--- title: 'QGSJet-II-04: Hadronic Interaction Model' url: https://www.emergentmind.com/topics/qgsjet-ii-04 type: topic --- # QGSJet-II-04: Hadronic Interaction Model QGSJet-II-04 is a high-energy hadronic interaction model used primarily in Monte Carlo descriptions of extensive air showers (EAS), atmospheric muons, and related detector-response calculations. In the studies summarized here, it is implemented mainly through CORSIKA and supplies the high-energy hadron–air interaction kernel for analyses spanning roughly the TeV-to-EeV domain. Its standard characterization is a non-linear Reggeon Field Theory framework with multiple-Pomeron exchange, enhanced Pomeron screening, a semihard component for minijet production, and post-LHC retuning of cross sections and forward particle production. The model is therefore both a microscopic interaction generator and a practical inference engine: it is used to predict muon densities, attenuation lengths, multimuon multiplicity distributions, lateral distribution functions, and surface-detector energy calibrations [1609.05764] [2410.17771]. ## 1. Theoretical basis and post-LHC retuning QGSJET-II-04 is described in the cited studies as a Reggeon-Field-Theory or Gribov–Regge framework in which hadronic collisions are represented through multiple Pomeron exchanges in an eikonal formalism. Soft and semihard processes are treated in a unified way, non-linear screening is incorporated through enhanced Pomeron diagrams, and diffraction is included through the model’s standard treatment of diffractive channels. Several summaries further note a continuous transition from soft to hard interactions and explicit treatment of semihard minijet production [1609.05764] [2410.17771] [2404.16948]. Representative parameterizations quoted in applications include an inelastic cross section scaling of the form $$ \sigma_{\mathrm{inel}}(s)\simeq \sigma_0\Bigl(\frac{s}{s_0}\Bigr)^\Delta, $$ with $\Delta\sim 0.1\mbox{–}0.15$ in the ALICE summary, and a proton–air energy dependence at PeV energies consistent with $$ \sigma_{p\text{-air}}(E)=\sigma_0\Bigl(\frac{E}{E_0}\Bigr)^\alpha, \qquad \sigma_0=265~\mathrm{mb},\quad E_0=0.2~\mathrm{TeV},\quad \alpha=0.079\pm0.010, $$ corresponding to an $8\%\pm1\%$ rise per decade and $\sigma_{p\text{-air}}(1\,\mathrm{PeV})=350\pm15~\mathrm{mb}$ in the Tien Shan analysis [2410.17771] [1506.04291]. A central post-LHC modification emphasized in the ALICE study is the retuning to early LHC data, including total and elastic $pp$ cross sections and forward particle spectra. That retuning included a new pion-exchange mechanism in forward neutral hadron production, which increased the $\rho^0$ yield and hence the EAS muon content by $\approx20\%$ relative to previous QGSJET versions [2410.17771]. The CTA comparison likewise characterizes QGSJET-II-04 as a retuned successor to QGSJET-II-03, with slightly softer forward spectra of leading baryons and neutral pions at TeV energies [2105.05822]. ## 2. Computational implementation in air-shower simulations In published applications, QGSJET-II-04 is most often interfaced through CORSIKA, with the low-energy hadronic sector supplied by FLUKA, GHEISHA, or UrQMD depending on the experiment. The thresholds summarized in the data vary by configuration: some studies use QGSJET-II-04 above $E_{\rm lab}\gtrsim80$ GeV, ALICE uses UrQMD below 100 GeV and QGSJET-II-04 above, and the KASCADE-Grande muon study uses FLUKA below 200 GeV and QGSJET-II-04 above [2409.10880] [2410.17771] [1609.05764] [1308.3202]. Detector modeling is typically not limited to particle transport in the atmosphere. Yakutsk folds the shower output through full simulations of the surface and underground scintillation detectors with the real detector geometry and