# Multiplicity dependence of (multi-)strange hadrons in oxygen-oxygen
collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV using EPOS4 and AMPT

M. U. Ashraf<EMAIL_ADDRESS> Centre for Cosmology, Particle Physics
and Phenomenology (CP3), Université Catholique de Louvain, B-1348 Louvain-la-
Neuve, Belgium
A. M. Khan<EMAIL_ADDRESS>(Corresponding Author) University of
Science & Technology of China, Hefei 230026, People’s Republic of China
J. Singh<EMAIL_ADDRESS>Instituto de Alta Investigación,
Universidad de Tarapacá, Casilla 7D, Arica, Chile
N. Kumar<EMAIL_ADDRESS>Department of Physics, Panjab University,
Chandigarh 160014, India

###### Abstract

LHC is anticipated to collect data from oxygen-oxygen ($O+O$) collisions at
center-of-mass energy $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV to further
investigate the particle production mechanisms. In the present work, we report
on the predictions of transverse momentum ($p_{\rm T}$-spectra), $dN/dy$,
yield ratios relative to pions, $p_{\rm T}$-differential ratios of
(multi-)strange hadrons in $O+O$ collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV using EPOS4 and AMPT models. Both models
differ fundamentally, EPOS4 incorporates a QGP phase, while AMPT focuses on
pre-formed hadron interactions. We observed that AMPT qualitatively fails to
predict strangeness enhancement in $O+O$ collisions, while EPOS4 predicts a
significant enhancement. We also observed the hints of stronger radial flow in
EPOS4 compared to AMPT in $O+O$ collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$
TeV. AMPT incorporates some flow effects, but EPOS4’s implementation of full
hydrodynamic flow appears to be significantly more effective in reproducing
the experimental data. Both models interestingly predict the final state
multiplicity overlap with $pp$, $p+Pb$, and $Pb+Pb$ collisions. The upcoming
data on $O+O$ collisions at the LHC is expected to play a crucial role both,
constraining the model parameters and significantly refining our understanding
of these theoretical models.

##  I Introduction

In recent years, there has been a lot of debate in our understanding of the
limit of the smallest possible droplet of the Quark-Gluon plasma (QGP) formed
at sufficient high temperature and energy density. High-energy heavy-ion
collisions recreate this exotic state of strongly interacting matter predicted
by Quantum Chromodynamics (QCD) in the laboratory [1, 2, 3]. Experiments at
the Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC)
have facilitated the investigations on the properties of the QGP. Collisions
of symmetric heavy-ions, such as lead-lead ($Pb+Pb$) and gold-gold ($Au+Au$),
at these facilities have revealed that the QGP exhibits hydrodynamic behavior,
flowing like a nearly perfect fluid [4, 5]. The interpretation of nucleus-
nucleus ($AA$) results depends critically on the comparison with the results
from small colliding systems, such as proton-proton ($pp$) or proton-nucleus
($pA$) collisions because these systems serve as a baseline for comparison.

Strangeness enhancement has long been proposed and observed as a signature of
the QGP since the hot medium facilitates thermal production of the strange
quarks [6]. Strangeness production has been extensively measured and reported
by many experimental facilities [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20]. The mass of a strange quark is close to the temperature at which
ordinary matter transitions into the QGP. Due to this reason strange quarks
are expected to be produced abundantly in the QGP [6, 21]. Therefore, one
would expect to see a significant enhancement in the strangeness production in
relativistic heavy-ion collisions. However, the ratios of production yields
for various strange hadrons relative to pions in heavy-ion collisions from SPS
to LHC shows significant centrality and energy dependence [17].

