Measurement of the proton-air cross-section at sqrt(s) = 57 TeV with the Pierre Auger Observatory
aa r X i v : . [ h e p - e x ] D ec Proceedings of the PIC 2012, ˇStrbsk´e Pleso, Slovakia
MEASUREMENT OF THE PROTON-AIR CROSS-SECTION ATSQRT(S) = 57 TEV WITH THE PIERRE AUGER OBSERVATORY
JAN EBR ∗ FOR THE PIERRE AUGER COLLABORATION † Observatorio Pierre Auger, Av. San Mart´ın Norte 304, 5613 Malarg¨ue, ArgentinaE-mail: [email protected]
Using measured events from the fluorescence detector of the Pierre Auger Obser-vatory, an unbiased distribution of the atmospheric slant depths where showersreach their maxima has been obtained. Analyzing the tail of this distribution theproton-air cross-section for particle production at center-of-mass energies per nu-cleon of 57 TeV is determined to be [505 ± − The Pierre Auger Observatory is a hybrid detector for ultra-high energy cosmicrays. The surface detector (SD), which detects secondary particles at ground level,consists of 1660 water-Cherenkov detectors spread over 3000 km on a triangulargrid with 1500 m spacing. The array is overlooked by 27 fluorescence telescopes (thefluorescence detector, FD) which measure the longitudinal development of extensiveair showers (EAS) initiated by the ultra-high energy particles in the atmosphereabove the array by detecting the fluorescence and Cherenkov light produced alongthe shower trajectory as the charged particles cross the atmosphere [1]. The FDcan measure events with energies from approximately 10 . eV, while full triggerefficiency in hybrid mode (a fluorescence event in coincidence with at least onetank) is achieved at energies greater than 10 eV [2]. The number of particles in the EAS (or shower size) as a function of the atmosphericslant depth (the amount of atmosphere traversed from its upper edge in g/cm )is called the shower longitudinal profile. Most of the EAS energy is dissipatedthrough the electromagnetic component. Therefore, the shower size increases untilthe average energy of the e ± in the EAS is about the critical energy of 81 MeV,when the rate of energy loss due to collisions and ionization begins to exceed thatdue to radiation. Photons have a similar attenuation length due to pair production.The slant depth at which the longitudinal profile of a shower reaches its maximumis called X max and is one of the primary observables of the fluorescence detector. *Institute of Physics of the Academy of Sciences of the Czech Republic, Na Slovance 1999/2,18221 Prague 8, Czech Republic † c (cid:13) Institute of Experimental Physics SAS, Koˇsice, Slovakia Jan Ebr for The Pierre Auger Collaboration ] [g/cm max X
500 600 700 800 900 1000 1100 1200 / g ] [ c m m ax d N / d X -1 ± = 55.8 η Λ Figure 1. The X max distribution used to obtain the value of Λ. The distribution of observed values of X max is widely used to estimate the masscomposition of the primary beam and it also carries information on the cross-sectionof the first interaction in the atmosphere [3,4].The differences in X max between showers of the same primary energy can bedue to fluctuations in interactions as well as to different masses of the primaryparticles. For purely proton primaries, the X max distribution is a convolution ofthe fluctuations in the shower development from the point of the first interaction tothe shower maximum (which is dependent on details of the hadronic interactions)and the exponential distribution of the depth of the first interaction with mean freepath λ p − air = h m air i /σ p − air , with the mean target mass of air h m air i ≈ . m p ≈ . / cm and the proton-air cross section σ p − air [4]. In a simple model, heaviernuclei can be considered as the superposition of many nucleons. For an iron nucleuswith energy E , each nucleon would have an energy E/
56, and the superposition of56 lower energy subshowers would reach X max earlier (higher in the atmosphere).Because the shape of the X max distribution (at least in the range between 10 and 10 . eV which we consider) suggests that there is a significant fraction ofprotons in the primary beam (for details on the determination of the primarycomposition see [5]), we can obtain a proton-enriched sample by using only thedeepest observed events. The remaining dependence on both the mass compositionand possible photon contamination is evaluated using simulations and included inthe systematic uncertainties. The slant depth range used in the analysis is definedby the slant depths of 20 % of the most penetrating events, which is a definitionthat can be easily applied also on simulated events. As the primary observable, weuse the exponential slope Λ of the tail of the X max distribution [6]. roton-air cross-section at 57 TeV with Auger We use events collected by the fluorescence detector between 1 December 2004 and20 September 2010 that have a signal in at least one of the SD stations measuredin coincidence with the FD. The geometry for these events is determined with anangular uncertainty of 0 . ◦ . Further we reject events • without reliable measurement of the aerosol optical depth [7], • with excessive cloud coverage (more than 25 % of the sky), • when χ /Ndf is greater than 2.5 when the profile is fitted to a suitable functionas this could indicate the presence of residual clouds, • with the total uncertainty of X max greater than 40 g/cm • when the angle between the shower and the telescope is smaller than 20 ◦ due tothe difficulties of reconstructing their geometry and high fraction of Cherenkovlight in such showers, • when the reconstructed X max lies outside the field of view of the fluorescencetelescopes.In total, applying these selection criteria yields 11,628 high-quality events [6]. The fluorescence telescopes have a limited field of view in elevation ranging fromabout 2 ◦ to 30 ◦ . The