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The number of muons in an air shower is a strong indicator of the mass of the primary particle and increases with a small power of the cosmic ray mass by the $\beta$-exponent, $N_{\mu} \sim A^{(1-\beta)}$. This behaviour can be explained in terms of the Heitler-Matthews model of hadronic air showers. In this paper, we present a method for calculating $\beta$ from the Heitler-Matthews model. The method has been successfully verified with a series of simulated events observed by the Pierre Auger Observatory at $10^{19}$ eV. To follow real measurements of the mass composition at this energy, the generated sample consists of a certain fraction of events produced with p, He, N and Fe primary energies. Since hadronic interactions at the highest energies can differ from those observed at energies reached by terrestrial accelerators, we generate a mock data set with $\beta =0.92$ (the canonical value) and $\beta =0.96$ (a more exotic scenario). The method can be applied to measured events to determine the muon signal for each primary particle as well as the muon scaling factor and the $\beta$-exponent. Determining the $\beta$-exponent can effectively constrain the parameters that govern hadronic interactions and help solve the so-called muon problem, where hadronic interaction models predict too few muons relative to observed events. In this paper, we lay the foundation for the future analysis of measured data from the Pierre Auger Observatory with a simulation study., Comment: Proccedings of 38th International Cosmic Ray Conference (ICRC2023)

Simulations of extensive air showers using current hadronic interaction models predict too small numbers of muons compared to events observed in the air-shower experiments, which is known as the muon-deficit problem. In this work, we present a new method to calculate the factor by which the muon signal obtained via Monte-Carlo simulations must be rescaled to match the data, as well as the beta exponent from the Heitler-Matthews model which governs the number of muons found in an extensive air shower as a function of the mass and the energy of the primary cosmic ray. This method uses the so-called z variable (difference between the total reconstructed and the simulated signals), which is connected to the muon signal and is roughly independent of the zenith angle, but depends on the mass of the primary cosmic ray. Using a mock dataset built from QGSJetII-04, we show that such a method allows us to reproduce the average muon signal from this dataset using Monte-Carlo events generated with the EPOS-LHC hadronic model, with accuracy better than 6%. As a consequence of the good recovery of the muon signal for each primary included in the analysis, also the beta exponent can be obtained with accuracy of less than 1% for the studied system. Detailed simulations show a dependence of the beta exponent on hadronic interaction properties, thus the determination of this parameter is important for understanding the muon deficit problem., Comment: 8 pages, 5 figures, 2 tables, accepted for publication in the proceedings of the 27th European Cosmic Ray Symposium

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 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 $\beta$ 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 $\beta$ 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 showing that this method allows us to recover the ratio of the muon signal between EPOS-LHC and QGSJetII-04 and the average $\beta$ 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., Comment: This work corresponds to the presentation at the ICNFP 2022 at Kolymbari, Crete, in September 2022. The proceedings will be published in Physica Scripta. arXiv admin note: text overlap with arXiv:2108.07527

The Pierre Auger Observatory is the world's largest detector for observation of ultra-high-energy cosmic rays (UHECRs) (above the energy of $10^{17}$ 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. 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., Comment: Proceedings of the ISMD-2022 conference, accepted for publication SciPost Proceedings

The measurement of the individual charged particles especially muons in an extended air shower (EAS) resulting from primary cosmic rays provides important distinguishing parameters to identify the chemical composition of the cosmic primary particles. For Neutrino Telescope experiments like Baikal-GVD, the estimation of underwater muon flux is of importance to study atmospheric muons. In this paper, a GEANT4-based simulation is presented to estimate the atmospheric muon flux underwater taking Baikal-GVD as an example. The location of the Baikal-GVD experiment at Lake Baikal provides a unique opportunity to study the passage of muons through its northern shore and the water. The muons arriving from the north direction will lose more energy as compared to those arriving from the south. An approximation for the northern shore is also simulated in the GEANT4 geometry and the results of the simulation are compared with the measurements from the NT-96 detector. The results of the simulations are consistent with the shore shadow observed in the measurements in the NT-96. This approach can also be used to propagate the muons from generators like CORSIKA through long distances in matter like water, ice, earth, etc. for simulations in such experiments.

