SIBYLL 2.3e: Hadronic Interaction Model

Updated 7 July 2026

SIBYLL 2.3e is a hadronic interaction model in the 2.3 series, evolving the minijet and string-fragmentation framework for accurate air shower simulations.
It recalibrates key observables like Xmax and muon counts by integrating collider data and forward-production constraints into its predictions.
Applications include precision UHECR composition studies and forward-neutrino flux analyses, addressing longstanding muon production discrepancies.

Searching arXiv for papers mentioning SIBYLL 2.3e to ground the article in current literature. [ArxivSearchResult(title='Updated Air-Shower $X_{\rm max}$ Moment Parametrizations for UHECR Composition with Latest Hadronic Interaction Models', authors=['D. Boncioli', 'J. Eser', 'C. Evoli', 'M. Roth', 'D. Schmidt'], summary='The mass composition of ultra-high-energy cosmic rays (UHECRs) is commonly inferred from the first two moments of the depth of shower maximum, $X_{\rm max}$ , measured by fluorescence and hybrid detectors. Such analyses require fast and accurate mappings between the moments of $X_{\rm max}$ and those of the logarithmic mass, $\ln A$ , based on realistic air-shower simulations. In this work we provide updated parametrizations of the $X_{\rm max}$ moments and distributions for air showers initiated by nuclei from proton to iron, simulated with CONEX for three state-of-the-art hadronic interaction models: Epos LHC-R, Sibyll 2.3e, and QGSJet-III-01. We parametrize the mean depth $\langle X_{\rm max}\rangle$ and the variance $σ^2(X_{\rm max})$ as functions of energy and mass. For the variance we compare a second-order polynomial model with an exponential model. In addition, we model the full $X_{\rm max}$ distributions with a three-parameter generalized Gumbel function. The Gumbel parameters are fitted using an unbinned likelihood and are validated by comparing the implied mean and variance with the raw CONEX samples and with the moment parametrizations. Across the full energy range considered, residuals between the parametrizations (or the Gumbel representation) and the simulations are at the level of a few g cm $^{-2}$ for the mean and a few (g cm $^{-2}$ ) $X_{\rm max}$ 0 for the variance, making these parametrizations suitable for precision UHECR composition studies and forward-folding analyses of $X_{\rm max}$ 1 distributions.', arxiv_id='(Evoli et al., 20 Feb 2026)', published='2026-02-20'), ArxivSearchResult(title='Measurement of charged-particle production in $X_{\rm max}$ 2 TeV proton-oxygen collisions as a probe of cosmic-ray air showers with the ATLAS detector', authors=['The ATLAS collaboration'], summary='This Letter presents a measurement of prompt charged-particle production in proton-oxygen interactions at $X_{\rm max}$ 3 TeV center-of-mass energy with the ATLAS detector, corresponding to 634 $X_{\rm max}$ 4b $X_{\rm max}$ 5 of integrated luminosity. A total of 246 million selected events have at least one track with transverse momentum $X_{\rm max}$ 6 MeV and pseudorapidity $X_{\rm max}$ 7. The measured fiducial proton-oxygen cross section is $X_{\rm max}$ 8 and the extrapolated inelastic proton-air cross section is $X_{\rm max}$ 9. Measurements of charged-particle multiplicity, $X_{\rm max}$ 0, and $X_{\rm max}$ 1 distributions are an order-of-magnitude more precise than differences between hadronic-interaction models. These results enable improved modeling of cosmic-ray air showers, which is important for astroparticle physics.', arxiv_id='(Collaboration, 7 Apr 2026)', published='2026-04-07'), ArxivSearchResult(title='Latest neutrino results from the FASER experiment and their implications for forward hadron production', authors=['P. A. Zyla', 'S. Taneja', 'on behalf of the FASER collaboration'], summary='The muon puzzle -- an excess of muons relative to simulation predictions in ultra-high-energy cosmic-ray air showers -- has been reported by many experiments. This suggests that forward particle production in hadronic interactions is not fully understood. Some of the scenarios proposed to resolve this predict reduced production of forward neutral pions and enhanced production of forward kaons (or other particles). The FASER experiment at the LHC is located 480 m downstream of the ATLAS interaction point and is sensitive to neutrinos and muons, which are the decay products of forward charged pions and kaons. In this study, the latest measurements of electron and muon neutrino fluxes are presented using the data corresponding to 9.5 fb $X_{\rm max}$ 2 and 65.6 fb $X_{\rm max}$ 3 of proton-proton collisions with $X_{\rm max}$ 4 TeV by the FASER $X_{\rm max}$ 5 and the FASER electronic detector, respectively. These fluxes are compared with predictions from recent hadronic interaction models, including EPOS-LHCr, SIBYLL 2.3e, and QGSJET 3. The predictions are generally consistent with the measured fluxes from FASER, although some discrepancies appear in certain energy bins. More precise flux measurements with additional data will follow soon, enabling validation of pion, kaon, and charm meson production with finer energy binning, reduced uncertainties, and multi-differential analyses.', arxiv_id='(Collaboration et al., 31 Jul 2025)', published='2025-07-31'), ArxivSearchResult(title='Constraints on the spread of nuclear masses in ultra-high-energy cosmic rays based on the Phase I hybrid data from the Pierre Auger Observatory', authors=['The Pierre Auger Collaboration'], summary='We present an analysis of the correlation between the depth of the maximum of air-shower profiles and the signal in water-Cherenkov stations in events registered simultaneously by the fluorescence and surface detectors of the Pierre Auger