32ND INTERNATIONAL COSMIC RAY CONFERENCE,BEIJING 2011 Estimate of the proton-air cross-section with the Pierre Auger Observatory RALF ULRICH1 FOR THE PIERRE AUGER COLLABORATION2 1Karlsruhe Institute of Technology, Karlsruhe, Germany 2Observatorio Pierre Auger, Av. San Martin Norte 304, 5613 Malargue,¨ Argentina (Full author list: http://www.auger.org/archive/authors 2011 05.html) auger [email protected] Abstract: Using the tail of the distribution of the depth of shower maxima observed with the Pierre Auger Observatory, we derive an estimate of the proton-air cross-section for particle production at center-of-mass energies of 57 TeV. Air showers observed with the fluorescence detector and at least one station of the surface detector array are analysed in the energy range from 1018 to 1018.5 eV. Systematic uncertainties in the cross-section estimate arising from the limited knowledge of the primary mass composition, the need to use shower simulations and the selection of showers are studied in detail. Keywords: Proton-air, Cross-section, Pierre Auger Observatory 1 Introduction An over-riding concern of the analysis has been the assign- ment of realistic systematic uncertainties to the result. We One of the biggest challenges towards a better understand- recognise and identify the unknown mass composition of ing of the nature of ultra-high energy cosmic rays is to im- cosmic rays as the major source of systematic uncertainty prove the modeling of hadronic interaction in air showers. for the proton-air cross-section analysis and we evaluate Currently, none of the models is able to consistently de- its impact on the final result. The analysis is optimised to scribe cosmic ray data, which most importantly prevents a minimise the impact of contamination by the presence of precise determination of the primary cosmic ray mass com- particles other than protons in the primary beam. position. Studies to exploit the sensitivity of cosmic ray data to the 2 Analysis approach characteristics of hadronic interactions at energies beyond state-of-the-art accelerator technology began over 50 years The method used to estimate the proton-air cross-section ago. While first measurements were based on the direct is the comparison of an appropriate air shower observable observation of cosmic ray particles [1], the rapidly shifting with Monte Carlo predictions. A disagreement between focus towards higher energies required the use of extensive data and predictions is then attributed to a modified value air shower observations [2,3]. The property of interactions of the proton-air cross-section. The present analysis is a most directly linked to the development of extensive air two-step process. showers is the cross-section for the production of hadronic particles (e.g. [4, 5]). Firstly, we measure an air shower observable with high sen- sitivity to the cross-section. Secondly, we convert this mea- We present the first analysis of the proton-air cross-section surement into an estimate of the proton-air cross-section based on hybrid data from the Pierre Auger Observatory. 18 for particle production, σ − , in the energy interval 10 For this purpose we analyse the shape of the distribution of p air to 1018.5 eV. The selection of this energy range has the fol- the largest values of the depth of shower maxima, X , max lowing advantages and features: the position at which air showers deposit the maximum en- ergy per unit of mass of atmosphere traversed. This tail Statistics: A large number of events are recorded. of the Xmax-distribution is very sensitive to the proton-air Composition: The shape of the Xmax-distribution is com- cross-section, a technique first exploited in the pioneering patible with there being a substantial fraction of protons in work of Fly’s Eye [3]. To obtain accurate measurements the cosmic ray beam. The situation is less clear at higher of Xmax, the timing data from the fluorescence telescopes energies. is combined with that from the surface detector array for a Energy: The average center-of-mass energy for a cosmic precise reconstruction of the geometry of events. ray proton interacting with a nucleon in the atmosphere R. ULRICH et al. ESTIMATE OF THE PROTON-AIR CROSS-SECTION WITH THE PIERRE AUGER OBSERVATORY is 57 TeV, significantly above what will be reached at the the Xmax and RMS(Xmax) [6,8] to extract a data sample LHC. that has an unbiased Xmax distribution. In the first step we derive the range of values of X As the primary observable we define Λ via the exponen- max f that corresponds to the deepest f = 20 % of the mea- tial shape dN/dX exp( X /Λ ) of the X - max max f max sured showers. We select