EPOS-LHCr: Retuned Forward Hadronic Model

• EPOS-LHCr is a retuned multiple-scattering Monte Carlo framework that models forward hadron production in high-energy proton collisions.
• It employs advanced string fragmentation, core–corona separation, and collective flow dynamics to simulate forward particle spectra including pions, kaons, and charm mesons.
• The model’s retuning aims to resolve discrepancies in neutrino flux and the muon puzzle observed in ultra-high-energy air showers, guiding future experimental constraints.

Searching arXiv for EPOS-LHCr and closely related sources. EPOS-LHCr is an LHC-retuned incarnation of the EPOS multiple-scattering Monte Carlo framework, used in forward-production studies as a model of proton–proton collisions in which a high-energy interaction is represented as a superposition of parton “cut Pomerons” or ladders, each evolving into a colored flux tube. In the FASER neutrino analysis at $\sqrt{s}=13.6~\mathrm{TeV}$, EPOS-LHCr is one of the recent hadronic interaction models used to predict forward pion, kaon, neutral-kaon, and charm production, and thereby the neutrino flux at a detector located $480~\mathrm{m}$ downstream of the ATLAS interaction point. The model is generally consistent with the measured FASER fluxes, although discrepancies appear in specific energy bins; these discrepancies are central to its interpretation as a forward-hadron baseline and as a candidate response to the long-standing muon puzzle in ultra-high-energy air showers (Collaboration et al., 31 Jul 2025).

1. Model identity within the EPOS family

EPOS is a multiple-scattering event generator based on Gribov–Regge theory. In the EPOS-LHC and EPOS-LHCr incarnations, a high-energy $pp$ collision is modeled as a superposition of parton ladders, with several ladders potentially excited in a single event. Each ladder is mapped onto a relativistic flux tube, and its hadronization overlaps with that of other ladders in the transverse plane. EPOS also includes collective effects through a core–corona picture in which overlapping strings thermalize and expand hydrodynamically, modifying soft transverse-momentum spectra and particle ratios at low $p_T$ (Collaboration et al., 31 Jul 2025).

EPOS-LHCr differs from EPOS-LHC mainly by retuning a small number of parameters in parton-ladder fragmentation and in the core–corona transition, with the explicit aim of improving the description of ultra-forward particle production, $\eta \gtrsim 8$, and addressing the muon excess in air-shower data. In the description used for the FASER study, the suffix “r” denotes a retuning of string-tension and string–string interaction parameters, giving slightly harder di-jet fragmentation and an enhanced yield of forward kaons, together with somewhat reduced $\pi^0$, relative to EPOS-LHC. The benchmarks for this tuning include the LHCf forward photon and neutron spectra at $\sqrt{s}=13~\mathrm{TeV}$ and central-rapidity identified-particle spectra from ALICE and CMS. Charm production remains perturbative, implemented as POWHEG+PYTHIA, while charm-hadron fragmentation fractions are adjusted to match LHCb forward measurements (Collaboration et al., 31 Jul 2025).

2. Microscopic structure and collective dynamics

The underlying EPOS-LHC family organizes hadronic final-state formation through three coupled elements: multiple scattering, core–corona separation, and collective hadronization. Each hadron–hadron or nucleus–nucleus collision is decomposed into many cut Pomerons, identified with parton ladders and mapped onto strings in transverse space. Hard scale-independent nonlinear corrections regulate the rise of the total cross section and the overall multiplicity. At an early proper time $\tau_0$, each string is broken into space–time segments carrying four-momentum and position; the local segment density $\rho(x,y,\eta)$ is then evaluated on a three-dimensional grid. Cells with $\rho>\rho_0$ define the core, while low-density cells define the corona. Corona segments hadronize via ordinary Lund-type string fragmentation, whereas core segments are grouped into clusters and undergo collective expansion before microcanonical decay at a freeze-out energy density $480~\mathrm{m}$0 (Pierog et al., 2013).

For a cluster assembled from core segments, the invariant mass is

$480~\mathrm{m}$1

The event-level core mass $480~\mathrm{m}$2 determines the flow. A minimum mass

$480~\mathrm{m}$3

is required for any collective flow to develop. The heavy-ion-like radial flow is parametrized as

$480~\mathrm{m}$4

while the proton–proton-like radial flow uses

$480~\mathrm{m}$5

$480~\mathrm{m}$6

$480~\mathrm{m}$7

The longitudinal Bjorken-like flow is written

$480~\mathrm{m}$8

Event by event, the active radial-flow rapidity is chosen by comparing $480~\mathrm{m}$9 and $pp$0; if the former is larger, the “pp” formula is used, otherwise the “AA” formula is used (Pierog et al., 2013).

The corresponding tuned parameters are quoted as $pp$1, $pp$2, $pp$3, $pp$4, $pp$5, $pp$6, and $pp$7. Soft segments with $pp$8 are fully absorbed into the core; hard segments with $pp$9 lose part of their momentum according to the BDMPS energy-loss formula but remain in the high-$p_T$0 tail. This structure explains why EPOS-LHCr is not merely a forward-fragmentation retune: it inherits a unified multiple-scattering and core–corona formalism spanning $p_T$1, $p_T$2, and $p_T$3 systems (Pierog et al., 2013).

