EPOS-LHC: Post-LHC Hadronic Model

• EPOS-LHC is a Monte-Carlo event generator that simulates hadronic interactions and cosmic-ray air showers using a parton-based Gribov-Regge and core–corona approach.
• The model is retuned with LHC Run 1 data, employing distinct pp and AA flow parametrizations to accurately reproduce multiplicity distributions and identified-hadron yields.
• EPOS-LHC is widely used in extensive air-shower simulations, though it underestimates ground-level muon counts by around 30%, highlighting ongoing tuning challenges.

EPOS-LHC is the post-LHC update of the EPOS hadronic interaction model, released as EPOS-LHC (v3400), and used for minimum-bias hadronic interactions, heavy-ion interactions, and cosmic-ray air-shower simulations. In the LHC-era formulation, it is an evolved Monte-Carlo event generator built on Parton-Based Gribov Regge Theory and on a parton-based Gribov-Regge multiple scattering picture in which parton ladders are split into color strings. Its defining feature is a core–corona organization of particle production together with collective hadronization, with distinct flow parametrizations for small high-density cores in $p$-$p$ and large-volume cores in heavy-ion collisions; these parametrizations depend on the geometry and the amount of secondary particles entering the core and not on the beam mass or energy (Pierog et al., 2013, Calcagni et al., 2017).

1. Theoretical framework and model architecture

EPOS-LHC descends from the EPOS line of hadronic models that treat hadron–hadron and hadron–nucleus collisions through multiple Pomeron exchanges, understood as effective representations of QCD parton cascades. In this picture, particle production proceeds through both the decay of the hadronic remnant and the hadronization of a cut Pomeron, the latter acting as color strings with quarks, antiquarks, or diquarks as ends. The broader EPOS framework also emphasizes exact energy conservation in both cross-section calculations and particle production, and it includes off-shell remnants as explicit sources of baryon-rich final states (Pierog et al., 2010, Calcagni et al., 2017).

The post-LHC update retained the model’s core–corona separation while revising the treatment of collective hadronization. Regions where string segment density exceeds a critical threshold form a core, whereas low-density regions remain corona and fragment through conventional string dynamics. In EPOS-LHC, the total mass of the core, $M_{\rm core}$, is the key organizing variable for collective flow. The model introduces separate “pp flow” and “AA flow” parametrizations, reflecting the distinction between a small volume with high density of thermalized matter in $p$-$p$ and a large volume produced in heavy-ion collisions. A smooth transition between these regimes is part of the model design and was identified as testable with $p$-Pb data (Pierog et al., 2013).

This architecture has direct phenomenological consequences. Diquark string ends enhance forward baryon and antibaryon production, a feature that is important in extensive air-shower modeling because baryon production feeds the hadronic cascade and thus the final muon content. A plausible implication is that EPOS-LHC’s collider and cosmic-ray applications are linked by the same forward-physics sector rather than by independent phenomenological modules (Calcagni et al., 2017, 0905.1198).

2. LHC retuning and minimum-bias collider phenomenology

EPOS-LHC was introduced as a post-LHC update of EPOS 1.99, with the retuning constrained by LHC Run 1 measurements. The update incorporated total, elastic, and inelastic proton–proton cross-sections from TOTEM and ATLAS, together with $p$-Pb and Pb-Pb yield measurements from ALICE and ATLAS. In the same retuning cycle, string-fragmentation parameters were harmonized with $e^+e^-$ and LEP constraints, and earlier artificial enhancements were removed (Pierog et al., 2013, Calcagni et al., 2017).

Within this retuned setup, EPOS-LHC was reported to describe multiplicity distributions and $dN_{\rm ch}/d\eta$ across energies, to improve the description of identified particle yields and ratios, and to reproduce the increase of $\langle p_t\rangle$ with multiplicity. Because the flow parameters depend solely on $p$0, the model was presented as automatically matching the observed energy-independent scaling of $p$1 versus multiplicity across systems. In $p$2-Pb, the interpolation between $p$3-like and $p$4-like flow was used to account for the slope change in $p$5 versus $p$6 at high multiplicity, while in Pb-Pb the model gave good agreement for multiplicity and $p$7 distributions across centrality bins (Pierog et al., 2013).

The model’s most characteristic collider claim concerns collective hadronization below the hard-scattering regime. EPOS-LHC was designed to describe the $p$8 GeV/$p$9 region, identified strange and multistrange baryon yields, and soft–intermediate-$M_{\rm core}$0 spectra in minimum-bias data. At the same time, the model description of hard-$M_{\rm core}$1 suppression in Pb-Pb was explicitly noted as incomplete and identified as an issue being addressed in EPOS 3. This distinguishes the model’s collective sector from an all-scale treatment of jet quenching or high-$M_{\rm core}$2 energy loss (Pierog et al., 2013).

