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

undergroundunderground

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

FLUKA MeetingFLUKA Meeting2828thth April 2009 April 2009

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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.

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First application:

Analyze the predictions for thecharge ratio of underground muons.

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

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

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), 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).

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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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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−).

↓ N(K+)/N(K−)is larger than N(π+)/N(π−).

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.

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critical energycritical energy εε::beyond this energybeyond this energyinteraction processinteraction processdominates on decay.dominates on decay.

As energy increases,the fraction of muons from kaon decays

also increases:

the longer-lived the longer-lived pions pions ((ππ±± : : ccττ00 = 780 cm, = 780 cm, εε = 115 GeV) = 115 GeV)

start to start to interact more before decaying thaninteract more before decaying thanthe shorter-lived the shorter-lived kaonskaons ((KK±± : : cτcτ00 = 371 cm, = 371 cm, εε = 850 GeV). = 850 GeV).

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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 ratiois expected to

increase with energy

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MINOS Charge Ratio at the Surface = 1.371± 0.003

hep-ex 0705.3815

RFLUKA μ+/μ− = 1.362 ± 0.012

L3L3 ++ COSMICCOSMIC((hep-ex/0408114).RFLUKA = 1.295 0.048Rexp = 1.28 0.48

Agreement Agreement between FLUKA between FLUKA simulation and simulation and

MINOS data MINOS data within 0.7%within 0.7%

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Muon charge ratio VS Muon charge ratio VS muon bundle multiplicitymuon 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.

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Primary mass groups distribution mean valuegrows with underground muon multiplicity

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

Muon charge ratio decreases with growing multiplicity

PRELIMINARY

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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.

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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

L3L3 ++ COSMICCOSMIC((hep-ex/0408114).RFLUKA = 1.295 0.048Rexp = 1.28 0.48

??

??

VERY PRELIMINARY

VERY PRELIMINARYWORK IN PROGRESS

WORK IN PROGRESS

RFLUKA μ+/μ− = 1.362 ± 0.012

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fromfrom K K

fromfrom K K

fromfrom ππ

fromfrom ππ

μμ++ / / μμ-- FLUKAFLUKA

1.362 ± 0.0121.362 ± 0.012

μμ++ / / μμ-- FLUKAFLUKA from from ππ

1.26 ± 0.011.26 ± 0.01

μμ++ / / μμ-- FLUKAFLUKA from K from K

1.98 ± 0.041.98 ± 0.04

μμ++ / / μμ-- DPMJET IIDPMJET II

1.27 ± 0.011.27 ± 0.01

μμ++ / / μμ-- DPMJET IIDPMJET II from from ππ

1.22 ± 0.011.22 ± 0.01

μμ++ / / μμ-- DPMJET IIDPMJET II from K from K

1.46 ± 0.031.46 ± 0.03

VERY PRELIMINARY

VERY PRELIMINARYWORK IN PROGRESS

WORK IN PROGRESS

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DPMJET II.5 & FLUKAp + N → K± + X Ep = 10 TeV

DPMJET II.5 DPMJET II.5 standalonestandalone & & by means ofby means of FLUKA FLUKA

FLUKAFLUKA

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p + N → K± + X

Ep = 10 TeV

DPMJET II.5&

DPMJET III

DPMJET II.5&

DPMJET II.5with rejection of

strange sea-quark pairs

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

Benchmark for the CNGSbeam construction.

Limited phase spacefor cosmic rays physics.

EElablab = 450 GeV = 450 GeV

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

SPY experiment (CERN North Area)SPY experiment (CERN North Area)

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The end

Volcano’s radiography with Volcano’s radiography with cosmic ray muons (MU-RAY)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 Muon radiography below the Asama volcano’s crater. It can Asama volcano’s crater. It can be noted an high-density region be noted an high-density region around the caldera, and a around the caldera, and a cavity below.cavity below.

Status of the workStatus 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

Detectorsite

Fake air box(100 m side)

Result of the testResult of the test(simulated ~250 days)(simulated ~250 days)

Plans and perspectivesPlans 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?

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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.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

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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),

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

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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Primary energy distributions for different underground muon multiplicities

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Muon bundle fromprimary iron nuclei

(E ≈ 105 TeV) in the ICARUST600 detector