3. Forward hadron production and flux construction

In the FASER application, EPOS-LHCr is used to generate forward hadron spectra

$p_T$4

or, equivalently,

$p_T$5

for $p_T$6, $p_T$7, $p_T$8, $p_T$9, and $\eta \gtrsim 8$0 mesons. The predictions quoted for EPOS-LHCr include a forward charged-pion spectrum peaking at $\eta \gtrsim 8$1 and falling roughly exponentially for $\eta \gtrsim 8$2; for $\eta \gtrsim 8$3, the integrated yield per inelastic event is $\eta \gtrsim 8$4. Relative to EPOS-LHC, the forward charged-kaon spectrum is $\eta \gtrsim 8$5 harder in $\eta \gtrsim 8$6, with a slightly increased normalization at high $\eta \gtrsim 8$7. Neutral-kaon spectra, $\eta \gtrsim 8$8 and $\eta \gtrsim 8$9, are similar in shape but $\pi^0$0 enhanced. Charm $\pi^0$1-meson spectra are computed perturbatively, with a total forward $\pi^0$2 yield $\pi^0$3 per event in the rapidity range $\pi^0$4 (Collaboration et al., 31 Jul 2025).

The neutrino flux at FASER is then obtained by folding these hadron spectra with the relevant two-body and three-body decays, including full decay kinematics, Lorentz boosts, and geometric acceptance. Schematically,

$\pi^0$5

where $\pi^0$6, $\pi^0$7 is the neutrino energy distribution from decay, and $\pi^0$8 is the FASER acceptance, specified as rapidity $\pi^0$9 and radius $\sqrt{s}=13~\mathrm{TeV}$0. The final neutrino interaction rate in the emulsion detector is written

$\sqrt{s}=13~\mathrm{TeV}$1

and after introducing a signal strength $\sqrt{s}=13~\mathrm{TeV}$2,

$\sqrt{s}=13~\mathrm{TeV}$3

These expressions make explicit that the experimental neutrino yield is a derived observable whose sensitivity is inherited from the underlying forward hadron spectra (Collaboration et al., 31 Jul 2025).

4. FASER confrontation at $\sqrt{s}=13~\mathrm{TeV}$4

The FASER study presents electron- and muon-neutrino flux measurements using data corresponding to $\sqrt{s}=13~\mathrm{TeV}$5 and $\sqrt{s}=13~\mathrm{TeV}$6 of proton–proton collisions with $\sqrt{s}=13~\mathrm{TeV}$7 by the FASER$\sqrt{s}=13~\mathrm{TeV}$8 and FASER electronic detectors, respectively. EPOS-LHCr, SIBYLL 2.3e, and QGSJET 3 are compared against these data, and the predictions are described as generally consistent with the measured fluxes, although some discrepancies appear in certain energy bins (Collaboration et al., 31 Jul 2025).

For the emulsion detector sample quoted as $\sqrt{s}=13~\mathrm{TeV}$9, the reported comparison is:

Interaction mode	Data (90% CL)	EPOS-LHCr prediction
$\tau_0$0 CC	$\tau_0$1	10.5
$\tau_0$2 CC	$\tau_0$3	28.0

In the combined energy range, EPOS-LHCr lies within $\tau_0$4 for electron neutrinos, with data/prediction $\tau_0$5, and underpredicts muon neutrinos by $\tau_0$6, with data/prediction $\tau_0$7. When binned in reconstructed neutrino energy, the comparison separates into three regimes: $\tau_0$8–$\tau_0$9, where data are $\rho(x,y,\eta)$0 the prediction and $\rho(x,y,\eta)$1 high; $\rho(x,y,\eta)$2–$\rho(x,y,\eta)$3, where data are $\rho(x,y,\eta)$4 the prediction and within $\rho(x,y,\eta)$5; and above $\rho(x,y,\eta)$6, where data are $\rho(x,y,\eta)$7 the prediction and $\rho(x,y,\eta)$8 low (Collaboration et al., 31 Jul 2025).

The model decomposition of the neutrino spectrum is also informative. In the quoted FASER description, $\rho(x,y,\eta)$9 dominates below $\rho>\rho_0$0, $\rho>\rho_0$1 contributes in the $\rho>\rho_0$2–$\rho>\rho_0$3 region and is slightly low in EPOS-LHCr, and charm $\rho>\rho_0$4 emerges above $\rho>\rho_0$5, where EPOS-LHCr overshoots the data. This motivates a specific interpretation: the mid-energy excess suggests that EPOS-LHCr still underestimates forward charged-pion and/or kaon production by $\rho>\rho_0$6–$\rho>\rho_0$7, while the high-energy deficit implies that the model’s combined kaon-plus-charm yield may be too large at ultra-forward rapidities. Since one of the stated motivations of EPOS-LHCr was to enhance forward kaons in order to address the muon puzzle, FASER provides a direct test of that tuning; the study concludes that the kaon enhancement is not yet optimal, and that a somewhat larger kaon yield around $\rho>\rho_0$8–$\rho>\rho_0$9 and/or a softer charm component would improve agreement (Collaboration et al., 31 Jul 2025).