Recent studies at the Large Hadron Collider (LHC) have observed features in
high-multiplicity $pp$ and proton-lead ($p+Pb$) collisions that are
surprisingly similar to those observed in $AA$ collisions, despite the
significant difference in system size [22, 23]. These findings exhibit
qualitative agreement with the predictions of the statistical hadronization
model [24]. This model incorporates the effect of canonical suppression, which
accounts for strangeness suppression due to strangeness conservation [25, 26].
Additionally, these findings are also consistent with the core-corona model
[27, 28, 29] based on the assumption that strange quarks are produced
thermally in the core, a high-density region of the colliding nuclei. On the
other hand, the most commonly used Monte-Carlo (MC) models for $pp$ collisions
like Pythia [30, 31] and EPOS LHC [32] failed to describe the experimental
data [22]. These observations present a significant challenge to current
theoretical understanding of QGP formation, as they suggest the possibility of
QGP-like behavior in smaller collision systems than previously anticipated.
Therefore, to understand the enhanced production of strange hadrons in small
systems, both experimental investigation and development of a comprehensive
microscopic model are crucial.

To enhance our understanding of QGP formation mechanisms in small systems, LHC
experiments are anticipated to collect data from Oxygen-Oxygen ($O+O$)
collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV [33, 34]. This could offer
a unique opportunity to explore the effects observed in high-multiplicity
$p+Pb$ collisions. $O+O$ system has a larger geometric overlap area, but with
a similar small number of participating nucleons and a similar number of
final-state multiplicity [34]. The underlying mechanisms of particle
production in $O+O$ collisions have recently been explored in several
theoretical studies [35, 36, 37, 38, 39, 40, 41, 42, 43, 44]. $O+O$ collisions
serve as a bridge between small systems ($pp$ and $p+Pb$) and large systems
($Xe+Xe$ and $Pb+Pb$). By studying particle production, transverse collective
flow, and the production of light-nuclei in $O+O$ collisions across a range of
multiplicities, deeper insights into the underlying mechanisms governing these
phenomena can be explored. The oxygen-16 (${}^{16}O$) is a doubly magic
nucleus, characterized by exceptional stability due to its closed shell
structure [45] with a notable feature of involving a similar number of
participating nucleons similar to that of the $p+Pb$ system. However, the
nucleons in ${}^{16}O$ are more evenly distributed in the transverse plane,
leading to a distinct initial state and potentially different subsequent
evolution of the collision system. The investigation of the ultra-relativistic
$O+O$ collisions at the LHC energies could have a profound impact on our
understanding of high-energy physics with the new idea of final-state
multiplicity plays a crucial role in determining the properties of the system.
$O+O$ collisions also provide a unique opportunity to bridge the gap between
different collision systems (species and centrality) and to gain a deeper
understanding of how these factors influence final-state multiplicity and
system behavior [42, 43, 44].

In this paper, we report on the predictions of (multi-)strange hadrons
($\mathrm{K}^{0}_{\mathrm{S}}$, $\Lambda$ ($\overline{\Lambda}$),
$\Xi^{-}+\overline{\Xi}^{+}$, $\Omega^{-}+\overline{\Omega}^{+}$, and $\phi$)
production in $O+O$ collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV using
AMPT [46, 47] and recently released EPOS4 [48, 49, 50, 51] models. The
observable include $p_{\rm T}$-spectra, $dN/dy$, multiplicity dependence of
the yield ratios of (multi-)strange hadrons relative to pions and $p_{\rm
T}$-differential ratio of (multi-)strange baryons to meson.

The paper is organized as follows. In Section I, we described the significance
of $O+O$ collisions. In Section II, the brief description of event generation
methodology with AMPT and EPOS4 models are discussed. The results are
presented and discussed in Section III. Finally, the summary, main findings
and potential outlook for future research is given in Section IV.

##  II Event Generator

In this section, a short description of the AMPT and EPOS4 models are
discussed.

