Constraints and measurements of hadronic interactions in extensive air showers with the Pierre Auger Observatory
CConstraints and measurements of hadronic interactions in extensiveair showers with the Pierre Auger Observatory
L. Cazon for the Pierre Auger Collaboration LIP, Av. Elias Garcia 14 - 1 1000-149 Lisbon,Portugal Abstract
The characteristics of extensive air showers are sensitive to the details of hadronic interactions atenergies and in kinematic regions beyond those tested by human-made accelerators. Uncertainties onextrapolations of the hadronic interaction models in these regions hamper the interpretation of the ultrahigh energy cosmic ray data in terms of primary mass composition. We report on how the Pierre AugerObservatory is able to constrain the hadronic interaction models by measuring the muon content andmuon production depth of air showers and also by measuring the proton-air cross section for particleproduction at a center-of-mass energy per nucleon of 57 TeV.
Interactions at a center of mass energy above those attained at the LHC are continuously happening in theupper layers of the Earth’s atmosphere. They occur when ultra high energy cosmic rays (UHECR) collidewith air nuclei, being the highest energy so far recorded at √ s ∼
700 TeV, by Fly’s Eye [1]. In the decadesto come, UHECR are the only way to explore such gigantic energies. Our current understanding of particleinteractions at these energies relies on extrapolations made from experimental data collected in terrestrialhuman-made accelerators, which in addition are hampered by the difficulties of placing detectors in the mostforward region.After the first cosmic ray interaction, thousands of secondaries interact again and cascade down to theEarth’s surface, producing extensive air showers (EAS) of particles. The Pierre Auger Observatory detectsthose showers by sampling the EAS at ground with a surface detector array (SD), consisting of 1600 waterCherenkov stations separated by 1.5 km and spread over 3000 km . Fluorescence detectors (FD) collect lightemitted by the passage of the charged particles of the shower through the air, allowing the reconstructionof the longitudinal profile (LP) of the shower and a calorimetric measurement of its energy. Simultaneousdetection by the SD and the FD is called hybrid detection and it has a dark night duty cycle of ∼
15% dueto the FD. More details on the Observatory can be found in [2, 3, 4] and references therein.The main goal of the Pierre Auger Observatory is to unveil the origin and nature of UHECR. A numberof breakthroughs and some very important steps towards this goal have already happened: stringent photonlimits have ruled out most top-down production mechanisms, favoring the acceleration scenarios in astro-physical sources. In addition, current neutrino limits have ruled out some exotic production models and areto reach the fluxes of cosmological origin [5], guaranteed if protons were the primaries. A flux suppressionat E = 4 × eV has been confirmed [6], being compatible with a GZK cut-off, but also with an energyexhaustion of the sources. Arrival directions of the highest energy cosmic rays have been shown to be un-evenly distributed in the sky, being correlated with the positions of nearby AGNs, which act as tracers ofthe extragalactic matter distribution [7][8]. The depth of the LP shower maximum is known to be sensitiveto the primary mass composition, given that the deepest air showers occur for the smallest mass number A .As the energy of the shower increases, the shower gets larger and reaches its maximum development deeperin the atmosphere. In general, a detailed simulation of the whole cascading process, accounting for all themultiparticle production details, is necessary to predict the position of the shower maximum as a functionof mass and energy. Thus, mass interpretation can only be achieved by comparing the actual experimentalreadings with the predictions of full air shower simulations using the different high energy hadronic models.1 a r X i v : . [ a s t r o - ph . H E ] M a y esults from the Pierre Auger Observatory show a composition which steadily becomes heavier with energywhen compared to the latest available models [9]. The number of muons at the ground is also sensitive tothe mass of the primaries [10], but it is also hampered by the ambiguity of the predictions of the high energyinteraction models. The phase space of shower observables occupied by different primary masses often over-laps with that of the different model predictions. Disentangling one from the other is of utmost importanceand is one of the most compelling challenges in UHECR physics.In this paper we focus on the Pierre Auger measurements relevant to constrain our knowledge of highenergy physics. In section 2 a measurement of proton-air cross section is presented and in section 3, measure-ments are presented related to the muon production in extensive air showers, namely, different measurementsof the muon number at the ground are described in subsections 3.1, 3.2, and 3.3, and the longitudinalproduction profile is described in subsection 3.4. The depth at