EPOS4: Unified Event Generator Framework

• EPOS4 is a unified event-generator framework combining Gribov–Regge theory, explicit pQCD ladders, and viscous hydrodynamics to simulate collisions.
• It enforces exact energy–momentum conservation via multiple scattering and dynamical saturation scales while distinguishing core–corona regions.
• The framework effectively bridges soft bulk production with hard probes across a broad energy range from pp to AA collisions.

EPOS4 is a unified event-generator framework for hadronic and nuclear collisions that combines a Gribov–Regge multiple-scattering description of the primary interaction stage with explicit pQCD ladders, dynamical saturation scales, event-by-event core–corona separation, viscous hydrodynamics, microcanonical hadronization, and a hadronic cascade. It is designed to describe collision systems from $pp$ to $AA$, and energies from several TeV per nucleon down to several GeV, with the explicit aim of reconciling rigorous parallel scattering and exact energy sharing with high-$p_T$ factorization and binary scaling (Werner, 2023, Werner et al., 2024).

1. Conceptual scope and historical position

EPOS4 emerged from a sequence of theoretical developments addressing a longstanding inconsistency in high-energy event generation. At ultrarelativistic energies, multiple parton–parton interactions occur effectively in parallel, so an S-matrix treatment with simultaneous sub-collisions is required. However, exact energy–momentum sharing among such parallel sub-collisions generically spoils the usual factorization properties of inclusive high-$p_T$ observables and also breaks binary scaling in nucleus–nucleus collisions. EPOS4 was formulated to retain rigorous parallel scattering while recovering factorization at high $p_T$ through dynamical saturation scales (Werner, 2023, Werner, 2023).

In this framework, earlier EPOS ingredients—multiple strings, a core–corona split, hydrodynamic evolution, and hadronic transport—are embedded in a more explicit pQCD-plus-unitarity construction. The literature repeatedly presents EPOS4 as a “general purpose” approach meant to accommodate soft bulk observables, collective flow, identified-particle production, hard probes, heavy flavor, and small-system phenomenology within one parameter set or one common architecture rather than through system-specific retuning (Werner, 10 Aug 2025, Werner, 2024).

A central organizing idea is that EPOS4 is not merely a hydrodynamic afterburner attached to a conventional Monte Carlo. Its initial state is itself formulated as a multiple-scattering theory in which each elementary interaction is a Pomeron or parton ladder, and the later hydrodynamic and hadronic stages are derived from the space–time distribution of the resulting string segments or prehadrons (Werner et al., 2024, Werner, 2023).

2. Parallel multiple scattering, saturation, and generalized AGK restoration

The high-energy primary stage is formulated in terms of parallel Pomeron exchanges in impact-parameter space. In the small-system flow formulation, the total S-matrix for an $A+B$ collision is written as

$$S_{AB}(s,b)=\prod_{i=1}^{N_{\rm scatt}}\bigl[1-T_i(s,b;\{x_i^\pm\})\bigr],$$

with exact light-cone momentum conservation enforced by

$\sum_i x_i^+=\sum_i x_i^-=1.$

Each elementary amplitude $T_i$ is a parton ladder with a saturation scale $Q_{\rm sat}^2$ that increases toward small $AA$0 (Werner, 10 Aug 2025).

In the heavy-ion implementation, the eikonal is decomposed as

$AA$1

and the total and inelastic nucleon–nucleon cross sections follow the usual eikonal form,

$AA$2

Here $AA$3 is associated with soft Pomeron exchange, while $AA$4 is built from DGLAP-evolved QCD ladders with a dynamical saturation scale $AA$5 (Werner et al., 2024).

The key theoretical innovation is the compensation of deformation effects induced by exact energy sharing. In the foundational formulation, EPOS4 introduces a “fundamental EPOS4 equation,”

$AA$6

where $AA$7 counts the number of ladders attached to a given nucleon, $AA$8 corrects the deformation of the light-cone momentum distribution caused by multiple parallel connections, and $AA$9 is a normalization constant. By imposing that the physical cut-Pomeron function $p_T$0 be independent of $p_T$1, the model fixes a dynamical $p_T$2 that absorbs the deformation (Werner, 2023, Werner et al., 2024).