###  II.1 AMPT

The AMPT model was developed to study the dynamics of relativistic heavy-ion
collisions and has been extensively used for various studies at RHIC and LHC
energies [46, 47]. For current study, both default (AMPT) and string melting
(AMPT-SM) versions have been used to produce simulations. In AMPT, hadrons are
produced by the HIJING model [52], which includes the initial spatial and
momentum distributions of minijet partons and the soft string excitations. The
subsequent space-time evolution of these partons is then governed by the ZPC
parton cascade model [53]. Following the parton cascade evolution, the model
employs either string fragmentation or quark coalescence mechanisms to convert
the remaining partonic degrees of freedom into final-state hadrons.
Subsequently, the interactions of these newly formed hadrons are governed by
the Hadronic Transport Model (ART) [54]. The default version of the AMPT model
reasonably reproduces the rapidity distributions and $p_{\rm T}$ spectra of
identified particles at SPS and RHIC energies due to the fact that it only
involves minijet partons from HIJING in the parton cascade and uses Lund
string fragmentation for the hadronization [30]. However, the default version
significantly underestimates the elliptic flow at RHIC energies [55]. In the
AMPT model with string melting (AMPT-SM) [55], the initial hadrons produced by
Lund string fragmentation are converted to their valence quarks. A simple
quark coalescence model is then employed to convert these quarks back into
hadrons after the ZPC. This approach has been successful in describing
anisotropic flows in both large and small collision systems [55, 56, 57].

The scattering cross-section are evaluated according to;

$\sigma_{p}\approx\frac{9\pi\alpha^{2}_{s}}{2(t-\mu^{2})^{2}}$ (1)

In this study, we employ both, the default and string melting versions of the
AMPT model to simulate $O+O$ collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$
TeV. A dataset of $\sim$ 2.5 million minimum-bias $O+O$ events were processed
in this analysis.

###  II.2 EPOS4

The EPOS model simulates nucleus-nucleus (AA) collisions based on 3+1D viscous
hydrodynamic approach [27]. The initial conditions in the EPOS are defined in
terms of flux tubes and are estimated using Gribov-Regge multiple scattering
theory [58]. The core-corona, hydrodynamical evolution and the hadronic
cascade are three main components of EPOS. The fragmentation of flux tubes
into core and corona (which later hadronize into hadron jets) is determined by
the probability of a fragment escaping the bulk matter. This probability
depends on the fragment transverse momentum and the local string density. EPOS
[51] further incorporates a mechanism to distinguish between the core and
corona zones of particle production within the colliding nuclei. To account
for the varying density, the model employs different approaches: Regge theory
[58] for the low-density (corona) and hydrodynamic equations for the high-
density (core) to study the particle production. The core utilizes a Cooper-
Frye freeze-out mechanism to describe hadronization. The $vHLLE$ algorithm, a
viscous hydrodynamic approach implemented in a 3D+1 framework, is employed
with a realistic Equation of State derived from lattice QCD [59]. The hadronic
afterburner, a hadronic cascade model based on the UrQMD model [60, 61], is
employed to study the late stages of ultra-relativistic heavy-ion collisions
[60, 61, 62]. This core-corona model successfully reproduces many features of
$pp$ and $d-Au$ collisions. The inclusion of the core-corona distinction has
significantly improved the model to describe the centrality dependence of
resonance as well as strange particle production in $AA$ collisions [63]. A
recent release, EPOS4, incorporates a novel concept providing a new
understanding on the fundamental interplay between four key principles in $pp$
and $AA$ collisions: rigorous parallel scattering, energy conservation,
factorization, and saturation. Furthermore, a core-corona approach based on
new micro-canonical hadronization procedures employed in EPOS4 to effectively
realize the role of collective flow in the monotonically increase in
strangeness enhancement in the transition from small to large systems [51].
More details on the latest release of EPOS4 is reported in Ref. [51].

A total of $\sim$ 1.5 million minimum-bias $O+O$ events were simulated from
EPOS4 to study the strangeness enhancement in $O+O$ collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV. Recent versions of both models are
considerably successful in describing various observables at RHIC and LHC but
have also encountered limitations.