The Pierre Auger Observatory is the world's largest detector of ultra--high energy cosmic rays (UHECRs). It uses an array of fluorescence telescopes and particle detectors at the ground to obtain detailed measurements of the energy spectrum, mass composition and arrival directions of primary cosmic rays (above the energy of $10^{17}$ eV) with accuracy not attainable until now.Observations of extensive air showers performed by the Pierre Auger Observatory can also be used to probe hadronic interactions at high energy, in a kinematic and energy region not accessible by man-made accelerators. Indeed, exploiting Auger data, we reach center-of-mass energies up to 400 TeV, i.e. more than 30 times of those attainable at the LHC, and explore interactions in the very forward region of phase space on targets of atomic mass of 14. In addition, a precise measurement of the muon component of air showers at the ground is more sensitive to the details of the hadronic interactions along many steps of the cascade development, such as the multiplicity of the secondaries and the fraction of electromagnetic component with respect to the total signal. On the other hand, the intrinsic muon fluctuations mostly depend on the first interaction. In this paper we overview the new Auger studies exploring the connection between the dynamics of the air shower and the multi-particle production, and how this knowledge can be translated into constraints of the high energy hadronic models as well as direct measurements, complementary to, and beyond the reach of, accelerator experiments., Comment: Proceedings of 9th International Conference on New Frontiers in Physics (ICNFP 2020), paper submitted to IJMPA

The number of muons in extensive air showers predicted using LHC-tuned hadronic interaction models, such as EPOS-LHC and QGSJetII-04, is smaller than observed in showers recorded by leading cosmic ray experiments. In this paper, we present a new method to derive muon rescaling factors by analyzing reconstructions of simulated showers. The z-variable used (difference of initially simulated and reconstructed total signal in detectors) is connected to the muon signal and is roughly independent of the zenith angle but depends on the mass of primary cosmic ray. The performance of the method is tested using Monte Carlo shower simulations for the hybrid detector of the Pierre Auger Observatory. Having an individual z-value from each simulated hybrid event, the corresponding signal at 1000 m from the shower axis, and using a parametrization of the muon fraction in simulated showers, we can calculate the multiplicative rescaling parameters of the muon signals in the ground detector even for an individual event. We can also study its dependence as a function of zenith angle and the mass of primary cosmic ray. This gives a possibility not only to test/calibrate the hadronic interaction models, but also to derive the $\beta$-exponent, describing an increase of the number of muons as a function of primary energy and mass of the cosmic ray. Detailed simulations show dependence of the $\beta$-exponent on hadronic interaction properties, thus the determination of this parameter is important for understanding the muon deficit problem., Comment: Proceedings of 37th International Cosmic Ray Conference (ICRC 2021), July 12th -- 23rd, 2021

The Cosmic Ray Extremely Distributed Observatory (CREDO) is a newly formed, global collaboration dedicated to observing and studying cosmic rays (CR) and cosmic ray ensembles (CRE): groups of a minimum of two CR with a common primary interaction vertex or the same parent particle. The CREDO program embraces testing known CR and CRE scenarios, and preparing to observe unexpected physics, it is also suitable for multi-messenger and multi-mission applications. Perfectly matched to CREDO capabilities, CRE could be formed both within classical models (e.g. as products of photon-photon interactions), and exotic scenarios (e.g. as results of decay of Super Heavy Dark Matter particles). Their fronts might be significantly extended in space and time, and they might include cosmic rays of energies spanning the whole cosmic ray energy spectrum, with a footprint composed of at least two extensive air showers with correlated arrival directions and arrival times. Since CRE are mostly expected to be spread over large areas and, because of the expected wide energy range of the contributing particles, CRE detection might only be feasible when using available cosmic ray infrastructure collectively, i.e. as a globally extended network of detectors. Thus, with this review article, the CREDO Collaboration invites the astroparticle physics community to actively join or to contribute to the research dedicated to CRE, and in particular to share any cosmic ray data useful for the specific CRE detection strategies., Comment: 59 pages, 23 figures

