Hadronic Interaction Models Research Articles

Proton-air interactions at ultra-high energies in muon-depleted air showers with different depths

The hardness of the energy spectrum of neutral pions produced in proton-air interactions at ultra-high energies, above 1018 eV, is constrained by the steepness of the shower-to-shower distribution of the number of muons in muon-depleted extensive air showers.In this work, we find that this steepness, quantified by the parameter Λμ, evolves with the depth of the shower maximum, Xmax, assuming a universal value for shallow showers and an enhanced dependence on the high-energy hadronic interaction model for deep showers. We show that Xmax probes the so-called hadronic activity of the first proton-air interaction, thus allowing direct access to the energy spectrum of neutral pions in different regions of its kinematic phase space.We verify that the unbiased measurement of Λμ is possible for realistic mass composition expectations. Finally, we infer that the statistical precision in Λμ required to distinguish between hadronic interaction models can be achieved in current extensive air shower detectors, given their resolution and exposure.

Explaining Muon Excess in Cosmic Rays Using the Gluon Condensation Model

Ultrahigh-energy cosmic rays are often characterized indirectly by analyzing the properties of secondary cosmic ray particles produced in the collisions with air nuclei. The particle number N μ of muon and the depth of shower maximum X max after air shower cascade are mostly studied to infer the energy and mass of the incident cosmic rays. Research has shown that there is a significant excess in the observed number of muons arriving at the ground from extensive air showers compared to the simulations using the existing cosmic ray hadronic interaction model. To explain this muon excess phenomenon, a new theoretical model, the gluon condensation model, is introduced in this paper and simulated by using the AIRES engine. We assume that the gluon condensation (GC) effect appears mainly in the first collision of the cascade, leading to a significant increase in the strangeness production, consequently, the production rate of kaons is increased, and n K /n π is greater than the value of the usual hadronic interaction process. In the calculation, the model assumes that only pions and kaons are produced in the GC state. The increase of strange particle yield would mean that the energy transferred from the hadronic cascade to the electromagnetic cascade through π 0 → 2γ decay is reduced. This would in turn increase the number of muons at the ground level due to meson decays. Our model provides a new theoretical possibility to explain the muon excess puzzle.

Modeling hadronic interactions in ultra-high-energy cosmic rays within astrophysical environments: A parametric approach

Interactions of ultra-high energy cosmic-rays (UHECRs) accelerated in astrophysical environments have been shown to shape the energy production rate of nuclei escaping from the confinement zone. To address the influence of hadronic interactions, Hadronic Interaction Models (HIMs) come into play. In this context, we present a parameterization capable of capturing the outcomes of two distinct HIMs, namely EPOS-LHC and Sibyll2.3d, in terms of secondary fluxes, including escaping nuclei, nucleons, neutrinos, photons, and electrons. Our parameterization is systematically evaluated against the source codes, both at fixed energy and mass, as well as in a physical case scenario. The comparison demonstrates that our parameterization aligns well with the source codes, establishing its reliability as a viable alternative for analytical or fast Monte Carlo approaches dedicated to the study of UHECR propagation within source environments. This suggests the potential for utilizing our parameterization as a practical substitute in studies focused on the intricate dynamics of ultra-high energy cosmic rays.

Atmospheric muons measured with the KM3NeT detectors in comparison with updated numeric predictions

The measurement of the flux of muons produced in cosmic ray air showers is essential for the study of primary cosmic rays. Such measurements are important in extensive air shower detectors to assess the energy spectrum and the chemical composition of the cosmic ray flux, complementary to the information provided by fluorescence detectors. Detailed simulations of the cosmic ray air showers are carried out, using codes such as CORSIKA, to estimate the muon flux at sea level. These simulations are based on the choice of hadronic interaction models, for which improvements have been implemented in the post-LHC era. In this work, a deficit in simulations that use state-of-the-art QCD models with respect to the measurement deep underwater with the KM3NeT neutrino detectors is reported. The KM3NeT/ARCA and KM3NeT/ORCA neutrino telescopes are sensitive to TeV muons originating mostly from primary cosmic rays with energies around 10 TeV. The predictions of state-of-the-art QCD models show that the deficit with respect to the data is constant in zenith angle; no dependency on the water overburden is observed. The observed deficit at a depth of several kilometres is compatible with the deficit seen in the comparison of the simulations and measurements at sea level.

