---
title: 'QGSJET-III: Advanced Cosmic-Ray Simulator'
url: https://www.emergentmind.com/topics/qgsjet-3
type: topic
---

# QGSJET-III: Advanced Cosmic-Ray Simulator

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 [2208.05889].

## 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 [1504.05853]. 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 [2208.05889].

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 [1112.0356]. 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 [1010.1869].

| Version | Role in the literature | Note |
|---|---|---|
| QGSJET-01 | Earlier benchmark in CORSIKA EAS studies | Used in proton/iron shower comparisons [1112.0356] |
| QGSJET-II-03 | Pre-LHC QGSJET-II release | Sometimes loosely conflated with “QGSJET 3,” but distinct [1504.05853] |
| QGSJET-II-04 | LHC-retuned QGSJET-II release | Used in collider and EAS benchmarking [1604.08536] |
| QGSJET-III | Newest QGSJET generation | Formalism, hadronization, EAS predictions, and uncertainty studies [2401.06202] |

## 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 [2208.05889]. 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 [2208.05889].

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
\[
\propto s^{\Delta_{\rm soft}},\qquad \Delta_{\rm soft}\simeq 0.1,
\]
so the early stages of semihard cascades become increasingly important for projectile-fragmentation-region production and thus for EAS development [2208.05889].

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 [2401.06202]. The latter is introduced because ordinary leading-twist minijet production rises too rapidly as \(p_t\) decreases, making predictions strongly dependent on the arbitrary soft-hard separation scale. QGSJET-III models coherent rescattering of produced \(s\)-channel partons on soft gluon pairs and introduces one new phenomenological parameter, \(K_{\rm HT}\), to control the strength of this higher-twist contribution. The reported consequences are a drastic reduction in sensitivity to the cutoff \(Q_0^2\), moderation of the energy rise of cross sections and multiplicities, and stronger damping of low-\(p_\perp\) jet production in more central collisions [2208.05889].

## 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 \(t\)- and \(s\)-channel parton evolution above \(Q_0^2\). Second, each cut Pomeron is converted into two color strings, and these strings are hadronized by an iterative string-fragmentation procedure [2403.16106].

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-\(x\) exponent for constituent sea quarks,
\[
0.5 \le \alpha_{\text{sea}} < 1,
\]
with the implemented value
\[
\alpha_{\text{sea}}=0.65.
\]
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 \(\xi\) of Pomeron–Pomeron interactions [2403.16106].

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 \(\Delta^{++}\), \(\Delta^-\), \(\rho\) mesons, and \(\eta\) mesons. The resonance weights quoted for QGSJET-III are
\[
w_\eta=0.11,\qquad w_\rho=0.33,
\]
with the latter chosen so that roughly 50% of final pions arise from \(\rho\) decays [2403.16106].

A distinctive update relative to QGSJET-II-04 is the more systematic treatment of pion exchange. QGSJET-III includes explicit RRP contributions with \(R=\pi\), important for forward neutron production and for forward \(\rho\)-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 [2403.16106].

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 \(pp\) and \(pC\) interactions at 158 GeV/\(c\), and it describes \(\rho\)-meson production in \(\pi C\) and \(\pi p\) rather well, with pion exchange dominating the forward part of the \(\rho\) spectra [2403.16106]. At the same time, important deficiencies remain. Antiproton \(x_F\) spectra in \(pp\) and \(pC\) at 158 GeV/\(c\) are too hard, charged kaon production in \(\pi^- C\) is underestimated by about \(30\%\), and proton and antiproton production in \(\pi^- C\) is considerably underestimated [2403.16106].

At collider energies, QGSJET-III reproduces charged-particle pseudorapidity densities in \(pp\) at \(\sqrt{s}=0.9, 2.36, 7,\) and \(13\) TeV satisfactorily, and it gives a substantially better description of \(pPb\) pseudorapidity densities than QGSJET-II-04 [2403.16106]. By contrast, identified-hadron \(p_T\) spectra at central rapidity in 7 TeV \(pp\) collisions are described only imperfectly, a limitation the paper connects to the simplified fragmentation model and approximate resonance treatment [2403.16106]. Forward neutron spectra agree satisfactorily with LHCf at 13 TeV but show some underestimation at 7 TeV, while forward \(\pi^0\) spectra are reproduced satisfactorily overall, with some underestimation around \(p_z\sim 1\) TeV [2403.16106].

## 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 \(X_{\max}\) for proton-induced showers changes by about \(5\ \mathrm{g/cm^2}\), the variation of the new parameter \(K_{\rm HT}\) by \(\pm 10\%\) shifts \(X_{\max}\) by only about \(\pm 2\ \mathrm{g/cm^2}\), and the EAS muon content \(N_\mu\) differs by only about \(1\%\) [2208.05889]. A later uncertainty study phrases the comparison somewhat differently, stating that QGSJET-III predicts \(X_{\max}\) values up to \(10\ \mathrm{g/cm^2}\) larger than QGSJET-II-04 and about \(5\%\) fewer sea-level muons for \(E_\mu>1\) GeV [2410.23465]. 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
\[
N_\mu^p(E_0)\propto E_0^{\alpha_\mu},\qquad \alpha_\mu\simeq 0.9,
\]
and the controlling pion-air quantity is the spectrum-weighted stable-hadron moment
\[
\left\langle x_E^{\alpha_{\mu}}\, n_{\rm stable}^{\pi\text{-air}}(E_0)\right\rangle
= \int dx_E\, x_E^{\alpha_{\mu}}\, \frac{dn_{\rm stable}^{\pi\text{-air}}(E_0,x_E)}{dx_E}.
\]
Because \(\alpha_\mu\) 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 \(\pi^0\) production [2410.23465].

