EPOS-LHC-R: Revised EPOS Hadronic Model

• EPOS-LHC-R is a retuned version of the EPOS-LHC model that recalibrates forward particle production to better match cosmic-ray air-shower observations.
• The retune adjusts hadronization processes, elasticity, and cross sections to address the muon deficit seen in previous air-shower simulations.
• Validation against accelerator and cosmic-ray data shows deeper shower maxima and increased muon yields, improving overall model consistency.

Searching arXiv for papers on EPOS-LHC-R and related EPOS-LHC work. EPOS-LHC-R is a revised, post-LHC retune of the EPOS-LHC hadronic interaction model, developed within the EPOS global approach to describe reactions from $e^+e^-$ to $pp$, $p$–$A$, and $A$–$A$, with particular emphasis on the forward particle production that controls extensive air shower development. It inherits the EPOS-LHC framework of multiple scattering, string-based initial conditions, core–corona separation, and collective hadronization, but reworks the correlation between collider observables at mid-rapidity and forward production relevant to cosmic-ray cascades. In the historical record, the reference EPOS-LHC tune is EPOS-LHC v3400; the original EPOS-LHC paper does not define a variant named “EPOS-LHC-R,” so the explicit “-R” label belongs to later revised retunes rather than to the baseline v3400 itself (Pierog et al., 2013, Pierog et al., 9 Aug 2025).

1. Definition, lineage, and nomenclature

EPOS originated as a Monte Carlo event generator for minimum-bias hadronic interactions, with applications to $pp$, $p$–$A$, $A$–$pp$0, and cosmic-ray air-shower simulations. The EPOS-LHC tune, described as version v3400, was a public, stable release derived from EPOS 1.99 and retuned to LHC minimum-bias data. Its underlying architecture remained the Parton-Based Gribov–Regge picture in which events are built from multiple elementary scatterings represented by cut Pomerons, implemented as longitudinal color flux tubes that later fragment or hadronize collectively (Pierog et al., 2013).

The designation “EPOS-LHC-R” is therefore not part of the original EPOS-LHC definition. In later usage, particularly in cosmic-ray and shower-reconstruction studies, the label denotes a revised, post-LHC hadronic interaction model tested against KASCADE-Grande data and contrasted with QGSJet-II-04, EPOS-LHC, and SIBYLL 2.3d. In that later sense, EPOS-LHC-R is not a new microscopic framework disconnected from EPOS-LHC; it is a retuned continuation of EPOS-LHC with updated proton–proton, proton–air, and nuclear-fragmentation treatments, intended to improve the simultaneous description of shower maximum and muon production (Kang et al., 29 Aug 2025).

A recurrent source of confusion is the relation between EPOS-LHC and EPOS-LHC-R. The baseline EPOS-LHC tune is the model validated against LHC minimum-bias data and used broadly in collider and air-shower simulations; EPOS-LHC-R is the subsequent revision that modifies how the same global EPOS framework maps accelerator constraints into forward particle production and air-shower observables. This suggests that “-R” should be read as a retune of a known model family rather than as a separate generator line.

2. Baseline EPOS-LHC framework inherited by EPOS-LHC-R

The retune remains grounded in the EPOS-LHC architecture. EPOS is based on Parton-Based Gribov–Regge theory, with multiple scattering and energy–momentum sharing among parallel ladders in the Drescher–Werner formalism. Nonlinear screening corrections are used to control the high-energy growth of cross sections and multiplicities. Initial conditions are built from strings rather than from partons, and an early-time density criterion separates the event into a dense core and a dilute corona (Pierog et al., 2013).

Core formation is determined at an early proper time $pp$1 by counting string segments per unit volume. If the local segment density exceeds a critical threshold $pp$2, a core forms; otherwise the region is treated as corona. In each $pp$3 bin, dense clusters are identified in $pp$4 cells, and the cluster mass is computed from the segment four-momenta as

$pp$5

Core clusters hadronize microcanonically with collective longitudinal and radial flow while conserving energy, momentum, and flavor; corona regions hadronize through standard string fragmentation.

EPOS-LHC introduced a complete reparametrization of collective flow. The relevant rapidities depend only on the geometry and on the amount of secondary particles entering the core, quantified by $pp$6, and not explicitly on beam species or $pp$7. The onset of flow is fixed by $pp$8. The longitudinal and radial flow parametrizations are

$pp$9

$p$0

$p$1

with a smooth $p$2 transition for $p$3–$p$4 based on the contribution of the most active nucleon–nucleon pair. The transverse expansion velocity is related to the radial rapidity by $p$5.

A further structural element is the explicit handling of high-$p$6 segments. EPOS-LHC introduces a cutoff $p$7 such that soft segments with $p$8 are absorbed into the core, whereas hard segments with $p$9 survive as jet fragments after losing energy according to system size. The best value quoted for this cutoff is $A$0. These baseline mechanisms—core–corona separation, collective hadronization, and explicit soft–hard partition—remain the conceptual substrate on which EPOS-LHC-R is built.