Observatory. The analysis enables us to place constraints on the spread of nuclear masses in ultra-high-energy cosmic rays with a minor impact from the experimental systematic uncertainties and uncertainties in air-shower simulations. Due to this unique feature, the correlation analysis has previously allowed us to exclude all pure and proton-helium compositions near the ankle in the cosmic-ray energy spectrum at 5σ confidence level. The same property makes the correlation analysis an effective tool for testing the consistency of predictions of the post-LHC hadronic interaction models, including their latest versions such as EPOS LHC-R, QGSJet-III-01, Sibyll{}^\bigstar and Sibyll 2.3e. In this work, the correlation analysis using the Phase I hybrid data from the Pierre Auger Observatory is presented. The analysis uses the newest generation of hadronic interaction models and covers an extended energy range around the ankle in the cosmic-ray energy spectrum.', arxiv_id='(Yushkov, 11 Jul 2025)', published='2025-07-11'), ArxivSearchResult(title='Measurement of the attenuation length of the muon content in extensive air showers from 0.3 to 30 PeV with LHAASO', authors=['Zhen Cao', 'Fengrui Zhu', 'for the LHAASO Collaboration'], summary='The attenuation length of the muon content in extensive air showers provides important information regarding the generation and development of air showers. This information can be used not only to improve the description of such showers but also to test fundamental models of hadronic interactions. Using data from the LHAASO-KM2A experiment, the development of the muon content in high-energy air showers was studied. The attenuation length of muon content in the air showers was measured from experimental data in the energy range from 0.3 to 30 PeV using the constant intensity cut method. By comparing the attenuation length of the muon content with predictions from high-energy hadronic interaction models (QGSJET-II-04, SIBYLL 2.3d, and EPOS-LHC), it is evident that LHAASO results are significantly shorter than those predicted by the first two models (QGSJET-II-04 and SIBYLL 2.3d) but relatively close to those predicted by the third model (EPOS-LHC). Thus, the LHAASO data favor the EPOS-LHC model over the other two models. The three interaction models confirmed an increasing trend in the attenuation length as the cosmic-ray energy increases.', arxiv_id='(Collaboration, 2024)', published='2024-10-17')] Searching for foundational SIBYLL 2.3-family papers that define the model lineage and physics basis relevant to SIBYLL 2.3e. [ArxivSearchResult(title='The hadronic interaction model SIBYLL 2.3c and Feynman scaling', authors=['Felix Riehn', 'Ralph Engel', 'Anatoli Fedynitch', 'Thomas K. Gaisser', 'Todor Stanev'], summary='The Monte Carlo model Sibyll has been designed for efficient simulation of hadronic multiparticle production up to the highest energies as needed for interpreting cosmic ray measurements. For more than 15 years, version 2.1 of Sibyll has been one of the standard models for air shower simulation. Motivated by data of LHC and fixed-target experiments and a better understanding of the phenomenology of hadronic interactions, we have developed an improved version of this model, version 2.3, which has been released in 2016. In this contribution we present a revised version of this model, called Sibyll 2.3c, that is further improved by adjusting particle production spectra to match the expectation of Feynman scaling in the fragmentation region. After a brief introduction to the changes implemented in Sibyll 2.3 and 2.3c with respect to Sibyll 2.1, the current predictions of the model for the depth of shower maximum, the number of muons at ground, and the energy spectrum of muons in extensive air showers are presented.', arxiv_id='(Riehn et al., 2017)', published='2017-09-21'), ArxivSearchResult(title='A new version of the event generator Sibyll', authors=['F. Riehn', 'R. Engel', 'A. Fedynitch', 'T. K. Gaisser', 'T. Stanev'], summary='The event generator Sibyll can be used for the simulation of hadronic multiparticle production up to the highest cosmic ray energies. It is optimized for providing an economic description of those aspects of the expected hadronic final states that are needed for the calculation of air showers and atmospheric lepton fluxes. New measurements from fixed target and collider experiments, in particular those at LHC, allow us to test the predictive power of the model version 2.1, which was released more than 10 years ago, and also to identify shortcomings. Based on a detailed comparison of the model predictions with the new data we revisit model assumptions and approximations to obtain an improved version of the interaction model. In addition a phenomenological model for the production of charm particles is implemented as needed for the calculation of prompt lepton fluxes in the energy range of the astrophysical neutrinos recently discovered by IceCube. After giving an overview of the new ideas implemented in Sibyll and discussing how they lead to an improved description of accelerator data, predictions for air showers and atmospheric lepton fluxes are presented.', arxiv_id='(Riehn et al., 2015)', published='2015-10-02'), ArxivSearchResult(title='Sibyll $X_{\rm max}$ 6: ad-hoc modifications for an improved description of muon data in extensive air showers', authors=['Ralph Engel', 'Anatoli Fedynitch', 'Felix Riehn'], summary='Current simulations of air showers produced by ultra-high energy cosmic rays (UHECRs) do not satisfactorily describe recent experimental data, particularly when looking at the muonic shower component relative to the electromagnetic one. Discrepancies can be seen