistical
and total systematic uncertainties are shown by bars and boxes, respectively.
The curves represent different model predictions of the same measurement.

The rope hadronization framework in PYTHIA 8.2 predicts both the single and
double ratios reasonably well. It is remarkable that even though PYTHIA 8.2
Monash fails to predict the single ratios, both PYTHIA 8.2 Monash and Rope
predictions show no significant deviations for the double ratios. The ${\rm
K}^{0}_{\rm{S}}$/K ratios for the different multiplicity estimators are
presented in Fig. 12. The ratios highlight a consistency with unity, and
showcase no significant $S_{\text{O}}^{p_{\rm T}=1}$ dependence. These results
verify that the modified $S_{\text{O}}^{p_{\rm T}=1}$ estimator is robust
through a data-driven approach, complementing the studies discussed in Sec. 3.

Figure 12: The neutral-to-charged ${\rm K}^{0}_{\rm{S}}$/K ratios as a
function of different multiplicity estimators and $S_{\text{O}}^{p_{\rm
T}=1}$. Statistical and total systematic uncertainties are shown by bars and
boxes, respectively. The curves represent PYTHIA 8.2 model predictions of the
same measurement.

###  7.4 Integrated yields as a function of $S_{\text{O}}^{p_{\rm T}=1}$

The integrated double ratio over the full $p_{\rm T}$ range is presented in
Fig. 13, for p, $\Lambda$, and $\Xi$. The fully integrated yields are obtained
by extrapolating the measured $p_{\rm T}$ spectra for each particle species.
Therefore, the systematic uncertainties shown in Fig. 13 also account for the
added uncertainty due to the extrapolation procedure. This added uncertainty
is particle species dependent given the different measured $p_{\rm T}$ ranges
for each particle species, particularly affecting the $\Lambda$ yields, which,
as shown in Tab. 1, can only be measured down to 1.0 ${\rm GeV}/c$ after
$S_{\text{O}}^{p_{\rm T}=1}$ selection.

The results demonstrate that the strange-hadron yield increases as a function
of $S_{\text{O}}^{p_{\rm T}=1}$, with indications of an ordering with
strangeness content. In previous ALICE publications it was observed that in pp
collisions at $\sqrt{s}$ $=13$ TeV the charge particle density,
$\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$, is a driving quantity for the
enhancement of strange hadrons [1]. For the results presented in Fig. 13, the
$\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$ at midrapidity is restricted (see
Fig. 2), which allows one to directly test if $S_{\text{O}}^{p_{\rm T}=1}$ is
directly sensitive to strangeness enhancement. We find that the strangeness
production is suppressed in events with jet-like topologies, and slightly
enhanced in softer, isotropic event topologies.

Figure 13: The double ratios of integrated yields as a function of
$S_{\text{O}}^{p_{\rm T}=1}$ for the spectra of top-1%
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$. The yield is estimated by
extrapolating the spectra over the full $p_{\rm T}$ range. Statistical and
systematic uncertainties are shown by bars and boxes, respectively. The grey
band around unity represents the systematic uncertainty of the pion
measurement.

In order to make the most precise comparison between the measured data and
model predictions, the integrated double ratios are presented as a function of
$S_{\text{O}}^{p_{\rm T}=1}$ for the measured $p_{\rm T}$ ranges in Fig. 14
and Fig. 15, for p, $\Lambda$ and $\Xi$. The two figures contain the same data
points, but use different ordinate ranges in the ratio to accommodate the MC-
generator predictions. The yields for the measured $p_{\rm T}$ ranges are
estimated by counting the bin entries in each $p_{\rm T}$ spectra, without the
use of the Levy–Tsallis extrapolation. Therefore, the systematic uncertainties
for the integrated yields utilizing the measured $p_{\rm T}$ ranges are
significantly reduced compared to the extrapolated yields presented in Fig.
13. Moreover, while the fraction of yields gained from the extrapolation is
species dependent, it was tested that the relative increase of yields is
consistent across all spherocity classes and the high-multiplicity reference.
As the integrated yields presented in Figs. 13 – 15 are self-normalized, the
relative yields obtained from the extrapolation therefore largely cancels. As
such, one obtains the same physics conclusions by utilizing either
extrapolated or measured $p_{\rm T}$ ranges, which is reflected in the
comparison between Fig. 13 and Fig. 14.

