Multiple experiments reported evidences of a muon deficit in air shower simulations with respect to data, which increases with the primary energy. In this work, we study the muon deficit using measurements of the muon density at 1000 m from the shower axis obtained by the Akeno Giant Air Shower Array (AGASA). The selected events have reconstructed energies in the range $18.83\,\leq\,\log_{10}(E_{R}/\textrm{eV})\,\leq\,19.46$ and zenith angles $\theta\leq 36^{\circ}$. We compare these muon density measurements to proton, iron, and mixed composition scenarios, obtained by using the high-energy hadronic interaction models EPOS-LHC, QGSJetII-04, and Sibyll2.3c. We find that AGASA data are compatible with a heavier composition, lying above the predictions of the mixed composition scenarios. The average muon density divided by the energy in AGASA data is greater than in the mixed composition scenarios by a factor of $1.49\pm0.11\,\textrm{(stat)}\pm^{0.49}_{0.30}\,\textrm{(syst)}$, $1.54\pm0.12\,\textrm{(stat)}\pm^{0.50}_{0.31}\,\textrm{(syst)}$, and $1.66\pm0.13\,\textrm{(stat)} \pm ^{0.54}_{0.34}\,\textrm{(syst)}$ for EPOS-LHC, Sibyll2.3c, and QGSJetII-04, respectively. We interpret this as further evidence of a muon deficit in air shower simulations at the highest energies

Etchegoyen, A.

Gesualdi, F.

Supanitsky, D.

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ICRC 2021THE ASTROPARTICLE PHYSICS CONFERENCEBerlin |  GermanyONLINE ICRC 2021THE ASTROPARTICLE PHYSICS CONFERENCEBerlin |  Germany37th International Cosmic Ray Conference12–23 July 2021Muon deficit in simulations of air showers inferred fromAGASA dataFlavia Gesualdi,𝑎,𝑏,∗ Daniel Supanitsky𝑎 and Alberto Etchegoyen𝑎𝑎Instituto de Tecnologías en Detección y Astropartículas (CNEA, CONICET, UNSAM), San Martín,Buenos Aires, Argentina𝑏Karlsruhe Institute of Technology, Institute for Astroparticle Physics, Karlsruhe, GermanyE-mail: flavia.gesualdi@iteda.cnea.gov.arMultiple experiments reported evidences of a muon deficit in air shower simulations with respectto data, which increases with the primary energy. In this work, we study the muon deficitusing measurements of the muon density at 1000 m from the shower axis obtained by the AkenoGiant Air Shower Array (AGASA). The selected events have reconstructed energies in the range18.83 ≤ log10 (𝐸𝑅/eV) ≤ 19.46 and zenith angles \ ≤ 36◦. We compare these muon densitymeasurements to proton, iron, and mixed composition scenarios, obtained by using the high-energy hadronic interaction models EPOS-LHC, QGSJetII-04, and Sibyll2.3c. We find thatAGASA data are compatible with a heavier composition, lying above the predictions of the mixedcomposition scenarios. The average muon density divided by the energy in AGASA data isgreater than in the mixed composition scenarios by a factor of 1.49 ± 0.11 (stat) ±0.490.30 (syst),1.54 ± 0.12 (stat) ±0.500.31 (syst), and 1.66 ± 0.13 (stat) ±0.540.34 (syst) for EPOS-LHC, Sibyll2.3c, andQGSJetII-04, respectively. We interpret this as further evidence of a muon deficit in air showersimulations at the highest energies.37th International Cosmic Ray Conference (ICRC 2021)July 12th – 23rd, 2021Online – Berlin, Germany∗Presenter© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/arXiv:2108.04829v1  [astro-ph.HE]  10 Aug 2021Muon deficit from AGASA data Flavia Gesualdi1. IntroductionIt is well known that high-energy cosmic rays can only be