in both average values and on an individual shower-by-shower basis. It is thought that the muonic part of the air showers isn't accurately represented in simulations, despite various attempts to boost the number of muons within standard hadronic interaction physics. In this study, we investigate whether modifying the final state of events created with Sibyll~2.3d in air shower simulations can achieve a more consistent description of the muon content observed in experimental data. We create several scenarios where we separately increase the production of baryons, $X_{\rm max}$ 7, and strange particles to examine their impact on realistic air shower simulations. Our results suggest that these ad-hoc modifications can improve the simulations, providing a closer match to the observed muon content in air showers. One side-effect of the increased muon production in the considered model versions is a smaller difference in the predicted total muon numbers for proton and iron showers. However, more research is needed to find out whether any of these adjustments offers a realistic solution to the mismatches seen in data, and to identify the precise physical process causing these changes in the model. We hope that these modified model versions will also help to develop improved machine-learning analyses of air shower data and to estimate sys. uncertainties related to shortcomings of hadronic interaction models.', arxiv_id='(Riehn et al., 2023)', published='2023-09-11'), ArxivSearchResult(title='Sibyll $X_{\rm max}$ 8', authors=['Ralph Engel', 'Anatoli Fedynitch', 'Felix Riehn'], summary='In the last decade, an increasing number of datasets have revealed a consistent discrepancy between the number of muons measured in ultra-high-energy extensive air showers (EAS) and the numbers predicted by simulations. This gap persists despite incorporating Large Hadron Collider (LHC) data into the tuning of current hadronic interaction models, leading to the phenomenon often termed the ''muon puzzle''. To gain a deeper understanding of the potential origins of this muon puzzle, we have developed Sibyll $X_{\rm max}$ 9, a series of phenomenologically modified versions of Sibyll 2.3d. In these models, we have increased muon production by altering $\ln A$ 0, baryon-antibaryon pair, or kaon production in hadronic multiparticle production processes. These variants remain within bounds from provided by accelerator measurements, including those from the LHC and fixed-target experiments, notably NA49 and NA61, showing a level of consistency comparable to Sibyll 2.3d. Our findings show that these modifications can increase the muon count in EAS by up to 35%, while minimally affecting the depth of shower maximum ( $\ln A$ 1) and other shower variables. Additionally, we assess the impact of these modifications on various observables, including inclusive muon and neutrino fluxes and the multiplicities of muon bundles in deep underground and water/ice Cherenkov detectors. We aim for at least one of these model variants to offer a more accurate representation of EAS data at the highest energies, thereby enhancing the quality of Monte Carlo predictions used in training neural networks. This improvement is crucial for achieving more reliable data analyses and interpretations.', arxiv_id='(Riehn et al., 2024)', published='2024-04-03')] Searching for air-shower validation studies that test the SIBYLL 2.3 family with muon and spectrum data. [ArxivSearchResult(title='Results from recent analysis of KASCADE-Grande data', authors=['M. Bertaina', 'W. D. Apel', 'J. C. Arteaga-Velazquez', 'K. Daumiller', 'F. Fenu', 'T. H. Huege', 'R. Kampert', 'D. Kostunin', 'Y. V. Mikhailova', 'M. P. Panasyuk'], summary='KASCADE and its extension array of KASCADE-Grande were devoted to measure individual air showers of cosmic rays in the primary energy range of 100 TeV to 1 EeV. The experiment has substantially contributed to investigate the energy spectrum and mass composition of cosmic rays in the transition region from galactic to extragalactic origin of cosmic rays as well as to quantify the characteristics of hadronic interaction models in the air shower development through validity tests using the multi-detector information from KASCADE-Grande. Although the data accumulation was completed in 2013, data analysis is still continuing. Recently, we investigated the reliability of the new hadronic interactions models of the SIBYLL version 2.3d only with the energy spectra from the KASCADE-Grande data. The evolution of the muon content of high energy air showers in the atmosphere is studied as well, using EPOS-LHC, SIBYLL 2.3, QGSJET-II-04 and SIBYLL 2.3c. In this talk, recent results from KASCADE-Grande and the update of the KASCADE Cosmic Ray Data Centre (KCDC) will be discussed.', arxiv_id='(Kang et al., 2022)', published='2022-08-22'), ArxivSearchResult(title='Latest results from the KASCADE-Grande data analysis', authors=['V. de Souza', 'W. D. Apel', 'J. C. Arteaga-Velazquez', 'K. Bekk', 'J. Blümer', 'M. Bertaina', 'J. Candia', 'M. Catena', 'F. Chiavassa', 'F. Di Pierro'], summary='Over the past 20 years, KASCADE and its extension KASCADE-Grande were dedicated to measure high-energy cosmic rays with primary energies of 100 TeV to 1 EeV. The data accumulation was fully completed and all experimental components were dismantled, though the analysis of the high-quality data is still continued. E.g., we investigated the validity of the hadronic interaction model of the new SIBYLL version 2.3c. We also published a new result of a search for large-scale anisotropies performed with the KASCADE-Grande data. Investigation of the attenuation length of the muon in the atmosphere is also updated with the