The Cosmic-Ray Extremely Distributed Observatory (CREDO) is a project created a few years ago in the Institute of Nuclear Physics PAS in Krak\'ow and dedicated is to global studies of extremely extended cosmic-ray phenomena. The main reason for creating such a project was that the cosmic-ray ensembles (CRE) are beyond the capabilities of existing detectors and observatories. Until now, cosmic ray studies, even in major observatories, have been limited to the recording and analysis of individual air showers therefore ensembles of cosmic-rays, which may spread over a significant fraction of the Earth were neither recorded nor analyzed. In this paper the status and perspectives of the CREDO project are presented., Comment: 8 pages, 5 figures

We study the feasibility of detecting preshower initiated by ultra-high energy photons using Monte-Carlo simulations of nearly horizontal air showers for the example of the La Palma site of the Cherenkov Telescope Array. We investigate the efficiency of multivariate analysis in correctly identifying preshower events initiated by 40 EeV photons and cosmic-ray dominated background simulated in the energy range 10 TeV -- 10 EeV. The effective areas for such kind of events are also investigated and event rate predictions related to different ultra-high energy photons production models are presented. While the expected number of preshowers from diffuse emission of UHE photon for 30 hours of observation is estimated around $3.3\times10^{-5}$ based on the upper limits put by the Pierre Auger Observatory, this value is at the level of $2.7\times10^{-4}$ ($5.7\times 10^{-5}$) when considering the upper limits of the Pierre Auger Observatory (Telescope Array) on UHE photon point sources. However, UHE photon emission may undergo possible "boosting" due to gamma-ray burst, increasing the expected number of preshower events up to 0.17 and yielding a minimum required flux of $\sim 0.2$ $\mathrm{km^{-2}yr^{-1}}$ to obtain one preshower event, which is about a factor 10 higher than upper limits put by the Pierre Auger Observatory and Telescope Array (0.034 and 0.019 $\mathrm{km^{-2}yr^{-1}}$, respectively)., Comment: 16 pages, 16 figures, 4 tables

Muons and other ionizing radiation produced by cosmic rays and radiative decays affect CMOS/CCD sensor. When particles colliding with sensors atoms cause specific kind of noise on images recorded by cameras. We present a concept and preliminary implementation of method for recognizing those events and algorithms for image processing and their classification by machine learning. Our method consists of analyzing the shape of traces present in images recorded by a camera sensor and metadata related to an image like camera model, GPS location of camera, vertical and horizontal orientation of a camera sensor, timestamp of image acquisition, and other events recognized near-by sensors. The so created feature vectors are classified as either a muon-like event, an electron-like event or the other event, possibly noise. For muon-like events our method estimates azimuth of a muon track. Source of the data is database of CREDO (Cosmic-Ray Extremely Distributed Observatory) project and ESO (European Southern Observatory) archives. The telescope dark frames from ESO are analysed. CREDO project collected so far over 2 millions images of events from many kinds of cameralike: smartphones camera, laptop webcams and Internet of Things cameras localised around the globe., Comment: 36th International Cosmic Ray Conference (ICRC2019)

The search for Cosmic-Ray Ensembles (CRE), groups of correlated cosmic rays that might be distributed over very large areas, even of the size of the planet, requires a globally spread and dense network of detectors, as proposed by the Cosmic-Ray Extremely Distributed Observatory (CREDO) Collaboration. This proposal motivates an effort towards exploring the potential of using even very much diversified detection technologies within one system, with detection units located even in hard-to-reach places, where, nevertheless, the sensors could work independently - without human intervention. For these reasons we have developed a dedicated communication solution enabling the connection of many different types of detectors, in a range of environments. The proposed data transmission system uses radio waves as an information carrier on the 169MHz frequency band in a contrast to the typical commercially used frequencies in a IoT systems (868MHz). The connectivity within the system is based on the star topology, which ensures the least energy consumption. The solution is now being prepared to being implemented using the prototype detection system based on the CosmicWatch open hardware design: a portable, pocket size, and economy particle detector using the scintillation technique. Our prototype detector is equipped with a dedicated software that integrates it with the already operational CREDO server system., Comment: ICRC2019

