QGSJET-III: Advanced Cosmic-Ray Simulator

• QGSJET-III is a Monte Carlo generator for high-energy hadronic interactions that uses Reggeon Field Theory to model soft, semihard, and diffractive processes.
• It incorporates a novel microscopic treatment of higher-twist corrections and a detailed implementation of pion exchange to improve particle production predictions.
• QGSJET-III maintains close agreement with previous models on air shower observables while offering enhanced precision in hadronization and muon production profiles.

QGSJET-III, often referred to informally as “QGSJET 3,” is the newest generation of Sergey Ostapchenko’s QGSJET family of Monte Carlo generators for high-energy hadronic interactions, developed primarily for simulations of cosmic-ray induced extensive air showers (EAS). It is formulated as a Reggeon Field Theory (RFT) model in which soft and semihard multiple scattering, diffraction, nonlinear screening, nuclear interactions, and forward hadron production are treated within a common framework. In the published characterization of the model, QGSJET-III is presented less as a radical departure from QGSJET-II-04 than as a substantial theoretical refinement, notably through a new microscopic treatment of higher-twist corrections to hard scattering and a more complete treatment of pion exchange, while retaining the earlier QGSJET machinery for soft and semihard Pomeron dynamics and enhanced-diagram resummation (Ostapchenko, 2022).

1. Terminology and lineage

A recurrent source of confusion is that the phrase “QGSJET 3” has been used loosely for different members of the QGSJET family. In the supplied literature, QGSJET-II-03 is a distinct model version and is not the same object as QGSJET-III; several papers explicitly analyze QGSJET-II-03 or QGSJET-II-04 while not addressing QGSJET-III at all (Dedenko et al., 2015). By contrast, the papers that directly define QGSJET-III are the formal and phenomenological studies published in 2022 and 2024, together with the later charm-production extension (Ostapchenko, 2022).

The family history visible in the literature runs from the original QGSJET and QGSJET-01, through QGSJET-II and its tuned release QGSJET-II-04, to QGSJET-III. Older work used QGSJET-01 as a benchmark high-energy model in CORSIKA studies of proton- and iron-induced showers, while later collider-oriented benchmark studies employed QGSJET-II-04 as the contemporary QGSJET implementation (Thakuria et al., 2011). QGSJET-III inherits the QGSJET-II treatment of multichannel Good–Walker diffraction, soft-plus-semihard Pomerons, and enhanced Pomeron diagrams, whose Monte Carlo realization had already been formulated in detail for QGSJET-II (Ostapchenko, 2010).

Version	Role in the literature	Note
QGSJET-01	Earlier benchmark in CORSIKA EAS studies	Used in proton/iron shower comparisons (Thakuria et al., 2011)
QGSJET-II-03	Pre-LHC QGSJET-II release	Sometimes loosely conflated with “QGSJET 3,” but distinct (Dedenko et al., 2015)
QGSJET-II-04	LHC-retuned QGSJET-II release	Used in collider and EAS benchmarking (d'Enterria et al., 2016)
QGSJET-III	Newest QGSJET generation	Formalism, hadronization, EAS predictions, and uncertainty studies (Ostapchenko, 2024)

2. Formal architecture

The theoretical backbone of QGSJET-III is RFT expressed in a partonic language through Pomeron exchange and multiple scattering in impact-parameter space. In the standard eikonal picture, the total proton-proton cross section is written as

$$\sigma^{\rm tot}_{pp}(s)=2\int d^2b\left[1-e^{-\chi_{pp}(s,b)}\right],$$

where $s$ is the squared center-of-mass energy and $\chi_{pp}(s,b)$ is the interaction eikonal (Ostapchenko, 2022). In the older Quark–Gluon String / Dual Parton formulation inherited by QGSJET, the elementary rescattering channel is represented by a Pomeron eikonal,

$$\chi_{pp}^{\mathbb P}(s,b)=\frac{\gamma_p^2\, s^{\Delta}}{2R_p^2+\alpha_{\mathbb P}'\ln s}\, \exp\!\left[- \frac{b^2/4}{2R_p^2+\alpha_{\mathbb P}'\ln s}\right],$$

with $\gamma_p$, $\Delta$, $R_p$, and $\alpha_{\mathbb P}'$ controlling the coupling, energy growth, transverse size, and transverse diffusion, respectively (Ostapchenko, 2022).