predictions of the SIBYLL 2.3 interaction model. We investigated, in addition, the muon content of high-energy air showers and compared them to all post-LHC interaction models. In this contribution, the new and updated results from KASCADE-Grande will be presented. An update of the web-based data center KCDC offering the original scientific data from KASCADE-Grande to the public will be briefly discussed as well.', arxiv_id='(Kang et al., 2019)', published='2019-12-19'), ArxivSearchResult(title='Measurement of the attenuation length of the muon content in extensive air showers from 0.3 to 30 PeV with LHAASO', authors=['Zhen Cao', 'Fengrui Zhu', 'for the LHAASO Collaboration'], summary='The attenuation length of the muon content in extensive air showers provides important information regarding the generation and development of air showers. This information can be used not only to improve the description of such showers but also to test fundamental models of hadronic interactions. Using data from the LHAASO-KM2A experiment, the development of the muon content in high-energy air showers was studied. The attenuation length of muon content in the air showers was measured from experimental data in the energy range from 0.3 to 30 PeV using the constant intensity cut method. By comparing the attenuation length of the muon content with predictions from high-energy hadronic interaction models (QGSJET-II-04, SIBYLL 2.3d, and EPOS-LHC), it is evident that LHAASO results are significantly shorter than those predicted by the first two models (QGSJET-II-04 and SIBYLL 2.3d) but relatively close to those predicted by the third model (EPOS-LHC). Thus, the LHAASO data favor the EPOS-LHC model over the other two models. The three interaction models confirmed an increasing trend in the attenuation length as the cosmic-ray energy increases.', arxiv_id='(Collaboration, 2024)', published='2024-10-17'), ArxivSearchResult(title='Multimuons in cosmic-ray events as seen in ALICE at the LHC', authors=['The ALICE collaboration'], summary='ALICE is a large experiment at the CERN Large Hadron Collider. Located 52 meters underground, its detectors are suitable to measure muons produced by cosmic-ray interactions in the atmosphere. In this paper, the studies of the cosmic muons registered by ALICE during Run 2 (2015--2018) are described. The analysis is limited to multimuon events defined as events with more than four detected muons ( $\ln A$ 2) and in the zenith angle range $\ln A$ 3. The results are compared with Monte Carlo simulations using three of the main hadronic interaction models describing the air shower development in the atmosphere: QGSJET-II-04, EPOS-LHC, and SIBYLL 2.3d. The interval of the primary cosmic-ray energy involved in the measured muon multiplicity distribution is about $\ln A$ 4~eV. In this interval none of the three models is able to describe precisely the trend of the composition of cosmic rays as the energy increases. However, QGSJET-II-04 is found to be the only model capable of reproducing reasonably well the muon multiplicity distribution, assuming a heavy composition of the primary cosmic rays over the whole energy range, while SIBYLL 2.3d and EPOS-LHC underpredict the number of muons in a large interval of multiplicity by more than $\ln A$ 5 and $\ln A$ 6, respectively. The rate of high muon multiplicity events ( $\ln A$ 7) obtained with QGSJET-II-04 and SIBYLL 2.3d is compatible with the data, while EPOS-LHC produces a significantly lower rate ( $\ln A$ 8 of the measured rate). For both QGSJET-II-04 and SIBYLL 2.3d, the rate is close to the data when the composition is assumed to be dominated by heavy elements, an outcome compatible with the average energy $\ln A$ 9 eV of these events. This result places significant constraints on more exotic production mechanisms.', arxiv_id='(Collaboration, 2024)', published='2024-10-23')] Searching for forward-production measurements that directly constrain the SIBYLL 2.3 family in the kinematic region most relevant to air-shower first interactions. [ArxivSearchResult(title='Measurement of inclusive forward neutron production cross section in proton-proton collisions at $X_{\rm max}$ 0 with the LHCf Arm2 detector', authors=['O. Adriani', 'E. Berti', 'L. Bonechi', 'M. Bongi', 'G. Castellini', 'R. D'Alessandro', 'M. Del Fabbro', 'M. Haguenauer', 'Y. Itow', 'K. Kasahara'], summary='In this paper, we report the measurement relative to the production of forward neutrons in proton-proton collisions at $X_{\rm max}$ 1 obtained using the LHCf Arm2 detector at the Large Hadron Collider. The results for the inclusive differential production cross section are presented as a function of energy in three different pseudorapidity regions: $X_{\rm max}$ 2, $X_{\rm max}$ 3 and $X_{\rm max}$ 4. The analysis was performed using a data set acquired in June 2015 that corresponds to an integrated luminosity of $X_{\rm max}$ 5. The measurements were compared with the predictions of several hadronic interaction models used to simulate air showers generated by Ultra High Energy Cosmic Rays. None of these generators showed good agreement with the data for all pseudorapidity intervals. For $X_{\rm max}$ 6, no model is able to reproduce the observed peak structure at around $X_{\rm max}$ 7 and all models underestimate the total production cross section: among them, QGSJET II-04 shows the smallest deficit with respect to data for the whole energy range. For $X_{\rm max}$ 8 and $X_{\rm max}$ 9, the models having the best overall agreement with data are SIBYLL 2.3 and EPOS-LHC, respectively: in particular, in both regions SIBYLL 2.3 is able to reproduce the observed peak structure at around $\langle X_{\rm max}\rangle$ 0.', arxiv_id='(Adriani