##  III Discussion

In this section, we present the results on transverse momentum $p_{\rm
T}$-spectra of (multi-)strange hadrons ($\mathrm{K}^{0}_{\mathrm{S}}$,
$\Lambda$ \+ $\overline{\Lambda}$), $\Xi^{-}+\overline{\Xi}^{+}$,
$\Omega^{-}+\overline{\Omega}^{+}$, and $\phi$), yields of (multi-)strange
hadrons as a function of event charged-particle multiplicity density
($\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$), $p_{\rm
T}$-integrated yield ratios relative to pions ($\pi^{+}+\pi^{-}$), $p_{\rm
T}$-differential baryon to meson ratios and mean transverse momentum ($\langle
p_{\mathrm{T}}\rangle$) as a function of charged-particle multiplicity
($\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$) at mid-rapidity
($|y|<0.5$) in $O+O$ collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV.
Herein, we refer to the ($\Lambda$ \+ $\overline{\Lambda}$),
($\Xi^{-}+\overline{\Xi}^{+}$), ($\Omega^{-}+\overline{\Omega}^{+}$) particles
as $\Lambda$, $\Xi$, and $\Omega$ respectively.

###  III.1 Transverse momentum $p_{\rm T}$ spectra

The transverse momentum ($p_{\rm T}$) distribution of
$\mathrm{K}^{0}_{\mathrm{S}}$, $\Lambda$, $\Xi$, $\Omega$, and $\phi$ from
EPOS4, AMPT-SM, and AMPT-default in 0–5% central $O+O$ collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV is shown in Fig. 1. EPOS4 simulations are
compared with the AMPT model. The results for EPOS4 are depicted by the solid
line, whereas the dashed and dotted lines represent AMPT-SM and the AMPT-
default model, respectively.

Figure 1: (Color online) $p_{\rm T}$-spectra of (multi-)strange hadrons
($\mathrm{K}^{0}_{\mathrm{S}}$, $\Lambda$, $\Xi$, $\Omega$, and $\phi$) from
EPOS4, AMPT-default, and AMPT-SM in $O+O$ collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV for 0–5% centrality. The $p_{\rm T}$
spectra for (multi-)strange hadrons are scaled by a factor of $10$ for better
visualization. Solid lines are used for EPOS4, whereas the dashed and dotted
lines represent AMPT-SM and the default AMPT model, respectively.

The $p_{\rm T}$ distributions of different particle species exhibit a clear
evolution. At low-$p_{\rm T}$, the distributions tend to flatten, with this
effect being stronger for heavier particles compared to lighter ones,
demonstrating a mass ordering behavior. This is expected in hydrodynamic
models as a consequence of the blue-shift induced by the collective expansion
of the system. Both models predict suppressed production of $\phi$ compared to
$\Lambda$, which is a clear violation of mass ordering. This has been reported
in $pp$ and $p+Pb$ collisions by the ALICE experiment [64]. At
intermediate-$p_{\rm T}$, the spectra of heavier particles seem to converge
towards those of lighter particles. This convergence may be attributed to the
influence of radial flow within the medium. As the system expands, the radial
flow can impart additional momentum to particles with lower $p_{\rm T}$,
pushing them towards intermediate-$p_{\rm T}$ [65, 66]. Additionally, the
spectra become harder with increasing centrality, especially for heavier
particles. This behavior is qualitatively reminiscent of what is observed in
$Pb+Pb$ collisions [67]. This suggests a progressively stronger radial flow
with increasing collision centrality. The observed changes in the shapes of
$p_{\rm T}$ spectra may be attributed to coalescence mechanisms [68] and/or
high-$p_{\rm T}$ jet production [69, 70] caused by fragmentation mechanisms.
However, the effects of jets are typically dominant beyond the
intermediate-$p_{\rm T}$ region.