Figures 14 and 15 highlight that the relative decrease of $\Xi$ production in
the most jet-like events is of order 20%. We estimate, based on Ref. [1], that
to obtain a similar effect driven solely by multiplicity, one would have to
decrease the multiplicity by approximately 60 to 70%. Given that the
difference in multiplicity between the spherocity event classes is roughly
10%, this indicates a substantial lifting of the strangeness suppression due
to the event topology selection.

Figure 14: The double ratios of integrated yield as a function of
$S_{\text{O}}^{p_{\rm T}=1}$ are represented in the top-1% of
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$. The yields are integrated in the
measured $p_{\rm T}$ ranges for each particle species. Statistical and
systematic uncertainties are shown by bars and boxes, respectively. The curves
represent different model predictions of the same measurement. The grey band
around unity represents the systematic uncertainty of the pion measurement.

This novel feature can help to further elucidate the underlying mechanism(s)
that drives the strangeness enhancement. Remarkably, these findings suggest
that charged particle production is not driven by a single source, but instead
driven by several sources with varying strangeness-to-$\pi$ production rates,
with the jet-like events showcasing a level of strangeness production usually
found at lower multiplicities. In combination with the $p_{\rm
T}$-differential ratios from Figs. 7 – 10, as well as the baryon-to-meson
ratios in Fig. 11, one can characterize jet-like events as exhibiting a large
decrease of relative production at intermediate $p_{\rm T}$, with an overall
high degree of strangeness suppression in the total yields. Isotropic events
can be characterized completely opposite to jet-like events, containing a
boost of particles at intermediate $p_{\rm T}$, with enhanced strangeness
production in the $p_{\rm T}$-integrated yields. These findings suggest that
one is able to control the degree of QGP-like effects in small systems by
categorizing events based on the azimuthal topology. Furthermore, it
demonstrates that $S_{\text{O}}^{p_{\rm T}=1}$-integrated high-multiplicity
events are dominated by soft processes, and provides an important input to
understanding the ALICE observation of universal scaling of strangeness
enhancement with multiplicity [1].

Figure 15: The double ratios of integrated yield as a function of
$S_{\text{O}}^{p_{\rm T}=1}$ are represented in the top-1% of
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$. The yields are integrated in
measured $p_{\rm T}$ ranges for each particle species. Statistical and
systematic uncertainties are shown by bars and boxes, respectively. Figure 14
and Fig. 15 both contain the same experimental data, but the vertical ranges
are modified to accommodate the model predictions. The curves represent
different model predictions of the same measurement. The grey band around
unity represents the systematic uncertainty of the pion measurement.

The PYTHIA 8.2 Rope hadronization framework and EPOS-LHC models, which
incorporate two-component phenomenologies, are able to predict the qualitative
trend of enhancement and suppression of strange particle production as a
function of $S_{\text{O}}^{p_{\rm T}=1}$, albeit with a different mass-
ordering for $\Lambda$ and $\Xi$. In contrast, both the PYTHIA8 Monash and
Herwig 7.2 predictions are unable to describe the reported experimental
observation. Surprisingly, Herwig 7.2 predicts the opposite trend; enhancement
of all three baryons in jet-like events and a suppression in isotropic events.
If this is a generic feature of the new strangeness-enhancement process
introduced in Herwig 7. 2[6], then the results presented in this article
appear to rule out this mechanism. Furthermore, it might seem counterintuitive
that there can be large differences between model predictions in Fig. 14 and
Fig. 15, while those same models had similar trends for the $p_{\rm
T}$-differential double-ratios presented in Figs. 7–10. However, it is
important to note that the integrated double-ratios are weighted by the
relative yields in each $p_{\rm T}$ interval. Therefore, the $\left<p_{\rm
T}\right>$ of each particle species play a major part in the integrated
particle yields, see Fig. 6.

The comparison between model and data suggests that models without a universal
hadronization scheme, either through the core–corona in EPOS-LHC, or through
the color ropes in PYTHIA 8.2, are able to qualitatively reproduce the
observed trends. In contrast, the default PYTHIA 8.2 Monash variation, based
on the concept of jet universality, is unable to capture the feature presented
in the data.

