EPOS LHC-R Model: Global Hadronic Update

• The paper presents a global retuning of the EPOS model that integrates collective hadronization, rescattering, and core-corona adjustments to reconcile collider observables with air shower data.
• The update implements resonance-sector modifications that boost muon production by up to 10% and deepen Xmax by about 25 g/cm², addressing the longstanding muon discrepancy.
• Using a multi-system accelerator dataset, the model unifies midrapidity and forward production predictions, implying a heavier cosmic-ray composition at the highest energies.

EPOS.LHC-R is a new retuning and physics update of the EPOS hadronic interaction model, designed specifically to improve the simultaneous description of collider observables and extensive air shower observables, with special emphasis on the long-standing “muon puzzle.” It is framed as an extension of the “global approach” developed for EPOS4, where the same physical ingredients are applied consistently across systems ranging from $e^+e^-$ to $pp$, $pA$, and $AA$. Its central thesis is that the same accelerator data can still permit different air-shower predictions once one models collective hadronization and rescattering more globally, in particular by changing the correlation between measured midrapidity observables and unmeasured large-rapidity production (Pierog et al., 9 Aug 2025).

1. Lineage within the EPOS family

EPOS.LHC-R belongs to the EPOS line of parton-based, multiple-scattering interaction models, but it should be situated after the public EPOS LHC release rather than identified with the earlier heavy-ion EPOS3 or EPOS4 literature. EPOS LHC was presented as the public LHC-retuned successor of EPOS 1.99, identified in that context as EPOS LHC v3400. Its defining structure combined parton-based Gribov-Regge multiple scattering, parton ladders or cut Pomerons realized as flux tubes or strings, a core-corona separation, and collective hadronization with distinct $pp$-type and $AA$-type radial-flow parametrizations governed by the core mass $M_{\rm core}$ (Pierog et al., 2013).

A later review of ultrahigh-energy cosmic-ray modeling described EPOS-LHC as one of the post-Run-I hadronic interaction models retuned using $pp$ data at 7 and 8 TeV. In that review, the relevant tuning observables were the inelastic $pp$ cross section, central charged-particle multiplicity, forward energy flow or inelasticity, and mean hadron transverse momentum. The retuned models gave improved consistency with collider data, but the total number of muons still remained significantly underestimated and the maximum muon production depth remained overestimated (d'Enterria, 2019).

EPOS.LHC-R is presented against that background as a revised EPOS-LHC-type air-shower model. Its novelty is not only a parameter retune but a coordinated update of hadronization, rescattering, core-corona usage, remnant treatment, and elasticity, all organized around the claim that collider measurements do not uniquely determine the forward hadron production that drives shower development (Pierog et al., 9 Aug 2025).

2. Motivation: the muon puzzle and the midrapidity–forward problem

The immediate motivation for EPOS.LHC-R is the persistent discrepancy between observed and simulated muon production in extensive air showers. The 2025 model paper states that data show more muons, different muon production heights, and tensions with shower-development observables than predicted by standard hadronic models, and it emphasizes the WHISP compilation as evidence that the discrepancy grows with energy (Pierog et al., 9 Aug 2025). Earlier review work had already summarized the problem in similar terms: from about $E_{\rm CR}\gtrsim 10^{17}\ {\rm eV}$, the number of muons is underestimated by about $pp$0 by all models, while the muon production or penetration depth is overestimated (d'Enterria, 2019).

In the EPOS.LHC-R formulation, the central control variable is the ratio $pp$1, defined as the ratio of average electromagnetic to average hadronic energy. A smaller $pp$2 leaves more energy in the hadronic cascade, allowing more generations of hadronic interactions and ultimately more muons. In the idealized pion-only, exact-isospin case, the model paper states that $pp$3; once baryons, kaons, and realistic resonance production are included, $pp$4 decreases and becomes hadronization-model dependent (Pierog et al., 9 Aug 2025).

This motivation was strengthened by post-LHC tests of standard EPOS-LHC. In underground multimuon data from ALICE, EPOS-LHC underpredicted the muon multiplicity distribution by more than $pp$5 over a large multiplicity interval and yielded only $pp$6 of the measured high-muon-multiplicity rate in the iron case (Collaboration, 2024). A more cautious Yakutsk analysis also found a trend toward a muon deficit above $pp$7 EeV, but stated that the discrepancy could not be confirmed decisively because the data remained compatible with a heavy composition and the total uncertainty on the $pp$8 parameter was about $pp$9 (Knurenko et al., 2022). Taken together, these results suggest a genuine model-building problem, but also explain why EPOS.LHC-R is formulated as a revision of standard hadronic physics rather than as a response to a single unambiguous anomaly.