Figure 2: (Color online) Multiplicity dependence of particle yield ($dN/dy$)
of (multi-)strange hadrons ($\mathrm{K}^{0}_{\mathrm{S}}$, $\Lambda$, $\Xi$,
$\Omega$, and $\phi$) in $O+O$ collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$
TeV using EPOS4, AMPT-SM, and AMPT-default. Solid lines are used for EPOS4,
whereas the dashed and dotted lines represent AMPT-SM and the default AMPT
model, respectively.

Figure 2 shows the predictions from EPOS4, AMPT-SM, and AMPT-default models
for the yields ($dN/dy$) of (multi-)strange hadrons as a function of event
charged-particle multiplicity density
($\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$) in $O+O$ collisions
at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV. It is observed that the average
yields of multi-strange hyperons decrease systematically with increasing
number of strange quarks for all models. On the other hand, all models
consistently predict an increase in $dN/dy$ with increasing
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$. The predictions for
$\Lambda$, $\Xi$, and $\Omega$ by EPOS4 are relatively larger compared to
those from AMPT-SM and AMPT-default.

Figure 3: (Color online) $p_{\rm T}$-integrated yield ratios of
$\mathrm{K}^{0}_{\mathrm{S}}$, $\Lambda$, $\Xi$, $\Omega$, and $\phi$ to pions
($\pi^{+}+\pi^{-}$) as a function of
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$ in $O+O$ collisions
at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV using EPOS4, AMPT-SM, and AMPT-
default. Solid lines are used for EPOS4, whereas the dashed and dotted lines
represent AMPT-SM and the default AMPT model, respectively. The values are
compared to the published results from $pp$, $p+Pb$, and $Pb+Pb$ collisions
[22, 67, 71, 72, 73, 74].

To investigate the relative production of strange particles compared to non-
strange particles, the yield ratios of strange particles to pions were
calculated as a function of charged particle multiplicity. Figure 3 shows the
$p_{\rm T}$-integrated ratios of (multi-)strange hadrons
($\mathrm{K}^{0}_{\mathrm{S}}$, $\Lambda$, $\Xi$, $\Omega$, and $\phi$) over
pions as a function of charged-particle multiplicity
($\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$) in $O+O$ collisions
at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV using EPOS4, AMPT-SM, and AMPT-default
model. The results are then compared with $pp$, $p+Pb$, and $Pb+Pb$ collisions
at available energies [22, 67, 71, 72, 73, 74]. Our analysis reveals a
significant increase in the production of strange hadrons relative to non-
strange hadrons in $O+O$ collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV
using various models. However, none of the model quantitatively describe the
relative yield ratio when compared to the different systems. The enhancement
becomes more pronounced with increasing multiplicity. It seems that
strangeness production is strongly correlated with event multiplicity. This
behavior is consistent with observations from previous studies of $pp$,
$p+Pb$, and $Pb+Pb$ collisions at different energies [22, 67, 71, 72, 73, 74].
Notably, this consistency extends not only to the magnitude of the ratios but
also to their evolution with multiplicity across different collision systems.
The AMPT default model predicts no significant multiplicity dependence on the
ratios except for multi-strange baryons, where the model fails to reproduce
the observed trend qualitatively and quantitatively. On the other hand, AMPT-
SM is flat for $\Xi/\pi$ and $\Omega/\pi$ ratios and completely failed to
describe strangeness enhancement in $O+O$ collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV. Both versions of AMPT failed to describe
$\phi/\pi$ ratio and over predict $pp$, $p+Pb$, and $Pb+Pb$ data. It would be
interesting to investigate strangeness enhancement with the extended AMPT
model [75]. This model incorporates improved coalescence parameters and is not
yet publicly available. Notably, the extended AMPT model provides a reasonable
description of the observed multiplicity dependence of strangeness enhancement
in high-multiplicity $pp$, $p+Pb$ collisions. Furthermore, the model suggests
that coalescence factors depend on the system size but not significantly on
whether the system is produced from $A+A$ or $p+A$ collisions [75].