Historically important in QGSJET is the “semihard Pomeron” concept. QGSJET-III retains the split between a nonperturbative part of the cascade, represented phenomenologically by Pomerons below the cutoff $Q_0^2$, and a perturbative part treated with pQCD above that scale. The model emphasizes that semihard processes rise much faster with energy than purely soft ones, with rates summarized as

$$\propto s^{\Delta_{\rm hard}},\qquad \Delta_{\rm hard}\simeq 0.3,$$

versus

$s$0

so the early stages of semihard cascades become increasingly important for projectile-fragmentation-region production and thus for EAS development (Ostapchenko, 2022).

QGSJET-III also retains the QGSJET-II treatment of nonlinear interaction effects through Pomeron–Pomeron interactions and all-order resummation of enhanced diagrams. In the formal presentation of QGSJET-III, this earlier structure is supplemented by two major additions: an explicit treatment of color fluctuations via Good–Walker-type Fock states of different transverse sizes and parton densities, and a phenomenological implementation of higher-twist corrections to hard scattering (Ostapchenko, 2024). The latter is introduced because ordinary leading-twist minijet production rises too rapidly as $s$1 decreases, making predictions strongly dependent on the arbitrary soft-hard separation scale. QGSJET-III models coherent rescattering of produced $s$2-channel partons on soft gluon pairs and introduces one new phenomenological parameter, $s$3, to control the strength of this higher-twist contribution. The reported consequences are a drastic reduction in sensitivity to the cutoff $s$4, moderation of the energy rise of cross sections and multiplicities, and stronger damping of low-$s$5 jet production in more central collisions (Ostapchenko, 2022).

3. Hadronization and particle production

In QGSJET-III, event generation proceeds in two stages. First, the model constructs the macro-configuration of the interaction, determining the network of cut Pomerons and, where relevant, perturbative $s$6- and $s$7-channel parton evolution above $s$8. Second, each cut Pomeron is converted into two color strings, and these strings are hadronized by an iterative string-fragmentation procedure (Ostapchenko, 2024).

The constituent partons attached to a projectile or target hadron share light-cone momentum fractions according to Regge-motivated distributions. A central parameter in QGSJET-III is the effective small-$s$9 exponent for constituent sea quarks,

$\chi_{pp}(s,b)$0

with the implemented value

$\chi_{pp}(s,b)$1

This differs from earlier QGSJET/QGSJET-II practice, where the corresponding behavior was tied more directly to Regge expectations, and it is used to absorb effects associated with the minimal rapidity size $\chi_{pp}(s,b)$2 of Pomeron–Pomeron interactions (Ostapchenko, 2024).

The hadronization itself is a phenomenological string-fragmentation model. Most short-lived resonances are not generated explicitly; their effects are assumed to be included by duality in the stable-hadron yields. Explicit exceptions are $\chi_{pp}(s,b)$3, $\chi_{pp}(s,b)$4, $\chi_{pp}(s,b)$5 mesons, and $\chi_{pp}(s,b)$6 mesons. The resonance weights quoted for QGSJET-III are

$\chi_{pp}(s,b)$7

with the latter chosen so that roughly 50% of final pions arise from $\chi_{pp}(s,b)$8 decays (Ostapchenko, 2024).

A distinctive update relative to QGSJET-II-04 is the more systematic treatment of pion exchange. QGSJET-III includes explicit RRP contributions with $\chi_{pp}(s,b)$9, important for forward neutron production and for forward $$\chi_{pp}^{\mathbb P}(s,b)=\frac{\gamma_p^2\, s^{\Delta}}{2R_p^2+\alpha_{\mathbb P}'\ln s}\, \exp\!\left[- \frac{b^2/4}{2R_p^2+\alpha_{\mathbb P}'\ln s}\right],$$0-meson production in pion-induced collisions. The model samples the leading hadron from the pion-exchange distribution and then treats the rest of the event as an inelastic interaction of the exchanged virtual pion with the target at reduced center-of-mass energy (Ostapchenko, 2024).