###  7.5 $S_{\text{O}}^{p_{\rm T}=1}$ results with a broadened multiplicity
range

In Sec. 7.3, it was shown that the 0–1% topology selection produced the
largest effects, seen in Fig. 9 and Fig. 10. However, the resonance particles
had to be excluded in those measurements due to statistical limitations
related to the signal extraction. Therefore, in this Section, we report on
$S_{\text{O}}^{p_{\rm T}=1}$ measurements with a broader multiplicity
selection for the different $S_{\text{O}}^{p_{\rm T}=1}$ classes. We implement
the broadening of the multiplicity estimation in two different ways:

  1. 1.

First, we broaden the midrapidity multiplicity estimation to 0–10%, while
simultaneously constricting the $S_{\text{O}}^{p_{\rm T}=1}$ event selection
to the top 1% quantile. This allows for a broader multiplicity range, while
retaining the extreme topology selection, gaining a factor 10 in the number of
events.

  2. 2.

Secondly, we investigate top-1% multiplicity at forward rapidity in 0–10%
$S_{\text{O}}^{p_{\rm T}=1}$ quantiles. This is to study the impact of a
broader $\langle\rm{d}\it{N}_{\pi}/\rm{d}\it{y}\rangle$, as well as being able
to compare midrapidity to forward rapidity multiplicity estimation between
roughly similar $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$, as is seen in Fig.
2.

Fig. 16 illustrates the $S_{\text{O}}^{p_{\rm T}=1}$-differential ratios to
$(\pi^{+}+\pi^{-})$ with multiplicity measured at midrapidity, with a
simultaneous broadened multiplicity
($N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ 0–10%) and tightened
$S_{\text{O}}^{p_{\rm T}=1}$ selection criteria, compared to the measurement
presented in Sec. 7.3.

The double ratios for $\rm K^{*0}$ suggest that the production in isotropic
topologies is similar to that of average high-multiplicity events. In
contrast, there is a pronounced structure of the ratio for jet-like
topologies, highlighting an overall suppression of $\rm K^{*0}$ production.
The $\phi$ has similar features: suppression in jet-like events (qualitatively
the same trend as for $\Xi$), and consistent with unity for isotropic events.
For all presented particle species, an overall narrower $S_{\text{O}}^{p_{\rm
T}=1}$ selection highlights a large suppression of the $p_{\rm
T}$-differential yield of strange hadrons relative to pions in events with
extreme jet-like topologies. Furthermore, there is a larger deviation among
the four different models compared to the more constrained multiplicity
quantile, in particular in jet-like topologies for protons, $\Xi$, and $\rm
K^{*0}$. However, the overall trends are well predicted. Both resonance
particles favor production in softer events containing QGP-like features,
where the decrease of $\rm K^{*0}$ production in jet-like events could
potentially be due to a rescattering effect. While the origin of the
suppression of $\phi$ production in jet-like events is not fully understood,
the behavior is consistent with the strange particles measured in this study.

The particle ratios to $(\pi^{+}+\pi^{-})$ for events with forward rapidity
multiplicity estimations are presented in 0–10% $S_{\text{O}}^{p_{\rm T}=1}$
event classes in Fig. 17. The reported effects of $S_{\text{O}}^{p_{\rm T}=1}$
event-selection while estimating multiplicity through the V0M is comparatively
weak to either percentile of tracklets, both for the looser and stricter
multiplicity $S_{\text{O}}^{p_{\rm T}=1}$ criteria. Both PYTHIA models and
Herwig 7.2 are able to accurately describe the interplay between different
$S_{\text{O}}^{p_{\rm T}=1}$ event classes, while estimating multiplicity in
the forward rapidity region. In contrast, EPOS-LHC overestimates the relative
enhancement and suppression of $\Xi$ and $\Lambda$ in isotropic and jet-like
topologies, respectively. The midrapidity multiplicity estimations (both 0–1%
and 0–10%) showcase an increased sensitivity of strange hadron production as a
function of $S_{\text{O}}^{p_{\rm T}=1}$ compared to the forward rapidity
multiplicity estimation, even though the fractional
$\langle\rm{d}\it{N}_{\pi}/\rm{d}\it{y}\rangle$ difference

Figure 16: Top panels show hadron-to-$\pi$ ratios for 0–1%
$S_{\text{O}}^{p_{\rm T}=1}$ classes selected for the 0–10%
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ multiplicity events. Bottom
panels present the hadron-to-$\pi$ double-ratios of $S_{\text{O}}^{p_{\rm
T}=1}$ classes relative to $S_{\text{O}}^{p_{\rm T}=1}$ integrated high-
multiplicity events. Statistical and systematic uncertainties are shown by
bars and boxes, respectively. Experimental results are compared with
predictions from PYTHIA 8.2 Monash and Rope variants.