which the parent cosmic ray interacts, X , follows an exponential distribution ∝ exp (cid:0) − X λ (cid:1) where λ is inversely proportional to the p-air cross section, σ prodp − air , that accounts for all interactions whichproduce particles, and thus contribute to the air shower development; it implicitly also includes diffractiveinteractions. The depth required for the shower to fully develop is ∆ X , being the tail of the X max -distributionof proton showers directly related to the distribution of the first interaction point X through X max = X + ∆ X . Thus, dNdX max = N exp (cid:18) − X max Λ η (cid:19) (1)where η represents the fraction of the most deeply penetrating air showers used. Thus, η is a key parameter:a small value enhances the proton fraction, but reduces the number of events available for the analysis. Wehave chosen η = 0 . X max distribution for selected events, resulting in a valueΛ η = 55 . ± . ± . − . (2)The average energy is 10 . eV which corresponds to a center-of-mass energy of √ s = 57 TeV in proton-proton collisions.Figure 1: Left panel:Unbinned likelihood fit to the X max -distribution to obtain Λ η (thick line). Right panel:Resulting p-air cross section compared to other measurements and different model predictions. The innererror bars are statistical, while the outer include systematic uncertainties for a helium fraction of 25% and10 mb for the systematic uncertainty attributed to the fraction of photons. See [11] for details.The hadronic cross sections of the different high energy interaction models were multiplied by an energy-dependent factor f ( E, f ) = 1 + ( f −
1) log( E/ eV)log 10 / (3)2o produce different predictions of the slope, Λ MCη . This allows us to directly relate the measured Λ η to thecorresponding σ prodp − air for a given model.After averaging the four values of the cross section obtained with the different available hadronic inter-action models we obtain: σ prodp − air = 505 ± +28 − (sys) mb (4)at a center-of-mass energy of 57 ± . ± The hadronic cascade is the main engine that drives the development of nuclei-induced EAS. Approximately80% of the particles produced in high energy collisions are pions, of which approximately 1/3 are neutralpions. They rapidly decay into photons, feeding the electromagnetic (EM) cascade. After only three hadronicgenerations, ∼
50% of the energy is already transferred to the EM cascade [12], causing it to rapidly decouplefrom the hadronic cascade. After each interaction, the other 2/3 of the energy keeps feeding the hadroniccascade through charged pions every generation, until they decay into muons at a few tens of meters fromthe shower axis [13], and then leaving the central region of the shower. Muons travel to the ground almost instraight lines, as Coulomb scattering is less important than for electrons. They act as true messengers fromthe hadronic skeleton of the shower, and allow us to peer into details of the hadronic physics at the core ofthe EAS.Despite of the Pierre Auger Observatory being an experiment not having been originally designed toseparately measure air shower components, we have developed techniques that allow us to assess the muonand the electromagnetic contributions, either by analyzing the time structure of the signals in the SD stations,or by analyzing different regions in terms of core distance and zenith angle of the showers, where the muoncomponent is dominant.Whenever a charged particle of sufficient energy passes through water of a SD station, it producesCherenkov photons. After a few reflections into the wall material, made of Tyvek, their distribution isisotropized. Their concentration is sampled by the FADCs from three photomultiplier tubes viewing the wa-ter volume, before being absorbed by the water after ∼
100 ns. The observed signal is basically proportionalto the track-length that the particle traverses in water, and therefore there is not a basic difference betweensignals produced by muons compared to those produced by electrons or positrons.Given that electrons are far more numerous than muons and that they typically cascade down insidethe water, while muons typically traverse the water without interactions but energy loss, the typical track-lengths of electrons in water are shorter. As a consequence, the EM component of the shower produces asignal distribution in time which is smoother than the muonic one, which is spiky and can be discriminatedunder some conditions. Note nevertheless that converting photons might also produce signals with verysimilar characteristics to those of muons.In addition, the relative richness of muons compared to EM particles in EAS increases with the distanceto the shower core, and also with the zenith angle of the EAS.The Pierre Auger Collaboration has developed different techniques to assess the muon content of EASunder different conditions, namely, 1) analysis of the muon fraction through the temporal structure of the SDsignals in vertical showers, 2) measurement of a hadronic scale factor by analyzing the signal size in verticalhybrid events, and finally 3) analysis of the muon content in inclined hybrid showers.