5. Connection to air showers and the muon puzzle

The wider significance of EPOS-LHCr derives from the persistent excess of muons in ultra-high-energy air showers relative to simulation predictions. In Yakutsk analyses using EPOS LHC and QGSjetII-04, a muon deficit is reported in the models at energies greater than $480~\mathrm{m}$00, with EPOS LHC underpredicting the absolute muon yield by $480~\mathrm{m}$01–$480~\mathrm{m}$02 at the highest energies when light primaries are assumed. The same source states that further tuning of the models is required, and explicitly associates the shortfall with missing physics in the forward hadronization stage, including forward-hadron production, inelasticity, and multiplicity (Knurenko et al., 2022).

Against that background, the retuned branch denoted EPOS.LHC-R in later air-shower literature makes several specific modifications: perfect isospin symmetry in string fragmentation, addition of the neutral resonances $480~\mathrm{m}$03 and $480~\mathrm{m}$04 to the string-fragmentation decay table, and inclusion of hadronic rescattering via UrQMD after string breakup. It also retunes the correlation between mid-rapidity multiplicity and forward production, targeting both $480~\mathrm{m}$05 and the Feynman-$480~\mathrm{m}$06 spectra of $480~\mathrm{m}$07 and $480~\mathrm{m}$08 at $480~\mathrm{m}$09 (Pierog et al., 9 Aug 2025).

In that formulation, EPOS.LHC-R yields $480~\mathrm{m}$10 and $480~\mathrm{m}$11, compared with an older fragmentation pattern with $480~\mathrm{m}$12 everywhere. For air showers, the quoted consequences relative to EPOS-LHC are $480~\mathrm{m}$13 by $480~\mathrm{m}$14, $480~\mathrm{m}$15 by $480~\mathrm{m}$16, and $480~\mathrm{m}$17 by $480~\mathrm{m}$18 at $480~\mathrm{m}$19, producing $480~\mathrm{m}$20 for proton primaries at $480~\mathrm{m}$21 and an overall $480~\mathrm{m}$22 increase in $480~\mathrm{m}$23 at the same energy (Pierog et al., 9 Aug 2025).

A plausible implication is that EPOS-LHCr in collider-forward studies and EPOS.LHC-R in air-shower studies represent closely related retuned branches of the EPOS-LHC framework, both motivated by the same forward-production problem. The cited sources, however, do not provide a formal statement of naming equivalence. What they do establish unambiguously is the physical link: the collider-forward neutrino data now test precisely the pion, kaon, and charm components that dominate the hadronic cascade and, ultimately, the ground-level muon content.

6. Retuning prospects and outstanding uncertainties

The FASER results define a concrete program for further constraint. According to the forward-neutrino study, once the full Run 3 data set is analyzed, FASER will provide flux measurements in $480~\mathrm{m}$24 energy bins up to several $480~\mathrm{m}$25 with $480~\mathrm{m}$26 uncertainties. The same study states that multi-differential analyses in $480~\mathrm{m}$27 and even hadron-parent $480~\mathrm{m}$28–$480~\mathrm{m}$29 correlations will allow retuning of the EPOS-LHCr string-fragmentation parameters and the core–corona threshold. It further suggests that a global fit including LHCf forward photons, FASER neutrinos, and cosmic-ray muon data could determine the correct mixture of $480~\mathrm{m}$30, $480~\mathrm{m}$31, $480~\mathrm{m}$32, and charm in the forward direction (Collaboration et al., 31 Jul 2025).

The related air-shower retuning program identifies additional unresolved inputs: the branching fractions $480~\mathrm{m}$33 and $480~\mathrm{m}$34 at multi-TeV string masses, the strength and phase-space dependence of hadronic rescattering in dilute $480~\mathrm{m}$35 environments, and the dependence of the core–corona switching threshold on multiplicity. Proposed future constraints include forward $480~\mathrm{m}$36 versus $480~\mathrm{m}$37 measurements in $480~\mathrm{m}$38 at $480~\mathrm{m}$39, leading-baryon spectra beyond $480~\mathrm{m}$40, two-particle correlations between mid- and forward multiplicities, and cosmic-ray measurements of the muon energy spectrum at ground as a function of radial distance (Pierog et al., 9 Aug 2025).

EPOS-LHCr therefore occupies a specific methodological position. It is a retuned forward-production model embedded in a broader multiple-scattering, string, and core–corona framework; it is already sufficiently constrained to provide realistic FASER neutrino predictions; yet its comparison with data isolates remaining tensions in the kaon and charm sectors. Those tensions are not peripheral. They are exactly the tensions that determine whether the same framework can simultaneously describe collider forward observables and extensive-air-shower muon data.