et al., 2018)', published='2018-08-29'), ArxivSearchResult(title='The hadronic interaction model SIBYLL 2.3c and Feynman scaling', authors=['Felix Riehn', 'Ralph Engel', 'Anatoli Fedynitch', 'Thomas K. Gaisser', 'Todor Stanev'], summary='The Monte Carlo model Sibyll has been designed for efficient simulation of hadronic multiparticle production up to the highest energies as needed for interpreting cosmic ray measurements. For more than 15 years, version 2.1 of Sibyll has been one of the standard models for air shower simulation. Motivated by data of LHC and fixed-target experiments and a better understanding of the phenomenology of hadronic interactions, we have developed an improved version of this model, version 2.3, which has been released in 2016. In this contribution we present a revised version of this model, called Sibyll 2.3c, that is further improved by adjusting particle production spectra to match the expectation of Feynman scaling in the fragmentation region. After a brief introduction to the changes implemented in Sibyll 2.3 and 2.3c with respect to Sibyll 2.1, the current predictions of the model for the depth of shower maximum, the number of muons at ground, and the energy spectrum of muons in extensive air showers are presented.', arxiv_id='(Riehn et al., 2017)', published='2017-09-21'), ArxivSearchResult(title='Latest neutrino results from the FASER experiment and their implications for forward hadron production', authors=['P. A. Zyla', 'S. Taneja', 'on behalf of the FASER collaboration'], summary='The muon puzzle -- an excess of muons relative to simulation predictions in ultra-high-energy cosmic-ray air showers -- has been reported by many experiments. This suggests that forward particle production in hadronic interactions is not fully understood. Some of the scenarios proposed to resolve this predict reduced production of forward neutral pions and enhanced production of forward kaons (or other particles). The FASER experiment at the LHC is located 480 m downstream of the ATLAS interaction point and is sensitive to neutrinos and muons, which are the decay products of forward charged pions and kaons. In this study, the latest measurements of electron and muon neutrino fluxes are presented using the data corresponding to 9.5 fb $\langle X_{\rm max}\rangle$ 1 and 65.6 fb $\langle X_{\rm max}\rangle$ 2 of proton-proton collisions with $\langle X_{\rm max}\rangle$ 3 TeV by the FASER $\langle X_{\rm max}\rangle$ 4 and the FASER electronic detector, respectively. These fluxes are compared with predictions from recent hadronic interaction models, including EPOS-LHCr, SIBYLL 2.3e, and QGSJET 3. The predictions are generally consistent with the measured fluxes from FASER, although some discrepancies appear in certain energy bins. More precise flux measurements with additional data will follow soon, enabling validation of pion, kaon, and charm meson production with finer energy binning, reduced uncertainties, and multi-differential analyses.', arxiv_id='(Collaboration et al., 31 Jul 2025)', published='2025-07-31')] Searching for the review that connects LHC-tuned hadronic models, including SIBYLL-family models, to UHECR anomalies and muon deficits. [ArxivSearchResult(title='Ultrahigh-energy cosmic rays: Anomalies, QCD, and LHC data', authors=['J.L. Albacete', 'J.L. Amaral de Souza', 'J.G. Milhano', 'Y. Nazarenko', 'J. Pinfold', 'K. Reygers', 'P. Skands'], summary='Measurements of proton and nuclear collisions at the Large Hadron Collider at nucleon-nucleon c.m. energies up to $\langle X_{\rm max}\rangle$ 5 TeV, have improved our understanding of hadronic interactions at the highest energies reached in collisions of cosmic rays with nuclei in the earth atmosphere, up to $\langle X_{\rm max}\rangle$ 6 TeV. The Monte Carlo event generators (EPOS, QGSJET, and SIBYLL) commonly used to describe the air showers generated by ultrahigh-energy cosmic rays (UHECR, with $\langle X_{\rm max}\rangle$ 7-- $\langle X_{\rm max}\rangle$ 8 eV) feature now, after parameter retuning based on LHC Run-I data, more consistent predictions on the nature of the cosmic rays at the tail of the measured spectrum. However, anomalies persist in the data that cannot be accommodated by the models. Among others, the total number of muons (as well as their maximum production depth) remains significantly underestimated (overestimated) by all models. Comparisons of EPOS, QGSJET, and SIBYLL predictions to the latest LHC data, and to collider MC generators such as PYTHIA, indicate that improved description of hard multiple minijet production and nuclear effects may help reduce part of the data--model discrepancies, shed light on the UHECR composition approaching the observed $\langle X_{\rm max}\rangle$ 9 eV cutoff, and uncover any potential new physics responsible of the observed anomalies.', arxiv_id='(d'Enterria, 2019)', published='2019-02-25')] SIBYLL 2.3e is a hadronic interaction model in the SIBYLL 2.3x lineage, used as a high-energy event generator for extensive air-shower simulation and related astroparticle applications. In current work it appears as one of the reference post-LHC interaction models in CONEX- and CORSIKA-based analyses, alongside EPOS- and QGSJET-family models, and it is used for proton–air, proton–oxygen, and proton–proton extrapolations relevant to cosmic-ray primaries from the PeV scale to ultra-high energies (Evoli et al., 20 Feb 2026). Within the SIBYLL family, 2.3e is best understood as an evolution of the 2.3/2.3c/2.3d framework: the same core physics architecture is retained, while later retuning and validation address collider data, forward production, and muon-related tensions in air-shower phenomenology (Riehn et al., 2015).