3. Hadron production, strangeness, and baryon transport

EPOS-LHC has been used extensively as a generator for identified-hadron systematics. In studies of strangeness enhancement at LHC energies, EPOSlhc was run through the CRMC interface with 100,000 events per energy and compared with the Hadron Resonance Gas model and available data. In that context it was used for Pb–Pb and $M_{\rm core}$3–$M_{\rm core}$4 collisions at 0.9, 2.76, 5.02, 7, and 13 TeV, focusing on ratios such as $M_{\rm core}$5, $M_{\rm core}$6, $M_{\rm core}$7, $M_{\rm core}$8, $M_{\rm core}$9, and $p$0. The reported outcome was good agreement with HRG calculations and experimental measurements at LHC energies, together with freeze-out estimates from HRG fits to EPOSlhc ratios of $p$1 MeV with $p$2 MeV for 5.02 TeV Pb–Pb and $p$3 MeV with $p$4 MeV for 13 TeV $p$5–$p$6 (Hanafy et al., 2021).

In $p$7 baryon-transport studies, EPOS-LHC was used alongside DPMJET-III, Pythia 8, and EPOS 1.99 to predict $p$8, $p$9, and $p$0 from $p$1 to 13.6 TeV. The anti-baryon to baryon ratios were found to converge to unity with increasing energy, and to display a mass hierarchy in which the hyperon species containing more strange quarks approach unity faster than $p$2. The proton asymmetry,

$p$3

was reported to decrease with energy and to become nearly zero by 13.6 TeV, consistent with the picture that pair production dominates and baryon-number transport to midrapidity becomes negligible at the highest LHC energies (Ashraf et al., 2022).

Related $p$4 studies used EPOS-LHC from SPS to LHC energies and up to 14 TeV predictions. The generator was reported to reproduce the qualitative horn-like structure in $p$5 and $p$6 at SPS energies, although it overpredicts the peak at $p$7 GeV, and to predict saturation of these ratios at 13 and 14 TeV. For the total ratio,

$p$8

EPOS-LHC, HIJING, and Sibyll2.3d were described as being in good quantitative agreement with available data and as indicating saturation at LHC energies (Khan et al., 2022).

At lower LHC energy, $p$9 GeV $p$0, EPOS-LHC was compared to ALICE $p$1 spectra for pions, kaons, and protons using a modified Hagedorn function with embedded transverse flow velocity. The fitted $p$2 and $p$3 values from EPOS-LHC were reported to match those extracted from the data, while the model reproduced pions in most of the measured $p$4 range, kaons up to $p$5 GeV/$p$6, and protons up to $p$7 GeV/$p$8. In the same analysis, the model reproduced the increase of average transverse momentum with particle mass (Ajaz et al., 2021).

4. Femtoscopy and event-by-event source structure

EPOS-LHC has also been used as a realistic event generator for event-by-event femtoscopic source reconstruction. In $p$9 GeV Au+Au collisions, the model was described as including initial parton interactions, hydrodynamical evolution, hadronization, and hadronic rescattering through UrQMD. The analysis focused on the most central $p$0–$p$1 events, same-charge pion pairs, three $p$2 classes, and the acceptance cut $p$3 (Árpási et al., 2024).

The central result of that study was that non-Gaussian source functions arise in individual EPOS events even in a three-dimensional setting and without event averaging. The reconstructed source distributions were fitted with Lévy-stable forms rather than Gaussian ones, with $p$4 corresponding to the Gaussian limit and $p$5 producing power-law tails. The best-fit Lévy exponent was reported to lie typically in the range $p$6–$p$7, consistently across pair transverse-momentum bins, while the extracted source radii satisfy $p$8, and the source size decreases with increasing transverse momentum (Árpási et al., 2024).

The same analysis also identified a systematic discrepancy with experiment: the reconstructed Lévy exponent in EPOS is larger than the values observed experimentally. This was explicitly presented as a possible indication of missing physics, with examples such as critical phenomena or anomalous diffusion. A plausible implication is that EPOS-LHC reproduces intrinsic non-Gaussianity but not the full strength of the long-range structure inferred from femtoscopic data (Árpási et al., 2024).

5. Cosmic-ray air showers and the muon problem

EPOS-LHC is one of the standard post-LHC hadronic interaction packages used in extensive air-shower simulation codes such as CORSIKA and CONEX. Comparative analyses of pre- and post-LHC versions of EPOS, QGSJET, and SIBYLL found that the post-LHC models show smaller discrepancies among themselves than the pre-LHC generations, especially for quantities such as inelasticity and the fraction of very energetic leading particle events. For EPOS specifically, the transition from EPOS 1.99 to EPOS-LHC increased the VELP fraction, modestly increased pion production, left baryon yields nearly unchanged, and did not significantly alter the overall shape or normalization of the muon production depth distribution or the location of $p$9 (Calcagni et al., 2017).