This construction yields what the EPOS4 literature calls a generalized Abramovskii–Gribov–Kancheli theorem. At $p_T$3, inclusive spectra recover the single-Pomeron, factorized result in $p_T$4, and binary scaling in $p_T$5 is restored. At lower scales, the same mechanism suppresses soft production through the increase of $p_T$6 with connection number and decreasing $p_T$7 (Werner, 2023, Werner, 2024).

Because the single-scattering module is explicitly connected to pQCD, EPOS4 can construct effective EPOS PDFs and compute inclusive jet and heavy-flavor cross sections in a factorized form at high transverse momentum. The same formalism is then used as the building block of full-event simulations that also include collective dynamics at low $p_T$8 (Werner et al., 2023, Werner, 2023).

3. From flux tubes to a fluid: core–corona separation and hydrodynamic evolution

After the primary interactions, each cut Pomeron is mapped onto strings or flux tubes, often described as “kinky strings” once hard transverse momentum kicks are included. These strings fragment into prehadrons or string segments at an early proper time $p_T$9, after which EPOS4 performs a dynamical split between dense and dilute matter (Werner et al., 2024, Werner, 2023).

The published implementations use several equivalent criteria for this split. One formulation classifies regions according to the local energy density $p_T$0 or local segment density $p_T$1: if $p_T$2, the region becomes part of the hydrodynamic core; otherwise, it remains corona and hadronizes directly. Another formulation uses the energy loss of a prehadron moving through dense matter; prehadrons with $p_T$3 are absorbed into the core, while those with $p_T$4 escape as corona (Werner et al., 2024, Werner, 2023, Koley et al., 28 Aug 2025).

The initial energy–momentum tensor is obtained by smearing the momenta of the prehadron segments. In one explicit formulation,

$p_T$5

with analogous expressions for conserved currents such as

$p_T$6

where $p_T$7 is a normalized Gaussian, $p_T$8 is the segment four-momentum, and $p_T$9 denotes flavor content. Diagonalization in the local rest frame yields $p_T$0 and $p_T$1 (Werner et al., 2024).

The hydrodynamic stage is event-by-event and viscous, with both $p_T$2D and $p_T$3D or $p_T$4D variants appearing in the published studies. The basic conservation laws are

$p_T$5

with

$p_T$6

or, in the Israel–Stewart form used in small-system and oxygen–oxygen applications,

$p_T$7

Published implementations employ lattice-QCD-based equations of state matched to hadron-gas sectors, and typical shear-viscosity values range from $p_T$8 to $p_T$9, depending on the application. In oxygen–oxygen studies, the core is evolved with the vHLLE code, described as a $A+B$0D Israel–Stewart-type solver (Ashraf et al., 2024, Bashir et al., 12 May 2025, Werner et al., 2024).

The initialization time and freeze-out conditions are not fixed universally across the literature. For example, $A+B$1 fm/$A+B$2 is typical in the RHIC Beam Energy Scan heavy-ion study, except at 7.7 GeV where $A+B$3 fm/$A+B$4; $A+B$5 fm/$A+B$6 appears in the small-system flow study; $A+B$7 fm/$A+B$8 is used in one oxygen–oxygen setup; and $A+B$9 fm/$$S_{AB}(s,b)=\prod_{i=1}^{N_{\rm scatt}}\bigl[1-T_i(s,b;\{x_i^\pm\})\bigr],$$0 appears in several LHC bulk studies (Werner et al., 2024, Werner, 10 Aug 2025, Ashraf et al., 2024, Koley et al., 12 Jan 2026). This suggests that EPOS4 is a common framework with context-dependent published parameterizations rather than a single immutable tune.

4. Hadronization, exact conservation laws, and the hadronic cascade

EPOS4 distinguishes sharply between core and corona hadronization. Corona segments hadronize through string fragmentation, described in several papers as Lund-like or standard flux-tube fragmentation, with updated breakup functions in some studies (Ashraf et al., 2024, Khan et al., 2024). The core is hadronized statistically but microcanonically, so that energy, momentum, baryon number, electric charge, strangeness, and related abelian charges are conserved exactly.