EPOS4 predictions suggest that the amount of strangeness produced in $O+O$
collisions does not seems to depend on the center of mass energy and the final
state of the collision, plays a cruicial role to study the strangeness
production rather than the type of colliding system or the energy. The yield
ratios of $\mathrm{K}^{0}_{\mathrm{S}}$/$\pi$, $\Lambda/\pi$, and $\phi/\pi$
from recently updated EPOS4 model qualitatively produce the strangeness
enhancement in $O+O$ collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV and
show reasonable agreement with previously published results from $pp$, $p+Pb$,
and $Pb+Pb$ collisions at the LHC [22, 67, 71, 72, 73, 74]. EPOS4 predicts an
increase in the yield ratios for heavier particles ($\Xi/\pi$ and
$\Omega/\pi$) in $O+O$ collisions compared to data from $pp$, $p+Pb$, and
$Pb+Pb$ collisions at similar collision energy. It has been reported recently
in Ref. [76] that EPOS4 exhibits relatively larger yield ratio particularly at
lower final-state multiplicities in $pp$ and $Pb+Pb$ collisions. This is
expected because when the system size decreases, the production of heavier
particles becomes reduced due to the microcanonical procedure (with its energy
and flavor conservation constraints), whereas in a grand canonical treatment,
one would expect a flat curve down to the small multiplicities. This effect
shows increasing trend with increasing particle mass and it is larger for
$\Omega$ baryon. Similar observations has already been reported for
$\Omega/\pi$ ratios in $pp$ and $Pb+Pb$ collisions from EPOS4 [51].
Interestingly, the yield ratios of strange particles to pions in $O+O$
collisions at $\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV from all models under study
shows a clear final state multiplicity overlap with $pp$, $p+Pb$, and $Pb+Pb$
collisions. The future $O+O$ collisions at the LHC is anticipated to cover
final state multiplicities from few particles at mid-rapidity up to the values
measured in semi-peripheral $Pb+Pb$ collisions. It will be interesting to
study the evolution of hadrochemistry in the whole range of variability below
the flattening in semicentral and central $Pb+Pb$ collisions. Furthermore, the
upcoming data will be hepful to put possible constraints on the model
parameters to study the particle production and system evolution in $O+O$
collisions.

Figure 4: (Color online) $p_{\rm T}$-differential ratios of (multi-)strange
($K$, $\Lambda$, $\phi$, and $\Xi$) hadrons to pions in $O+O$ collisions using
EPOS4, AMPT-SM, and AMPT-default. Solid lines are used for EPOS4, whereas the
dashed and dotted lines represent AMPT-SM and the default AMPT model,
respectively.

