Hadronic Interaction Models Research Articles

The all-particle energy spectrum of cosmic rays from 10 TeV to 1 PeV measured with HAWC

The HAWC observatory is an air-shower detector, which is designed to study both astrophysical gamma-rays in the TeV region and galactic cosmic rays in the energy interval from 1 TeV to 1 PeV. This energy regime is interesting for cosmic ray research, since indirect observations overlap with direct measurements, which offers the opportunity for cross calibration and studies of experimental systematic errors in both techniques. One quantity that could help for this purpose is the all-particle energy spectrum of cosmic rays. In this work, we present an update of HAWC measurements on the total cosmic-ray energy spectrum between 10 TeV and 1 PeV. The spectrum was obtained from an unfolding analysis of almost two years of HAWC’s data, which was collected from January, 2018 to December, 2019. For the energy estimation, we employed the high-energy hadronic interaction model QGSJET-II-04. As in a previous work of HAWC, published in 2017, we observed the presence of a knee-like feature in the region of tens of TeV.

Updated results on the cosmic ray energy spectrum and composition from the GRAPES-3 experiment

Here, we present the updated results on the cosmic ray energy spectrum and composition analysis from the GRAPES-3 experiment over the energy range of 50 TeV to 1000 TeV since ICRC 2021. The simulation of cosmic ray showers was performed using the post-LHC high energy hadronic interaction model QGSJetII-04 and low energy hadronic model FLUKA. A detailed GEANT4 simulation of the GRAPES-3 muon telescope was performed. The composition was obtained by fitting simulated muon multiplicity distributions for proton, helium, nitrogen, aluminium, and iron primaries to the observed data. The energy spectrum connects to the direct measurements with a fairly good agreement in flux.

Muon puzzle in inclined muon bundles detected by NEVOD-DECOR

The data of cosmic ray NEVOD-DECOR experiment on the investigation of inclined muon bundles for a long time period (May 2012 - March 2021) are presented. The analysis showed that the observed intensity of muon bundles at primary cosmic ray energies of about 1 EeV and higher can be compatible with the expectation in frame of widely used hadron interaction models only under the assumption of an extremely heavy mass composition. This conclusion is consistent with data of several experiments on investigations of muon content in air showers, but contradicts the available fluorescence data on X_{max}Xmax which favor a light mass composition at these energies. In order to clarify the nature of the "muon puzzle", investigations of the muon bundle energy deposit in the detector material were carried out. For the first time, experimental estimates of the average energy of muons in the bundles of inclined air showers initiated by primary particles with energies from 10 to 1000 PeV have been obtained.

Uncertainty in mean $X_{\rm max}$ from diffractive dissociation estimated using measurements of accelerator experiments

Mass composition is important for understanding the origin of ultra-high-energy cosmic rays. However, interpretation of mass composition from air shower experiments is challenging, owing to significant uncertainty in hadronic interaction models adopted in air shower simulation. A particular source of uncertainty is diffractive dissociation, as its measurements in accelerator experiments demonstrated significant systematic uncertainty. In this research, we estimate the uncertainty in \langle X_{max}\rangle〈Xmax⟩ from the uncertainty of the measurement of diffractive dissociation by the ALICE experiment. The maximum uncertainty size of the entire air shower was estimated to be ^{+4.0}_{-5.6} \mathrm{g/cm^2}−5.6+4.0g/cm2 for air showers induced by 10^{17}1017~eV proton, which is not negligible in the uncertainty of \langle X_{max}\rangle〈Xmax⟩ predictions.

Cosmic ray measurements with IceCube and IceTop

IceCube is a cubic-kilometer Cherenkov detector in the deep ice at the geographic South Pole. The dominant event yield in the deep ice detector consists of penetrating atmospheric muons with energies above approximately 300 GeV, produced in cosmic ray air showers. In addition, the surface array, IceTop, measures the electromagnetic component and GeV muons of air showers. Hence, IceCube and IceTop yield unique opportunities to study cosmic rays with unprecedented statistics in great detail. We will present recent results of comic ray measurements from IceCube and IceTop. In this overview, we will highlight measurements of the energy spectrum of cosmic rays from 250 TeV up to the EeV range and their mass composition above 3 PeV. We will also report recent results from measurements of the muon content in air showers and discuss their consistency with predictions from current hadronic interaction models.