On a freeze-out hypersurface $$S_{AB}(s,b)=\prod_{i=1}^{N_{\rm scatt}}\bigl[1-T_i(s,b;\{x_i^\pm\})\bigr],$$1, one may write the standard Cooper–Frye expression,

$$S_{AB}(s,b)=\prod_{i=1}^{N_{\rm scatt}}\bigl[1-T_i(s,b;\{x_i^\pm\})\bigr],$$2

but EPOS4 emphasizes microcanonical sampling rather than purely grand-canonical emission. In the microcanonical framework, freeze-out elements carry

$$S_{AB}(s,b)=\prod_{i=1}^{N_{\rm scatt}}\bigl[1-T_i(s,b;\{x_i^\pm\})\bigr],$$3

with invariant mass

$$S_{AB}(s,b)=\prod_{i=1}^{N_{\rm scatt}}\bigl[1-T_i(s,b;\{x_i^\pm\})\bigr],$$4

Hadronic final states are then sampled subject to exact conservation of energy–momentum and charges (Werner, 2023).

One explicit microcanonical weight used in the literature is

$$S_{AB}(s,b)=\prod_{i=1}^{N_{\rm scatt}}\bigl[1-T_i(s,b;\{x_i^\pm\})\bigr],$$5

with

$$S_{AB}(s,b)=\prod_{i=1}^{N_{\rm scatt}}\bigl[1-T_i(s,b;\{x_i^\pm\})\bigr],$$6

This construction is used to discuss both exact charge conservation and finite-cluster effects such as microcanonical suppression of strange hadrons in small systems or small droplets (Werner, 2023, Koley et al., 28 Aug 2025).

A major phenomenological use of this hadronization scheme is the treatment of strangeness. The EPOS4 strangeness literature argues that the rise of strange-to-pion ratios with multiplicity is driven primarily by the growth of the core fraction, while microcanonical suppression provides an additional reduction at very low multiplicity or small invariant mass. In one published $$S_{AB}(s,b)=\prod_{i=1}^{N_{\rm scatt}}\bigl[1-T_i(s,b;\{x_i^\pm\})\bigr],$$7 study at 7 TeV, the core fraction for $$S_{AB}(s,b)=\prod_{i=1}^{N_{\rm scatt}}\bigl[1-T_i(s,b;\{x_i^\pm\})\bigr],$$8 rises from approximately $$S_{AB}(s,b)=\prod_{i=1}^{N_{\rm scatt}}\bigl[1-T_i(s,b;\{x_i^\pm\})\bigr],$$9 at $\sum_i x_i^+=\sum_i x_i^-=1.$0 to approximately $\sum_i x_i^+=\sum_i x_i^-=1.$1 at $\sum_i x_i^+=\sum_i x_i^-=1.$2 (Bierlich et al., 2024). Another study states that in $\sum_i x_i^+=\sum_i x_i^-=1.$3 at 7 TeV the overall core fraction grows from approximately zero at $\sum_i x_i^+=\sum_i x_i^-=1.$4 to approximately one by $\sum_i x_i^+=\sum_i x_i^-=1.$5 (Werner, 2023). The differing numerical contexts reflect different observables and definitions, but both studies assign the dominant multiplicity dependence to core–corona mixing.

After hadronization, EPOS4 passes all hadrons—core and corona alike—into a hadronic transport stage, usually UrQMD and in some low-energy discussions alternatively SMASH. This afterburner handles resonance decays and hadronic rescattering, including channels such as $\sum_i x_i^+=\sum_i x_i^-=1.$6, $\sum_i x_i^+=\sum_i x_i^-=1.$7, and baryon–antibaryon annihilation, until interactions cease (Werner et al., 2024, Sumberia et al., 2024). Several application papers use UrQMD ON/OFF comparisons as a diagnostic tool for the role of the hadronic phase.

5. Systematics across beam energy and collision system

A defining claim of EPOS4 is that it uses the same theoretical architecture for $\sum_i x_i^+=\sum_i x_i^-=1.$8, $\sum_i x_i^+=\sum_i x_i^-=1.$9, and $T_i$0. In heavy ions above $T_i$1 GeV, the model adopts the parallel-scattering-plus-hydrodynamics scenario; below about 4 GeV, the published heavy-ion study argues that a sequential hadronic cascade is more appropriate because the hadron formation time exceeds the time between successive scatterings (Werner et al., 2024).