Given that the number of muons at 1000 m from the core scales nearly linearly with the energy of the shower,the fraction of the signal attributed to muons to the total signal, f µ = S µ /S is insensitive to the systematicuncertainty of the energy, which is 14% ([14]). Two different methods were used to assess f µ : a multivariatemethod, and a smoothing method. 3he basic idea of the multivariate method is to combine muon-content sensitive characteristics of theFADC signal to reconstruct f µ using: ˆ f µ = a + b ˆ θ + cf . + d ˆ θP + e ˆ r (5)where ˆ θ is the reconstructed zenith angle of the shower and ˆ r is the distance of the detector from thereconstructed shower axis. f . is the portion of the signal in FADC bins larger than 0.5 Vertical EquivalentMuons (VEM), and P is the normalized zero-frequency component of the power spectrum [15].Both f . and P are sensitive to large relative fluctuations and short signals, which are the signatures ofhigh muon content. We estimate the fit parameters ( a, b, c, d, e ) using simulations described in [15].Figure 2: The measured muon signal rescaling to E = 10 eV and at 1000 m from the shower axis vs. zenithangle, with respect to QGSJetII-04 proton simulations as a baseline. The rectangles represent the systematicuncertainties, and the error bars represent the statistical uncertainties added to the systematic uncertainties.See [15] for details.The smoothing method is a low-pass filter, which was run a few times on the signal to gradually separatethe low-frequency EM component from the high-frequency one which is attributed to muons. Firstly, thesignal is smoothed by a moving average of size L over the FADC. The window size L was adjusted usingsimulations to follow the low frequencies corresponding to the EM signal at large angles, while narrowerwindows are needed to extract it in vertical showers, where the EM component is more similar to the muonicsignal, resulting in L = 7 .
83 + 0 . θ/ deg. The procedure was repeated four times, re-smoothing each time theoutput of the previous iteration. The final muonic signal is the sum of the non-smooth positive differencesat each step.The muon signal can be retrieved by multiplying ˆ f µ by the total signal. The results respect to QGSJetII-04 [16] proton simulations are shown in Fig. 2 for E = 10 eV and r = 1000 m, with a value ∼ . − . The ground signal of simulated showers with longitudinal profiles matching those of detected showers wasanalyzed. The data used for this study were narrowed down to the energy bin 10 . < E < . eV,sufficient to have adequate statistics while being narrow enough that the primary cosmic ray mass compositiondoes not evolve significantly.Each event was compared with the results obtained from simulations using two different hadronic models(QGSJetII-04 and EPOS-LHC [17]) and for four different primary masses (proton, helium, nitrogen, andiron), for all of the events in the dataset. 4igure 3: Value of the hadronic rescaling parameter R µ and the energy rescaling parameter R E for Augerhybrid data at 10 EeV. See [19] for more details.To explore the potential sources of the muon count discrepancy between measurements and model ex-pectations, the ground signal was modified in the simulated events to fit the ground signal in the data. Tworescaling factors were introduced: R E and R µ . R E acts as a rescaling of the energy of the primary cosmicray, affecting the total ground signal. R µ acts as a rescaling factor of the contribution to the ground signal ofinherently hadronic origin. R E and R µ are then fitted to minimize the discrepancy between the ensemble ofobserved and simulated signals at ground, which can also reproduce the observed X max -distribution, and islabeled as “mixed” in Fig. 3. The observed hadronic signal is a factor 1.3 to 1.6 larger than predicted usingthe hadronic interaction models tuned to fit LHC and lower energy accelerator data. None of the testedmodels calls for an energy rescaling. More details of this analysis can be found in [19]. After the arrival direction ( θ , φ ) of the cosmic ray is determined from the relative arrival times of the showerfront, the shower size parameter N is defined through the following relation: ρ µ = N ρ µ, ( x, y, θ, φ ) , (6)where ρ µ is the model prediction for the muon density at the ground used to fit the signals recorded atthe detectors. ρ µ, is a reference profile corresponding to the inferred arrival direction, obtained as aparametrization [18] of the muon density at ground for proton showers of 10 eV, simulated using theQGSJetII-03 interaction model. N is sensitive