Garcia-Gamez, D.

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Studies of hadronic interactions at ultra-high energieswith the Pierre Auger ObservatoryD. Garcia-GamezTo cite this version:D. Garcia-Gamez. Studies of hadronic interactions at ultra-high energies with the Pierre AugerObservatory. E. Auge´, J. Dumarchez, B. Pietrzyk, J. Traˆn Thanh Vaˆn. XLVIIth Rencontres deMoriond - QCD AND HIGH ENERGY INTERACTIONS, Mar 2012, La Thuile, Italy. ARISF,pp.307-312, 2012. <in2p3-00679927>HAL Id: in2p3-00679927http://hal.in2p3.fr/in2p3-00679927Submitted on 14 Dec 2012HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.STUDIES OF HADRONIC INTERACTIONS AT ULTRA-HIGH ENERGIESWITH THE PIERRE AUGER OBSERVATORYDIEGO GARCIA-GAMEZ1 FOR THE PIERRE AUGER COLLABORATION21Laboratoire de l’Acce´le´rateur line´aire (LAL), Universite´ Paris 11, CNRS-IN2P3, Orsay, France2Observatorio Pierre Auger, Av. San Martin Norte 304, 5613 Malargu¨e, Argentina(Full author list: http://www.auger.org/archive/authors 2012 01.html)The hybrid design of the Pierre Auger Observatory allows one to measure the longitudinalproﬁle of ultra-high energy air showers and the depth at which the shower reaches its max-imum size, Xmax. It also provides a record of the shower front by sampling the secondaryparticles at ground level. These measurements give a variety of independent experimentalobservables with information about the nature of the primary particle and its interactions. Inthis contribution we present a comparison of our mass sensitive observables with the predic-tion of different hadronic interaction models. Furthermore we show how the analysis of thetail of the distribution of Xmax allows one to estimate the proton-air cross-section for particleproduction at center-of-mass energies of 57 TeV.1 IntroductionThe Pierre Auger Observatory is the largest cosmic ray observatory ever built. It was conceivedto study the properties of ultra-high energy cosmic rays (UHECR). It is a hybrid detector thatcombines both surface and ﬂuorescence detectors at the same site1. The Surface Detector (SD)2consists of a triangular grid of over 1600 water Cherenkov detectors spaced 1.5 km and covering asurface of about 3000 km2. The purpose of these detectors is to measure the density of particlesat the ground. The Fluorescence Detector (FD) 3,4 consists of 27 telescopes placed at four sitessurrounding the SD and looking to the atmosphere. Their aim is to collect the UV light trackemitted by the de-excitation of air molecules. The detection of this radiation is only possibleduring dark nights without moon. That results in a small duty cycle of about 13 %, which con-trasts with the nearly 100 % of the SD. As the atmosphere is where extensive air showers (EAS)develop, a good knowledge of its state is of great importance for an experiment like the PierreAuger Observatory. In any FD measurement, the atmosphere is the medium where emissionand transmission of recorded light occur. The particle density at ground sampled by the SD,particularly the electromagnetic component, is also sensitive to the amount of matter traversed.Hence, ﬂuctuations in the atmospheric conditions have an effect over both the longitudinal 5and the lateral 6 developments of the showers. Different monitoring devices are placed at theobservatory site to record atmospheric conditions. This is crucial to be able to understand thefunctioning of the detector and correct the different measurements.The goal of any UHECR detector is to measure the development of EAS. This development isextremely sensitive to the hadronic interaction properties at ultra-high energies. Although theresults coming from LHC will be of great help, the range of energies that governs the featuresof these showers is not accessible by any current accelerator. Therefore the different models areE [eV]18101910]2> [g/cmmax<X65070075080085014071251998 781619 457331 230 188143186 10647EPOSv1.99pFeQGSJET01SIBYLL2.1QGSJETIIE [eV]18101910]2) [g/cmmaxRMS(X01020304050607014071251998 781 619457331230 188143 18610647pFeFigure 1: 〈Xmax〉 (left) and RMS(Xmax) (right) as a function of the energy. The number of real data events ineach energy bin is indicated. The predictions for proton and iron, following different hadronic models, are shownas well. The shaded region represents the systematic uncertainties.built over different extrapolations and approximations7,8,9. Differences in multi-particle produc-tion models are directly reﬂected in shower observables like Xmax and the number of muons atground