Strangeness Enhancement in Hadronic Collisions

• Strangeness enhancement is defined as the relative increase in strange hadron production with greater system size, multiplicity, and centrality, reflecting complex QGP and hadronization dynamics.
• Canonical suppression, rope hadronization, and core-corona separation are key methodologies used to model the observed enhancement trends across diverse collision systems and energies.
• Event topology and rapidity-resolved studies indicate that both soft underlying processes and jet-correlated interactions contribute distinctively to the enhanced strange-hadron yields.

Strangeness enhancement scenario denotes the class of observations and models in which the relative production of strange hadrons increases as the produced system becomes larger, denser, more central, or more multiplicity-rich. In its historical heavy-ion form, it was proposed as a signature of QGP formation, because strange quarks are produced during the collision and their yields can encode the collision dynamics; in its modern form, it also encompasses exact-strangeness-conservation effects in small systems, core-corona separation, rope and closepacking modifications of string fragmentation, rapidity- and jet-resolved observables, and even forward kaon-over-pion modifications in UHECR air-shower phenomenology (Collaboration et al., 2010, Cleymans et al., 2020, Koley et al., 28 Aug 2025, Ohashi et al., 28 Sep 2025).

1. Heavy-ion origin and canonical formulation

The canonical heavy-ion formulation compares strange-hadron yields in nucleus-nucleus collisions to an elementary baseline, normalized by participant measures. In the NA57 study of Pb-Pb and p-Be interactions at $40\,A\,\mathrm{GeV}/c$, the enhancement is defined as

$$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$

where $Y$ is the yield per event extrapolated to one unit of rapidity around mid-rapidity and the full measured $m_T$ range. That study established the classic hierarchy: the enhancement increases with the strangeness content of the hyperons and with the centrality of collision; $K^0_S$ and $\Lambda$ show comparable enhancements, $\Xi^-$ is enhanced more strongly and reaches roughly an order of magnitude in the most central collisions, and $\Omega^-+\bar{\Omega}^+$ also show very large enhancement, while $\bar{\Lambda}$ remains an exception with no clear enhancement and no strong centrality trend (Collaboration et al., 2010).

The same work also sharpened the energy-systematics statement. At $40\,A\,\mathrm{GeV}/c$, the centrality dependence of the Pb-Pb yields and enhancements is steeper than at $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$0, and for the most central classes the measured enhancements for $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$1, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$2, and $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$3 are larger at 40 than at 158 $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$4. This made explicit that the enhancement magnitude is not simply monotonic with beam energy, even though the hierarchy with strangeness content persists across SPS and RHIC energies (Collaboration et al., 2010).

A related reformulation replaces wounded-nucleon scaling by constituent-quark scaling. In the nuclear overlap analysis of $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$5, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$6, and $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$7, the usual participant-normalized enhancement grows monotonically with centrality, but the same observable becomes approximately centrality independent at top RHIC energy when normalized to the number of constituent quark participants, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$8. When further normalized to the strangeness content, it becomes approximately strangeness independent at RHIC, whereas only weak $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$9-scaling and violated strangeness scaling are found at top SPS energy. This was interpreted as evidence that partonic degrees of freedom dominate at RHIC, while SPS energies correspond to a coexistence of hadronic and partonic phases (Behera et al., 2012).

A chemically non-equilibrated freeze-out variant appears in the multicomponent HRGM with $Y$0. There the strange-sector density is modified as

$Y$1

and the best fits yield $Y$2 below about $Y$3, with quoted low-energy enhancement around $Y$4. The same framework gives $Y$5 for 111 independent hadron yield ratios at 14 beam energies and improves the description of the Strangeness Horn, reaching $Y$6, while leaving the multi-strange baryons and antibaryons insufficiently described (Sagun et al., 2014).