thresholds; ALICE transports muons through 80 m w.e. of rock and the underground hall via GEANT3; IceTop/IceCube uses a Geant4-based detector simulation for both surface tanks and in-ice DOMs; HAWC passes CORSIKA output through a full GEANT4 model of the 300 water Cherenkov detectors [2409.10880] [2410.17771] [2307.14689] [2509.17273]. The same model output can enter very different reconstruction pipelines. In the Yakutsk muon-correlation analysis, QGSJET-II-04 provides benchmark muon and surface densities for proton and iron primaries at a fixed reference energy. In IceCube, the model defines the simulated relation between primary energy and the multiplicity of muons with $E_\mu>500$ GeV. In HAWC, QGSJET-II-04 is treated as a fixed generator whose outputs populate the bidimensional response matrix $P_j(s,E_{\rm rec}\mid E_{\rm true})$ used in Gold-method unfolding [2409.10880] [2307.14689] [2509.17273]. This broad implementation pattern suggests that QGSJET-II-04 functions less as a standalone theoretical object than as infrastructure for inverse problems in cosmic-ray physics: composition inference, energy-scale setting, attenuation measurements, and detector-background estimation all depend on its forward model. ## 3. Model observables and analysis relations QGSJET-II-04 enters air-shower analyses through a restricted set of observables that are strongly model dependent. The most common are the muon lateral distribution, the total or local muon content, the attenuation of muons with slant depth, and the surface-detector signal at a reference core distance. In the Yakutsk muon-correlation method, one measures $S_{600}(E,\theta)$ and $\rho_\mu^{\rm exp}(E,\theta,r)$ and uses QGSJET-II-04 tables of $\rho_\mu(E^\*,\theta,r)$ and $S_{600}(E^\*,\theta)$ at a fixed reference energy $E^\*=3.16\times10^{19}$ eV. The model prediction for an observed shower is then obtained through $$ \rho_\mu(E,\theta,r)=\rho_\mu(E^\*,\theta,r)\; \frac{S_{600}(E,\theta)}{S_{600}(E^\*,\theta)}. $$ This avoids rerunning full Monte Carlo for each event while preserving the proton and iron benchmark lines used in composition classification [2409.10880]. The same Yakutsk analysis defines a mass-sensitive estimator $$ \xi= \frac{\ln \rho_\mu^{\rm exp}-\ln \rho_\mu^p} {\ln \rho_\mu^{\rm Fe}-\ln \rho_\mu^p}, \qquad \ln A_{\rm exp}=\xi\ln 56, $$ and uses the ratio $$ \eta=\frac{\rho_\mu^{\rm exp}(E,\theta,r)}{\rho_\mu^p(E,\theta,r)} $$ to separate proton-like, iron-like, muon-rich, and muon-deficient event groups [2409.10880]. For atmospheric development studies, the model is tested through the muon-attenuation length $\Lambda_\mu$, defined by $$ N_\mu(X)=N_\mu(X_0)\exp\!\bigl[-(X-X_0)/\Lambda_\mu\bigr], $$ or equivalently $$ \ln N_\mu(\theta)=\ln N_\mu^0-\frac{X_0}{\Lambda_\mu}\sec\theta. $$ This observable is used in both KASCADE-Grande and LHAASO to compare the measured zenith-angle dependence of muon content against QGSJET-II-04 predictions [2410.13173] [1801.05513]. For surface-detector calibration, QGSJET-II-04 is used to derive energy–signal mappings. In the Yakutsk/Telescope Array comparison, the attenuation-corrected signal density at 800 m is converted into the SD energy estimator through $$ E_{SD}=A\,[\rho(800,0)]^\beta, $$ with $\beta=1.025\pm0.010$ and $A=(2.29\pm0.08)\times10^{17}$ eV for the TA SD calibration. The same study reports the hybrid relation $$ E_{FD}=0.787\,E_{SD} $$ for the Telescope Array fluorescence and surface energy scales [2404.16948]. ## 4. Experimental performance across energy regimes Published comparisons do not yield a single global verdict on QGSJET-II-04. Instead, the model performs well for some observables and regimes, while exhibiting systematic discrepancies for others. | Context | QGSJET-II-04 