level. Other hadronic interaction features like the particle production cross-section, elas-ticity or charge-ratio (fraction of particles going into the electromagnetic (EM) cascade) havealso their own impact on the different shower observables. They have been studied in detailin 10. This interconnection allows the study of hadronic interactions at ultra-high energies usingcosmic ray data. The main problem for this kind of analysis is that the cosmic ray composi-tion is unknown at these energies. Furthermore, the mass of the primary particles can only bedetermined by comparing air shower observables with simulations. All this, along with theirorigin and mechanisms of acceleration, is the complex cosmic ray puzzle that experiments likethe Pierre Auger Observatory try to solve. In Sec. 2 we describe the main observables and anal-ysis carried out by the Auger collaboration to infer the mass of the primary particles measuredwith both the FD and the SD. The measurement of the proton-air cross-section from the tail ofthe Xmax distribution is discussed in Sec. 3. We ﬁnish this document (in Sec. 4) with differentstudies that highlight the muon deﬁcit found in simulations when compared with real data.2 Measurements of the Longitudinal Shower Development2.1 Fluorescence Detector MeasurementsWith the ﬂuorescence detector of the Pierre Auger Observatory it is possible to measure thelongitudinal development of cosmic rays in the atmosphere. The preferred observable used forcomposition studies is the depth of the maximum in the shower development, Xmax. A simpleway to understand the sensitivity of this variable to the mass of the primary particle is thesuperposition model. It states that the interaction of a nucleus with mass A and energy E canbe seen as the superposition of A nucleons interacting with an energy E/A. All this, in theframework of the extended Heitler model 11,12, leads to the following expresion where the massdependence is shown:〈XAmax〉 = c+Dp ln(E/A). (1)The elongation rate Dp = dXmax/dlnE and the parameter c contain the dependency on thehadronic interaction properties. Also the ﬂuctuations in Xmax carry information about the pri-E [eV]19102010max?1.51.551.6EPOSv1.99QGSJETII-0.3SIBYLL 2.1protonironSyst. Unc.85174423 25881815987251E [eV]19102010]-2 [g cm?max!X?50055060065011872 503316Figure 2: The azimuthal rise-time asymmetry Θmax (left panel) and 〈Xµmax〉 (right panel) as a function of theenergy. The number of events in each bin is indicated.mary particles. They are supposed to be smaller for heavy than for light nuclei.When we analyse real data we have to compare them with simulations. Given that acceleratordata do not cover the energy range of the ﬁrst interactions produced in the cascade develop-ment, models must rely in theoretical extrapolations. Differences between them are often usedas an estimation of the systematic uncertainties due to the lack of knowledge in the hadronicinteractions at ultra-high energies.The measurement of the longitudinal proﬁle of the energy deposited in the atmosphere with thePierre Auger Observatory is described in 14. Only hybrid events (showers measured with the FDand at least one SD station in coincidence) are considered in this analysis, to provide an accuratereconstruction of the geometry. To ensure a good Xmax resolution and an unbiased mean mea-surement (not undersampling the tails of the Xmax distributions) different set of cuts are appliedover the data sample 15. Figure 1 shows the results for the 〈Xmax〉 analysis. Along with thepredictions for different hadronic interaction models and primaries, the mean values (left panel)and the RMS (right panel) of the Xmax distributions are shown as a function of the primary en-ergy. The elongation rate is well described with a linear ﬁt broken at log(E/eV)=18.38+0.07−0.1716.This change in the elongation rate can be interpreted as a transition from lighter to heavierprimaries as the energy increases. The values for the Xmax ﬂuctuations shown in Figure 1 havebeen corrected by the detector resolution 16. Again, assuming that the hadronic interactionproperties do not change much within the observed energy range, this result is an independentsignature of an increasing average mass of the primary particles with energy. The compatibilityof the Auger results for 〈Xmax〉 and RMS(Xmax) with different hadronic interaction models hasbeen studied in 17. A direct comparison between the shape of the measured Xmax distributionswith different hadronic models and primaries is discussed in 