geometrical acceptance as well as the limitations relatedto atmospheric light transmission introduce a bias into the distribution of X max .The bias is even enhanced by demanding that X max be within the observed profile.For example, many showers landing close to the FD will have their X max abovethe field of view. Some vertical showers, on the other hand, may have their X max below the ground. In both cases such events will be rejected and the observed X max distribution will be biased.To avoid such a bias, we apply the fiducial volume selection. First, we determinefrom the data the range of values where most (99.8 %) of the events lie (550–1004g/cm ). Then, we select only showers with such geometries that each of the showerswould be observable for any X max in the whole range of slant depths (irregardlessof the actual X max of the shower). From this unbiased distribution of 1635 eventswe find that the 20 % most deeply penetrating events fall within the range 768 to1004 g/cm . Repeating the same procedure for this range, we obtain a set of 3082events (shown in Fig. 1), of which 783 events contribute to the estimated value ofΛ, yielding Λ = 55 . ± . ± . / cm , where the systematic error is estimated as the RMS of the distribution of Λ cal-culated using different selection procedures. The average energy of these eventsis 10 . ± . eV, corresponding to a center-of-mass energy of 57 ± . Jan Ebr for The Pierre Auger Collaboration (cid:0)(cid:0)(cid:1)(cid:2)(cid:3)(cid:4) (cid:5)(cid:6)(cid:7)(cid:8)(cid:9) (cid:10) (cid:11)(cid:12)(cid:12) (cid:13)(cid:12)(cid:12) (cid:14)(cid:12)(cid:12) (cid:15)(cid:12)(cid:12) (cid:16)(cid:12)(cid:12) (cid:4) (cid:17) (cid:0)(cid:0)(cid:1)(cid:18)(cid:19)(cid:20)(cid:2) (cid:21)(cid:22)(cid:23) (cid:24) (cid:13)(cid:12)(cid:14)(cid:12)(cid:15)(cid:12)(cid:16)(cid:12) (cid:25)(cid:26)(cid:27)(cid:28)(cid:29)(cid:30)(cid:31) !(cid:25)(cid:26)(cid:27)(cid:28)(cid:29)(cid:30)""
Figure 2. Relation between the slope Λ in the simulations and the proton-air particle productioncross-section [8]. (Energy/eV) log
11 12 13 14 15 16 17 18 19 20 C r o ss sec t i on ( p r o t on - a i r ) [ m b ] QGSJet01cQGSJetII.3Sibyll 2.1Epos 1.99
Energy [eV]
10 [TeV] pp sEquivalent c.m. energy -1
10 1 10 Nam et al. 1975Siohan et al. 1978Baltrusaitis et al. 1984Mielke et al. 1994Knurenko et al. 1999Honda et al. 1999Belov et al. 2007Aglietta et al. 2009Aielli et al. 2009This work
LHC
Figure 3. Resulting proton-air particle production cross-section compared to other measurementsand model predictions. The inner error bars are statistical, while the outer ones include also thesystematic uncertainties for a helium fraction of 25 % and 10 mb for the systematic uncertaintyconnected with the fraction of photons.
We have used the four high-energy hadronic interaction models: QGSJET01 [9],QGSJETII.3 [10], SIBYLL 2.1 [11], and EPOS1.99 [12] to perform Monte Carlosimulations, where we smoothly modify all hadronic cross sections by an energy- roton-air cross-section at 57 TeV with Auger Table 1. Summary of the systematic uncertainties
Description Impact on σ prodp − air Λ systematics ±
15 mbHadronic interaction models − , +19 mbEnergy scale ± σ prodp − air ± < . < +10 mbHelium, 10 % −
12 mbHelium, 25 % −
30 mbHelium, 50 % −
80 mb
Total (25% helium) − mb, +28 mb dependent factor f , given by f ( E, f ) = 1 + ( f −
1) ln (cid:0) E/ eV (cid:1) ln (10 eV / eV)( f = 1 for E < eV) where E denotes the shower energy and f is the factorby which the cross section is rescaled at 10 eV. For each hadronic interactionmodel, we find a value of f that reproduces the measured value of Λ and useit to evaluate the cross-section at E = 10 . eV. The proton-air cross sectionsfor particle production obtained by this procedure deviate from the original modelpredictions by less than 5 % in all cases, except for SIBYLL, for which it is 12 %smaller than the original prediction.Additional sources of systematic uncertainties are (see Table 1): • the systematic uncertainty of 22 % in the absolute value of the energy scale ofthe primary particles [13], • the dependence of the procedure for retrieving the cross-section from Λ onadditional parameters such as the energy distribution, energy and X max reso-lution, • the presence of photons (observational limits on the fraction of photons are < . σ prodp − air = 505 ± +28 − (syst) mbat a center-of-mass energy of 57 ± . ± We also calculate the inelastic and total proton-proton cross sections using theGlauber model extended by a two-channel implementation of inelastic intermedi-ate states to account for diffraction dissociation [14]. This calculation is model-dependent since neither the parameters nor the physical processes involved are
Jan Ebr for The Pierre Auger Collaboration ( P r o t on - P r o t on ) [ m b ] i n e l σ ATLAS 2011CMS 2011ALICE 2011TOTEM 2011UA5CDF/E710This work (Glauber) QGSJet01QGSJetII.3Sibyll2.1Epos1.99Pythia 6.115Phojet
Figure 4. Comparison of the estimated inelastic pp cross-section, accelerator data and some modelpredictions. The inner error bars are statistical, while the outer ones include also the systematicuncertainties. For references to the data, see [6]. known accurately at the cosmic-ray energies. In particular, this applies to the elas-tic slope parameter B , the correlation of B with the cross section, and the crosssection for diffractive dissociation. The result for the inelastic proton-proton crosssection is σ inelp − p = 92 ± +9 − (syst) ± σ totp − p = 133 ± +17 − (syst) ± Acknowledgements
This contribution is prepared with the support of Ministry of Education, Youth andSports of the Czech Republic within the project LA08016 and with the support ofthe Charles University in Prague within the project 119810.
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