QGSJET-III model of high energy hadronic interactions. II. Particle production and extensive air shower characteristics

The hadronization procedure of the QGSJET-III Monte Carlo (MC) generator of high energy hadronic interactions is discussed. Selected results of the model, regarding production spectra of secondary particles, are presented in comparison to experimental data and to the corresponding predictions of the QGSJET-II-04 MC generator. The model is applied to calculations of basic characteristics of extensive air showers initiated by cosmic ray interactions in the atmosphere and the results are compared to predictions of other MC generators of cosmic ray interactions. Published by the American Physical Society 2024

Testing hadronic-model predictions of depth of maximum of air-shower profiles and ground-particle signals using hybrid data of the Pierre Auger Observatory

We test the predictions of hadronic interaction models regarding the depth of maximum of air-shower profiles, Xmax, and ground-particle signals in water-Cherenkov detectors at 1000 m from the shower core, S(1000), using the data from the fluorescence and surface detectors of the Pierre Auger Observatory. The test consists of fitting the measured two-dimensional (S(1000), Xmax) distributions using templates for simulated air showers produced with hadronic interaction models pos-, et--04, 2.3d and leaving the scales of predicted Xmax and the signals from hadronic component at ground as free-fit parameters. The method relies on the assumption that the mass composition remains the same at all zenith angles, while the longitudinal shower development and attenuation of ground signal depend on the mass composition in a correlated way. The analysis was applied to 2239 events detected by both the fluorescence and surface detectors of the Pierre Auger Observatory with energies between 1018.5 eV to 1019.0 eV and zenith angles below 60°. We found, that within the assumptions of the method, the best description of the data is achieved if the predictions of the hadronic interaction models are shifted to deeper Xmax values and larger hadronic signals at all zenith angles. Given the magnitude of the shifts and the data sample size, the statistical significance of the improvement of data description using the modifications considered in the paper is larger than 5σ even for any linear combination of experimental systematic uncertainties. Published by the American Physical Society 2024

Studies of ultra-high-energy cosmic rays by the Yakutsk air shower array, based on the Cherenkov light detection technique

The paper presents the results of long-term, continuous observations of the Cherenkov light at the Yakutsk array. The Cherenkov light measurements allow one to reconstruct the longitudinal development of the shower, which is associated with both the model of hadron interactions and the mass composition of cosmic rays. The paper also provides a review of the results that are important for the physics of air showers and the astrophysics of cosmic rays, obtained over a long period of time at the Yakutsk array.

Energy spectra of elemental groups of cosmic rays with the KASCADE experiment data and machine learning

We report the reconstruction of the mass component spectra of cosmic rays (protons, helium, carbon, silicon and iron) and their mean mass composition, at energies from 1.4 to 100 PeV. The results are derived from the archival data of the extensive air shower experiment KASCADE. We use a novel machine learning technique developed specifically for this reconstruction, and post-LHC hadronic interaction models: QGSJet-II.04, EPOS-LHC and Sibyll 2.3c. We have found an excess of the proton component and a deficit of intermediate and heavy nuclei components compared to the original KASCADE results. The spectra of protons and helium show a knee-like behavior at ∼ 4.4 PeV and ∼ 11 PeV, with significances 5.2σ and 3.9σ, respectively. The spectrum of the iron component has a hint (2.4σ) of a hardening at ∼ 4.5 PeV, which can be interpreted as a counterpart of a hardening in the proton spectrum at 166 TeV, recently reported by the GRAPES-3 experiment. The systematic uncertainties of our analysis were found to be smaller than those of the original KASCADE, as well as those of IceTop and TALE experiments, over the most part of the energy range studied. We also estimated separately the uncertainty related to the difference between the three mentioned hadronic interaction models. We also compute a mean logarithm mass of CR flux as a function of energy. It is in agreement with the results of IceTop, TALE and LHAASO within the uncertainties.