only event geometries that al- distribution of the fraction∝ f of the− most deeply penetrating low, for each shower, the complete observation of the slant air showers. Considering only these events enhances the depth range from 550 to 1004 g/cm2, which corresponds to contribution of protons in the sample as the average depth 99.8 % of the observed X -distribution. These fiducial at which showers maximise is higher in the atmosphere for max volume cuts reduce the data sample to 1635 events, pro- non-proton primaries. viding a good estimate of the unbiased Xmax-distribution. The choice of the fraction f is a crucial part of the def- This distribution is then used to find the range of values inition of the observable Λ . While a small value of f f of Xmax that contains the 20 % deepest showers, which is will enhances the proton fraction, since protons penetrate identified to extend from 768 to 1004 g/cm2. Due to the most deeply of all primary nuclei, it also reduces the num- limited statistics involved in this range estimation, there is ber of events for the analysis. By varying f we investigate a 1.5 g/cm2 uncertainty on the definition of the range of how much the bias due to non-proton induced showers can the± tail, which will be included in the estimation of the sys- be reduced without statistical uncertainties being dominant. tematic uncertainties. Following these studies we have chosen f = 20 % so that In the second step we select those events from the orig- for helium-fractions up to 15 % biases induced by helium inal data sample of 11628 high quality events that allow are kept below the level of the statistical resolution. At the the complete observation of values of X from 768 to same time this choice suppresses elements heavier than he- max 1004 g/cm2, corresponding to the 20 %-tail of the unbiased lium very efficiently. distribution. This is a more relaxed fiducial volume cut since we are not requiring that a shower track can be ob- 2 3 The Measurement of Λf served at depths higher in the atmosphere than 768 g/cm , which maximises the event statistics and still guarantees an We use events collected between December 2004 and unbiased Xmax distribution in the range of interest. In total September 2010. The atmospheric and event-quality cuts there are 3082 showers passing the fiducial volume cuts, of applied are identical to those used for the analysis of which 783 events have their Xmax in the selected range and X and RMS(X ) [6,8]. This results in 11628 high thus directly contribute to the measurement of Λf . The av- max max 18.24 quality events between 1018 and 1018.5 eV. erage energy of these events is 10 eV, corresponding to a center-of-mass energy of √s = 57 TeV in proton-proton collisions. Λ +2.4 2 In Fig. 1 we show the data and the result of an unbinned f = 55.8 -2.3 g/cm maximum likelihood fit of an exponential function over the 10 range 768 to 1004 g/cm2. This yields /g] 2 2 Λf = (55.8 2.3stat 0.6syst) g/cm . (1) ± ± [cm max 1 The systematic uncertainty arises from the precision with which the range of depths that are used can be defined. dN/dX Values of Λf have been calculated for modified event selec- tions and for different ranges of atmospheric depths. It is 10-1 found that the changes in Λr lie within the statistical uncer- 500 600 700 800 900 1000 1100 1200 2 tainties. The re-analysis of sub-samples selected according Xmax [g/cm ] to zenith-angle, shower-telescope distance and energy pro- duces variations of the value of Λf consistent with statis- Figure 1: Unbinned likelihood fit of Λf to the tail of the tical fluctuations. We conclude that the systematic uncer- Xmax distribution. tainties related to the measurement are below 5 %. The Xmax distribution of the data is affected by the known geometrical acceptance of the fluorescence telescopes as 4 Determination of the cross-section well as by detection limitations related to atmospheric light transmission. The impact of the telescope acceptance on We must resort to Monte Carlo simulations to derive an the Xmax distribution is well understood and can be stud- estimate of the proton-air cross-section from the measure- ied by using data (see [8]) and with detailed Monte Carlo ment of Λf . These have been made using the same energy simulations of the shower detection process. In the follow- distribution as in the data, and the events from the simula- ing we use the strategy developed for the measurement of tions have been analysed with the identical procedures used for the data. 32ND INTERNATIONAL COSMIC RAY CONFERENCE,BEIJING 2011 lations (Sibyll2.1 [9], QGSJet01 [10], QGSJetII.3 [11] and 80 Auger Data QGSJet01c EPOS1.99 [12]).