studied through the extensive airshowers they produce, because the flux drops steeply above 1015 eV. These primaries can reachenergies beyond those accessible at the Large Hadron Collider. Therefore, high-energy hadronicinteraction models can only be tested at ultrahigh energies via air showers. Furthermore, to elucidatethe origin of cosmic rays, it is important to know the mass composition as a function of the energy.The composition is determined through the comparison of data to air shower simulations. The twomost sensitive observables to the composition are the depth of the shower maximum 𝑋max and thenumber of muons 𝑁` [1].The muonic component of air showers, which originates mainly from the decay of hadrons,serves as a tracer of the hadronic component because most muons (and anti-muons) reach theground before decaying. Recently, several experiments reported a muon deficit in simulations withrespect to data. At the energies considered in this work, the Pierre Auger Observatory reporteda deficit between 30 % and 80 % against the mixed composition scenarios [2, 3]. The TelescopeArray Collaboration reported a deficit of ∼ 67 % against proton QGSJetII-04 showers (compatiblewith their observed composition) [4]. Finally, preliminary data of Yakutsk Array are compatiblewith no muon deficit [5, 6]. It is not yet understood the cause of said deficit: it could be dueto new high-energy phenomena, or to a partial mismodeling of hadronic interactions at low orhigh energies. Solving the muon deficit would improve both hadronic interaction models and thesystematic uncertainties in the inferred comsic-ray mass composition.In this work, we use data measured by the Akeno Giant Air Shower Array (AGASA) to studythe muon deficit. This experiment was able to detect air showers with energies above ∼ 3× 1018 eVand zenith angles \ ≤ 45◦. It consisted of 111 scintillation counters, covering ∼ 100 m2, and 27proportional counters shielded with 30 cm of iron or 1 m of concrete, covering ∼ 30 km2. Thelatter served as the muon detectors, and had a vertical muon energy threshold of 0.5 GeV [8]. Theexperiment was decomissioned in 2004.2. AnalysisWe analyze the AGASA measurements of the muon density at 1000 m from the shower axis,measured on the shower plane. The data is extracted from Fig. 7 of Ref. [7] (see also Table IV inAppendix B of Ref. [9]). The energies of these events are reduced by a factor of 0.68 to take themto the referece energy scale defined by the Spectrum working group [10]. This factor is obtainedby matching the features of the cosmic ray flux measurements (see Ref. [9] and references therein).The idea behind matching fluxes is that, assuming isotropy, all experiments should measure thesame flux. Furthermore, most of the difference between the AGASA and the reference energy scalearises from the muon deficit in the simulations used to calibrate the AGASA scale (especially inthose using older-generation hadronic models). Considering the energies in the reference scale, theanalyzed events have reconstructed energies in 18.83 ≤ log10(𝐸𝑅/eV) ≤ 19.46, as well as zenithangles \ ≤ 36◦.Moreover, we use a library of proton, helium, nitrogen, and iron-initiated air showers, simulatedusing EPOS-LHC, QGSJetII-04, and Sibyll2.3c, as well as Fluka 2011.2x for the low-energy2Muon deficit from AGASA data Flavia Gesualdiinteractions, and employing CORSIKA. The library consists of ∼ 20 showers (∼ 30 in the case ofproton primaries) per model, primary, and input energy, the latter taking discrete values in the range18.0 ≤ log10(𝐸/eV) ≤ 19.8 in steps of Δ log10(𝐸/eV) = 0.2. This library is further described inRef. [9]. For every primary and model, the mean muon density as a function of the energy 〈?