STUDY OF HIGH ENERY HADRONIC INTERACTION MODELS USING CORSIKA SIMULATION Raghunath Ganugapati (Newt), John Kelley, Teresa Montaruli, and Albrecht Karle

Motivation-I Downgoing muon analysis to understand atmospheric neutrino spectrum at High Energies (Newt’s Thesis) The atmospheric neutrino fluxes are not completely understood at high energies due to the uncertainties associated with the hadronic Interaction Models and the level of Charm Flux The hadronic Interaction models don’t agree with each other as the Physics that goes into each is different. They start to differ widely at large energies so it becomes very important to understand the region of large Feynman-X. It might be important to separate the conventional muons and understand the uncertainties in their fluxes from a hadronic Interaction model point of View

Motivation-II To understand the level of Prompt muon flux it is important to separate them from Conventional muons. After all both of them are muons! One suggestion was to use the assumption that prompt muons would take large momentum of the primary and hence when they reach AMANDA they would be low multiplicity events (My earlier work). Did not have the simulation to verify it. It has also been suggested by some Physicists that prompt muon events would be much spread out when they reached the detector (lateral separation). Our simulations using the DPMJET-II interaction model seem to show that might not be the case even if one take the first Interaction alone and this is further destroyed once the full air-shower develops

Scheme The Various hadronic interaction models are introduced The energy fractions taken by the secondary particles that are produced (Pions, Kaons and Charmed particles) during the first interaction (Pre-Shower) of cosmic ray with the atmosphere for the case of fixed primary energy and zenith angle using various interaction models are shown. Dig deep into the analytics of this presenting the multiplicity of secondaries for mono-energetic beams of primary and also present their Z-moments. The transverse and longitudinal momentum distributions for the secondaries are shown and there is a very important conclusion derived (Stay tuned!) The results for muon multiplicity, surface energy and lateral separation for the muons are studied. This has been done for the hypothetical case of first Interaction alone and after the full air shower develops isolating the Prompt muons from Conventional muons (facilitated through DPMJET-II interaction model)

Interaction Models DPMJET-II QGSJET01-c SYBILL 2.1 QGSJET-II-03 FLUKA+DPMJET-III

CORSIKA MUON FLUX COMPARISON Simulated Data bumped up by 30% in this Zenith Angle plot Ref: ICRC,Hamburg,Paolo Desiati With Convoluted Pandel Reco And 3 months worth simulated data

Energy Fraction For 1PeV Primary

Energy Fraction For Mono-Energetic Primary Interactions-II

First Interaction Analytics

Transverse and Longitudinal Momentum Distributions In the case of charm PT is higher but so is PL and the angle from the direction of primary is approximately PT/PL.The lateral separation which is the lever arm times PT/PL is not considerably different between conventional and prompt muons Pions Kaons Baryons Mesons PT PL  tan  ~  = PT/PL AB C AB=BC*  Muon Primary Proton

Surface Energy Spectra Muon Tracks produced from Charmed particles were tagged separately and this was done on a track by track basis and energy at surface of Earth shown

Surface Energy Spectra Prompts have a much harder surface energy spectrum!

Muon Multiplicity Spectra Prompts produce much more muons at detector for 65 degrees Zenith Angle (A natural energy cut)

Lateral Separation From Shower Core-I Notice the first bin of the plot on left the maximum lateral separation is zero

Lateral Separation From Shower Core-II Hardly and difference between Conventional and Prompt muons though as Expected lateral separation increases as the full shower develops

Conclusions and Future Work Air shower simulations using the DPMJET-II model reveal that Prompt muon events don’t look much different from the Conventional muons from a topological perspective after the entire air shower development is accounted for. The only possible strategy would be to try and do an analysis based on zenith angle and energy only. The uncertainties in the Hadronic Interaction models in the high energy region even just taking conventional muons alone become huge so in the long run we might have to start thinking of ways to account for this is uncertainty properly rather than use an average normalization as most of our analysis use an energy cut.