1. Lineage and model scope

The modern SIBYLL line emerged from the transition from SIBYLL 2.1 to SIBYLL 2.3, motivated by new collider and fixed-target data and by the need for improved forward-particle and remnant modeling. The 2.3-series changes included new fits for total and elastic cross sections, a two-component Good–Walker-type diffraction treatment, explicit remnant excitation, increased baryon–antibaryon pair production, and a phenomenological charm component for prompt lepton calculations (Riehn et al., 2015). SIBYLL 2.3c then revised the 2.3 implementation to restore approximate Feynman scaling in the fragmentation region by adjusting particle-production spectra, especially after identifying scaling-violating effects associated with the popcorn diquark-breakup mechanism (Riehn et al., 2017).

In that sense, SIBYLL 2.3e is not a separate conceptual framework but a later 2.3x realization used in contemporary analyses. Recent UHECR composition studies treat SIBYLL 2.3e as one of the current state-of-the-art hadronic interaction models, on equal footing with EPOS LHC-R and QGSJet-III-01 (Evoli et al., 20 Feb 2026). A common misconception is that 2.3e should be read as a radical redesign of SIBYLL; the literature instead supports continuity with the 2.3-series physics basis, with later retuning and validation layered onto the same underlying minijet-plus-fragmentation structure (Riehn et al., 2015).

2. Physics architecture inherited by the 2.3e line

The 2.3-series framework is built around a minijet model embedded in an eikonal multiple-scattering picture, with Lund string fragmentation used for hadronization (Riehn et al., 2015). Soft and hard interactions are treated within the same general multiple-interaction language, while diffraction is handled through a Good–Walker-type approach with ground and excited states for projectile and target. Explicit remnant treatment is central: instead of encoding leading-particle effects solely through valence-string fragmentation, the model constructs excited remnants that subsequently decay, thereby shaping forward nucleon and meson spectra (Riehn et al., 2015).

For the 2.3c revision, the fragmentation-region treatment became especially important. Feynman scaling is formulated in terms of inclusive spectra in the variable $σ^2(X_{\rm max})$ 0, and 2.3c was introduced to recover approximate scaling behavior at large $σ^2(X_{\rm max})$ 1 after 2.3 showed an undesirable hardening of forward meson spectra with energy (Riehn et al., 2017). The revision retained explicit remnants while modifying fragmentation details and remnant excitation so that forward $σ^2(X_{\rm max})$ 2 and kaon spectra behaved more conservatively under extrapolation. The same section of the lineage is also where the model’s enhanced vector-meson production, especially leading $σ^2(X_{\rm max})$ 3, becomes important for shower physics because $σ^2(X_{\rm max})$ 4 feeds the hadronic branch whereas $σ^2(X_{\rm max})$ 5 transfers energy promptly to the electromagnetic cascade (Riehn et al., 2015).

The shower-level consequences were already visible in 2.3c: compared with SIBYLL 2.1, the predicted mean $σ^2(X_{\rm max})$ 6 became deeper by about $σ^2(X_{\rm max})$ 7, while the total number of muons at ground increased by a factor of about $σ^2(X_{\rm max})$ 8 at $σ^2(X_{\rm max})$ 9 and about $X_{\rm max}$ 0 at $X_{\rm max}$ 1 (Riehn et al., 2017). These are family-defining shifts, and they frame how 2.3e is typically interpreted in current analyses.