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 \(N_\mu\) by less than \(1\%\) [2410.23465]. Neglecting absorptive corrections in pion exchange entirely makes the predicted muon number decrease by up to \(10\%\) at \(E_0=10^{19}\) eV, because elastic virtual-pion scattering then becomes important and produces little hadronic multiplication [2410.23465]. The only modification identified as significantly effective for muons is enhanced kaon and \((\bar)N\) production in pion-air collisions: using approximately \(40\%\) larger kaon yields and \(60\%\) larger \((\bar)N\) yields, as suggested by comparison to NA61 \(\pi^-C\) data at 158 GeV/\(c\), raises \(N_\mu\) by up to about \(10\%\), but at the price of serious tension with other accelerator data [2410.23465].

The corresponding limits on delaying shower development are similarly restrictive. A \(30\%\) increase in the low-mass diffractive \(pp\) cross section, still said to be compatible with TOTEM, yields about \(15\%\) more diffractive-like proton-air interactions with leading nucleon energy loss below 10% and increases \(X_{\max}\) by only about \(8\ \mathrm{g/cm^2}\) [2410.23465]. Modifying the constituent sea-quark exponent from the default \(\alpha_{\rm sea}=0.65\) to \(\alpha_{\rm sea}=0.9\) reduces \(K^{\rm inel}_{pN}\) by up to about \(6\%\) and increases \(X_{\max}\) by up to about \(12\ \mathrm{g/cm^2}\) at the highest energies [2410.23465]. More exotic collective modifications could, in the author’s wording, increase \(X_{\max}\) by as much as about \(30\ \mathrm{g/cm^2}\), but such scenarios are described as strongly disfavored by LHCf forward-neutron data and by Pierre Auger measurements of the muon production depth [2410.23465].

## 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 [2208.05889]. 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 \(X_{\max}\) [2208.05889]. SIBYLL-2.3 is also said to underestimate absorptive damping in the pion-exchange sector, producing too little energy dependence in forward \(\rho^0\) production and potentially an artificial enhancement of the EAS muon content [2208.05889].

Against EPOS-LHC, the critique is more model-specific. The forward \((\bar)B\) yield in QGSJET-III remains about an order of magnitude below the charged-pion yield over energies \(10^2\), \(10^4\), and \(10^6\) 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 [2208.05889]. This behavior is attributed to isospin violation in EPOS-LHC, and it is invoked to explain why EPOS-LHC predicts deeper \(X_{\max}\) than QGSJET. The treatment of nuclear breakup in EPOS-LHC is likewise criticized as erroneous and as the origin of unusually small \(X_{\max}\) fluctuations for nucleus-induced showers [2208.05889].

The 2024 QGSJET-III EAS paper reaches a more observationally framed conclusion. It reports that QGSJET-III and QGSJET-II-04 remain close in \(X_{\max}\), \(\sigma(X_{\max})\), \(N_\mu\), and \(X_{\max}^{\mu}\), whereas EPOS-LHC and SIBYLL-2.3 predict substantially larger \(N_\mu\) and especially larger \(X_{\max}^{\mu}\), which the paper describes as being in strong contradiction with Pierre Auger Observatory measurements [2403.16106]. This supports a common QGSJET claim: the decisive discriminator among contemporary hadronic models is not only \(X_{\max}\), 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 [1902.09505]. This does not directly evaluate QGSJET-III, but it explains why QGSJET-III’s modest allowed shifts in \(N_\mu\) and \(X_{\max}\) 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 [2508.12095]. In this implementation, perturbative charm is treated at leading order through
\[
gg\to c\bar c,\qquad q\bar q\to c\bar c,
\]
with charm mass
\[
m_c=1.3~\mathrm{GeV},
\]
default scales
\[
\mu_F^c=\mu_R^c=2m_{c,\perp},
\]
and an effective perturbative normalization
\[
K_f^c=3,
\]
chosen from comparison with LHCb \(D+\bar D\) data [2508.12095]. The calculation is done in a three-flavor evolution scheme, so charm does not appear as an active initial-state flavor and the produced \(c,\bar c\) quarks do not undergo final-state cascading in this implementation [2508.12095].

The same work adds a nonperturbative intrinsic-charm sector using Good–Walker-state dependence,
\[
w_h^{\mathrm{IC}(i)}=w_0^{\mathrm{IC}}\frac{R_p^2(1)}{R_h^2(i)},
\]
with normalization
\[
w_0^{\mathrm{IC}}=3\times 10^{-4},
\]
chosen from forward \(\Lambda_c^+\) data [2508.12095]. The resulting prompt atmospheric \(\nu_\mu+\bar\nu_\mu\) flux is dominated by perturbative charm, but intrinsic charm contributes a substantial correction of about \(25\%\)–\(35\%\) to the total prompt flux for the chosen parameters, while the full prediction remains below the current IceCube upper limit [2508.12095]. In this extension, \(D\)-meson production moments remain perturbatively dominated, whereas \(\Lambda_c\) production moments are almost entirely intrinsic-charm driven [2508.12095].

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.

Source: https://www.emergentmind.com/topics/qgsjet-3