result | Comparison with data | |---|---|---| | Tien Shan, $0.5$–$10$ PeV | $\sigma_{p\text{-air}}(1\,\mathrm{PeV})=350\pm15$ mb, $8\%\pm1\%$ rise per decade [1506.04291] | Reported as better matched than earlier QGSJET-II versions | | EAS-MSU, $10^{17}$–$10^{18}$ eV, $E_\mu\gtrsim10$ GeV | $k=N_\mu^{\rm obs}/N_\mu^{\rm sim}=0.92\pm0.06$ with 43% p + 57% Fe [1609.05764] | No significant muon excess in inner region | | ALICE multimuons, $4\times10^{15}500$ GeV | Simulated and measured $\langle N_\mu\rangle$ agree within 15–20% systematics [2307.14689] | Absolute TeV-muon multiplicity is consistent | | KASCADE-Grande, $10^{16.3}$–$10^{17.0}$ eV | $\Lambda_\mu^{\rm MC}=768\pm65^{+208}_{-219}$ g/cm$^2$ [1801.05513] | Below $\Lambda_\mu^{\rm exp}=1256\pm85^{+229}_{-232}$ g/cm$^2$ | | LHAASO, 0.3–30 PeV | $\Lambda_\mu$ predictions are systematically longer than measured [2410.13173] | Data favor EPOS-LHC over QGSJET-II-04 | | SUGAR, $10^{17.6}$–$10^{18.6}$ eV | LDF too flat; data are higher near core and lower at large $r$ [2202.01200] | Shape mismatch rather than pure normalization mismatch | The model’s strongest reported successes in the data block are its compatibility with EAS-MSU inner-core muon densities once a surface-derived composition is imposed, and its simultaneous description of the ALICE multimuon multiplicity distribution and the high-multiplicity tail under a heavy-composition hypothesis [1609.05764] [2410.17771]. The Yakutsk muon-correlation analysis further shows that QGSJET-II-04 can act as a stable benchmark for event-by-event classification at ultra-high energies, with the full 127-event sample yielding $\xi_{\rm total}=-0.03\pm0.02$, consistent with a predominantly light composition but with heavy, muon-rich, and muon-poor admixtures [2409.10880]. The principal weaknesses reported here concern the atmospheric evolution and spatial profile of the muon component. KASCADE-Grande and LHAASO both find that QGSJET-II-04 predicts steeper or deeper muon attenuation than observed, while SUGAR finds a lateral distribution that falls off too slowly with core distance [1801.05513] [2410.13173] [2202.01200]. ## 5. Muon-related tensions and the “muon puzzle” The model’s record on muons is explicitly non-uniform. In some configurations QGSJET-II-04 removes or greatly reduces previously reported discrepancies, whereas in others it appears to shift rather than eliminate them. At EAS-MSU, where the analysis is restricted to the inner shower region, $r\lesssim3R_0$, and to muons above $\sim10$ GeV, the measured and simulated $\rho_\mu(100)$ distributions overlap within statistical errors and the fitted scaling factor is $k=0.92\pm0.06$; the paper concludes that no ad hoc muon rescaling is required in that regime [1609.05764]. By contrast, KASCADE-Grande reports that the measured attenuation of the muon content in the atmosphere is lower than predicted, with QGSJET-II-04 still underestimating $\Lambda_\mu$ despite being closer than older pre-LHC models [1801.05513]. LHAASO extends that discrepancy across 0.3–30 PeV, with QGSJET-II-04 overpredicting the attenuation length by about $110$ g/cm$^2$ at 0.3 PeV and about $630$ g/cm$^2$ at 30 PeV, corresponding to approximately 25% and 78% respectively [2410.13173]. The tension is not only longitudinal. SUGAR finds that, after normalizing to the same total muon number, QGSJET-II-04 places relatively too few muons near the core and too many at large distances. The reported residuals are up to $+10$–$15\%$ for $r\lesssim200$ m and roughly $-10$–$15\%$ for $r\gtrsim500$ m, with a chance probability $p\approx0.007$ for such a coherent slope difference [2202.01200]. IceCube identifies a different inconsistency: under QGSJET-II-04, TeV-muon multiplicities agree with simulation-based