̃?`〉 isfitted using a power-law.We derive a simulated muon density for a mixed composition scenario by using the massfractions obtained from the fits to the 𝑋max distributions of the Pierre Auger Observatory [11].For each model, we compute the mixed composition mean muon density as 〈?̃?`,mix〉(𝐸) =∑𝐴 𝑓𝐴(𝐸)〈?̃?`,𝐴〉(𝐸), where 𝐴 = {p, He, N, Fe}, 𝑓𝐴(𝐸) are the mass fractions, and 〈?̃?`,𝐴〉(𝐸)are the single-primary mean muon densities.The mean muon density from simulations at 1000 m from the shower axis 〈?̃?`〉, which dependson the Monte-Carlo energy 𝐸 , cannot be directly compared to that of data, which depends on thereconstructed energy 𝐸𝑅, even if 𝐸𝑅 is an unbiased estimator of 𝐸 [12]. We therefore compute theenergy reconstruction and binning effects on simulations analytically. The mean simulated muondensity divided by the reconstructed energy as a function of the center of the 𝑖-th reconstructedenergy bin 𝐸𝑅𝑖 can be expressed as〈𝜌`𝐸𝑅〉(𝐸𝑅𝑖) =∫ 𝐸+𝑅𝑖𝐸−𝑅𝑖𝑑𝐸𝑅∫ ∞0𝑑𝐸 〈?̃?`〉(𝐸) 𝐸−1𝑅 𝐽 (𝐸)𝐺 (𝐸𝑅 |𝐸)∫ 𝐸+𝑅𝑖𝐸−𝑅𝑖𝑑𝐸𝑅∫ ∞0𝑑𝐸 𝐽 (𝐸)𝐺 (𝐸𝑅 |𝐸), (1)where 𝐸−𝑅𝑖and 𝐸+𝑅𝑖are the lower and upper limits of the energy bin; 〈?̃?` (𝐸)〉 is the mean muondensity as a function of the Monte-Carlo/true energy of the simulation (i.e. the power-law fits); 𝐽 (𝐸)is the cosmic ray flux, obtained by fitting the Telescope Array measurements [13]; and 𝐺 (𝐸𝑅 |𝐸) isthe conditional probability distribution of 𝐸𝑅 conditioned to 𝐸 , modeled as a log-normal distribution[14] with a standard deviation that decreases with energy [15]. A more extensive explanation ofEq. (1) can be found in Ref. [9].Both the energy reconstruction and binning have the effect of making〈𝜌`/𝐸𝑅〉(𝐸𝑅𝑖 = 𝐸∗)smaller than 〈?̃?`/𝐸〉(𝐸 = 𝐸∗), when evaluating both at a same numerical value 𝐸∗. The energy re-construction effect, which is the dominant, increases for broader conditioned distributions𝐺 (𝐸𝑅 |𝐸)and in regions where the flux 𝐽 (𝐸) is steeper.Figure 1 shows a comparison between 〈?̃?`/𝐸〉(𝐸) and 〈𝜌`/𝐸𝑅〉(𝐸𝑅𝑖). It can be seen in thefigure that 〈𝜌`/𝐸𝑅〉(𝐸𝑅𝑖) can be 11 % to 22 % smaller than 〈?̃?`/𝐸〉(𝐸) in the studied energy range.At low energies, this difference is explained by the large uncertainty in the reconstructed energy(∼28 % at 1018.83 eV). At high energies, the dominant effect is the flux suppression. The effect ofbinning in reconstructed energy with a bin width of Δ log10(𝐸𝑅/eV) = 0.2 is small in comparison.It is relevant to add that〈𝜌`/𝐸𝑅〉(𝐸𝑅𝑖) is computed from the integration of 〈?̃?`,mix〉(𝐸) usingEq. (1). It is not equivalent to calculate it as the linear combination of〈𝜌`,𝐴/𝐸𝑅〉(𝐸𝑅𝑖), becausethe mass fractions 𝑓𝐴(𝐸) depend on the energy 𝐸 , which is an integration variable in Eq. (1).Finally, we consider the systematic uncertainties as presented in Ref. [16]. The systematicuncertainty in the energy constitutes the dominant source, ranging between ±22 % to ±26 % (thisincludes a ±10 % systematic uncertainty of the reference energy scale). The systematics in the3Muon deficit from AGASA data Flavia Gesualdi18.9 19.0 19.1 19.2 19.3 19.4log10(E(Ri)/eV)1.001.251.501.752.002.252.50pFeEPOS− LHCp 〈(ρ̃µ/m2)/(E/1019eV)〉p 〈(ρµ/m2)/(ER/1019eV)〉Fe 