3. Defining updates relative to EPOS LHC

EPOS.LHC-R is presented as a “global approach” update rather than an isolated retune. The model paper states that, relative to EPOS LHC, it restores perfect isospin conservation in the fragmentation step itself, whereas EPOS LHC had slightly broken isospin by assigning different effective masses to $pA$0 and $pA$1 quarks in order to better fit $pA$2 data. At the same time, EPOS.LHC-R enlarges the set of neutral resonances by adding the high-mass states $pA$3 and $pA$4. Because $pA$5 decays feed $pA$6 but not $pA$7, the final observable $pA$8 ratio is shifted upward after decays even though the fragmentation stage is isospin-symmetric (Pierog et al., 9 Aug 2025).

This resonance-sector modification is quantitatively central. The paper states that the change raises the $pA$9 ratio by about $AA$0 relative to the generic “CR model” pattern and leads overall to about $AA$1 more $AA$2 without changing charged $AA$3 yields. Since $AA$4 decays into charged pions rather than feeding the electromagnetic component in the way $AA$5 does, this reduces $AA$6 by about $AA$7 and increases the number of muons by about $AA$8. In the summary, the authors state that, including indirect effects from core-corona and hadronic rescattering, the muon number increases by almost $AA$9 (Pierog et al., 9 Aug 2025).

A second major update is the extension of hadronic rescattering to systems beyond heavy ions. EPOS.LHC-R applies hadronic rescattering, simulated with UrQMD 3.4, in $pp$0 and $pp$1 collisions whenever relevant. The stated effect is rapidity dependent: slow, nearby particles at midrapidity can rescatter, reducing the finally observed yield of heavy resonances such as the $pp$2, whereas at large rapidity particles are too fast and too separated in phase space for this effect to be strong. This gives the model a mechanism to reconcile a larger forward $pp$3 component, important for air showers, with more moderate midrapidity yields compatible with collider data (Pierog et al., 9 Aug 2025).

The model also keeps the EPOS core-corona framework but applies it more strongly and at lower multiplicity than before. In parallel, baryon production from the beam remnant is reduced relative to EPOS LHC in order to better reproduce NA61 data, and beam-particle color transparency is introduced to improve the description of multiplicity fluctuations and elasticity in $pp$4 collisions. A plausible implication is that EPOS.LHC-R does not seek a single “more muons” knob; it redistributes the relative roles of resonances, core-corona hadronization, remnants, and rescattering while preserving the collider description (Pierog et al., 9 Aug 2025).

4. Air-shower predictions and composition implications

The principal air-shower observables emphasized for EPOS.LHC-R are the number of muons at ground, the muon energy spectrum at ground, $pp$5, the inelastic cross section, elasticity, and multiplicity. The model paper uses the plotting normalization

$pp$6

and repeatedly stresses that both fixed-primary muon production and the $pp$7–$pp$8 correlation are relevant for composition inference (Pierog et al., 9 Aug 2025).

Relative to EPOS LHC, EPOS.LHC-R is reported to have a $pp$9-air cross section about $AA$0 lower over the full energy range, elasticity increased by around $AA$1, and multiplicity increased by about $AA$2 at the highest energy only. The increase in elasticity is singled out as especially important: deeper leading-particle propagation increases $AA$3 by about $AA$4, which the paper states is larger than the difference between EPOS LHC and SIBYLL 2.3, and deeper than the new QGSJET-III as well (Pierog et al., 9 Aug 2025).

These changes have direct composition consequences. Because heavier primaries produce shallower showers, a model that predicts deeper $AA$5 for a fixed primary implies a heavier mass composition when fitted to measured $AA$6. The EPOS.LHC-R paper states explicitly that, with this model, the mean logarithmic mass inferred from $AA$7 becomes compatible with iron showers at the highest energies. That in turn reduces the muon deficit relative to data, because a heavier inferred composition naturally produces more muons. The model also predicts more muons at fixed primary type, so the $AA$8–$AA$9 correlation is shifted in what the authors describe as a favorable direction (Pierog et al., 9 Aug 2025).

