PROCEEDINGS OF THE 31 st ICRC, L ´ OD ´ Z 2009 1 Systematic uncertainties in air shower measurements from high-energy hadronic interaction models C. Bleve * , R.D. Parsons † , J. Knapp † and S.S. Ostapchenko ‡ * Dipartimento di Fisica, Universit` a del Salento & INFN, Sezione di Lecce, I-73100, Lecce, Italy † School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK ‡ NTNU, Institutt for Fysikk, 7491 Trondheim, Norway Abstract. Hadronic interaction models at cosmic ray energies are inherently uncertain due to the lack of a fundamental theoretical description of soft hadronic and nuclear interactions and the large extrapolation required from collider energies to the range of the most energetic Cosmic Rays observed (> 10 20 eV). Model uncertainties are evaluated within the QGSjet-II model, by varying some of the crucial parameters in the limits allowed by collider data, and between QGSjet-II and other mod- els commonly used in air shower simulations. The crucial parameters relate to hard processes, string fragmentation, diffraction and baryon production. Results on inelastic cross sections, on secondary particle production and on the properties of air showers measured by ground detectors from energies of 10 12 to 10 19 eV are discussed. Keywords: hadronic interaction models, air show- ers, CORSIKA-QGSjet I. I NTRODUCTION Primary cosmic rays with energies > 10 14 eV can not be measured directly, due to their exceedingly low flux. Instead, their properties are reconstructed from the shape and particle content of the extensive air showers they produce in the atmosphere. The reconstruction is based on numerical models of the air shower development. As there is currently no reliable fundamental theory describing soft hadronic interactions at high energies, large systematic uncertainties limit the precision of the results. Most current hadronic interaction models use Gribov-Regge theory (GRT) of multi-Pomeron exchange between nucleons as basis for the treatment of high- energy, soft interactions, which are prevalent in air show- ers. Perturbative quantum chromodynamics (pQCD) can describe hard interactions with high p ⊥ , which are rare in cosmic ray interactions, but become more important at higher energies. In addition, diffractive interactions, collisions of nuclei, and interactions and decays of all possible secondary particles at energies from MeV to beyond 10 20 eV are needed for a complete simulation of an air shower. Nuclear interactions are usually de- duced from nucleon-nucleon collision via the Glauber formalism. Particle tracking and their electromagnetic interactions are straight forward to simulate. The major problem is the seamless and coherent combination of the different parts of hadronic models. Different numerical codes implement the same theoretical ideas in different ways, with approximate agreement at lower energies where collider data are used for tuning, but diverging in the region where extrapolations are required, e.g. to ultra high energies, or to very forward emission directions. In this paper we study the systematic uncertainties, within the QGSjet-II-3 model ([1], released in 2006), due to the variation of some crucial model parameters within the limits still allowed by collider data. The results of the model variation (options 2-6) are compared with pre- dictions with the standard version of QGSjet-II (option 1), SIBYLL 2.1 [2] and the new EPOS 1.99 model [3]. The distinctive feature of EPOS is an enhanced baryon production, in agreement with data from heavy ion colliders, which leads to more energy in the muonic component of showers. The standard versions of these models are available in the framework of the CORSIKA 6.735 air shower simulation package [4]. II. PARAMETER VARIATIONS IN QGSJET-II The crucial model parameters relate to the treatment of diffraction, the cut-off between hard and soft inter- actions and the distribution of momentum in secondary particles. Six versions of the QGSjet-II model have been created, with varying parameter settings, and tuned to reproduce the collider data within errors. The effects of these variations are then investigated for both single interactions and air showers as a whole. The first option (1) corresponds to the standard parameter settings of QGSjet-II (see Tab. I). Diffractive interactions are very important for the shower development, as they transport the primary en- ergy effectively through the atmosphere. Both, projectile option diffraction Q 2 0 BJM SE λ 1 λ 2 (p) λ 1 λ 2 (π) (GeV 2 ) 1 (std) 4 4.7 2.25 on 0.5 2 9 4.7 2.25 on 0.5 3 4 4.7 4 on 0.5 4 4 4,7 2.25 off 0.5 5 4 4.7 2.25 off 0.7 6 4 3 2.25 on 0.5 TABLE I Parameter settings of six options of QGSjet-II. Option 1 represents the standard settings of QGSjet-II (See text for explanation.)