Within the RHIC Beam Energy Scan analysis, the initial central energy density at $T_i$2 decreases from approximately $T_i$3 GeV/fm$T_i$4 at 5.02 ATeV to approximately $T_i$5 GeV/fm$T_i$6 at 11.5 GeV, and falls below the freeze-out density near $T_i$7 GeV, so that no core is formed. The same study introduces a rough interpolation for the core fraction,

$T_i$8

implying $T_i$9 for $Q_{\rm sat}^2$0 GeV, $Q_{\rm sat}^2$1 at $Q_{\rm sat}^2$2 GeV, and $Q_{\rm sat}^2$3 at 4 GeV (Werner et al., 2024). This supports the interpretation of EPOS4 as a model for the gradual disappearance of fluid behavior rather than a framework with a hard external switch at intermediate RHIC energies.

In $Q_{\rm sat}^2$4 Au+Au collisions from $Q_{\rm sat}^2$5 to $Q_{\rm sat}^2$6 GeV, EPOS4 reproduces identified-hadron $Q_{\rm sat}^2$7 spectra and their centrality dependence within approximately $Q_{\rm sat}^2$8. At 11.5 GeV, the published comparison shows an excess of low-$Q_{\rm sat}^2$9 protons and $AA$00 mesons; at 7.7 GeV, all spectra are too soft. For midrapidity yields, the model agrees well for $AA$01, $AA$02, and antibaryons above 19.6 GeV, but below that it overestimates $AA$03, $AA$04, $AA$05, and especially $AA$06, which is interpreted there as being consistent with too-strong stopping and fluidization at low energy (Werner et al., 2024).

In the same energy range, elliptic flow remains a major strength. Using the event-plane method with a rapidity gap $AA$07, EPOS4 reproduces the centrality and mass ordering of $AA$08 for $AA$09, $AA$10, $AA$11, $AA$12, $AA$13, $AA$14, and $AA$15 to better than approximately $AA$16 from $AA$17 down to $AA$18 GeV (Werner et al., 2024).

At LHC energies, the framework is used for large, intermediate, and small systems. In oxygen–oxygen collisions at $AA$19 TeV, EPOS4 predicts harder $AA$20 spectra than AMPT for $AA$21, $AA$22, $AA$23, $AA$24, and $AA$25, with stronger radial flow and a monotonic rise of strange-hadron yields with multiplicity. At a given $AA$26, EPOS4 predicts approximately $AA$27 larger $AA$28 and $AA$29 yields than AMPT, and its strange-to-pion ratios follow the empirical $AA$30–$AA$31Pb–PbPb trend reported by ALICE more closely than AMPT-SM or AMPT-default (Ashraf et al., 2024).

A complementary oxygen–oxygen study reports $AA$32 for the $AA$33 class and $AA$34 for the $AA$35 class, with identified-particle spectra exhibiting mass-ordered hardening and $AA$36 peaking around $AA$37 near $AA$38 GeV/$AA$39 in central events (Khan et al., 2024). The same work notes that EPOS4 systematically overestimates integrated $AA$40 and especially $AA$41 relative to observed multiplicity trends across $AA$42, $AA$43Pb, and PbPb, with the $AA$44 overestimate reaching approximately $AA$45 (Khan et al., 2024).

In $AA$46 and $AA$47Pb at 5.02 TeV, EPOS4 reproduces qualitative features such as multiplicity-dependent spectral hardening, hierarchical strangeness enhancement, and characteristic modifications of particle-yield ratios with $AA$48 and multiplicity, but the published comparison also emphasizes remaining discrepancies in intermediate-$AA$49 spectra, $AA$50 production, and blast-wave parameters (Koley et al., 28 Aug 2025).

6. Validation, specialized applications, and documented limitations

EPOS4 has been benchmarked against a wide range of observables that go beyond bulk hadron spectra. In $AA$51 at 7 TeV, a comparative jet-and-underlying-event analysis finds that EPOS4$AA$52 reproduces CMS measurements for all charged particles, underlying events, intrajet particles, and leading charged particles; for charged-jet rates with $AA$53 GeV/$AA$54, EPOS4$AA$55 and Pythia8 agree with data to better than $AA$56 across the full multiplicity range, while EPOS4$AA$57 underestimates the rate by $AA$58 above $AA$59 (Waqar et al., 2024). The same study attributes the improved high-multiplicity agreement to the conversion of energy into flow when hydrodynamics is enabled.

