The FLUKA high energy The FLUKA high energy cosmic ray generator:cosmic ray generator:

predictions for the charge ratio predictions for the charge ratio of muons detected of muons detected

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

(University and INFN of Bologna and Milano)

for the FLUKA collaboration

44th Rencontres de MoriondVery High Energy Phenomena in the Universe

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In the environment of the FLUKA Monte Carlo code application to cosmic rays physics, a new generator for high energy cosmic rays is under development, with the aim of extend the existing FLUKA cosmic rays library to include the TeV region.

The application of FLUKA in cosmic ray physics arises from the interest in applied physics topics (radioprotection in space or in atmosphere) and in basic research (calculation of atmospheric neutrino fluxes).

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.

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Work under way within the ICARUS and OPERA collaborations at Gran Sasso.

First application:

Analyze the predictions for thecharge ratio of underground muons.

Compare preliminary results with datafrom an ongoing experiment (MINOS).

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Authors: A. Fasso`1, A. Ferrari2, J. Ranft3, P.R. Sala4

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 (Shielding, Radiobiology, High energy physics, Cosmic Ray physics, Nuclear and reactor physics).•Built and maintained with the aim of including the best possible physical models in terms of completeness and precision.•Continuously benchmarked with a wide set of experimental data from well controlled accelerator experiments.

FLUKAFLUKA http://www.fluka.org

Hadronic interaction models: based on a theoretical microscopic approach (no parametrizations). Free parameters are set (thin target experiments at accelerators) and kept fixed for all projectile-target combinations and energies. => High predictivity also in regions where experimental data are not available.

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The FLUKA hadronic Modelsfor a detailed study of the validity for CR studies see hep-ph/0612075 and 0711.2044

Hadron-HadronElastic,exchange

Phase shiftsdata, eikonal

P<3-5GeV/cResonance prod

and decay

low E π,KSpecial

High EnergyDPM

hadronization

Hadron-Nucleus Nucleus-NucleusE < 5 GeVPEANUT

Sophisticated GINCPreequilibriumCoalescence

High EnergyGlauber-Gribov

multiple interactions

Coarser GINCCoalescence

E< 0.1GeV/uBME

Complete fusion+

peripheral

0.1< E< 5 GeV/u

rQMD-2.4modifiednew QMD

E> 5 GeV/uDPMJET

DPM+Glauber+

GINC

Evaporation/Fission/Fermi break-up deexcitation

> 5 GeV Elab

DPM: soft physics based on (multi)Pomeron exchangeDPMJET: soft physics of DPM plus 2+2 processes from pQCD

Relevant forRelevant forHE C.R. physicsHE C.R. physics

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The underground muons generator:The underground muons generator: main features main features

Geometry setupEarth:

sphere of radius R = 6378.14 kmAtmospheric 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).

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Primary spectrumSampled from a primary mass composition model (a description of the relative abundances of cosmic rays and their energy spectra), at present, derived from the analysis of the MACRO experiment at Gran Sasso.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).

Hadronic interaction modelHigh energy cosmic ray interactions relevant for this work are treated in FLUKA by means of the interface to DPMJET.II.5. (hadron-hadron, hadron-nucleus and also nucleus-nucleus collision by means of the Glauber-Gribov mechanism)

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Muon bundle fromprimary iron nuclei

(E ≈ 105 TeV) in the ICARUST600 detector

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First application: prediction for theFirst application: prediction for thecharge ratiocharge ratio of underground muons of underground muons

Muons that reach the Earthcome from mesons with enough energy:

to reflect the forward fragmentation regionof 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 reflectsthe excess of π+ over π- and K+ over K−.