Figure 4 shows the predictions of $p_{\rm T}$-differential particle ratios of
$K$, $\Lambda$, $\phi$, and $\Xi$ to pions in 0–5% $O+O$ collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV. The results are presented for the EPOS4,
AMPT-SM, and AMPT-default models. Particle ratios, particularly those
involving different hadron species, serve as a direct probe of the relative
abundances and interaction dynamics of the underlying quark constituents
within the hot and dense medium. Similar to $K/\pi$ ratio, $\Lambda/\pi$ ratio
serve as a measure of strangeness enhancement due to similar strangeness
content. We observe enhancement of strangeness production as a function of
$p_{\rm T}$ from all of the models used for the current study. The strangeness
enhancement observed in the $K/\pi$ ratio at intermediate-$p_{\rm T}$ for
EPOS4 exhibits qualitative agreement with the AMPT-SM model. However,
$\Lambda/\pi$ ratio predicted by EPOS4 is relatively larger compared to both
AMPT models. The rise in the $\phi/\pi$ ratio is more gradual compared to the
$K/\pi$ and $\Lambda/\pi$ ratios, which exhibit a rapid increase at
low-$p_{\rm T}$. This observed trend may be attributed to a higher probability
of strange quark coalescence with abundantly produced $u$ and $d$ quarks in
the dense medium, compared to the less probable interaction with their anti-
strange partners to form $\phi$ mesons at the low-$p_{\rm T}$ region. At the
intermediate-$p_{\rm T}$ region where the momentum of particle becomes
comparable or more than the mass of strange quark, the production probability
of $s\bar{s}$ increases significantly. This leads to a corresponding rise in
the observed $\phi/\pi$ ratio at intermediate-$p_{\rm T}$, as $\phi$ mesons
are composed of $s$ and $\bar{s}$ quark. In contrast, at high-$p_{\rm T}$, $u$
and $d$ quarks are abundantly produced compared to the $s$ quarks and the
ratio starts to drop at high-$p_{\rm T}$. This trend is similar to that
observed in $pp$, $p+Pb$, and $Pb+Pb$ collisions at the LHC [22, 67, 71, 72,
73, 74]. The AMPT model predicts a relatively larger $\phi/\pi$ ratio compared
to EPOS4. This difference might be attributed to the influence of Lund string
fragmentation parameters on the yields of strange quarks carrying hadron like
$\phi$ mesons. AMPT may implement these parameters more effectively, leading
to a stronger preference for strange quark hadronization compared to EPOS4
[77]. This, in turn, would result in a higher $\phi/\pi$ ratio for AMPT. The
EPOS4 model predicts a larger $\Xi/\pi$ ratio compared to both AMPT versions
at intermediate-$p_{\rm T}$. However, this ratio exhibits a stronger
suppression compared to the $\phi/\pi$ ratio due to the presence of two
strange quarks in the $\Xi$ baryon compared to the single strange quark in the
$\phi$ meson. Clearly $O+O$ collisions exhibit a final-state charged-particle
multiplicity that overlaps significantly with those observed in $pp$, $p+Pb$,
and $Pb+Pb$ collisions. This shared characteristic, a relatively similar
number of participant nucleons interacting in the collision, is believed to be
a key factor influencing the behavior of certain particle production ratios.

Figure 5: (Color online) $p_{\rm T}$-differential baryon-to-meson ($p/\pi$ and
$\Lambda$/$\mathrm{K}^{0}_{\mathrm{S}}$) ratios in $O+O$ collisions using
EPOS4, AMPT-SM, and AMPT-default. Solid lines are used for EPOS4, whereas the
dashed and dotted lines represent AMPT-SM and the default AMPT model,
respectively.

The $p_{\rm T}$-differential $p/\pi$ (lightest baryon to lightest meson) ratio
serves as an indicator of the relative production of baryons compared to
mesons. EPOS4 shows an increasing trend in the ratio (up to a maximum of 0.45)
at intermediate-$p_{\rm T}$ for 0–5% central collisions while both versions of
AMPT predicts slightly higher ratios. It is also observed that the trend
appears to be plateau at intermediate-$p_{\rm T}$ for mid-central and
peripheral collisions similar to that observed in $pp$, $p+Pb$, and $Pb+Pb$
collisions at the LHC [22, 67, 71, 72, 73, 74]. EPOS4 model reproduces the
qualitative behavior of the $p/\pi$ ratio observed in $O+O$ collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV. This trend is consistent with $p/\pi$
ratios measured in $pp$, $p+Pb$, and $Pb+Pb$ collisions. EPOS4 is based on
parton-based Gribov-Regge framework and incorporates hydrodynamic elements
[32], predicts an enhancement in $p/\pi$ ratios at intermediate-$p_{\rm T}$
attributed to radial flow effects. The EPOS4 model predicts a relatively
larger $\Lambda$/$\mathrm{K}^{0}_{\mathrm{S}}$ ratio at the
intermediate-$p_{\rm T}$ region compared to AMPT. This suggests a higher
relative abundance of strange baryons compared to strange mesons produced in
EPOS4. This difference might be attributed to the presence of stronger radial
flow in EPOS4, which affects baryons like $\Lambda$ at higher multiplicities.
This finding aligns well with the observed collision dynamics at this center-
of-mass energy, suggesting that EPOS4’s treatment of strangeness production
mechanisms, particularly for these particles, is more consistent with the
data. AMPT incorporates some flow effects, but EPOS4’s implementation of full
hydrodynamic flow appears to be significantly more effective in reproducing
the experimental data [51]. The upcoming data on $O+O$ collisions at the LHC
is expected to play a crucial role both, constraining the model parameters and
significantly refining our understanding of these theoretical models.