For flow in very small systems, the small-system EPOS4 study reports that the default “symmetric scenario” for the proton yields $AA$60 at large multiplicity in $AA$61 at 13 TeV, whereas a “dipole scenario” with two transverse centers separated by $AA$62 fm produces a flat $AA$63 in agreement with ATLAS data and also improves $AA$64 and $AA$65. In PbPb at 2.76 TeV, by contrast, the dipole versus symmetric choice makes almost no difference because geometric eccentricities are dominated by nuclear overlap (Werner, 10 Aug 2025). This is one of the clearest examples of an explicitly documented model uncertainty tied to subnucleonic structure rather than hydrodynamic transport alone.

Heavy flavor and quarkonium have also been embedded in the EPOS4 architecture. One study classifies heavy-quark pair production into flavor creation, flavor excitation, and gluon splitting, with corresponding back-to-back, broad, and near-side heavy-quark azimuthal correlations. When coupled to a Wigner-density projection for quarkonium formation, EPOS4 reproduces prompt $AA$66 $AA$67 spectra at $AA$68 TeV up to $AA$69 GeV, and neglecting heavy-flavor correlations suppresses the high-$AA$70 charmonium yield by up to $AA$71 (Zhao et al., 29 Sep 2025).

The framework has also been used for fluctuation and correlation observables. In Au+Au collisions at RHIC Beam Energy Scan energies, second-order conserved-charge cumulant ratios computed from hadronic proxies show that improved variance-based proxies $AA$72, $AA$73, and $AA$74 track the true charge cumulant ratios to within a few percent across all studied $AA$75, while traditional STAR-style proxies can differ from the conserved-charge ratios by up to $AA$76 (Jahan et al., 2024). In PbPb at 5.02 TeV, an intermittency study finds larger intermittency exponents $AA$77 and generalized dimensions $AA$78 in EPOS4 than in PYTHIA 8, but concludes that neither generator exhibits the scale-invariant intermittency expected near a QCD critical point (Haider et al., 25 May 2026).

For hadronic resonances, EPOS4 plus UrQMD has been used to isolate rescattering and regeneration effects. In central Pb–Pb at 5.36 TeV and high-multiplicity $AA$79 at 13.6 TeV, low-$AA$80 suppression of short-lived resonances such as $AA$81 is strong when UrQMD is turned on, whereas the longer-lived $AA$82 is much less affected. By comparing resonance-to-stable-hadron ratios, one study extracts a hadronic-phase duration of approximately $AA$83 fm/$AA$84 in most-central Pb–Pb and a nonzero value of approximately $AA$85 fm/$AA$86 in high-multiplicity $AA$87 (Sumberia et al., 2024).

Femtoscopic applications further illustrate the breadth of the framework. In minimum-bias Au+Au from $AA$88 to $AA$89 GeV, a Lévy-source analysis finds that $AA$90 and $AA$91 increase gradually with collision energy, $AA$92 shows little energy dependence, and the Lévy index $AA$93 remains sub-Gaussian in the range $AA$94. A comparison with EPOS3 shows agreement within approximately $AA$95 for most parameters, with the notable exception that $AA$96 is systematically smaller in EPOS4 (Huang et al., 2 Dec 2025).

Taken together, these studies portray EPOS4 as a broad, internally connected framework rather than a narrowly tuned heavy-ion hydro model. Its strengths are most consistently reported in the unified treatment of parallel scattering, collective flow, multiplicity dependence, and exact local conservation at hadronization. Its limitations are also explicit in the published record: sensitivity to the assumed proton shape in small systems, overestimation of some low-energy baryon and kaon yields, spectra that become too soft near the lower end of the Beam Energy Scan, and residual discrepancies in $AA$97 production, baryon-to-meson ratios, and some femtoscopic radii (Werner, 10 Aug 2025, Werner et al., 2024, Koley et al., 28 Aug 2025, Huang et al., 2 Dec 2025). This suggests that EPOS4 is best understood as a unified but still evolving framework whose principal scientific value lies in making soft, hard, and intermediate observables calculable within a common dynamical scheme.