Figure 17: Top panels show hadron-to-$\pi$ ratios for 0–10%
$S_{\text{O}}^{p_{\rm T}=1}$ classes selected for the 0–1% V0M multiplicity
events. Bottom panels present the hadron-to-$\pi$ double-ratios of
$S_{\text{O}}^{p_{\rm T}=1}$ classes relative to $S_{\text{O}}^{p_{\rm T}=1}$
integrated high-multiplicity events. Statistical and systematic uncertainties
are shown by bars and boxes, respectively. Experimental results are compared
with predictions from PYTHIA 8.2 Monash and Rope variants.

between the $S_{\text{O}}^{p_{\rm T}=1}$ event classes in this case are
similar. This finding suggests that the effects of the relative enhancement
(suppression) of light-flavor hadron production to $\pi$ mesons in isotropic
(jet-like) topologies are smaller while estimating multiplicity with V0M, and
that one can study different physical properties relative to the rapidity
ranges in which the multiplicity is estimated.

Finally, in Fig. 18 the $p_{\rm T}$-integrated yields are presented as a
function of $S_{\text{O}}^{p_{\rm T}=1}$ following the two expanded
multiplicity estimations. It was shown in Sec. 7.4 that the results utilizing
the measured $p_{\rm T}$ ranges were consistent with yields obtained from
integrating over the full, extrapolated $p_{\rm T}$ range. Therefore, for the
sake of brevity, this section will only include yields integrated over the
measured $p_{\rm T}$ ranges, to allow for maximal precision when compared with
model predictions. Remarkably, the $S_{\text{O}}^{p_{\rm T}=1}$-dependent
enhancement of strange hadrons seems to vanish once the multiplicity
estimation is performed at forward rapidity. Similarly to Figs. 14 and 15, the
effect of strangeness enhancement is consistent between different ranges of
the midrapidity multiplicity estimation, and the effect is suggested to be
slightly stronger in the more extreme multiplicity case.

Figure 18: The double ratios of integrated yield as a function of
$S_{\text{O}}^{p_{\rm T}=1}$ are presented for V0M 0–1% (upper) and
$N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$ 0–10% (lower). Left and right
panels show the same data points, but with different model predictions.
Statistical and total systematic uncertainties are shown by bars and boxes,
respectively. The curves represent different model predictions of the same
measurement.

Both EPOS-LHC and the PYTHIA 8.2 rope hadronization framework are able to
qualitatively describe the enhancement of $\Lambda$ and $\Xi$ with increasing
$S_{\text{O}}^{p_{\rm T}=1}$, while simultaneously predicting the
insensitivity of strange particle production as a function of
$S_{\text{O}}^{p_{\rm T}=1}$ when estimating multiplicity at forward rapidity.

Finally, due to the increase of the number of events from the broader
multiplicity interval, it is possible to measure the integrated $\phi$ over
the full $S_{\text{O}}^{p_{\rm T}=1}$ range. This is presented in Fig. 19,
where integrated $\phi$ yields are compared to $\Xi$ yields as function of
$S_{\text{O}}^{p_{\rm T}=1}$, for $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$
0–10%, relative to the equivalent ($\pi^{+}\pi^{-}$) yields. It is observed
that there is no significant modification of the relative $\phi$ meson yield
as a function of $S_{\text{O}}^{p_{\rm T}=1}$ within systematic uncertainties.
This is in clear contrast to the features exhibited when measuring the
relative $\Xi$ production. Given the similarity of the proton curves in Fig.
18, these results imply that the $\phi$ meson has the properties of particles
with net-zero strangeness content, when measured as a function of
$S_{\text{O}}^{p_{\rm T}=1}$. The resulting suppression or enhancement of
relative hadron yields as a function of $S_{\text{O}}^{p_{\rm T}=1}$ are
therefore suggested to be driven by the hadron mass, rather than by the
effective strangeness of the hadron.

