1. Atmospheric Muon Simulation using the FLUKA MC Model G.Battistoni, A.Ferrari, S.Muraro, T.Montaruli P.R. Sala INFN & Univ.Milano, CERN, Madison Univ. of Winscosin

2. Work carried on within the program of the FLUKA Collaboration F.Ballarini, G.Battistoni, M.Campanella, M.Carboni, F.Cerutti, A.Empl, A.Fassò, A.Ferrari, E.Gadioli, M.V.Garzelli, M.Lantz, A.Mairani, A.Mostacci, S.Muraro, A.Ottolenghi, M.Pelliccioni, L.Pinsky, J.Ranft, S.Roesler, P.R.Sala, D.Scannicchio, S.Trovati, V.Vlachoudis, R.Villari, T.Wilson, N.Zapp INFN-Mi, LNF, Pv, Univ. Milano, Univ. Pavia, CERN, Univ. of Houston, SLAC, Univ. of Siegen, NASA-Houston Outline: 1)Motivations 2)The key features of FLUKA hadronic models at high energy 3)the FLUKA cosmic ray library 4)Results 1: up to 100 GeV region 5)Results 2: beyond the 100 GeV region 6)The TeV region: prediction about the prompt component at very high energy and multimuon events 7)Conclusions

3. Authors: A. Fasso` 1, A. Ferrari 2, J. Ranft 3, P.R. Sala 4 1 SLAC Stanford, 2 CERN, 3 Siegen University, 4 INFN Milan Interaction and Transport Monte Carlo code FLUKA is a general purpose tool for calculations of particle transport and interactions with matter, covering an extended range of applications spanning from proton and electron accelerator shielding to target design, calorimetry, activation, dosimetry, detector design, Accelerator Driven Systems, radioprotection, radiotherapy etc.,  therefore can be used in cosmic rays Maintained and developed under INFN-CERN agreement and copyright 1989-2006; More than 1000 users all over the world; see http://www.fluka.org FLUKA

4. Specific Motivations FLUKA is designed and maintained searching for high degree of quality in physics models and algorithms. Model building based on “microscopic” concepts that allow to be predictive even where data do not yet exist. We do not rely on parametrizations. Minimiz. of the number of free parameters. Not flexible everywhere: cannot be forced at pleasure. Benchmarked ONLY with data from well controlled situations (typically thin target exp at accelerators) The interest in c.r. physics arises from a twofold necessity: 1.Basic research: investigate how a model based upon the above principles is able to explain/predict c.r. fluxes (e.g. the calculation of atmospheric neutrinos). Muons are a good subject. 2.FLUKA groups working in fields like radioprotection in space and in atmosphere need these comparisons to take confidence on the reliability of their calculations.

5. The FLUKA hadronic Models Hadron-Hadron Elastic,exchange Phase shifts data, eikonal P<3-5GeV/c Resonance prod and decay low E π, K Special High Energy DPM hadronization Hadron-NucleusNucleus-Nucleus E < 5 GeV PEANUT Sophisticated GINC Preequilibrium Coalescence High Energy Glauber-Gribov multiple interactions Coarser GINC Coalescence E< 0.1GeV/u BME Complete fusion+ peripheral 0.1< E< 5 GeV/u rQMD-2.4 modified new QMD E> 5 GeV/u DPMJET DPM+ Glauber+ GINC Evaporation/Fission/Fermi break-up  deexcitation > 5 GeV Elab DPM: soft physics based on (multi)Pomeron exchange DPMJET: soft physics of DPM plus 2+2 processes from pQCD Relevant for HE C.R. physics

6. Comparison with the HARP experiment Data from the HARP experiment at CERN particle production with p beams in the 1.5-15 GeV/c range on several targets First published results : 12.9 GeV/c protons on Aluminum,  + production cross section as a function of emission momentum and angle

7. The relevant key features (mostly for inclusive calculations) Above few tens of GeV: approximate Feynman scaling

8. the “Z-moments” from FLUKA in p-Air interaction ++ -- K-K- K+K+

9. Muon and Neutrino fluxes: Semi-analytic calculations The above distributions can be inserted in the formalism described by T.K.Gaisser in Astropart.Phys. 16 (2002) 285 (1-dimensional, exponential atmosphere, exact Feynman scaling, ecc.) X dn/dX  flux weight by E 3

10. FLUKA+DPMJET: behaviour @1000 TeV As expected: violation of scaling in the “central’ region (low rapidity) naive behaviour ~(1-x) b