16.2.2 Surface Detector MeasurementsIn the development of EAS, the atmosphere acts as a huge calorimeter absorbing part of theEM component in its path to ground. This means that the number of these particles at groundrelates with the depth of the shower maximum. Furthermore, the arrival time for the muon com-ponent is earlier than for EM particles, since they travel in almost straight lines with smallermultiple scattering. Based on this, it is possible to ﬁnd observables relating to primary particlecomposition in the time structure of particles at ground, recorded by the water Cherenkov de-tectors of the Pierre Auger Observatory.]2  [g/cmmaxX500 600 700 800 900 1000 1100 1200/g]2  [cmmaxdN/dX-1101102 g/cm+2.4-2.3 = 55.8 f?(Energy/eV)10log11 12 13 14 15 16 17 18 19 20Cross section (proton-air)   [mb]200300400500600700QGSJet01cQGSJetII.3Sibyll 2.1Epos 1.99Energy    [eV]1110 12101310 141015101610 1710181019102010    [TeV]ppsEquivalent c.m. energy -110 1 10 210Nam et al. 1975Siohan et al. 1978Baltrusaitis et al. 1984Mielke et al. 1994Honda et al. 1999Knurenko et al. 1999ICRC07 HiResAglietta et al. 2009Aielli et al. 2009This work0.9TeV 2.36TeV 7TeV 14TeVLHCFigure 3: Left: Unbinned likelihood ﬁt of the tail of Xmax distribution in the energy interval 1018-1018.5 eV.Right: Proton-air cross-section measured by Auger and other cosmic ray experiments along with different modelpredictions.The so called rise-time of the signal (the time to go from the 10% to the 50% of the totalintegrated signal), t1/2, is a measurement of the muon to electron ratio in a SD detector. Itdepends on the primary mass, the zenith angle θ and the distance to the shower axis r. Theazimuthal asymmetry of t1/2 for non vertical events carries information about the longitudinaldevelopment of the shower 18. The maximum of this asymmetry, Θmax, has been used to studythe composition of cosmic rays.Using signals dominated by muons (in inclined events and far from the shower core) it is pos-sible to reconstruct the muon production depth distribution (MPD) 19. In this technique thearrival times of the muons are converted into their production distances along the shower axisassuming they travel undeﬂected from birth until reaching the ground. These distributions carryinformation about the hadronic longitudinal development of the shower. The maximum Xµmaxof these proﬁles is strongly correlated with the depth of the ﬁrst interaction X1, and Xmax, soit is also sensitive to the nature of primary particles.Figure 2 shows the values of Θmax and 〈Xµmax〉 as a function of the energy. Both results arecompatible with showers that develop earlier than pure proton showers in the highest energyregion.3 Proton-air cross-sectionThe Pierre Auger Collaboration has measured the proton-air cross-section, σp−air, for particleproduction at ultra-high energies using hybrid data. This cross-section is directly related withthe exponential distribution of X1. The strong correlation between X1 and Xmax makes thetail of the Xmax distribution still sensitive to the proton-air cross-section. This quality was ﬁrstexploited for this purpose by the Fly’s Eye Collaboration20. The idea is to ﬁt the deep tail of theXmax distribution with an exponential function and use the slope as an estimator of σp−air. Thetranslation to a cross-section is done using Monte Carlo simulations with a consistent rescalingof the original cross-section to reproduce the value of the measurement 21.One of the main difficulties in this analysis is the poor knowledge of mass composition at theseenergies. The tail of Xmax distribution is supposed to be proton-rich as protons are the mostpenetrating nuclei. However we cannot exclude the presence of other primaries, mainly heliumand photons. The possible photon impact is almost under control thanks to the strong limitsreported on the photon fraction in Auger data 22. But no limit exists on the helium fraction ofcosmic rays at these energies. This lack of knowledge translates into the main contribution toFigure 4: Data from the Pierre Auger Observatory showing the measured number of muons at 1000 m from theshower axis and 1019 eV relative to the predictions of the hadronic model QGSJETII for proton initiated showers(Nrelµ ) as a function of the zenith angle. The ﬁgure shows the results derived from the multivariate, showeruniversality and inclined events (N19) methods. The result for pure iron simulations is also shown.the systematic uncertainty of this measurement. Figure 3 left panel shows the selected Xmaxdistribution