The experimental data is compared with both PYTHIA 8.2 Ropes and EPOS-LHC,
which, as shown in previous sections of this article, give the most accurate
predictions of the observed trends. Both generator models are also able to
quantitatively predict the dynamics of the relative $\phi$ yields as a
function of $S_{\text{O}}^{p_{\rm T}=1}$. However, in PYTHIA 8.2, one would
naively expect that the $\phi$ dynamics should follow the same trend as $\Xi$,
as both are effectively double-strange. This observed difference suggests that
the $\Xi$ enhancement in the PYTHIA 8.2 rope model can mainly be attributed to
addition of Junction formations, which only enhances baryon production.

Figure 19: The double ratios of integrated yield as a function of
$S_{\text{O}}^{p_{\rm T}=1}$ in $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$
0–10% for $\phi$ and $\Xi$. Statistical and total systematic uncertainties are
shown by bars and boxes, respectively. The curves represent different model
predictions of the same measurement

##  8 Summary and conclusions

In this article, we have presented the production of strange and non-strange
light-flavor particles at midrapidity ($\left|\eta\right|~{}<~{}0$.8) in high-
multiplicity pp collisions at $\sqrt{s}$ $=$ 13 TeV, as a function of the
unweighted transverse spherocity $S_{\text{O}}^{p_{\rm T}=1}$. In order to
account for the biases between weakly-decaying and charged primary hadrons, we
elaborate on how the observable was updated from the traditional transverse
spherocity.

The multiplicity was estimated in two different kinematic regions: at
midrapidity ($\left|\eta\right|~{}<~{}0$.8) by measuring the activity in the
SPD ($N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$), and at forward rapidities
($2.8<\eta<5.1$ and $-3.7<\eta<-1.7$) by measuring the activity in both sides
of the V0 forward detector (V0M amplitude). In Fig. 2, we report that the
different $S_{\text{O}}^{p_{\rm T}=1}$ event classes have a large variance in
local charged particle density when estimating the multiplicity through the
V0M, while being roughly equal in terms of $\left<p_{\rm T}\right>$. In
contrast, the $N_{\text{tracklets}}^{\text{$|\eta|<0.8$}}$-selected
$S_{\text{O}}^{p_{\rm T}=1}$ events are constrained in terms of
$\langle\rm{d}\it{N}_{\pi}/\rm{d}\it{y}\rangle$ within $~{}10\%$, while having
a large variance in $\left<p_{\rm T}\right>$. We conclude that estimating
multiplicity at midrapidity allows one to isolate and study the dynamics of
particle production in events that are driven by either soft or hard-QCD
physics.

The main features of this analysis are reported in the particle-to-pion ratios
in Figs. 7– 10, highlighting an enhancement of strange hadrons in events with
an isotropic topology, and a strong suppression in events with a jet-like
topology. This indicates that events with an isotropic topology describe the
average high-multiplicity event fairly well, while events heavily influenced
by jet-like physics are outliers. For the baryon-to-meson ratios presented in
Fig. 11, the $S_{\text{O}}^{p_{\rm T}=1}$ selection also highlights an
enhancement at intermediate $p_{\rm T}$ in the p/$\pi$, $\Lambda$/${\rm
K}^{0}_{\rm{S}}$ and $\Xi$/$\phi$ ratios, but without a depletion of
low-$p_{\rm T}$ particles for jet-like events. The effects are consistent
among the three ratios, and the $\phi$ exhibits a behavior similar to the
other strange particles. However, the $p_{\rm T}$-integrated yield of $\phi$
as a function of $S_{\text{O}}^{p_{\rm T}=1}$ presented in Fig. 19 highlights
features similar to other non-strange particles, reporting no observed
modification of relative $\phi$ meson production as a function of
$S_{\text{O}}^{p_{\rm T}=1}$.

The presented models are not able to describe the quantitative observations
found in data for the particle ratios, but are overall able to describe the
interplay between $S_{\text{O}}^{p_{\rm T}=1}$ classified events at high-
multiplicity with good accuracy in the double ratios. Remarkably, even though
the production mechanisms for the PYTHIA 8.2 Monash and PYTHIA 8.2 Ropes
variations (ropes formed by layers of overlapping strings) are qualitatively
different, they both predict the interplay with only minor differences between
them.

