G. Battistoni, A. Margiotta, S. Muraro, M. Sioli

1. The FLUKA high energy cosmic ray generator:predictions for the charge ratio of muons detected underground G. Battistoni, A. Margiotta, S. Muraro, M. Sioli FLUKA Meeting 28th April 2009

2. The generator for high energy cosmic rays that is under development, has the aim of extend the existing FLUKA cosmic rays library to include the TeV region. • Work under way within the ICARUS (Milano) and OPERA (Bologna) collaborations at Gran Sasso. • Generator dedicated to: • physics of high energy underground muons • exploiting the full integration in the calculation of both air shower development and muons transport in the rock. • Aim: predict multiple muon rates for different primary masses and energy within the framework of a unique simulation model.

3. First application: Analyze the predictions for the charge ratio of underground muons. Compare the results with data from an ongoing experiment (MINOS).

4. The underground muons generator: main features • Geometry setup • Earth: • sphere of radius R = 6378.14 km • Atmospheric geometry & profile: • 100 concentric spherical shells whose density and composition is varied according to the U.S. Standard Atmospheric Model. • Gran Sasso mountain: • spherical body whose radius is dynamically changed, according to the primary direction and to the Gran Sasso mountain map. • LNGS laboratory: • experimental underground halls • ICARUS and OPERA detectors volumes • rock box where muon–induced secondary are activated • (e.m. & hadronic showers from photo-nuclear interaction).

5. Primary spectrum Sampled from a primary mass composition model (a description of the relative abundances of cosmic rays and their energy spectra), derived from the Hörandel composition model [Astrop. Phys. 19 (2003) 193-220]. For each primary nucleus and for each amount of rock to be crossed, we compute the minimum energy required to produce at least one muon underground (probability < 10-5 to survive).

6. First application: prediction for thecharge ratio of underground muons • Muons that reach the Earth • come from mesonswith enough energy: • to reflect the forward fragmentation region • of the primary initiated interaction and • to “remember” the nature of the projectile • (there are more protons than neutrons • in the primary spectrum) • The muon charge ratio reflects the excess of π+ over π- and K+ over K−. • NOTE: • π and K hadronic production are affected by • uncertainties up to 20%

7. The muons result from pions and kaons that decay before they interact in the atmosphere. Because of their strangeness (S = +1), K+ and K0 can be yielded in association with a leading barion Λ o Σ. On the other hand, the production of K−,K0 requires the creation of a sea-quark pair s − s together with the leading nucleon and this is a superior order process. For this region K+ yield is greater than K− yield, differently from π+ and π− yields because of their isospin symmetry. ↓ N(K+)/N(K−) is larger than N(π+)/N(π−).

8. As energy increases, the fraction of muons from kaon decays also increases: the longer-lived pions (π± : cτ0= 780 cm, ε = 115 GeV) start to interact more before decaying than the shorter-lived kaons (K± : cτ0 = 371 cm, ε = 850 GeV). critical energyε: beyond this energy interaction process dominates on decay.

9. As energy increases, kaon decays became a more important contribution to the muon charge ratio. Since Nμ+/Nμ- (fromK)> Nμ+/Nμ− (fromπ) the total muons charge ratio is expected to increase with energy

10. hep-ex 0705.3815 MINOS Charge Ratio at the Surface = 1.371± 0.003 RFLUKA μ+/μ− = 1.362 ± 0.012 Agreement between FLUKA simulation and MINOS data within 0.7% L3+COSMIC (hep-ex/0408114). RFLUKA = 1.295  0.048 Rexp = 1.28  0.48

11. Muon charge ratio VS muon bundle multiplicity In the primary heavy elements the ratio of primary protons to neutrons decreases with respect to primary protons ↓ the muon charge ratio is expected to decrease with growing primary mass number. Muon bundle high multiplicity ↕ High primary energy and High primary mass number

12. Primary mass groups distribution mean valuegrows with underground muon multiplicity

13. Muon charge ratio VS muon bundle multiplicity PRELIMINARY Muon charge ratio decreases with growing multiplicity

14. This work has been presented at the 44th Rencontres de Moriond (Very High Energy Phenomena in the Universe) and has been accepted for the 31st ICRC conference. Work in progress: Comparison between FLUKA and DPMJET II.5 interaction models.

15. hep-ex 0705.3815 MINOS Charge Ratio at the Surface = 1.371± 0.003 RFLUKA μ+/μ− = 1.362 ± 0.012 VERY PRELIMINARY WORK IN PROGRESS ? R DPMJET II μ+/μ− = 1.27 ± 0.01 DPMJET II.5 L3+COSMIC (hep-ex/0408114). RFLUKA = 1.295  0.048 Rexp = 1.28  0.48 ?