and the ﬁt of its exponential tail. Only events with E∈ [1018eV, 1018.5eV ] are usedin this analysis, resulting in an averaged center-of-mass energy of√s = 57 TeV. If we neglectthe possible presence of helium in our data sample, then the measured proton-air cross-sectionisσp−air = (505± 22stat ± (+20−15)sys)mb. (2)Using simulations we ﬁnd that a 50 % fraction of helium would reduce the actual value ofthe measured cross-section by 80 mb 21. In Figure 3, right panel, we show the measured σp−airtogether with different model predictions and other measurements derived from cosmic ray data.Our result favors a moderately slow rise of the cross-section towards higher energies.4 Muon shower contentA good description of shower data is essential to draw the right conclusions when comparingthe measurements with simulations. As mentioned in the text, the number of muons at grounddepends on several properties of hadronic interactions10, becoming a powerful tool in the difficulttask of validate the various existing models. Different methods have been developed to derivethe fraction of the signals, collected by the surface detectors, coming from the muonic or theelectromagnetic component of the shower using the Auger data. Some of these methods are basedon the different time structure showed by both components 23. Muons typically deposit moreenergy in the water Cherenkov detectors than electrons and photons, producing spikes over thesmoother EM contribution in the signals. The multivariate method exploits this feature in thetime traces to build an estimator correlated with the number of muons. The universality methoduses a recently found shower universality property which relates the muon to electromagneticsignal ratio with the maximum in the shower development24. This property can be described bya simple parameterization for showers with zenith angle between 45◦ and 65◦. Then, for hybridevents, this method derives the muonic signal in a SD detector from the shower maximumdepth and the total signal. The most direct way to investigate the muon content of cosmic rayshowers is by studying very inclined events, where the dominant particles at ground are muonsbecause most of the electrons and photons have been absorbed in the atmosphere25. Using hybridinclined events, the measured shower size N19, which is a muon estimator itself, can be calibratedwith the calorimetric energy reconstructed by the FD. This calibration procedure can be usedto obtain the number of muons as a function of energy. A summary of the results obtainedwhen we apply these methods to real data is presented in Figure 4. It shows the estimatednumber of muons at 1000 m in data relative to the predictions of simulations using the hadronicmodel QGSJETII 7 with proton primaries. In view of this ﬁgure, the considered simulations arefound to present underestimations of the muon fraction at ground level for the events measuredwith the Pierre Auger Observatory. The observed relative excess is angle dependent, growingfrom about 1.6 23, at the lower zenith angles, to more than 2 25, for the more inclined events.Understanding this discrepancy is critical to an appropriate interpretation of cosmic ray data.Different efforts are focused on that. For example, it has been recently demonstrated that alarger baryon anti-baryon pair production yields to a higher number of low energy muons 8.AcknowledgmentsThis work was supported by the ANR-2010-COSI-002 grant of the French National ResearchAgency.References1. J. Abraham et al, (Pierre Auger Collab.), Nucl. Instr. and Meth. A, 523, 50-95, (2004)2. J. Abraham et al, (Pierre Auger Collab.), Nucl. Instr. and Meth. A, 613, 29-39, (2010)3. J. Abraham et al, (Pierre Auger Collab.), Nucl. Instr. and Meth. A, 620, 2-3, (2010)4. 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Phys. 31, 312-319, (2009)19. D. Garcia-Gamez et al, (Pierre Auger Collab.), Proc. 32nd ICRC, (2011),arXiv:1107.4804v120. R. Ellsworth et al, Phys. Rev. D 26, 336 (1982)21. R. Ulrich et al, (Pierre Auger Collab.), Proc. 32nd ICRC, (2011), arXiv:1107.4804v122. M. Settimo et al, (Pierre Auger Collab.), Proc. 32nd ICRC, (2011), arXiv:1107.4805v123. J. Allen et al, (Pierre Auger Collab.), Proc. 32nd ICRC, (2011), arXiv:1107.4804v124. A. Yushkov et al, Phys. Rev. D 81, 123004 (2010)25. G. Rodriguez et al, (Pierre Auger Collab.), Proc. 32nd ICRC, (2011), arXiv:1107.4809v1

Studies of hadronic interactions at ultra-high energies with the Pierre Auger Observatory

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