NOTE:π and K hadronic production are affected by

uncertainties up to 20%

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Validation of the DPMJET-III hadronic models:

Comparison with the NA49 experimentData 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),

343hep-ex/0606028hep-ex/0606029+ , - production

p + p p + C+ , - production as a function of Feynman-x

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p + Be => p + Be => ππ++ + X + X p + Be => p + Be => ππ-- + X + X

Nucl. Instr. Meth. A449, 609 (2000) SPY experiment (CERN North Area)

EEcmcm = 450 GeV = 450 GeV

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p + Be => p + Be => KK++ + X + X p + Be => p + Be => KK-- + X + X

Benchmark for the CNGS beam construction.Limited phase space for cosmic rays physics.

EEcmcm = 450 GeV = 450 GeV

Nucl. Instr. Meth. A449, 609 (2000)

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FLUKA for Cosmic Rays validationFLUKA for Cosmic Rays validationat low energy (Eat low energy (Eμμ< 100 GeV)< 100 GeV)

Black points: exp. DataOpen symb: FLUKA Simulation

- +

FLUKA simulations comparison with the experimental data of atmospheric muons taken at the top of Mt. Norikura, Japan, with

the BESS detector. (Phys. Lett. B 564 (2003), 8 – 20)•2770 m above sea level •Geomagnetic Cut-off: 11.2 GV•cone of ~11o

The energy range for muons extends up to 100 GeV. Results within 20%.

S.MuraroPhD Thesis

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The muons result from pions and kaons that decay before they interact in the atmosphere.

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).

→ the K+/K− ratio is larger than the π+/π− ratio.

Instead of π production, because of the strangeness of K, inclusive cross section for K+ production is bigger then inclusive cross section for K-

critical energy ε: beyond this energy interaction process dominates on decay.

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FLUKA in the TeV region:μ/All from π and K

μμ (from (from ππ) / All) / All

μμ (from (from KK) / All) / All

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As energy increases, kaon decays became a more important contribution to the muon charge ratio.

Since Nμ+ Nμ+

(from K) > (from π) Nμ- Nμ−

the total muons charge ratiois expected to

increase with energy

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FLUKA for Cosmic Rays FLUKA for Cosmic Rays validation (Evalidation (Eμμ < 1 TeV) < 1 TeV)

RFLUKA = 1.295 0.0482Rexp = 1.285 0.484

Vertical0.975 < cosθ < 1.

Black points: exp. DataOpen symb: FLUKA

At large angle0.525 < cosθ < 0.6

FLUKA simulations comparison with the experimental data of atmospheric muons charge ratiocharge ratio from L3 L3 ++ COSMIC experiment COSMIC experiment ((hep-ex/0408114).

(S.Muraro PhD Thesis)

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FLUKA in the FLUKA in the TeV region:TeV region:

muon charge muon charge ratioratio

μμ++ / / μμ-- FLUKAFLUKA 1.312 1.312 0.0155 0.0155

μμ++ / / μμ-- FLUKAFLUKA fromfrom ππ 1.220171.22017 0.0163948 0.0163948

μμ++ / / μμ-- FLUKAFLUKA fromfrom K K 1.78605 1.78605 0.04586390.0458639

fromfrom ππ

fromfrom K K

PRELIMINARY

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MINOS Charge Ratio at the Surface = 1.371± 0.003

hep-ex 0705.3815

RFLUKA = 1.295 0.0482RFLUKA = 1.312 0.0155

FLUKA prediction ~5% lower

then MINOS exp. data

=> Possible lack of K

production in FLUKA

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ConclusionsFLUKA models have been benchmarked with experimental data from accelerator experiments and from atmospheric

muons experiments (BESS: Eμ < 100 GeV; L3+C: Eμ < 1 TeV)

The FLUKA charge ratio prediction in the TeV regionis ~5% lower then MINOS experimental results

Uncertenties on π and K production in hadronic models can reach 20% because of lack of data from K production

experiments at high energy

=> Possible lack of K production in FLUKA

We are waiting for OPERA data

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Thank you

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Muon charge ratio VS Muon charge ratio VS muon bundle multiplicitymuon bundle multiplicity

Muon charge ratio is expected decreases

with growing 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.

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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.

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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 productionof K requires production of a strange-antistrange pair from the sea in addition to the leading nucleon