3. Retuning principles and specific modifications in EPOS-LHC-R

EPOS-LHC-R was introduced in response to the persistent “muon puzzle”: LHC-informed hadronic interaction models improved consistency relative to pre-LHC generations, yet still failed to reproduce air-shower data in $A$1 and muon production jointly. The retune uses the EPOS global approach to alter the correlation between measured mid-rapidity collider data and the predicted particle production at large rapidities, which drive air-shower development (Pierog et al., 9 Aug 2025).

The retune is constrained by several data classes. At the hadronization level it uses global $A$2 hadron yields and isospin constraints; at low energy it uses NA61/SHINE $A$3 data at $A$4, especially forward $A$5 production versus $A$6; at the LHC it uses LHCf leading neutral production to constrain elasticity and pion-exchange contributions, CMS $A$7–Pb multiplicity fluctuations to constrain fluctuations of elasticity via color transparency, and $A$8–air inelastic cross-section trends compared to PDG data.

Several modifications are stated explicitly.

Aspect	EPOS-LHC-R change	Stated consequence
Corona fragmentation	Isospin symmetry enforced; $A$9 and $A$0 added	Neutral/charged resonance balance revised
Hadronic rescattering	UrQMD applied where phase space allows	Mid-rapidity resonance yields reduced
Final $A$1 content	About $A$2 more $A$3 than $A$4 in final state	$A$5 lowered by roughly $A$6; $A$7 increased by around $A$8
Elasticity in $A$9–air	Increased by about $A$0 relative to EPOS-LHC	$A$1 deepened
$A$2–air inelastic cross section	Reduced by roughly $A$3 versus EPOS-LHC	Deeper shower development
Multiplicity	Increased by about $A$4 at the highest energies only	Larger secondary production

The retune also reduces baryon production from beam remnants relative to EPOS-LHC in order to better match NA61 forward baryons. Taken alone, that change would decrease muon production, but the larger core fraction at lower multiplicity partly compensates via increased charged-hadron production. Likewise, color transparency in $A$5–$A$6 introduces event-by-event fluctuations linking low multiplicity to high elasticity and high multiplicity to lower elasticity, improving the description of multiplicity fluctuations and the correlation between leading-particle energy and mid-rapidity activity.

The kinematic variables emphasized in this reformulation are the usual rapidity,

$A$7

pseudorapidity,

$A$8

Feynman-$A$9,

$pp$0

leading energy fraction $pp$1, inelasticity $pp$2, and the cascade energy-flow parameter $pp$3, defined as the ratio of average electromagnetic to average hadronic energy. In EPOS-LHC-R, larger forward elasticity and a reduced effective $pp$4 fraction decrease $pp$5, leaving more energy in the hadronic channel and thereby increasing the muon yield.

4. Consequences for air-shower development

The central air-shower consequences of EPOS-LHC-R are a deeper shower maximum and a higher muon yield. The retune predicts $pp$6 values deeper by about $pp$7 relative to EPOS-LHC for proton-induced showers, with an even larger shift for iron. This is attributed primarily to the roughly $pp$8 increase in elasticity, together with the modest reduction of the $pp$9–air inelastic cross section. Relative to other contemporary models, EPOS-LHC-R is stated to give deeper $p$0 than Sibyll 2.3 and deeper than the latest QGSJet-III (Pierog et al., 9 Aug 2025).

For the muon component, the retune modifies the hadronic-to-electromagnetic energy balance in the first generations of the cascade. The enhancement of final-state $p$1 relative to $p$2 reduces electromagnetic leakage through $p$3 production and lowers $p$4 by roughly $p$5. The resulting increase in $p$6 is around $p$7 at fixed energy, and up to nearly $p$8 when indirect multiplicity effects from the larger core fraction are included. The paper frames this within Heitler–Matthews scaling,

$p$9

with the retune effectively increasing the charged fraction per generation and reducing the energy transferred to the electromagnetic channel.

The change in $A$0 also affects composition inference. For a given measured $A$1, the deeper baseline predicted by EPOS-LHC-R implies a heavier composition interpretation than EPOS-LHC. This is a central reason the retune improves the consistency of the $A$2–$A$3 plane: heavier inferred composition raises the expected muon content while the model simultaneously produces more muons intrinsically.

A subtle detector-level consequence appears at the KASCADE-Grande observation level near sea level. Although EPOS-LHC-R generates more muons overall, the larger electromagnetic component associated with the deeper $A$4 increases $A$5 relatively more than $A$6. As a result, the ground-level muon fraction encoded by

$A$7

is slightly smaller than in EPOS-LHC and closer to QGSJet-II-04 and SIBYLL 2.3d in that specific detector context (Kang et al., 29 Aug 2025).