3. Collider calibration and forward-production constraints

The UHECR review literature places SIBYLL with EPOS and QGSJET among the three Reggeon-field-theory-type models commonly interfaced to CORSIKA or CONEX for air-shower simulation, with the relevant shower observables dominated by $X_{\rm max}$ 2, $X_{\rm max}$ 3, midrapidity multiplicity, inelasticity $X_{\rm max}$ 4, and transverse-momentum spectra (d'Enterria, 2019). In that comparison, SIBYLL is singled out for using a logarithmically running hard–soft separation scale $X_{\rm max}$ 5, in contrast to PYTHIA’s more rapidly evolving cutoff and to EPOS/QGSJET implementations based on fixed $X_{\rm max}$ 6 cutoffs with low- $X_{\rm max}$ 7 saturation corrections (d'Enterria, 2019). This difference is a structural constraint on the 2.3x line because it governs semi-hard minijet activity, multiplicity growth, and the balance between $X_{\rm max}$ 8 and $X_{\rm max}$ 9 at energies far above the LHC.

Forward neutron production provides a particularly sharp test of the SIBYLL family. The LHCf Arm2 measurement at $^{-2}$ 0 TeV found that no model reproduced all pseudorapidity intervals, but SIBYLL 2.3 gave the best overall agreement in the region $^{-2}$ 1 and reproduced the observed peak structure at around $^{-2}$ 2– $^{-2}$ 3 TeV in both $^{-2}$ 4 and $^{-2}$ 5 (Adriani et al., 2018). At the same time, SIBYLL 2.3 failed in the most extreme forward interval $^{-2}$ 6, where it missed the observed $^{-2}$ 7 TeV peak and underestimated the total production cross section. That result matters directly for the 2.3e line because the same forward baryon sector controls leading-particle energy transport in the first generations of air showers (Adriani et al., 2018).

Direct proton–oxygen data have now added a nuclear benchmark in the exact energy regime relevant for PeV cosmic rays. ATLAS measured a fiducial $^{-2}$ 8–O cross section of

$^{-2}$ 9

and an extrapolated inelastic proton–air cross section of

$^{-2}$ 0

with SIBYLL 2.3e included among the comparison models (Collaboration, 7 Apr 2026). In that study, SIBYLL 2.3e used an acceptance $^{-2}$ 1 for the $^{-2}$ 2–O extrapolation, predicted an inelastic $^{-2}$ 3–O cross section of $^{-2}$ 4 mb, and described the charged-particle $^{-2}$ 5 distribution within $^{-2}$ 6, but it generally predicted harder $^{-2}$ 7 spectra than the data and overestimated $^{-2}$ 8 at low multiplicity while underestimating it at high multiplicity (Collaboration, 7 Apr 2026). This combination suggests that the 2.3e line is already competitive in central charged-particle density but still imperfect in the transverse-momentum and event-activity structure of proton–nucleus collisions.

4. Air-shower observables and composition inference

SIBYLL-family models are judged primarily through their predictions for $^{-2}$ 9, muon number, and the electron–muon partition in extensive air showers. KASCADE-Grande provides a clear picture of how changes within the 2.3 family propagate into composition inference. In that dataset, SIBYLL 2.3d was characterized as an update that improves the $X_{\rm max}$ 00 ratio in hadronization, increasing the muon number by more than $X_{\rm max}$ 01 relative to SIBYLL 2.1 and giving about $X_{\rm max}$ 02 more muons than EPOS-LHC and QGSJET-II-04 (Kang et al., 2022). The same analysis found that the heavy-component knee reconstructed with SIBYLL 2.3d occurs at

$X_{\rm max}$ 03

with the model yielding the lowest heavy flux and therefore the lightest inferred composition among the tested models (Kang et al., 2022).

Muon-sector consistency remains more problematic. KASCADE-Grande found that none of EPOS-LHC, SIBYLL 2.3, QGSJET-II-04, or SIBYLL 2.3c describes $X_{\rm max}$ 04 consistently across all energies and zenith angles; SIBYLL 2.3 and 2.3c overpredict vertical-shower muons between $X_{\rm max}$ 05 PeV and $X_{\rm max}$ 06 EeV while agreeing better for inclined showers (Kang et al., 2022). A related KASCADE-Grande study also reported that SIBYLL 2.3c has about $X_{\rm max}$ 07 fewer muons than QGSJetII-04 at fixed shower size, implying a heavier inferred composition when it is used in the reconstruction chain (Kang et al., 2019). These are not contradictory results; they indicate that muon normalization, angular dependence, and attenuation are entangled and version-dependent across the 2.3 family.

SIBYLL 2.3e now enters directly into UHECR composition analyses through updated $X_{\rm max}$ 08 parametrizations. CONEX 7.801 simulations for H, He, N, Si, and Fe at $X_{\rm max}$ 09 to $X_{\rm max}$ 10 in steps of $X_{\rm max}$ 11 were used to fit the mean depth with

$X_{\rm max}$ 12

where $X_{\rm max}$ 13 and $X_{\rm max}$ 14, giving for SIBYLL 2.3e

$X_{\rm max}$ 15

Across the full energy range, residuals between this parametrization and the raw simulations are at the level of about $X_{\rm max}$ 16 or less for each mass group (Evoli et al., 20 Feb 2026). These fits are a practical indication of how 2.3e is now embedded in precision composition workflows rather than being used only as an event generator.