〈(ρ̃µ/m2)/(E/1019eV)〉Fe 〈(ρµ/m2)/(ER/1019eV)〉Figure 1: Mean muon density divided by the energy (reconstructed energy), as a function of the loga-rithm of the Monte-Carlo energy (center of the 𝑖-th reconstructed energy bin) in dashed lines (solid lines),obtained from the power-law fits (from Eq. (1)). The shown muon densities correspond to proton andiron-initiated simulated air showers generated by using EPOS-LHC. The binwidth considered in Eq. (1) isΔ log10 (𝐸𝑅/eV) = 0.2.muon density are negligible in comparison. The propagation of uncertainties is applied followingRef. [9].3. ResultsFigure 2 shows 〈𝜌`/𝐸𝑅〉(𝐸𝑅𝑖) as a function of the logarithm of the reconstructed energybin obtained for AGASA data, proton and iron simulations, and for the mixed composition sce-narios. The data from the 120 events are grouped into three energy bins, each of a binwidth ofΔ log10(𝐸/eV) = 0.2. The data points constitute the average of 67, 33, and 20 events (from lowerto higher energy). The square brackets associated to the AGASA data represent the systematicuncertainties corresponding to the energy (hence they are diagonal) and muon density. The squarebrackets associated to the mixed composition scenarios include those of the energy, and also includethe systematic uncertainties propagated from the mass fractions, which are small in comparison tothe first. It can be seen from Fig. 2 that for all models, the AGASA data are compatible with ironnuclei. The AGASA data points lie above the mixed composition scenarios. The lowest energydata point is not compatible with the mixed composition scenarios for all three models. This is alsotrue for the highest-energy data point in the case of QGSJetII-04. However, all the remaining datapoints are compatible with the mixed composition scnearios when considering total uncertainties.To summarize the information in a unique value, we compute 〈𝜌`/𝐸𝑅〉 taking the averagein the whole energy range (18.83 ≤ log10(𝐸𝑅/eV) ≤ 19.46). It is reasonable to compute suchaverage since 𝜌`/𝐸𝑅 is nearly constant within the analyzed energy range. Fig. 3 shows the values4Muon deficit from AGASA data Flavia Gesualdi18.8 18.9 19.0 19.1 19.2 19.3 19.4log10(ERi/eV)0.81.01.21.41.61.82.02.22.42.6〈(ρµ/m2 )/(ER/1019eV)〉Sibyll2.3cData Fe Mixed p18.8 18.9 19.0 19.1 19.2 19.3 19.4log10(ERi/eV)0.81.01.21.41.61.82.02.22.42.6〈(ρµ/m2 )/(ER/1019eV)〉EPOS− LHCData Fe Mixed p18.8 18.9 19.0 19.1 19.2 19.3 19.4log10(ERi/eV)0.81.01.21.41.61.82.02.22.42.6〈(ρµ/m2 )/(ER/1019eV)〉QGSJetII− 04Data Fe Mixed pFigure 2: Average muon density divided by the reconstructed energy, as a function of the logarithm ofthe reconstructed energy in the center of the 𝑖-th bin. Superimposed to AGASA data points [7] are thepredictions for proton (red) and iron (blue) primaries, and for the mixed composition scenario correspondingto the models Sibyll2.3c (top left panel), EPOS-LHC (top right panel), and QGSJetII-04 (bottom panel). Thesystematic uncertainties are enclosed by square brackets. The vertical dashed lines mark the limits of thereconstructed energy bins.of 〈𝜌`/𝐸𝑅〉 computed from AGASA measurements, and the ones corresponding to proton, iron,and mixed composition scenarios for the three considered models.Fig. 3 shows that the composition inferred from 〈𝜌`/𝐸𝑅〉 obtained from AGASA data iscompatible with heavy primaries, for the three models considered. The values from AGASA dataare larger than those of the mixed composition