16. VERY PRELIMINARY WORK IN PROGRESS μ+/ μ-FLUKA 1.362 ± 0.012 μ+/ μ-FLUKA from π 1.26 ± 0.01 μ+/ μ-FLUKA from K 1.98 ± 0.04 from K fromπ μ+/ μ-DPMJET II 1.27 ± 0.01 μ+/ μ-DPMJET II from π 1.22 ± 0.01 μ+/ μ-DPMJET II from K 1.46 ± 0.03 from K fromπ

17. DPMJET II.5 & FLUKAp + N → K± + X Ep = 10 TeV FLUKA DPMJET II.5 standalone & by means of FLUKA

18. p + N → K± + X Ep = 10 TeV DPMJET II.5&DPMJET III DPMJET II.5&DPMJET II.5 with rejection of strange sea-quark pairs

19. Benchmark for the CNGS beam construction. Limited phase space for cosmic rays physics. SPY experiment (CERN North Area) Nucl. Instr. Meth. A449, 609 (2000) p + Be => K+ + X p + Be => K- + X Elab = 450 GeV

20. The end

21. This idea has a long history: measurement of muon intensity attenuation to detect heterogeneities in large matter volumes (e.g. snow layers, Georg, 1955) 1970: Alvarez (search for hidden chambers in the Chefren pyramid) Since 2003: muon radiography of volcano’s structures with quasi-horizontal muons spatial resolution ~ some tens of m “quasi” online monitoring Interest for Vesuvio, Stromboli etc MU-RAY project, use of scintillation counters along the mountain profile(P. Strolin et al.) FLUKA: full simulation of cosmic ray muon flux starting from primary interactions and using detailed volcano’s topography map (use of m-TeV library) Volcano’s radiography with cosmic ray muons (MU-RAY) Muon radiography below the Asama volcano’s crater. It can be noted an high-density region around the caldera, and a cavity below.

22. Status of the work • As soon as FLUKA was chosen as the official simulation tool, much work has been done in collaboration with INFN-Naples: • Translation of the Vesuvius’s DEM into a FLUKA-voxel geometry • Each voxel is a cube of 20 m side (granularity high enough for the moment) • 3 organs: air, rock, “detector” (two boxes on the volcano’s lateral surface) • Embedding of voxel geometry into muTeV geometry • Adaptation and optimization for the code for this new site • Thresholds changed according to volcano’s profile • Extension of the primary spectrum in the low energy region • First test with ad-hoc geometries with air holes into the caldera • Good resolution for bodies 1.5 km away from the detector site

23. SimpleGeoview Fake air box (100 m side) Detector site

24. Result of the test(simulated ~250 days)

25. Plans and perspectives • The code is ready to be used • All the main changes can be performed at data-card level (thresholds, directions, spectra and so on…) • Practical problem: the nature of this work, requires a full control of the code by Naples group (detector location, setting of the exposure time, performances and so on), under our supervision: how to proceed?

26. xlab = Ej/Ei ratio of the total energies of the secondary particle j over the primary particle i dNij/dxlab differential multiplicity distributions of secondary j as produced by primary i in collisions with air nuclei as a function of xlab ”spectrum weighted moments” Zij : the multiplicity of secondary particles j as produced by primary particles i in interaction, weighted for the primary spectrum. Strictly bound to inclusive cross sections. γ= 2.7 approximate spectral index of the differential cosmic ray spectrum.

27. For isospin symmetry: On the other hand: where N is a nucleon. K+ and 0 (S = +1), can be produced in association with a leading Λ or Σ barion, whereas production of K requires production of a strange-antistrange pair from the sea in addition to the leading nucleon So the K+/K− ratio is larger than the π+/π− ratio. Spectrum weighted moments (γ = 2.7) for secondary particles produced in p-air collisions as a function of the projectile kinetic energy in the FLUKA code.

28. Validation of the DPMJET-III hadronic models: Comparison with the NA49 experiment Data from the NA49 experiment at CERN SPS particle production by p beams on p, C targets: 158 GeV/c beam momentum First published results: Eur. Phys. J. 45 (2006), 343 hep-ex/0606028 hep-ex/0606029 + , - production p + p p + C + , - production as a function of Feynman-x

29. SPY experiment (CERN North Area) Nucl. Instr. Meth. A449, 609 (2000) p + Be => π+ + X p + Be => π- + X Ecm = 450 GeV

30. FLUKA for Cosmic Rays validation (Eμ < 1 TeV) FLUKA simulations comparison with the experimental data of atmospheric muons charge ratio from L3+COSMIC experiment (hep-ex/0408114). Vertical 0.975 < cosθ < 1. RFLUKA = 1.295  0.0482 Rexp = 1.285  0.484 Black points: exp. Data Open symb: FLUKA At large angle 0.525 < cosθ < 0.6 (S.Muraro PhD Thesis)

31. Primary energy distributions for different underground muon multiplicities

32. Muon bundle from primary iron nuclei (E ≈ 105 TeV) in the ICARUS T600 detector