The particle-production validation program spans fixed-target and collider data. QGSJET-III gives satisfactory descriptions of proton, charged-pion, charged-kaon, and neutron production in $$\chi_{pp}^{\mathbb P}(s,b)=\frac{\gamma_p^2\, s^{\Delta}}{2R_p^2+\alpha_{\mathbb P}'\ln s}\, \exp\!\left[- \frac{b^2/4}{2R_p^2+\alpha_{\mathbb P}'\ln s}\right],$$1 and $$\chi_{pp}^{\mathbb P}(s,b)=\frac{\gamma_p^2\, s^{\Delta}}{2R_p^2+\alpha_{\mathbb P}'\ln s}\, \exp\!\left[- \frac{b^2/4}{2R_p^2+\alpha_{\mathbb P}'\ln s}\right],$$2 interactions at 158 GeV/$$\chi_{pp}^{\mathbb P}(s,b)=\frac{\gamma_p^2\, s^{\Delta}}{2R_p^2+\alpha_{\mathbb P}'\ln s}\, \exp\!\left[- \frac{b^2/4}{2R_p^2+\alpha_{\mathbb P}'\ln s}\right],$$3, and it describes $$\chi_{pp}^{\mathbb P}(s,b)=\frac{\gamma_p^2\, s^{\Delta}}{2R_p^2+\alpha_{\mathbb P}'\ln s}\, \exp\!\left[- \frac{b^2/4}{2R_p^2+\alpha_{\mathbb P}'\ln s}\right],$$4-meson production in $$\chi_{pp}^{\mathbb P}(s,b)=\frac{\gamma_p^2\, s^{\Delta}}{2R_p^2+\alpha_{\mathbb P}'\ln s}\, \exp\!\left[- \frac{b^2/4}{2R_p^2+\alpha_{\mathbb P}'\ln s}\right],$$5 and $$\chi_{pp}^{\mathbb P}(s,b)=\frac{\gamma_p^2\, s^{\Delta}}{2R_p^2+\alpha_{\mathbb P}'\ln s}\, \exp\!\left[- \frac{b^2/4}{2R_p^2+\alpha_{\mathbb P}'\ln s}\right],$$6 rather well, with pion exchange dominating the forward part of the $$\chi_{pp}^{\mathbb P}(s,b)=\frac{\gamma_p^2\, s^{\Delta}}{2R_p^2+\alpha_{\mathbb P}'\ln s}\, \exp\!\left[- \frac{b^2/4}{2R_p^2+\alpha_{\mathbb P}'\ln s}\right],$$7 spectra (Ostapchenko, 2024). At the same time, important deficiencies remain. Antiproton $$\chi_{pp}^{\mathbb P}(s,b)=\frac{\gamma_p^2\, s^{\Delta}}{2R_p^2+\alpha_{\mathbb P}'\ln s}\, \exp\!\left[- \frac{b^2/4}{2R_p^2+\alpha_{\mathbb P}'\ln s}\right],$$8 spectra in $$\chi_{pp}^{\mathbb P}(s,b)=\frac{\gamma_p^2\, s^{\Delta}}{2R_p^2+\alpha_{\mathbb P}'\ln s}\, \exp\!\left[- \frac{b^2/4}{2R_p^2+\alpha_{\mathbb P}'\ln s}\right],$$9 and $\gamma_p$0 at 158 GeV/$\gamma_p$1 are too hard, charged kaon production in $\gamma_p$2 is underestimated by about $\gamma_p$3, and proton and antiproton production in $\gamma_p$4 is considerably underestimated (Ostapchenko, 2024).

At collider energies, QGSJET-III reproduces charged-particle pseudorapidity densities in $\gamma_p$5 at $\gamma_p$6 and $\gamma_p$7 TeV satisfactorily, and it gives a substantially better description of $\gamma_p$8 pseudorapidity densities than QGSJET-II-04 (Ostapchenko, 2024). By contrast, identified-hadron $\gamma_p$9 spectra at central rapidity in 7 TeV $\Delta$0 collisions are described only imperfectly, a limitation the paper connects to the simplified fragmentation model and approximate resonance treatment (Ostapchenko, 2024). Forward neutron spectra agree satisfactorily with LHCf at 13 TeV but show some underestimation at 7 TeV, while forward $\Delta$1 spectra are reproduced satisfactorily overall, with some underestimation around $\Delta$2 TeV (Ostapchenko, 2024).

4. Extensive air showers and uncertainty bounds

For EAS applications, QGSJET-III is presented as theoretically improved but phenomenologically conservative. The 2022 overview reports that, relative to QGSJET-II-04, the average shower maximum depth $\Delta$3 for proton-induced showers changes by about $\Delta$4, the variation of the new parameter $\Delta$5 by $\Delta$6 shifts $\Delta$7 by only about $\Delta$8, and the EAS muon content $\Delta$9 differs by only about $R_p$0 (Ostapchenko, 2022). A later uncertainty study phrases the comparison somewhat differently, stating that QGSJET-III predicts $R_p$1 values up to $R_p$2 larger than QGSJET-II-04 and about $R_p$3 fewer sea-level muons for $R_p$4 GeV (Ostapchenko, 2024). Taken together, these studies agree that the bulk shower observables of QGSJET-III remain very close to those of QGSJET-II-04.