expectations, but the composition implied by those TeV muons is significantly heavier than the composition inferred from GeV-muon lateral densities measured by IceTop, with the two $z$ values differing by up to $\sim0.4$ in $\ln A/\ln 56$, or about $4$–$5\sigma$ in the 5–50 PeV range [2307.14689]. A further constraint comes from the vertical atmospheric muon spectrum. In that comparison, QGSJET-II-04 predicts a vertical muon intensity $D(E_\mu)$ larger than data by a factor rising from about 1.4 at $10^2$ GeV to about 1.7 at $10^4$ GeV, and is therefore interpreted as producing too many very-forward secondary $\pi^\pm$ and $K^\pm$ mesons [1504.05853]. This does not contradict the ALICE result, but it does indicate that improvement in one muon observable does not guarantee consistency across all muon thresholds, radial regions, and phase-space domains. A plausible implication is that the remaining discrepancies are differential: they concern energy partition, forward production, and transverse development rather than a single universal muon normalization. ## 6. Calibration, extensions, and related variants Beyond shower-composition studies, QGSJET-II-04 serves as a calibration model for detector systems and as a reference generator in broader astroparticle pipelines. In the Yakutsk/Telescope Array calibration study, QGSJET-II-04 proton simulations are used to connect the particle density at 800 m to the SD energy scale, to compare Yakutsk and TA vertical-shower calibrations, and to interpret the hybrid result $E_{FD}=0.787\,E_{SD}$ for TA [2404.16948]. In the Yakutsk surface-detector composition analysis, QGSJET-II-04 is reported to give one of the best agreements with measured charged-particle lateral steepness, supporting an inferred decrease of $\langle\ln A\rangle$ from about 3 at $10^{17}$ eV to about 1.5 at $2\times10^{18}$ eV [1411.5088]. In gamma-ray instrumentation, QGSJET-II-04 is close to QGSJET-II-03 in its practical impact on CTA sensitivity estimates. The CTA study attributes this to very similar $\pi^0$ production spectra: the QGSJET-II-04 spectrum is about 13% softer than QGSJET-II-03 at $x=0.1$, remains within about 10% over $x=0.1$–0.8, yields an average total residual background ratio $R_{\rm tot,04}/R_{\rm tot,03}=1.03\pm0.12$ across 1–30 TeV, and changes the 50 h point-source sensitivity by only $S_{04}/S_{03}=1.02\pm0.06$ [2105.05822]. A closely related derivative is QGSJET-II-04m, used in the AAfrag interpolation package for inclusive secondary production in $pp$, $pA$, $Ap$, and $AA$ collisions. QGSJET-II-04m is described as a successor with improved low-energy secondary production, retuned hadronization, and validation against LHCf, LHCb, and NA61 data. AAfrag exposes tabulated differential yields for photons, neutrinos, leptons, and antinucleons through interpolation routines rather than through full air-shower simulations [1904.05129]. This suggests an important bifurcation in the model family: QGSJET-II-04 remains the standard EAS interaction engine in many detector simulations, while QGSJET-II-04m extends the framework toward precision secondary-production calculations relevant to Galactic cosmic-ray transport. Overall, QGSJET-II-04 occupies a technically central but empirically conditional position in high-energy cosmic-ray phenomenology. It is well enough constrained to underpin detector calibration, response-matrix construction, and event-by-event mass-sensitive benchmarks, yet current measurements of attenuation lengths, muon spectra, and lateral distributions show that its description of muon production and transport remains incomplete in several energy and phase-space regimes [2404.16948] [2509.17273] [2410.13173]. Source: https://www.emergentmind.com/topics/qgsjet-ii-04