scenarios, and are not compatible within totaluncertainties. Considering the upper uncertainties for the mixed composition models, and the loweruncertianties for the AGASA data point, the discrepancies are of 1.9𝜎 for QGSJetII-04, 1.6𝜎 forEPOS-LHC, and 1.7𝜎 for Sibyll2.3c. It follows that the AGASA data support a muon deficit insimulations.We therefore quantify the average muon deficit in the reconstructed energy range 18.83 ≤log10(𝐸𝑅/eV) ≤ 19.46 with a correction factor 𝐹. This is defined as the ratio between theexperimental average muon density divided by the energy and the one obtained from air shower5Muon deficit from AGASA data Flavia Gesualdi1.82± 0.13±0.580.351.471.19± 0.03±0.070.080.951.591.23± 0.04±0.080.081.051.501.10± 0.03±0.060.081.00DataFeMixedpFeMixedpFeMixedpAGASASibyll2.3cEPOS - LHCQGSJetII - 04〈(ρµ/m2)/(ER/1019 eV)〉 ± (stat)± (syst) 1.00 1.25 1.50 1.75 2.00 2.25Figure 3: Average muon density divided by the reconstructed energy for AGASA data and for proton,iron, and mixed composition scenarios, for the three considered models. The obtained values are reportedin the table (left) and are also plotted (right) on the same line. The average is taken in the energy range18.83 ≤ log10 (𝐸𝑅/eV) ≤ 19.46. The square brackets show the systematic uncertainties.simulations,𝐹 =〈𝜌data` /𝐸𝑅〉〈𝜌S`/𝐸𝑅〉, (2)where S denotes the scenario under analysis, i.e. S={mix, p, Fe}. The uncertainties in 𝐹 are derivedby standard error propagation. Fig. 4 shows the obtained values of the correction factor 𝐹, togetherwith their statistic and systematic uncertainties, for the three considered models, and for the singlenuclei and mixed composition scenarios. Note that the latter do not overlap with 1 even consideringtotal uncertainties.1.24± 0.09±0.400.241.54± 0.12±0.500.311.91± 0.14±0.610.371.14± 0.08±0.370.221.49± 0.12±0.490.301.74± 0.13±0.560.331.21± 0.09±0.390.231.66± 0.13±0.540.341.82± 0.13±0.580.35FeMixedpFeMixedpFeMixedpSibyll2.3cEPOS - LHCQGSJetII - 04F± (stat)± (syst) 1.00 1.25 1.50 1.75 2.00 2.25 2.5Figure 4: Muon density correction factor 𝐹 corresponding to the single nuclei and mixed compositionscenarios, for the three considered models. The obtained values are reported in the table (left) and are alsoplotted (right) on the same line. The square brackets correspond to the systematic uncertainties. The energyrange under consideration is 18.83 ≤ log10 (𝐸𝑅/eV) ≤ 19.46.It is interesting to add that the results presented in Figs. 3 and 4 are essentially independent ofthe chosen flux parameterization. If the fit to the flux measurements of the Pierre Auger Observatory[17] are used instead of that of Telescope Array [9, 13], the values of 〈𝜌S`/𝐸𝑅〉 and 𝐹 change in lessthan ∼ 1 %.6Muon deficit from AGASA data Flavia GesualdiThe muon deficit found in this analysis is qualitatively compatible with those reported by thePierre Auger [3] and Telescope Array Collaborations [4]. A quantitative comparison to the findingsof other experiments can be found in Ref. [16].4. ConclusionsWe analyzed the measurements of the muon density at 1000 m from the shower axis obtainedby the AGASA experiment, and compared them to the predictions corresponding to single protonand iron-initiated air shower simulations, as well as four-component mixed composition scenar-ios. The latter are based on the 𝑋max measurements performed by the Pierre Auger Observatory.The simulations were generated with the high-energy