Muon measurements at the Pierre Auger Observatory

The Pierre Auger Observatory is the world’s largest detector for observation of ultra-high-energy cosmic rays (UHECRs) (above the energy of 10^{17}1017 eV). It consists of a Fluorescence Detector (FD) and an array of particle detectors known as the Surface Detector (SD). Observations of extensive air showers by the Observatory can be used to probe hadronic interactions at high energy, in a kinematic and energy region inaccessible to experiments at man-made accelerators and to measure the muon component of the shower. Air showers induced by different primaries have different muon contents. With increasing mass of the primary cosmic ray particle, it is expected that the muon content in the corresponding air showers should also increase. Therefore, the determination of the muon component in the air shower is crucial to infer the mass of the primary particle. This is a key ingredient in the searches conducted to pinpoint the sources of UHECRs. Recent results obtained from the Pierre Auger Observatory and other experiments indicate that all the shower simulations underestimate the number of muons in the showers compared to the data. This is the so-called muon deficit. In this paper we briefly review the muon measurements, and present in more detail recent results on fluctuations in the muon number. These results provide new insights into the origin of the muon deficit in air shower simulations and constrain the models of hadronic interactions at ultrahigh energies. With the current design of the surface detectors it is also difficult to reliably separate the contributions of muons to the SD signal from the contributions of photons, electrons, and positrons. Therefore, we also present a new method to extract the muon component of the signal time traces recorded by each SD station using recurrent neural networks. The combination of such algorithms, with the future data collected by the upgraded Pierre Auger Observatory, will be a major step forward, as we are likely to achieve an unprecedented resolution in mass estimation on an event-by-event basis.

Sub-TeV hadronic interaction model differences and their impact on air showers

In the sub-TeV regime, the most widely used hadronic interaction models disagree significantly in their predictions of particle spectra from cosmic ray induced air showers. We investigate the nature and impact of model uncertainties, focussing on air shower primaries with energies around the transition between high and low energy hadronic interaction models, where the dissimilarities are largest and which constitute the bulk of the interactions in air showers.

Sibyll[formula omitted]

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★, a series of phenomenologically modified versions of Sibyll 2.3d. In these models, we have increased muon production by altering ρ0, 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 (Xmax) 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.

QGSJET-III model of high energy hadronic interactions: The formalism

The physics content of the QGSJET-III Monte Carlo generator of high energy hadronic collisions is described. In particular, a phenomenological implementation of higher twist corrections to hard parton scattering processes is discussed in some detail. Additionally addressed is the treatment of the so-called “color fluctuation” effects related to a decomposition of hadron wave functions into a number of Fock states characterized by different spatial sizes and different parton densities. Selected model results regarding the energy dependence of the total, elastic, and diffractive proton-proton cross sections are presented. Published by the American Physical Society 2024

Constraints on the proton fraction of cosmic rays at the highest energies and the consequences for cosmogenic neutrinos and photons

Over the last decade, observations have shown that the mean mass of ultra-high-energy cosmic rays (UHECRs) increases progressively toward the highest energies. However, the precise composition is still unknown and several theoretical studies hint at the existence of a subdominant proton component up to the highest energies. Motivated by the exciting prospect of performing charged-particle astronomy with ultra-high-energy (UHE) protons we quantify the level of UHE-proton flux that is compatible with present multimessenger observations and the associated fluxes of neutral messengers produced in the interactions of the protons. We study this scenario with numerical simulations of two independent populations of extragalactic sources and perform a fit to the combined UHECR energy spectrum and composition observables, constrained by diffuse gamma-ray and neutrino observations. We find that up to of order 10% of the cosmic rays at the highest energies can be UHE protons, although the result depends critically on the selected hadronic interaction model for the air showers. Depending on the maximum proton energy (E max p) and the redshift evolution of sources, the associated flux of cosmogenic neutrinos and UHE gamma rays can significantly exceed the multimessenger signal of the mixed-mass cosmic rays. Moreover, if E max p is above the GZK limit, we predict a large flux of UHE neutrinos above EeV energies that is absent in alternate scenarios for the origin of UHECRs. We present the implications and opportunities afforded by these UHE proton, neutrino and photon fluxes for future multimessenger observations.

Simulation of Hadronic Interactions with Deep Generative Models

Accurate simulation of detector responses to hadrons is paramount for all physics programs at the Large Hadron Collider (LHC). Central to this simulation is the modeling of hadronic interactions. Unfortunately, the absence of first-principle theoretical guidance has made this a formidable challenge. The state-of-the-art simulation tool, Geant4, currently relies on phenomenology-inspired parametric models. Each model is designed to simulate hadronic interactions within specific energy ranges and for particular types of hadrons. Despite dedicated tuning efforts, these models sometimes fail to describe the data in certain physics processes accurately. Furthermore, finetuning these models with new measurements is laborious. Our research endeavors to leverage generative models to simulate hadronic interactions. While our ultimate goal is to train a generative model using experimental data, we have taken a crucial step by training conditional normalizing flow models with Geant4 simulation data. Our work marks a significant stride toward developing a fully differentiable and data-driven model for hadronic interactions in High Energy and Nuclear Physics.