Finally, we report the relative integrated strange particle yield to pions as
function of $S_{\text{O}}^{p_{\rm T}=1}$ in Fig. 14. It is found that one can
achieve a similar strangeness enhancement found in multiplicity differential
analyses, by fixing the local charged particle density and varying the
azimuthal topology, instead of only varying the charged-particle density. This
indicates that particle production at high multiplicities is driven by more
than a single source, with different strangeness-to-pion production rates. The
same measurement is then performed in high-multiplicity events selected at
forward rapidities. Fig. 2 highlights that the
differential-$S_{\text{O}}^{p_{\rm T}=1}$ selection in this event-class
primarily varies the local charged particle density approximately a factor of
two. Therefore, when contrasted to the multiplicity-dependent ALICE
measurements in Ref. [1], one could naively expect to observe strangeness
suppression and enhancement due to the difference in charged particle density
alone. Surprisingly, we show in Fig. 18 that this effect is negligible when
estimating multiplicity in the forward-rapidity region, with no significant
strangeness enhancement or suppression within systematic uncertainties. This
goes contrary to expectations based on previous ALICE publications, and the
effect is currently not well understood. PYTHIA 8.2 Monash and Herwig 7.2 are
unable to describe this effect, but PYTHIA 8.2 Ropes and EPOS-LHC
qualitatively capture the trend, showcasing a large suppression of strangeness
production in jet-like events, although with a mass ordering that is
incompatible with the experimental data.

We conclude that with $S_{\text{O}}^{p_{\rm T}=1}$, one is able to categorize
events into classes based on characteristic azimuthal topologies, from jet-
like events associated with hard-QCD physics, to isotropic events associated
with soft-QCD physics. Furthermore, the findings presented in this article
suggest that average high-multiplicity events, even in the most extreme cases,
are dominated by soft processes, where rare hard processes play little or no
role for bulk observables.

## 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) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. In addition, individual groups or members have received support from: European Research Council, Strong 2020 - Horizon 2020 (grant nos. 950692, 824093), European Union; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland.

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##  Appendix A The ALICE Collaboration