2. Canonical suppression, thermal limits, and core-corona dynamics

In small systems, the most widely used statistical explanation is canonical suppression from exact strangeness conservation. In the HRG treatment of multiplicity dependence in pp, p-Pb, and Pb-Pb, the grand-canonical yield

$Y$7

is replaced by a canonical partition function

$Y$8

so that strange particles must be produced with compensating strange partners. For kaons the suppression factor is

$Y$9

and for a hadron with strangeness $m_T$0,

$m_T$1

The physical content is that the suppression becomes stronger with increasing $m_T$2, so $m_T$3 is most suppressed at low multiplicity and therefore shows the largest enhancement trend as multiplicity increases. With hadronic interactions included through the S-matrix kernel

$m_T$4

the same framework quantifies ALICE multiplicity-dependent data at a universal freeze-out temperature $m_T$5, consistent with the chiral-crossover temperature; it also reports about a $m_T$6 reduction in proton yield and a $m_T$7 enhancement in $m_T$8 yield relative to the simpler HRG treatment (Cleymans et al., 2020).

A dynamical realization of finite-size and conservation effects is provided by EPOS4. In that framework, multiple partonic scatterings generate flux tubes that are separated into a dense core and a dilute corona. The core is evolved with $m_T$9D viscous hydrodynamics using $K^0_S$0, hadronizes on a fixed energy-density hypersurface

$K^0_S$1

corresponding to $K^0_S$2 MeV, and is followed by hadronic rescattering through UrQMD, while the corona hadronizes through standard string fragmentation. The central claim is that microcanonical core hadronization enforces exact conservation of energy, momentum, baryon number, charge, and strangeness over the full hadronization hypersurface, so small core droplets suppress strange and especially multi-strange hadrons, whereas increasing multiplicity makes the results approach the GCE limit (Koley et al., 28 Aug 2025).

In that EPOS4 picture, the most direct enhancement observables are the integrated strange-to-pion ratios

$K^0_S$3

which rise with $K^0_S$4 from pp to p-Pb. The rise is hierarchical,

$K^0_S$5

and the steepest enhancement appears in pp, while pp and p-Pb converge when plotted versus multiplicity. The core fraction grows with multiplicity; for multi-strange hadrons it exceeds $K^0_S$6 of the total yield at high multiplicity, and for $K^0_S$7 it can contribute $K^0_S$8 even in peripheral events and up to $K^0_S$9 in some intermediate-$\Lambda$0 regions. At the same time, the model retains quantitative tensions: intermediate-$\Lambda$1 discrepancies can reach about $\Lambda$2, $\Lambda$3 is underestimated, $\Lambda$4 is sometimes overestimated, $\Lambda$5 is overestimated, and the self-normalized strange-hadron yields rise too nearly linearly compared with data (Koley et al., 28 Aug 2025).

3. Multiplicity-driven enhancement in small systems and string-based mechanisms

ALICE established that, at the LHC, strange-hadron-to-pion yield ratios rise with increasing charged-particle multiplicity at midrapidity across pp, p-Pb, and Pb-Pb, largely independently of collision energy and system size. In small systems, the same program has been extended from mean yields to full event-by-event multiplicity distributions $\Lambda$6 in pp at $\Lambda$7 TeV. Those measurements reach up to 7 $\Lambda$8, 5 $\Lambda$9, 4 $\Xi^-$0, and 2 $\Xi^-$1 per event, show that the probability of observing $\Xi^-$2 strange hadrons increases with multiplicity, and that the difference between low- and high-multiplicity classes becomes more pronounced at larger $\Xi^-$3, indicating a stronger-than-linear growth in the high-multiplicity tail. The distributions are well described by a Negative Binomial Distribution, and model agreement worsens as the number of strange particles in the event increases (Pucillo, 18 Jun 2026).

The same event-by-event program isolates effects not fixed by total strangeness alone. Ratios with balanced strangeness content, such as $\Xi^-$4, still show nontrivial multiplicity dependence, and the comparison to PYTHIA 8 Monash, PYTHIA 8 QCD-CR Ropes, and EPOS LHC indicates that the production rate of strange quarks remains difficult to model even when color-reconnection mechanisms capture some of the $\Xi^-$5 observables. A closely related ALICE analysis emphasized that present QCD-based models only partially reproduce the observed patterns and that canonical suppression, rope hadronization with colour reconnection, and core-corona models each capture only parts of the phenomenon (Collaboration, 13 Nov 2025, Pucillo, 3 Apr 2025).