Observation of seasonal variations of the flux of high-energy atmospheric neutrinos with IceCube

Atmospheric muon neutrinos are produced by meson decays in cosmic-ray-induced air showers. The flux depends on meteorological quantities such as the air temperature, which affects the density of air. Competition between decay and re-interaction of those mesons in the first particle production generations gives rise to a higher neutrino flux when the air density in the stratosphere is lower, corresponding to a higher temperature. A measurement of a temperature dependence of the atmospheric nu _{mu } flux provides a novel method for constraining hadronic interaction models of air showers. It is particularly sensitive to the production of kaons. Studying this temperature dependence for the first time requires a large sample of high-energy neutrinos as well as a detailed understanding of atmospheric properties. We report the significant (> 10 ; sigma ) observation of a correlation between the rate of more than 260,000 neutrinos, detected by IceCube between 2012 and 2018, and atmospheric temperatures of the stratosphere, measured by the Atmospheric Infrared Sounder (AIRS) instrument aboard NASA’s AQUA satellite. For the observed 10% seasonal change of effective atmospheric temperature we measure a 3.5(3)% change in the muon neutrino flux. This observed correlation deviates by about 2-3 standard deviations from the expected correlation of 4.3% as obtained from theoretical predictions under the assumption of various hadronic interaction models.

Cosmic ray mass composition at the knee using azimuthal fluctuations of air shower particles detected at ground by the KASCADE experiment

The presence of hadronic sub-showers causes azimuthal non-uniformity in the particle distributions on the ground in vertical air showers. The LCm parameter, which quantifies the non-uniformity of the signal recorded in detectors located at a given distance on a ring around the shower axis, has been successfully introduced as a gamma/hadron discriminator at PeV energies [23]. In this work, we demonstrate that the LCm parameter can effectively serve as a mass composition discriminator in experiments that employ a compact array of detectors, like KASCADE. We reconstruct the LCm parameter distributions in the energy range lg(E/eV) = [15.0 – 16.0] using measurements from the KASCADE experiment, with intervals of lg(E/eV) = 0.2, which are then fitted with MC templates for five primary nuclei species p, He, C, Si, and Fe considering three hadronic interaction models: QGSjet-II-04, EPOS-LHC and SIBYLL 2.3d. We find that the LCm parameter exhibits minimal dependence on the specific hadronic interaction model considered. The reconstructed fractions of individual species demonstrate a linear decrease in the abundance of protons and He nuclei with increasing energy, while the heavier components become prevalent above the knee as predicted by all three hadronic interaction models. Our findings indicate that the abundance of particle types as a function of energy aligns with different astrophysical models that link the knee to the acceleration and propagation of cosmic rays within the Galaxy. Furthermore, they also demonstrate excellent agreement with three more recent data-driven astrophysical models. These findings suggest that the LCm parameter could be a valuable tool for forthcoming measurements of the LHAASO experiment to enhance our knowledge about the origin and acceleration mechanisms of cosmic rays.

A multi-channel U-Matrix model of hadron interaction at high energy

The present phenomenological study investigates a multi-channel model of high-energy hadron interactions by considering a full parton configurations space and the U-matrix unitarisation scheme of the elastic amplitude, comparing it to the two-channel model, and examining the consequences of up-to-date high-energy collider data on the best fits to various hadronic observables in pp and poverline{p} collisions. The findings of this study reveal that the data are well-fitted with the multi-channel model and that the difference compared to the two-channel one is negligible. Of particular significance is the observation that the U-matrix unitarisation is likely incompatible with uncorrelated pomeron exchange, as suggested by the equivalence between the U-matrix multi-channel and eikonal two-channel descriptions. Based on our best fit, predictions for the ρ parameter, the double diffractive cross-section, and the elastic differential cross-section are provided. We shed light on the effect of taking into account a multi-channel model on present and future cosmic ray data.

Average muon energies in inclined bundles according to NEVOD-DECOR data

Results of measurements of the energy characteristics of muon bundles in inclined extensive air showers in the NEVOD-DECOR experiment are presented. Estimates of the average energy of muons in the bundles in the energy range of primary particles from 10 to 1000 PeV were obtained and compared with the calculated expected values for various assumptions about the composition of cosmic radiation and models of hadronic interactions. An excess of experimental values of the average muon energy in comparison with calculations for high local densities corresponding to energies of primary particles above 100 PeV was found.

Content of Muons in Extensive Air Showers Measured by Yakutsk Array

Lateral distribution of muons in extensive air showers registered at the Yakutsk array was investigated. The analysis covers two periods of observation: before 2018 and after 2020, when the revision of muon detectors with 1-GeV threshold was complete. Measured values of muon density are compared to computational results obtained within the framework of two hadron interaction models. Within the energy domain above 1018 eV the best agreement is observed for proton composition primary cosmic rays.

Muon Puzzle in Ultra-High Energy EASs According to Yakutsk Array and Auger Experiment Data

The lateral distribution of particles in extensive air showers from cosmic rays with energy above $10^{17}$ eV registered at the Yakutsk complex array was analyzed. Experimentally measured particle densities were compared to the predictions obtained within frameworks of three ultra-high energy hadron interaction models. The cosmic ray mass composition estimated by the readings of surface-based and underground detectors of the array is consistent with results based on the Cherenkov light lateral distribution data. A comparison was made with the results of direct measurement of the muon component performed at the Pierre Auger Observatory. It is demonstrated that the densities of muon flux measured at Yakutsk array are consistent with results of fluorescent light measurements and disagree with results on muons obtained at the Auger array.