The scaling of the proton-shower muon number is summarized as

$R_p$5

and the controlling pion-air quantity is the spectrum-weighted stable-hadron moment

$R_p$6

Because $R_p$7 is close to unity, this is approximately the energy fraction that remains in stable hadronic secondaries rather than being transferred promptly to the electromagnetic channel through $R_p$8 production (Ostapchenko, 2024).

The uncertainty analysis built on QGSJET-III is unusually explicit about what cannot be achieved by standard microscopic retuning. An extreme modification of pion PDFs, reducing the valence-quark light-cone momentum fraction by a factor of two and increasing the gluon share, changes $R_p$9 by less than $\alpha_{\mathbb P}'$0 (Ostapchenko, 2024). Neglecting absorptive corrections in pion exchange entirely makes the predicted muon number decrease by up to $\alpha_{\mathbb P}'$1 at $\alpha_{\mathbb P}'$2 eV, because elastic virtual-pion scattering then becomes important and produces little hadronic multiplication (Ostapchenko, 2024). The only modification identified as significantly effective for muons is enhanced kaon and $\alpha_{\mathbb P}'$3 production in pion-air collisions: using approximately $\alpha_{\mathbb P}'$4 larger kaon yields and $\alpha_{\mathbb P}'$5 larger $\alpha_{\mathbb P}'$6 yields, as suggested by comparison to NA61 $\alpha_{\mathbb P}'$7 data at 158 GeV/$\alpha_{\mathbb P}'$8, raises $\alpha_{\mathbb P}'$9 by up to about $Q_0^2$0, but at the price of serious tension with other accelerator data (Ostapchenko, 2024).

The corresponding limits on delaying shower development are similarly restrictive. A $Q_0^2$1 increase in the low-mass diffractive $Q_0^2$2 cross section, still said to be compatible with TOTEM, yields about $Q_0^2$3 more diffractive-like proton-air interactions with leading nucleon energy loss below 10% and increases $Q_0^2$4 by only about $Q_0^2$5 (Ostapchenko, 2024). Modifying the constituent sea-quark exponent from the default $Q_0^2$6 to $Q_0^2$7 reduces $Q_0^2$8 by up to about $Q_0^2$9 and increases $$\propto s^{\Delta_{\rm hard}},\qquad \Delta_{\rm hard}\simeq 0.3,$$0 by up to about $$\propto s^{\Delta_{\rm hard}},\qquad \Delta_{\rm hard}\simeq 0.3,$$1 at the highest energies (Ostapchenko, 2024). More exotic collective modifications could, in the author’s wording, increase $$\propto s^{\Delta_{\rm hard}},\qquad \Delta_{\rm hard}\simeq 0.3,$$2 by as much as about $$\propto s^{\Delta_{\rm hard}},\qquad \Delta_{\rm hard}\simeq 0.3,$$3, but such scenarios are described as strongly disfavored by LHCf forward-neutron data and by Pierre Auger measurements of the muon production depth (Ostapchenko, 2024).

5. Model comparisons and disputes

QGSJET-III is compared primarily with QGSJET-II-04, EPOS-LHC, and SIBYLL-2.3/2.3d. The explicit stance of the 2022 QGSJET-III review is polemical: it argues that differences between QGSJET-III and other interaction models are not merely irreducible model spread but are partly caused by severe deficiencies in those alternatives (Ostapchenko, 2022). The most substantial criticisms are directed at SIBYLL and EPOS-LHC.

Against SIBYLL-2.3, the criticism is foundational. QGSJET-III’s author argues that SIBYLL effectively keeps only the hardest parton-parton scattering and neglects the full initial-state parton cascade, leading to underestimated fragmentation-region production, conflict with forward LHC data, and a slower-than-correct shower development, hence deeper $$\propto s^{\Delta_{\rm hard}},\qquad \Delta_{\rm hard}\simeq 0.3,$$4 (Ostapchenko, 2022). SIBYLL-2.3 is also said to underestimate absorptive damping in the pion-exchange sector, producing too little energy dependence in forward $$\propto s^{\Delta_{\rm hard}},\qquad \Delta_{\rm hard}\simeq 0.3,$$5 production and potentially an artificial enhancement of the EAS muon content (Ostapchenko, 2022).