Despite these improvements, the muon problem remained. A review of ultrahigh-energy cosmic-ray modeling concluded that all leading models, including EPOS-LHC, systematically underestimate the measured number of muons at ground level and overestimate the maximum muon production depth. In that comparison, EPOS-LHC predicts slightly more muons than QGSJET-II-04 but still falls short of Auger data, with the deficit described as around $e^+e^-$0 for vertical showers and larger at very large radial distances from the shower axis (d'Enterria, 2019).

Dedicated comparisons to data reinforce that conclusion. In Yakutsk air-shower measurements with $e^+e^-$1 GeV and $e^+e^-$2 EeV, the observable $e^+e^-$3 was compared with EPOS-LHC and QGSJETII-04 predictions for proton and iron primaries. Up to $e^+e^-$4 EeV, EPOS-LHC was reported to be in reasonable agreement with the data, but above $e^+e^-$5 EeV the $e^+e^-$6 parameter trends upward, so that the data approach or exceed the iron prediction. The study stated that this may indicate a muon deficit in the model, although the total uncertainty in $e^+e^-$7 is about $e^+e^-$8 and the deficit was not claimed as statistically significant in that dataset alone; the stated conclusion was that further tuning of the models is required (Knurenko et al., 2022).

Underground cosmic-muon data from ALICE point in the same direction. In multimuon events with $e^+e^-$9 and $dN_{\rm ch}/d\eta$0, EPOS-LHC underpredicts the muon multiplicity distribution by more than $dN_{\rm ch}/d\eta$1 over a large multiplicity interval, even for pure iron primaries, and for high-muon-multiplicity events with $dN_{\rm ch}/d\eta$2 it gives only $dN_{\rm ch}/d\eta$3 of the measured rate. The same analysis also concluded that there is no need to invoke exotic production mechanisms, because QGSJET-II-04 and SIBYLL 2.3d can account for the rate under a heavy-composition assumption, whereas EPOS-LHC remains significantly low (Collaboration, 2024).

6. Comparative position, later retunings, and open problems

EPOS-LHC occupies an intermediate position in several later comparative studies. In minimum-bias Au+Au collisions at $dN_{\rm ch}/d\eta$4, $dN_{\rm ch}/d\eta$5, and $dN_{\rm ch}/d\eta$6 GeV, it was compared to EPOS-4 and SMASH. For pions, the three models gave broadly similar yields and spectral shapes, but for strange hadrons EPOS-LHC was generally intermediate between the larger yields and harder spectra of EPOS-4 and the lower strange-hadron production of SMASH. In the same study, the best approximate NCQ scaling in $dN_{\rm ch}/d\eta$7 versus $dN_{\rm ch}/d\eta$8 was seen in EPOS-LHC, which was interpreted as indicating a more coherent partonic anisotropy carried to the hadronic stage in that energy range (Badshah et al., 23 Mar 2026).

The most direct retuning beyond EPOS-LHC is EPOS-LHC-R, introduced as a global approach to the muon puzzle. That model keeps the EPOS emphasis on correlations between midrapidity measurements and the forward particle production that drives air-shower development, but adds perfect isospin conservation in string fragmentation, an expanded resonance list, and hadronic rescattering through UrQMD. The reported consequences relative to EPOS-LHC were a $dN_{\rm ch}/d\eta$9-air cross-section about $\langle p_t\rangle$0 lower, elasticity about $\langle p_t\rangle$1 higher, multiplicity up to about $\langle p_t\rangle$2 higher at ultrahigh energy, an increase of $\langle p_t\rangle$3 production by about $\langle p_t\rangle$4, a decrease of the electromagnetic-to-hadronic energy ratio $\langle p_t\rangle$5 by about $\langle p_t\rangle$6, and a deeper $\langle p_t\rangle$7 by about $\langle p_t\rangle$8 g/cm$\langle p_t\rangle$9, together with more muons at ground (Pierog et al., 9 Aug 2025).

Tests with KASCADE-Grande indicate that these later model updates refine rather than overturn the main spectral interpretations. Using EPOS-LHC, QGSJet-II-04, SIBYLL 2.3d, and EPOS-LHC-R, the heavy component retained a knee-like break near $p$00, while the light component retained a hardening above $p$01 eV. EPOS-LHC-R produced somewhat different heavy and light flux normalizations than EPOS-LHC, but the major astrophysical conclusion—a heavy knee and a light-component hardening interpreted as a Galactic-to-extragalactic transition—remained stable across models (Kang et al., 29 Aug 2025).

Taken together, these results define the contemporary status of EPOS-LHC. It is a unified generator linking minimum-bias LHC phenomenology, heavy-ion collective effects, and cosmic-ray air-shower development through a common parton-ladder and core–corona framework. At the same time, collider-correlation studies, femtoscopic source reconstructions, and air-shower muon measurements all expose tensions that have driven continuing retuning and the development of variants such as EPOS-LHC-R (Pierog et al., 2013, Árpási et al., 2024).