to the cosmic-ray energy and nuclear mass composition.The quantity R µ ( R µ (cid:39) N ) was introduced to account for the difference between the real number ofmuons, given by the integral of the distribution of muons at the ground, and the estimate obtained by thefitting procedure of eq. 6. The difference between N and R µ is less than 5%.The averaged scaled quantity R µ / ( E F D / 10 eV) is shown in Fig. 4 divided in five energy binscontaining roughly equal statistics. The measurement of R µ / ( E F D / 10 eV) is dominated by systematicuncertainties in the energy scale (shown as open circles in the figure). The measured number of muons between4 × eV and 2 × eV is marginally comparable to predictions for iron showers simulated either withQGSJetII-04 or EPOS-LHC if we allow the FD energy scale to increase by its systematic uncertainty of about14% ([14]).Given that the observed distribution of the depth of shower maximum between 4 × eV and 2 × eV is not compatible with an iron dominated composition, we conclude that the observed number of muonsis not well reproduced by the shower simulations. More details of this analysis can be found in [20].5igure 4: Average value of R µ /( E F D / eV) as a function of shower energy. The gray thick error barsindicate the systematic uncertainty. Theoretical curves for proton and iron showers simulated with QGSJetII-04 and EPOS LHC are shown for comparison. Open circles indicate the result if the FD energy scale is variedby its systematic uncertainty. See [20] for more details. The distribution of muon arrival times to the ground is closely related to the distribution of their productiondepths. To a first approximation, there is a one-to-one map between the time elapsed between the arrivaltime of a hypothetical shower front plane, traveling at the speed of light, and the arrival time of the muonswhose trajectories are not parallel to the shower axis: ct g = (cid:112) r + ( z − ∆) − ( r − ∆) , where r is thedistance to the shower core in the perpendicular plane, z is the distance from the ground to the productionpoint, and ∆ is the z -coordinate of the observation point. Both ∆ and z are measured along the shower axis.The second most important source of delay is the subluminal velocities of the muons, due to their finiteenergy [13]. The so called kinematic time is a second order correction to the total arrival time delay, ( < ∼
10% above 1000 m from the core), that decreases as r increases. Its average (cid:104) ct (cid:15) (cid:105) is calculated from ananalytic model for the energy spectrum of muons [21].The production distance z is approximated as z (cid:39) r ct − (cid:104) ct (cid:15) (cid:105) + ∆ (7)which is later transformed into a production depth using the density profiles provided by the instrumentsdedicated to monitor the atmosphere above the Auger Observatory.The data set used in this analysis comprises the events recorded in the angular range from 55 ◦ to 65 ◦ .The evolution of the measured average maximum of the muon production depth distribution (cid:104) X µ max (cid:105) as afunction of log ( E/ eV) is shown in Fig. 5. The uncertainties represent the standard error on the mean,whereas the gray bars represents the systematic uncertainty, which amounts to 17 g cm − . Fig. 5 alsodisplays QGSJetII-04 and EPOS-LHC predictions for both proton and iron primaries. Both models have thesame muonic elongation rate but with considerable differences in the absolute value of (cid:104) X µ max (cid:105) . More detailsof this analysis can be found in [22].It is possible to linearly convert (cid:104) X max (cid:105) and (cid:104) X µ max (cid:105) into the mean logarithmic mass of the primary, (cid:104) lnA (cid:105) ,for a given high-energy interaction model. A mismatch of this conversion would necessarily imply that such6igure 5: (cid:104) X µ max (cid:105) as a function of energy. The prediction of different hadronic models for proton and ironprimaries are shown. Numbers indicate the number of events in each energy bin and the gray rectanglesrepresent the systematic uncertainty. See [22] for details.model is unable to consistently predict for the same primary the values of (cid:104) X max (cid:105) and the values of (cid:104) X µ max (cid:105) [23].For the EPOS-LHC model, this conversion procedure results into incompatible (cid:104) ln A (cid:105) values, and themass conversion of (cid:104) X µ max (cid:105) resulting in (cid:104) ln A (cid:105) ∼
5, a value that corresponds to a nuclei which is muchheavier than iron lnA (cid:39)
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