5. Validation, first applications, and empirical status

The validation strategy for EPOS-LHC-R is explicitly multi-scale. At the accelerator level, the retune is constrained simultaneously by global $A$8 hadronization, NA61 $A$9 forward $A$0, LHCf leading neutral production, CMS $A$1–Pb multiplicity fluctuations, and $A$2–air cross-section trends. A key point is that hadronic rescattering reduces resonance yields only in the slow, mid-rapidity region, leaving forward production largely unaffected; this allows the model to reproduce forward $A$3 without overproducing it at mid-rapidity (Pierog et al., 9 Aug 2025).

The first explicit KASCADE-Grande test of EPOS-LHC-R uses about $A$4 million events over $A$5 days. Simulations were performed in CORSIKA for five primaries ($A$6, He, C, Si, Fe) from $A$7 to $A$8 eV and zenith angles $A$9–$pp$00, with events generated at spectral index $pp$01 and reweighted to $pp$02. Mass-group separation is done event-by-event with the attenuation-corrected variable $pp$03; for EPOS-LHC-R the heavy–light decision boundary is $pp$04. Energy calibration uses $pp$05 only, through

$pp$06

with $pp$07, $pp$08 for the heavy group and $pp$09, $pp$10 for the light group. Shower-to-shower fluctuations are corrected through a response matrix $pp$11 and iterative Bayesian unfolding, with forward model

$pp$12

The stated effect of unfolding is below $pp$13 in all energy bins (Kang et al., 29 Aug 2025).

In the heavy component, all post-LHC models show a knee-like break just below $pp$14 eV. For EPOS-LHC-R, using the raw spectrum, the fitted parameters are

$pp$15

All models also show a gradual ankle-like hardening in the light component beginning around $pp$16 eV. EPOS-LHC-R yields a slightly higher heavy-component flux than EPOS-LHC and a lower light-component flux at lower energies, while above $pp$17 eV the two EPOS variants are very similar.

The empirical motivation for this retune is the documented shortfall of EPOS-LHC in air-shower muon observables. In ALICE Run 2 multimuon data, EPOS-LHC underpredicts the muon multiplicity distribution by about $pp$18 even for iron primaries across much of $pp$19, and its iron prediction for the high-muon-multiplicity rate is only about $pp$20 of the measured value (Collaboration, 2024). Yakutsk data at $pp$21 EeV similarly motivate further tuning: up to about $pp$22 EeV EPOS-LHC brackets the muon density when proton and iron are used as composition extremes, but above that energy the data trend toward higher muon densities and the authors call for further tuning of EPOS-LHC and QGSjetII-04 (Knurenko et al., 2022).

6. Interpretation, limitations, and unresolved issues

EPOS-LHC-R is best understood as an attempt to solve the muon puzzle by changing the mapping between accelerator-constrained hadronization and the forward production that governs air showers, not by abandoning the EPOS framework. The model’s stated gains come from a coordinated change in resonance content, hadronic rescattering, remnant treatment, elasticity, and cross sections, all within a single Gribov–Regge and core–corona description. This suggests that the decisive issue is not only the absolute normalization of collider observables, but also the correlation structure between mid-rapidity and forward phase space (Pierog et al., 9 Aug 2025).

At the same time, the model is not presented as fully closing the problem. Remaining uncertainties explicitly include diffractive channels and pion-exchange contributions, $pp$23–air and Fe–air extrapolations, remnant excitation, color transparency, and the treatment of strangeness, charm, and minijets. Residual discrepancies at the highest energies are stated to persist, and further joint analyses of $pp$24, $pp$25, and muon spectra are still needed. In the KASCADE-Grande study, the EPOS-LHC-R spectra shown are raw rather than unfolded, so small changes are expected once unfolding is applied (Kang et al., 29 Aug 2025).

A second limitation is historical and terminological. Because the original EPOS-LHC publication does not define a model called EPOS-LHC-R, uses of the suffix “-R” outside the later dedicated retune papers can remain implementation-specific. The stable reference for the baseline model is EPOS-LHC v3400, whereas EPOS-LHC-R denotes the later revised tune explicitly aimed at improving air-shower consistency.

A final misconception is that a higher absolute muon yield must imply a larger ground-level muon fraction in every detector configuration. KASCADE-Grande shows that this is not generally true: the deeper $pp$26 predicted by EPOS-LHC-R increases the electromagnetic component sufficiently that $pp$27 can grow more than $pp$28 at the observation level, shifting $pp$29 slightly downward even while the model produces more muons in the cascade as a whole. EPOS-LHC-R is therefore best characterized not by a single monotonic change in “muon richness,” but by a global retuning of shower development, composition inference, and ground-observable correlations.