33 RD I NTERNATIONAL COSMIC RAY CONFERENCE,RIO DE JANEIRO 2013 THE ASTROPARTICLE PHYSICS CONFERENCE Estimate of the non-calorimetric energy of showers observed with the fluores- cence and surface detectors of the Pierre Auger Observatory MATIAS J. TUEROS 1 FOR THE PIERRE AUGER COLLABORATION 2 1 Departamento de F´ ısica de Part´ ıculas, Universidad de Santiago de Compostela, Espa˜ na 2 Full author list: http://www.auger.org/archive/authors 2013 05.html auger spokespersons@fnal.gov Abstract: The determination of the primary energy of extensive air showers using the fluorescence technique requires an estimation of the energy carried away by particles that do not deposit all of their energy in the atmosphere. This estimation is typically made using Monte Carlo simulations and thus depends on the assumed primary particle composition and model predictions for neutrino and muon production. In this contribution we introduce a new method to obtain the invisible energy directly from events measured simultaneously with the fluorescence and the surface detectors of the Pierre Auger Observatory. The robustness of the method, which is based on the correlation of the invisible energy with the muon number at ground, is demonstrated by applying it to different sets of Monte Carlo events. An event-by-event estimate of the invisible energy is given for the hybrid data set used for the energy calibration of the surface detector of the Pierre Auger Observatory. Keywords: Pierre Auger Observatory, Ultra High Energy Cosmic Rays, Invisible Energy 1 Intoduction When an ultra-high energy cosmic ray interacts in the at- mosphere a cascade of particles is generated. In this cas- cade, an important fraction of the energy is deposited in the atmosphere as ionisation of the air molecules and atoms. A fraction of the deposited energy is then re-emitted during the de-excitation of the ionized molecules as fluorescence light that can be detected by fluorescence telescopes. Since the fluorescence intensity is proportional to the deposited energy, the integral of the fluorescence profile yields an accurate measurement of the energy of the pri- mary particle (E 0 ) that was deposited in the atmosphere by the charged particles due to electromagnetic energy losses. This is usually referred to as the calorimetric energy (E Cal ). The remaining energy, carried away mostly by neutrinos and high-energy muons that do not deposit all their energy in the atmosphere, is a priori unknown. An estimation of this “invisible” energy is required to derive the primary energy (E 0 ) from the measured E Cal . Historically, this non- calorimetric energy has been called “missing energy” [1]. However, we will use the name “invisible energy” (E Inv ) deeming it more appropriate. Generally, the invisible energy correction is parame- terized as a function of E Cal (E Inv (E Cal )) and it is typi- cally estimated using Monte Carlo simulations averaging over many showers. The average value depends on the high-energy hadronic interaction model and on the primary mass, ranging from 8.5 to 17% of the primary energy at 1 EeV and from 7 to 13.5 % at 10 EeV. Selecting a particular interaction model when analysing real events could introduce a bias to the reconstruction of the primary energy that is ultimately unknowable. An ac- curate knowledge of the invisible energy is thus essential in experiments using the fluorescence technique if a reli- able measurement of the primary energy of cosmic rays is to be obtained. In a previous work [2] we have described a method that relies on the properties of shower universality and a sim- ple model of extensive air showers to find a parameteri- zation of E Inv . This method is robust to changes in the hadronic interaction models used in Monte Carlo simula- tions. In this work, the method has been updated to take into account the fact that the signal attenuation curve and the muon content measured in extensive air showers may not be properly described simultaneously by current Monte Carlo simulations.[3, 4, 5]. 2 A simple model for the invisible energy In the Heitler model extended to hadronic cascades by Matthews [6], the primary energy is distributed between the electromagnetic and muonic components of the air shower as E 0 = ξ e c N max e + ξ π c N μ , (1) where E 0 is the primary energy, N max e is the number of elec- trons at the shower maximum, and ξ e c is the critical energy for the electromagnetic particles. The second term is the energy transferred to the muonic component of the cascade and is considered to be proportional to the total number of muons (N μ ). The critical energy of the pion, ξ π c , is cho- sen as the proportionality factor to account for the fact that, in this model, the muons are considered to originate from pion decays with an associated muon neutrino (or muon antineutrino), transferring all of the energy into the non- calorimetric channel independently of how much energy goes to each muon. With these considerations, the second term of Eq.(1) can be identified directly with the invisible energy. The model presented is clearly an oversimplification, as there are also muons being produced by other processes, the next in importance being kaon decay (roughly 10 times less frequent). Therefore, ξ π c should be considered as an “effective” critical energy, that averages the different con- tributions to the muonic component. If we pick cascades at the same stage of shower development at ground level, measured by the slant depth from shower maximum to