hadronic interaction models QGSJetII-04,EPOS-LHC, and Sibyll2.3c. Furthermore, we worked in the reference energy scale defined bythe Spectrum Working Group [10]. To compare data to simulations, we analytically computed thebiases introduced by binning in energy and by reconstructing the energy with a broad resolution.In this work, we take into account the systematics in the energy (between ±22 % to ±26 %) asdescribed in Ref. [16].The AGASA measurements are found to be compatible with iron primaries for all the consideredmodels. The measurements lie above the predictions corresponding to the mixed compositionscenarios for the three models. When considering the average throughout the complete energy range,the estimate of 〈𝜌`/𝐸〉 from AGASA data does not overlap with those of the mixed compositionscenarios. Thus, AGASA data support a muon deficit in simulations.We computed a muon density correction factor 𝐹 in the energy range 18.83 ≤ log10(𝐸𝑅/eV) ≤19.46 for the three models considered. For the mixed composition scenarios to be in perfectagreement with AGASA measurements, the muon density should be incremented by a factor of1.49 ± 0.11 (stat) ± 0.490.30 (syst) for EPOS-LHC, 1.54 ± 0.12 (stat) ±0.500.31 (syst) for Sibyll2.3c, and1.66 ± 0.13 (stat) ±0.540.34 (syst) for QGSJetII-04. It is worth mentioning that the estimated muondeficits are qualitatively in agreement with the ones reported by the Pierre Auger and TelescopeArray Collaborations.AcknowledgementsThe authors acknowledge the members of the WHISP group, specially K. Shinozaki and H.Dembinski, for useful discussions about the systematic uncertainties of the AGASA data.7Muon deficit from AGASA data Flavia GesualdiReferences[1] R. R. Prado, EPJ Web Conf. 208, 08003 (2019).[2] A. Aab et al. (Pierre Auger Collaboration), Phys. Rev. D 91, 032003 (2015).[3] A. Aab et al. (Pierre Auger Collaboration), Phys. Rev. Lett. 117, 192001 (2016).[4] R. U. Abbasi et al. (Telescope Array Collaboration), Phys. Rev. D 98, 022002 (2018).[5] H. P. Dembinski et al. for the EAS-MSU, IceCube, KASCADE-Grande, NEVOD-DECOR,Pierre Auger, SUGAR, Telescope Array, and Yakutsk EAS Array collaborations, EPJ WebConf. 210, 02004 (2019).[6] L. Cazon for the EAS-MSU, IceCube, KASCADE-Grande, NEVOD-DECOR, Pierre Auger,SUGAR, Telescope Array, and Yakutsk EAS Array collaborations, PoS (ICRC2019), 214(2019).[7] K. Shinozaki and M. Teshima, Nucl. Phys. B (Proc. Suppl.) 136, 18 (2004).[8] N. Hayashida et al., J. Phys. G: Nucl. Part. Phys. 21, 1101 (1995).[9] F. Gesualdi, A. D. Supanitsky, and A. Etchegoyen, Phys. Rev. D 101, 083025 (2020).[10] D. Ivanov for the Pierre Auger Collaboration and the Telescope Array Collaboration, PoS(ICRC2017), 498 (2018).[11] J. Bellido for the Pierre Auger Collaboration, PoS (ICRC2017), 301 (2018).[12] H. P. Dembinski, Astroparticle Physics 102, 89 (2018).[13] C. Jui for the Telescope Array Collaboration, PoS (ICRC2015), 035 (2016).[14] M. Takeda et al., Astropart. Phys. 19, 447 (2003).[15] S. Yoshida et al., Astropart. Phys. 3, 105 (1995).[16] F. Gesualdi et al. for the WHISP Group, PoS (ICRC2021), 473 (2021).[17] F. Fenu for the Pierre Auger Collaboration, PoS (ICRC2017), 486 (2018).8

Muon deficit in simulations of air showers inferred from AGASA data

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Muon deficit in simulations of air showers inferred from AGASA data

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