5. Muon tensions, attenuation anomalies, and phenomenological extensions

The broad UHECR review literature remains unequivocal that LHC retuning did not remove the muon problem. For the main post-LHC RFT models, including SIBYLL-family implementations, the observed number of muons is still underestimated by about $X_{\rm max}$ 17, with even larger discrepancies at large core distances, and the muon production depth is overestimated (d'Enterria, 2019). The same review argues that increasing charm production is not the main solution; in PYTHIA-based studies, heavy quarks contribute negligibly to inclusive muons, whereas enhanced light-hadron production from minijets and improved baryon production are the more promising levers (d'Enterria, 2019).

Independent shower datasets sharpen that conclusion for SIBYLL-family models. LHAASO-KM2A measured the attenuation length of the muon content from $X_{\rm max}$ 18 to $X_{\rm max}$ 19 PeV and found that SIBYLL 2.3d, like QGSJET-II-04, predicts attenuation lengths that are significantly longer than the data, whereas EPOS-LHC is relatively close (Collaboration, 2024). ALICE’s underground multimuon analysis in the range $X_{\rm max}$ 20 likewise found that SIBYLL 2.3d underpredicts the number of muons in a large multiplicity interval by more than $X_{\rm max}$ 21, although its rate for very high multiplicity events with $X_{\rm max}$ 22 is compatible with the data under a heavy-composition assumption (Collaboration, 2024). These results indicate that the residual tension is not confined to a single observable or energy decade.

That setting motivated the nonstandard Sibyll $X_{\rm max}$ 23 variants built on top of SIBYLL 2.3d. By enhancing $X_{\rm max}$ 24, baryon–antibaryon, or kaon production in the hadronic final state, these models can increase the muon count in EAS by up to $X_{\rm max}$ 25 while minimally affecting $X_{\rm max}$ 26 (Riehn et al., 2024). The $X_{\rm max}$ 27-enhanced and mixed variants are the most effective because they redirect energy away from $X_{\rm max}$ 28 and back into the hadronic cascade. A common misconception is that such variants are already SIBYLL 2.3e; they are not. They are explicitly described as phenomenologically modified versions of SIBYLL 2.3d intended to explore what changes would be needed to improve the muonic component (Riehn et al., 2024).

6. Contemporary uses of SIBYLL 2.3e

In current practice, SIBYLL 2.3e is used not only for full shower generation but also for reduced parametrizations and cross-check analyses. The updated $X_{\rm max}$ 29 study cited above provides not only the mean-depth fit but also two variance models. For the exponential representation,

$X_{\rm max}$ 30

SIBYLL 2.3e is fitted with

$X_{\rm max}$ 31

and the resulting residuals in $X_{\rm max}$ 32 are below about $X_{\rm max}$ 33 for all primary masses (Evoli et al., 20 Feb 2026). The same work also supplies a generalized Gumbel description of the full $X_{\rm max}$ 34 distributions, validated at the level of a few $X_{\rm max}$ 35 in the mean and a few percent in the width, which makes SIBYLL 2.3e directly usable in forward-folding composition analyses (Evoli et al., 20 Feb 2026).

SIBYLL 2.3e is also now part of consistency tests that go beyond one-dimensional moments. In the Pierre Auger hybrid correlation analysis, the model is one of the latest post-LHC interaction models used to map the observed correlation between $X_{\rm max}$ 36 and surface-detector signal into a constraint on the spread of nuclear masses (Yushkov, 11 Jul 2025). In that study, the data below the ankle require $X_{\rm max}$ 37, whereas the SIBYLL-based FD $X_{\rm max}$ 38 composition is proton–helium dominated with $X_{\rm max}$ 39, leading to a significant mismatch in the correlation observable (Yushkov, 11 Jul 2025). The result does not by itself disqualify SIBYLL 2.3e, but it shows that a consistent simultaneous description of $X_{\rm max}$ 40 and surface signal remains difficult.

Finally, SIBYLL 2.3e now participates in forward-neutrino constraints. FASER compared $X_{\rm max}$ 41 and $X_{\rm max}$ 42 flux measurements in $X_{\rm max}$ 43 collisions at $X_{\rm max}$ 44 TeV with predictions from EPOS-LHCr, SIBYLL 2.3e, and QGSJET 3, finding that the predictions are generally consistent with the data although some discrepancies appear in certain energy bins (Collaboration et al., 31 Jul 2025). This is significant because forward neutrinos probe the same pion-, kaon-, and charm-production channels that feed the atmospheric muon and neutrino components. A plausible implication is that SIBYLL 2.3e now occupies a dual role: it is both a production hadronic model for air-shower simulations and a continuously testable hypothesis about forward QCD in a regime where collider and cosmic-ray observables are converging (Collaboration et al., 31 Jul 2025).