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 28 th April 2009

2. 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. 3 First application: Analyze the predictions for the charge ratio of underground muons. Compare the results with data from an ongoing experiment (MINOS).

4. 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. 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. 6 First application: prediction for the charge ratio of underground muons Muons that reach the Earth come from mesons with 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. 7 The muons result from pions and kaons that decay before they interact in the atmosphere. ↓ N(K + )/N(K − ) is larger than N(π + )/N(π − ). Because of their strangeness (S = +1), K + and K 0 can be yielded in association with a leading barion Λ o Σ. On the other hand, the production of K −,K 0 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.

8. 8 critical energy ε : beyond this energy interaction process dominates on decay. As energy increases, the fraction of muons from kaon decays also increases: the longer-lived pions (π ± : cτ 0 = 780 cm, ε = 115 GeV) start to interact more before decaying than the shorter-lived kaons (K ± : cτ 0 = 371 cm, ε = 850 GeV).

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

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

11. 11 Muon charge ratio VS muon bundle multiplicity Muon bundle high multiplicity ↕ High primary energy and High primary mass number 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.

12. 12 Primary mass groups distribution mean value grows with underground muon multiplicity

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

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

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

16. 16 from K from π 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 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 VERY PRELIMINARY WORK IN PROGRESS

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

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

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

20. 20 The end

21. Volcano’s radiography with cosmic ray muons (MU-RAY) 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  -TeV library) 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. Detector site Fake air box (100 m side)

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. 26 x lab = E j /E i ratio of the total energies of the secondary particle j over the primary particle i dN ij /dx lab differential multiplicity distributions of secondary j as produced by primary i in collisions with air nuclei as a function of x lab ”spectrum weighted moments” Z ij : 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. 27 For isospin symmetry: On the other hand: where N is a 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. 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

28. 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. 29 p + Be => π + + X p + Be => π - + X Nucl. Instr. Meth. A449, 609 (2000) SPY experiment (CERN North Area) E cm = 450 GeV

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

31. 31 Primary energy distributions for different underground muon multiplicities

32. 32 Muon bundle from primary iron nuclei (E ≈ 10 5 TeV) in the ICARUS T600 detector