##  IV Conclusions

We present predictions of various observables for (mutli-)strange hadrons
($\mathrm{K}^{0}_{\mathrm{S}}$, $\Lambda$($\overline{\Lambda}$),
$\Xi^{-}$($\overline{\Xi}^{+}$), $\phi$, and
$\Omega^{-}$($\overline{\Omega}^{+}$)) in $O+O$ collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV using the recently updated hydrodynamics-
based model EPOS4 and two different versions the AMPT model. The strangeness
production mechanisms in the EPOS4 and AMPT models differ fundamentally. EPOS4
incorporates the formation of a Quark-Gluon Plasma (QGP) phase, where strange
quarks can be abundantly created. In contrast, AMPT is a transport model that
focuses on the interactions and collisions of pre-formed hadrons, including
strange particles, without explicitly simulating the QGP phase. Interestingly,
both EPOS4 and AMPT reasonably reproduce the overall strangeness enhancement
results from the ALICE experiment. An extensive model studies have been
performed to study the transverse momentum ($p_{\rm T}$-spectra), multiplicity
dependence of particle yield ($dN/dy$) and yield ratio of various
(multi-)strange hadrons relative to pions, $p_{\rm T}$-differential ratios of
different strange meson and baryons relative to pions and $p_{\rm
T}$-differential baryon to meson ratio in $O+O$ collisions at
$\sqrt{s_{\mathrm{NN}}}~{}=~{}7$ TeV. All of the models successfully reproduce
the general shape of the $p_{\rm T}$ spectra for all (mutli-)strange hadrons.
The EPOS4 model predict relative larger enhancement for (multi-)strange
baryons ($\Xi^{-}$($\overline{\Xi}^{+}$) and
$\Omega^{-}$($\overline{\Omega}^{+}$)) while preforms well for strange hadrons
($\mathrm{K}^{0}_{\mathrm{S}}$, $\Lambda$($\overline{\Lambda}$), and $\phi$).
However, none of the models quantitatively describe the strangeness
enhancement. Similar enhancement is also observed in $p_{\rm T}$-differential
strange hadron to pion ratios. AMPT predicts strong enhancement in $\phi/\pi$
ratio compared to EPOS4, due to the effective implementation of the Lund
string fragmentation parameters leading to a stronger preference for strange
quark hadronization and may effect the yield of $\phi$ mesons compared to
EPOS4. The larger enhancement in $\Lambda$/$\mathrm{K}^{0}_{\mathrm{S}}$ ratio
at the intermediate-$p_{\rm T}$ region from EPOS4 compared to AMPT might be
attributed to the implementation of full hydrodynamic flow in EPOS4, while
AMPT incorporates some flow effects. The implementation of full hydrodynamic
flow in EPOS4 seems to play an important role and appears to be significantly
more effective in reproducing the experimental data. We observed a clear final
state multiplicity overlap with $pp$, $p+Pb$ and $Pb+Pb$ collisions from both
of the models which is very interesting in our opinion. Our comprehensive
investigation of $O+O$ collisions lays the groundwork for a deeper
understanding of these interactions at LHC energies. Future LHC $O+O$ run with
enhanced detectors and significantly larger datasets will be crucial for
validating and refining these theoretical predictions.

##  V Acknowledgements

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