S. Acharya 127, D. Adamová 86, G. Aglieri Rinella 33, M. Agnello 30, N.
Agrawal 51, Z. Ahammed 135, 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 126, 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 130, 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 127, L. Barreto 110, C. Bartels 118, K. Barth 33, E.
Bartsch 64, N. Bastid 127, 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 129, A.D.C. Bell Hechavarria 126, 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 135, 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 129, 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 134,55, H.
Borel 130, 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 128, L.A.D. Carvalho 110,
J. Castillo Castellanos 130, F. Catalano 33,25, C. Ceballos Sanchez 143, I.
Chakaberia 74, P. Chakraborty 47, S. Chandra 135, S. Chapeland 33, M. Chartier
118, S. Chattopadhyay 135, S. Chattopadhyay 99, T.G. Chavez 45, T. Cheng 97,6,
C. Cheshkov 128, B. Cheynis 128, V. Chibante Barroso 33, D.D. Chinellato 111,
E.S. Chizzali II,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. ClaiIII,51, F.
Colamaria 50, J.S. Colburn100, D. Colella 96,32, M. Colocci 26, M. Concas
IV,33, G. Conesa Balbastre 73, Z. Conesa del Valle 131, G. Contin 24, J.G.
Contreras 36, M.L. Coquet 130, P. Cortese 133,56, M.R. Cosentino 112, F. Costa
33, S. Costanza 22,55, C. Cot 131, J. Crkovská 94, P. Crochet 127, 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 126, 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 134, R. Del Grande 95, L.
Dello Stritto 29, W. Deng 6, P. Dhankher 19, D. Di Bari 32, A. Di Mauro 33, B.
Diab 130, R.A. Diaz 143,7, T. Dietel 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 136, A. Dubla 97, S. Dudi 90, P. Dupieux 127, M. Durkac106,
N. Dzalaiova13, T.M. Eder 126, R.J. Ehlers 74, F. Eisenhut 64, R. Ejima92, D.
Elia 50, B. Erazmus 103, F. Ercolessi 26, B. Espagnon 131, G. Eulisse 33, D.
Evans 100, S. Evdokimov 142, L. Fabbietti 95, M. Faggin 28, J. Faivre 73, F.
Fan 6, W. Fan 74, A. Fantoni 49, M. Fasel 87, A. Feliciello 56, G. Feofilov
142, A. Fernández Téllez 45, L. Ferrandi 110, M.B. Ferrer 33, A. Ferrero 130,
C. Ferrero 56, A. Ferretti 25, V.J.G. Feuillard 94, V. Filova 36, D. Finogeev
142, F.M. Fionda 52, E. Flatland33, F. Flor 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. Garcia 131, J.R.A. Garcia
45, E. Garcia-Solis 9, C. Gargiulo 33, P. Gasik 97, A. Gautam 117, M.B. Gay
Ducati 66, M. Germain 103, A. Ghimouz124, C. Ghosh135, M. Giacalone 51, G.
Gioachin 30, P. Giubellino 97,56, P. Giubilato 28, A.M.C. Glaenzer 130, P.
Glässel 94, E. Glimos 121, D.J.Q. Goh76, V. Gonzalez 137, P. Gordeev 142, M.
Gorgon 2, K. Goswami 48, S. Gotovac34, V. Grabski 67, L.K. Graczykowski 136,
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.
Gulbrandsen 83, T. Gündem 64, T. Gunji 123, W. Guo 6, A. Gupta 91, R. Gupta
91, R. Gupta 48, S.P. Guzman 45, K. Gwizdziel 136, L. Gyulai 138, C.
Hadjidakis 131, F.U. Haider 91, S. Haidlova 36, H. Hamagaki 76, A. Hamdi 74,
Y. Han 140, B.G. Hanley 137, R. Hannigan 108, J. Hansen 75, M.R. Haque 136,
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. Herrmann126, S. Herrmann 128, K.F.
Hetland 35, B. Heybeck 64, H. Hillemanns 33, B. Hippolyte 129, F.W. Hoffmann
70, B. Hofman 59, G.H. Hong 140, M. Horst 95, A. Horzyk 2, 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. Ippolitov 142, A. Isakov 84,86, T. Isidori 117, M.S. Islam
99, M. Ivanov 97, M. Ivanov13, V. Ivanov 142, K.E. Iversen 75, M. Jablonski 2,
B. Jacak 74, N. Jacazio 26, P.M. Jacobs 74, S. Jadlovska106, J. Jadlovsky106,
S. Jaelani 82, C. Jahnke 110, M.J. Jakubowska 136, M.A. Janik 136, T.
Janson70, S. Ji 17, S. Jia 10, A.A.P. Jimenez 65, F. Jonas 87, D.M. Jones 118,
J.M. Jowett 33,97, J. Jung 64, M. Jung 64, A. Junique 33, A. Jusko 100, M.J.
Kabus 33,136, J. Kaewjai105, P. Kalinak 60, A.S. Kalteyer 97, A. Kalweit 33,
V. Kaplin 142, A. Karasu Uysal 72, D. Karatovic 89, O. Karavichev 142, T.
Karavicheva 142, P. Karczmarczyk 136, E. Karpechev 142, U. Kebschull 70, R.
Keidel 141, D.L.D. Keijdener59, M. Keil 33, B. Ketzer 43, S.S. Khade 48, A.M.
Khan 119, S. Khan 16, A. Khanzadeev 142, Y. Kharlov 142, A. Khatun 117, A.
Khuntia 36, B. Kileng 35, B. Kim 104, C. Kim 17, D.J. Kim 116, E.J. Kim 69, J.
Kim 140, J.S. Kim 41, J. Kim 58, J. Kim 69, M. Kim 19, S. Kim 18, T. Kim 140,
K. Kimura 92, S. Kirsch 64, I. Kisel 39, S. Kiselev 142, A. Kisiel 136, J.P.
Kitowski 2, J.L. Klay 5, J. Klein 33, S. Klein 74, C. Klein-Bösing 126, M.
Kleiner 64, T. Klemenz 95, A. Kluge 33, A.G. Knospe 115, C. Kobdaj 105, T.
Kollegger97, A. Kondratyev 143, N. Kondratyeva 142, E. Kondratyuk 142, J.