The Cosmic-Ray Extremely Distributed Observatory (CREDO) uses the hunt for particle cascades from deep space as a vehicle for a unique "bottom-up" approach to scientific research. By engaging the non-specialist public of all ages as "citizen scientists" we create opportunities for lifelong learning for individuals as well as for cooperation and the sharing of common educational tools amongst institutions. The discoveries of these citizen scientists will feed directly into a pioneering new area of scientific research oriented on Cosmic Ray Ensembles (CRE). The detection (or non-detection) of such particle groups promises to open up a new method for exploring our universe, and a new channel on the multi-messenger stage, oriented on both astro- and geo-investigations. The opportunities this would create for cross-disciplinary research are significant and beneficial for individuals, networks of institutions and the global communities of both professional scientists and science enthusiasts., Comment: 4 pages, 3 figures, Proceedings The New Era of Multi-Messenger Astrophysics - Asterics2019, 25 - 29 March, 2019 Groningen, The Netherlands

Ultra-high energy photons constitute one of the most important pieces of the astroparticle physics problems. Their observation may provide new insight on several phenomena such as supermassive particle annihilation or the GZK effect. Because of the absence of any significant photon identification by a leading experiments such as the Pierre Auger Observatory, we consider a screening phenomenon called preshower effect which could efficiently affect ultra-high energy photon propagation. This effect is a consequence of photon interactions with the geomagnetic field and results in large electromagnetic cascade of particles several thousands kilometers above the atmosphere. This collection of particles, called cosmic-ray ensembles (CRE), may reach the atmosphere and produce the well-known air showers. In this paper we propose to use gamma-ray telescopes to look for air showers induced by CRE. Possible sources of ultra-high energy photons include the GZK effect and Super Heavy Dark Matter particles. Simulations involving the preshower effect and detectors response are performed and properties of these peculiar air showers are investigated. The use of boosted decision trees to obtain the best cosmic-ray ensemble/hadron separation, the aperture and event rate predictions for a few models of photon production are also presented., Comment: 8 pages, 3 figures, International Cosmic Ray Conference 2019

The Cosmic-Ray Extremely Distributed Observatory (CREDO) is a project dedicated to global studies of extremely extended cosmic-ray phenomena, the cosmic-ray ensembles (CRE), beyond the capabilities of existing detectors and observatories. Up to date cosmic-ray research has been focused on detecting single air showers, while the search for ensembles of cosmic-rays, which may spread over a significant fraction of the Earth, is a scientific terra incognita. The key idea of CREDO is to combine existing cosmic-ray detectors (large professional arrays, educational instruments, individual detectors, such as smartphones, etc.) into a worldwide network, thus enabling a global analysis. The second goal of CREDO involves a large number of participants (citizen science!), assuring the geographical spread of the detectors and managing manpower necessary to deal with vast amount of data to search for evidence for cosmic-ray ensembles. In this paper the status and perspectives of the project are presented., Comment: Proceedings of 36th International Cosmic Ray Conference - ICRC2019 - July 24th - August 1st, 2019 Madison, WI, U.S.A

One of the main objectives of cosmic-ray studies are precise measurements of energy and chemical composition of particles with extreme energies. Large and sophisticated detectors are used to find events seen as showers starting in the Earth's atmosphere with recorded energies larger than 100 EeV. However, a Cosmic-Ray Ensemble (CRE) developing before reaching the Earth as a bunch of correlated particles may spread over larger areas and requires an extended set of detectors to be discovered. The Cosmic-Ray Extremely Distributed Observatory (CREDO) is a solution to find such phenomena. Even simple detectors measuring the particle arrival time only are useful in this approach, as they are sufficient both to provide candidate CRE events and to determine the direction from which they are arriving., Comment: 20th International Symposium on Very High Energy Cosmic Ray Interactions, May 21-15, 2018, Nagoya, Japan