String-based microscopic scenarios replace thermal suppression by enhanced string tension in dense events. In rope hadronization, overlapping Lund strings form higher color multiplets whose effective tension obeys a Casimir-scaling-inspired relation, and pair production follows a Schwinger-like form

$\Xi^-$6

As $\Xi^-$7 grows, the suppression of strange quarks and diquarks weakens, so strange-meson and baryon yields increase coherently with average charged central multiplicity $\Xi^-$8 across pp, pPb, and PbPb. This reproduces the overall rise of strange-hadron enhancement qualitatively, but in PbPb the model tends to overshoot baryonic yields at high multiplicity, motivating additional ingredients such as colour reconnections and string shoving (Bierlich et al., 2022).

A fluctuation-based variant attributes the effect to event-by-event fluctuations of the string tension. Starting from

$\Xi^-$9

with a Gaussian distribution of $\Omega^-+\bar{\Omega}^+$0, the averaged spectrum becomes exponential in $\Omega^-+\bar{\Omega}^+$1. Fits to ATLAS charged-hadron $\Omega^-+\bar{\Omega}^+$2 spectra in pp at $\Omega^-+\bar{\Omega}^+$3 TeV over $\Omega^-+\bar{\Omega}^+$4 give $\Omega^-+\bar{\Omega}^+$5 and $\Omega^-+\bar{\Omega}^+$6 as $\Omega^-+\bar{\Omega}^+$7 increases from $\Omega^-+\bar{\Omega}^+$8 to $\Omega^-+\bar{\Omega}^+$9, while the inferred $\bar{\Lambda}$0 ratio rises from $\bar{\Lambda}$1 to $\bar{\Lambda}$2. Fed into PYTHIA 8.235 string decay, this produces the hierarchy $\bar{\Lambda}$3 in strange-hadron enhancement (Pirner et al., 2018).

A related momentum-space implementation is string closepacking in PYTHIA 8.3. There the modified suppression is written as

$\bar{\Lambda}$4

so overlapping strings create a background field with larger effective tension $\bar{\Lambda}$5, reducing strangeness suppression. The Trieste tunes combine closepacking with popcorn destructive interference and strange junctions; they improve the description of $\bar{\Lambda}$6, $\bar{\Lambda}$7, and $\bar{\Lambda}$8 relative to Monash and default Rope Hadronization, while the $\bar{\Lambda}$9 ratio and the shape of the $40\,A\,\mathrm{GeV}/c$0 spectra remain challenging (Altmann et al., 30 Apr 2026).

Generator-level pp studies at lower energy reproduce the same qualitative trend. A PYTHIA 8.309 analysis at $40\,A\,\mathrm{GeV}/c$1 reports that high-multiplicity events yield more $40\,A\,\mathrm{GeV}/c$2, $40\,A\,\mathrm{GeV}/c$3, $40\,A\,\mathrm{GeV}/c$4, and $40\,A\,\mathrm{GeV}/c$5 than low-multiplicity events, quoting high-to-low production ratios of approximately $40\,A\,\mathrm{GeV}/c$6, $40\,A\,\mathrm{GeV}/c$7, $40\,A\,\mathrm{GeV}/c$8, and $40\,A\,\mathrm{GeV}/c$9, respectively, and interprets the low- and intermediate-$$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$00 enhancement together with high-$$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$01 suppression as QGP-like behavior in pp collisions (Hamed et al., 2024).

4. Rapidity-dependent and quark-content-resolved scenario

The rapidity-dependent extension asks whether enhancement is uniform in $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$02 and whether it depends on hadron quark content. In UrQMD-3.3 at FAIR energies, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$03 collisions at $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$04 GeV show a strong rapidity dependence of the enhancement factor. The analysis distinguishes hadrons containing at least one leading quark, such as $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$05, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$06, and $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$07, from hadrons containing only produced quarks, such as $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$08, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$09, and ideally $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$10. The conventional reference definition is

$$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$11

but the study itself uses a centrality-based ratio of yield per produced pion in central to peripheral collisions (Dey et al., 2015).