The same paper is explicit, however, that the discrepancy is reduced but not fully eliminated. It also notes that the changes appear over the full cosmic-ray energy scale, not only at the highest energies, so further studies are needed to understand whether the model captures the observed energy dependence of the muon discrepancy or primarily improves its normalization (Pierog et al., 9 Aug 2025).

5. Accelerator constraints and first applications

EPOS.LHC-R is constrained by a deliberately broad accelerator dataset rather than by a single collider observable. The model paper lists early 7 TeV LHC data used for EPOS LHC, newer and more precise 13 TeV data, lead projectile data, LHCf measurements constraining elasticity and leading-particle energy flow, CMS $M_{\rm core}$0 multiplicity fluctuation data, ALICE indications of stronger collective behavior or core contribution, and NA61 $M_{\rm core}$1 measurements in $M_{\rm core}$2. This multi-system strategy is presented as essential to the “global approach” argument: the same accelerator data can be made compatible with different forward hadron production once collective hadronization and rescattering are treated more globally (Pierog et al., 9 Aug 2025).

A first explicit test of EPOS-LHC-R with KASCADE-Grande describes it as a newly released revision of EPOS-LHC with revisions to proton-proton cross sections, multiplicity of proton-proton and proton-air interactions, nuclear fragmentation processes, and hadronization tuned according to LHC data. That study states that EPOS-LHC-R predicts more muons and a deeper $M_{\rm core}$3 by about $M_{\rm core}$4 relative to EPOS-LHC (Kang et al., 29 Aug 2025).

The KASCADE-Grande result is nevertheless subtle. In the ground-level mass-sensitive variable

$M_{\rm core}$5

EPOS-LHC-R gives a value slightly lower than EPOS-LHC and closer to QGSJet-II-04 and SIBYLL 2.3d. The authors interpret this as showing that, at KASCADE-Grande observation level, the effect of the deeper $M_{\rm core}$6 on the electromagnetic component outweighs the increase in generated muon number. In that first application, the heavy component still exhibits a knee-like structure with

$M_{\rm core}$7

and the paper concludes that EPOS-LHC-R preserves the main KASCADE-Grande spectral structures rather than removing them (Kang et al., 29 Aug 2025).

6. Scope, distinctions, and open issues

A common misconception is to treat EPOS.LHC-R as a generic label for any modern EPOS implementation. The literature summarized here does not support that identification. Heavy-ion femtoscopy papers based on EPOS359 or EPOS3, including source-function studies in $M_{\rm core}$8 GeV Au+Au, explicitly state that they do not discuss an “EPOS LHC-R” model by name; they are RHIC heavy-ion applications of EPOS-family hybrid frameworks with Parton-Based Gribov-Regge initial states, core-corona separation, hydrodynamics, and optional hadronic cascades (Stefaniak et al., 2020, Kincses et al., 2022). Similarly, EPOS-HQ is a heavy-flavor extension built on EPOS3 rather than an LHC-R model, and EPOS4 Pb-Pb prediction papers present EPOS4 heavy-ion phenomenology without defining an EPOS LHC-R variant (Gossiaux et al., 2019, Koley et al., 12 Jan 2026).

The current EPOS.LHC-R picture is therefore specific: it is an air-shower-oriented revision of EPOS-LHC grounded in the EPOS global approach, not a synonym for EPOS3, EPOS4, EPOS359, or EPOS-HQ. Its distinguishing idea is that collective hadronization, hadronic rescattering, and resonance content can change the mapping between collider observables at midrapidity and the forward hadron production that controls shower development (Pierog et al., 9 Aug 2025).

The model also carries explicit limitations. The 2025 EPOS.LHC-R paper provides no formal uncertainty band or parameter error propagation, and it acknowledges that the muon discrepancy is reduced but not fully eliminated (Pierog et al., 9 Aug 2025). The first KASCADE-Grande application further states that the EPOS-LHC-R spectra shown there are still raw, not yet unfolded for shower-to-shower fluctuations, even though the main spectral features appear robust (Kang et al., 29 Aug 2025). This suggests that EPOS.LHC-R should be regarded as a substantive but still evolving intervention in post-LHC hadronic interaction modeling rather than as a final resolution of the muon puzzle.