The Pierre Auger Observatory is the world's largest operating detection system for the observation of ultra high energy cosmic rays (UHECRs). The detector allows detailed measurements of their energy spectrum, mass composition and arrival directions of primary cosmic rays in the energy range above $10^{17}$ eV. The data collected at the Observatory over the last decade show the suppression of the cosmic ray flux at energies above $4\times10^{19}$ eV. However, it is still unclear if this suppression is caused by the propagation of cosmic rays or rather by energy limitation of their sources. The other puzzle is the origin of UHECRs. Some clues can be drawn from studying the distribution of their arrival directions. The recently observed dipole anisotropy has an orientation which indicates an extragalactic origin of UHECRs. The Auger surface detector array is also sensitive to showers due to ultra high energy neutrinos of all flavours and photons, and recent neutrino and photon limits provided by the Observatory can constrain models of the cosmogenic neutrino production and exotic scenarios of the UHECRs origin, such as the decays of super heavy particles. In this paper the recent results on measurements of the energy spectrum, mass composition and arrival directions of cosmic rays, and future prospects are presented., Comment: This article belongs to the Special Issue Selected Papers from the 7th International Conference on New Frontiers in Physics (ICNFP 2018)

This paper investigates the potential to detect tau neutrinos in the energy range of 1-1000 PeV searching for very inclined showers with imaging Cherenkov telescopes. A neutrino induced tau lepton escaping from the Earth may decay and initiate an air shower which can be detected by a fluorescence or Cherenkov telescope. We present here a study of the detection potential of Earth-skimming neutrinos taking into account neutrino interactions in the Earth crust, local matter distributions at various detector sites, the development of tau-induced showers in air and the detection of Cherenkov photons with IACTs. We analyzed simulated shower images on the camera focal plane and implemented generic reconstruction chains based on Hillas parameters. We find that present IACTs can distinguish air showers induced by tau neutrinos from the background of hadronic showers in the PeV-EeV energy range. We present the neutrino trigger efficiency obtained for a few configurations being considered for the next-generation Cherenkov telescopes, i.e. the Cherenkov Telescope Array. Finally, for a few representative neutrino spectra expected from astrophysical sources, we compare the expected event rates at running IACTs to what is expected for the dedicated IceCube neutrino telescope., Comment: Paper accepted for publication in Astroparticle Physics

This paper investigates the potential to detect tau neutrinos in the energy range of 1-1000 PeV searching for very inclined showers with imaging Cherenkov telescopes. A neutrino induced tau lepton escaping from the Earth may decay and initiate an air shower which can be detected by a fluorescence or Cherenkov telescope. We present here a study of the detection potential of Earth-skimming neutrinos taking into account neutrino interactions in the Earth crust, local matter distributions at various detector sites, the development of tau-induced showers in air and the detection of Cherenkov photons with IACTs. We analysed simulated shower images on the camera focal plane and implemented generic reconstruction chains based on Hillas parameters. We find that present IACTs can distinguish air showers induced by tau neutrinos from the background of hadronic showers in the PeV-EeV energy range. We present the neutrino trigger efficiency obtained for a few configurations being considered for the next-generation Cherenkov telescopes, i.e. the Cherenkov Telescope Array. Finally, for a few representative neutrino spectra expected from astrophysical sources, we compare the expected event rates at running IACTs to what expected for the dedicated IceCube neutrino telescope., Comment: Proceedings of the 34th International Cosmic Ray Conference, 30 July- 6 August, 2015, The Hague, The Netherlands

Cherenkov telescopes could have the capability of detecting high energy tau neutrinos by searching for very inclined showers. If a tau lepton, produced by a tau neutrino, escapes from the Earth crust, it will decay and initiate an air shower which can be detected by a fluorescence/Cherenkov telescope. Here we present a detailed Monte Carlo simulation of event rates induced by tau neutrinos in the energy range from 1 PeV to 1 EeV. Topographic conditions are taken into account for a set of example locations. As expected, we find a neutrino sensitivity which depends on the shape of the energy spectrum from astrophysical sources. We compare our findings with the sensitivity of the dedicated IceCube neutrino telescope under different conditions. We also find that a difference of several factors can be observed depending on the topographic conditions of the sites sampled., Comment: Proceedings of 33nd International Cosmic Ray Conference - 2013 - Rio de Janeiro, Brazil