The central finding is that $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$12 is not flat. For particles containing leading quarks, the enhancement is maximum at mid-rapidity; for particles consisting only of produced quarks, it is minimum at mid-rapidity and rises away from mid-rapidity. $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$13 is special: a rise-and-fall shape is seen, but with a dip near mid-rapidity. This difference is traced to the centrality dependence of the rapidity width and, through it, to the rapidity distribution of net-baryon density. For leading-quark hadrons, the rapidity width increases as collisions become more peripheral; for produced-quark hadrons it tends to decrease with decreasing centrality (Dey et al., 2015).

The link to baryon transport is made explicit through $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$14 as a proxy for baryon stopping. Its width decreases from central to peripheral collisions, consistent with baryon transport toward larger $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$15. At $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$16 GeV, where net-baryon density is largest near mid-rapidity, hadrons with leading quarks track the baryon-rich region, whereas produced-quark hadrons respond differently to the size of the central fireball and to secondary dynamics. This makes rapidity-resolved enhancement a probe of baryon-rich matter rather than a single global number (Dey et al., 2015).

The $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$17 case further shows how reaction channels can blur the leading/non-leading distinction. In UrQMD, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$18 production is influenced by $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$19, and because $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$20 and $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$21 contain leading quarks, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$22 inherits some leading-quark-like behavior. When these $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$23 channels are switched off, the rise-and-fall pattern disappears and the mid-rapidity minimum becomes more evident. Turning off baryon-antibaryon annihilation has little effect on leading-quark hadrons, but it strongly increases the mid-rapidity values for produced-quark hadrons, sometimes changing suppression $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$24 into enhancement $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$25, while leaving the overall mid-rapidity minimum intact (Dey et al., 2015).

5. Event structure, soft production, and jet-correlated enhancement

In small systems, a central controversy concerns whether the enhancement is generated by hard jets or by soft underlying-event activity. ALICE addressed this with ZDC-based effective-energy selections and with the separation of toward-leading and transverse-to-leading regions in pp. The reported pattern is that self-normalized strange-hadron yields divided by the average charged-particle multiplicity increase with multiplicity and are anti-correlated with very forward energy; at fixed multiplicity, strangeness enhancement persists and still correlates strongly with effective energy. In the soft-hard separation, full and transverse-to-leading yields increase with multiplicity, whereas toward-leading yields show very mild or no dependence on midrapidity multiplicity. This led to the conclusion that the increased relative strangeness production emerges from the growth of the underlying event and that soft processes are the dominant contribution to strange hadron production and strangeness enhancement (Bhasin et al., 2022).

A dedicated h-$$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$26 correlation measurement in p-Pb at $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$27 TeV sharpened this distinction. Using a high-$$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$28 trigger hadron with $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$29 GeV/$$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$30 as a jet proxy, the analysis decomposes near-side jet, away-side jet, and underlying-event yields. The $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$31 proxy ratio, constructed from $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$32, is much larger in the underlying event than in the jets; in both momentum intervals the UE ratio exceeds the jet ratio by about $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$33. As multiplicity increases, the fraction of the total hadron yield coming from jets decreases from $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$34 to $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$35 in the lower-$$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$36 range and from $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$37 to $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$38 in the higher-$$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$39 range, so high-multiplicity events become dominated by underlying-event production. PYTHIA8 reproduces the jet-region ratios at low multiplicity reasonably well but underpredicts the UE and total ratios by roughly a factor of 3 (Collaboration, 2024).