A Method to Estimate the Primary Mass of Ultrahigh-energy Cosmic Rays from Measurements of the Depth of the Shower Maximum and the Muon Content

The origin and mass composition of ultrahigh-energy cosmic rays is one of the big open questions of modern physics. Estimating the mass of ultrahigh-energy cosmic rays always involves the comparison of data with simulations using hadronic interaction models. The state-of-the-art hadronic interaction models, however, fail to agree with each other on the expected depths of the shower maxima, and on the average number of muons produced in air showers initiated by the same primary particles. Thus the interpretation of data in terms of the primary masses of cosmic rays differs depending on which hadronic interaction model is considered as a reference. Good agreement, however, can be found in the implications from hadronic interaction models in the prediction of the change of the average depth of the shower maximum and in the relative change in the number of produced muons as a function of the nuclear mass of the primary cosmic ray. Considering these, a model-independent estimation of the primary mass of ultrahigh-energy cosmic rays can be given in relative terms. In this work we propose a method to estimate the primary mass of ultrahigh-energy cosmic rays from the depth of the shower maximum and the number of muons produced in the shower, utilizing the similarities of modern hadronic interaction models. We discuss a geometric approach that combines the depth of the shower maximum and the number of muons produced in a shower to estimate the mass of the primary particle.

Calculation of rescaling factors and nuclear multiplication of muons in extensive air showers

Recent results obtained from leading cosmic ray experiments indicate that simulations using LHC-tuned hadronic interaction models underestimate the number of muons in extensive air showers compared to experimental data. This is the so-called muon deficit problem. Determination of the muon component in the air shower is crucial for inferring the mass of the primary particle, which is a key ingredient in the efforts to pinpoint the sources of ultra-high energy cosmic rays. In this paper, we present a new method to derive the muon signal in detectors, which uses the difference between the total reconstructed (‘data’) and simulated signals, and is in turn related to the muon signal which is roughly independent of the zenith angle, but depends on the mass of the primary cosmic ray. Such a method offers an opportunity not only to test/calibrate the hadronic interaction models, but also to derive the β exponent, which describes an increase of the number of muons in a shower as a function of the energy and mass of the primary cosmic ray. Detailed simulations show a dependence of the β exponent on hadronic interaction properties, thus the determination of this parameter is important for understanding the muon deficit problem. We validate the method by using Monte-Carlo simulations for the EPOS-LHC and QGSJetII-04 hadronic interaction models, and show that this method allows us to recover the ratio of the muon signal between EPOS-LHC and QGSJetII-04 and the average β exponent for the studied system, within less than a few percent. This is a consequence of the good recovery of the muon signal for each primary included in the analysis.

Universality of the muon component of extensive air showers

In extensive air shower experiments, the number of muons crossing a detector at a given position, as well as their arrival time, arrival direction, and energy, are determined by a more fundamental 3-dimensional distribution linked to the hadronic core of the shower. Muons are produced high up in the atmosphere after the decay of mesons in the hadronic cascade. The distributions of production depth, energy, and transverse momentum of muons are enough to fully predict the muon component of air showers in any particular observational condition. By using air-shower simulations with the state-of-the-art hadronic interaction models, the mentioned distributions at production are analyzed as a function of zenith angle, primary mass, and hadronic interaction model, and their level of universality is studied and assessed in an exhaustive manner for the first time.

Cosmic ray mass independent energy reconstruction method using Cherenkov light and muon content in LHAASO

The wide field-of-view Cherenkov telescope array of the Large High Altitude Air Shower Observatory (LHAASO) measures the longitudinal development of Cherenkov light in the air shower of cosmic rays, while the kilometer-square array of LHAASO measures the number of muons in the air shower. The unique detector arrangement of LHAASO can facilitate the precise reconstruction of the cosmic ray energy in the knee region. Thus, this study proposed a new energy reconstruction method by simultaneously using the Cherenkov light size and the number of muons, which is insensitive to the primary particle type. Using this method, the energy bias and resolution of the light component (proton and helium) were less than 1% and 10% at approximately 1 PeV, respectively. Moreover, the difference in energy bias between helium and proton was less than 1% at approximately 1 PeV. In addition, the dependence of this energy reconstruction method on hadronic interaction models and cosmic ray components was also discussed.