Against EPOS-LHC, the critique is more model-specific. The forward $$\propto s^{\Delta_{\rm hard}},\qquad \Delta_{\rm hard}\simeq 0.3,$$6 yield in QGSJET-III remains about an order of magnitude below the charged-pion yield over energies $$\propto s^{\Delta_{\rm hard}},\qquad \Delta_{\rm hard}\simeq 0.3,$$7, $$\propto s^{\Delta_{\rm hard}},\qquad \Delta_{\rm hard}\simeq 0.3,$$8, and $$\propto s^{\Delta_{\rm hard}},\qquad \Delta_{\rm hard}\simeq 0.3,$$9 GeV, whereas EPOS-LHC is said to predict a steeply rising forward baryon and antibaryon yield with energy, to the point that it exceeds charged pions away from the extreme diffractive endpoint (Ostapchenko, 2022). This behavior is attributed to isospin violation in EPOS-LHC, and it is invoked to explain why EPOS-LHC predicts deeper $s$00 than QGSJET. The treatment of nuclear breakup in EPOS-LHC is likewise criticized as erroneous and as the origin of unusually small $s$01 fluctuations for nucleus-induced showers (Ostapchenko, 2022).

The 2024 QGSJET-III EAS paper reaches a more observationally framed conclusion. It reports that QGSJET-III and QGSJET-II-04 remain close in $s$02, $s$03, $s$04, and $s$05, whereas EPOS-LHC and SIBYLL-2.3 predict substantially larger $s$06 and especially larger $s$07, which the paper describes as being in strong contradiction with Pierre Auger Observatory measurements (Ostapchenko, 2024). This supports a common QGSJET claim: the decisive discriminator among contemporary hadronic models is not only $s$08, but also the treatment of pion-air interactions and the resulting muon-production profile.

A broader contextual point, drawn from pre-QGSJET-III review literature, is that even LHC-retuned generators such as QGSJET-II-04, EPOS-LHC, and SIBYLL 2.3c still left persistent anomalies: the total number of muons remained underestimated by about 30%, with even larger deficits at large radial distance, and the muon production depth was overestimated (d'Enterria, 2019). This does not directly evaluate QGSJET-III, but it explains why QGSJET-III’s modest allowed shifts in $s$09 and $s$10 are so consequential for UHECR composition analysis and for the interpretation of the muon puzzle.

6. Extensions and specialized applications

QGSJET-III has also become a platform for more specialized high-energy atmospheric calculations. A 2025 extension develops charm production within the QGSJET-III framework for prompt atmospheric neutrino calculations (Ostapchenko et al., 16 Aug 2025). In this implementation, perturbative charm is treated at leading order through

$s$11

with charm mass

$s$12

default scales

$s$13

and an effective perturbative normalization

$s$14

chosen from comparison with LHCb $s$15 data (Ostapchenko et al., 16 Aug 2025). The calculation is done in a three-flavor evolution scheme, so charm does not appear as an active initial-state flavor and the produced $s$16 quarks do not undergo final-state cascading in this implementation (Ostapchenko et al., 16 Aug 2025).

The same work adds a nonperturbative intrinsic-charm sector using Good–Walker-state dependence,

$s$17

with normalization

$s$18

chosen from forward $s$19 data (Ostapchenko et al., 16 Aug 2025). The resulting prompt atmospheric $s$20 flux is dominated by perturbative charm, but intrinsic charm contributes a substantial correction of about $s$21–$s$22 to the total prompt flux for the chosen parameters, while the full prediction remains below the current IceCube upper limit (Ostapchenko et al., 16 Aug 2025). In this extension, $s$23-meson production moments remain perturbatively dominated, whereas $s$24 production moments are almost entirely intrinsic-charm driven (Ostapchenko et al., 16 Aug 2025).

This later development clarifies the status of QGSJET-III within current cosmic-ray phenomenology. It is not only a hadronic interaction model for standard EAS observables, but also a basis for quantitative calculations of forward-heavy-flavor production and atmospheric lepton backgrounds. A plausible implication is that QGSJET-III should be understood as a continuing program of RFT-based high-energy interaction modeling rather than as a closed, single-release generator family.