In heavy-ion collisions, jet-resolved strangeness enhancement has been proposed as a medium-response observable. In the AMPT string-melting setup, Pb+Pb and $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$40 collisions at $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$41 TeV are analyzed with anti-$$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$42 jets reconstructed by FastJet, using $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$43, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$44 GeV, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$45, and a partonic cross section of $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$46 mb. The observables are jet-correlated $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$47, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$48, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$49, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$50, and $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$51, extracted from mixed-event-corrected and side-band-subtracted jet-particle correlations. All of these ratios are larger around quenched jets in Pb+Pb than in $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$52, the enhancement grows with centrality, is stronger at larger radial distance from the jet axis, and for $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$53, $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$54, and $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$55 peaks at intermediate $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$56. The interpretation is a chain of jet-QGP interaction, jet-induced medium excitation, partial thermalization, and coalescence hadronization, rather than modified fragmentation alone (Luo et al., 2024).

Taken together, these results support a bifurcated picture. In pp and p-Pb, the dominant driver of multiplicity-dependent strangeness production is the soft underlying event; in Pb+Pb, additional enhancement can be localized around quenched jets as a signature of medium response. This suggests that the same hadrochemical observable can diagnose very different microscopic mechanisms depending on system size and kinematic selection (Bhasin et al., 2022, Luo et al., 2024).

6. Domain of validity, external applications, and unresolved issues

The scenario does not appear universal across all reaction types. In $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$57 annihilation, the proposed control variable is the initial parton density in the transverse plane. Using a Statistical Hadronization Model with a suppression factor $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$58, the analysis argues that strangeness saturation requires roughly $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$59, corresponding to $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$60, whereas LEP and lower-energy $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$61 data correspond to only $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$62. The paper therefore concludes that there is no strangeness enhancement and no flow-like effect at currently available $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$63 energies, and estimates that suppression might begin to disappear only around $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$64 and $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$65 TeV (Castorina et al., 2020).

A different extension appears in the UHECR muon puzzle, where the strangeness enhancement scenario means increasing kaon production at the expense of pions in forward, high-energy hadronic interactions. The strangeball model retains only the pion-kaon swapping part of an earlier fireball picture and finds that the successful solutions require no extra inelasticity enhancement, but roughly $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$66 of interactions to be strangeballs at Tevatron and LHC energies, corresponding to a $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$67 increase of the average fraction of energy retained in the hadronic cascade. LHCf does not directly exclude this, while LHCb already suggests tension and motivates a stringent test at 14 TeV (Manshanden et al., 2022).

A more differential collider-to-air-shower framework then parameterizes the swapped pion fraction as

$$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$68

applied only above thresholds in projectile energy and forward energy fraction. Using MCEQ response matrices, the dominant phase space for the muon yield is identified as projectile energies above $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$69 GeV and $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$70. The same study finds that direct tests become possible if LHCb reaches $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$71 precision on the $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$72 ratio and FASER $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$73; under a null result, nearly the entire Auger-compatible parameter space is excluded at $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$74, except very high-threshold scenarios (Ohashi et al., 28 Sep 2025).

Within collider phenomenology itself, the remaining issue is not whether enhancement exists, but which mechanism dominates in which regime. Heavy-ion data retain the original hierarchy and centrality dependence, but no single conventional hadronic model fully reproduces the magnitudes and steepness of the SPS enhancements (Collaboration et al., 2010). Small-system data show smooth multiplicity scaling, yet present models remain incomplete: rope, core-corona, canonical, and color-reconnection scenarios each reproduce selected trends while missing others, and the full event-by-event $$E=\left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{Pb-Pb}} \Bigg/ \left(\frac{Y}{\langle N_{\mathrm{wound}}\rangle}\right)_{\mathrm{p-Be}},$$75 measurements make those deficiencies more visible (Pucillo, 3 Apr 2025, Pucillo, 18 Jun 2026).

This suggests a modern, composite definition of the strangeness enhancement scenario. It is no longer a single observable or a unique QGP signature, but a family of chemically sensitive probes whose interpretation depends on rapidity, centrality, system size, event topology, effective energy, and hadronization mechanism. The persistent empirical regularities are the rise of strange-to-non-strange production with multiplicity or system density, and the stronger response of multi-strange hadrons; the open problem is the microscopic decomposition of that pattern into canonical constraints, collective core formation, string-field amplification, coalescence, and medium response.