11. Dedicated FLUKA library + additional off-line packages including: Primary spectra from Z = 1 to Z = 28 (derived from NASA and updated to most recent measurements.) Solar Modulation model (correlated to neutron monitors) Atmospheric model (MSIS Mass-Spectrometer-Incoherent-Scatter) 3D geometry of Earth + atmosphere Geomagnetic model The FLUKA C.R. library FLUKA: superposition model  nucleon-Air interaction FLUKA+DPMJET(II or III): full N-Air interactions other primary choices possible, for instance the Bartol all-nucleon spectrum Basic primary fluxes modulated for a given date, location according to geomag. model, solar modulation

12. 100 layers Cone amplitude Depending on allowed tolerance On geomagnetic cut-off 50 or 200 as options For the special case of atmospheric neutrinos the whole earth is instead considered Example of geometry setup for earth + local atmosphere

13. The output of the cosmic FLUKA library: At user request: Fluences or currents of charged/neutral particles in atmosphere at different altitudes (@boundary X-ing between layers) in the form of double differential distributions with respect to energy or momentum or angles or x F or x Lab or etc. etc. AND/OR: spatial distributions in x-y-z or R-z-  coordinates AND/OR: event by event output AND/OR: particle trajectories  shower drawing The simulation of muon fluxes: In the recent years many new data sets have been published. In particular the BESS spectrometer has collected data at different cut-offs, altitudes, solar modulation

14. Up to 10-20 GeV: BESS muons @Lynn Lake (1997) cone of ~25 o -- Very Low Cut-off: 0.4 GV ++

15. Up to 100 GeV: BESS muons @Mnt Norikura (1999) -- ++ Cut-off: 11.2 GV 2,700 m asl

16. BESS: high altitude hadron fluxes FLUKA simulation exp. data here: atmospheric profile from MSIS different from data, cut-off might be too approximated

17. BESS: high altitude muon fluxes Here, unspectedly, simulation exceed REAL DATA The difference in atmospheric profile could have relevance for decay prob. of pions

18. The all-nucleon spectrum of the simulation towards higher energies: constrained to join KASKADE measurements

19. Beyond the 100 GeV region: L3 Muons exp. data FLUKA simulation Vertical at larger angle

20. Very High Energies: convntional + prompt muons and neutrinos A benchmark on charmed meson production (OLD) Presented at ICRC 2005 Knee model: following KASCADE results

21. Kaons Pions A look at particle production at 1 PeV Charm (Meson+Baryon) A comparison with results from the models contained in CORSIKA (with R.Ganugapati, A.Karle, J.L.Kelley, Univ. of Winsconsin)

22. Muons in EAS: 1 TeV vertical p prim. Integral at sea level: ~ 21  /p sea level 2800 m 6200 m 10200 m

23. The aim is to predict multiple muon rates for different primary masses and energy within the framework of a unique simulation model Four steps: 1)atmospheric shower generation 2)transport in Gran Sasso rock 3)folding with the detector (spatial randomization of event) 4)full simulation in ICARUS T600 Interaction model: Interaction model: FLUKA + DPMJET-II for nucleus-nucleus collisions Secondary threshold = 1 TeV Output : Output : muons (E > 1 TeV) event by event Using FLUKA for underground  -bundles Within ICARUS collaboration Voxel geometry description of GranSasso

24. Muon Yield underground 3100 hg cm -2  ~ 30 o Fe nuclei protons Continuos lines are the parametrization obtained from the MC code used for MACRO analysis [C.Forti et al. (1990)] Systematic differences at the level of 15% exist between FLUKA FLUKA+DPMJET2 FLUKA+DPMJET3 in yield and radial distr.

25. First results: folding with FLUKA full simulation in ICARUS Fe nuclei, 1000 TeV/nucleon

26. Conclusions FLUKA results for muon fluxes in atmosphere are in general satisfactory The numerical results are strongly dependent on the choice of primary flux. To a lesser extent, other details still seem to be important: atmosphere, algorithm of solar modulation and geomagnetic cutoff FLUKA can be successfully operated also at very high energy (tested in part up to 10 6 GeV) At these energy the coupling FLUKA+DPMJET (2 or 3) is probably more reliable, at least for theoretical reasons (the hard QCD contribution must not be neglected) The FLUKA library for c.r. fluxes can be made available to interested people (documentation is still in progress) The primary fluxes of FLUKA library for C.R. physics in the atmosphere should probably be improved dN/dX distributions for semi-analytic calculations can be made available for fast numerical evaluation