Reconstruction of high-energy shower cores in MATHUSLA

In this work, we show the results of a comparative analysis of different reconstruction methods of shower cores produced by Cosmic Rays (CR’s) in a layer of Resistive Plate Chambers (RPC’s) that is under consideration for MATHUSLA (Massive Timing Hodoscope for Ultra-Stable neutraL pArticles). The analysis was performed with Monte Carlo simulations. Extensive air showers were simulated with CORSIKA using the GEISHA and QGSJET-II-04 hadronic interaction models for primary protons and iron nuclei in the energy range from 10 TeV to 100 PeV and zenith angles: θ ≤ 20°. The detector response was simulated with a simplified Python-based program. The location of the shower core was found using the center of mass of the deposited charge distribution, the maximum of the charge distribution, a fit with an exponential function to the projected distributions on the X and Y horizontal directions of the 2D charge distributions, and fits with an exponential and a Nishimura-Kamata-Greisen (NKG) lateral functions to the 3D charge distributions of the RPC. We found that the fits of the X and Y projections with an exponential function and the fits with a NKG function to the 3D signal distributions have a better performance than the other methods.

Measurement of the forward η meson production rate in p-p collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{\ extrm{s}} $$\\end{document} = 13 TeV with the LHCf-Arm2 detector

The forward η mesons production has been observed by the Large Hadron Collider forward (LHCf) experiment in proton-proton collision at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV. This paper presents the measurement of the inclusive production rate of η in pT< 1.1 GeV/c, expressed as a function of the Feynman-x variable. These results are compared with the predictions of several hadronic interaction models commonly used for the modelling of the air showers produced by ultra-high energy cosmic rays. This is both the first measurement of η mesons from LHCf and the first time a particle containing strange quarks has been observed in the forward region for high-energy collisions. These results will provide a powerful constraint on hadronic interaction models for the purpose of improving the understanding of the processes underlying the air showers produced in the Earth’s atmosphere by ultra-energetic cosmic rays.

Atmospheric muons at PeV energies in radio neutrino detectors

Experiments seeking to detect radio emission stemming from neutrino interactions will soon reach sensitivities that bring a detection within reach. Since experiments like RNO-G or the future IceCube-Gen2 target more than an order of magnitude more effective volume than existing experiments, the renewed and detailed study of rare backgrounds is needed. In this paper, we study the potential background from energy losses of highly energetic atmospheric muons. Due to both limited experimental measurements and limited modeling in hadronic interaction models, the expected event rate is subject to large uncertainties. Here, we estimate rate predictions and their uncertainties for different models and instrumental parameters. We also study possible routes towards mitigation of the muon background, such as parent air shower detection, and illustrate what is needed to make the first measurement of the prompt muon flux at energies above 10 PeV.

Probing hadronic interaction models with the hybrid data of the Pierre Auger Observatory

Presently large systematic uncertainties remain in the description of hadronic interactions at ultra-high energies and a fully consistent description of air-shower experimental data is yet to be reached. The amount of data collected by the Pierre Auger Observatory using simultaneously the fluorescence and surface detectors in the energy range 10^{18.5}18.5 -10^{19.0}19.0 eV has provided opportunity to perform a multi-parameter test of model predictions. We apply a global method to simultaneously fit the mass composition of cosmic rays and adjustments to the simulated depth of shower maximum, and hadronic signal at ground level. The best description of the hybrid data is obtained for a deeper scale of simulated depth of shower maximum than predicted by hadronic interaction models tuned to the LHC data. Consequently, the deficit of the simulated hadronic signal at ground level, dominated by muons, is alleviated with respect to the unmodified hadronic interaction models. Because of the size of the adjustments to simulated depth of shower maximum and hadronic signal and the large number of events in the sample, the statistical significance of these assumed adjustments is large, greater than 5\sigma_{stat}σstat, even for the combination of the systematic experimental shifts within 1\sigma_{sys}σsys that are the most favorable for the models.

Results from recent analysis of KASCADE-Grande data

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.

Muons in showers with energy $\boldsymbol{E_{0} \geq}$ 5 EeV and QGSjetII-04 and EPOS LHC models of hadronic interactions. Is there a muon deficit in the models?

The paper presents data on the muon component with a threshold\varepsilon_{thr} \geqεthr≥ 1 GeV. Air showers were registered at the Yakutsk array during almost 50 years of continuous air shower observations. The characteristics of muons are compared with calculations of QGSjetII-04 and EPOS LHC models for a proton and an iron nucleus. There is a muon deficit in the models, at energies greater than 5 EeV. To make an agreement between experimental data and simulations on muons, further tuning of the models is required.