Supernova connection of unidentified ultra-high-energy gamma-ray source LHAASO J2108+5157

ABSTRACT We present a simple phenomenological model of hadronic interaction between protons accelerated in an old supernova remnant (SNR) and cold protons situated within the associated molecular clouds (MCs). The accelerated protons from the old SNR escaped the SNR shock front, and got injected into the MCs at an earlier time, producing ultra-high-energy gamma-rays and neutrinos through inelastic proton–proton interaction. We also take into account the acceleration and subsequent escape of electrons from the SNR shock front. The escaped electrons produce gamma-rays through various radiative cooling mechanisms, after getting injected into the MCs. We use the model discussed in this letter to explain the multiwavelength spectral energy distribution of unidentified Galactic ultra-high-energy gamma-ray source LHAASO J2108+5157. We also discuss the feasibility of applying this model in other cases as well. Future observations can test the viability of the model discussed in this letter, which will in turn confirm that the SNRs can, in fact, accelerate particles up to PeV energies.

Muons in EASs with E0 = 1019 eV According to Data of the Yakutsk Array

Lateral distribution functions of particles in extensive air showers with the energy {{E}_{0}} approx {{10}^{{19}}}{kern 1pt} eV recorded by ground-based and underground scintillation detectors with a threshold of {{E}_{mu }} approx {kern 1pt} 1.0 times {text{sec}}{kern 1pt} theta GeV at the Yakutsk array during the continuous observations from 1986 to 2016 have been analyzed using events with zenith angles θ ≤ 60°. Experimental functions have been compared to the predictions obtained with the QGSJet-01-d hadron interaction model by applying the CORSIKA code. The entire dataset indicates that cosmic rays consist predominantly of protons.

Modeling strangeness enhancements to resolve the muon excess in cosmic ray extensive air shower data

Experimental observations of extensive air showers have revealed an excess of the muon content with respect to their theoretical simulations, which we refer to as the muon puzzle. This muon puzzle hampers a precise determination of the ultra-high-energy cosmic ray mass composition. We investigate the potential of producing states of dense quark-gluon matter (which we call fireballs) to resolve the muon puzzle as quantified with data from the Pierre Auger Observatory on the depth of the shower maximum and the number of muons at ground. Adopting a phenomenological fireball model, we find that the inelasticity enhancement associated with the formation of a plasma state is in tension with data on the electromagnetic longitudinal shower development. Instead, we restrict the fireball model to only enhance the strangeness produced in Standard Model hadronic interactions, and dub this model the strangeball model. With an analytic approach based on the Heitler-Matthews model we then find explicit sets of strangeball parameters that resolve the muon puzzle. Constraints from data on shower-to-shower fluctuations of the muon number require strangeness enhancements already at energies accessible to current-generation collider experiments. At Tevatron and LHC energies we estimate 40% of the interactions to produce strangeballs, corresponding to a 5–9% increase of the average fraction of energy retained in the hadronic cascade compared to predictions from current hadronic interaction models. A comparison with relevant measurements of the LHCf and LHCb detectors does not directly exclude this scenario, though the obtained tension with LHCb suggests a stringent test at 14 TeV.

Hadronic interaction model dependence in cosmic Gamma-ray flux estimation using an extensive air shower array with a muon detector

Observation techniques of high-energy gamma rays using air showers have remarkably progressed via the Tibet ASγ, HAWC, and LHAASO experiments. These observations have significantly contributed to gamma-ray astronomy in the northern sky’s sub-PeV region. Moreover, in the southern sky, the ALPACA experiment is underway at 4,740 m altitude on the Chacaltaya plateau in Bolivia. This experiment estimates the gamma-ray flux from the difference between the number of on-source and off-source events by real data, utilizing the gamma-ray detection efficiency calculated through Monte Carlo simulations, which in turn depends on the hadronic interaction models. Even though the number of cosmic-ray background events can be experimentally estimated, this model dependence affects the estimation of gamma-ray detection efficiency. However, previous reports have assumed that the model dependence is negligible and have not included it in the error of gamma-ray flux estimation. Using ALPAQUITA, the prototype experiment of ALPACA, we quantitatively evaluated the model dependence on hadronic interaction models for the first time. We evaluate the model dependence on hadronic interactions as less than 3.6 % in the typical gamma-ray flux estimation performed by ALPAQUITA; this is negligible compared with other uncertainties such as energy scale uncertainty in the energy range from 6 to 300 TeV, which is dominated by the Monte Carlo statistics. This upper limit of 3.6 % model dependence is expected to apply to ALPACA.

Pythia 8 as hadronic interaction model in air shower simulations

Hadronic interaction models are a core ingredient of simulations of extensive air showers and pose the major source of uncertainties of predictions of air shower observables. Recently, Pythia 8, a hadronic interaction model popular in accelerator-based high-energy physics, became usable in air shower simulations as well. We have integrated Pythia 8 with its new capabilities into the air shower simulation framework CORSIKA 8. First results show significantly shallower shower development, which we attribute to higher cross-section predictions by the new simplified nuclear model of Pythia.